id	sid	tid	token	lemma	pos
ejpam-4643	1	1	european	european	PROPN
ejpam-4643	1	2	journal	journal	PROPN
ejpam-4643	1	3	of	of	ADP
ejpam-4643	1	4	pure	pure	ADJ
ejpam-4643	1	5	and	and	CCONJ
ejpam-4643	1	6	applied	apply	VERB
ejpam-4643	1	7	mathematics	mathematic	NOUN
ejpam-4643	1	8	vol	vol	NOUN
ejpam-4643	1	9	.	.	PUNCT
ejpam-4643	2	1	16	16	NUM
ejpam-4643	2	2	,	,	PUNCT
ejpam-4643	2	3	no	no	INTJ
ejpam-4643	2	4	.	.	NOUN
ejpam-4643	2	5	1	1	NUM
ejpam-4643	2	6	,	,	PUNCT
ejpam-4643	2	7	2023	2023	NUM
ejpam-4643	2	8	,	,	PUNCT
ejpam-4643	2	9	18	18	NUM
ejpam-4643	2	10	-	-	SYM
ejpam-4643	2	11	28	28	NUM
ejpam-4643	2	12	issn	issn	PROPN
ejpam-4643	2	13	1307	1307	NUM
ejpam-4643	2	14	-	-	SYM
ejpam-4643	2	15	5543	5543	NUM
ejpam-4643	2	16	–	–	PUNCT
ejpam-4643	2	17	ejpam.com	ejpam.com	X
ejpam-4643	2	18	published	publish	VERB
ejpam-4643	2	19	by	by	ADP
ejpam-4643	2	20	new	new	PROPN
ejpam-4643	2	21	york	york	PROPN
ejpam-4643	2	22	business	business	PROPN
ejpam-4643	2	23	global	global	ADJ
ejpam-4643	2	24	resolving	resolving	NOUN
ejpam-4643	2	25	domination	domination	NOUN
ejpam-4643	2	26	in	in	ADP
ejpam-4643	2	27	graphs	graph	NOUN
ejpam-4643	2	28	under	under	ADP
ejpam-4643	2	29	some	some	DET
ejpam-4643	2	30	binary	binary	ADJ
ejpam-4643	2	31	operations	operations	PROPN
ejpam-4643	2	32	gerald	gerald	PROPN
ejpam-4643	2	33	b.	b.	PROPN
ejpam-4643	2	34	monsanto1,∗	monsanto1,∗	PROPN
ejpam-4643	2	35	,	,	PUNCT
ejpam-4643	3	1	helen	helen	PROPN
ejpam-4643	3	2	m.	m.	PROPN
ejpam-4643	3	3	rara2	rara2	PROPN
ejpam-4643	4	1	1	1	NUM
ejpam-4643	4	2	college	college	NOUN
ejpam-4643	4	3	of	of	ADP
ejpam-4643	4	4	teacher	teacher	NOUN
ejpam-4643	4	5	education	education	NOUN
ejpam-4643	4	6	,	,	PUNCT
ejpam-4643	4	7	arts	art	NOUN
ejpam-4643	4	8	and	and	CCONJ
ejpam-4643	4	9	sciences	science	NOUN
ejpam-4643	4	10	,	,	PUNCT
ejpam-4643	4	11	visayas	visayas	PROPN
ejpam-4643	4	12	state	state	PROPN
ejpam-4643	4	13	university	university	PROPN
ejpam-4643	4	14	villaba	villaba	NOUN
ejpam-4643	4	15	,	,	PUNCT
ejpam-4643	4	16	6537	6537	NUM
ejpam-4643	4	17	villaba	villaba	NOUN
ejpam-4643	4	18	,	,	PUNCT
ejpam-4643	4	19	leyte	leyte	PROPN
ejpam-4643	4	20	,	,	PUNCT
ejpam-4643	4	21	philippines	philippines	PROPN
ejpam-4643	4	22	2	2	NUM
ejpam-4643	4	23	department	department	NOUN
ejpam-4643	4	24	of	of	ADP
ejpam-4643	4	25	mathematics	mathematic	NOUN
ejpam-4643	4	26	and	and	CCONJ
ejpam-4643	4	27	statistics	statistic	NOUN
ejpam-4643	4	28	,	,	PUNCT
ejpam-4643	4	29	college	college	NOUN
ejpam-4643	4	30	of	of	ADP
ejpam-4643	4	31	science	science	NOUN
ejpam-4643	4	32	and	and	CCONJ
ejpam-4643	4	33	mathematics	mathematic	NOUN
ejpam-4643	4	34	,	,	PUNCT
ejpam-4643	4	35	center	center	NOUN
ejpam-4643	4	36	of	of	ADP
ejpam-4643	4	37	graph	graph	NOUN
ejpam-4643	4	38	theory	theory	NOUN
ejpam-4643	4	39	,	,	PUNCT
ejpam-4643	4	40	algebra	algebra	NOUN
ejpam-4643	4	41	,	,	PUNCT
ejpam-4643	4	42	and	and	CCONJ
ejpam-4643	4	43	analysis	analysis	NOUN
ejpam-4643	4	44	-	-	PUNCT
ejpam-4643	4	45	premier	premier	NOUN
ejpam-4643	4	46	research	research	NOUN
ejpam-4643	4	47	institute	institute	PROPN
ejpam-4643	4	48	of	of	ADP
ejpam-4643	4	49	science	science	NOUN
ejpam-4643	4	50	and	and	CCONJ
ejpam-4643	4	51	mathematics	mathematic	NOUN
ejpam-4643	4	52	,	,	PUNCT
ejpam-4643	4	53	mindanao	mindanao	PROPN
ejpam-4643	4	54	state	state	PROPN
ejpam-4643	4	55	university	university	PROPN
ejpam-4643	4	56	-	-	PUNCT
ejpam-4643	4	57	iligan	iligan	PROPN
ejpam-4643	4	58	institute	institute	PROPN
ejpam-4643	4	59	of	of	ADP
ejpam-4643	4	60	technology	technology	PROPN
ejpam-4643	4	61	,	,	PUNCT
ejpam-4643	4	62	9200	9200	NUM
ejpam-4643	4	63	iligan	iligan	ADJ
ejpam-4643	4	64	city	city	NOUN
ejpam-4643	4	65	,	,	PUNCT
ejpam-4643	4	66	philippines	philippine	NOUN
ejpam-4643	4	67	abstract	abstract	ADJ
ejpam-4643	4	68	.	.	PUNCT
ejpam-4643	5	1	in	in	ADP
ejpam-4643	5	2	this	this	DET
ejpam-4643	5	3	paper	paper	NOUN
ejpam-4643	5	4	,	,	PUNCT
ejpam-4643	5	5	we	we	PRON
ejpam-4643	5	6	investigate	investigate	VERB
ejpam-4643	5	7	the	the	DET
ejpam-4643	5	8	concept	concept	NOUN
ejpam-4643	5	9	of	of	ADP
ejpam-4643	5	10	resolving	resolve	VERB
ejpam-4643	5	11	dominating	dominating	NOUN
ejpam-4643	5	12	set	set	VERB
ejpam-4643	5	13	in	in	ADP
ejpam-4643	5	14	a	a	DET
ejpam-4643	5	15	graph	graph	NOUN
ejpam-4643	5	16	.	.	PUNCT
ejpam-4643	6	1	in	in	ADP
ejpam-4643	6	2	particular	particular	ADJ
ejpam-4643	6	3	,	,	PUNCT
ejpam-4643	6	4	we	we	PRON
ejpam-4643	6	5	characterize	characterize	VERB
ejpam-4643	6	6	the	the	DET
ejpam-4643	6	7	resolving	resolve	VERB
ejpam-4643	6	8	dominating	dominating	NOUN
ejpam-4643	6	9	sets	set	NOUN
ejpam-4643	6	10	in	in	ADP
ejpam-4643	6	11	the	the	DET
ejpam-4643	6	12	join	join	NOUN
ejpam-4643	6	13	,	,	PUNCT
ejpam-4643	6	14	corona	corona	NOUN
ejpam-4643	6	15	and	and	CCONJ
ejpam-4643	6	16	lexicographic	lexicographic	ADJ
ejpam-4643	6	17	product	product	NOUN
ejpam-4643	6	18	of	of	ADP
ejpam-4643	6	19	two	two	NUM
ejpam-4643	6	20	graphs	graph	NOUN
ejpam-4643	6	21	and	and	CCONJ
ejpam-4643	6	22	determine	determine	VERB
ejpam-4643	6	23	the	the	DET
ejpam-4643	6	24	resolving	resolve	VERB
ejpam-4643	6	25	domination	domination	NOUN
ejpam-4643	6	26	number	number	NOUN
ejpam-4643	6	27	of	of	ADP
ejpam-4643	6	28	these	these	DET
ejpam-4643	6	29	graphs	graph	NOUN
ejpam-4643	6	30	.	.	PUNCT
ejpam-4643	7	1	2020	2020	NUM
ejpam-4643	7	2	mathematics	mathematic	NOUN
ejpam-4643	7	3	subject	subject	NOUN
ejpam-4643	7	4	classifications	classification	NOUN
ejpam-4643	7	5	:	:	PUNCT
ejpam-4643	7	6	05c69	05c69	X
ejpam-4643	7	7	key	key	ADJ
ejpam-4643	7	8	words	word	NOUN
ejpam-4643	7	9	and	and	CCONJ
ejpam-4643	7	10	phrases	phrase	NOUN
ejpam-4643	7	11	:	:	PUNCT
ejpam-4643	7	12	resolving	resolve	VERB
ejpam-4643	7	13	dominating	dominating	NOUN
ejpam-4643	7	14	set	set	NOUN
ejpam-4643	7	15	,	,	PUNCT
ejpam-4643	7	16	resolving	resolve	VERB
ejpam-4643	7	17	domination	domination	NOUN
ejpam-4643	7	18	number	number	NOUN
ejpam-4643	7	19	,	,	PUNCT
ejpam-4643	7	20	join	join	NOUN
ejpam-4643	7	21	,	,	PUNCT
ejpam-4643	7	22	corona	corona	PROPN
ejpam-4643	7	23	,	,	PUNCT
ejpam-4643	7	24	lexicographic	lexicographic	ADJ
ejpam-4643	7	25	product	product	NOUN
ejpam-4643	7	26	1	1	NUM
ejpam-4643	7	27	.	.	PUNCT
ejpam-4643	8	1	introduction	introduction	NOUN
ejpam-4643	8	2	all	all	DET
ejpam-4643	8	3	graphs	graph	NOUN
ejpam-4643	8	4	considered	consider	VERB
ejpam-4643	8	5	in	in	ADP
ejpam-4643	8	6	this	this	DET
ejpam-4643	8	7	study	study	NOUN
ejpam-4643	8	8	are	be	AUX
ejpam-4643	8	9	finite	finite	ADJ
ejpam-4643	8	10	,	,	PUNCT
ejpam-4643	8	11	simple	simple	ADJ
ejpam-4643	8	12	,	,	PUNCT
ejpam-4643	8	13	and	and	CCONJ
ejpam-4643	8	14	undirected	undirected	ADJ
ejpam-4643	8	15	connected	connected	ADJ
ejpam-4643	8	16	graphs	graph	NOUN
ejpam-4643	8	17	,	,	PUNCT
ejpam-4643	8	18	that	that	ADV
ejpam-4643	8	19	is	is	ADV
ejpam-4643	8	20	,	,	PUNCT
ejpam-4643	8	21	without	without	ADP
ejpam-4643	8	22	loops	loop	NOUN
ejpam-4643	8	23	and	and	CCONJ
ejpam-4643	8	24	multiple	multiple	ADJ
ejpam-4643	8	25	edges	edge	NOUN
ejpam-4643	8	26	.	.	PUNCT
ejpam-4643	9	1	for	for	ADP
ejpam-4643	9	2	some	some	DET
ejpam-4643	9	3	basic	basic	ADJ
ejpam-4643	9	4	concepts	concept	NOUN
ejpam-4643	9	5	in	in	ADP
ejpam-4643	9	6	graph	graph	NOUN
ejpam-4643	9	7	theory	theory	NOUN
ejpam-4643	9	8	,	,	PUNCT
ejpam-4643	9	9	we	we	PRON
ejpam-4643	9	10	refer	refer	VERB
ejpam-4643	9	11	readers	reader	NOUN
ejpam-4643	9	12	to	to	ADP
ejpam-4643	9	13	[	[	X
ejpam-4643	9	14	5	5	NUM
ejpam-4643	9	15	]	]	PUNCT
ejpam-4643	9	16	.	.	PUNCT
ejpam-4643	10	1	let	let	VERB
ejpam-4643	10	2	g	g	NOUN
ejpam-4643	10	3	=	=	PUNCT
ejpam-4643	10	4	(	(	PUNCT
ejpam-4643	10	5	v	v	NOUN
ejpam-4643	10	6	(	(	PUNCT
ejpam-4643	10	7	g	g	NOUN
ejpam-4643	10	8	)	)	PUNCT
ejpam-4643	10	9	,	,	PUNCT
ejpam-4643	10	10	e(g	e(g	PROPN
ejpam-4643	10	11	)	)	PUNCT
ejpam-4643	10	12	)	)	PUNCT
ejpam-4643	11	1	be	be	AUX
ejpam-4643	11	2	a	a	DET
ejpam-4643	11	3	connected	connected	ADJ
ejpam-4643	11	4	graph	graph	NOUN
ejpam-4643	11	5	.	.	PUNCT
ejpam-4643	12	1	the	the	DET
ejpam-4643	12	2	open	open	ADJ
ejpam-4643	12	3	neighborhood	neighborhood	NOUN
ejpam-4643	12	4	of	of	ADP
ejpam-4643	12	5	v	v	NUM
ejpam-4643	12	6	∈	∈	NOUN
ejpam-4643	12	7	v	v	NOUN
ejpam-4643	12	8	(	(	PUNCT
ejpam-4643	12	9	g	g	NOUN
ejpam-4643	12	10	)	)	PUNCT
ejpam-4643	12	11	is	be	AUX
ejpam-4643	12	12	ng(v	ng(v	PUNCT
ejpam-4643	12	13	)	)	PUNCT
ejpam-4643	12	14	=	=	PRON
ejpam-4643	13	1	{	{	PUNCT
ejpam-4643	13	2	u	u	NOUN
ejpam-4643	13	3	∈	∈	PROPN
ejpam-4643	13	4	v	v	NOUN
ejpam-4643	13	5	(	(	PUNCT
ejpam-4643	13	6	g	g	NOUN
ejpam-4643	13	7	)	)	PUNCT
ejpam-4643	13	8	:	:	PUNCT
ejpam-4643	13	9	uv	uv	PROPN
ejpam-4643	13	10	∈	∈	PROPN
ejpam-4643	13	11	e(g	e(g	PROPN
ejpam-4643	13	12	)	)	PUNCT
ejpam-4643	13	13	}	}	PUNCT
ejpam-4643	13	14	.	.	PUNCT
ejpam-4643	14	1	any	any	DET
ejpam-4643	14	2	element	element	NOUN
ejpam-4643	14	3	u	u	NOUN
ejpam-4643	14	4	of	of	ADP
ejpam-4643	14	5	ng(v	ng(v	PUNCT
ejpam-4643	14	6	)	)	PUNCT
ejpam-4643	14	7	is	be	AUX
ejpam-4643	14	8	called	call	VERB
ejpam-4643	14	9	a	a	DET
ejpam-4643	14	10	neighbor	neighbor	NOUN
ejpam-4643	14	11	of	of	ADP
ejpam-4643	14	12	v.	v.	ADP
ejpam-4643	14	13	the	the	DET
ejpam-4643	14	14	closed	closed	ADJ
ejpam-4643	14	15	neighborhood	neighborhood	NOUN
ejpam-4643	14	16	of	of	ADP
ejpam-4643	14	17	v	v	NUM
ejpam-4643	14	18	∈	∈	NOUN
ejpam-4643	14	19	v	v	NOUN
ejpam-4643	14	20	(	(	PUNCT
ejpam-4643	14	21	g	g	NOUN
ejpam-4643	14	22	)	)	PUNCT
ejpam-4643	14	23	is	be	AUX
ejpam-4643	14	24	ng[v	ng[v	NOUN
ejpam-4643	14	25	]	]	X
ejpam-4643	14	26	=	=	SYM
ejpam-4643	14	27	ng(v	ng(v	X
ejpam-4643	14	28	)	)	PUNCT
ejpam-4643	14	29	∪	∪	ADP
ejpam-4643	14	30	{	{	PUNCT
ejpam-4643	14	31	v	v	NOUN
ejpam-4643	14	32	}	}	PUNCT
ejpam-4643	14	33	.	.	PUNCT
ejpam-4643	15	1	thus	thus	ADV
ejpam-4643	15	2	,	,	PUNCT
ejpam-4643	15	3	the	the	DET
ejpam-4643	15	4	degree	degree	NOUN
ejpam-4643	15	5	of	of	ADP
ejpam-4643	15	6	v	v	NUM
ejpam-4643	15	7	∈	∈	NOUN
ejpam-4643	15	8	v	v	NOUN
ejpam-4643	15	9	(	(	PUNCT
ejpam-4643	15	10	g	g	NOUN
ejpam-4643	15	11	)	)	PUNCT
ejpam-4643	15	12	is	be	AUX
ejpam-4643	15	13	given	give	VERB
ejpam-4643	15	14	by	by	ADP
ejpam-4643	15	15	degg(v	degg(v	PROPN
ejpam-4643	15	16	)	)	PUNCT
ejpam-4643	15	17	=	=	SYM
ejpam-4643	15	18	|ng(v)|	|ng(v)|	NOUN
ejpam-4643	15	19	.	.	PUNCT
ejpam-4643	16	1	customarily	customarily	ADV
ejpam-4643	16	2	,	,	PUNCT
ejpam-4643	16	3	for	for	ADP
ejpam-4643	16	4	s	s	PROPN
ejpam-4643	16	5	⊆	⊆	NUM
ejpam-4643	16	6	v	v	NOUN
ejpam-4643	16	7	(	(	PUNCT
ejpam-4643	16	8	g	g	NOUN
ejpam-4643	16	9	)	)	PUNCT
ejpam-4643	16	10	,	,	PUNCT
ejpam-4643	16	11	ng(s	ng(s	NUM
ejpam-4643	16	12	)	)	PUNCT
ejpam-4643	17	1	=	=	SYM
ejpam-4643	18	1	⋃	⋃	ADP
ejpam-4643	18	2	v∈s	v∈s	NOUN
ejpam-4643	18	3	ng(v	ng(v	NOUN
ejpam-4643	18	4	)	)	PUNCT
ejpam-4643	18	5	and	and	CCONJ
ejpam-4643	18	6	ng[s	ng[	NOUN
ejpam-4643	18	7	]	]	PUNCT
ejpam-4643	18	8	=	=	PUNCT
ejpam-4643	18	9	⋃	⋃	VERB
ejpam-4643	18	10	v∈s	v∈s	ADJ
ejpam-4643	18	11	ng[v	ng[v	NOUN
ejpam-4643	18	12	]	]	PUNCT
ejpam-4643	18	13	.	.	PUNCT
ejpam-4643	19	1	a	a	DET
ejpam-4643	19	2	nonempty	nonempty	ADV
ejpam-4643	19	3	set	set	VERB
ejpam-4643	19	4	s	s	PROPN
ejpam-4643	19	5	⊆	⊆	NUM
ejpam-4643	19	6	v	v	NOUN
ejpam-4643	19	7	(	(	PUNCT
ejpam-4643	19	8	g	g	NOUN
ejpam-4643	19	9	)	)	PUNCT
ejpam-4643	19	10	is	be	AUX
ejpam-4643	19	11	a	a	DET
ejpam-4643	19	12	dominating	dominating	NOUN
ejpam-4643	19	13	set	set	VERB
ejpam-4643	19	14	in	in	ADP
ejpam-4643	19	15	graph	graph	NOUN
ejpam-4643	19	16	g	g	NOUN
ejpam-4643	19	17	if	if	SCONJ
ejpam-4643	19	18	ng[s	ng[	NOUN
ejpam-4643	19	19	]	]	PUNCT
ejpam-4643	19	20	=	=	SYM
ejpam-4643	19	21	v	v	NOUN
ejpam-4643	19	22	(	(	PUNCT
ejpam-4643	19	23	g	g	NOUN
ejpam-4643	19	24	)	)	PUNCT
ejpam-4643	19	25	.	.	PUNCT
ejpam-4643	20	1	otherwise	otherwise	ADV
ejpam-4643	20	2	,	,	PUNCT
ejpam-4643	20	3	we	we	PRON
ejpam-4643	20	4	say	say	VERB
ejpam-4643	20	5	s	s	PRON
ejpam-4643	20	6	is	be	AUX
ejpam-4643	20	7	a	a	DET
ejpam-4643	20	8	non	non	ADJ
ejpam-4643	20	9	-	-	ADJ
ejpam-4643	20	10	dominating	dominating	ADJ
ejpam-4643	20	11	set	set	NOUN
ejpam-4643	20	12	of	of	ADP
ejpam-4643	20	13	g.	g.	PROPN
ejpam-4643	20	14	the	the	DET
ejpam-4643	20	15	domination	domination	NOUN
ejpam-4643	20	16	number	number	NOUN
ejpam-4643	20	17	of	of	ADP
ejpam-4643	20	18	a	a	DET
ejpam-4643	20	19	graph	graph	NOUN
ejpam-4643	20	20	g	g	NOUN
ejpam-4643	20	21	,	,	PUNCT
ejpam-4643	20	22	denoted	denote	VERB
ejpam-4643	20	23	by	by	ADP
ejpam-4643	20	24	γ(g	γ(g	PROPN
ejpam-4643	20	25	)	)	PUNCT
ejpam-4643	20	26	,	,	PUNCT
ejpam-4643	20	27	is	be	AUX
ejpam-4643	20	28	given	give	VERB
ejpam-4643	20	29	by	by	ADP
ejpam-4643	20	30	γ(g	γ(g	PROPN
ejpam-4643	20	31	)	)	PUNCT
ejpam-4643	21	1	=	=	SYM
ejpam-4643	21	2	min|s|	min|s|	PROPN
ejpam-4643	21	3	:	:	PUNCT
ejpam-4643	21	4	s	s	VERB
ejpam-4643	21	5	is	be	AUX
ejpam-4643	21	6	a	a	DET
ejpam-4643	21	7	dominating	dominating	NOUN
ejpam-4643	21	8	set	set	NOUN
ejpam-4643	21	9	of	of	ADP
ejpam-4643	21	10	g.	g.	PROPN
ejpam-4643	21	11	if	if	SCONJ
ejpam-4643	21	12	s	s	X
ejpam-4643	21	13	is	be	AUX
ejpam-4643	21	14	a	a	DET
ejpam-4643	21	15	dominating	dominating	NOUN
ejpam-4643	21	16	set	set	NOUN
ejpam-4643	21	17	of	of	ADP
ejpam-4643	21	18	g	g	PROPN
ejpam-4643	21	19	and	and	CCONJ
ejpam-4643	21	20	if	if	SCONJ
ejpam-4643	21	21	|s|	|s|	PROPN
ejpam-4643	21	22	=	=	SYM
ejpam-4643	21	23	γ(g	γ(g	PROPN
ejpam-4643	21	24	)	)	PUNCT
ejpam-4643	21	25	,	,	PUNCT
ejpam-4643	21	26	then	then	ADV
ejpam-4643	21	27	s	s	VERB
ejpam-4643	21	28	is	be	AUX
ejpam-4643	21	29	called	call	VERB
ejpam-4643	21	30	a	a	DET
ejpam-4643	21	31	minimum	minimum	ADJ
ejpam-4643	21	32	dominating	dominating	NOUN
ejpam-4643	21	33	set	set	NOUN
ejpam-4643	21	34	or	or	CCONJ
ejpam-4643	21	35	a	a	DET
ejpam-4643	21	36	γ	γ	NOUN
ejpam-4643	21	37	-	-	PUNCT
ejpam-4643	21	38	set	set	NOUN
ejpam-4643	21	39	of	of	ADP
ejpam-4643	21	40	g.	g.	PROPN
ejpam-4643	21	41	∗corresponding	∗corresponde	VERB
ejpam-4643	21	42	author	author	NOUN
ejpam-4643	21	43	.	.	PUNCT
ejpam-4643	22	1	doi	doi	NOUN
ejpam-4643	22	2	:	:	PUNCT
ejpam-4643	22	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4643	https://doi.org/10.29020/nybg.ejpam.v16i1.4643	NOUN
ejpam-4643	22	4	email	email	NOUN
ejpam-4643	22	5	addresses	address	VERB
ejpam-4643	22	6	:	:	PUNCT
ejpam-4643	22	7	gerald.monsanto@vsu.edu.ph	gerald.monsanto@vsu.edu.ph	PROPN
ejpam-4643	22	8	(	(	PUNCT
ejpam-4643	22	9	g.	g.	PROPN
ejpam-4643	22	10	monsanto	monsanto	PROPN
ejpam-4643	22	11	)	)	PUNCT
ejpam-4643	22	12	,	,	PUNCT
ejpam-4643	22	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4643	22	14	(	(	PUNCT
ejpam-4643	22	15	h.	h.	PROPN
ejpam-4643	22	16	rara	rara	PROPN
ejpam-4643	22	17	)	)	PUNCT
ejpam-4643	22	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4643	22	19	18	18	NUM
ejpam-4643	22	20	©	©	PROPN
ejpam-4643	22	21	2023	2023	NUM
ejpam-4643	22	22	ejpam	ejpam	NOUN
ejpam-4643	22	23	all	all	DET
ejpam-4643	22	24	rights	right	NOUN
ejpam-4643	22	25	reserved	reserve	VERB
ejpam-4643	22	26	.	.	PUNCT
ejpam-4643	23	1	g.	g.	PROPN
ejpam-4643	23	2	monsanto	monsanto	PROPN
ejpam-4643	23	3	,	,	PUNCT
ejpam-4643	23	4	h.	h.	PROPN
ejpam-4643	23	5	rara	rara	PROPN
ejpam-4643	23	6	/	/	SYM
ejpam-4643	23	7	eur	eur	PROPN
ejpam-4643	23	8	.	.	PUNCT
ejpam-4643	24	1	j.	j.	PROPN
ejpam-4643	24	2	pure	pure	PROPN
ejpam-4643	24	3	appl	appl	PROPN
ejpam-4643	24	4	.	.	PROPN
ejpam-4643	24	5	math	math	PROPN
ejpam-4643	24	6	,	,	PUNCT
ejpam-4643	24	7	16	16	NUM
ejpam-4643	24	8	(	(	PUNCT
ejpam-4643	24	9	1	1	NUM
ejpam-4643	24	10	)	)	PUNCT
ejpam-4643	24	11	(	(	PUNCT
ejpam-4643	24	12	2023	2023	NUM
ejpam-4643	24	13	)	)	PUNCT
ejpam-4643	24	14	,	,	PUNCT
ejpam-4643	24	15	18	18	NUM
ejpam-4643	24	16	-	-	SYM
ejpam-4643	24	17	28	28	NUM
ejpam-4643	24	18	19	19	NUM
ejpam-4643	24	19	the	the	DET
ejpam-4643	24	20	distance	distance	NOUN
ejpam-4643	24	21	dg(u	dg(u	X
ejpam-4643	24	22	,	,	PUNCT
ejpam-4643	24	23	v	v	NOUN
ejpam-4643	24	24	)	)	PUNCT
ejpam-4643	24	25	in	in	ADP
ejpam-4643	24	26	g	g	NOUN
ejpam-4643	24	27	of	of	ADP
ejpam-4643	24	28	two	two	NUM
ejpam-4643	24	29	vertices	vertex	NOUN
ejpam-4643	24	30	u	u	NOUN
ejpam-4643	24	31	,	,	PUNCT
ejpam-4643	24	32	v	v	PROPN
ejpam-4643	24	33	is	be	AUX
ejpam-4643	24	34	the	the	DET
ejpam-4643	24	35	length	length	NOUN
ejpam-4643	24	36	of	of	ADP
ejpam-4643	24	37	a	a	DET
ejpam-4643	24	38	shortest	short	ADJ
ejpam-4643	24	39	u	u	NOUN
ejpam-4643	24	40	-	-	NOUN
ejpam-4643	24	41	v	v	ADJ
ejpam-4643	24	42	path	path	NOUN
ejpam-4643	24	43	in	in	ADP
ejpam-4643	24	44	g.	g.	PROPN
ejpam-4643	24	45	a	a	DET
ejpam-4643	24	46	vertex	vertex	NOUN
ejpam-4643	24	47	x	x	X
ejpam-4643	24	48	of	of	ADP
ejpam-4643	24	49	a	a	DET
ejpam-4643	24	50	connected	connected	ADJ
ejpam-4643	24	51	graph	graph	NOUN
ejpam-4643	24	52	g	g	NOUN
ejpam-4643	24	53	is	be	AUX
ejpam-4643	24	54	said	say	VERB
ejpam-4643	24	55	to	to	PART
ejpam-4643	24	56	resolve	resolve	VERB
ejpam-4643	24	57	two	two	NUM
ejpam-4643	24	58	vertices	vertex	NOUN
ejpam-4643	24	59	u	u	NOUN
ejpam-4643	24	60	and	and	CCONJ
ejpam-4643	24	61	v	v	NOUN
ejpam-4643	24	62	of	of	ADP
ejpam-4643	24	63	g	g	PROPN
ejpam-4643	24	64	if	if	SCONJ
ejpam-4643	24	65	dg(x	dg(x	NUM
ejpam-4643	24	66	,	,	PUNCT
ejpam-4643	24	67	u	u	NOUN
ejpam-4643	24	68	)	)	PUNCT
ejpam-4643	24	69	̸=	̸=	PROPN
ejpam-4643	24	70	dg(x	dg(x	NUM
ejpam-4643	24	71	,	,	PUNCT
ejpam-4643	24	72	v	v	NOUN
ejpam-4643	24	73	)	)	PUNCT
ejpam-4643	24	74	.	.	PUNCT
ejpam-4643	25	1	for	for	ADP
ejpam-4643	25	2	an	an	DET
ejpam-4643	25	3	ordered	order	VERB
ejpam-4643	25	4	set	set	NOUN
ejpam-4643	25	5	w	w	NOUN
ejpam-4643	25	6	=	=	PUNCT
ejpam-4643	25	7	{	{	PUNCT
ejpam-4643	25	8	x1	x1	PROPN
ejpam-4643	25	9	,	,	PUNCT
ejpam-4643	25	10	.	.	PUNCT
ejpam-4643	25	11	.	.	PUNCT
ejpam-4643	25	12	.	.	PUNCT
ejpam-4643	26	1	,	,	PUNCT
ejpam-4643	26	2	xk	xk	ADJ
ejpam-4643	26	3	}	}	PUNCT
ejpam-4643	26	4	⊆	⊆	NUM
ejpam-4643	26	5	v	v	NOUN
ejpam-4643	26	6	(	(	PUNCT
ejpam-4643	26	7	g	g	NOUN
ejpam-4643	26	8	)	)	PUNCT
ejpam-4643	26	9	and	and	CCONJ
ejpam-4643	26	10	a	a	DET
ejpam-4643	26	11	vertex	vertex	NOUN
ejpam-4643	26	12	v	v	NOUN
ejpam-4643	26	13	in	in	ADP
ejpam-4643	26	14	g	g	PROPN
ejpam-4643	26	15	,	,	PUNCT
ejpam-4643	26	16	the	the	DET
ejpam-4643	26	17	k	k	NOUN
ejpam-4643	26	18	-	-	NOUN
ejpam-4643	26	19	vector	vector	NOUN
ejpam-4643	26	20	rg(v	rg(v	NOUN
ejpam-4643	26	21	/	/	SYM
ejpam-4643	26	22	w	w	NOUN
ejpam-4643	26	23	)	)	PUNCT
ejpam-4643	26	24	=	=	PRON
ejpam-4643	26	25	(	(	PUNCT
ejpam-4643	26	26	dg(v	dg(v	X
ejpam-4643	26	27	,	,	PUNCT
ejpam-4643	26	28	x1	x1	PROPN
ejpam-4643	26	29	)	)	PUNCT
ejpam-4643	26	30	,	,	PUNCT
ejpam-4643	26	31	dg(v	dg(v	X
ejpam-4643	26	32	,	,	PUNCT
ejpam-4643	26	33	x2	x2	PROPN
ejpam-4643	26	34	)	)	PUNCT
ejpam-4643	26	35	,	,	PUNCT
ejpam-4643	26	36	.	.	PUNCT
ejpam-4643	26	37	.	.	PUNCT
ejpam-4643	27	1	.	.	PUNCT
ejpam-4643	28	1	,	,	PUNCT
ejpam-4643	28	2	dg(v	dg(v	X
ejpam-4643	28	3	,	,	PUNCT
ejpam-4643	28	4	xk	xk	NOUN
ejpam-4643	28	5	)	)	PUNCT
ejpam-4643	28	6	)	)	PUNCT
ejpam-4643	28	7	is	be	AUX
ejpam-4643	28	8	called	call	VERB
ejpam-4643	28	9	the	the	DET
ejpam-4643	28	10	representation	representation	NOUN
ejpam-4643	28	11	of	of	ADP
ejpam-4643	28	12	v	v	NOUN
ejpam-4643	28	13	with	with	ADP
ejpam-4643	28	14	respect	respect	NOUN
ejpam-4643	28	15	to	to	ADP
ejpam-4643	28	16	w	w	PROPN
ejpam-4643	28	17	.	.	PUNCT
ejpam-4643	29	1	the	the	DET
ejpam-4643	29	2	set	set	NOUN
ejpam-4643	29	3	w	w	NOUN
ejpam-4643	29	4	is	be	AUX
ejpam-4643	29	5	a	a	DET
ejpam-4643	29	6	resolving	resolving	NOUN
ejpam-4643	29	7	set	set	VERB
ejpam-4643	29	8	for	for	ADP
ejpam-4643	29	9	g	g	PROPN
ejpam-4643	29	10	if	if	SCONJ
ejpam-4643	30	1	and	and	CCONJ
ejpam-4643	30	2	only	only	ADV
ejpam-4643	30	3	if	if	SCONJ
ejpam-4643	30	4	no	no	DET
ejpam-4643	30	5	two	two	NUM
ejpam-4643	30	6	distinct	distinct	ADJ
ejpam-4643	30	7	bvertices	bvertice	NOUN
ejpam-4643	30	8	of	of	ADP
ejpam-4643	30	9	g	g	PROPN
ejpam-4643	30	10	have	have	VERB
ejpam-4643	30	11	the	the	DET
ejpam-4643	30	12	same	same	ADJ
ejpam-4643	30	13	representation	representation	NOUN
ejpam-4643	30	14	with	with	ADP
ejpam-4643	30	15	respect	respect	NOUN
ejpam-4643	30	16	to	to	ADP
ejpam-4643	30	17	w	w	PROPN
ejpam-4643	30	18	.	.	PUNCT
ejpam-4643	31	1	the	the	DET
ejpam-4643	31	2	metric	metric	ADJ
ejpam-4643	31	3	dimension	dimension	NOUN
ejpam-4643	31	4	of	of	ADP
ejpam-4643	31	5	g	g	NOUN
ejpam-4643	31	6	,	,	PUNCT
ejpam-4643	31	7	denoted	denote	VERB
ejpam-4643	31	8	by	by	ADP
ejpam-4643	31	9	,	,	PUNCT
ejpam-4643	31	10	dim(g	dim(g	PROPN
ejpam-4643	31	11	)	)	PUNCT
ejpam-4643	31	12	,	,	PUNCT
ejpam-4643	31	13	is	be	AUX
ejpam-4643	31	14	the	the	DET
ejpam-4643	31	15	minimum	minimum	ADJ
ejpam-4643	31	16	cardinality	cardinality	NOUN
ejpam-4643	31	17	over	over	ADP
ejpam-4643	31	18	all	all	DET
ejpam-4643	31	19	resolving	resolve	VERB
ejpam-4643	31	20	sets	set	NOUN
ejpam-4643	31	21	of	of	ADP
ejpam-4643	31	22	g.	g.	PROPN
ejpam-4643	31	23	a	a	DET
ejpam-4643	31	24	resolving	resolve	VERB
ejpam-4643	31	25	set	set	NOUN
ejpam-4643	31	26	of	of	ADP
ejpam-4643	31	27	cardinality	cardinality	PROPN
ejpam-4643	31	28	dim(g	dim(g	PROPN
ejpam-4643	31	29	)	)	PUNCT
ejpam-4643	31	30	is	be	AUX
ejpam-4643	31	31	called	call	VERB
ejpam-4643	31	32	a	a	DET
ejpam-4643	31	33	basis	basis	NOUN
ejpam-4643	31	34	.	.	PUNCT
ejpam-4643	32	1	slater	slater	NOUN
ejpam-4643	33	1	[	[	X
ejpam-4643	33	2	10	10	NUM
ejpam-4643	33	3	]	]	PUNCT
ejpam-4643	33	4	brought	bring	VERB
ejpam-4643	33	5	in	in	ADP
ejpam-4643	33	6	the	the	DET
ejpam-4643	33	7	notion	notion	NOUN
ejpam-4643	33	8	of	of	ADP
ejpam-4643	33	9	locating	locate	VERB
ejpam-4643	33	10	sets	set	NOUN
ejpam-4643	33	11	and	and	CCONJ
ejpam-4643	33	12	its	its	PRON
ejpam-4643	33	13	minimum	minimum	ADJ
ejpam-4643	33	14	cardinality	cardinality	NOUN
ejpam-4643	33	15	as	as	ADP
ejpam-4643	33	16	locating	locate	VERB
ejpam-4643	33	17	number	number	NOUN
ejpam-4643	33	18	.	.	PUNCT
ejpam-4643	34	1	the	the	DET
ejpam-4643	34	2	same	same	ADJ
ejpam-4643	34	3	concept	concept	NOUN
ejpam-4643	34	4	was	be	AUX
ejpam-4643	34	5	also	also	ADV
ejpam-4643	34	6	introduced	introduce	VERB
ejpam-4643	34	7	by	by	ADP
ejpam-4643	34	8	harary	harary	NOUN
ejpam-4643	34	9	and	and	CCONJ
ejpam-4643	34	10	melter	melter	NOUN
ejpam-4643	35	1	[	[	X
ejpam-4643	35	2	5	5	NUM
ejpam-4643	35	3	]	]	PUNCT
ejpam-4643	35	4	but	but	CCONJ
ejpam-4643	35	5	using	use	VERB
ejpam-4643	35	6	the	the	DET
ejpam-4643	35	7	terms	term	NOUN
ejpam-4643	35	8	resolving	resolve	VERB
ejpam-4643	35	9	sets	set	NOUN
ejpam-4643	35	10	and	and	CCONJ
ejpam-4643	35	11	metric	metric	ADJ
ejpam-4643	35	12	dimension	dimension	NOUN
ejpam-4643	35	13	to	to	PART
ejpam-4643	35	14	refer	refer	VERB
ejpam-4643	35	15	to	to	ADP
ejpam-4643	35	16	locating	locate	VERB
ejpam-4643	35	17	sets	set	NOUN
ejpam-4643	35	18	and	and	CCONJ
ejpam-4643	35	19	locating	locate	VERB
ejpam-4643	35	20	number	number	NOUN
ejpam-4643	35	21	,	,	PUNCT
ejpam-4643	35	22	respectively	respectively	ADV
ejpam-4643	35	23	.	.	PUNCT
ejpam-4643	36	1	some	some	DET
ejpam-4643	36	2	variations	variation	NOUN
ejpam-4643	36	3	of	of	ADP
ejpam-4643	36	4	locating	locate	VERB
ejpam-4643	36	5	sets	set	NOUN
ejpam-4643	36	6	and	and	CCONJ
ejpam-4643	36	7	resolving	resolve	VERB
ejpam-4643	36	8	sets	set	NOUN
ejpam-4643	36	9	are	be	AUX
ejpam-4643	36	10	studied	study	VERB
ejpam-4643	36	11	in	in	ADP
ejpam-4643	36	12	[	[	X
ejpam-4643	36	13	2	2	NUM
ejpam-4643	36	14	,	,	PUNCT
ejpam-4643	36	15	6	6	NUM
ejpam-4643	36	16	–	–	PUNCT
ejpam-4643	36	17	9	9	NUM
ejpam-4643	36	18	,	,	PUNCT
ejpam-4643	36	19	11	11	NUM
ejpam-4643	36	20	,	,	PUNCT
ejpam-4643	36	21	12	12	NUM
ejpam-4643	36	22	]	]	PUNCT
ejpam-4643	36	23	.	.	PUNCT
ejpam-4643	37	1	let	let	VERB
ejpam-4643	37	2	g	g	PRON
ejpam-4643	37	3	be	be	AUX
ejpam-4643	37	4	a	a	DET
ejpam-4643	37	5	connected	connected	ADJ
ejpam-4643	37	6	graph	graph	NOUN
ejpam-4643	37	7	.	.	PUNCT
ejpam-4643	38	1	a	a	DET
ejpam-4643	38	2	set	set	NOUN
ejpam-4643	38	3	s	s	NOUN
ejpam-4643	38	4	⊆	⊆	NUM
ejpam-4643	38	5	v	v	NOUN
ejpam-4643	38	6	(	(	PUNCT
ejpam-4643	38	7	g	g	NOUN
ejpam-4643	38	8	)	)	PUNCT
ejpam-4643	38	9	is	be	AUX
ejpam-4643	38	10	a	a	DET
ejpam-4643	38	11	locating	locating	NOUN
ejpam-4643	38	12	set	set	NOUN
ejpam-4643	38	13	of	of	ADP
ejpam-4643	38	14	g	g	PROPN
ejpam-4643	38	15	if	if	SCONJ
ejpam-4643	38	16	for	for	ADP
ejpam-4643	38	17	every	every	DET
ejpam-4643	38	18	two	two	NUM
ejpam-4643	38	19	distinct	distinct	ADJ
ejpam-4643	38	20	vertices	vertex	NOUN
ejpam-4643	38	21	u	u	NOUN
ejpam-4643	38	22	and	and	CCONJ
ejpam-4643	38	23	v	v	NOUN
ejpam-4643	38	24	of	of	ADP
ejpam-4643	38	25	v	v	NOUN
ejpam-4643	38	26	(	(	PUNCT
ejpam-4643	38	27	g	g	NOUN
ejpam-4643	38	28	)	)	PUNCT
ejpam-4643	38	29	\	\	PROPN
ejpam-4643	39	1	s	s	X
ejpam-4643	39	2	,	,	PUNCT
ejpam-4643	39	3	ng(u)∩	ng(u)∩	PROPN
ejpam-4643	39	4	s	s	PART
ejpam-4643	39	5	̸=	̸=	PROPN
ejpam-4643	39	6	ng(v)∩	ng(v)∩	ADP
ejpam-4643	39	7	s.	s.	PROPN
ejpam-4643	40	1	the	the	DET
ejpam-4643	40	2	locating	locate	VERB
ejpam-4643	40	3	number	number	NOUN
ejpam-4643	40	4	of	of	ADP
ejpam-4643	40	5	g	g	NOUN
ejpam-4643	40	6	,	,	PUNCT
ejpam-4643	40	7	denoted	denote	VERB
ejpam-4643	40	8	by	by	ADP
ejpam-4643	40	9	ln(g	ln(g	NOUN
ejpam-4643	40	10	)	)	PUNCT
ejpam-4643	40	11	,	,	PUNCT
ejpam-4643	40	12	is	be	AUX
ejpam-4643	40	13	the	the	DET
ejpam-4643	40	14	smallest	small	ADJ
ejpam-4643	40	15	cardinality	cardinality	NOUN
ejpam-4643	40	16	of	of	ADP
ejpam-4643	40	17	a	a	DET
ejpam-4643	40	18	locating	locating	NOUN
ejpam-4643	40	19	set	set	NOUN
ejpam-4643	40	20	of	of	ADP
ejpam-4643	40	21	g.	g.	PROPN
ejpam-4643	40	22	a	a	DET
ejpam-4643	40	23	locating	locate	VERB
ejpam-4643	40	24	set	set	NOUN
ejpam-4643	40	25	of	of	ADP
ejpam-4643	40	26	g	g	PROPN
ejpam-4643	40	27	of	of	ADP
ejpam-4643	40	28	cardinality	cardinality	PROPN
ejpam-4643	40	29	ln(g	ln(g	PUNCT
ejpam-4643	40	30	)	)	PUNCT
ejpam-4643	40	31	is	be	AUX
ejpam-4643	40	32	referred	refer	VERB
ejpam-4643	40	33	to	to	ADP
ejpam-4643	40	34	as	as	ADP
ejpam-4643	40	35	an	an	DET
ejpam-4643	40	36	ln	ln	ADV
ejpam-4643	40	37	-	-	PUNCT
ejpam-4643	40	38	set	set	NOUN
ejpam-4643	40	39	of	of	ADP
ejpam-4643	40	40	g.	g.	PROPN
ejpam-4643	40	41	let	let	VERB
ejpam-4643	40	42	g	g	NOUN
ejpam-4643	40	43	be	be	AUX
ejpam-4643	40	44	a	a	DET
ejpam-4643	40	45	connected	connected	ADJ
ejpam-4643	40	46	graph	graph	NOUN
ejpam-4643	40	47	.	.	PUNCT
ejpam-4643	41	1	a	a	DET
ejpam-4643	41	2	set	set	NOUN
ejpam-4643	41	3	s	s	NOUN
ejpam-4643	41	4	⊆	⊆	NUM
ejpam-4643	41	5	v	v	NOUN
ejpam-4643	41	6	(	(	PUNCT
ejpam-4643	41	7	g	g	NOUN
ejpam-4643	41	8	)	)	PUNCT
ejpam-4643	41	9	is	be	AUX
ejpam-4643	41	10	a	a	DET
ejpam-4643	41	11	strictly	strictly	ADV
ejpam-4643	41	12	locating	locate	VERB
ejpam-4643	41	13	set	set	NOUN
ejpam-4643	41	14	of	of	ADP
ejpam-4643	41	15	g	g	NOUN
ejpam-4643	41	16	if	if	SCONJ
ejpam-4643	41	17	it	it	PRON
ejpam-4643	41	18	is	be	AUX
ejpam-4643	41	19	a	a	DET
ejpam-4643	41	20	locating	locating	NOUN
ejpam-4643	41	21	set	set	NOUN
ejpam-4643	41	22	of	of	ADP
ejpam-4643	41	23	g	g	PROPN
ejpam-4643	41	24	and	and	CCONJ
ejpam-4643	41	25	ng(u)∩s	ng(u)∩s	PROPN
ejpam-4643	41	26	̸=	̸=	PROPN
ejpam-4643	41	27	s	s	PART
ejpam-4643	41	28	,	,	PUNCT
ejpam-4643	41	29	for	for	ADP
ejpam-4643	41	30	all	all	DET
ejpam-4643	41	31	u	u	PROPN
ejpam-4643	41	32	∈	∈	PROPN
ejpam-4643	41	33	v	v	NOUN
ejpam-4643	41	34	(	(	PUNCT
ejpam-4643	41	35	g)\s	g)\s	NOUN
ejpam-4643	41	36	.	.	PUNCT
ejpam-4643	42	1	the	the	DET
ejpam-4643	42	2	strictly	strictly	ADV
ejpam-4643	42	3	locating	locate	VERB
ejpam-4643	42	4	number	number	NOUN
ejpam-4643	42	5	of	of	ADP
ejpam-4643	42	6	g	g	NOUN
ejpam-4643	42	7	,	,	PUNCT
ejpam-4643	42	8	denoted	denote	VERB
ejpam-4643	42	9	by	by	ADP
ejpam-4643	42	10	sln(g	sln(g	PROPN
ejpam-4643	42	11	)	)	PUNCT
ejpam-4643	42	12	,	,	PUNCT
ejpam-4643	42	13	is	be	AUX
ejpam-4643	42	14	the	the	DET
ejpam-4643	42	15	smallest	small	ADJ
ejpam-4643	42	16	cardinality	cardinality	NOUN
ejpam-4643	42	17	of	of	ADP
ejpam-4643	42	18	a	a	DET
ejpam-4643	42	19	strictly	strictly	ADV
ejpam-4643	42	20	locating	locate	VERB
ejpam-4643	42	21	set	set	NOUN
ejpam-4643	42	22	of	of	ADP
ejpam-4643	42	23	g.	g.	PROPN
ejpam-4643	42	24	a	a	DET
ejpam-4643	42	25	strictly	strictly	ADV
ejpam-4643	42	26	locating	locate	VERB
ejpam-4643	42	27	set	set	NOUN
ejpam-4643	42	28	of	of	ADP
ejpam-4643	42	29	g	g	PROPN
ejpam-4643	42	30	of	of	ADP
ejpam-4643	42	31	cardinality	cardinality	PROPN
ejpam-4643	42	32	sln(g	sln(g	PROPN
ejpam-4643	42	33	)	)	PUNCT
ejpam-4643	42	34	is	be	AUX
ejpam-4643	42	35	referred	refer	VERB
ejpam-4643	42	36	to	to	ADP
ejpam-4643	42	37	as	as	SCONJ
ejpam-4643	42	38	sln	sln	NOUN
ejpam-4643	42	39	-	-	PUNCT
ejpam-4643	42	40	set	set	NOUN
ejpam-4643	42	41	of	of	ADP
ejpam-4643	42	42	g.	g.	PROPN
ejpam-4643	42	43	a	a	DET
ejpam-4643	42	44	connected	connected	ADJ
ejpam-4643	42	45	graph	graph	NOUN
ejpam-4643	42	46	g	g	NOUN
ejpam-4643	42	47	of	of	ADP
ejpam-4643	42	48	order	order	NOUN
ejpam-4643	42	49	n	n	PRON
ejpam-4643	42	50	≥	≥	NOUN
ejpam-4643	42	51	3	3	NUM
ejpam-4643	42	52	is	be	AUX
ejpam-4643	42	53	point	point	NOUN
ejpam-4643	42	54	distinguishing	distinguish	VERB
ejpam-4643	42	55	if	if	SCONJ
ejpam-4643	42	56	for	for	ADP
ejpam-4643	42	57	any	any	DET
ejpam-4643	42	58	two	two	NUM
ejpam-4643	42	59	distinct	distinct	ADJ
ejpam-4643	42	60	vertices	vertex	NOUN
ejpam-4643	42	61	u	u	NOUN
ejpam-4643	42	62	and	and	CCONJ
ejpam-4643	42	63	v	v	NOUN
ejpam-4643	42	64	of	of	ADP
ejpam-4643	42	65	g	g	NOUN
ejpam-4643	42	66	,	,	PUNCT
ejpam-4643	42	67	ng(u	ng(u	NOUN
ejpam-4643	42	68	)	)	PUNCT
ejpam-4643	42	69	̸=	̸=	PROPN
ejpam-4643	42	70	ng(v	ng(v	PUNCT
ejpam-4643	42	71	)	)	PUNCT
ejpam-4643	43	1	[	[	X
ejpam-4643	43	2	3	3	NUM
ejpam-4643	43	3	]	]	PUNCT
ejpam-4643	43	4	.	.	PUNCT
ejpam-4643	44	1	it	it	PRON
ejpam-4643	44	2	is	be	AUX
ejpam-4643	44	3	totally	totally	ADV
ejpam-4643	44	4	point	point	NOUN
ejpam-4643	44	5	determining	determine	VERB
ejpam-4643	44	6	if	if	SCONJ
ejpam-4643	44	7	for	for	ADP
ejpam-4643	44	8	any	any	DET
ejpam-4643	44	9	two	two	NUM
ejpam-4643	44	10	distinct	distinct	ADJ
ejpam-4643	44	11	vertices	vertex	NOUN
ejpam-4643	44	12	u	u	NOUN
ejpam-4643	44	13	and	and	CCONJ
ejpam-4643	44	14	v	v	NOUN
ejpam-4643	44	15	of	of	ADP
ejpam-4643	44	16	g	g	NOUN
ejpam-4643	44	17	,	,	PUNCT
ejpam-4643	44	18	ng(u	ng(u	NOUN
ejpam-4643	44	19	)	)	PUNCT
ejpam-4643	44	20	̸=	̸=	PROPN
ejpam-4643	44	21	ng(v	ng(v	PUNCT
ejpam-4643	44	22	)	)	PUNCT
ejpam-4643	44	23	and	and	CCONJ
ejpam-4643	44	24	ng[u	ng[u	PROPN
ejpam-4643	44	25	]	]	X
ejpam-4643	44	26	̸=	̸=	PROPN
ejpam-4643	44	27	ng[v	ng[v	X
ejpam-4643	44	28	]	]	PUNCT
ejpam-4643	45	1	[	[	X
ejpam-4643	45	2	13	13	NUM
ejpam-4643	45	3	]	]	PUNCT
ejpam-4643	45	4	.	.	PUNCT
ejpam-4643	46	1	brigham	brigham	PROPN
ejpam-4643	46	2	et	et	PROPN
ejpam-4643	46	3	al	al	PROPN
ejpam-4643	46	4	.	.	PUNCT
ejpam-4643	47	1	[	[	X
ejpam-4643	47	2	1	1	X
ejpam-4643	47	3	]	]	PUNCT
ejpam-4643	47	4	defined	define	VERB
ejpam-4643	47	5	a	a	DET
ejpam-4643	47	6	resolving	resolve	VERB
ejpam-4643	47	7	dominating	dominating	NOUN
ejpam-4643	47	8	set	set	VERB
ejpam-4643	47	9	as	as	ADP
ejpam-4643	47	10	a	a	DET
ejpam-4643	47	11	set	set	NOUN
ejpam-4643	47	12	s	s	NOUN
ejpam-4643	47	13	of	of	ADP
ejpam-4643	47	14	vertices	vertex	NOUN
ejpam-4643	47	15	of	of	ADP
ejpam-4643	47	16	a	a	DET
ejpam-4643	47	17	connected	connected	ADJ
ejpam-4643	47	18	graph	graph	NOUN
ejpam-4643	47	19	g	g	NOUN
ejpam-4643	47	20	that	that	PRON
ejpam-4643	47	21	is	be	AUX
ejpam-4643	47	22	both	both	PRON
ejpam-4643	47	23	resolving	resolve	VERB
ejpam-4643	47	24	and	and	CCONJ
ejpam-4643	47	25	dominating	dominating	NOUN
ejpam-4643	47	26	.	.	PUNCT
ejpam-4643	48	1	the	the	DET
ejpam-4643	48	2	cardinality	cardinality	NOUN
ejpam-4643	48	3	of	of	ADP
ejpam-4643	48	4	a	a	DET
ejpam-4643	48	5	minimum	minimum	ADJ
ejpam-4643	48	6	resolving	resolving	NOUN
ejpam-4643	48	7	dominating	dominating	NOUN
ejpam-4643	48	8	set	set	NOUN
ejpam-4643	48	9	is	be	AUX
ejpam-4643	48	10	called	call	VERB
ejpam-4643	48	11	the	the	DET
ejpam-4643	48	12	resolving	resolve	VERB
ejpam-4643	48	13	domination	domination	NOUN
ejpam-4643	48	14	number	number	NOUN
ejpam-4643	48	15	of	of	ADP
ejpam-4643	48	16	g	g	NOUN
ejpam-4643	48	17	and	and	CCONJ
ejpam-4643	48	18	is	be	AUX
ejpam-4643	48	19	denoted	denote	VERB
ejpam-4643	48	20	by	by	ADP
ejpam-4643	48	21	γr(g	γr(g	PROPN
ejpam-4643	48	22	)	)	PUNCT
ejpam-4643	48	23	.	.	PUNCT
ejpam-4643	49	1	a	a	DET
ejpam-4643	49	2	resolving	resolve	VERB
ejpam-4643	49	3	dominating	dominating	NOUN
ejpam-4643	49	4	set	set	NOUN
ejpam-4643	49	5	of	of	ADP
ejpam-4643	49	6	cardinality	cardinality	PROPN
ejpam-4643	49	7	γr(g	γr(g	PROPN
ejpam-4643	49	8	)	)	PUNCT
ejpam-4643	49	9	is	be	AUX
ejpam-4643	49	10	called	call	VERB
ejpam-4643	49	11	a	a	DET
ejpam-4643	49	12	γr	γr	PROPN
ejpam-4643	49	13	-	-	PUNCT
ejpam-4643	49	14	set	set	NOUN
ejpam-4643	49	15	of	of	ADP
ejpam-4643	49	16	g.	g.	PROPN
ejpam-4643	49	17	canoy	canoy	PROPN
ejpam-4643	49	18	and	and	CCONJ
ejpam-4643	49	19	malacas	malacas	NOUN
ejpam-4643	49	20	[	[	X
ejpam-4643	49	21	11	11	NUM
ejpam-4643	49	22	]	]	PUNCT
ejpam-4643	49	23	defined	define	VERB
ejpam-4643	49	24	a	a	DET
ejpam-4643	49	25	locating	locate	VERB
ejpam-4643	49	26	-	-	PUNCT
ejpam-4643	49	27	dominating	dominate	VERB
ejpam-4643	49	28	(	(	PUNCT
ejpam-4643	49	29	resp	resp	NOUN
ejpam-4643	49	30	.	.	PUNCT
ejpam-4643	50	1	strictly	strictly	ADV
ejpam-4643	50	2	locating	locate	VERB
ejpam-4643	50	3	-	-	PUNCT
ejpam-4643	50	4	dominating	dominating	NOUN
ejpam-4643	50	5	)	)	PUNCT
ejpam-4643	50	6	as	as	ADP
ejpam-4643	50	7	a	a	DET
ejpam-4643	50	8	locating	locating	NOUN
ejpam-4643	50	9	(	(	PUNCT
ejpam-4643	50	10	resp	resp	NOUN
ejpam-4643	50	11	.	.	PUNCT
ejpam-4643	51	1	strictly	strictly	ADV
ejpam-4643	51	2	locating	locate	VERB
ejpam-4643	51	3	)	)	PUNCT
ejpam-4643	51	4	subset	subset	NOUN
ejpam-4643	51	5	s	s	PROPN
ejpam-4643	51	6	of	of	ADP
ejpam-4643	51	7	v	v	NOUN
ejpam-4643	51	8	(	(	PUNCT
ejpam-4643	51	9	g	g	NOUN
ejpam-4643	51	10	)	)	PUNCT
ejpam-4643	51	11	which	which	PRON
ejpam-4643	51	12	is	be	AUX
ejpam-4643	51	13	also	also	ADV
ejpam-4643	51	14	dominating	dominate	VERB
ejpam-4643	51	15	set	set	VERB
ejpam-4643	51	16	in	in	ADP
ejpam-4643	51	17	a	a	DET
ejpam-4643	51	18	connected	connected	ADJ
ejpam-4643	51	19	graph	graph	NOUN
ejpam-4643	51	20	g.	g.	VERB
ejpam-4643	51	21	the	the	DET
ejpam-4643	51	22	minimum	minimum	ADJ
ejpam-4643	51	23	cardinality	cardinality	NOUN
ejpam-4643	51	24	of	of	ADP
ejpam-4643	51	25	a	a	DET
ejpam-4643	51	26	locating	locate	VERB
ejpam-4643	51	27	-	-	PUNCT
ejpam-4643	51	28	dominating	dominate	VERB
ejpam-4643	51	29	(	(	PUNCT
ejpam-4643	51	30	resp	resp	NOUN
ejpam-4643	51	31	.	.	PUNCT
ejpam-4643	52	1	strictly	strictly	ADV
ejpam-4643	52	2	locating	locate	VERB
ejpam-4643	52	3	-	-	PUNCT
ejpam-4643	52	4	dominating	dominating	NOUN
ejpam-4643	52	5	)	)	PUNCT
ejpam-4643	52	6	set	set	VERB
ejpam-4643	52	7	in	in	ADP
ejpam-4643	52	8	g	g	NOUN
ejpam-4643	52	9	,	,	PUNCT
ejpam-4643	52	10	denoted	denote	VERB
ejpam-4643	52	11	by	by	ADP
ejpam-4643	52	12	γl(g	γl(g	NUM
ejpam-4643	52	13	)	)	PUNCT
ejpam-4643	52	14	(	(	PUNCT
ejpam-4643	52	15	resp	resp	NOUN
ejpam-4643	52	16	.	.	PUNCT
ejpam-4643	53	1	(	(	PUNCT
ejpam-4643	53	2	γsl	γsl	NOUN
ejpam-4643	53	3	)	)	PUNCT
ejpam-4643	53	4	)	)	PUNCT
ejpam-4643	53	5	,	,	PUNCT
ejpam-4643	53	6	is	be	AUX
ejpam-4643	53	7	called	call	VERB
ejpam-4643	53	8	the	the	DET
ejpam-4643	53	9	l	l	NOUN
ejpam-4643	53	10	-	-	NOUN
ejpam-4643	53	11	domination	domination	NOUN
ejpam-4643	53	12	(	(	PUNCT
ejpam-4643	53	13	resp	resp	NOUN
ejpam-4643	53	14	.	.	PUNCT
ejpam-4643	54	1	sl	sl	NOUN
ejpam-4643	54	2	-	-	PUNCT
ejpam-4643	54	3	domination	domination	NOUN
ejpam-4643	54	4	)	)	PUNCT
ejpam-4643	54	5	number	number	NOUN
ejpam-4643	54	6	of	of	ADP
ejpam-4643	54	7	g.	g.	PROPN
ejpam-4643	54	8	any	any	DET
ejpam-4643	54	9	l	l	NOUN
ejpam-4643	54	10	-	-	ADJ
ejpam-4643	54	11	dominating	dominate	VERB
ejpam-4643	54	12	(	(	PUNCT
ejpam-4643	54	13	resp	resp	NOUN
ejpam-4643	54	14	.	.	PUNCT
ejpam-4643	55	1	sl	sl	NOUN
ejpam-4643	55	2	-	-	PUNCT
ejpam-4643	55	3	dominating	dominating	NOUN
ejpam-4643	55	4	)	)	PUNCT
ejpam-4643	55	5	set	set	NOUN
ejpam-4643	55	6	of	of	ADP
ejpam-4643	55	7	cardinality	cardinality	PROPN
ejpam-4643	55	8	γl(g	γl(g	NUM
ejpam-4643	55	9	)	)	PUNCT
ejpam-4643	55	10	(	(	PUNCT
ejpam-4643	55	11	resp	resp	NOUN
ejpam-4643	55	12	.	.	PUNCT
ejpam-4643	55	13	γsl(g	γsl(g	X
ejpam-4643	55	14	)	)	PUNCT
ejpam-4643	55	15	)	)	PUNCT
ejpam-4643	55	16	is	be	AUX
ejpam-4643	55	17	then	then	ADV
ejpam-4643	55	18	referred	refer	VERB
ejpam-4643	55	19	to	to	ADP
ejpam-4643	55	20	as	as	ADP
ejpam-4643	55	21	a	a	DET
ejpam-4643	55	22	γl	γl	NOUN
ejpam-4643	55	23	-	-	PUNCT
ejpam-4643	55	24	set	set	VERB
ejpam-4643	55	25	(	(	PUNCT
ejpam-4643	55	26	γsl	γsl	NOUN
ejpam-4643	55	27	-	-	PUNCT
ejpam-4643	55	28	set	set	NOUN
ejpam-4643	55	29	)	)	PUNCT
ejpam-4643	55	30	of	of	ADP
ejpam-4643	55	31	g.	g.	PROPN
ejpam-4643	55	32	let	let	VERB
ejpam-4643	55	33	g	g	NOUN
ejpam-4643	55	34	be	be	AUX
ejpam-4643	55	35	a	a	DET
ejpam-4643	55	36	connected	connected	ADJ
ejpam-4643	55	37	graph	graph	NOUN
ejpam-4643	55	38	.	.	PUNCT
ejpam-4643	56	1	a	a	DET
ejpam-4643	56	2	set	set	NOUN
ejpam-4643	56	3	s	s	NOUN
ejpam-4643	56	4	⊆	⊆	NUM
ejpam-4643	56	5	v	v	NOUN
ejpam-4643	56	6	(	(	PUNCT
ejpam-4643	56	7	g	g	NOUN
ejpam-4643	56	8	)	)	PUNCT
ejpam-4643	56	9	is	be	AUX
ejpam-4643	56	10	strictly	strictly	ADV
ejpam-4643	56	11	resolving	resolve	VERB
ejpam-4643	56	12	dominating	dominating	NOUN
ejpam-4643	56	13	set	set	NOUN
ejpam-4643	56	14	of	of	ADP
ejpam-4643	56	15	g	g	PROPN
ejpam-4643	56	16	if	if	SCONJ
ejpam-4643	56	17	it	it	PRON
ejpam-4643	56	18	is	be	AUX
ejpam-4643	56	19	a	a	DET
ejpam-4643	56	20	resolving	resolve	VERB
ejpam-4643	56	21	dominating	dominating	NOUN
ejpam-4643	56	22	set	set	NOUN
ejpam-4643	56	23	of	of	ADP
ejpam-4643	56	24	g	g	PROPN
ejpam-4643	56	25	and	and	CCONJ
ejpam-4643	56	26	ng	ng	PROPN
ejpam-4643	56	27	∩	∩	PROPN
ejpam-4643	56	28	s	s	PART
ejpam-4643	56	29	̸=	̸=	PROPN
ejpam-4643	56	30	s	s	X
ejpam-4643	56	31	for	for	ADP
ejpam-4643	56	32	u	u	PROPN
ejpam-4643	56	33	∈	∈	PROPN
ejpam-4643	56	34	v	v	ADP
ejpam-4643	56	35	(	(	PUNCT
ejpam-4643	56	36	g	g	NOUN
ejpam-4643	56	37	)	)	PUNCT
ejpam-4643	56	38	\	\	PUNCT
ejpam-4643	57	1	s.	s.	PROPN
ejpam-4643	57	2	the	the	DET
ejpam-4643	57	3	strictly	strictly	ADV
ejpam-4643	57	4	resolving	resolve	VERB
ejpam-4643	57	5	dominating	dominating	NOUN
ejpam-4643	57	6	number	number	NOUN
ejpam-4643	57	7	of	of	ADP
ejpam-4643	57	8	g	g	NOUN
ejpam-4643	57	9	,	,	PUNCT
ejpam-4643	57	10	denoted	denote	VERB
ejpam-4643	57	11	by	by	ADP
ejpam-4643	57	12	γsr(g	γsr(g	PROPN
ejpam-4643	57	13	)	)	PUNCT
ejpam-4643	57	14	,	,	PUNCT
ejpam-4643	57	15	is	be	AUX
ejpam-4643	57	16	the	the	DET
ejpam-4643	57	17	smallest	small	ADJ
ejpam-4643	57	18	cardinality	cardinality	NOUN
ejpam-4643	57	19	of	of	ADP
ejpam-4643	57	20	a	a	DET
ejpam-4643	57	21	strictly	strictly	ADV
ejpam-4643	57	22	resolving	resolve	VERB
ejpam-4643	57	23	dominating	dominating	NOUN
ejpam-4643	57	24	set	set	NOUN
ejpam-4643	57	25	of	of	ADP
ejpam-4643	57	26	g.	g.	PROPN
ejpam-4643	57	27	a	a	DET
ejpam-4643	57	28	strictly	strictly	ADV
ejpam-4643	57	29	resolving	resolve	VERB
ejpam-4643	57	30	dominating	dominating	NOUN
ejpam-4643	57	31	set	set	NOUN
ejpam-4643	57	32	of	of	ADP
ejpam-4643	57	33	g	g	NOUN
ejpam-4643	57	34	of	of	ADP
ejpam-4643	57	35	cardinality	cardinality	PROPN
ejpam-4643	57	36	γsr(g	γsr(g	NOUN
ejpam-4643	57	37	)	)	PUNCT
ejpam-4643	57	38	is	be	AUX
ejpam-4643	57	39	referred	refer	VERB
ejpam-4643	57	40	to	to	ADP
ejpam-4643	57	41	as	as	SCONJ
ejpam-4643	57	42	γsr	γsr	PROPN
ejpam-4643	57	43	-	-	PUNCT
ejpam-4643	57	44	set	set	NOUN
ejpam-4643	57	45	of	of	ADP
ejpam-4643	57	46	g.	g.	PROPN
ejpam-4643	57	47	this	this	DET
ejpam-4643	57	48	study	study	NOUN
ejpam-4643	57	49	aims	aim	VERB
ejpam-4643	57	50	to	to	PART
ejpam-4643	57	51	define	define	VERB
ejpam-4643	57	52	and	and	CCONJ
ejpam-4643	57	53	characterize	characterize	VERB
ejpam-4643	57	54	the	the	DET
ejpam-4643	57	55	resolving	resolve	VERB
ejpam-4643	57	56	dominating	dominating	NOUN
ejpam-4643	57	57	sets	set	NOUN
ejpam-4643	57	58	in	in	ADP
ejpam-4643	57	59	the	the	DET
ejpam-4643	57	60	join	join	NOUN
ejpam-4643	57	61	,	,	PUNCT
ejpam-4643	57	62	corona	corona	NOUN
ejpam-4643	57	63	and	and	CCONJ
ejpam-4643	57	64	lexicographic	lexicographic	ADJ
ejpam-4643	57	65	product	product	NOUN
ejpam-4643	57	66	of	of	ADP
ejpam-4643	57	67	graphs	graph	NOUN
ejpam-4643	57	68	and	and	CCONJ
ejpam-4643	57	69	determine	determine	VERB
ejpam-4643	57	70	their	their	PRON
ejpam-4643	57	71	corresponding	correspond	VERB
ejpam-4643	57	72	resolving	resolving	NOUN
ejpam-4643	57	73	domination	domination	NOUN
ejpam-4643	57	74	number	number	NOUN
ejpam-4643	57	75	.	.	PUNCT
ejpam-4643	58	1	g.	g.	PROPN
ejpam-4643	58	2	monsanto	monsanto	PROPN
ejpam-4643	58	3	,	,	PUNCT
ejpam-4643	58	4	h.	h.	PROPN
ejpam-4643	58	5	rara	rara	PROPN
ejpam-4643	58	6	/	/	SYM
ejpam-4643	58	7	eur	eur	PROPN
ejpam-4643	58	8	.	.	PUNCT
ejpam-4643	59	1	j.	j.	PROPN
ejpam-4643	59	2	pure	pure	PROPN
ejpam-4643	59	3	appl	appl	PROPN
ejpam-4643	59	4	.	.	PROPN
ejpam-4643	59	5	math	math	PROPN
ejpam-4643	59	6	,	,	PUNCT
ejpam-4643	59	7	16	16	NUM
ejpam-4643	59	8	(	(	PUNCT
ejpam-4643	59	9	1	1	NUM
ejpam-4643	59	10	)	)	PUNCT
ejpam-4643	59	11	(	(	PUNCT
ejpam-4643	59	12	2023	2023	NUM
ejpam-4643	59	13	)	)	PUNCT
ejpam-4643	59	14	,	,	PUNCT
ejpam-4643	59	15	18	18	NUM
ejpam-4643	59	16	-	-	SYM
ejpam-4643	59	17	28	28	NUM
ejpam-4643	59	18	20	20	NUM
ejpam-4643	59	19	2	2	NUM
ejpam-4643	59	20	.	.	PUNCT
ejpam-4643	59	21	preliminary	preliminary	ADJ
ejpam-4643	59	22	results	result	NOUN
ejpam-4643	59	23	remark	remark	VERB
ejpam-4643	59	24	1	1	NUM
ejpam-4643	59	25	.	.	PUNCT
ejpam-4643	60	1	every	every	DET
ejpam-4643	60	2	locating	locate	VERB
ejpam-4643	60	3	-	-	PUNCT
ejpam-4643	60	4	dominating	dominate	VERB
ejpam-4643	60	5	set	set	NOUN
ejpam-4643	60	6	of	of	ADP
ejpam-4643	60	7	a	a	DET
ejpam-4643	60	8	connected	connected	ADJ
ejpam-4643	60	9	graph	graph	NOUN
ejpam-4643	60	10	g	g	PROPN
ejpam-4643	60	11	is	be	AUX
ejpam-4643	60	12	a	a	DET
ejpam-4643	60	13	resolving	resolve	VERB
ejpam-4643	60	14	dominating	dominating	NOUN
ejpam-4643	60	15	set	set	NOUN
ejpam-4643	60	16	and	and	CCONJ
ejpam-4643	60	17	every	every	DET
ejpam-4643	60	18	resolving	resolve	VERB
ejpam-4643	60	19	dominating	dominating	NOUN
ejpam-4643	60	20	set	set	NOUN
ejpam-4643	60	21	is	be	AUX
ejpam-4643	60	22	a	a	DET
ejpam-4643	60	23	dominating	dominating	NOUN
ejpam-4643	60	24	set	set	NOUN
ejpam-4643	60	25	of	of	ADP
ejpam-4643	60	26	g.	g.	PROPN
ejpam-4643	60	27	hence	hence	ADV
ejpam-4643	60	28	,	,	PUNCT
ejpam-4643	60	29	γ(g	γ(g	PROPN
ejpam-4643	60	30	)	)	PUNCT
ejpam-4643	60	31	≤	≤	NOUN
ejpam-4643	60	32	γr(g	γr(g	NOUN
ejpam-4643	60	33	)	)	PUNCT
ejpam-4643	60	34	≤	≤	NUM
ejpam-4643	60	35	γl(g	γl(g	NUM
ejpam-4643	60	36	)	)	PUNCT
ejpam-4643	60	37	.	.	PUNCT
ejpam-4643	61	1	example	example	NOUN
ejpam-4643	62	1	1	1	X
ejpam-4643	62	2	.	.	X
ejpam-4643	62	3	consider	consider	VERB
ejpam-4643	62	4	the	the	DET
ejpam-4643	62	5	graph	graph	NOUN
ejpam-4643	62	6	g	g	NOUN
ejpam-4643	62	7	in	in	ADP
ejpam-4643	62	8	figure	figure	NOUN
ejpam-4643	62	9	1	1	NUM
ejpam-4643	62	10	and	and	CCONJ
ejpam-4643	62	11	let	let	VERB
ejpam-4643	62	12	s	s	AUX
ejpam-4643	62	13	=	=	NOUN
ejpam-4643	62	14	{	{	PUNCT
ejpam-4643	62	15	v1	v1	PROPN
ejpam-4643	62	16	,	,	PUNCT
ejpam-4643	62	17	v5	v5	PROPN
ejpam-4643	62	18	}	}	PUNCT
ejpam-4643	62	19	.	.	PUNCT
ejpam-4643	63	1	observe	observe	VERB
ejpam-4643	63	2	that	that	SCONJ
ejpam-4643	63	3	ng[s	ng[	NOUN
ejpam-4643	63	4	]	]	X
ejpam-4643	63	5	=	=	SYM
ejpam-4643	63	6	v	v	NOUN
ejpam-4643	63	7	(	(	PUNCT
ejpam-4643	63	8	g	g	NOUN
ejpam-4643	63	9	)	)	PUNCT
ejpam-4643	63	10	,	,	PUNCT
ejpam-4643	63	11	that	that	ADV
ejpam-4643	63	12	is	is	ADV
ejpam-4643	63	13	,	,	PUNCT
ejpam-4643	63	14	s	s	VERB
ejpam-4643	63	15	is	be	AUX
ejpam-4643	63	16	a	a	DET
ejpam-4643	63	17	dominating	dominating	NOUN
ejpam-4643	63	18	set	set	VERB
ejpam-4643	63	19	in	in	ADP
ejpam-4643	63	20	g.	g.	PROPN
ejpam-4643	63	21	moreover	moreover	ADV
ejpam-4643	63	22	,	,	PUNCT
ejpam-4643	63	23	s	s	VERB
ejpam-4643	63	24	is	be	AUX
ejpam-4643	63	25	a	a	DET
ejpam-4643	63	26	resolving	resolving	NOUN
ejpam-4643	63	27	set	set	VERB
ejpam-4643	63	28	since	since	SCONJ
ejpam-4643	63	29	the	the	DET
ejpam-4643	63	30	representation	representation	NOUN
ejpam-4643	63	31	of	of	ADP
ejpam-4643	63	32	each	each	DET
ejpam-4643	63	33	vertex	vertex	NOUN
ejpam-4643	63	34	in	in	ADP
ejpam-4643	63	35	g	g	NOUN
ejpam-4643	63	36	,	,	PUNCT
ejpam-4643	63	37	with	with	ADP
ejpam-4643	63	38	respect	respect	NOUN
ejpam-4643	63	39	to	to	ADP
ejpam-4643	63	40	s	s	NOUN
ejpam-4643	63	41	is	be	AUX
ejpam-4643	63	42	unique	unique	ADJ
ejpam-4643	63	43	:	:	PUNCT
ejpam-4643	63	44	rg(v1	rg(v1	VERB
ejpam-4643	63	45	/	/	SYM
ejpam-4643	63	46	s	s	NOUN
ejpam-4643	63	47	)	)	PUNCT
ejpam-4643	63	48	=	=	SYM
ejpam-4643	63	49	(	(	PUNCT
ejpam-4643	63	50	0	0	NUM
ejpam-4643	63	51	,	,	PUNCT
ejpam-4643	63	52	1	1	NUM
ejpam-4643	63	53	)	)	PUNCT
ejpam-4643	63	54	,	,	PUNCT
ejpam-4643	63	55	rg(v2	rg(v2	NOUN
ejpam-4643	63	56	/	/	SYM
ejpam-4643	63	57	s	s	NOUN
ejpam-4643	63	58	)	)	PUNCT
ejpam-4643	63	59	=	=	SYM
ejpam-4643	63	60	(	(	PUNCT
ejpam-4643	63	61	1	1	NUM
ejpam-4643	63	62	,	,	PUNCT
ejpam-4643	63	63	2	2	NUM
ejpam-4643	63	64	)	)	PUNCT
ejpam-4643	63	65	,	,	PUNCT
ejpam-4643	63	66	rg(v3	rg(v3	NOUN
ejpam-4643	63	67	/	/	SYM
ejpam-4643	63	68	s	s	NOUN
ejpam-4643	63	69	)	)	PUNCT
ejpam-4643	63	70	=	=	SYM
ejpam-4643	63	71	(	(	PUNCT
ejpam-4643	63	72	2	2	NUM
ejpam-4643	63	73	,	,	PUNCT
ejpam-4643	63	74	1	1	NUM
ejpam-4643	63	75	)	)	PUNCT
ejpam-4643	63	76	,	,	PUNCT
ejpam-4643	63	77	rg(v4	rg(v4	PROPN
ejpam-4643	63	78	/	/	SYM
ejpam-4643	63	79	s	s	NOUN
ejpam-4643	63	80	)	)	PUNCT
ejpam-4643	63	81	=	=	SYM
ejpam-4643	63	82	(	(	PUNCT
ejpam-4643	63	83	1	1	NUM
ejpam-4643	63	84	,	,	PUNCT
ejpam-4643	63	85	1	1	NUM
ejpam-4643	63	86	)	)	PUNCT
ejpam-4643	63	87	and	and	CCONJ
ejpam-4643	63	88	rg(v5	rg(v5	PROPN
ejpam-4643	63	89	/	/	SYM
ejpam-4643	63	90	s	s	NOUN
ejpam-4643	63	91	)	)	PUNCT
ejpam-4643	63	92	=	=	SYM
ejpam-4643	63	93	(	(	PUNCT
ejpam-4643	63	94	1	1	NUM
ejpam-4643	63	95	,	,	PUNCT
ejpam-4643	63	96	0	0	NUM
ejpam-4643	63	97	)	)	PUNCT
ejpam-4643	63	98	.	.	PUNCT
ejpam-4643	64	1	hence	hence	ADV
ejpam-4643	64	2	,	,	PUNCT
ejpam-4643	64	3	γr(g	γr(g	PROPN
ejpam-4643	64	4	)	)	PUNCT
ejpam-4643	64	5	≤	≤	NUM
ejpam-4643	64	6	|s|	|s|	PROPN
ejpam-4643	64	7	=	=	SYM
ejpam-4643	64	8	2	2	NUM
ejpam-4643	64	9	.	.	PUNCT
ejpam-4643	64	10	since	since	SCONJ
ejpam-4643	64	11	any	any	DET
ejpam-4643	64	12	singleton	singleton	NOUN
ejpam-4643	64	13	is	be	AUX
ejpam-4643	64	14	not	not	PART
ejpam-4643	64	15	a	a	DET
ejpam-4643	64	16	resolving	resolving	NOUN
ejpam-4643	64	17	set	set	NOUN
ejpam-4643	64	18	,	,	PUNCT
ejpam-4643	64	19	γr(g	γr(g	PROPN
ejpam-4643	64	20	)	)	PUNCT
ejpam-4643	64	21	=	=	SYM
ejpam-4643	65	1	2	2	X
ejpam-4643	65	2	.	.	PUNCT
ejpam-4643	65	3	also	also	ADV
ejpam-4643	65	4	,	,	PUNCT
ejpam-4643	65	5	s	s	VERB
ejpam-4643	65	6	is	be	AUX
ejpam-4643	65	7	a	a	DET
ejpam-4643	65	8	locating	locate	VERB
ejpam-4643	65	9	-	-	PUNCT
ejpam-4643	65	10	dominating	dominate	VERB
ejpam-4643	65	11	set	set	NOUN
ejpam-4643	65	12	of	of	ADP
ejpam-4643	65	13	a	a	DET
ejpam-4643	65	14	graph	graph	NOUN
ejpam-4643	65	15	g	g	NOUN
ejpam-4643	65	16	since	since	SCONJ
ejpam-4643	65	17	ng(v2	ng(v2	NOUN
ejpam-4643	65	18	)	)	PUNCT
ejpam-4643	65	19	∩	∩	NOUN
ejpam-4643	65	20	s	s	PART
ejpam-4643	65	21	=	=	X
ejpam-4643	65	22	{	{	PUNCT
ejpam-4643	65	23	v1	v1	NOUN
ejpam-4643	65	24	}	}	PUNCT
ejpam-4643	65	25	,	,	PUNCT
ejpam-4643	65	26	ng(v3	ng(v3	NOUN
ejpam-4643	65	27	)	)	PUNCT
ejpam-4643	65	28	∩	∩	NOUN
ejpam-4643	65	29	s	s	PART
ejpam-4643	65	30	=	=	PUNCT
ejpam-4643	65	31	{	{	PUNCT
ejpam-4643	65	32	v5	v5	PROPN
ejpam-4643	65	33	}	}	PUNCT
ejpam-4643	65	34	,	,	PUNCT
ejpam-4643	65	35	and	and	CCONJ
ejpam-4643	65	36	ng(v4	ng(v4	PRON
ejpam-4643	65	37	)	)	PUNCT
ejpam-4643	65	38	∩	∩	NOUN
ejpam-4643	65	39	s	s	PART
ejpam-4643	65	40	=	=	X
ejpam-4643	65	41	{	{	PUNCT
ejpam-4643	65	42	v1	v1	PROPN
ejpam-4643	65	43	,	,	PUNCT
ejpam-4643	65	44	v5	v5	PROPN
ejpam-4643	65	45	}	}	PUNCT
ejpam-4643	65	46	.	.	PUNCT
ejpam-4643	66	1	thus	thus	ADV
ejpam-4643	66	2	,	,	PUNCT
ejpam-4643	66	3	γl(g	γl(g	NUM
ejpam-4643	66	4	)	)	PUNCT
ejpam-4643	66	5	=	=	SYM
ejpam-4643	67	1	2	2	X
ejpam-4643	67	2	.	.	X
ejpam-4643	67	3	figure	figure	NOUN
ejpam-4643	67	4	1	1	NUM
ejpam-4643	67	5	:	:	PUNCT
ejpam-4643	67	6	a	a	DET
ejpam-4643	67	7	graph	graph	NOUN
ejpam-4643	67	8	g	g	NOUN
ejpam-4643	67	9	with	with	ADP
ejpam-4643	67	10	γ(g	γ(g	PROPN
ejpam-4643	67	11	)	)	PUNCT
ejpam-4643	67	12	=	=	SYM
ejpam-4643	67	13	γr(g	γr(g	NOUN
ejpam-4643	67	14	)	)	PUNCT
ejpam-4643	67	15	=	=	SYM
ejpam-4643	68	1	γl(g	γl(g	X
ejpam-4643	68	2	)	)	PUNCT
ejpam-4643	68	3	=	=	SYM
ejpam-4643	68	4	2	2	NUM
ejpam-4643	68	5	example	example	NOUN
ejpam-4643	68	6	2	2	NUM
ejpam-4643	68	7	.	.	X
ejpam-4643	68	8	consider	consider	VERB
ejpam-4643	68	9	the	the	DET
ejpam-4643	68	10	graph	graph	NOUN
ejpam-4643	68	11	g	g	NOUN
ejpam-4643	68	12	in	in	ADP
ejpam-4643	68	13	figure	figure	NOUN
ejpam-4643	68	14	2	2	NUM
ejpam-4643	68	15	.	.	PUNCT
ejpam-4643	69	1	let	let	VERB
ejpam-4643	69	2	s1	s1	PROPN
ejpam-4643	69	3	=	=	PUNCT
ejpam-4643	69	4	{	{	PUNCT
ejpam-4643	69	5	x	x	PROPN
ejpam-4643	69	6	,	,	PUNCT
ejpam-4643	69	7	y	y	PROPN
ejpam-4643	69	8	,	,	PUNCT
ejpam-4643	69	9	z	z	NOUN
ejpam-4643	69	10	}	}	PUNCT
ejpam-4643	69	11	.	.	PUNCT
ejpam-4643	70	1	observe	observe	VERB
ejpam-4643	70	2	that	that	SCONJ
ejpam-4643	70	3	ng[s1	ng[s1	PROPN
ejpam-4643	70	4	]	]	X
ejpam-4643	70	5	=	=	SYM
ejpam-4643	70	6	v	v	X
ejpam-4643	70	7	(	(	PUNCT
ejpam-4643	70	8	g	g	NOUN
ejpam-4643	70	9	)	)	PUNCT
ejpam-4643	70	10	,	,	PUNCT
ejpam-4643	70	11	that	that	ADV
ejpam-4643	70	12	is	is	ADV
ejpam-4643	70	13	,	,	PUNCT
ejpam-4643	70	14	s1	s1	PROPN
ejpam-4643	70	15	is	be	AUX
ejpam-4643	70	16	a	a	DET
ejpam-4643	70	17	dominating	dominating	NOUN
ejpam-4643	70	18	set	set	VERB
ejpam-4643	70	19	in	in	ADP
ejpam-4643	70	20	g.	g.	PROPN
ejpam-4643	70	21	hence	hence	ADV
ejpam-4643	70	22	,	,	PUNCT
ejpam-4643	70	23	γ(g	γ(g	PROPN
ejpam-4643	70	24	)	)	PUNCT
ejpam-4643	70	25	=	=	SYM
ejpam-4643	71	1	3	3	X
ejpam-4643	71	2	.	.	PUNCT
ejpam-4643	71	3	moreover	moreover	ADV
ejpam-4643	71	4	,	,	PUNCT
ejpam-4643	71	5	let	let	VERB
ejpam-4643	71	6	s2	s2	VERB
ejpam-4643	71	7	=	=	SYM
ejpam-4643	71	8	{	{	PUNCT
ejpam-4643	71	9	w1	w1	NOUN
ejpam-4643	71	10	,	,	PUNCT
ejpam-4643	71	11	w2	w2	NOUN
ejpam-4643	71	12	,	,	PUNCT
ejpam-4643	71	13	w3	w3	PROPN
ejpam-4643	71	14	,	,	PUNCT
ejpam-4643	71	15	w4	w4	NOUN
ejpam-4643	71	16	}	}	PUNCT
ejpam-4643	71	17	.	.	PUNCT
ejpam-4643	72	1	then	then	ADV
ejpam-4643	72	2	rg(x	rg(x	VERB
ejpam-4643	72	3	/	/	SYM
ejpam-4643	72	4	s2	s2	PROPN
ejpam-4643	72	5	)	)	PUNCT
ejpam-4643	72	6	=	=	PUNCT
ejpam-4643	72	7	(	(	PUNCT
ejpam-4643	72	8	1	1	NUM
ejpam-4643	72	9	,	,	PUNCT
ejpam-4643	72	10	1	1	NUM
ejpam-4643	72	11	,	,	PUNCT
ejpam-4643	72	12	1	1	NUM
ejpam-4643	72	13	,	,	PUNCT
ejpam-4643	72	14	2	2	NUM
ejpam-4643	72	15	)	)	PUNCT
ejpam-4643	72	16	,	,	PUNCT
ejpam-4643	72	17	rg(y	rg(y	NOUN
ejpam-4643	72	18	/	/	SYM
ejpam-4643	72	19	s2	s2	PROPN
ejpam-4643	72	20	)	)	PUNCT
ejpam-4643	72	21	=	=	PUNCT
ejpam-4643	72	22	(	(	PUNCT
ejpam-4643	72	23	1	1	NUM
ejpam-4643	72	24	,	,	PUNCT
ejpam-4643	72	25	1	1	NUM
ejpam-4643	72	26	,	,	PUNCT
ejpam-4643	72	27	1	1	NUM
ejpam-4643	72	28	,	,	PUNCT
ejpam-4643	72	29	4	4	NUM
ejpam-4643	72	30	)	)	PUNCT
ejpam-4643	72	31	,	,	PUNCT
ejpam-4643	72	32	rg(z	rg(z	PROPN
ejpam-4643	72	33	/	/	SYM
ejpam-4643	72	34	s2	s2	PROPN
ejpam-4643	72	35	)	)	PUNCT
ejpam-4643	72	36	=	=	PUNCT
ejpam-4643	72	37	(	(	PUNCT
ejpam-4643	72	38	2	2	NUM
ejpam-4643	72	39	,	,	PUNCT
ejpam-4643	72	40	2	2	NUM
ejpam-4643	72	41	,	,	PUNCT
ejpam-4643	72	42	2	2	NUM
ejpam-4643	72	43	,	,	PUNCT
ejpam-4643	72	44	1	1	NUM
ejpam-4643	72	45	)	)	PUNCT
ejpam-4643	72	46	,	,	PUNCT
ejpam-4643	72	47	rg(w1	rg(w1	PROPN
ejpam-4643	72	48	/	/	SYM
ejpam-4643	72	49	s2	s2	PROPN
ejpam-4643	72	50	)	)	PUNCT
ejpam-4643	72	51	=	=	SYM
ejpam-4643	72	52	(	(	PUNCT
ejpam-4643	72	53	0	0	NUM
ejpam-4643	72	54	,	,	PUNCT
ejpam-4643	72	55	2	2	NUM
ejpam-4643	72	56	,	,	PUNCT
ejpam-4643	72	57	2	2	NUM
ejpam-4643	72	58	,	,	PUNCT
ejpam-4643	72	59	3	3	NUM
ejpam-4643	72	60	)	)	PUNCT
ejpam-4643	72	61	,	,	PUNCT
ejpam-4643	72	62	rg(w2	rg(w2	NOUN
ejpam-4643	72	63	/	/	SYM
ejpam-4643	72	64	s2	s2	PROPN
ejpam-4643	72	65	)	)	PUNCT
ejpam-4643	72	66	=	=	PUNCT
ejpam-4643	72	67	(	(	PUNCT
ejpam-4643	72	68	2	2	NUM
ejpam-4643	72	69	,	,	PUNCT
ejpam-4643	72	70	0	0	NUM
ejpam-4643	72	71	,	,	PUNCT
ejpam-4643	72	72	2	2	NUM
ejpam-4643	72	73	,	,	PUNCT
ejpam-4643	72	74	3	3	NUM
ejpam-4643	72	75	)	)	PUNCT
ejpam-4643	72	76	,	,	PUNCT
ejpam-4643	72	77	rg(w3	rg(w3	PROPN
ejpam-4643	72	78	/	/	SYM
ejpam-4643	72	79	s2	s2	PROPN
ejpam-4643	72	80	)	)	PUNCT
ejpam-4643	72	81	=	=	PUNCT
ejpam-4643	72	82	(	(	PUNCT
ejpam-4643	72	83	2	2	NUM
ejpam-4643	72	84	,	,	PUNCT
ejpam-4643	72	85	2	2	NUM
ejpam-4643	72	86	,	,	PUNCT
ejpam-4643	72	87	0	0	NUM
ejpam-4643	72	88	,	,	PUNCT
ejpam-4643	72	89	3	3	NUM
ejpam-4643	72	90	)	)	PUNCT
ejpam-4643	72	91	,	,	PUNCT
ejpam-4643	72	92	and	and	CCONJ
ejpam-4643	72	93	rg(w4	rg(w4	ADJ
ejpam-4643	72	94	/	/	SYM
ejpam-4643	72	95	s2	s2	PROPN
ejpam-4643	72	96	)	)	PUNCT
ejpam-4643	72	97	=	=	PUNCT
ejpam-4643	72	98	(	(	PUNCT
ejpam-4643	72	99	3	3	NUM
ejpam-4643	72	100	,	,	PUNCT
ejpam-4643	72	101	2	2	NUM
ejpam-4643	72	102	,	,	PUNCT
ejpam-4643	72	103	2	2	NUM
ejpam-4643	72	104	,	,	PUNCT
ejpam-4643	72	105	0	0	NUM
ejpam-4643	72	106	)	)	PUNCT
ejpam-4643	72	107	.	.	PUNCT
ejpam-4643	73	1	thus	thus	ADV
ejpam-4643	73	2	,	,	PUNCT
ejpam-4643	73	3	s2	s2	PROPN
ejpam-4643	73	4	is	be	AUX
ejpam-4643	73	5	a	a	DET
ejpam-4643	73	6	resolving	resolve	VERB
ejpam-4643	73	7	dominating	dominating	NOUN
ejpam-4643	73	8	set	set	NOUN
ejpam-4643	73	9	of	of	ADP
ejpam-4643	73	10	a	a	DET
ejpam-4643	73	11	graph	graph	NOUN
ejpam-4643	73	12	g.	g.	NOUN
ejpam-4643	73	13	hence	hence	ADV
ejpam-4643	73	14	,	,	PUNCT
ejpam-4643	73	15	γr(g	γr(g	PROPN
ejpam-4643	73	16	)	)	PUNCT
ejpam-4643	73	17	=	=	SYM
ejpam-4643	74	1	4	4	X
ejpam-4643	74	2	.	.	X
ejpam-4643	75	1	furthermore	furthermore	ADV
ejpam-4643	75	2	,	,	PUNCT
ejpam-4643	75	3	let	let	VERB
ejpam-4643	75	4	s3	s3	PROPN
ejpam-4643	75	5	=	=	SYM
ejpam-4643	75	6	{	{	PUNCT
ejpam-4643	75	7	x	x	PROPN
ejpam-4643	75	8	,	,	PUNCT
ejpam-4643	75	9	w1	w1	NOUN
ejpam-4643	75	10	,	,	PUNCT
ejpam-4643	75	11	w2	w2	NOUN
ejpam-4643	75	12	,	,	PUNCT
ejpam-4643	75	13	w3	w3	PROPN
ejpam-4643	75	14	,	,	PUNCT
ejpam-4643	75	15	w4	w4	NOUN
ejpam-4643	75	16	}	}	PUNCT
ejpam-4643	75	17	.	.	PUNCT
ejpam-4643	76	1	then	then	ADV
ejpam-4643	76	2	s3	s3	PROPN
ejpam-4643	76	3	is	be	AUX
ejpam-4643	76	4	a	a	DET
ejpam-4643	76	5	locating	locate	VERB
ejpam-4643	76	6	-	-	PUNCT
ejpam-4643	76	7	dominating	dominate	VERB
ejpam-4643	76	8	set	set	NOUN
ejpam-4643	76	9	of	of	ADP
ejpam-4643	76	10	a	a	DET
ejpam-4643	76	11	graph	graph	NOUN
ejpam-4643	76	12	g	g	NOUN
ejpam-4643	76	13	since	since	SCONJ
ejpam-4643	76	14	ng(y)∩s3	ng(y)∩s3	NOUN
ejpam-4643	76	15	=	=	SYM
ejpam-4643	76	16	{	{	PUNCT
ejpam-4643	76	17	w1	w1	NOUN
ejpam-4643	76	18	,	,	PUNCT
ejpam-4643	76	19	w2	w2	NOUN
ejpam-4643	76	20	,	,	PUNCT
ejpam-4643	76	21	w3	w3	PROPN
ejpam-4643	76	22	}	}	PUNCT
ejpam-4643	76	23	and	and	CCONJ
ejpam-4643	76	24	ng(z)∩s3	ng(z)∩s3	NOUN
ejpam-4643	76	25	=	=	SYM
ejpam-4643	76	26	{	{	PUNCT
ejpam-4643	76	27	w4	w4	NOUN
ejpam-4643	76	28	}	}	PUNCT
ejpam-4643	76	29	.	.	PUNCT
ejpam-4643	77	1	thus	thus	ADV
ejpam-4643	77	2	,	,	PUNCT
ejpam-4643	77	3	γl(g	γl(g	NUM
ejpam-4643	77	4	)	)	PUNCT
ejpam-4643	77	5	=	=	SYM
ejpam-4643	78	1	5	5	X
ejpam-4643	78	2	.	.	X
ejpam-4643	78	3	figure	figure	NOUN
ejpam-4643	78	4	2	2	NUM
ejpam-4643	78	5	:	:	PUNCT
ejpam-4643	78	6	a	a	DET
ejpam-4643	78	7	graph	graph	NOUN
ejpam-4643	78	8	g	g	NOUN
ejpam-4643	78	9	with	with	ADP
ejpam-4643	78	10	γ(g	γ(g	PROPN
ejpam-4643	78	11	)	)	PUNCT
ejpam-4643	78	12	=	=	SYM
ejpam-4643	78	13	3	3	NUM
ejpam-4643	78	14	,	,	PUNCT
ejpam-4643	78	15	γr(g	γr(g	NUM
ejpam-4643	78	16	)	)	PUNCT
ejpam-4643	78	17	=	=	SYM
ejpam-4643	78	18	4	4	NUM
ejpam-4643	78	19	,	,	PUNCT
ejpam-4643	78	20	and	and	CCONJ
ejpam-4643	78	21	γl(g	γl(g	NUM
ejpam-4643	78	22	)	)	PUNCT
ejpam-4643	78	23	=	=	SYM
ejpam-4643	78	24	5	5	NUM
ejpam-4643	78	25	remark	remark	NOUN
ejpam-4643	78	26	2	2	NUM
ejpam-4643	78	27	.	.	PUNCT
ejpam-4643	79	1	every	every	DET
ejpam-4643	79	2	resolving	resolve	VERB
ejpam-4643	79	3	dominating	dominating	NOUN
ejpam-4643	79	4	set	set	NOUN
ejpam-4643	79	5	of	of	ADP
ejpam-4643	79	6	a	a	DET
ejpam-4643	79	7	connected	connected	ADJ
ejpam-4643	79	8	graph	graph	NOUN
ejpam-4643	79	9	g	g	PROPN
ejpam-4643	79	10	is	be	AUX
ejpam-4643	79	11	a	a	DET
ejpam-4643	79	12	resolving	resolving	NOUN
ejpam-4643	79	13	set	set	NOUN
ejpam-4643	79	14	of	of	ADP
ejpam-4643	79	15	g.	g.	PROPN
ejpam-4643	79	16	thus	thus	ADV
ejpam-4643	79	17	,	,	PUNCT
ejpam-4643	79	18	dim(g	dim(g	PROPN
ejpam-4643	79	19	)	)	PUNCT
ejpam-4643	79	20	≤	≤	NOUN
ejpam-4643	79	21	γr(g	γr(g	NUM
ejpam-4643	79	22	)	)	PUNCT
ejpam-4643	79	23	.	.	PUNCT
ejpam-4643	80	1	g.	g.	PROPN
ejpam-4643	80	2	monsanto	monsanto	PROPN
ejpam-4643	80	3	,	,	PUNCT
ejpam-4643	80	4	h.	h.	PROPN
ejpam-4643	80	5	rara	rara	PROPN
ejpam-4643	80	6	/	/	SYM
ejpam-4643	80	7	eur	eur	PROPN
ejpam-4643	80	8	.	.	PUNCT
ejpam-4643	81	1	j.	j.	PROPN
ejpam-4643	81	2	pure	pure	PROPN
ejpam-4643	81	3	appl	appl	PROPN
ejpam-4643	81	4	.	.	PROPN
ejpam-4643	81	5	math	math	PROPN
ejpam-4643	81	6	,	,	PUNCT
ejpam-4643	81	7	16	16	NUM
ejpam-4643	81	8	(	(	PUNCT
ejpam-4643	81	9	1	1	NUM
ejpam-4643	81	10	)	)	PUNCT
ejpam-4643	81	11	(	(	PUNCT
ejpam-4643	81	12	2023	2023	NUM
ejpam-4643	81	13	)	)	PUNCT
ejpam-4643	81	14	,	,	PUNCT
ejpam-4643	81	15	18	18	NUM
ejpam-4643	81	16	-	-	SYM
ejpam-4643	81	17	28	28	NUM
ejpam-4643	81	18	21	21	NUM
ejpam-4643	81	19	example	example	NOUN
ejpam-4643	81	20	3	3	NUM
ejpam-4643	81	21	.	.	X
ejpam-4643	81	22	consider	consider	VERB
ejpam-4643	81	23	the	the	DET
ejpam-4643	81	24	graph	graph	NOUN
ejpam-4643	81	25	g	g	NOUN
ejpam-4643	81	26	in	in	ADP
ejpam-4643	81	27	figure	figure	NOUN
ejpam-4643	81	28	3	3	NUM
ejpam-4643	81	29	.	.	PUNCT
ejpam-4643	82	1	the	the	DET
ejpam-4643	82	2	set	set	NOUN
ejpam-4643	82	3	s	s	PART
ejpam-4643	82	4	=	=	NOUN
ejpam-4643	82	5	{	{	PUNCT
ejpam-4643	82	6	v1	v1	PROPN
ejpam-4643	82	7	,	,	PUNCT
ejpam-4643	82	8	v2	v2	PROPN
ejpam-4643	82	9	}	}	PUNCT
ejpam-4643	82	10	is	be	AUX
ejpam-4643	82	11	a	a	DET
ejpam-4643	82	12	resolving	resolving	NOUN
ejpam-4643	82	13	set	set	NOUN
ejpam-4643	82	14	.	.	PUNCT
ejpam-4643	83	1	since	since	SCONJ
ejpam-4643	83	2	no	no	DET
ejpam-4643	83	3	single	single	ADJ
ejpam-4643	83	4	vertex	vertex	NOUN
ejpam-4643	83	5	constitutes	constitute	VERB
ejpam-4643	83	6	a	a	DET
ejpam-4643	83	7	resolving	resolving	NOUN
ejpam-4643	83	8	set	set	VERB
ejpam-4643	83	9	for	for	ADP
ejpam-4643	83	10	g	g	NOUN
ejpam-4643	83	11	,	,	PUNCT
ejpam-4643	83	12	it	it	PRON
ejpam-4643	83	13	follows	follow	VERB
ejpam-4643	83	14	that	that	SCONJ
ejpam-4643	83	15	w	w	NOUN
ejpam-4643	83	16	is	be	AUX
ejpam-4643	83	17	a	a	DET
ejpam-4643	83	18	minimum	minimum	ADJ
ejpam-4643	83	19	resolving	resolving	NOUN
ejpam-4643	83	20	set	set	NOUN
ejpam-4643	83	21	.	.	PUNCT
ejpam-4643	84	1	hence	hence	ADV
ejpam-4643	84	2	,	,	PUNCT
ejpam-4643	84	3	dim(g	dim(g	PROPN
ejpam-4643	84	4	)	)	PUNCT
ejpam-4643	84	5	=	=	SYM
ejpam-4643	85	1	2	2	X
ejpam-4643	85	2	.	.	PUNCT
ejpam-4643	85	3	moreover	moreover	ADV
ejpam-4643	85	4	,	,	PUNCT
ejpam-4643	85	5	s	s	VERB
ejpam-4643	85	6	is	be	AUX
ejpam-4643	85	7	a	a	DET
ejpam-4643	85	8	resolving	resolve	VERB
ejpam-4643	85	9	dominating	dominating	NOUN
ejpam-4643	85	10	set	set	NOUN
ejpam-4643	85	11	of	of	ADP
ejpam-4643	85	12	a	a	DET
ejpam-4643	85	13	graph	graph	NOUN
ejpam-4643	85	14	g	g	NOUN
ejpam-4643	85	15	since	since	SCONJ
ejpam-4643	85	16	ng[s	ng[	NOUN
ejpam-4643	85	17	]	]	PUNCT
ejpam-4643	85	18	=	=	SYM
ejpam-4643	85	19	v	v	NOUN
ejpam-4643	85	20	(	(	PUNCT
ejpam-4643	85	21	g	g	NOUN
ejpam-4643	85	22	)	)	PUNCT
ejpam-4643	85	23	.	.	PUNCT
ejpam-4643	86	1	thus	thus	ADV
ejpam-4643	86	2	,	,	PUNCT
ejpam-4643	86	3	γr(g	γr(g	PROPN
ejpam-4643	86	4	)	)	PUNCT
ejpam-4643	86	5	=	=	SYM
ejpam-4643	87	1	2	2	X
ejpam-4643	87	2	.	.	X
ejpam-4643	87	3	figure	figure	NOUN
ejpam-4643	87	4	3	3	NUM
ejpam-4643	87	5	:	:	PUNCT
ejpam-4643	87	6	a	a	DET
ejpam-4643	87	7	graph	graph	NOUN
ejpam-4643	87	8	g	g	NOUN
ejpam-4643	87	9	with	with	ADP
ejpam-4643	87	10	dim(g	dim(g	PROPN
ejpam-4643	87	11	)	)	PUNCT
ejpam-4643	87	12	=	=	SYM
ejpam-4643	87	13	2	2	NUM
ejpam-4643	87	14	=	=	SYM
ejpam-4643	87	15	γr(g	γr(g	NOUN
ejpam-4643	87	16	)	)	PUNCT
ejpam-4643	87	17	example	example	NOUN
ejpam-4643	88	1	4	4	X
ejpam-4643	88	2	.	.	PUNCT
ejpam-4643	88	3	consider	consider	VERB
ejpam-4643	88	4	the	the	DET
ejpam-4643	88	5	graph	graph	NOUN
ejpam-4643	88	6	g	g	NOUN
ejpam-4643	88	7	in	in	ADP
ejpam-4643	88	8	figure	figure	NOUN
ejpam-4643	88	9	4	4	NUM
ejpam-4643	88	10	.	.	PUNCT
ejpam-4643	89	1	let	let	VERB
ejpam-4643	89	2	s1	s1	PROPN
ejpam-4643	89	3	=	=	PUNCT
ejpam-4643	89	4	{	{	PUNCT
ejpam-4643	89	5	v	v	NOUN
ejpam-4643	89	6	,	,	PUNCT
ejpam-4643	89	7	y	y	NOUN
ejpam-4643	89	8	}	}	PUNCT
ejpam-4643	89	9	is	be	AUX
ejpam-4643	89	10	a	a	DET
ejpam-4643	89	11	resolving	resolving	NOUN
ejpam-4643	89	12	set	set	NOUN
ejpam-4643	89	13	of	of	ADP
ejpam-4643	89	14	a	a	DET
ejpam-4643	89	15	graph	graph	NOUN
ejpam-4643	89	16	g	g	NOUN
ejpam-4643	89	17	since	since	SCONJ
ejpam-4643	89	18	the	the	DET
ejpam-4643	89	19	representation	representation	NOUN
ejpam-4643	89	20	of	of	ADP
ejpam-4643	89	21	each	each	DET
ejpam-4643	89	22	vertex	vertex	NOUN
ejpam-4643	89	23	in	in	ADP
ejpam-4643	89	24	g	g	NOUN
ejpam-4643	89	25	,	,	PUNCT
ejpam-4643	89	26	with	with	SCONJ
ejpam-4643	89	27	respect	respect	NOUN
ejpam-4643	89	28	to	to	ADP
ejpam-4643	89	29	s1	s1	PROPN
ejpam-4643	89	30	is	be	AUX
ejpam-4643	89	31	unique	unique	ADJ
ejpam-4643	89	32	:	:	PUNCT
ejpam-4643	89	33	rg(x	rg(x	NOUN
ejpam-4643	89	34	/	/	SYM
ejpam-4643	89	35	s1	s1	NOUN
ejpam-4643	89	36	)	)	PUNCT
ejpam-4643	89	37	=	=	PUNCT
ejpam-4643	90	1	(	(	PUNCT
ejpam-4643	90	2	2	2	NUM
ejpam-4643	90	3	,	,	PUNCT
ejpam-4643	90	4	2	2	NUM
ejpam-4643	90	5	)	)	PUNCT
ejpam-4643	90	6	,	,	PUNCT
ejpam-4643	90	7	rg(u1	rg(u1	NOUN
ejpam-4643	90	8	/	/	SYM
ejpam-4643	90	9	s1	s1	NOUN
ejpam-4643	90	10	)	)	PUNCT
ejpam-4643	90	11	=	=	PUNCT
ejpam-4643	90	12	(	(	PUNCT
ejpam-4643	90	13	2	2	NUM
ejpam-4643	90	14	,	,	PUNCT
ejpam-4643	90	15	1	1	NUM
ejpam-4643	90	16	)	)	PUNCT
ejpam-4643	90	17	,	,	PUNCT
ejpam-4643	90	18	rg(u2	rg(u2	NOUN
ejpam-4643	90	19	/	/	SYM
ejpam-4643	90	20	s1	s1	PROPN
ejpam-4643	90	21	)	)	PUNCT
ejpam-4643	90	22	=	=	PUNCT
ejpam-4643	90	23	(	(	PUNCT
ejpam-4643	90	24	1	1	NUM
ejpam-4643	90	25	,	,	PUNCT
ejpam-4643	90	26	2	2	NUM
ejpam-4643	90	27	)	)	PUNCT
ejpam-4643	90	28	,	,	PUNCT
ejpam-4643	90	29	rg(u3	rg(u3	PROPN
ejpam-4643	90	30	/	/	SYM
ejpam-4643	90	31	s1	s1	NOUN
ejpam-4643	90	32	)	)	PUNCT
ejpam-4643	90	33	=	=	PUNCT
ejpam-4643	90	34	(	(	PUNCT
ejpam-4643	90	35	1	1	NUM
ejpam-4643	90	36	,	,	PUNCT
ejpam-4643	90	37	3	3	NUM
ejpam-4643	90	38	)	)	PUNCT
ejpam-4643	90	39	,	,	PUNCT
ejpam-4643	90	40	rg(z	rg(z	PROPN
ejpam-4643	90	41	/	/	SYM
ejpam-4643	90	42	s1	s1	NOUN
ejpam-4643	90	43	)	)	PUNCT
ejpam-4643	90	44	=	=	PUNCT
ejpam-4643	90	45	(	(	PUNCT
ejpam-4643	90	46	2	2	NUM
ejpam-4643	90	47	,	,	PUNCT
ejpam-4643	90	48	3	3	NUM
ejpam-4643	90	49	)	)	PUNCT
ejpam-4643	90	50	,	,	PUNCT
ejpam-4643	90	51	rg(v	rg(v	X
ejpam-4643	90	52	/	/	SYM
ejpam-4643	90	53	s1	s1	NOUN
ejpam-4643	90	54	)	)	PUNCT
ejpam-4643	90	55	=	=	SYM
ejpam-4643	90	56	(	(	PUNCT
ejpam-4643	90	57	0	0	NUM
ejpam-4643	90	58	,	,	PUNCT
ejpam-4643	90	59	3	3	NUM
ejpam-4643	90	60	)	)	PUNCT
ejpam-4643	90	61	,	,	PUNCT
ejpam-4643	90	62	and	and	CCONJ
ejpam-4643	90	63	rg(y	rg(y	NOUN
ejpam-4643	90	64	/	/	SYM
ejpam-4643	90	65	s1	s1	NOUN
ejpam-4643	90	66	)	)	PUNCT
ejpam-4643	90	67	=	=	PUNCT
ejpam-4643	90	68	(	(	PUNCT
ejpam-4643	90	69	3	3	NUM
ejpam-4643	90	70	,	,	PUNCT
ejpam-4643	90	71	0	0	NUM
ejpam-4643	90	72	)	)	PUNCT
ejpam-4643	90	73	.	.	PUNCT
ejpam-4643	91	1	hence	hence	ADV
ejpam-4643	91	2	,	,	PUNCT
ejpam-4643	91	3	dim(g	dim(g	PROPN
ejpam-4643	91	4	)	)	PUNCT
ejpam-4643	91	5	=	=	SYM
ejpam-4643	92	1	2	2	X
ejpam-4643	92	2	.	.	PUNCT
ejpam-4643	92	3	moreover	moreover	ADV
ejpam-4643	92	4	,	,	PUNCT
ejpam-4643	92	5	let	let	VERB
ejpam-4643	92	6	s2	s2	VERB
ejpam-4643	92	7	=	=	SYM
ejpam-4643	92	8	{	{	PUNCT
ejpam-4643	92	9	u1	u1	NOUN
ejpam-4643	92	10	,	,	PUNCT
ejpam-4643	92	11	u2	u2	NOUN
ejpam-4643	92	12	,	,	PUNCT
ejpam-4643	92	13	u3	u3	NOUN
ejpam-4643	92	14	}	}	PUNCT
ejpam-4643	92	15	.	.	PUNCT
ejpam-4643	93	1	then	then	ADV
ejpam-4643	93	2	s2	s2	PROPN
ejpam-4643	93	3	is	be	AUX
ejpam-4643	93	4	a	a	DET
ejpam-4643	93	5	resolving	resolve	VERB
ejpam-4643	93	6	dominating	dominating	NOUN
ejpam-4643	93	7	set	set	NOUN
ejpam-4643	93	8	of	of	ADP
ejpam-4643	93	9	a	a	DET
ejpam-4643	93	10	graph	graph	NOUN
ejpam-4643	93	11	g.	g.	PROPN
ejpam-4643	93	12	thus	thus	ADV
ejpam-4643	93	13	,	,	PUNCT
ejpam-4643	93	14	γr(g	γr(g	PROPN
ejpam-4643	93	15	)	)	PUNCT
ejpam-4643	93	16	=	=	SYM
ejpam-4643	94	1	3	3	X
ejpam-4643	94	2	.	.	X
ejpam-4643	94	3	figure	figure	VERB
ejpam-4643	94	4	4	4	NUM
ejpam-4643	94	5	:	:	PUNCT
ejpam-4643	94	6	a	a	DET
ejpam-4643	94	7	graph	graph	NOUN
ejpam-4643	94	8	g	g	NOUN
ejpam-4643	94	9	with	with	ADP
ejpam-4643	94	10	dim(g	dim(g	PROPN
ejpam-4643	94	11	)	)	PUNCT
ejpam-4643	94	12	=	=	SYM
ejpam-4643	94	13	2	2	NUM
ejpam-4643	94	14	and	and	CCONJ
ejpam-4643	94	15	γr(g	γr(g	NUM
ejpam-4643	94	16	)	)	PUNCT
ejpam-4643	95	1	=	=	SYM
ejpam-4643	95	2	3	3	NUM
ejpam-4643	95	3	proposition	proposition	NOUN
ejpam-4643	95	4	1	1	NUM
ejpam-4643	95	5	.	.	PUNCT
ejpam-4643	96	1	[	[	X
ejpam-4643	96	2	1	1	X
ejpam-4643	96	3	]	]	PUNCT
ejpam-4643	96	4	let	let	VERB
ejpam-4643	96	5	g	g	PRON
ejpam-4643	96	6	be	be	AUX
ejpam-4643	96	7	a	a	DET
ejpam-4643	96	8	connected	connected	ADJ
ejpam-4643	96	9	graph	graph	NOUN
ejpam-4643	96	10	of	of	ADP
ejpam-4643	96	11	order	order	NOUN
ejpam-4643	96	12	n	n	PRON
ejpam-4643	96	13	≥	≥	NOUN
ejpam-4643	96	14	2	2	NUM
ejpam-4643	96	15	,	,	PUNCT
ejpam-4643	96	16	then	then	ADV
ejpam-4643	96	17	(	(	PUNCT
ejpam-4643	96	18	i	i	NOUN
ejpam-4643	96	19	)	)	PUNCT
ejpam-4643	96	20	γr(p3	γr(p3	ADJ
ejpam-4643	96	21	)	)	PUNCT
ejpam-4643	96	22	=	=	SYM
ejpam-4643	96	23	2	2	NUM
ejpam-4643	96	24	and	and	CCONJ
ejpam-4643	96	25	for	for	ADP
ejpam-4643	96	26	n	n	PRON
ejpam-4643	96	27	≥	≥	NUM
ejpam-4643	96	28	4	4	NUM
ejpam-4643	96	29	,	,	PUNCT
ejpam-4643	96	30	γr(pn	γr(pn	PROPN
ejpam-4643	96	31	)	)	PUNCT
ejpam-4643	96	32	=	=	VERB
ejpam-4643	96	33	⌈n3	⌈n3	ADJ
ejpam-4643	96	34	⌉	⌉	X
ejpam-4643	96	35	(	(	PUNCT
ejpam-4643	96	36	ii	ii	NOUN
ejpam-4643	96	37	)	)	PUNCT
ejpam-4643	96	38	for	for	ADP
ejpam-4643	96	39	n	n	X
ejpam-4643	96	40	≥	≥	NUM
ejpam-4643	96	41	3	3	NUM
ejpam-4643	96	42	,	,	PUNCT
ejpam-4643	96	43	γr(cn	γr(cn	PROPN
ejpam-4643	96	44	)	)	PUNCT
ejpam-4643	96	45	=	=	VERB
ejpam-4643	97	1	⌈n3	⌈n3	ADJ
ejpam-4643	97	2	⌉	⌉	X
ejpam-4643	97	3	if	if	SCONJ
ejpam-4643	97	4	n	n	PRON
ejpam-4643	97	5	̸=	̸=	PROPN
ejpam-4643	97	6	6	6	NUM
ejpam-4643	97	7	and	and	CCONJ
ejpam-4643	97	8	γr(c6	γr(c6	NOUN
ejpam-4643	97	9	)	)	PUNCT
ejpam-4643	97	10	=	=	SYM
ejpam-4643	97	11	3	3	X
ejpam-4643	97	12	.	.	X
ejpam-4643	97	13	proposition	proposition	NOUN
ejpam-4643	97	14	2	2	NUM
ejpam-4643	97	15	.	.	X
ejpam-4643	97	16	for	for	ADP
ejpam-4643	97	17	any	any	DET
ejpam-4643	97	18	connected	connected	ADJ
ejpam-4643	97	19	graph	graph	NOUN
ejpam-4643	97	20	g	g	NOUN
ejpam-4643	97	21	of	of	ADP
ejpam-4643	97	22	order	order	NOUN
ejpam-4643	97	23	n	n	PRON
ejpam-4643	97	24	≥	≥	NOUN
ejpam-4643	97	25	2	2	NUM
ejpam-4643	97	26	,	,	PUNCT
ejpam-4643	97	27	1	1	NUM
ejpam-4643	97	28	≤	≤	NUM
ejpam-4643	97	29	γr(g	γr(g	NUM
ejpam-4643	97	30	)	)	PUNCT
ejpam-4643	97	31	≤	≤	NOUN
ejpam-4643	98	1	n−1	n−1	PROPN
ejpam-4643	98	2	.	.	PUNCT
ejpam-4643	99	1	moreover	moreover	ADV
ejpam-4643	99	2	,	,	PUNCT
ejpam-4643	99	3	(	(	PUNCT
ejpam-4643	99	4	i	i	NOUN
ejpam-4643	99	5	)	)	PUNCT
ejpam-4643	99	6	γr(g	γr(g	PROPN
ejpam-4643	99	7	)	)	PUNCT
ejpam-4643	99	8	=	=	PUNCT
ejpam-4643	99	9	1	1	NUM
ejpam-4643	99	10	if	if	SCONJ
ejpam-4643	99	11	and	and	CCONJ
ejpam-4643	99	12	only	only	ADV
ejpam-4643	99	13	if	if	SCONJ
ejpam-4643	99	14	g	g	NOUN
ejpam-4643	99	15	=	=	NOUN
ejpam-4643	99	16	p2	p2	PROPN
ejpam-4643	99	17	and	and	CCONJ
ejpam-4643	99	18	(	(	PUNCT
ejpam-4643	99	19	ii	ii	NOUN
ejpam-4643	99	20	)	)	PUNCT
ejpam-4643	99	21	γr(g	γr(g	PROPN
ejpam-4643	99	22	)	)	PUNCT
ejpam-4643	100	1	=	=	PUNCT
ejpam-4643	100	2	n−	n−	NOUN
ejpam-4643	100	3	1	1	NUM
ejpam-4643	100	4	if	if	SCONJ
ejpam-4643	100	5	and	and	CCONJ
ejpam-4643	100	6	only	only	ADV
ejpam-4643	100	7	if	if	SCONJ
ejpam-4643	100	8	g	g	PROPN
ejpam-4643	100	9	=	=	VERB
ejpam-4643	100	10	kn	kn	PROPN
ejpam-4643	100	11	or	or	CCONJ
ejpam-4643	100	12	k1,n−1	k1,n−1	ADJ
ejpam-4643	100	13	.	.	PUNCT
ejpam-4643	101	1	proof	proof	NOUN
ejpam-4643	101	2	:	:	PUNCT
ejpam-4643	101	3	suppose	suppose	VERB
ejpam-4643	101	4	that	that	SCONJ
ejpam-4643	101	5	γr(g	γr(g	PROPN
ejpam-4643	101	6	)	)	PUNCT
ejpam-4643	101	7	=	=	SYM
ejpam-4643	102	1	1	1	X
ejpam-4643	102	2	,	,	PUNCT
ejpam-4643	102	3	say	say	VERB
ejpam-4643	102	4	w	w	NOUN
ejpam-4643	102	5	=	=	PRON
ejpam-4643	102	6	{	{	PUNCT
ejpam-4643	102	7	v	v	NOUN
ejpam-4643	102	8	}	}	PUNCT
ejpam-4643	102	9	is	be	AUX
ejpam-4643	102	10	a	a	DET
ejpam-4643	102	11	minimum	minimum	ADJ
ejpam-4643	102	12	resolving	resolving	NOUN
ejpam-4643	102	13	dominating	dominating	NOUN
ejpam-4643	102	14	set	set	NOUN
ejpam-4643	102	15	of	of	ADP
ejpam-4643	102	16	g.	g.	PROPN
ejpam-4643	102	17	since	since	SCONJ
ejpam-4643	102	18	g	g	PROPN
ejpam-4643	102	19	is	be	AUX
ejpam-4643	102	20	connected	connect	VERB
ejpam-4643	102	21	and	and	CCONJ
ejpam-4643	102	22	non	non	ADJ
ejpam-4643	102	23	-	-	ADJ
ejpam-4643	102	24	trivial	trivial	ADJ
ejpam-4643	102	25	,	,	PUNCT
ejpam-4643	102	26	there	there	PRON
ejpam-4643	102	27	exists	exist	VERB
ejpam-4643	102	28	x	x	X
ejpam-4643	102	29	∈	∈	PROPN
ejpam-4643	102	30	v	v	X
ejpam-4643	102	31	(	(	PUNCT
ejpam-4643	102	32	g	g	NOUN
ejpam-4643	102	33	)	)	PUNCT
ejpam-4643	102	34	\	\	NOUN
ejpam-4643	102	35	{	{	PUNCT
ejpam-4643	102	36	v	v	NOUN
ejpam-4643	102	37	}	}	PUNCT
ejpam-4643	102	38	such	such	ADJ
ejpam-4643	102	39	that	that	SCONJ
ejpam-4643	102	40	xv	xv	PROPN
ejpam-4643	102	41	∈	∈	PROPN
ejpam-4643	102	42	e(g	e(g	PROPN
ejpam-4643	102	43	)	)	PUNCT
ejpam-4643	102	44	.	.	PUNCT
ejpam-4643	103	1	if	if	SCONJ
ejpam-4643	103	2	|v	|v	PROPN
ejpam-4643	103	3	(	(	PUNCT
ejpam-4643	103	4	g)|	g)|	NOUN
ejpam-4643	103	5	=	=	SYM
ejpam-4643	103	6	2	2	NUM
ejpam-4643	103	7	,	,	PUNCT
ejpam-4643	103	8	then	then	ADV
ejpam-4643	103	9	g	g	PROPN
ejpam-4643	103	10	=	=	PROPN
ejpam-4643	103	11	k2	k2	NOUN
ejpam-4643	103	12	=	=	NOUN
ejpam-4643	103	13	p2	p2	PROPN
ejpam-4643	103	14	.	.	PUNCT
ejpam-4643	104	1	therefore	therefore	ADV
ejpam-4643	104	2	,	,	PUNCT
ejpam-4643	104	3	(	(	PUNCT
ejpam-4643	104	4	i	i	NOUN
ejpam-4643	104	5	)	)	PUNCT
ejpam-4643	104	6	holds	hold	VERB
ejpam-4643	104	7	.	.	PUNCT
ejpam-4643	105	1	g.	g.	PROPN
ejpam-4643	105	2	monsanto	monsanto	PROPN
ejpam-4643	105	3	,	,	PUNCT
ejpam-4643	105	4	h.	h.	PROPN
ejpam-4643	105	5	rara	rara	PROPN
ejpam-4643	105	6	/	/	SYM
ejpam-4643	105	7	eur	eur	PROPN
ejpam-4643	105	8	.	.	PUNCT
ejpam-4643	106	1	j.	j.	PROPN
ejpam-4643	106	2	pure	pure	PROPN
ejpam-4643	106	3	appl	appl	PROPN
ejpam-4643	106	4	.	.	PROPN
ejpam-4643	106	5	math	math	PROPN
ejpam-4643	106	6	,	,	PUNCT
ejpam-4643	106	7	16	16	NUM
ejpam-4643	106	8	(	(	PUNCT
ejpam-4643	106	9	1	1	NUM
ejpam-4643	106	10	)	)	PUNCT
ejpam-4643	106	11	(	(	PUNCT
ejpam-4643	106	12	2023	2023	NUM
ejpam-4643	106	13	)	)	PUNCT
ejpam-4643	106	14	,	,	PUNCT
ejpam-4643	106	15	18	18	NUM
ejpam-4643	106	16	-	-	SYM
ejpam-4643	106	17	28	28	NUM
ejpam-4643	106	18	22	22	NUM
ejpam-4643	106	19	suppose	suppose	VERB
ejpam-4643	106	20	g	g	PROPN
ejpam-4643	106	21	̸=	̸=	PROPN
ejpam-4643	106	22	kn	kn	PROPN
ejpam-4643	106	23	.	.	PUNCT
ejpam-4643	107	1	let	let	VERB
ejpam-4643	107	2	v	v	X
ejpam-4643	107	3	(	(	PUNCT
ejpam-4643	107	4	g	g	NOUN
ejpam-4643	107	5	)	)	PUNCT
ejpam-4643	107	6	\	\	NOUN
ejpam-4643	108	1	{	{	PUNCT
ejpam-4643	108	2	v	v	NOUN
ejpam-4643	108	3	}	}	PUNCT
ejpam-4643	108	4	=	=	PUNCT
ejpam-4643	108	5	w	w	NOUN
ejpam-4643	108	6	is	be	AUX
ejpam-4643	108	7	γr	γr	PROPN
ejpam-4643	108	8	-	-	PUNCT
ejpam-4643	108	9	set	set	NOUN
ejpam-4643	108	10	.	.	PUNCT
ejpam-4643	109	1	let	let	VERB
ejpam-4643	109	2	w	w	NOUN
ejpam-4643	109	3	∈	∈	PROPN
ejpam-4643	109	4	ng(v	ng(v	NOUN
ejpam-4643	109	5	)	)	PUNCT
ejpam-4643	109	6	.	.	PUNCT
ejpam-4643	110	1	consider	consider	VERB
ejpam-4643	110	2	that	that	DET
ejpam-4643	110	3	|ng(v)|	|ng(v)|	NOUN
ejpam-4643	110	4	=	=	SYM
ejpam-4643	110	5	1	1	X
ejpam-4643	110	6	.	.	X
ejpam-4643	110	7	claim	claim	NOUN
ejpam-4643	110	8	:	:	PUNCT
ejpam-4643	111	1	g	g	X
ejpam-4643	111	2	=	=	PUNCT
ejpam-4643	111	3	⟨w⟩+kn−1	⟨w⟩+kn−1	VERB
ejpam-4643	111	4	∼=	∼=	ADV
ejpam-4643	111	5	k1,n−1	k1,n−1	ADJ
ejpam-4643	111	6	.	.	PUNCT
ejpam-4643	111	7	suppose	suppose	VERB
ejpam-4643	111	8	there	there	PRON
ejpam-4643	111	9	exists	exist	VERB
ejpam-4643	111	10	u	u	PROPN
ejpam-4643	111	11	∈	∈	PROPN
ejpam-4643	111	12	v	v	ADP
ejpam-4643	111	13	(	(	PUNCT
ejpam-4643	111	14	g	g	NOUN
ejpam-4643	111	15	)	)	PUNCT
ejpam-4643	111	16	\	\	NOUN
ejpam-4643	111	17	{	{	PUNCT
ejpam-4643	111	18	v	v	NOUN
ejpam-4643	111	19	,	,	PUNCT
ejpam-4643	111	20	w	w	NOUN
ejpam-4643	111	21	}	}	PUNCT
ejpam-4643	111	22	such	such	ADJ
ejpam-4643	111	23	that	that	DET
ejpam-4643	111	24	uv	uv	NOUN
ejpam-4643	111	25	/∈	/∈	PUNCT
ejpam-4643	111	26	e(g	e(g	PROPN
ejpam-4643	111	27	)	)	PUNCT
ejpam-4643	111	28	.	.	PUNCT
ejpam-4643	112	1	let	let	VERB
ejpam-4643	112	2	w	w	NOUN
ejpam-4643	112	3	=	=	SYM
ejpam-4643	112	4	v	v	X
ejpam-4643	112	5	(	(	PUNCT
ejpam-4643	112	6	g	g	NOUN
ejpam-4643	112	7	)	)	PUNCT
ejpam-4643	112	8	\	\	NOUN
ejpam-4643	113	1	{	{	PUNCT
ejpam-4643	113	2	u	u	NOUN
ejpam-4643	113	3	,	,	PUNCT
ejpam-4643	113	4	v	v	NOUN
ejpam-4643	113	5	}	}	PUNCT
ejpam-4643	113	6	.	.	PUNCT
ejpam-4643	114	1	clearly	clearly	ADV
ejpam-4643	114	2	,	,	PUNCT
ejpam-4643	114	3	w	w	PROPN
ejpam-4643	114	4	is	be	AUX
ejpam-4643	114	5	a	a	DET
ejpam-4643	114	6	dominating	dominating	NOUN
ejpam-4643	114	7	set	set	NOUN
ejpam-4643	114	8	of	of	ADP
ejpam-4643	114	9	g.	g.	PROPN
ejpam-4643	114	10	since	since	SCONJ
ejpam-4643	114	11	v	v	NUM
ejpam-4643	114	12	∈	∈	PROPN
ejpam-4643	114	13	ng(w	ng(w	NOUN
ejpam-4643	114	14	)	)	PUNCT
ejpam-4643	114	15	and	and	CCONJ
ejpam-4643	114	16	u	u	PROPN
ejpam-4643	114	17	∈	∈	PROPN
ejpam-4643	114	18	ng(w	ng(w	NOUN
ejpam-4643	114	19	)	)	PUNCT
ejpam-4643	114	20	,	,	PUNCT
ejpam-4643	114	21	r(u	r(u	PROPN
ejpam-4643	114	22	/	/	SYM
ejpam-4643	114	23	w	w	NOUN
ejpam-4643	114	24	)	)	PUNCT
ejpam-4643	114	25	̸=	̸=	PROPN
ejpam-4643	114	26	r(v	r(v	PROPN
ejpam-4643	114	27	/	/	SYM
ejpam-4643	114	28	w	w	PROPN
ejpam-4643	114	29	)	)	PUNCT
ejpam-4643	114	30	.	.	PUNCT
ejpam-4643	115	1	hence	hence	ADV
ejpam-4643	115	2	,	,	PUNCT
ejpam-4643	115	3	w	w	PROPN
ejpam-4643	115	4	is	be	AUX
ejpam-4643	115	5	a	a	DET
ejpam-4643	115	6	resolving	resolve	VERB
ejpam-4643	115	7	dominating	dominating	NOUN
ejpam-4643	115	8	set	set	NOUN
ejpam-4643	115	9	of	of	ADP
ejpam-4643	115	10	g	g	PROPN
ejpam-4643	115	11	and	and	CCONJ
ejpam-4643	115	12	γr(g	γr(g	NUM
ejpam-4643	115	13	)	)	PUNCT
ejpam-4643	115	14	≤	≤	NOUN
ejpam-4643	116	1	n	n	CCONJ
ejpam-4643	116	2	−	−	PROPN
ejpam-4643	116	3	2	2	NUM
ejpam-4643	116	4	,	,	PUNCT
ejpam-4643	116	5	a	a	DET
ejpam-4643	116	6	contradiction	contradiction	NOUN
ejpam-4643	116	7	.	.	PUNCT
ejpam-4643	117	1	thus	thus	ADV
ejpam-4643	117	2	,	,	PUNCT
ejpam-4643	117	3	w	w	PROPN
ejpam-4643	117	4	∈	∈	PROPN
ejpam-4643	117	5	ng(z	ng(z	NUM
ejpam-4643	117	6	)	)	PUNCT
ejpam-4643	117	7	for	for	ADP
ejpam-4643	117	8	all	all	DET
ejpam-4643	117	9	z	z	NOUN
ejpam-4643	117	10	∈	∈	PROPN
ejpam-4643	117	11	v	v	ADP
ejpam-4643	117	12	(	(	PUNCT
ejpam-4643	117	13	g	g	NOUN
ejpam-4643	117	14	)	)	PUNCT
ejpam-4643	117	15	\	\	NOUN
ejpam-4643	117	16	{	{	PUNCT
ejpam-4643	117	17	w	w	NOUN
ejpam-4643	117	18	}	}	PUNCT
ejpam-4643	117	19	.	.	PUNCT
ejpam-4643	118	1	next	next	ADV
ejpam-4643	118	2	,	,	PUNCT
ejpam-4643	118	3	suppose	suppose	VERB
ejpam-4643	118	4	there	there	PRON
ejpam-4643	118	5	exist	exist	VERB
ejpam-4643	118	6	distinct	distinct	ADJ
ejpam-4643	118	7	vertices	vertex	NOUN
ejpam-4643	118	8	a	a	PRON
ejpam-4643	118	9	,	,	PUNCT
ejpam-4643	118	10	b	b	PROPN
ejpam-4643	118	11	∈	∈	PROPN
ejpam-4643	118	12	v	v	NOUN
ejpam-4643	118	13	(	(	PUNCT
ejpam-4643	118	14	g	g	NOUN
ejpam-4643	118	15	)	)	PUNCT
ejpam-4643	118	16	\	\	NOUN
ejpam-4643	119	1	{	{	PUNCT
ejpam-4643	119	2	w	w	PROPN
ejpam-4643	119	3	,	,	PUNCT
ejpam-4643	119	4	v	v	NOUN
ejpam-4643	119	5	}	}	PUNCT
ejpam-4643	119	6	such	such	ADJ
ejpam-4643	119	7	that	that	SCONJ
ejpam-4643	119	8	ab	ab	PROPN
ejpam-4643	119	9	∈	∈	PROPN
ejpam-4643	119	10	e(g	e(g	PROPN
ejpam-4643	119	11	)	)	PUNCT
ejpam-4643	119	12	.	.	PUNCT
ejpam-4643	120	1	let	let	VERB
ejpam-4643	120	2	w1	w1	NOUN
ejpam-4643	120	3	=	=	SYM
ejpam-4643	120	4	v	v	PROPN
ejpam-4643	120	5	(	(	PUNCT
ejpam-4643	120	6	g	g	NOUN
ejpam-4643	120	7	)	)	PUNCT
ejpam-4643	120	8	\	\	NOUN
ejpam-4643	120	9	{	{	PUNCT
ejpam-4643	120	10	a	a	NOUN
ejpam-4643	120	11	,	,	PUNCT
ejpam-4643	120	12	v	v	NOUN
ejpam-4643	120	13	}	}	PUNCT
ejpam-4643	120	14	.	.	PUNCT
ejpam-4643	121	1	then	then	ADV
ejpam-4643	121	2	w1	w1	PROPN
ejpam-4643	121	3	is	be	AUX
ejpam-4643	121	4	a	a	DET
ejpam-4643	121	5	dominating	dominating	NOUN
ejpam-4643	121	6	set	set	NOUN
ejpam-4643	121	7	of	of	ADP
ejpam-4643	121	8	g.	g.	PROPN
ejpam-4643	121	9	since	since	SCONJ
ejpam-4643	121	10	w	w	PROPN
ejpam-4643	121	11	∈	∈	PROPN
ejpam-4643	121	12	ng(v	ng(v	PUNCT
ejpam-4643	121	13	)	)	PUNCT
ejpam-4643	121	14	and	and	CCONJ
ejpam-4643	121	15	b	b	X
ejpam-4643	121	16	/∈	/∈	PUNCT
ejpam-4643	121	17	ng(v	ng(v	NUM
ejpam-4643	121	18	)	)	PUNCT
ejpam-4643	121	19	,	,	PUNCT
ejpam-4643	121	20	r(w	r(w	PROPN
ejpam-4643	121	21	/	/	SYM
ejpam-4643	121	22	w1	w1	NOUN
ejpam-4643	121	23	)	)	PUNCT
ejpam-4643	121	24	̸=	̸=	PROPN
ejpam-4643	121	25	r(b	r(b	PROPN
ejpam-4643	121	26	/	/	SYM
ejpam-4643	121	27	w1	w1	NOUN
ejpam-4643	121	28	)	)	PUNCT
ejpam-4643	121	29	.	.	PUNCT
ejpam-4643	122	1	hence	hence	ADV
ejpam-4643	122	2	,	,	PUNCT
ejpam-4643	122	3	w1	w1	NOUN
ejpam-4643	122	4	is	be	AUX
ejpam-4643	122	5	a	a	DET
ejpam-4643	122	6	resolving	resolve	VERB
ejpam-4643	122	7	dominating	dominating	NOUN
ejpam-4643	122	8	set	set	NOUN
ejpam-4643	122	9	of	of	ADP
ejpam-4643	122	10	g.	g.	PROPN
ejpam-4643	122	11	thus	thus	ADV
ejpam-4643	122	12	,	,	PUNCT
ejpam-4643	122	13	γr(g	γr(g	PROPN
ejpam-4643	122	14	)	)	PUNCT
ejpam-4643	122	15	≤	≤	NUM
ejpam-4643	122	16	|w1|	|w1|	NOUN
ejpam-4643	122	17	=	=	SYM
ejpam-4643	122	18	n−2	n−2	PROPN
ejpam-4643	122	19	,	,	PUNCT
ejpam-4643	122	20	a	a	DET
ejpam-4643	122	21	contradiction	contradiction	NOUN
ejpam-4643	122	22	.	.	PUNCT
ejpam-4643	123	1	therefore	therefore	ADV
ejpam-4643	123	2	,	,	PUNCT
ejpam-4643	123	3	ab	ab	PROPN
ejpam-4643	123	4	/∈	/∈	PUNCT
ejpam-4643	123	5	e(g	e(g	PROPN
ejpam-4643	123	6	)	)	PUNCT
ejpam-4643	123	7	.	.	PUNCT
ejpam-4643	124	1	accordingly	accordingly	ADV
ejpam-4643	124	2	,	,	PUNCT
ejpam-4643	124	3	g	g	PROPN
ejpam-4643	124	4	=	=	PUNCT
ejpam-4643	124	5	⟨w⟩+kn−1	⟨w⟩+kn−1	VERB
ejpam-4643	124	6	∼=	∼=	ADV
ejpam-4643	124	7	k1,n−1	k1,n−1	ADJ
ejpam-4643	124	8	.	.	PUNCT
ejpam-4643	125	1	for	for	ADP
ejpam-4643	125	2	the	the	DET
ejpam-4643	125	3	converse	converse	NOUN
ejpam-4643	125	4	,	,	PUNCT
ejpam-4643	125	5	suppose	suppose	VERB
ejpam-4643	125	6	g	g	PROPN
ejpam-4643	125	7	=	=	PROPN
ejpam-4643	125	8	kn	kn	PROPN
ejpam-4643	125	9	or	or	CCONJ
ejpam-4643	125	10	g	g	PROPN
ejpam-4643	125	11	=	=	PUNCT
ejpam-4643	125	12	k1,n−1	k1,n−1	PROPN
ejpam-4643	125	13	.	.	PUNCT
ejpam-4643	126	1	then	then	ADV
ejpam-4643	126	2	γr(g	γr(g	NUM
ejpam-4643	126	3	)	)	PUNCT
ejpam-4643	126	4	=	=	SYM
ejpam-4643	127	1	n	n	CCONJ
ejpam-4643	128	1	−	−	NOUN
ejpam-4643	128	2	1	1	NUM
ejpam-4643	128	3	.	.	PUNCT
ejpam-4643	129	1	hence	hence	ADV
ejpam-4643	129	2	,	,	PUNCT
ejpam-4643	129	3	(	(	PUNCT
ejpam-4643	129	4	ii	ii	NOUN
ejpam-4643	129	5	)	)	PUNCT
ejpam-4643	129	6	holds	hold	VERB
ejpam-4643	129	7	.	.	PUNCT
ejpam-4643	130	1	3	3	X
ejpam-4643	130	2	.	.	X
ejpam-4643	130	3	resolving	resolve	VERB
ejpam-4643	130	4	domination	domination	NOUN
ejpam-4643	130	5	in	in	ADP
ejpam-4643	130	6	the	the	DET
ejpam-4643	130	7	join	join	NOUN
ejpam-4643	130	8	of	of	ADP
ejpam-4643	130	9	graphs	graph	NOUN
ejpam-4643	130	10	the	the	DET
ejpam-4643	130	11	join	join	NOUN
ejpam-4643	130	12	of	of	ADP
ejpam-4643	130	13	two	two	NUM
ejpam-4643	130	14	graphs	graph	NOUN
ejpam-4643	130	15	g	g	NOUN
ejpam-4643	130	16	and	and	CCONJ
ejpam-4643	130	17	h	h	NOUN
ejpam-4643	130	18	is	be	AUX
ejpam-4643	130	19	the	the	DET
ejpam-4643	130	20	graph	graph	NOUN
ejpam-4643	130	21	g	g	NOUN
ejpam-4643	130	22	+	+	CCONJ
ejpam-4643	130	23	h	h	NOUN
ejpam-4643	130	24	with	with	ADP
ejpam-4643	130	25	vertex	vertex	NOUN
ejpam-4643	130	26	set	set	VERB
ejpam-4643	130	27	v	v	NOUN
ejpam-4643	130	28	(	(	PUNCT
ejpam-4643	130	29	g	g	PROPN
ejpam-4643	130	30	+	+	NOUN
ejpam-4643	130	31	h	h	NOUN
ejpam-4643	130	32	)	)	PUNCT
ejpam-4643	131	1	=	=	NOUN
ejpam-4643	131	2	v	v	X
ejpam-4643	131	3	(	(	PUNCT
ejpam-4643	131	4	g	g	NOUN
ejpam-4643	131	5	)	)	PUNCT
ejpam-4643	131	6	•	•	ADP
ejpam-4643	131	7	∪	∪	X
ejpam-4643	131	8	v	v	NOUN
ejpam-4643	131	9	(	(	PUNCT
ejpam-4643	131	10	h	h	NOUN
ejpam-4643	131	11	)	)	PUNCT
ejpam-4643	131	12	and	and	CCONJ
ejpam-4643	131	13	edge	edge	NOUN
ejpam-4643	131	14	set	set	VERB
ejpam-4643	131	15	e(g+h	e(g+h	NUM
ejpam-4643	131	16	)	)	PUNCT
ejpam-4643	131	17	=	=	SYM
ejpam-4643	131	18	e(g	e(g	PROPN
ejpam-4643	131	19	)	)	PUNCT
ejpam-4643	132	1	•	•	ADP
ejpam-4643	132	2	∪	∪	ADP
ejpam-4643	132	3	e(h	e(h	PROPN
ejpam-4643	132	4	)	)	PUNCT
ejpam-4643	132	5	∪	∪	NOUN
ejpam-4643	132	6	{	{	PUNCT
ejpam-4643	132	7	uv	uv	NOUN
ejpam-4643	132	8	:	:	PUNCT
ejpam-4643	132	9	u	u	PROPN
ejpam-4643	132	10	∈	∈	PROPN
ejpam-4643	132	11	v	v	ADP
ejpam-4643	132	12	(	(	PUNCT
ejpam-4643	132	13	g	g	NOUN
ejpam-4643	132	14	)	)	PUNCT
ejpam-4643	132	15	,	,	PUNCT
ejpam-4643	132	16	v	v	X
ejpam-4643	132	17	∈	∈	PROPN
ejpam-4643	132	18	v	v	NOUN
ejpam-4643	132	19	(	(	PUNCT
ejpam-4643	132	20	h	h	NOUN
ejpam-4643	132	21	)	)	PUNCT
ejpam-4643	132	22	}	}	PUNCT
ejpam-4643	132	23	.	.	PUNCT
ejpam-4643	133	1	theorem	theorem	NOUN
ejpam-4643	133	2	1	1	NUM
ejpam-4643	133	3	.	.	PUNCT
ejpam-4643	134	1	[	[	X
ejpam-4643	134	2	9	9	NUM
ejpam-4643	134	3	]	]	PUNCT
ejpam-4643	134	4	let	let	VERB
ejpam-4643	134	5	g	g	NOUN
ejpam-4643	134	6	and	and	CCONJ
ejpam-4643	134	7	h	h	PROPN
ejpam-4643	134	8	be	be	VERB
ejpam-4643	134	9	non	non	ADJ
ejpam-4643	134	10	-	-	ADJ
ejpam-4643	134	11	trivial	trivial	ADJ
ejpam-4643	134	12	connected	connected	ADJ
ejpam-4643	134	13	graphs	graph	NOUN
ejpam-4643	134	14	.	.	PUNCT
ejpam-4643	135	1	a	a	DET
ejpam-4643	135	2	set	set	NOUN
ejpam-4643	135	3	w	w	PROPN
ejpam-4643	135	4	⊆	⊆	NUM
ejpam-4643	135	5	v	v	NOUN
ejpam-4643	135	6	(	(	PUNCT
ejpam-4643	135	7	g+h	g+h	NOUN
ejpam-4643	135	8	)	)	PUNCT
ejpam-4643	135	9	is	be	AUX
ejpam-4643	135	10	a	a	DET
ejpam-4643	135	11	resolving	resolving	NOUN
ejpam-4643	135	12	set	set	NOUN
ejpam-4643	135	13	of	of	ADP
ejpam-4643	135	14	g+h	g+h	PROPN
ejpam-4643	135	15	if	if	SCONJ
ejpam-4643	135	16	and	and	CCONJ
ejpam-4643	135	17	only	only	ADV
ejpam-4643	135	18	if	if	SCONJ
ejpam-4643	135	19	w	w	PROPN
ejpam-4643	135	20	=	=	VERB
ejpam-4643	135	21	wg	wg	PROPN
ejpam-4643	135	22	∪wh	∪wh	NOUN
ejpam-4643	135	23	where	where	SCONJ
ejpam-4643	135	24	wg	wg	PROPN
ejpam-4643	135	25	⊆	⊆	NUM
ejpam-4643	135	26	v	v	NOUN
ejpam-4643	135	27	(	(	PUNCT
ejpam-4643	135	28	g	g	NOUN
ejpam-4643	135	29	)	)	PUNCT
ejpam-4643	135	30	and	and	CCONJ
ejpam-4643	135	31	wh	wh	VERB
ejpam-4643	135	32	⊆	⊆	NUM
ejpam-4643	135	33	v	v	NOUN
ejpam-4643	135	34	(	(	PUNCT
ejpam-4643	135	35	h	h	NOUN
ejpam-4643	135	36	)	)	PUNCT
ejpam-4643	135	37	are	be	AUX
ejpam-4643	135	38	locating	locate	VERB
ejpam-4643	135	39	sets	set	NOUN
ejpam-4643	135	40	of	of	ADP
ejpam-4643	135	41	g	g	PROPN
ejpam-4643	135	42	and	and	CCONJ
ejpam-4643	135	43	h	h	NOUN
ejpam-4643	135	44	,	,	PUNCT
ejpam-4643	135	45	respectively	respectively	ADV
ejpam-4643	135	46	,	,	PUNCT
ejpam-4643	135	47	where	where	SCONJ
ejpam-4643	135	48	wg	wg	NOUN
ejpam-4643	135	49	or	or	CCONJ
ejpam-4643	135	50	wh	wh	PROPN
ejpam-4643	135	51	is	be	AUX
ejpam-4643	135	52	a	a	DET
ejpam-4643	135	53	strictly	strictly	ADV
ejpam-4643	135	54	locating	locate	VERB
ejpam-4643	135	55	set	set	NOUN
ejpam-4643	135	56	.	.	PUNCT
ejpam-4643	136	1	theorem	theorem	NOUN
ejpam-4643	136	2	2	2	NUM
ejpam-4643	136	3	.	.	PUNCT
ejpam-4643	137	1	[	[	X
ejpam-4643	137	2	4	4	X
ejpam-4643	137	3	]	]	PUNCT
ejpam-4643	137	4	let	let	VERB
ejpam-4643	137	5	g	g	NOUN
ejpam-4643	137	6	and	and	CCONJ
ejpam-4643	137	7	h	h	NOUN
ejpam-4643	137	8	be	be	AUX
ejpam-4643	137	9	connected	connect	VERB
ejpam-4643	137	10	graphs	graph	NOUN
ejpam-4643	137	11	.	.	PUNCT
ejpam-4643	138	1	then	then	ADV
ejpam-4643	138	2	c	c	PROPN
ejpam-4643	138	3	⊆	⊆	NUM
ejpam-4643	138	4	v	v	NOUN
ejpam-4643	138	5	(	(	PUNCT
ejpam-4643	138	6	g+h	g+h	PROPN
ejpam-4643	138	7	)	)	PUNCT
ejpam-4643	138	8	is	be	AUX
ejpam-4643	138	9	a	a	DET
ejpam-4643	138	10	dominating	dominating	NOUN
ejpam-4643	138	11	set	set	VERB
ejpam-4643	138	12	in	in	ADP
ejpam-4643	138	13	g+h	g+h	PROPN
ejpam-4643	138	14	if	if	SCONJ
ejpam-4643	138	15	and	and	CCONJ
ejpam-4643	138	16	only	only	ADV
ejpam-4643	138	17	if	if	SCONJ
ejpam-4643	138	18	at	at	ADV
ejpam-4643	138	19	least	least	ADJ
ejpam-4643	138	20	one	one	NUM
ejpam-4643	138	21	of	of	ADP
ejpam-4643	138	22	the	the	DET
ejpam-4643	138	23	following	follow	VERB
ejpam-4643	138	24	is	be	AUX
ejpam-4643	138	25	true	true	ADJ
ejpam-4643	138	26	:	:	PUNCT
ejpam-4643	138	27	(	(	PUNCT
ejpam-4643	138	28	i	i	NOUN
ejpam-4643	138	29	)	)	PUNCT
ejpam-4643	138	30	c	c	PROPN
ejpam-4643	138	31	∩	∩	PROPN
ejpam-4643	138	32	v	v	X
ejpam-4643	138	33	(	(	PUNCT
ejpam-4643	138	34	g	g	NOUN
ejpam-4643	138	35	)	)	PUNCT
ejpam-4643	138	36	is	be	AUX
ejpam-4643	138	37	a	a	DET
ejpam-4643	138	38	dominating	dominating	NOUN
ejpam-4643	138	39	set	set	VERB
ejpam-4643	138	40	in	in	ADP
ejpam-4643	138	41	g.	g.	PROPN
ejpam-4643	138	42	(	(	PUNCT
ejpam-4643	138	43	ii	ii	PROPN
ejpam-4643	138	44	)	)	PUNCT
ejpam-4643	138	45	c	c	NOUN
ejpam-4643	138	46	∩	∩	PROPN
ejpam-4643	138	47	v	v	X
ejpam-4643	138	48	(	(	PUNCT
ejpam-4643	138	49	h	h	NOUN
ejpam-4643	138	50	)	)	PUNCT
ejpam-4643	138	51	is	be	AUX
ejpam-4643	138	52	a	a	DET
ejpam-4643	138	53	dominating	dominating	NOUN
ejpam-4643	138	54	set	set	NOUN
ejpam-4643	138	55	in	in	ADP
ejpam-4643	138	56	h.	h.	PROPN
ejpam-4643	138	57	(	(	PUNCT
ejpam-4643	138	58	iii	iii	NOUN
ejpam-4643	138	59	)	)	PUNCT
ejpam-4643	138	60	c	c	NOUN
ejpam-4643	138	61	∩	∩	X
ejpam-4643	138	62	v	v	X
ejpam-4643	138	63	(	(	PUNCT
ejpam-4643	138	64	g	g	NOUN
ejpam-4643	138	65	)	)	PUNCT
ejpam-4643	138	66	̸=	̸=	PROPN
ejpam-4643	138	67	∅	∅	NOUN
ejpam-4643	138	68	and	and	CCONJ
ejpam-4643	138	69	c	c	NOUN
ejpam-4643	138	70	∩	∩	ADJ
ejpam-4643	138	71	v	v	X
ejpam-4643	138	72	(	(	PUNCT
ejpam-4643	138	73	h	h	NOUN
ejpam-4643	138	74	)	)	PUNCT
ejpam-4643	138	75	̸=	̸=	PROPN
ejpam-4643	138	76	∅.	∅.	ADV
ejpam-4643	138	77	theorem	theorem	ADJ
ejpam-4643	138	78	3	3	X
ejpam-4643	138	79	.	.	PUNCT
ejpam-4643	139	1	let	let	VERB
ejpam-4643	139	2	g	g	NOUN
ejpam-4643	139	3	and	and	CCONJ
ejpam-4643	139	4	h	h	PROPN
ejpam-4643	139	5	be	be	VERB
ejpam-4643	139	6	non	non	ADJ
ejpam-4643	139	7	-	-	ADJ
ejpam-4643	139	8	trivial	trivial	ADJ
ejpam-4643	139	9	connected	connected	ADJ
ejpam-4643	139	10	graphs	graph	NOUN
ejpam-4643	139	11	.	.	PUNCT
ejpam-4643	140	1	a	a	DET
ejpam-4643	140	2	set	set	NOUN
ejpam-4643	140	3	w	w	PROPN
ejpam-4643	140	4	⊆	⊆	NUM
ejpam-4643	140	5	v	v	NOUN
ejpam-4643	140	6	(	(	PUNCT
ejpam-4643	140	7	g	g	PROPN
ejpam-4643	140	8	+	+	NOUN
ejpam-4643	140	9	h	h	NOUN
ejpam-4643	140	10	)	)	PUNCT
ejpam-4643	140	11	is	be	AUX
ejpam-4643	140	12	a	a	DET
ejpam-4643	140	13	resolving	resolve	VERB
ejpam-4643	140	14	dominating	dominating	NOUN
ejpam-4643	140	15	set	set	NOUN
ejpam-4643	140	16	of	of	ADP
ejpam-4643	140	17	g+h	g+h	PROPN
ejpam-4643	141	1	if	if	SCONJ
ejpam-4643	141	2	and	and	CCONJ
ejpam-4643	141	3	only	only	ADV
ejpam-4643	141	4	if	if	SCONJ
ejpam-4643	141	5	w	w	NOUN
ejpam-4643	141	6	is	be	AUX
ejpam-4643	141	7	a	a	DET
ejpam-4643	141	8	locating	locate	VERB
ejpam-4643	141	9	-	-	PUNCT
ejpam-4643	141	10	dominating	dominate	VERB
ejpam-4643	141	11	set	set	NOUN
ejpam-4643	141	12	of	of	ADP
ejpam-4643	141	13	g+h	g+h	PROPN
ejpam-4643	141	14	.	.	PUNCT
ejpam-4643	142	1	proof	proof	NOUN
ejpam-4643	142	2	:	:	PUNCT
ejpam-4643	142	3	suppose	suppose	VERB
ejpam-4643	142	4	that	that	SCONJ
ejpam-4643	142	5	w	w	NOUN
ejpam-4643	142	6	is	be	AUX
ejpam-4643	142	7	a	a	DET
ejpam-4643	142	8	resolving	resolve	VERB
ejpam-4643	142	9	dominating	dominating	NOUN
ejpam-4643	142	10	set	set	NOUN
ejpam-4643	142	11	of	of	ADP
ejpam-4643	142	12	g+h	g+h	PROPN
ejpam-4643	142	13	.	.	PUNCT
ejpam-4643	143	1	then	then	ADV
ejpam-4643	143	2	w	w	PROPN
ejpam-4643	143	3	is	be	AUX
ejpam-4643	143	4	a	a	DET
ejpam-4643	143	5	resolving	resolving	NOUN
ejpam-4643	143	6	set	set	NOUN
ejpam-4643	143	7	of	of	ADP
ejpam-4643	143	8	g	g	PROPN
ejpam-4643	143	9	+	+	PROPN
ejpam-4643	143	10	h.	h.	PROPN
ejpam-4643	143	11	by	by	ADP
ejpam-4643	143	12	theorem	theorem	NOUN
ejpam-4643	143	13	1	1	NUM
ejpam-4643	143	14	,	,	PUNCT
ejpam-4643	143	15	w	w	NOUN
ejpam-4643	143	16	=	=	PUNCT
ejpam-4643	143	17	wg	wg	PROPN
ejpam-4643	143	18	∪wh	∪wh	NOUN
ejpam-4643	143	19	where	where	SCONJ
ejpam-4643	143	20	wg	wg	PROPN
ejpam-4643	143	21	⊆	⊆	NUM
ejpam-4643	143	22	v	v	NOUN
ejpam-4643	143	23	(	(	PUNCT
ejpam-4643	143	24	g	g	NOUN
ejpam-4643	143	25	)	)	PUNCT
ejpam-4643	143	26	and	and	CCONJ
ejpam-4643	143	27	wh	wh	VERB
ejpam-4643	143	28	⊆	⊆	NUM
ejpam-4643	143	29	v	v	NOUN
ejpam-4643	143	30	(	(	PUNCT
ejpam-4643	143	31	h	h	NOUN
ejpam-4643	143	32	)	)	PUNCT
ejpam-4643	143	33	are	be	AUX
ejpam-4643	143	34	locating	locate	VERB
ejpam-4643	143	35	sets	set	NOUN
ejpam-4643	143	36	of	of	ADP
ejpam-4643	143	37	g	g	PROPN
ejpam-4643	143	38	and	and	CCONJ
ejpam-4643	143	39	h	h	NOUN
ejpam-4643	143	40	,	,	PUNCT
ejpam-4643	143	41	respectively	respectively	ADV
ejpam-4643	143	42	,	,	PUNCT
ejpam-4643	143	43	where	where	SCONJ
ejpam-4643	143	44	wg	wg	NOUN
ejpam-4643	143	45	or	or	CCONJ
ejpam-4643	143	46	wh	wh	PROPN
ejpam-4643	143	47	is	be	AUX
ejpam-4643	143	48	a	a	DET
ejpam-4643	143	49	strictly	strictly	ADV
ejpam-4643	143	50	locating	locate	VERB
ejpam-4643	143	51	set	set	NOUN
ejpam-4643	143	52	.	.	PUNCT
ejpam-4643	144	1	since	since	SCONJ
ejpam-4643	144	2	w	w	PROPN
ejpam-4643	144	3	is	be	AUX
ejpam-4643	144	4	a	a	DET
ejpam-4643	144	5	dominating	dominating	NOUN
ejpam-4643	144	6	set	set	NOUN
ejpam-4643	144	7	of	of	ADP
ejpam-4643	144	8	g	g	PROPN
ejpam-4643	144	9	+	+	CCONJ
ejpam-4643	144	10	h	h	NOUN
ejpam-4643	144	11	,	,	PUNCT
ejpam-4643	144	12	wg	wg	VERB
ejpam-4643	144	13	and	and	CCONJ
ejpam-4643	144	14	wh	wh	PROPN
ejpam-4643	144	15	are	be	AUX
ejpam-4643	144	16	also	also	ADV
ejpam-4643	144	17	dominating	dominate	VERB
ejpam-4643	144	18	sets	set	NOUN
ejpam-4643	144	19	of	of	ADP
ejpam-4643	144	20	g	g	PROPN
ejpam-4643	144	21	and	and	CCONJ
ejpam-4643	144	22	h	h	NOUN
ejpam-4643	144	23	,	,	PUNCT
ejpam-4643	144	24	respectively	respectively	ADV
ejpam-4643	144	25	.	.	PUNCT
ejpam-4643	145	1	by	by	ADP
ejpam-4643	145	2	theorem	theorem	NOUN
ejpam-4643	145	3	1	1	NUM
ejpam-4643	145	4	,	,	PUNCT
ejpam-4643	145	5	w	w	NOUN
ejpam-4643	145	6	is	be	AUX
ejpam-4643	145	7	a	a	DET
ejpam-4643	145	8	locating	locate	VERB
ejpam-4643	145	9	-	-	PUNCT
ejpam-4643	145	10	dominating	dominate	VERB
ejpam-4643	145	11	set	set	NOUN
ejpam-4643	145	12	of	of	ADP
ejpam-4643	145	13	g+h	g+h	PROPN
ejpam-4643	145	14	.	.	PUNCT
ejpam-4643	146	1	the	the	DET
ejpam-4643	146	2	converse	converse	NOUN
ejpam-4643	146	3	follows	follow	VERB
ejpam-4643	146	4	immediately	immediately	ADV
ejpam-4643	146	5	from	from	ADP
ejpam-4643	146	6	theorem	theorem	ADJ
ejpam-4643	146	7	1	1	NUM
ejpam-4643	146	8	and	and	CCONJ
ejpam-4643	146	9	theorem	theorem	VERB
ejpam-4643	146	10	2(iii	2(iii	NUM
ejpam-4643	146	11	)	)	PUNCT
ejpam-4643	146	12	.	.	PUNCT
ejpam-4643	147	1	theorem	theorem	ADJ
ejpam-4643	147	2	4	4	NUM
ejpam-4643	147	3	.	.	PUNCT
ejpam-4643	148	1	let	let	VERB
ejpam-4643	148	2	g	g	NOUN
ejpam-4643	148	3	and	and	CCONJ
ejpam-4643	148	4	h	h	PROPN
ejpam-4643	148	5	be	be	VERB
ejpam-4643	148	6	non	non	ADJ
ejpam-4643	148	7	-	-	ADJ
ejpam-4643	148	8	trivial	trivial	ADJ
ejpam-4643	148	9	connected	connected	ADJ
ejpam-4643	148	10	graphs	graph	NOUN
ejpam-4643	148	11	.	.	PUNCT
ejpam-4643	149	1	a	a	DET
ejpam-4643	149	2	set	set	NOUN
ejpam-4643	149	3	w	w	PROPN
ejpam-4643	149	4	⊆	⊆	NUM
ejpam-4643	149	5	v	v	NOUN
ejpam-4643	149	6	(	(	PUNCT
ejpam-4643	149	7	g	g	PROPN
ejpam-4643	149	8	+	+	NOUN
ejpam-4643	149	9	h	h	NOUN
ejpam-4643	149	10	)	)	PUNCT
ejpam-4643	149	11	is	be	AUX
ejpam-4643	149	12	a	a	DET
ejpam-4643	149	13	resolving	resolve	VERB
ejpam-4643	149	14	dominating	dominating	NOUN
ejpam-4643	149	15	set	set	NOUN
ejpam-4643	149	16	of	of	ADP
ejpam-4643	149	17	g+h	g+h	PROPN
ejpam-4643	150	1	if	if	SCONJ
ejpam-4643	150	2	and	and	CCONJ
ejpam-4643	150	3	only	only	ADV
ejpam-4643	150	4	if	if	SCONJ
ejpam-4643	150	5	w	w	PROPN
ejpam-4643	150	6	=	=	VERB
ejpam-4643	150	7	wg	wg	PROPN
ejpam-4643	150	8	∪wh	∪wh	NOUN
ejpam-4643	150	9	where	where	SCONJ
ejpam-4643	150	10	wg	wg	PROPN
ejpam-4643	150	11	=	=	SYM
ejpam-4643	150	12	v	v	NOUN
ejpam-4643	150	13	(	(	PUNCT
ejpam-4643	150	14	g	g	NOUN
ejpam-4643	150	15	)	)	PUNCT
ejpam-4643	150	16	∩w	∩w	NOUN
ejpam-4643	150	17	and	and	CCONJ
ejpam-4643	150	18	wh	wh	VERB
ejpam-4643	150	19	=	=	SYM
ejpam-4643	150	20	v	v	PROPN
ejpam-4643	150	21	(	(	PUNCT
ejpam-4643	150	22	h	h	NOUN
ejpam-4643	150	23	)	)	PUNCT
ejpam-4643	150	24	∩w	∩w	NOUN
ejpam-4643	150	25	are	be	AUX
ejpam-4643	150	26	locating	locate	VERB
ejpam-4643	150	27	sets	set	NOUN
ejpam-4643	150	28	of	of	ADP
ejpam-4643	150	29	g	g	PROPN
ejpam-4643	150	30	and	and	CCONJ
ejpam-4643	150	31	h	h	NOUN
ejpam-4643	150	32	,	,	PUNCT
ejpam-4643	150	33	respectively	respectively	ADV
ejpam-4643	150	34	,	,	PUNCT
ejpam-4643	150	35	where	where	SCONJ
ejpam-4643	150	36	wg	wg	NOUN
ejpam-4643	150	37	or	or	CCONJ
ejpam-4643	150	38	wh	wh	PROPN
ejpam-4643	150	39	is	be	AUX
ejpam-4643	150	40	a	a	DET
ejpam-4643	150	41	strictly	strictly	ADV
ejpam-4643	150	42	locating	locate	VERB
ejpam-4643	150	43	set	set	NOUN
ejpam-4643	150	44	.	.	PUNCT
ejpam-4643	151	1	g.	g.	PROPN
ejpam-4643	151	2	monsanto	monsanto	PROPN
ejpam-4643	151	3	,	,	PUNCT
ejpam-4643	151	4	h.	h.	PROPN
ejpam-4643	151	5	rara	rara	PROPN
ejpam-4643	151	6	/	/	SYM
ejpam-4643	151	7	eur	eur	PROPN
ejpam-4643	151	8	.	.	PUNCT
ejpam-4643	152	1	j.	j.	PROPN
ejpam-4643	152	2	pure	pure	PROPN
ejpam-4643	152	3	appl	appl	PROPN
ejpam-4643	152	4	.	.	PROPN
ejpam-4643	152	5	math	math	PROPN
ejpam-4643	152	6	,	,	PUNCT
ejpam-4643	152	7	16	16	NUM
ejpam-4643	152	8	(	(	PUNCT
ejpam-4643	152	9	1	1	NUM
ejpam-4643	152	10	)	)	PUNCT
ejpam-4643	152	11	(	(	PUNCT
ejpam-4643	152	12	2023	2023	NUM
ejpam-4643	152	13	)	)	PUNCT
ejpam-4643	152	14	,	,	PUNCT
ejpam-4643	152	15	18	18	NUM
ejpam-4643	152	16	-	-	SYM
ejpam-4643	152	17	28	28	NUM
ejpam-4643	152	18	23	23	NUM
ejpam-4643	152	19	proof	proof	NOUN
ejpam-4643	152	20	:	:	PUNCT
ejpam-4643	152	21	suppose	suppose	VERB
ejpam-4643	152	22	that	that	SCONJ
ejpam-4643	152	23	w	w	NOUN
ejpam-4643	152	24	is	be	AUX
ejpam-4643	152	25	a	a	DET
ejpam-4643	152	26	resolving	resolve	VERB
ejpam-4643	152	27	dominating	dominating	NOUN
ejpam-4643	152	28	set	set	NOUN
ejpam-4643	152	29	of	of	ADP
ejpam-4643	152	30	g+h	g+h	PROPN
ejpam-4643	152	31	.	.	PUNCT
ejpam-4643	153	1	then	then	ADV
ejpam-4643	153	2	w	w	PROPN
ejpam-4643	153	3	is	be	AUX
ejpam-4643	153	4	a	a	DET
ejpam-4643	153	5	resolving	resolving	NOUN
ejpam-4643	153	6	set	set	NOUN
ejpam-4643	153	7	of	of	ADP
ejpam-4643	153	8	g	g	PROPN
ejpam-4643	153	9	+	+	CCONJ
ejpam-4643	153	10	h.	h.	PROPN
ejpam-4643	153	11	by	by	ADP
ejpam-4643	153	12	theorem	theorem	NOUN
ejpam-4643	153	13	1	1	NUM
ejpam-4643	153	14	,	,	PUNCT
ejpam-4643	153	15	wg	wg	PROPN
ejpam-4643	154	1	=	=	NOUN
ejpam-4643	154	2	w	w	NOUN
ejpam-4643	154	3	∪	∪	X
ejpam-4643	154	4	v	v	NOUN
ejpam-4643	154	5	(	(	PUNCT
ejpam-4643	154	6	g	g	NOUN
ejpam-4643	154	7	)	)	PUNCT
ejpam-4643	154	8	where	where	SCONJ
ejpam-4643	154	9	wg	wg	PROPN
ejpam-4643	154	10	⊆	⊆	NUM
ejpam-4643	154	11	v	v	NOUN
ejpam-4643	154	12	(	(	PUNCT
ejpam-4643	154	13	g	g	NOUN
ejpam-4643	154	14	)	)	PUNCT
ejpam-4643	154	15	and	and	CCONJ
ejpam-4643	154	16	wh	wh	VERB
ejpam-4643	154	17	⊆	⊆	NUM
ejpam-4643	154	18	v	v	NOUN
ejpam-4643	154	19	(	(	PUNCT
ejpam-4643	154	20	h	h	NOUN
ejpam-4643	154	21	)	)	PUNCT
ejpam-4643	154	22	are	be	AUX
ejpam-4643	154	23	locating	locate	VERB
ejpam-4643	154	24	sets	set	NOUN
ejpam-4643	154	25	of	of	ADP
ejpam-4643	154	26	g	g	PROPN
ejpam-4643	154	27	and	and	CCONJ
ejpam-4643	154	28	h	h	NOUN
ejpam-4643	154	29	,	,	PUNCT
ejpam-4643	154	30	respectively	respectively	ADV
ejpam-4643	154	31	,	,	PUNCT
ejpam-4643	154	32	where	where	SCONJ
ejpam-4643	154	33	wg	wg	NOUN
ejpam-4643	154	34	or	or	CCONJ
ejpam-4643	154	35	wh	wh	PROPN
ejpam-4643	154	36	is	be	AUX
ejpam-4643	154	37	a	a	DET
ejpam-4643	154	38	strictly	strictly	ADV
ejpam-4643	154	39	locating	locate	VERB
ejpam-4643	154	40	set	set	NOUN
ejpam-4643	154	41	.	.	PUNCT
ejpam-4643	155	1	since	since	SCONJ
ejpam-4643	155	2	w	w	PROPN
ejpam-4643	155	3	is	be	AUX
ejpam-4643	155	4	a	a	DET
ejpam-4643	155	5	dominating	dominating	NOUN
ejpam-4643	155	6	set	set	NOUN
ejpam-4643	155	7	of	of	ADP
ejpam-4643	155	8	g+h	g+h	PROPN
ejpam-4643	155	9	,	,	PUNCT
ejpam-4643	155	10	wg	wg	VERB
ejpam-4643	155	11	and	and	CCONJ
ejpam-4643	155	12	wh	wh	PROPN
ejpam-4643	155	13	are	be	AUX
ejpam-4643	155	14	also	also	ADV
ejpam-4643	155	15	dominating	dominate	VERB
ejpam-4643	155	16	sets	set	NOUN
ejpam-4643	155	17	of	of	ADP
ejpam-4643	155	18	g	g	PROPN
ejpam-4643	155	19	and	and	CCONJ
ejpam-4643	155	20	h	h	NOUN
ejpam-4643	155	21	,	,	PUNCT
ejpam-4643	155	22	respectively	respectively	ADV
ejpam-4643	155	23	.	.	PUNCT
ejpam-4643	156	1	by	by	ADP
ejpam-4643	156	2	theorem	theorem	NOUN
ejpam-4643	156	3	3	3	NUM
ejpam-4643	156	4	,	,	PUNCT
ejpam-4643	156	5	w	w	PROPN
ejpam-4643	156	6	is	be	AUX
ejpam-4643	156	7	a	a	DET
ejpam-4643	156	8	locating	locate	VERB
ejpam-4643	156	9	-	-	PUNCT
ejpam-4643	156	10	dominating	dominate	VERB
ejpam-4643	156	11	set	set	NOUN
ejpam-4643	156	12	of	of	ADP
ejpam-4643	156	13	g+h	g+h	PROPN
ejpam-4643	156	14	.	.	PUNCT
ejpam-4643	157	1	conversely	conversely	ADV
ejpam-4643	157	2	,	,	PUNCT
ejpam-4643	157	3	let	let	VERB
ejpam-4643	157	4	wg	wg	VERB
ejpam-4643	157	5	=	=	SYM
ejpam-4643	157	6	v	v	NOUN
ejpam-4643	157	7	(	(	PUNCT
ejpam-4643	157	8	g	g	NOUN
ejpam-4643	157	9	)	)	PUNCT
ejpam-4643	157	10	∩w	∩w	NOUN
ejpam-4643	157	11	and	and	CCONJ
ejpam-4643	157	12	wh	wh	VERB
ejpam-4643	157	13	=	=	SYM
ejpam-4643	157	14	v	v	PROPN
ejpam-4643	157	15	(	(	PUNCT
ejpam-4643	157	16	h	h	NOUN
ejpam-4643	157	17	)	)	PUNCT
ejpam-4643	157	18	∩w	∩w	VERB
ejpam-4643	157	19	be	be	AUX
ejpam-4643	157	20	locating	locate	VERB
ejpam-4643	157	21	sets	set	NOUN
ejpam-4643	157	22	of	of	ADP
ejpam-4643	157	23	g	g	PROPN
ejpam-4643	157	24	and	and	CCONJ
ejpam-4643	157	25	h	h	NOUN
ejpam-4643	157	26	,	,	PUNCT
ejpam-4643	157	27	respectively	respectively	ADV
ejpam-4643	157	28	,	,	PUNCT
ejpam-4643	157	29	and	and	CCONJ
ejpam-4643	157	30	wg	wg	PROPN
ejpam-4643	157	31	or	or	CCONJ
ejpam-4643	157	32	wh	wh	PROPN
ejpam-4643	157	33	is	be	AUX
ejpam-4643	157	34	a	a	DET
ejpam-4643	157	35	strictly	strictly	ADV
ejpam-4643	157	36	locating	locate	VERB
ejpam-4643	157	37	set	set	NOUN
ejpam-4643	157	38	of	of	ADP
ejpam-4643	157	39	g	g	PROPN
ejpam-4643	157	40	+	+	CCONJ
ejpam-4643	157	41	h.	h.	PROPN
ejpam-4643	157	42	by	by	ADP
ejpam-4643	157	43	theorem	theorem	NOUN
ejpam-4643	157	44	2	2	NUM
ejpam-4643	157	45	,	,	PUNCT
ejpam-4643	157	46	w	w	NOUN
ejpam-4643	157	47	is	be	AUX
ejpam-4643	157	48	a	a	DET
ejpam-4643	157	49	dominating	dominating	NOUN
ejpam-4643	157	50	set	set	NOUN
ejpam-4643	157	51	of	of	ADP
ejpam-4643	157	52	g	g	PROPN
ejpam-4643	157	53	+	+	PROPN
ejpam-4643	157	54	h.	h.	PROPN
ejpam-4643	157	55	let	let	VERB
ejpam-4643	157	56	u	u	NOUN
ejpam-4643	157	57	,	,	PUNCT
ejpam-4643	157	58	v	v	PROPN
ejpam-4643	157	59	∈	∈	PROPN
ejpam-4643	157	60	v	v	NOUN
ejpam-4643	157	61	(	(	PUNCT
ejpam-4643	157	62	g	g	PROPN
ejpam-4643	157	63	+	+	NOUN
ejpam-4643	157	64	h	h	NOUN
ejpam-4643	157	65	)	)	PUNCT
ejpam-4643	157	66	\w	\w	ADJ
ejpam-4643	157	67	with	with	ADP
ejpam-4643	157	68	u	u	PROPN
ejpam-4643	157	69	̸=	̸=	PROPN
ejpam-4643	157	70	v.	v.	CCONJ
ejpam-4643	157	71	consider	consider	VERB
ejpam-4643	157	72	the	the	DET
ejpam-4643	157	73	following	follow	VERB
ejpam-4643	157	74	cases	case	NOUN
ejpam-4643	157	75	:	:	PUNCT
ejpam-4643	157	76	case	case	NOUN
ejpam-4643	157	77	1	1	NUM
ejpam-4643	157	78	.	.	X
ejpam-4643	157	79	u	u	NOUN
ejpam-4643	157	80	,	,	PUNCT
ejpam-4643	157	81	v	v	PROPN
ejpam-4643	157	82	∈	∈	PROPN
ejpam-4643	157	83	v	v	NOUN
ejpam-4643	157	84	(	(	PUNCT
ejpam-4643	157	85	g	g	NOUN
ejpam-4643	157	86	)	)	PUNCT
ejpam-4643	157	87	since	since	SCONJ
ejpam-4643	157	88	wg	wg	PROPN
ejpam-4643	157	89	is	be	AUX
ejpam-4643	157	90	a	a	DET
ejpam-4643	157	91	locating	locating	NOUN
ejpam-4643	157	92	set	set	NOUN
ejpam-4643	157	93	of	of	ADP
ejpam-4643	157	94	g	g	NOUN
ejpam-4643	157	95	,	,	PUNCT
ejpam-4643	157	96	ng(u	ng(u	NOUN
ejpam-4643	157	97	)	)	PUNCT
ejpam-4643	157	98	∩wg	∩wg	NOUN
ejpam-4643	157	99	̸=	̸=	PROPN
ejpam-4643	157	100	ng(v	ng(v	NOUN
ejpam-4643	157	101	)	)	PUNCT
ejpam-4643	157	102	∩wg	∩wg	NOUN
ejpam-4643	157	103	.	.	PUNCT
ejpam-4643	158	1	hence	hence	ADV
ejpam-4643	158	2	,	,	PUNCT
ejpam-4643	158	3	rg+h(u	rg+h(u	PROPN
ejpam-4643	158	4	/	/	SYM
ejpam-4643	158	5	w	w	PROPN
ejpam-4643	158	6	)	)	PUNCT
ejpam-4643	158	7	̸=	̸=	PROPN
ejpam-4643	158	8	rg+h(v	rg+h(v	PROPN
ejpam-4643	158	9	/	/	SYM
ejpam-4643	158	10	w	w	NOUN
ejpam-4643	158	11	)	)	PUNCT
ejpam-4643	158	12	.	.	PUNCT
ejpam-4643	159	1	case	case	NOUN
ejpam-4643	159	2	2	2	NUM
ejpam-4643	159	3	.	.	X
ejpam-4643	159	4	u	u	NOUN
ejpam-4643	159	5	,	,	PUNCT
ejpam-4643	159	6	v	v	PROPN
ejpam-4643	159	7	∈	∈	PROPN
ejpam-4643	159	8	v	v	NOUN
ejpam-4643	159	9	(	(	PUNCT
ejpam-4643	159	10	h	h	NOUN
ejpam-4643	159	11	)	)	PUNCT
ejpam-4643	159	12	the	the	DET
ejpam-4643	159	13	proof	proof	NOUN
ejpam-4643	159	14	is	be	AUX
ejpam-4643	159	15	similar	similar	ADJ
ejpam-4643	159	16	to	to	PART
ejpam-4643	159	17	case	case	NOUN
ejpam-4643	159	18	1	1	NUM
ejpam-4643	159	19	.	.	PUNCT
ejpam-4643	159	20	case	case	NOUN
ejpam-4643	159	21	3	3	NUM
ejpam-4643	159	22	.	.	X
ejpam-4643	159	23	u	u	PROPN
ejpam-4643	159	24	∈	∈	PROPN
ejpam-4643	159	25	v	v	ADP
ejpam-4643	159	26	(	(	PUNCT
ejpam-4643	159	27	g	g	NOUN
ejpam-4643	159	28	)	)	PUNCT
ejpam-4643	159	29	and	and	CCONJ
ejpam-4643	160	1	v	v	ADP
ejpam-4643	160	2	∈	∈	PROPN
ejpam-4643	160	3	v	v	NOUN
ejpam-4643	160	4	(	(	PUNCT
ejpam-4643	160	5	h	h	NOUN
ejpam-4643	160	6	)	)	PUNCT
ejpam-4643	160	7	rg+h(u	rg+h(u	PROPN
ejpam-4643	160	8	/	/	SYM
ejpam-4643	160	9	w	w	NOUN
ejpam-4643	160	10	)	)	PUNCT
ejpam-4643	160	11	=	=	SYM
ejpam-4643	160	12	(	(	PUNCT
ejpam-4643	160	13	dg+h(u	dg+h(u	PROPN
ejpam-4643	160	14	,	,	PUNCT
ejpam-4643	160	15	w1	w1	NOUN
ejpam-4643	160	16	)	)	PUNCT
ejpam-4643	160	17	,	,	PUNCT
ejpam-4643	160	18	.	.	PUNCT
ejpam-4643	160	19	.	.	PUNCT
ejpam-4643	161	1	.	.	PUNCT
ejpam-4643	162	1	,	,	PUNCT
ejpam-4643	162	2	dg+h(u	dg+h(u	PROPN
ejpam-4643	162	3	,	,	PUNCT
ejpam-4643	162	4	wn	wn	PROPN
ejpam-4643	162	5	)	)	PUNCT
ejpam-4643	162	6	,	,	PUNCT
ejpam-4643	162	7	1	1	NUM
ejpam-4643	162	8	,	,	PUNCT
ejpam-4643	162	9	1	1	NUM
ejpam-4643	162	10	,	,	PUNCT
ejpam-4643	162	11	.	.	PUNCT
ejpam-4643	162	12	.	.	PUNCT
ejpam-4643	163	1	.	.	PUNCT
ejpam-4643	164	1	,	,	PUNCT
ejpam-4643	164	2	1	1	X
ejpam-4643	164	3	)	)	PUNCT
ejpam-4643	164	4	and	and	CCONJ
ejpam-4643	164	5	rg+h(v	rg+h(v	PROPN
ejpam-4643	164	6	/	/	SYM
ejpam-4643	164	7	w	w	NOUN
ejpam-4643	164	8	)	)	PUNCT
ejpam-4643	164	9	=	=	PUNCT
ejpam-4643	165	1	(	(	PUNCT
ejpam-4643	165	2	1	1	NUM
ejpam-4643	165	3	,	,	PUNCT
ejpam-4643	165	4	1	1	NUM
ejpam-4643	165	5	,	,	PUNCT
ejpam-4643	165	6	.	.	PUNCT
ejpam-4643	165	7	.	.	PUNCT
ejpam-4643	166	1	.	.	PUNCT
ejpam-4643	167	1	,	,	PUNCT
ejpam-4643	167	2	1	1	X
ejpam-4643	167	3	,	,	PUNCT
ejpam-4643	167	4	dg+h(v	dg+h(v	NOUN
ejpam-4643	167	5	,	,	PUNCT
ejpam-4643	167	6	u1	u1	NOUN
ejpam-4643	167	7	)	)	PUNCT
ejpam-4643	167	8	,	,	PUNCT
ejpam-4643	167	9	.	.	PUNCT
ejpam-4643	167	10	.	.	PUNCT
ejpam-4643	168	1	.	.	PUNCT
ejpam-4643	169	1	,	,	PUNCT
ejpam-4643	169	2	dg+h(v	dg+h(v	PROPN
ejpam-4643	169	3	,	,	PUNCT
ejpam-4643	169	4	un	un	PROPN
ejpam-4643	169	5	)	)	PUNCT
ejpam-4643	169	6	)	)	PUNCT
ejpam-4643	169	7	suppose	suppose	VERB
ejpam-4643	169	8	there	there	PRON
ejpam-4643	169	9	exists	exist	VERB
ejpam-4643	169	10	j	j	PROPN
ejpam-4643	169	11	∈	∈	PROPN
ejpam-4643	169	12	{	{	PUNCT
ejpam-4643	169	13	1	1	NUM
ejpam-4643	169	14	,	,	PUNCT
ejpam-4643	169	15	2	2	NUM
ejpam-4643	169	16	,	,	PUNCT
ejpam-4643	169	17	.	.	PUNCT
ejpam-4643	169	18	.	.	PUNCT
ejpam-4643	170	1	.	.	PUNCT
ejpam-4643	171	1	,	,	PUNCT
ejpam-4643	171	2	n	n	CCONJ
ejpam-4643	171	3	}	}	PUNCT
ejpam-4643	171	4	such	such	ADJ
ejpam-4643	171	5	that	that	SCONJ
ejpam-4643	171	6	dg+h(u	dg+h(u	PROPN
ejpam-4643	171	7	,	,	PUNCT
ejpam-4643	171	8	wj	wj	NOUN
ejpam-4643	171	9	)	)	PUNCT
ejpam-4643	171	10	̸=	̸=	PROPN
ejpam-4643	171	11	1	1	NUM
ejpam-4643	171	12	or	or	CCONJ
ejpam-4643	171	13	there	there	PRON
ejpam-4643	171	14	exists	exist	VERB
ejpam-4643	171	15	k	k	PROPN
ejpam-4643	171	16	∈	∈	PROPN
ejpam-4643	171	17	{	{	PUNCT
ejpam-4643	171	18	1	1	NUM
ejpam-4643	171	19	,	,	PUNCT
ejpam-4643	171	20	2	2	NUM
ejpam-4643	171	21	,	,	PUNCT
ejpam-4643	171	22	.	.	PUNCT
ejpam-4643	171	23	.	.	PUNCT
ejpam-4643	172	1	.	.	PUNCT
ejpam-4643	173	1	,	,	PUNCT
ejpam-4643	173	2	m	m	VERB
ejpam-4643	173	3	}	}	PUNCT
ejpam-4643	173	4	such	such	ADJ
ejpam-4643	173	5	that	that	SCONJ
ejpam-4643	173	6	dg+h(v	dg+h(v	PROPN
ejpam-4643	173	7	,	,	PUNCT
ejpam-4643	173	8	uk	uk	PROPN
ejpam-4643	173	9	)	)	PUNCT
ejpam-4643	173	10	̸=	̸=	PROPN
ejpam-4643	173	11	1	1	NUM
ejpam-4643	173	12	.	.	PUNCT
ejpam-4643	174	1	hence	hence	ADV
ejpam-4643	174	2	,	,	PUNCT
ejpam-4643	174	3	rg+h(u	rg+h(u	PROPN
ejpam-4643	174	4	/	/	SYM
ejpam-4643	174	5	w	w	PROPN
ejpam-4643	174	6	)	)	PUNCT
ejpam-4643	174	7	̸=	̸=	PROPN
ejpam-4643	174	8	rg+h(v	rg+h(v	PROPN
ejpam-4643	174	9	/	/	SYM
ejpam-4643	174	10	w	w	NOUN
ejpam-4643	174	11	)	)	PUNCT
ejpam-4643	174	12	.	.	PUNCT
ejpam-4643	175	1	therefore	therefore	ADV
ejpam-4643	175	2	,	,	PUNCT
ejpam-4643	175	3	w	w	PROPN
ejpam-4643	175	4	is	be	AUX
ejpam-4643	175	5	a	a	DET
ejpam-4643	175	6	resolving	resolving	NOUN
ejpam-4643	175	7	set	set	NOUN
ejpam-4643	175	8	of	of	ADP
ejpam-4643	175	9	g	g	PROPN
ejpam-4643	175	10	+	+	PROPN
ejpam-4643	175	11	h.	h.	PROPN
ejpam-4643	175	12	accordingly	accordingly	ADV
ejpam-4643	175	13	,	,	PUNCT
ejpam-4643	175	14	w	w	PROPN
ejpam-4643	175	15	is	be	AUX
ejpam-4643	175	16	a	a	DET
ejpam-4643	175	17	resolving	resolve	VERB
ejpam-4643	175	18	dominating	dominating	NOUN
ejpam-4643	175	19	set	set	NOUN
ejpam-4643	175	20	of	of	ADP
ejpam-4643	175	21	g+h	g+h	PROPN
ejpam-4643	175	22	.	.	PUNCT
ejpam-4643	176	1	corollary	corollary	ADJ
ejpam-4643	176	2	1	1	NUM
ejpam-4643	176	3	.	.	PUNCT
ejpam-4643	177	1	let	let	VERB
ejpam-4643	177	2	g	g	NOUN
ejpam-4643	177	3	and	and	CCONJ
ejpam-4643	177	4	h	h	PROPN
ejpam-4643	177	5	be	be	VERB
ejpam-4643	177	6	non	non	ADJ
ejpam-4643	177	7	-	-	ADJ
ejpam-4643	177	8	trivial	trivial	ADJ
ejpam-4643	177	9	connected	connected	ADJ
ejpam-4643	177	10	graphs	graph	NOUN
ejpam-4643	177	11	.	.	PUNCT
ejpam-4643	178	1	then	then	ADV
ejpam-4643	178	2	γr(g+h	γr(g+h	NUM
ejpam-4643	178	3	)	)	PUNCT
ejpam-4643	178	4	=	=	SYM
ejpam-4643	178	5	min	min	NOUN
ejpam-4643	178	6	{	{	PUNCT
ejpam-4643	178	7	sln(h	sln(h	PROPN
ejpam-4643	178	8	)	)	PUNCT
ejpam-4643	178	9	+	+	NUM
ejpam-4643	178	10	ln(g	ln(g	NUM
ejpam-4643	178	11	)	)	PUNCT
ejpam-4643	178	12	,	,	PUNCT
ejpam-4643	178	13	sln(g	sln(g	PROPN
ejpam-4643	178	14	)	)	PUNCT
ejpam-4643	178	15	+	+	NUM
ejpam-4643	178	16	ln(h	ln(h	NUM
ejpam-4643	178	17	)	)	PUNCT
ejpam-4643	178	18	}	}	PUNCT
ejpam-4643	178	19	.	.	PUNCT
ejpam-4643	179	1	proof	proof	NOUN
ejpam-4643	179	2	:	:	PUNCT
ejpam-4643	179	3	let	let	VERB
ejpam-4643	179	4	w	w	PART
ejpam-4643	179	5	be	be	AUX
ejpam-4643	179	6	a	a	DET
ejpam-4643	179	7	minimum	minimum	ADJ
ejpam-4643	179	8	resolving	resolving	NOUN
ejpam-4643	179	9	dominating	dominating	NOUN
ejpam-4643	179	10	set	set	VERB
ejpam-4643	179	11	in	in	ADP
ejpam-4643	179	12	g+h	g+h	PROPN
ejpam-4643	179	13	.	.	PUNCT
ejpam-4643	180	1	let	let	VERB
ejpam-4643	180	2	wg	wg	VERB
ejpam-4643	180	3	=	=	SYM
ejpam-4643	180	4	v	v	NOUN
ejpam-4643	180	5	(	(	PUNCT
ejpam-4643	180	6	g)∩w	g)∩w	ADJ
ejpam-4643	180	7	and	and	CCONJ
ejpam-4643	180	8	wh	wh	VERB
ejpam-4643	180	9	=	=	SYM
ejpam-4643	180	10	v	v	PROPN
ejpam-4643	180	11	(	(	PUNCT
ejpam-4643	180	12	h	h	NOUN
ejpam-4643	180	13	)	)	PUNCT
ejpam-4643	180	14	∩	∩	PROPN
ejpam-4643	180	15	w	w	X
ejpam-4643	180	16	.	.	PUNCT
ejpam-4643	181	1	by	by	ADP
ejpam-4643	181	2	theorem	theorem	NOUN
ejpam-4643	181	3	4	4	NUM
ejpam-4643	181	4	,	,	PUNCT
ejpam-4643	181	5	wg	wg	VERB
ejpam-4643	181	6	and	and	CCONJ
ejpam-4643	181	7	wh	wh	PROPN
ejpam-4643	181	8	are	be	AUX
ejpam-4643	181	9	locating	locate	VERB
ejpam-4643	181	10	sets	set	NOUN
ejpam-4643	181	11	in	in	ADP
ejpam-4643	181	12	g	g	PROPN
ejpam-4643	181	13	and	and	CCONJ
ejpam-4643	181	14	h	h	NOUN
ejpam-4643	181	15	,	,	PUNCT
ejpam-4643	181	16	respectively	respectively	ADV
ejpam-4643	181	17	,	,	PUNCT
ejpam-4643	181	18	where	where	SCONJ
ejpam-4643	181	19	wg	wg	NOUN
ejpam-4643	181	20	or	or	CCONJ
ejpam-4643	181	21	wh	wh	PROPN
ejpam-4643	181	22	is	be	AUX
ejpam-4643	181	23	a	a	DET
ejpam-4643	181	24	strictly	strictly	ADV
ejpam-4643	181	25	locating	locate	VERB
ejpam-4643	181	26	set	set	NOUN
ejpam-4643	181	27	.	.	PUNCT
ejpam-4643	182	1	if	if	SCONJ
ejpam-4643	182	2	wg	wg	PROPN
ejpam-4643	182	3	is	be	AUX
ejpam-4643	182	4	strictly	strictly	ADV
ejpam-4643	182	5	locating	locate	VERB
ejpam-4643	182	6	,	,	PUNCT
ejpam-4643	182	7	then	then	ADV
ejpam-4643	182	8	sln(g	sln(g	PROPN
ejpam-4643	182	9	)	)	PUNCT
ejpam-4643	183	1	+	+	CCONJ
ejpam-4643	183	2	ln(h	ln(h	X
ejpam-4643	183	3	)	)	PUNCT
ejpam-4643	183	4	≤	≤	NOUN
ejpam-4643	183	5	|wg|+	|wg|+	ADV
ejpam-4643	183	6	|wh	|wh	ADP
ejpam-4643	183	7	|	|	ADV
ejpam-4643	183	8	=	=	SYM
ejpam-4643	183	9	|w	|w	NOUN
ejpam-4643	183	10	|	|	NOUN
ejpam-4643	183	11	=	=	SYM
ejpam-4643	183	12	γr(g+h	γr(g+h	PROPN
ejpam-4643	183	13	)	)	PUNCT
ejpam-4643	183	14	.	.	PUNCT
ejpam-4643	184	1	if	if	SCONJ
ejpam-4643	184	2	wh	wh	NOUN
ejpam-4643	184	3	is	be	AUX
ejpam-4643	184	4	strictly	strictly	ADV
ejpam-4643	184	5	locating	locate	VERB
ejpam-4643	184	6	,	,	PUNCT
ejpam-4643	184	7	then	then	ADV
ejpam-4643	184	8	sln(g	sln(g	PROPN
ejpam-4643	184	9	)	)	PUNCT
ejpam-4643	185	1	+	+	CCONJ
ejpam-4643	185	2	ln(h	ln(h	X
ejpam-4643	185	3	)	)	PUNCT
ejpam-4643	185	4	≤	≤	NUM
ejpam-4643	185	5	|wh	|wh	ADP
ejpam-4643	185	6	|+	|+	NOUN
ejpam-4643	185	7	|wg|	|wg|	NOUN
ejpam-4643	185	8	=	=	NOUN
ejpam-4643	185	9	|w	|w	NOUN
ejpam-4643	185	10	|	|	NOUN
ejpam-4643	185	11	=	=	SYM
ejpam-4643	185	12	γr(g+h	γr(g+h	PROPN
ejpam-4643	185	13	)	)	PUNCT
ejpam-4643	185	14	.	.	PUNCT
ejpam-4643	186	1	thus	thus	ADV
ejpam-4643	186	2	,	,	PUNCT
ejpam-4643	186	3	γr(g+h	γr(g+h	NUM
ejpam-4643	186	4	)	)	PUNCT
ejpam-4643	186	5	=	=	SYM
ejpam-4643	186	6	min	min	NOUN
ejpam-4643	186	7	{	{	PUNCT
ejpam-4643	186	8	sln(h	sln(h	PROPN
ejpam-4643	186	9	)	)	PUNCT
ejpam-4643	186	10	+	+	NUM
ejpam-4643	186	11	ln(g	ln(g	NUM
ejpam-4643	186	12	)	)	PUNCT
ejpam-4643	186	13	,	,	PUNCT
ejpam-4643	186	14	sln(g	sln(g	PROPN
ejpam-4643	186	15	)	)	PUNCT
ejpam-4643	186	16	+	+	NUM
ejpam-4643	186	17	ln(h	ln(h	NUM
ejpam-4643	186	18	)	)	PUNCT
ejpam-4643	186	19	}	}	PUNCT
ejpam-4643	186	20	.	.	PUNCT
ejpam-4643	187	1	next	next	ADV
ejpam-4643	187	2	,	,	PUNCT
ejpam-4643	187	3	suppose	suppose	VERB
ejpam-4643	187	4	that	that	SCONJ
ejpam-4643	187	5	sln(g)+	sln(g)+	NOUN
ejpam-4643	187	6	ln(h	ln(h	NUM
ejpam-4643	187	7	)	)	PUNCT
ejpam-4643	187	8	≤	≤	NUM
ejpam-4643	187	9	sln(h	sln(h	VERB
ejpam-4643	187	10	)	)	PUNCT
ejpam-4643	187	11	+	+	NUM
ejpam-4643	187	12	ln(g	ln(g	NUM
ejpam-4643	187	13	)	)	PUNCT
ejpam-4643	187	14	.	.	PUNCT
ejpam-4643	188	1	g.	g.	PROPN
ejpam-4643	188	2	monsanto	monsanto	PROPN
ejpam-4643	188	3	,	,	PUNCT
ejpam-4643	188	4	h.	h.	PROPN
ejpam-4643	188	5	rara	rara	PROPN
ejpam-4643	188	6	/	/	SYM
ejpam-4643	188	7	eur	eur	PROPN
ejpam-4643	188	8	.	.	PUNCT
ejpam-4643	189	1	j.	j.	PROPN
ejpam-4643	189	2	pure	pure	PROPN
ejpam-4643	189	3	appl	appl	PROPN
ejpam-4643	189	4	.	.	PROPN
ejpam-4643	189	5	math	math	PROPN
ejpam-4643	189	6	,	,	PUNCT
ejpam-4643	189	7	16	16	NUM
ejpam-4643	189	8	(	(	PUNCT
ejpam-4643	189	9	1	1	NUM
ejpam-4643	189	10	)	)	PUNCT
ejpam-4643	189	11	(	(	PUNCT
ejpam-4643	189	12	2023	2023	NUM
ejpam-4643	189	13	)	)	PUNCT
ejpam-4643	189	14	,	,	PUNCT
ejpam-4643	189	15	18	18	NUM
ejpam-4643	189	16	-	-	SYM
ejpam-4643	189	17	28	28	NUM
ejpam-4643	189	18	24	24	NUM
ejpam-4643	189	19	let	let	VERB
ejpam-4643	189	20	wg	wg	PRON
ejpam-4643	189	21	be	be	AUX
ejpam-4643	189	22	a	a	DET
ejpam-4643	189	23	minimum	minimum	NOUN
ejpam-4643	189	24	strictly	strictly	ADV
ejpam-4643	189	25	locating	locate	VERB
ejpam-4643	189	26	set	set	NOUN
ejpam-4643	189	27	of	of	ADP
ejpam-4643	189	28	g	g	PROPN
ejpam-4643	189	29	and	and	CCONJ
ejpam-4643	189	30	wh	wh	PROPN
ejpam-4643	189	31	be	be	AUX
ejpam-4643	189	32	a	a	DET
ejpam-4643	189	33	minimum	minimum	ADJ
ejpam-4643	189	34	locating	locating	NOUN
ejpam-4643	189	35	set	set	NOUN
ejpam-4643	189	36	of	of	ADP
ejpam-4643	189	37	h.	h.	PROPN
ejpam-4643	189	38	then	then	ADV
ejpam-4643	189	39	w	w	PROPN
ejpam-4643	189	40	=	=	PUNCT
ejpam-4643	189	41	wg	wg	PROPN
ejpam-4643	189	42	∪wh	∪wh	NOUN
ejpam-4643	189	43	is	be	AUX
ejpam-4643	189	44	a	a	DET
ejpam-4643	189	45	resolving	resolve	VERB
ejpam-4643	189	46	dominating	dominating	NOUN
ejpam-4643	189	47	set	set	NOUN
ejpam-4643	189	48	of	of	ADP
ejpam-4643	189	49	g+h	g+h	PROPN
ejpam-4643	189	50	by	by	ADP
ejpam-4643	189	51	theorem	theorem	NOUN
ejpam-4643	189	52	4	4	NUM
ejpam-4643	189	53	.	.	PUNCT
ejpam-4643	189	54	hence	hence	ADV
ejpam-4643	189	55	,	,	PUNCT
ejpam-4643	189	56	γr(g+h	γr(g+h	NOUN
ejpam-4643	189	57	)	)	PUNCT
ejpam-4643	189	58	≤	≤	NOUN
ejpam-4643	189	59	|w	|w	NOUN
ejpam-4643	190	1	|	|	NOUN
ejpam-4643	190	2	=	=	PUNCT
ejpam-4643	190	3	|wg|+	|wg|+	NOUN
ejpam-4643	190	4	|wh	|wh	X
ejpam-4643	190	5	|	|	NOUN
ejpam-4643	190	6	=	=	SYM
ejpam-4643	190	7	sln(g	sln(g	PROPN
ejpam-4643	190	8	)	)	PUNCT
ejpam-4643	190	9	+	+	NUM
ejpam-4643	190	10	ln(h	ln(h	NUM
ejpam-4643	190	11	)	)	PUNCT
ejpam-4643	190	12	.	.	PUNCT
ejpam-4643	191	1	therefore	therefore	ADV
ejpam-4643	191	2	,	,	PUNCT
ejpam-4643	191	3	γr(g+h	γr(g+h	NUM
ejpam-4643	191	4	)	)	PUNCT
ejpam-4643	191	5	=	=	SYM
ejpam-4643	191	6	min	min	NOUN
ejpam-4643	191	7	{	{	PUNCT
ejpam-4643	191	8	sln(h	sln(h	PROPN
ejpam-4643	191	9	)	)	PUNCT
ejpam-4643	191	10	+	+	NUM
ejpam-4643	191	11	ln(g	ln(g	NUM
ejpam-4643	191	12	)	)	PUNCT
ejpam-4643	191	13	,	,	PUNCT
ejpam-4643	191	14	sln(g	sln(g	PROPN
ejpam-4643	191	15	)	)	PUNCT
ejpam-4643	191	16	+	+	NUM
ejpam-4643	191	17	ln(h	ln(h	NUM
ejpam-4643	191	18	)	)	PUNCT
ejpam-4643	191	19	}	}	PUNCT
ejpam-4643	191	20	.	.	PUNCT
ejpam-4643	192	1	theorem	theorem	ADJ
ejpam-4643	192	2	5	5	NUM
ejpam-4643	192	3	.	.	PUNCT
ejpam-4643	193	1	[	[	X
ejpam-4643	193	2	11	11	NUM
ejpam-4643	193	3	]	]	PUNCT
ejpam-4643	193	4	let	let	VERB
ejpam-4643	193	5	g	g	PRON
ejpam-4643	193	6	be	be	AUX
ejpam-4643	193	7	a	a	DET
ejpam-4643	193	8	connected	connected	ADJ
ejpam-4643	193	9	graph	graph	NOUN
ejpam-4643	193	10	of	of	ADP
ejpam-4643	193	11	order	order	NOUN
ejpam-4643	193	12	n	n	PRON
ejpam-4643	193	13	≥	≥	NOUN
ejpam-4643	193	14	2	2	NUM
ejpam-4643	193	15	.	.	PUNCT
ejpam-4643	194	1	(	(	PUNCT
ejpam-4643	194	2	i	i	NOUN
ejpam-4643	194	3	)	)	PUNCT
ejpam-4643	194	4	if	if	SCONJ
ejpam-4643	194	5	ln(g	ln(g	NUM
ejpam-4643	194	6	)	)	PUNCT
ejpam-4643	194	7	<	<	X
ejpam-4643	194	8	sln(g	sln(g	PROPN
ejpam-4643	194	9	)	)	PUNCT
ejpam-4643	194	10	,	,	PUNCT
ejpam-4643	194	11	then	then	ADV
ejpam-4643	194	12	1	1	NUM
ejpam-4643	194	13	+	+	NUM
ejpam-4643	194	14	ln(g	ln(g	X
ejpam-4643	194	15	)	)	PUNCT
ejpam-4643	194	16	=	=	PUNCT
ejpam-4643	194	17	sln(g	sln(g	PROPN
ejpam-4643	194	18	)	)	PUNCT
ejpam-4643	194	19	.	.	PUNCT
ejpam-4643	195	1	(	(	PUNCT
ejpam-4643	195	2	ii	ii	NOUN
ejpam-4643	195	3	)	)	PUNCT
ejpam-4643	195	4	if	if	SCONJ
ejpam-4643	195	5	ln(g	ln(g	NUM
ejpam-4643	195	6	)	)	PUNCT
ejpam-4643	195	7	<	<	X
ejpam-4643	195	8	γl(g	γl(g	NUM
ejpam-4643	195	9	)	)	PUNCT
ejpam-4643	195	10	,	,	PUNCT
ejpam-4643	195	11	then	then	ADV
ejpam-4643	195	12	1	1	NUM
ejpam-4643	195	13	+	+	NUM
ejpam-4643	195	14	ln(g	ln(g	X
ejpam-4643	195	15	)	)	PUNCT
ejpam-4643	195	16	=	=	SYM
ejpam-4643	196	1	γl(g	γl(g	NUM
ejpam-4643	196	2	)	)	PUNCT
ejpam-4643	196	3	.	.	PUNCT
ejpam-4643	197	1	(	(	PUNCT
ejpam-4643	197	2	iii	iii	X
ejpam-4643	197	3	)	)	PUNCT
ejpam-4643	197	4	if	if	SCONJ
ejpam-4643	197	5	sln(g	sln(g	PROPN
ejpam-4643	197	6	)	)	PUNCT
ejpam-4643	197	7	<	<	X
ejpam-4643	197	8	γsl(g	γsl(g	X
ejpam-4643	197	9	)	)	PUNCT
ejpam-4643	197	10	,	,	PUNCT
ejpam-4643	197	11	then	then	ADV
ejpam-4643	197	12	1	1	NUM
ejpam-4643	197	13	+	+	CCONJ
ejpam-4643	197	14	sln(g	sln(g	NOUN
ejpam-4643	197	15	)	)	PUNCT
ejpam-4643	197	16	=	=	SYM
ejpam-4643	197	17	γsl(g	γsl(g	PROPN
ejpam-4643	197	18	)	)	PUNCT
ejpam-4643	197	19	.	.	PUNCT
ejpam-4643	198	1	corollary	corollary	ADJ
ejpam-4643	198	2	2	2	NUM
ejpam-4643	198	3	.	.	PUNCT
ejpam-4643	199	1	let	let	VERB
ejpam-4643	199	2	g	g	PRON
ejpam-4643	199	3	be	be	AUX
ejpam-4643	199	4	a	a	DET
ejpam-4643	199	5	non	non	ADJ
ejpam-4643	199	6	-	-	ADJ
ejpam-4643	199	7	trivial	trivial	ADJ
ejpam-4643	199	8	connected	connected	ADJ
ejpam-4643	199	9	graph	graph	NOUN
ejpam-4643	199	10	and	and	CCONJ
ejpam-4643	199	11	let	let	VERB
ejpam-4643	199	12	kn	kn	PROPN
ejpam-4643	199	13	be	be	AUX
ejpam-4643	199	14	a	a	DET
ejpam-4643	199	15	complete	complete	ADJ
ejpam-4643	199	16	graph	graph	NOUN
ejpam-4643	199	17	of	of	ADP
ejpam-4643	199	18	order	order	NOUN
ejpam-4643	199	19	n	n	PRON
ejpam-4643	199	20	≥	≥	NOUN
ejpam-4643	199	21	2	2	NUM
ejpam-4643	199	22	.	.	PUNCT
ejpam-4643	199	23	then	then	ADV
ejpam-4643	199	24	γr(g+kn	γr(g+kn	NOUN
ejpam-4643	199	25	)	)	PUNCT
ejpam-4643	200	1	=	=	PUNCT
ejpam-4643	200	2	sln(g	sln(g	NOUN
ejpam-4643	200	3	)	)	PUNCT
ejpam-4643	201	1	+	+	CCONJ
ejpam-4643	201	2	n−	n−	NOUN
ejpam-4643	201	3	1	1	NUM
ejpam-4643	201	4	.	.	PUNCT
ejpam-4643	202	1	proof	proof	NOUN
ejpam-4643	202	2	:	:	PUNCT
ejpam-4643	202	3	note	note	VERB
ejpam-4643	202	4	that	that	SCONJ
ejpam-4643	202	5	γr(kn	γr(kn	NOUN
ejpam-4643	202	6	)	)	PUNCT
ejpam-4643	203	1	=	=	PUNCT
ejpam-4643	203	2	n−	n−	NOUN
ejpam-4643	203	3	1	1	NUM
ejpam-4643	203	4	and	and	CCONJ
ejpam-4643	203	5	sln(kn	sln(kn	NOUN
ejpam-4643	203	6	)	)	PUNCT
ejpam-4643	203	7	=	=	VERB
ejpam-4643	203	8	n.	n.	ADJ
ejpam-4643	203	9	from	from	ADP
ejpam-4643	203	10	corollary	corollary	ADJ
ejpam-4643	203	11	1	1	NUM
ejpam-4643	203	12	,	,	PUNCT
ejpam-4643	203	13	γr(g+kn	γr(g+kn	NOUN
ejpam-4643	203	14	)	)	PUNCT
ejpam-4643	203	15	=	=	SYM
ejpam-4643	203	16	min	min	NOUN
ejpam-4643	203	17	{	{	PUNCT
ejpam-4643	203	18	sln(h	sln(h	PROPN
ejpam-4643	203	19	)	)	PUNCT
ejpam-4643	203	20	+	+	NUM
ejpam-4643	203	21	ln(g	ln(g	NUM
ejpam-4643	203	22	)	)	PUNCT
ejpam-4643	203	23	,	,	PUNCT
ejpam-4643	203	24	sln(g	sln(g	PROPN
ejpam-4643	203	25	)	)	PUNCT
ejpam-4643	203	26	+	+	NUM
ejpam-4643	203	27	ln(h	ln(h	NUM
ejpam-4643	203	28	)	)	PUNCT
ejpam-4643	203	29	}	}	PUNCT
ejpam-4643	203	30	.	.	PUNCT
ejpam-4643	204	1	by	by	ADP
ejpam-4643	204	2	theorem	theorem	NOUN
ejpam-4643	204	3	5	5	NUM
ejpam-4643	204	4	,	,	PUNCT
ejpam-4643	204	5	sln(g)−	sln(g)−	ADJ
ejpam-4643	204	6	1	1	NUM
ejpam-4643	204	7	≤	≤	NOUN
ejpam-4643	204	8	ln(g	ln(g	NUM
ejpam-4643	204	9	)	)	PUNCT
ejpam-4643	204	10	.	.	PUNCT
ejpam-4643	205	1	therefore	therefore	ADV
ejpam-4643	205	2	,	,	PUNCT
ejpam-4643	205	3	γr(g+kn	γr(g+kn	NOUN
ejpam-4643	205	4	)	)	PUNCT
ejpam-4643	205	5	=	=	SYM
ejpam-4643	205	6	min	min	NOUN
ejpam-4643	205	7	{	{	PUNCT
ejpam-4643	205	8	sln(g	sln(g	NOUN
ejpam-4643	205	9	)	)	PUNCT
ejpam-4643	206	1	+	+	CCONJ
ejpam-4643	206	2	n−	n−	NOUN
ejpam-4643	206	3	1	1	NUM
ejpam-4643	206	4	,	,	PUNCT
ejpam-4643	206	5	ln(g	ln(g	PUNCT
ejpam-4643	206	6	)	)	PUNCT
ejpam-4643	206	7	+	+	NUM
ejpam-4643	206	8	n	n	CCONJ
ejpam-4643	206	9	}	}	PUNCT
ejpam-4643	206	10	=	=	SYM
ejpam-4643	206	11	sln(g	sln(g	NOUN
ejpam-4643	206	12	)	)	PUNCT
ejpam-4643	207	1	+	+	CCONJ
ejpam-4643	207	2	n−	n−	NOUN
ejpam-4643	207	3	1	1	NUM
ejpam-4643	207	4	.	.	PUNCT
ejpam-4643	207	5	theorem	theorem	VERB
ejpam-4643	207	6	6	6	NUM
ejpam-4643	207	7	.	.	PUNCT
ejpam-4643	208	1	[	[	X
ejpam-4643	208	2	11	11	NUM
ejpam-4643	208	3	]	]	PUNCT
ejpam-4643	208	4	let	let	VERB
ejpam-4643	208	5	h	h	PRON
ejpam-4643	208	6	be	be	AUX
ejpam-4643	208	7	a	a	DET
ejpam-4643	208	8	non	non	ADJ
ejpam-4643	208	9	-	-	ADJ
ejpam-4643	208	10	trivial	trivial	ADJ
ejpam-4643	208	11	connected	connected	ADJ
ejpam-4643	208	12	graph	graph	NOUN
ejpam-4643	208	13	and	and	CCONJ
ejpam-4643	208	14	let	let	VERB
ejpam-4643	208	15	k1	k1	NOUN
ejpam-4643	208	16	=	=	SYM
ejpam-4643	208	17	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4643	208	18	then	then	ADV
ejpam-4643	208	19	w	w	PROPN
ejpam-4643	208	20	⊆	⊆	NUM
ejpam-4643	208	21	v	v	NOUN
ejpam-4643	208	22	(	(	PUNCT
ejpam-4643	208	23	h	h	NOUN
ejpam-4643	208	24	)	)	PUNCT
ejpam-4643	208	25	is	be	AUX
ejpam-4643	208	26	a	a	DET
ejpam-4643	208	27	locating	locate	VERB
ejpam-4643	208	28	-	-	PUNCT
ejpam-4643	208	29	dominating	dominate	VERB
ejpam-4643	208	30	set	set	NOUN
ejpam-4643	208	31	of	of	ADP
ejpam-4643	208	32	h	h	NOUN
ejpam-4643	208	33	+	+	CCONJ
ejpam-4643	208	34	k1	k1	NOUN
ejpam-4643	208	35	if	if	SCONJ
ejpam-4643	208	36	and	and	CCONJ
ejpam-4643	208	37	only	only	ADV
ejpam-4643	208	38	if	if	SCONJ
ejpam-4643	208	39	either	either	PRON
ejpam-4643	208	40	v	v	NOUN
ejpam-4643	208	41	/∈	/∈	PROPN
ejpam-4643	209	1	w	w	NOUN
ejpam-4643	209	2	and	and	CCONJ
ejpam-4643	209	3	w	w	PROPN
ejpam-4643	209	4	is	be	AUX
ejpam-4643	209	5	a	a	DET
ejpam-4643	209	6	strictly	strictly	ADV
ejpam-4643	209	7	locating	locate	VERB
ejpam-4643	209	8	dominating	dominating	NOUN
ejpam-4643	209	9	set	set	NOUN
ejpam-4643	209	10	of	of	ADP
ejpam-4643	209	11	h	h	NOUN
ejpam-4643	209	12	or	or	CCONJ
ejpam-4643	209	13	w	w	NOUN
ejpam-4643	209	14	=	=	PUNCT
ejpam-4643	209	15	{	{	PUNCT
ejpam-4643	209	16	v	v	NOUN
ejpam-4643	209	17	}	}	PUNCT
ejpam-4643	209	18	∪wh	∪wh	NOUN
ejpam-4643	209	19	,	,	PUNCT
ejpam-4643	209	20	where	where	SCONJ
ejpam-4643	209	21	wh	wh	NOUN
ejpam-4643	209	22	is	be	AUX
ejpam-4643	209	23	a	a	DET
ejpam-4643	209	24	locating	locate	VERB
ejpam-4643	209	25	set	set	NOUN
ejpam-4643	209	26	of	of	ADP
ejpam-4643	209	27	h.	h.	PROPN
ejpam-4643	209	28	theorem	theorem	PROPN
ejpam-4643	209	29	7	7	NUM
ejpam-4643	209	30	.	.	PUNCT
ejpam-4643	210	1	[	[	X
ejpam-4643	210	2	9	9	NUM
ejpam-4643	210	3	]	]	PUNCT
ejpam-4643	210	4	let	let	VERB
ejpam-4643	210	5	h	h	PRON
ejpam-4643	210	6	be	be	AUX
ejpam-4643	210	7	a	a	DET
ejpam-4643	210	8	non	non	ADJ
ejpam-4643	210	9	-	-	ADJ
ejpam-4643	210	10	trivial	trivial	ADJ
ejpam-4643	210	11	connected	connected	ADJ
ejpam-4643	210	12	graph	graph	NOUN
ejpam-4643	210	13	and	and	CCONJ
ejpam-4643	210	14	let	let	VERB
ejpam-4643	210	15	k1	k1	NOUN
ejpam-4643	210	16	=	=	SYM
ejpam-4643	210	17	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4643	210	18	then	then	ADV
ejpam-4643	210	19	w	w	PROPN
ejpam-4643	210	20	⊆	⊆	NUM
ejpam-4643	210	21	v	v	NOUN
ejpam-4643	210	22	(	(	PUNCT
ejpam-4643	210	23	h	h	NOUN
ejpam-4643	210	24	)	)	PUNCT
ejpam-4643	210	25	is	be	AUX
ejpam-4643	210	26	a	a	DET
ejpam-4643	210	27	resolving	resolving	NOUN
ejpam-4643	210	28	set	set	NOUN
ejpam-4643	210	29	of	of	ADP
ejpam-4643	210	30	h	h	NOUN
ejpam-4643	210	31	+	+	NOUN
ejpam-4643	210	32	k1	k1	NOUN
ejpam-4643	210	33	if	if	SCONJ
ejpam-4643	210	34	and	and	CCONJ
ejpam-4643	210	35	only	only	ADV
ejpam-4643	210	36	if	if	SCONJ
ejpam-4643	210	37	either	either	PRON
ejpam-4643	210	38	v	v	NOUN
ejpam-4643	210	39	/∈	/∈	PROPN
ejpam-4643	211	1	w	w	NOUN
ejpam-4643	211	2	and	and	CCONJ
ejpam-4643	211	3	w	w	PROPN
ejpam-4643	211	4	is	be	AUX
ejpam-4643	211	5	a	a	DET
ejpam-4643	211	6	strictly	strictly	ADV
ejpam-4643	211	7	locating	locate	VERB
ejpam-4643	211	8	set	set	NOUN
ejpam-4643	211	9	of	of	ADP
ejpam-4643	211	10	h	h	NOUN
ejpam-4643	211	11	or	or	CCONJ
ejpam-4643	211	12	w	w	NOUN
ejpam-4643	211	13	=	=	PUNCT
ejpam-4643	211	14	{	{	PUNCT
ejpam-4643	211	15	v	v	NOUN
ejpam-4643	211	16	}	}	PUNCT
ejpam-4643	211	17	∪wh	∪wh	NOUN
ejpam-4643	211	18	,	,	PUNCT
ejpam-4643	211	19	where	where	SCONJ
ejpam-4643	211	20	wh	wh	NOUN
ejpam-4643	211	21	is	be	AUX
ejpam-4643	211	22	a	a	DET
ejpam-4643	211	23	locating	locate	VERB
ejpam-4643	211	24	set	set	NOUN
ejpam-4643	211	25	of	of	ADP
ejpam-4643	211	26	h.	h.	PROPN
ejpam-4643	211	27	the	the	DET
ejpam-4643	211	28	next	next	ADJ
ejpam-4643	211	29	result	result	NOUN
ejpam-4643	211	30	follows	follow	VERB
ejpam-4643	211	31	immediately	immediately	ADV
ejpam-4643	211	32	from	from	ADP
ejpam-4643	211	33	theorem	theorem	ADJ
ejpam-4643	211	34	6	6	NUM
ejpam-4643	211	35	and	and	CCONJ
ejpam-4643	211	36	theorem	theorem	VERB
ejpam-4643	211	37	7	7	NUM
ejpam-4643	211	38	.	.	PUNCT
ejpam-4643	211	39	theorem	theorem	NOUN
ejpam-4643	211	40	8	8	NUM
ejpam-4643	211	41	.	.	PUNCT
ejpam-4643	212	1	let	let	VERB
ejpam-4643	212	2	h	h	PRON
ejpam-4643	212	3	be	be	AUX
ejpam-4643	212	4	a	a	DET
ejpam-4643	212	5	non	non	ADJ
ejpam-4643	212	6	-	-	ADJ
ejpam-4643	212	7	trivial	trivial	ADJ
ejpam-4643	212	8	connected	connected	ADJ
ejpam-4643	212	9	graph	graph	NOUN
ejpam-4643	212	10	and	and	CCONJ
ejpam-4643	212	11	let	let	VERB
ejpam-4643	212	12	k1	k1	NOUN
ejpam-4643	212	13	=	=	SYM
ejpam-4643	212	14	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4643	212	15	then	then	ADV
ejpam-4643	212	16	w	w	PROPN
ejpam-4643	212	17	⊆	⊆	NUM
ejpam-4643	212	18	v	v	NOUN
ejpam-4643	212	19	(	(	PUNCT
ejpam-4643	212	20	h	h	NOUN
ejpam-4643	212	21	)	)	PUNCT
ejpam-4643	212	22	is	be	AUX
ejpam-4643	212	23	a	a	DET
ejpam-4643	212	24	resolving	resolve	VERB
ejpam-4643	212	25	dominating	dominating	NOUN
ejpam-4643	212	26	set	set	NOUN
ejpam-4643	212	27	of	of	ADP
ejpam-4643	212	28	h	h	NOUN
ejpam-4643	212	29	+	+	NOUN
ejpam-4643	212	30	k1	k1	NOUN
ejpam-4643	212	31	if	if	SCONJ
ejpam-4643	212	32	and	and	CCONJ
ejpam-4643	212	33	only	only	ADV
ejpam-4643	212	34	if	if	SCONJ
ejpam-4643	212	35	either	either	PRON
ejpam-4643	212	36	v	v	NOUN
ejpam-4643	212	37	/∈	/∈	PROPN
ejpam-4643	213	1	w	w	NOUN
ejpam-4643	213	2	and	and	CCONJ
ejpam-4643	213	3	w	w	PROPN
ejpam-4643	213	4	is	be	AUX
ejpam-4643	213	5	a	a	DET
ejpam-4643	213	6	strictly	strictly	ADV
ejpam-4643	213	7	resolving	resolve	VERB
ejpam-4643	213	8	dominating	dominating	NOUN
ejpam-4643	213	9	set	set	NOUN
ejpam-4643	213	10	of	of	ADP
ejpam-4643	213	11	h	h	NOUN
ejpam-4643	213	12	or	or	CCONJ
ejpam-4643	213	13	w	w	NOUN
ejpam-4643	213	14	=	=	PUNCT
ejpam-4643	213	15	{	{	PUNCT
ejpam-4643	213	16	v	v	NOUN
ejpam-4643	213	17	}	}	PUNCT
ejpam-4643	213	18	∪wh	∪wh	NOUN
ejpam-4643	213	19	,	,	PUNCT
ejpam-4643	213	20	where	where	SCONJ
ejpam-4643	213	21	wh	wh	NOUN
ejpam-4643	213	22	is	be	AUX
ejpam-4643	213	23	a	a	DET
ejpam-4643	213	24	locating	locate	VERB
ejpam-4643	213	25	set	set	NOUN
ejpam-4643	213	26	of	of	ADP
ejpam-4643	213	27	h.	h.	PROPN
ejpam-4643	213	28	corollary	corollary	PROPN
ejpam-4643	213	29	3	3	X
ejpam-4643	213	30	.	.	PUNCT
ejpam-4643	214	1	let	let	VERB
ejpam-4643	214	2	h	h	PRON
ejpam-4643	214	3	be	be	AUX
ejpam-4643	214	4	a	a	DET
ejpam-4643	214	5	non	non	ADJ
ejpam-4643	214	6	-	-	ADJ
ejpam-4643	214	7	trivial	trivial	ADJ
ejpam-4643	214	8	connected	connected	ADJ
ejpam-4643	214	9	graph	graph	NOUN
ejpam-4643	214	10	.	.	PUNCT
ejpam-4643	215	1	then	then	ADV
ejpam-4643	215	2	γr(h	γr(h	PUNCT
ejpam-4643	216	1	+	+	NOUN
ejpam-4643	216	2	k1	k1	NOUN
ejpam-4643	216	3	)	)	PUNCT
ejpam-4643	216	4	=	=	SYM
ejpam-4643	216	5	min	min	PROPN
ejpam-4643	216	6	{	{	PUNCT
ejpam-4643	216	7	γsr(h	γsr(h	PROPN
ejpam-4643	216	8	)	)	PUNCT
ejpam-4643	216	9	,	,	PUNCT
ejpam-4643	216	10	ln(h	ln(h	PUNCT
ejpam-4643	216	11	)	)	PUNCT
ejpam-4643	217	1	+	+	CCONJ
ejpam-4643	217	2	1	1	NUM
ejpam-4643	217	3	}	}	PUNCT
ejpam-4643	217	4	.	.	PUNCT
ejpam-4643	218	1	4	4	X
ejpam-4643	218	2	.	.	X
ejpam-4643	218	3	resolving	resolve	VERB
ejpam-4643	218	4	domination	domination	NOUN
ejpam-4643	218	5	in	in	ADP
ejpam-4643	218	6	the	the	DET
ejpam-4643	218	7	corona	corona	NOUN
ejpam-4643	218	8	of	of	ADP
ejpam-4643	218	9	graphs	graph	NOUN
ejpam-4643	218	10	the	the	DET
ejpam-4643	218	11	corona	corona	NOUN
ejpam-4643	218	12	of	of	ADP
ejpam-4643	218	13	two	two	NUM
ejpam-4643	218	14	graphs	graph	NOUN
ejpam-4643	218	15	g	g	NOUN
ejpam-4643	218	16	and	and	CCONJ
ejpam-4643	218	17	h	h	NOUN
ejpam-4643	218	18	,	,	PUNCT
ejpam-4643	218	19	denoted	denote	VERB
ejpam-4643	218	20	by	by	ADP
ejpam-4643	218	21	g	g	PROPN
ejpam-4643	218	22	◦	◦	NOUN
ejpam-4643	218	23	h	h	NOUN
ejpam-4643	218	24	,	,	PUNCT
ejpam-4643	218	25	is	be	AUX
ejpam-4643	218	26	the	the	DET
ejpam-4643	218	27	graph	graph	NOUN
ejpam-4643	218	28	obtained	obtain	VERB
ejpam-4643	218	29	by	by	ADP
ejpam-4643	218	30	taking	take	VERB
ejpam-4643	218	31	one	one	NUM
ejpam-4643	218	32	copy	copy	NOUN
ejpam-4643	218	33	of	of	ADP
ejpam-4643	218	34	g	g	NOUN
ejpam-4643	218	35	of	of	ADP
ejpam-4643	218	36	order	order	NOUN
ejpam-4643	218	37	n	n	NOUN
ejpam-4643	218	38	and	and	CCONJ
ejpam-4643	218	39	n	n	PRON
ejpam-4643	218	40	copies	copy	NOUN
ejpam-4643	218	41	of	of	ADP
ejpam-4643	218	42	h	h	NOUN
ejpam-4643	218	43	,	,	PUNCT
ejpam-4643	218	44	and	and	CCONJ
ejpam-4643	218	45	then	then	ADV
ejpam-4643	218	46	joining	join	VERB
ejpam-4643	218	47	every	every	DET
ejpam-4643	218	48	vertex	vertex	NOUN
ejpam-4643	218	49	of	of	ADP
ejpam-4643	218	50	the	the	DET
ejpam-4643	218	51	ith	ith	PROPN
ejpam-4643	218	52	copy	copy	NOUN
ejpam-4643	218	53	of	of	ADP
ejpam-4643	218	54	h	h	NOUN
ejpam-4643	218	55	to	to	ADP
ejpam-4643	218	56	the	the	DET
ejpam-4643	218	57	ith	ith	PROPN
ejpam-4643	218	58	vertex	vertex	NOUN
ejpam-4643	218	59	of	of	ADP
ejpam-4643	218	60	g.	g.	PROPN
ejpam-4643	218	61	for	for	ADP
ejpam-4643	218	62	v	v	NOUN
ejpam-4643	218	63	∈	∈	PROPN
ejpam-4643	218	64	v	v	NOUN
ejpam-4643	218	65	(	(	PUNCT
ejpam-4643	218	66	g	g	NOUN
ejpam-4643	218	67	)	)	PUNCT
ejpam-4643	218	68	,	,	PUNCT
ejpam-4643	218	69	denoted	denote	VERB
ejpam-4643	218	70	by	by	ADP
ejpam-4643	218	71	hv	hv	PROPN
ejpam-4643	218	72	the	the	DET
ejpam-4643	218	73	copy	copy	NOUN
ejpam-4643	218	74	of	of	ADP
ejpam-4643	218	75	h	h	NOUN
ejpam-4643	218	76	whose	whose	DET
ejpam-4643	218	77	vertices	vertex	NOUN
ejpam-4643	218	78	are	be	AUX
ejpam-4643	218	79	attached	attach	VERB
ejpam-4643	218	80	one	one	NUM
ejpam-4643	218	81	by	by	ADP
ejpam-4643	218	82	one	one	NUM
ejpam-4643	218	83	to	to	ADP
ejpam-4643	218	84	the	the	DET
ejpam-4643	218	85	vertex	vertex	NOUN
ejpam-4643	218	86	v.	v.	ADP
ejpam-4643	218	87	subsequently	subsequently	ADV
ejpam-4643	218	88	,	,	PUNCT
ejpam-4643	218	89	denote	denote	VERB
ejpam-4643	218	90	by	by	ADP
ejpam-4643	218	91	v+hv	v+hv	NOUN
ejpam-4643	218	92	the	the	DET
ejpam-4643	218	93	subgraph	subgraph	NOUN
ejpam-4643	218	94	of	of	ADP
ejpam-4643	218	95	the	the	DET
ejpam-4643	218	96	corona	corona	NOUN
ejpam-4643	218	97	g	g	PROPN
ejpam-4643	218	98	◦	◦	NOUN
ejpam-4643	218	99	h	h	NOUN
ejpam-4643	218	100	corresponding	correspond	VERB
ejpam-4643	218	101	to	to	ADP
ejpam-4643	218	102	the	the	DET
ejpam-4643	218	103	join	join	NOUN
ejpam-4643	218	104	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4643	218	105	,	,	PUNCT
ejpam-4643	218	106	v	v	PROPN
ejpam-4643	218	107	∈	∈	PROPN
ejpam-4643	218	108	v	v	NOUN
ejpam-4643	218	109	(	(	PUNCT
ejpam-4643	218	110	g	g	NOUN
ejpam-4643	218	111	)	)	PUNCT
ejpam-4643	218	112	.	.	PUNCT
ejpam-4643	219	1	g.	g.	PROPN
ejpam-4643	219	2	monsanto	monsanto	PROPN
ejpam-4643	219	3	,	,	PUNCT
ejpam-4643	219	4	h.	h.	PROPN
ejpam-4643	219	5	rara	rara	PROPN
ejpam-4643	219	6	/	/	SYM
ejpam-4643	219	7	eur	eur	PROPN
ejpam-4643	219	8	.	.	PUNCT
ejpam-4643	220	1	j.	j.	PROPN
ejpam-4643	220	2	pure	pure	PROPN
ejpam-4643	220	3	appl	appl	PROPN
ejpam-4643	220	4	.	.	PROPN
ejpam-4643	220	5	math	math	PROPN
ejpam-4643	220	6	,	,	PUNCT
ejpam-4643	220	7	16	16	NUM
ejpam-4643	220	8	(	(	PUNCT
ejpam-4643	220	9	1	1	NUM
ejpam-4643	220	10	)	)	PUNCT
ejpam-4643	220	11	(	(	PUNCT
ejpam-4643	220	12	2023	2023	NUM
ejpam-4643	220	13	)	)	PUNCT
ejpam-4643	220	14	,	,	PUNCT
ejpam-4643	220	15	18	18	NUM
ejpam-4643	220	16	-	-	SYM
ejpam-4643	220	17	28	28	NUM
ejpam-4643	220	18	25	25	NUM
ejpam-4643	220	19	theorem	theorem	NOUN
ejpam-4643	220	20	9	9	NUM
ejpam-4643	220	21	.	.	PUNCT
ejpam-4643	221	1	[	[	X
ejpam-4643	221	2	9	9	NUM
ejpam-4643	221	3	]	]	PUNCT
ejpam-4643	221	4	let	let	VERB
ejpam-4643	221	5	g	g	NOUN
ejpam-4643	221	6	and	and	CCONJ
ejpam-4643	221	7	h	h	PROPN
ejpam-4643	221	8	be	be	VERB
ejpam-4643	221	9	non	non	ADJ
ejpam-4643	221	10	-	-	ADJ
ejpam-4643	221	11	trivial	trivial	ADJ
ejpam-4643	221	12	connected	connected	ADJ
ejpam-4643	221	13	graphs	graph	NOUN
ejpam-4643	221	14	.	.	PUNCT
ejpam-4643	222	1	then	then	ADV
ejpam-4643	222	2	w	w	PROPN
ejpam-4643	222	3	⊆	⊆	NUM
ejpam-4643	222	4	v	v	NOUN
ejpam-4643	222	5	(	(	PUNCT
ejpam-4643	222	6	g	g	PROPN
ejpam-4643	222	7	◦	◦	NOUN
ejpam-4643	222	8	h	h	NOUN
ejpam-4643	222	9	)	)	PUNCT
ejpam-4643	222	10	is	be	AUX
ejpam-4643	222	11	a	a	DET
ejpam-4643	222	12	resolving	resolving	NOUN
ejpam-4643	222	13	set	set	NOUN
ejpam-4643	222	14	of	of	ADP
ejpam-4643	222	15	g	g	PROPN
ejpam-4643	222	16	◦	◦	NOUN
ejpam-4643	222	17	h	h	NOUN
ejpam-4643	222	18	if	if	SCONJ
ejpam-4643	223	1	and	and	CCONJ
ejpam-4643	223	2	only	only	ADV
ejpam-4643	223	3	if	if	SCONJ
ejpam-4643	223	4	w	w	PROPN
ejpam-4643	223	5	∩	∩	ADJ
ejpam-4643	223	6	v	v	X
ejpam-4643	223	7	(	(	PUNCT
ejpam-4643	223	8	hv	hv	NOUN
ejpam-4643	223	9	)	)	PUNCT
ejpam-4643	223	10	̸=	̸=	PROPN
ejpam-4643	223	11	∅	∅	NOUN
ejpam-4643	223	12	for	for	ADP
ejpam-4643	223	13	all	all	PRON
ejpam-4643	223	14	v	v	ADP
ejpam-4643	223	15	∈	∈	NUM
ejpam-4643	223	16	v	v	NOUN
ejpam-4643	223	17	(	(	PUNCT
ejpam-4643	223	18	g	g	NOUN
ejpam-4643	223	19	)	)	PUNCT
ejpam-4643	223	20	and	and	CCONJ
ejpam-4643	223	21	w	w	NOUN
ejpam-4643	223	22	=	=	PUNCT
ejpam-4643	223	23	a	a	DET
ejpam-4643	223	24	∪	∪	X
ejpam-4643	223	25	b	b	NOUN
ejpam-4643	223	26	,	,	PUNCT
ejpam-4643	223	27	where	where	SCONJ
ejpam-4643	223	28	a	a	DET
ejpam-4643	223	29	⊆	⊆	NUM
ejpam-4643	223	30	v	v	NOUN
ejpam-4643	223	31	(	(	PUNCT
ejpam-4643	223	32	g	g	NOUN
ejpam-4643	223	33	)	)	PUNCT
ejpam-4643	223	34	and	and	CCONJ
ejpam-4643	223	35	b	b	X
ejpam-4643	223	36	=	=	SYM
ejpam-4643	223	37	∪{bv	∪{bv	NOUN
ejpam-4643	223	38	:	:	PUNCT
ejpam-4643	223	39	v	v	NUM
ejpam-4643	223	40	∈	∈	PROPN
ejpam-4643	223	41	v	v	NOUN
ejpam-4643	223	42	(	(	PUNCT
ejpam-4643	223	43	g	g	NOUN
ejpam-4643	223	44	)	)	PUNCT
ejpam-4643	223	45	and	and	CCONJ
ejpam-4643	223	46	bv	bv	PROPN
ejpam-4643	223	47	is	be	AUX
ejpam-4643	223	48	a	a	DET
ejpam-4643	223	49	locating	locate	VERB
ejpam-4643	223	50	set	set	NOUN
ejpam-4643	223	51	of	of	ADP
ejpam-4643	223	52	hv	hv	PROPN
ejpam-4643	223	53	}	}	PUNCT
ejpam-4643	223	54	.	.	PUNCT
ejpam-4643	224	1	theorem	theorem	ADJ
ejpam-4643	224	2	10	10	NUM
ejpam-4643	224	3	.	.	PUNCT
ejpam-4643	225	1	let	let	VERB
ejpam-4643	225	2	g	g	NOUN
ejpam-4643	225	3	and	and	CCONJ
ejpam-4643	225	4	h	h	PROPN
ejpam-4643	225	5	be	be	VERB
ejpam-4643	225	6	non	non	ADJ
ejpam-4643	225	7	-	-	ADJ
ejpam-4643	225	8	trivial	trivial	ADJ
ejpam-4643	225	9	connected	connected	ADJ
ejpam-4643	225	10	graphs	graph	NOUN
ejpam-4643	225	11	.	.	PUNCT
ejpam-4643	226	1	then	then	ADV
ejpam-4643	226	2	w	w	PROPN
ejpam-4643	226	3	⊆	⊆	NUM
ejpam-4643	226	4	v	v	NOUN
ejpam-4643	226	5	(	(	PUNCT
ejpam-4643	226	6	g	g	PROPN
ejpam-4643	226	7	◦	◦	NOUN
ejpam-4643	226	8	h	h	NOUN
ejpam-4643	226	9	)	)	PUNCT
ejpam-4643	226	10	is	be	AUX
ejpam-4643	226	11	a	a	DET
ejpam-4643	226	12	resolving	resolve	VERB
ejpam-4643	226	13	dominating	dominating	NOUN
ejpam-4643	226	14	set	set	NOUN
ejpam-4643	226	15	of	of	ADP
ejpam-4643	226	16	g	g	PROPN
ejpam-4643	226	17	◦	◦	NOUN
ejpam-4643	226	18	h	h	NOUN
ejpam-4643	226	19	if	if	SCONJ
ejpam-4643	227	1	and	and	CCONJ
ejpam-4643	227	2	only	only	ADV
ejpam-4643	227	3	if	if	SCONJ
ejpam-4643	227	4	w	w	PROPN
ejpam-4643	227	5	∩	∩	ADJ
ejpam-4643	227	6	v	v	X
ejpam-4643	227	7	(	(	PUNCT
ejpam-4643	227	8	hv	hv	NOUN
ejpam-4643	227	9	)	)	PUNCT
ejpam-4643	227	10	̸=	̸=	PROPN
ejpam-4643	227	11	∅	∅	NOUN
ejpam-4643	227	12	for	for	ADP
ejpam-4643	227	13	every	every	DET
ejpam-4643	227	14	v	v	NUM
ejpam-4643	227	15	∈	∈	PROPN
ejpam-4643	227	16	v	v	NOUN
ejpam-4643	227	17	(	(	PUNCT
ejpam-4643	227	18	g	g	NOUN
ejpam-4643	227	19	)	)	PUNCT
ejpam-4643	227	20	and	and	CCONJ
ejpam-4643	227	21	w	w	X
ejpam-4643	227	22	=	=	PUNCT
ejpam-4643	227	23	a	a	PRON
ejpam-4643	227	24	∪b	∪b	X
ejpam-4643	227	25	∪d	∪d	NUM
ejpam-4643	227	26	,	,	PUNCT
ejpam-4643	227	27	where	where	SCONJ
ejpam-4643	227	28	a	a	DET
ejpam-4643	227	29	⊆	⊆	NUM
ejpam-4643	227	30	v	v	NOUN
ejpam-4643	227	31	(	(	PUNCT
ejpam-4643	227	32	g	g	NOUN
ejpam-4643	227	33	)	)	PUNCT
ejpam-4643	227	34	,	,	PUNCT
ejpam-4643	227	35	b	b	X
ejpam-4643	227	36	=	=	SYM
ejpam-4643	227	37	∪{bv	∪{bv	NOUN
ejpam-4643	227	38	:	:	PUNCT
ejpam-4643	227	39	v	v	NUM
ejpam-4643	227	40	∈	∈	PROPN
ejpam-4643	227	41	a	a	PRON
ejpam-4643	227	42	and	and	CCONJ
ejpam-4643	227	43	bv	bv	PROPN
ejpam-4643	227	44	is	be	AUX
ejpam-4643	227	45	a	a	DET
ejpam-4643	227	46	locating	locate	VERB
ejpam-4643	227	47	set	set	NOUN
ejpam-4643	227	48	of	of	ADP
ejpam-4643	227	49	hv	hv	PROPN
ejpam-4643	227	50	}	}	PUNCT
ejpam-4643	227	51	and	and	CCONJ
ejpam-4643	227	52	d	d	NOUN
ejpam-4643	227	53	=	=	PUNCT
ejpam-4643	227	54	∪{du	∪{du	PROPN
ejpam-4643	227	55	:	:	PUNCT
ejpam-4643	227	56	u	u	NOUN
ejpam-4643	227	57	/∈	/∈	VERB
ejpam-4643	227	58	a	a	PRON
ejpam-4643	227	59	and	and	CCONJ
ejpam-4643	227	60	du	du	PROPN
ejpam-4643	227	61	is	be	AUX
ejpam-4643	227	62	a	a	DET
ejpam-4643	227	63	locating	locate	VERB
ejpam-4643	227	64	-	-	PUNCT
ejpam-4643	227	65	dominating	dominate	VERB
ejpam-4643	227	66	set	set	NOUN
ejpam-4643	227	67	of	of	ADP
ejpam-4643	227	68	hv	hv	PROPN
ejpam-4643	227	69	}	}	PUNCT
ejpam-4643	227	70	.	.	PUNCT
ejpam-4643	228	1	proof	proof	NOUN
ejpam-4643	228	2	:	:	PUNCT
ejpam-4643	228	3	letw	letw	NOUN
ejpam-4643	228	4	be	be	AUX
ejpam-4643	228	5	a	a	DET
ejpam-4643	228	6	resolving	resolve	VERB
ejpam-4643	228	7	dominating	dominating	NOUN
ejpam-4643	228	8	set	set	VERB
ejpam-4643	228	9	ofg	ofg	PROPN
ejpam-4643	228	10	◦	◦	NOUN
ejpam-4643	228	11	h.	h.	NOUN
ejpam-4643	228	12	then	then	ADV
ejpam-4643	228	13	by	by	ADP
ejpam-4643	228	14	theorem	theorem	ADJ
ejpam-4643	228	15	9,w∩v	9,w∩v	PROPN
ejpam-4643	228	16	(	(	PUNCT
ejpam-4643	228	17	hv	hv	NOUN
ejpam-4643	228	18	)	)	PUNCT
ejpam-4643	228	19	̸=	̸=	PROPN
ejpam-4643	228	20	∅	∅	NOUN
ejpam-4643	228	21	for	for	ADP
ejpam-4643	228	22	any	any	DET
ejpam-4643	228	23	v	v	NUM
ejpam-4643	228	24	∈	∈	NOUN
ejpam-4643	228	25	v	v	NOUN
ejpam-4643	228	26	(	(	PUNCT
ejpam-4643	228	27	g	g	NOUN
ejpam-4643	228	28	)	)	PUNCT
ejpam-4643	228	29	.	.	PUNCT
ejpam-4643	229	1	since	since	SCONJ
ejpam-4643	229	2	w	w	PROPN
ejpam-4643	229	3	is	be	AUX
ejpam-4643	229	4	a	a	DET
ejpam-4643	229	5	resolving	resolving	NOUN
ejpam-4643	229	6	set	set	NOUN
ejpam-4643	229	7	,	,	PUNCT
ejpam-4643	229	8	g	g	PROPN
ejpam-4643	229	9	=	=	PROPN
ejpam-4643	229	10	a	a	DET
ejpam-4643	229	11	∪b∗	∪b∗	NUM
ejpam-4643	229	12	,	,	PUNCT
ejpam-4643	229	13	where	where	SCONJ
ejpam-4643	229	14	a	a	DET
ejpam-4643	229	15	⊆	⊆	NUM
ejpam-4643	229	16	v	v	NOUN
ejpam-4643	229	17	(	(	PUNCT
ejpam-4643	229	18	g	g	NOUN
ejpam-4643	229	19	)	)	PUNCT
ejpam-4643	229	20	and	and	CCONJ
ejpam-4643	229	21	b∗	b∗	ADJ
ejpam-4643	229	22	=	=	SYM
ejpam-4643	229	23	∪{bv	∪{bv	NOUN
ejpam-4643	229	24	:	:	PUNCT
ejpam-4643	229	25	v	v	NUM
ejpam-4643	229	26	∈	∈	PROPN
ejpam-4643	229	27	v	v	NOUN
ejpam-4643	229	28	(	(	PUNCT
ejpam-4643	229	29	g	g	NOUN
ejpam-4643	229	30	)	)	PUNCT
ejpam-4643	229	31	and	and	CCONJ
ejpam-4643	229	32	bv	bv	PROPN
ejpam-4643	229	33	is	be	AUX
ejpam-4643	229	34	a	a	DET
ejpam-4643	229	35	locating	locate	VERB
ejpam-4643	229	36	set	set	NOUN
ejpam-4643	229	37	of	of	ADP
ejpam-4643	229	38	hv	hv	PROPN
ejpam-4643	229	39	}	}	PUNCT
ejpam-4643	229	40	by	by	ADP
ejpam-4643	229	41	theorem	theorem	NOUN
ejpam-4643	229	42	9	9	NUM
ejpam-4643	229	43	.	.	PUNCT
ejpam-4643	230	1	let	let	VERB
ejpam-4643	230	2	b	b	NOUN
ejpam-4643	230	3	=	=	SYM
ejpam-4643	230	4	∪{bv	∪{bv	NOUN
ejpam-4643	230	5	:	:	PUNCT
ejpam-4643	230	6	v	v	NUM
ejpam-4643	230	7	∈	∈	PROPN
ejpam-4643	230	8	a	a	PRON
ejpam-4643	230	9	}	}	PUNCT
ejpam-4643	230	10	and	and	CCONJ
ejpam-4643	230	11	d	d	NOUN
ejpam-4643	230	12	=	=	PUNCT
ejpam-4643	230	13	∪{bu	∪{bu	NOUN
ejpam-4643	230	14	:	:	PUNCT
ejpam-4643	230	15	u	u	NOUN
ejpam-4643	230	16	∈	∈	PROPN
ejpam-4643	230	17	v	v	ADP
ejpam-4643	230	18	(	(	PUNCT
ejpam-4643	230	19	g	g	NOUN
ejpam-4643	230	20	)	)	PUNCT
ejpam-4643	230	21	\a	\a	NUM
ejpam-4643	230	22	}	}	PUNCT
ejpam-4643	230	23	.	.	PUNCT
ejpam-4643	231	1	since	since	SCONJ
ejpam-4643	231	2	w	w	PROPN
ejpam-4643	231	3	is	be	AUX
ejpam-4643	231	4	a	a	DET
ejpam-4643	231	5	dominating	dominating	NOUN
ejpam-4643	231	6	set	set	NOUN
ejpam-4643	231	7	,	,	PUNCT
ejpam-4643	231	8	it	it	PRON
ejpam-4643	231	9	follows	follow	VERB
ejpam-4643	231	10	that	that	SCONJ
ejpam-4643	231	11	bu	bu	PROPN
ejpam-4643	231	12	is	be	AUX
ejpam-4643	231	13	a	a	DET
ejpam-4643	231	14	dominating	dominating	NOUN
ejpam-4643	231	15	set	set	NOUN
ejpam-4643	231	16	for	for	ADP
ejpam-4643	231	17	each	each	DET
ejpam-4643	231	18	u	u	PROPN
ejpam-4643	231	19	∈	∈	PROPN
ejpam-4643	231	20	v	v	ADP
ejpam-4643	231	21	(	(	PUNCT
ejpam-4643	231	22	g	g	NOUN
ejpam-4643	231	23	)	)	PUNCT
ejpam-4643	231	24	\a	\a	ADJ
ejpam-4643	231	25	.	.	PUNCT
ejpam-4643	232	1	for	for	ADP
ejpam-4643	232	2	the	the	DET
ejpam-4643	232	3	converse	converse	NOUN
ejpam-4643	232	4	,	,	PUNCT
ejpam-4643	232	5	suppose	suppose	VERB
ejpam-4643	232	6	w	w	ADP
ejpam-4643	232	7	=	=	PUNCT
ejpam-4643	232	8	a	a	DET
ejpam-4643	232	9	∪	∪	X
ejpam-4643	232	10	b	b	NOUN
ejpam-4643	232	11	∪d	∪d	NOUN
ejpam-4643	232	12	,	,	PUNCT
ejpam-4643	232	13	where	where	SCONJ
ejpam-4643	232	14	a	a	DET
ejpam-4643	232	15	,	,	PUNCT
ejpam-4643	232	16	b	b	NOUN
ejpam-4643	232	17	and	and	CCONJ
ejpam-4643	232	18	d	d	NOUN
ejpam-4643	232	19	are	be	AUX
ejpam-4643	232	20	the	the	DET
ejpam-4643	232	21	sets	set	NOUN
ejpam-4643	232	22	possesing	possese	VERB
ejpam-4643	232	23	the	the	DET
ejpam-4643	232	24	properties	property	NOUN
ejpam-4643	232	25	described	describe	VERB
ejpam-4643	232	26	.	.	PUNCT
ejpam-4643	233	1	then	then	ADV
ejpam-4643	233	2	by	by	ADP
ejpam-4643	233	3	theorem	theorem	NOUN
ejpam-4643	233	4	9	9	NUM
ejpam-4643	233	5	,	,	PUNCT
ejpam-4643	233	6	w	w	NOUN
ejpam-4643	233	7	is	be	AUX
ejpam-4643	233	8	a	a	DET
ejpam-4643	233	9	resolving	resolving	NOUN
ejpam-4643	233	10	set	set	NOUN
ejpam-4643	233	11	of	of	ADP
ejpam-4643	233	12	g	g	PROPN
ejpam-4643	233	13	◦	◦	PROPN
ejpam-4643	233	14	h.	h.	PROPN
ejpam-4643	233	15	since	since	SCONJ
ejpam-4643	233	16	du	du	PROPN
ejpam-4643	233	17	is	be	AUX
ejpam-4643	233	18	a	a	DET
ejpam-4643	233	19	dominating	dominating	NOUN
ejpam-4643	233	20	set	set	NOUN
ejpam-4643	233	21	of	of	ADP
ejpam-4643	233	22	hu	hu	PROPN
ejpam-4643	233	23	for	for	ADP
ejpam-4643	233	24	each	each	DET
ejpam-4643	233	25	u	u	NOUN
ejpam-4643	233	26	/∈	/∈	PUNCT
ejpam-4643	234	1	w	w	ADP
ejpam-4643	234	2	,	,	PUNCT
ejpam-4643	234	3	w	w	NOUN
ejpam-4643	234	4	is	be	AUX
ejpam-4643	234	5	a	a	DET
ejpam-4643	234	6	resolving	resolve	VERB
ejpam-4643	234	7	dominating	dominating	NOUN
ejpam-4643	234	8	set	set	NOUN
ejpam-4643	234	9	of	of	ADP
ejpam-4643	234	10	g	g	PROPN
ejpam-4643	234	11	◦	◦	PROPN
ejpam-4643	234	12	h.	h.	PROPN
ejpam-4643	234	13	remark	remark	NOUN
ejpam-4643	234	14	3	3	NUM
ejpam-4643	234	15	.	.	PUNCT
ejpam-4643	235	1	[	[	X
ejpam-4643	235	2	11	11	NUM
ejpam-4643	235	3	]	]	PUNCT
ejpam-4643	235	4	for	for	ADP
ejpam-4643	235	5	any	any	DET
ejpam-4643	235	6	connected	connected	ADJ
ejpam-4643	235	7	graph	graph	NOUN
ejpam-4643	235	8	g	g	NOUN
ejpam-4643	235	9	,	,	PUNCT
ejpam-4643	235	10	ln(g	ln(g	NUM
ejpam-4643	235	11	)	)	PUNCT
ejpam-4643	235	12	≤	≤	NUM
ejpam-4643	235	13	γl(g	γl(g	NUM
ejpam-4643	235	14	)	)	PUNCT
ejpam-4643	235	15	≤	≤	NUM
ejpam-4643	235	16	γsl(g	γsl(g	NOUN
ejpam-4643	235	17	)	)	PUNCT
ejpam-4643	235	18	.	.	PUNCT
ejpam-4643	236	1	corollary	corollary	ADJ
ejpam-4643	236	2	4	4	NUM
ejpam-4643	236	3	.	.	PUNCT
ejpam-4643	237	1	let	let	VERB
ejpam-4643	237	2	g	g	NOUN
ejpam-4643	237	3	and	and	CCONJ
ejpam-4643	237	4	h	h	PROPN
ejpam-4643	237	5	be	be	VERB
ejpam-4643	237	6	non	non	ADJ
ejpam-4643	237	7	-	-	ADJ
ejpam-4643	237	8	trivial	trivial	ADJ
ejpam-4643	237	9	connected	connected	ADJ
ejpam-4643	237	10	graphs	graph	NOUN
ejpam-4643	237	11	with	with	ADP
ejpam-4643	237	12	|v	|v	PROPN
ejpam-4643	237	13	(	(	PUNCT
ejpam-4643	237	14	g)|	g)|	NOUN
ejpam-4643	237	15	=	=	SYM
ejpam-4643	237	16	n.	n.	PROPN
ejpam-4643	237	17	then	then	ADV
ejpam-4643	237	18	γr(g	γr(g	VERB
ejpam-4643	237	19	◦	◦	NOUN
ejpam-4643	237	20	h	h	NOUN
ejpam-4643	237	21	)	)	PUNCT
ejpam-4643	237	22	=	=	SYM
ejpam-4643	238	1	n	n	X
ejpam-4643	238	2	·	·	PUNCT
ejpam-4643	238	3	γl(h	γl(h	NUM
ejpam-4643	238	4	)	)	PUNCT
ejpam-4643	238	5	.	.	PUNCT
ejpam-4643	239	1	proof	proof	NOUN
ejpam-4643	239	2	:	:	PUNCT
ejpam-4643	239	3	let	let	VERB
ejpam-4643	239	4	w	w	PART
ejpam-4643	239	5	be	be	AUX
ejpam-4643	239	6	a	a	DET
ejpam-4643	239	7	minimum	minimum	ADJ
ejpam-4643	239	8	resolving	resolving	NOUN
ejpam-4643	239	9	dominating	dominating	NOUN
ejpam-4643	239	10	set	set	VERB
ejpam-4643	239	11	in	in	ADP
ejpam-4643	239	12	g	g	PROPN
ejpam-4643	239	13	◦	◦	NOUN
ejpam-4643	239	14	h.	h.	NOUN
ejpam-4643	239	15	then	then	ADV
ejpam-4643	239	16	w	w	PROPN
ejpam-4643	239	17	=	=	SYM
ejpam-4643	239	18	a∪b	a∪b	NOUN
ejpam-4643	239	19	∪d	∪d	PUNCT
ejpam-4643	239	20	where	where	SCONJ
ejpam-4643	239	21	a	a	DET
ejpam-4643	239	22	,	,	PUNCT
ejpam-4643	239	23	b	b	NOUN
ejpam-4643	239	24	and	and	CCONJ
ejpam-4643	239	25	d	d	NOUN
ejpam-4643	239	26	are	be	AUX
ejpam-4643	239	27	the	the	DET
ejpam-4643	239	28	sets	set	NOUN
ejpam-4643	239	29	described	describe	VERB
ejpam-4643	239	30	in	in	ADP
ejpam-4643	239	31	theorem	theorem	ADJ
ejpam-4643	239	32	10	10	NUM
ejpam-4643	239	33	.	.	PUNCT
ejpam-4643	240	1	by	by	ADP
ejpam-4643	240	2	remark	remark	NOUN
ejpam-4643	240	3	3	3	NUM
ejpam-4643	240	4	and	and	CCONJ
ejpam-4643	240	5	theorem	theorem	VERB
ejpam-4643	240	6	5(ii	5(ii	NUM
ejpam-4643	240	7	)	)	PUNCT
ejpam-4643	240	8	,	,	PUNCT
ejpam-4643	240	9	it	it	PRON
ejpam-4643	240	10	follows	follow	VERB
ejpam-4643	240	11	that	that	SCONJ
ejpam-4643	240	12	γr(g	γr(g	PROPN
ejpam-4643	240	13	◦	◦	NOUN
ejpam-4643	240	14	h	h	NOUN
ejpam-4643	240	15	)	)	PUNCT
ejpam-4643	240	16	=	=	SYM
ejpam-4643	241	1	|w	|w	NOUN
ejpam-4643	241	2	|	|	NOUN
ejpam-4643	241	3	=	=	PUNCT
ejpam-4643	242	1	|a|+	|a|+	NOUN
ejpam-4643	242	2	|b|+	|b|+	NOUN
ejpam-4643	242	3	|d|	|d|	PROPN
ejpam-4643	242	4	≥	≥	AUX
ejpam-4643	242	5	|a|+	|a|+	VERB
ejpam-4643	242	6	|a|	|a|	PROPN
ejpam-4643	242	7	·	·	PUNCT
ejpam-4643	242	8	ln(h	ln(h	NUM
ejpam-4643	242	9	)	)	PUNCT
ejpam-4643	243	1	+	+	CCONJ
ejpam-4643	243	2	(	(	PUNCT
ejpam-4643	243	3	n−	n−	NOUN
ejpam-4643	243	4	|a|	|a|	NOUN
ejpam-4643	243	5	)	)	PUNCT
ejpam-4643	243	6	·	·	PUNCT
ejpam-4643	243	7	γl(h	γl(h	X
ejpam-4643	243	8	)	)	PUNCT
ejpam-4643	243	9	=	=	SYM
ejpam-4643	243	10	|a|	|a|	PROPN
ejpam-4643	243	11	(	(	PUNCT
ejpam-4643	243	12	1	1	NUM
ejpam-4643	243	13	+	+	CCONJ
ejpam-4643	243	14	ln(h	ln(h	NUM
ejpam-4643	243	15	)	)	PUNCT
ejpam-4643	243	16	)	)	PUNCT
ejpam-4643	244	1	+	+	CCONJ
ejpam-4643	244	2	(	(	PUNCT
ejpam-4643	244	3	n−	n−	NOUN
ejpam-4643	244	4	|a|	|a|	NOUN
ejpam-4643	244	5	)	)	PUNCT
ejpam-4643	244	6	·	·	PUNCT
ejpam-4643	244	7	γl(h	γl(h	X
ejpam-4643	244	8	)	)	PUNCT
ejpam-4643	244	9	=	=	SYM
ejpam-4643	244	10	|a|	|a|	PROPN
ejpam-4643	244	11	·	·	PUNCT
ejpam-4643	244	12	γl(h	γl(h	PUNCT
ejpam-4643	244	13	)	)	PUNCT
ejpam-4643	245	1	+	+	CCONJ
ejpam-4643	245	2	(	(	PUNCT
ejpam-4643	245	3	n−	n−	NOUN
ejpam-4643	245	4	|a|	|a|	NOUN
ejpam-4643	245	5	)	)	PUNCT
ejpam-4643	245	6	·	·	PUNCT
ejpam-4643	245	7	γl(h	γl(h	X
ejpam-4643	245	8	)	)	PUNCT
ejpam-4643	245	9	=	=	SYM
ejpam-4643	245	10	n	n	X
ejpam-4643	245	11	·	·	PUNCT
ejpam-4643	245	12	γl(h	γl(h	NUM
ejpam-4643	245	13	)	)	PUNCT
ejpam-4643	245	14	.	.	PUNCT
ejpam-4643	246	1	now	now	ADV
ejpam-4643	246	2	,	,	PUNCT
ejpam-4643	246	3	let	let	VERB
ejpam-4643	246	4	f	f	PRON
ejpam-4643	246	5	be	be	AUX
ejpam-4643	246	6	a	a	DET
ejpam-4643	246	7	minimum	minimum	ADJ
ejpam-4643	246	8	locating	locating	NOUN
ejpam-4643	246	9	dominating	dominating	NOUN
ejpam-4643	246	10	set	set	NOUN
ejpam-4643	246	11	of	of	ADP
ejpam-4643	246	12	h.	h.	PROPN
ejpam-4643	246	13	for	for	ADP
ejpam-4643	246	14	each	each	DET
ejpam-4643	246	15	v	v	NUM
ejpam-4643	246	16	∈	∈	PROPN
ejpam-4643	246	17	v	v	NOUN
ejpam-4643	246	18	(	(	PUNCT
ejpam-4643	246	19	g	g	NOUN
ejpam-4643	246	20	)	)	PUNCT
ejpam-4643	246	21	,	,	PUNCT
ejpam-4643	246	22	pick	pick	VERB
ejpam-4643	246	23	fv	fv	PROPN
ejpam-4643	246	24	⊆	⊆	NUM
ejpam-4643	246	25	v	v	PROPN
ejpam-4643	246	26	(	(	PUNCT
ejpam-4643	246	27	hv	hv	PROPN
ejpam-4643	246	28	)	)	PUNCT
ejpam-4643	246	29	with	with	ADP
ejpam-4643	246	30	⟨fv⟩	⟨fv⟩	NOUN
ejpam-4643	246	31	∼=	∼=	PROPN
ejpam-4643	246	32	⟨f	⟨f	PUNCT
ejpam-4643	246	33	⟩.	⟩.	NOUN
ejpam-4643	246	34	then	then	ADV
ejpam-4643	246	35	w	w	PROPN
ejpam-4643	246	36	=	=	PUNCT
ejpam-4643	246	37	⋃	⋃	NOUN
ejpam-4643	246	38	v∈v	v∈v	NOUN
ejpam-4643	246	39	(	(	PUNCT
ejpam-4643	246	40	g	g	NOUN
ejpam-4643	246	41	)	)	PUNCT
ejpam-4643	246	42	fv	fv	PROPN
ejpam-4643	246	43	is	be	AUX
ejpam-4643	246	44	a	a	DET
ejpam-4643	246	45	resolving	resolve	VERB
ejpam-4643	246	46	dominating	dominating	NOUN
ejpam-4643	246	47	set	set	NOUN
ejpam-4643	246	48	of	of	ADP
ejpam-4643	246	49	g	g	PROPN
ejpam-4643	246	50	◦	◦	NOUN
ejpam-4643	246	51	h	h	NOUN
ejpam-4643	246	52	by	by	ADP
ejpam-4643	246	53	theorem	theorem	NOUN
ejpam-4643	246	54	10	10	NUM
ejpam-4643	246	55	.	.	PUNCT
ejpam-4643	247	1	hence	hence	ADV
ejpam-4643	247	2	,	,	PUNCT
ejpam-4643	247	3	γr(g	γr(g	PUNCT
ejpam-4643	247	4	◦	◦	NOUN
ejpam-4643	247	5	h	h	NOUN
ejpam-4643	247	6	)	)	PUNCT
ejpam-4643	247	7	≤	≤	NOUN
ejpam-4643	247	8	|w	|w	NOUN
ejpam-4643	247	9	|	|	NOUN
ejpam-4643	247	10	=	=	SYM
ejpam-4643	247	11	n	n	NOUN
ejpam-4643	247	12	·	·	PUNCT
ejpam-4643	247	13	γl(h	γl(h	NUM
ejpam-4643	247	14	)	)	PUNCT
ejpam-4643	247	15	.	.	PUNCT
ejpam-4643	248	1	therefore	therefore	ADV
ejpam-4643	248	2	,	,	PUNCT
ejpam-4643	248	3	γr(g	γr(g	PROPN
ejpam-4643	248	4	◦	◦	NOUN
ejpam-4643	248	5	h	h	NOUN
ejpam-4643	248	6	)	)	PUNCT
ejpam-4643	248	7	=	=	SYM
ejpam-4643	248	8	n	n	X
ejpam-4643	248	9	·	·	PUNCT
ejpam-4643	248	10	γl(h	γl(h	NUM
ejpam-4643	248	11	)	)	PUNCT
ejpam-4643	248	12	.	.	PUNCT
ejpam-4643	249	1	g.	g.	PROPN
ejpam-4643	249	2	monsanto	monsanto	PROPN
ejpam-4643	249	3	,	,	PUNCT
ejpam-4643	249	4	h.	h.	PROPN
ejpam-4643	249	5	rara	rara	PROPN
ejpam-4643	249	6	/	/	SYM
ejpam-4643	249	7	eur	eur	PROPN
ejpam-4643	249	8	.	.	PUNCT
ejpam-4643	250	1	j.	j.	PROPN
ejpam-4643	250	2	pure	pure	PROPN
ejpam-4643	250	3	appl	appl	PROPN
ejpam-4643	250	4	.	.	PROPN
ejpam-4643	250	5	math	math	PROPN
ejpam-4643	250	6	,	,	PUNCT
ejpam-4643	250	7	16	16	NUM
ejpam-4643	250	8	(	(	PUNCT
ejpam-4643	250	9	1	1	NUM
ejpam-4643	250	10	)	)	PUNCT
ejpam-4643	250	11	(	(	PUNCT
ejpam-4643	250	12	2023	2023	NUM
ejpam-4643	250	13	)	)	PUNCT
ejpam-4643	250	14	,	,	PUNCT
ejpam-4643	250	15	18	18	NUM
ejpam-4643	250	16	-	-	SYM
ejpam-4643	250	17	28	28	NUM
ejpam-4643	250	18	26	26	NUM
ejpam-4643	250	19	5	5	NUM
ejpam-4643	250	20	.	.	PUNCT
ejpam-4643	250	21	resolving	resolve	VERB
ejpam-4643	250	22	domination	domination	NOUN
ejpam-4643	250	23	in	in	ADP
ejpam-4643	250	24	the	the	DET
ejpam-4643	250	25	lexicographic	lexicographic	ADJ
ejpam-4643	250	26	product	product	NOUN
ejpam-4643	250	27	of	of	ADP
ejpam-4643	250	28	graphs	graph	NOUN
ejpam-4643	250	29	the	the	DET
ejpam-4643	250	30	lexicographic	lexicographic	ADJ
ejpam-4643	250	31	product	product	NOUN
ejpam-4643	250	32	of	of	ADP
ejpam-4643	250	33	graphs	graph	NOUN
ejpam-4643	250	34	g	g	PROPN
ejpam-4643	250	35	and	and	CCONJ
ejpam-4643	250	36	h	h	NOUN
ejpam-4643	250	37	,	,	PUNCT
ejpam-4643	250	38	denoted	denote	VERB
ejpam-4643	250	39	by	by	ADP
ejpam-4643	250	40	g[h	g[h	NOUN
ejpam-4643	250	41	]	]	PUNCT
ejpam-4643	250	42	,	,	PUNCT
ejpam-4643	250	43	is	be	AUX
ejpam-4643	250	44	the	the	DET
ejpam-4643	250	45	graph	graph	NOUN
ejpam-4643	250	46	with	with	ADP
ejpam-4643	250	47	vertex	vertex	NOUN
ejpam-4643	250	48	set	set	VERB
ejpam-4643	250	49	v	v	NOUN
ejpam-4643	250	50	(	(	PUNCT
ejpam-4643	250	51	g[h	g[h	PROPN
ejpam-4643	250	52	]	]	PUNCT
ejpam-4643	250	53	)	)	PUNCT
ejpam-4643	250	54	=	=	SYM
ejpam-4643	250	55	v	v	X
ejpam-4643	250	56	(	(	PUNCT
ejpam-4643	250	57	g)×	g)×	NOUN
ejpam-4643	250	58	v	v	NOUN
ejpam-4643	250	59	(	(	PUNCT
ejpam-4643	250	60	h	h	NOUN
ejpam-4643	250	61	)	)	PUNCT
ejpam-4643	250	62	such	such	ADJ
ejpam-4643	250	63	that	that	SCONJ
ejpam-4643	250	64	(	(	PUNCT
ejpam-4643	250	65	v	v	NOUN
ejpam-4643	250	66	,	,	PUNCT
ejpam-4643	250	67	a)(u	a)(u	ADJ
ejpam-4643	250	68	,	,	PUNCT
ejpam-4643	250	69	b	b	X
ejpam-4643	250	70	)	)	PUNCT
ejpam-4643	250	71	∈	∈	NOUN
ejpam-4643	250	72	e(g[h	e(g[h	NOUN
ejpam-4643	250	73	]	]	PUNCT
ejpam-4643	250	74	)	)	PUNCT
ejpam-4643	250	75	if	if	SCONJ
ejpam-4643	250	76	and	and	CCONJ
ejpam-4643	250	77	only	only	ADV
ejpam-4643	250	78	if	if	SCONJ
ejpam-4643	250	79	either	either	DET
ejpam-4643	250	80	uv	uv	PROPN
ejpam-4643	250	81	∈	∈	PROPN
ejpam-4643	250	82	e(g	e(g	PROPN
ejpam-4643	250	83	)	)	PUNCT
ejpam-4643	250	84	or	or	CCONJ
ejpam-4643	250	85	u	u	X
ejpam-4643	250	86	=	=	PROPN
ejpam-4643	250	87	v	v	PROPN
ejpam-4643	250	88	and	and	CCONJ
ejpam-4643	250	89	ab	ab	PROPN
ejpam-4643	250	90	∈	∈	PROPN
ejpam-4643	250	91	e(h	e(h	PROPN
ejpam-4643	250	92	)	)	PUNCT
ejpam-4643	250	93	.	.	PUNCT
ejpam-4643	251	1	theorem	theorem	VERB
ejpam-4643	251	2	11	11	NUM
ejpam-4643	251	3	.	.	PUNCT
ejpam-4643	252	1	[	[	X
ejpam-4643	252	2	9	9	NUM
ejpam-4643	252	3	]	]	PUNCT
ejpam-4643	252	4	let	let	VERB
ejpam-4643	252	5	g	g	NOUN
ejpam-4643	252	6	and	and	CCONJ
ejpam-4643	252	7	h	h	PROPN
ejpam-4643	252	8	be	be	VERB
ejpam-4643	252	9	non	non	ADJ
ejpam-4643	252	10	-	-	ADJ
ejpam-4643	252	11	trivial	trivial	ADJ
ejpam-4643	252	12	connected	connected	ADJ
ejpam-4643	252	13	graphs	graph	NOUN
ejpam-4643	252	14	with	with	ADP
ejpam-4643	252	15	∆(h	∆(h	NOUN
ejpam-4643	252	16	)	)	PUNCT
ejpam-4643	252	17	≤	≤	NOUN
ejpam-4643	252	18	|v	|v	X
ejpam-4643	252	19	(	(	PUNCT
ejpam-4643	252	20	h)|	h)|	NOUN
ejpam-4643	252	21	−	−	PROPN
ejpam-4643	252	22	2	2	NUM
ejpam-4643	252	23	.	.	PUNCT
ejpam-4643	253	1	then	then	ADV
ejpam-4643	253	2	w	w	PROPN
ejpam-4643	253	3	=	=	PUNCT
ejpam-4643	253	4	⋃	⋃	PROPN
ejpam-4643	253	5	x∈s	x∈s	NOUN
ejpam-4643	253	6	[	[	PUNCT
ejpam-4643	253	7	{	{	PUNCT
ejpam-4643	253	8	x}×tx	x}×tx	X
ejpam-4643	253	9	]	]	PUNCT
ejpam-4643	253	10	,	,	PUNCT
ejpam-4643	253	11	where	where	SCONJ
ejpam-4643	253	12	s	s	VERB
ejpam-4643	253	13	⊆	⊆	NUM
ejpam-4643	253	14	v	v	NOUN
ejpam-4643	253	15	(	(	PUNCT
ejpam-4643	253	16	g	g	NOUN
ejpam-4643	253	17	)	)	PUNCT
ejpam-4643	253	18	and	and	CCONJ
ejpam-4643	253	19	tx	tx	VERB
ejpam-4643	253	20	⊆	⊆	NUM
ejpam-4643	253	21	v	v	NOUN
ejpam-4643	253	22	(	(	PUNCT
ejpam-4643	253	23	h	h	NOUN
ejpam-4643	253	24	)	)	PUNCT
ejpam-4643	253	25	for	for	ADP
ejpam-4643	253	26	each	each	DET
ejpam-4643	253	27	x	x	SYM
ejpam-4643	253	28	∈	∈	PROPN
ejpam-4643	253	29	s	s	NOUN
ejpam-4643	253	30	,	,	PUNCT
ejpam-4643	253	31	is	be	AUX
ejpam-4643	253	32	a	a	DET
ejpam-4643	253	33	resolving	resolving	NOUN
ejpam-4643	253	34	set	set	NOUN
ejpam-4643	253	35	of	of	ADP
ejpam-4643	253	36	g[h	g[h	NOUN
ejpam-4643	253	37	]	]	PUNCT
ejpam-4643	253	38	if	if	SCONJ
ejpam-4643	254	1	and	and	CCONJ
ejpam-4643	254	2	only	only	ADV
ejpam-4643	254	3	if	if	SCONJ
ejpam-4643	254	4	w	w	NOUN
ejpam-4643	254	5	is	be	AUX
ejpam-4643	254	6	a	a	DET
ejpam-4643	254	7	locating	locating	NOUN
ejpam-4643	254	8	set	set	NOUN
ejpam-4643	254	9	of	of	ADP
ejpam-4643	254	10	g[h	g[h	PROPN
ejpam-4643	254	11	]	]	PUNCT
ejpam-4643	254	12	.	.	PUNCT
ejpam-4643	255	1	theorem	theorem	NOUN
ejpam-4643	255	2	12	12	NUM
ejpam-4643	255	3	.	.	PUNCT
ejpam-4643	256	1	[	[	X
ejpam-4643	256	2	4	4	X
ejpam-4643	256	3	]	]	PUNCT
ejpam-4643	256	4	let	let	VERB
ejpam-4643	256	5	g	g	NOUN
ejpam-4643	256	6	and	and	CCONJ
ejpam-4643	256	7	h	h	PROPN
ejpam-4643	256	8	be	be	VERB
ejpam-4643	256	9	non	non	ADJ
ejpam-4643	256	10	-	-	ADJ
ejpam-4643	256	11	trivial	trivial	ADJ
ejpam-4643	256	12	be	be	AUX
ejpam-4643	256	13	connected	connect	VERB
ejpam-4643	256	14	graphs	graph	NOUN
ejpam-4643	256	15	.	.	PUNCT
ejpam-4643	257	1	then	then	ADV
ejpam-4643	257	2	c	c	PROPN
ejpam-4643	257	3	⊆	⊆	NUM
ejpam-4643	257	4	v	v	NOUN
ejpam-4643	257	5	(	(	PUNCT
ejpam-4643	257	6	g	g	PROPN
ejpam-4643	257	7	[	[	X
ejpam-4643	257	8	h	h	X
ejpam-4643	257	9	]	]	X
ejpam-4643	257	10	)	)	PUNCT
ejpam-4643	257	11	is	be	AUX
ejpam-4643	257	12	a	a	DET
ejpam-4643	257	13	dominating	dominating	NOUN
ejpam-4643	257	14	set	set	VERB
ejpam-4643	257	15	in	in	ADP
ejpam-4643	257	16	g[h	g[h	PROPN
ejpam-4643	257	17	]	]	PUNCT
ejpam-4643	257	18	if	if	SCONJ
ejpam-4643	257	19	and	and	CCONJ
ejpam-4643	257	20	only	only	ADV
ejpam-4643	257	21	if	if	SCONJ
ejpam-4643	257	22	w	w	PROPN
ejpam-4643	257	23	=	=	SYM
ejpam-4643	257	24	⋃	⋃	PROPN
ejpam-4643	257	25	x∈s	x∈s	NOUN
ejpam-4643	257	26	[	[	PUNCT
ejpam-4643	257	27	{	{	PUNCT
ejpam-4643	257	28	x	x	NOUN
ejpam-4643	257	29	}	}	PUNCT
ejpam-4643	257	30	×	×	NOUN
ejpam-4643	257	31	tx	tx	NOUN
ejpam-4643	257	32	]	]	PUNCT
ejpam-4643	257	33	and	and	CCONJ
ejpam-4643	257	34	either	either	CCONJ
ejpam-4643	257	35	(	(	PUNCT
ejpam-4643	257	36	i	i	NOUN
ejpam-4643	257	37	)	)	PUNCT
ejpam-4643	257	38	s	s	AUX
ejpam-4643	257	39	is	be	AUX
ejpam-4643	257	40	a	a	DET
ejpam-4643	257	41	total	total	ADJ
ejpam-4643	257	42	dominating	dominating	NOUN
ejpam-4643	257	43	set	set	NOUN
ejpam-4643	257	44	in	in	ADP
ejpam-4643	257	45	g	g	PROPN
ejpam-4643	257	46	or	or	CCONJ
ejpam-4643	257	47	(	(	PUNCT
ejpam-4643	257	48	ii	ii	NOUN
ejpam-4643	257	49	)	)	PUNCT
ejpam-4643	257	50	s	s	VERB
ejpam-4643	257	51	is	be	AUX
ejpam-4643	257	52	a	a	DET
ejpam-4643	257	53	dominating	dominating	NOUN
ejpam-4643	257	54	set	set	NOUN
ejpam-4643	257	55	in	in	ADP
ejpam-4643	257	56	g	g	PROPN
ejpam-4643	257	57	and	and	CCONJ
ejpam-4643	257	58	tx	tx	PROPN
ejpam-4643	257	59	is	be	AUX
ejpam-4643	257	60	a	a	DET
ejpam-4643	257	61	dominating	dominating	NOUN
ejpam-4643	257	62	set	set	VERB
ejpam-4643	257	63	in	in	ADP
ejpam-4643	257	64	h	h	NOUN
ejpam-4643	257	65	for	for	ADP
ejpam-4643	257	66	every	every	DET
ejpam-4643	257	67	x	x	SYM
ejpam-4643	257	68	∈	∈	PROPN
ejpam-4643	257	69	s	s	PART
ejpam-4643	257	70	\ng(s	\ng(s	NOUN
ejpam-4643	257	71	)	)	PUNCT
ejpam-4643	257	72	.	.	PUNCT
ejpam-4643	258	1	theorem	theorem	NOUN
ejpam-4643	258	2	13	13	NUM
ejpam-4643	258	3	.	.	PUNCT
ejpam-4643	259	1	let	let	VERB
ejpam-4643	259	2	g	g	NOUN
ejpam-4643	259	3	and	and	CCONJ
ejpam-4643	259	4	h	h	PROPN
ejpam-4643	259	5	be	be	VERB
ejpam-4643	259	6	non	non	ADJ
ejpam-4643	259	7	-	-	ADJ
ejpam-4643	259	8	trivial	trivial	ADJ
ejpam-4643	259	9	connected	connected	ADJ
ejpam-4643	259	10	graphs	graph	NOUN
ejpam-4643	259	11	with	with	ADP
ejpam-4643	259	12	∆(h	∆(h	NOUN
ejpam-4643	259	13	)	)	PUNCT
ejpam-4643	259	14	≤	≤	NOUN
ejpam-4643	259	15	|v	|v	X
ejpam-4643	259	16	(	(	PUNCT
ejpam-4643	259	17	h)|	h)|	NOUN
ejpam-4643	259	18	−	−	PROPN
ejpam-4643	259	19	2	2	NUM
ejpam-4643	259	20	.	.	PUNCT
ejpam-4643	260	1	then	then	ADV
ejpam-4643	260	2	w	w	PROPN
ejpam-4643	260	3	=	=	PUNCT
ejpam-4643	260	4	⋃	⋃	PROPN
ejpam-4643	260	5	x∈s	x∈s	NOUN
ejpam-4643	260	6	[	[	PUNCT
ejpam-4643	260	7	{	{	PUNCT
ejpam-4643	260	8	x}×tx	x}×tx	X
ejpam-4643	260	9	]	]	PUNCT
ejpam-4643	260	10	,	,	PUNCT
ejpam-4643	260	11	where	where	SCONJ
ejpam-4643	260	12	s	s	VERB
ejpam-4643	260	13	⊆	⊆	NUM
ejpam-4643	260	14	v	v	NOUN
ejpam-4643	260	15	(	(	PUNCT
ejpam-4643	260	16	g	g	NOUN
ejpam-4643	260	17	)	)	PUNCT
ejpam-4643	260	18	and	and	CCONJ
ejpam-4643	260	19	tx	tx	VERB
ejpam-4643	260	20	⊆	⊆	NUM
ejpam-4643	260	21	v	v	NOUN
ejpam-4643	260	22	(	(	PUNCT
ejpam-4643	260	23	h	h	NOUN
ejpam-4643	260	24	)	)	PUNCT
ejpam-4643	260	25	for	for	ADP
ejpam-4643	260	26	each	each	DET
ejpam-4643	260	27	x	x	SYM
ejpam-4643	260	28	∈	∈	PROPN
ejpam-4643	260	29	s	s	NOUN
ejpam-4643	260	30	,	,	PUNCT
ejpam-4643	260	31	is	be	AUX
ejpam-4643	260	32	a	a	DET
ejpam-4643	260	33	resolving	resolve	VERB
ejpam-4643	260	34	dominating	dominating	NOUN
ejpam-4643	260	35	set	set	NOUN
ejpam-4643	260	36	of	of	ADP
ejpam-4643	260	37	g[h	g[h	PROPN
ejpam-4643	260	38	]	]	PUNCT
ejpam-4643	260	39	if	if	SCONJ
ejpam-4643	261	1	and	and	CCONJ
ejpam-4643	261	2	only	only	ADV
ejpam-4643	261	3	if	if	SCONJ
ejpam-4643	261	4	w	w	NOUN
ejpam-4643	261	5	is	be	AUX
ejpam-4643	261	6	a	a	DET
ejpam-4643	261	7	locating	locate	VERB
ejpam-4643	261	8	-	-	PUNCT
ejpam-4643	261	9	dominating	dominate	VERB
ejpam-4643	261	10	set	set	NOUN
ejpam-4643	261	11	of	of	ADP
ejpam-4643	261	12	g[h	g[h	PROPN
ejpam-4643	261	13	]	]	PUNCT
ejpam-4643	261	14	.	.	PUNCT
ejpam-4643	262	1	proof	proof	NOUN
ejpam-4643	262	2	:	:	PUNCT
ejpam-4643	262	3	suppose	suppose	VERB
ejpam-4643	262	4	w	w	NOUN
ejpam-4643	262	5	is	be	AUX
ejpam-4643	262	6	a	a	DET
ejpam-4643	262	7	resolving	resolve	VERB
ejpam-4643	262	8	dominating	dominating	NOUN
ejpam-4643	262	9	set	set	NOUN
ejpam-4643	262	10	of	of	ADP
ejpam-4643	262	11	g[h	g[h	PROPN
ejpam-4643	262	12	]	]	PUNCT
ejpam-4643	262	13	.	.	PUNCT
ejpam-4643	263	1	then	then	ADV
ejpam-4643	263	2	by	by	ADP
ejpam-4643	263	3	theorem	theorem	NOUN
ejpam-4643	263	4	11	11	NUM
ejpam-4643	263	5	,	,	PUNCT
ejpam-4643	263	6	w	w	NOUN
ejpam-4643	263	7	is	be	AUX
ejpam-4643	263	8	a	a	DET
ejpam-4643	263	9	locating	locate	VERB
ejpam-4643	263	10	-	-	PUNCT
ejpam-4643	263	11	dominating	dominate	VERB
ejpam-4643	263	12	set	set	NOUN
ejpam-4643	263	13	of	of	ADP
ejpam-4643	263	14	g[h	g[h	NOUN
ejpam-4643	263	15	]	]	PUNCT
ejpam-4643	263	16	.	.	PUNCT
ejpam-4643	264	1	the	the	DET
ejpam-4643	264	2	converse	converse	NOUN
ejpam-4643	264	3	follows	follow	VERB
ejpam-4643	264	4	from	from	ADP
ejpam-4643	264	5	theorem	theorem	ADJ
ejpam-4643	264	6	11	11	NUM
ejpam-4643	264	7	and	and	CCONJ
ejpam-4643	264	8	theorem	theorem	VERB
ejpam-4643	264	9	12	12	NUM
ejpam-4643	264	10	.	.	PUNCT
ejpam-4643	265	1	theorem	theorem	VERB
ejpam-4643	265	2	14	14	NUM
ejpam-4643	265	3	.	.	PUNCT
ejpam-4643	266	1	[	[	X
ejpam-4643	266	2	11	11	NUM
ejpam-4643	266	3	]	]	PUNCT
ejpam-4643	266	4	let	let	VERB
ejpam-4643	266	5	g	g	NOUN
ejpam-4643	266	6	and	and	CCONJ
ejpam-4643	266	7	h	h	PROPN
ejpam-4643	266	8	be	be	VERB
ejpam-4643	266	9	non	non	ADJ
ejpam-4643	266	10	-	-	ADJ
ejpam-4643	266	11	trivial	trivial	ADJ
ejpam-4643	266	12	connected	connected	ADJ
ejpam-4643	266	13	graphs	graph	NOUN
ejpam-4643	266	14	with	with	ADP
ejpam-4643	266	15	∆(h	∆(h	NOUN
ejpam-4643	266	16	)	)	PUNCT
ejpam-4643	266	17	≤	≤	NOUN
ejpam-4643	266	18	|v	|v	X
ejpam-4643	266	19	(	(	PUNCT
ejpam-4643	266	20	h)|−2	h)|−2	PROPN
ejpam-4643	266	21	.	.	PUNCT
ejpam-4643	267	1	then	then	ADV
ejpam-4643	267	2	w	w	PROPN
ejpam-4643	267	3	=	=	PUNCT
ejpam-4643	267	4	⋃	⋃	PROPN
ejpam-4643	267	5	x∈s	x∈s	NOUN
ejpam-4643	267	6	[	[	PUNCT
ejpam-4643	267	7	{	{	PUNCT
ejpam-4643	267	8	x	x	NOUN
ejpam-4643	267	9	}	}	PUNCT
ejpam-4643	267	10	×	×	NOUN
ejpam-4643	267	11	tx	tx	PROPN
ejpam-4643	267	12	]	]	PUNCT
ejpam-4643	267	13	,	,	PUNCT
ejpam-4643	267	14	where	where	SCONJ
ejpam-4643	267	15	s	s	VERB
ejpam-4643	267	16	⊆	⊆	NUM
ejpam-4643	267	17	v	v	NOUN
ejpam-4643	267	18	(	(	PUNCT
ejpam-4643	267	19	g	g	NOUN
ejpam-4643	267	20	)	)	PUNCT
ejpam-4643	267	21	and	and	CCONJ
ejpam-4643	267	22	tx	tx	VERB
ejpam-4643	267	23	⊆	⊆	NUM
ejpam-4643	267	24	v	v	NOUN
ejpam-4643	267	25	(	(	PUNCT
ejpam-4643	267	26	h	h	NOUN
ejpam-4643	267	27	)	)	PUNCT
ejpam-4643	267	28	for	for	ADP
ejpam-4643	267	29	each	each	DET
ejpam-4643	267	30	x	x	SYM
ejpam-4643	267	31	∈	∈	PROPN
ejpam-4643	267	32	s	s	NOUN
ejpam-4643	267	33	,	,	PUNCT
ejpam-4643	267	34	is	be	AUX
ejpam-4643	267	35	a	a	DET
ejpam-4643	267	36	locating	locate	VERB
ejpam-4643	267	37	-	-	PUNCT
ejpam-4643	267	38	dominating	dominate	VERB
ejpam-4643	267	39	set	set	NOUN
ejpam-4643	267	40	of	of	ADP
ejpam-4643	267	41	g[h	g[h	NOUN
ejpam-4643	267	42	]	]	PUNCT
ejpam-4643	268	1	if	if	SCONJ
ejpam-4643	268	2	and	and	CCONJ
ejpam-4643	268	3	only	only	ADV
ejpam-4643	268	4	if	if	SCONJ
ejpam-4643	268	5	(	(	PUNCT
ejpam-4643	268	6	i	i	NOUN
ejpam-4643	268	7	)	)	PUNCT
ejpam-4643	268	8	s	s	PART
ejpam-4643	268	9	=	=	SYM
ejpam-4643	268	10	v	v	NOUN
ejpam-4643	268	11	(	(	PUNCT
ejpam-4643	268	12	g	g	NOUN
ejpam-4643	268	13	)	)	PUNCT
ejpam-4643	268	14	;	;	PUNCT
ejpam-4643	268	15	(	(	PUNCT
ejpam-4643	268	16	ii	ii	NOUN
ejpam-4643	268	17	)	)	PUNCT
ejpam-4643	268	18	tx	tx	PROPN
ejpam-4643	268	19	is	be	AUX
ejpam-4643	268	20	a	a	DET
ejpam-4643	268	21	locating	locating	NOUN
ejpam-4643	268	22	set	set	NOUN
ejpam-4643	268	23	of	of	ADP
ejpam-4643	268	24	h	h	NOUN
ejpam-4643	268	25	for	for	ADP
ejpam-4643	268	26	every	every	DET
ejpam-4643	268	27	x	x	SYM
ejpam-4643	268	28	∈	∈	PROPN
ejpam-4643	268	29	v	v	NOUN
ejpam-4643	268	30	(	(	PUNCT
ejpam-4643	268	31	g	g	NOUN
ejpam-4643	268	32	)	)	PUNCT
ejpam-4643	268	33	;	;	PUNCT
ejpam-4643	268	34	(	(	PUNCT
ejpam-4643	268	35	iii	iii	X
ejpam-4643	268	36	)	)	PUNCT
ejpam-4643	268	37	tx	tx	NOUN
ejpam-4643	269	1	or	or	CCONJ
ejpam-4643	269	2	ty	ty	INTJ
ejpam-4643	269	3	is	be	AUX
ejpam-4643	269	4	strictly	strictly	ADV
ejpam-4643	269	5	locating	locate	VERB
ejpam-4643	269	6	of	of	ADP
ejpam-4643	269	7	h	h	NOUN
ejpam-4643	269	8	whenever	whenever	SCONJ
ejpam-4643	269	9	x	x	PRON
ejpam-4643	269	10	and	and	CCONJ
ejpam-4643	269	11	y	y	PROPN
ejpam-4643	269	12	are	be	AUX
ejpam-4643	269	13	adjacent	adjacent	ADJ
ejpam-4643	269	14	vertices	vertex	NOUN
ejpam-4643	269	15	of	of	ADP
ejpam-4643	269	16	g	g	NOUN
ejpam-4643	269	17	with	with	ADP
ejpam-4643	269	18	ng[x	ng[x	PROPN
ejpam-4643	269	19	]	]	X
ejpam-4643	269	20	=	=	PUNCT
ejpam-4643	269	21	ng[y	ng[y	PROPN
ejpam-4643	269	22	]	]	X
ejpam-4643	269	23	;	;	PUNCT
ejpam-4643	269	24	and	and	CCONJ
ejpam-4643	269	25	(	(	PUNCT
ejpam-4643	269	26	iv	iv	X
ejpam-4643	269	27	)	)	PUNCT
ejpam-4643	269	28	tx	tx	NOUN
ejpam-4643	269	29	or	or	CCONJ
ejpam-4643	269	30	ty	ty	INTJ
ejpam-4643	269	31	is	be	AUX
ejpam-4643	269	32	(	(	PUNCT
ejpam-4643	269	33	locating	locate	VERB
ejpam-4643	269	34	)	)	PUNCT
ejpam-4643	269	35	dominating	dominating	NOUN
ejpam-4643	269	36	of	of	ADP
ejpam-4643	269	37	h	h	NOUN
ejpam-4643	269	38	whenever	whenever	SCONJ
ejpam-4643	269	39	x	x	PRON
ejpam-4643	269	40	and	and	CCONJ
ejpam-4643	269	41	y	y	PROPN
ejpam-4643	269	42	are	be	AUX
ejpam-4643	269	43	nonadjacent	nonadjacent	ADJ
ejpam-4643	269	44	vertices	vertex	NOUN
ejpam-4643	269	45	of	of	ADP
ejpam-4643	269	46	g	g	NOUN
ejpam-4643	269	47	with	with	ADP
ejpam-4643	269	48	ng(x	ng(x	NUM
ejpam-4643	269	49	)	)	PUNCT
ejpam-4643	269	50	=	=	PUNCT
ejpam-4643	269	51	ng(y	ng(y	NOUN
ejpam-4643	269	52	)	)	PUNCT
ejpam-4643	269	53	.	.	PUNCT
ejpam-4643	270	1	the	the	DET
ejpam-4643	270	2	next	next	ADJ
ejpam-4643	270	3	result	result	NOUN
ejpam-4643	270	4	follows	follow	VERB
ejpam-4643	270	5	immediately	immediately	ADV
ejpam-4643	270	6	from	from	ADP
ejpam-4643	270	7	theorem	theorem	ADJ
ejpam-4643	270	8	13	13	NUM
ejpam-4643	270	9	and	and	CCONJ
ejpam-4643	270	10	theorem	theorem	VERB
ejpam-4643	270	11	14	14	NUM
ejpam-4643	270	12	.	.	PUNCT
ejpam-4643	271	1	theorem	theorem	NOUN
ejpam-4643	271	2	15	15	NUM
ejpam-4643	271	3	.	.	PUNCT
ejpam-4643	272	1	let	let	VERB
ejpam-4643	272	2	g	g	NOUN
ejpam-4643	272	3	and	and	CCONJ
ejpam-4643	272	4	h	h	PROPN
ejpam-4643	272	5	be	be	VERB
ejpam-4643	272	6	non	non	ADJ
ejpam-4643	272	7	-	-	ADJ
ejpam-4643	272	8	trivial	trivial	ADJ
ejpam-4643	272	9	connected	connected	ADJ
ejpam-4643	272	10	graphs	graph	NOUN
ejpam-4643	272	11	with	with	ADP
ejpam-4643	272	12	∆(h	∆(h	NOUN
ejpam-4643	272	13	)	)	PUNCT
ejpam-4643	272	14	≤	≤	NOUN
ejpam-4643	272	15	|v	|v	X
ejpam-4643	272	16	(	(	PUNCT
ejpam-4643	272	17	h)|	h)|	NOUN
ejpam-4643	272	18	−	−	PROPN
ejpam-4643	272	19	2	2	NUM
ejpam-4643	272	20	.	.	PUNCT
ejpam-4643	273	1	then	then	ADV
ejpam-4643	273	2	w	w	PROPN
ejpam-4643	273	3	=	=	PUNCT
ejpam-4643	273	4	⋃	⋃	PROPN
ejpam-4643	273	5	x∈s	x∈s	NOUN
ejpam-4643	273	6	[	[	PUNCT
ejpam-4643	273	7	{	{	PUNCT
ejpam-4643	273	8	x}×tx	x}×tx	X
ejpam-4643	273	9	]	]	PUNCT
ejpam-4643	273	10	,	,	PUNCT
ejpam-4643	273	11	where	where	SCONJ
ejpam-4643	273	12	s	s	VERB
ejpam-4643	273	13	⊆	⊆	NUM
ejpam-4643	273	14	v	v	NOUN
ejpam-4643	273	15	(	(	PUNCT
ejpam-4643	273	16	g	g	NOUN
ejpam-4643	273	17	)	)	PUNCT
ejpam-4643	273	18	and	and	CCONJ
ejpam-4643	273	19	tx	tx	VERB
ejpam-4643	273	20	⊆	⊆	NUM
ejpam-4643	273	21	v	v	NOUN
ejpam-4643	273	22	(	(	PUNCT
ejpam-4643	273	23	h	h	NOUN
ejpam-4643	273	24	)	)	PUNCT
ejpam-4643	273	25	for	for	ADP
ejpam-4643	273	26	each	each	DET
ejpam-4643	273	27	x	x	SYM
ejpam-4643	273	28	∈	∈	PROPN
ejpam-4643	273	29	s	s	NOUN
ejpam-4643	273	30	,	,	PUNCT
ejpam-4643	273	31	is	be	AUX
ejpam-4643	273	32	a	a	DET
ejpam-4643	273	33	resolving	resolve	VERB
ejpam-4643	273	34	dominating	dominating	NOUN
ejpam-4643	273	35	set	set	NOUN
ejpam-4643	273	36	of	of	ADP
ejpam-4643	273	37	g[h	g[h	PROPN
ejpam-4643	273	38	]	]	PUNCT
ejpam-4643	273	39	if	if	SCONJ
ejpam-4643	273	40	and	and	CCONJ
ejpam-4643	273	41	only	only	ADV
ejpam-4643	273	42	if	if	SCONJ
ejpam-4643	273	43	(	(	PUNCT
ejpam-4643	273	44	i	i	NOUN
ejpam-4643	273	45	)	)	PUNCT
ejpam-4643	273	46	s	s	PART
ejpam-4643	273	47	=	=	SYM
ejpam-4643	273	48	v	v	NOUN
ejpam-4643	273	49	(	(	PUNCT
ejpam-4643	273	50	g	g	NOUN
ejpam-4643	273	51	)	)	PUNCT
ejpam-4643	273	52	;	;	PUNCT
ejpam-4643	273	53	references	reference	NOUN
ejpam-4643	273	54	27	27	NUM
ejpam-4643	273	55	(	(	PUNCT
ejpam-4643	273	56	ii	ii	NOUN
ejpam-4643	273	57	)	)	PUNCT
ejpam-4643	273	58	tx	tx	PROPN
ejpam-4643	273	59	is	be	AUX
ejpam-4643	273	60	a	a	DET
ejpam-4643	273	61	locating	locating	NOUN
ejpam-4643	273	62	set	set	NOUN
ejpam-4643	273	63	of	of	ADP
ejpam-4643	273	64	h	h	NOUN
ejpam-4643	273	65	for	for	ADP
ejpam-4643	273	66	every	every	DET
ejpam-4643	273	67	x	x	SYM
ejpam-4643	273	68	∈	∈	PROPN
ejpam-4643	273	69	v	v	NOUN
ejpam-4643	273	70	(	(	PUNCT
ejpam-4643	273	71	g	g	NOUN
ejpam-4643	273	72	)	)	PUNCT
ejpam-4643	273	73	;	;	PUNCT
ejpam-4643	273	74	(	(	PUNCT
ejpam-4643	273	75	iii	iii	X
ejpam-4643	273	76	)	)	PUNCT
ejpam-4643	273	77	tx	tx	NOUN
ejpam-4643	274	1	or	or	CCONJ
ejpam-4643	274	2	ty	ty	INTJ
ejpam-4643	274	3	is	be	AUX
ejpam-4643	274	4	strictly	strictly	ADV
ejpam-4643	274	5	locating	locate	VERB
ejpam-4643	274	6	of	of	ADP
ejpam-4643	274	7	h	h	NOUN
ejpam-4643	274	8	whenever	whenever	SCONJ
ejpam-4643	274	9	x	x	PRON
ejpam-4643	274	10	and	and	CCONJ
ejpam-4643	274	11	y	y	PROPN
ejpam-4643	274	12	are	be	AUX
ejpam-4643	274	13	adjacent	adjacent	ADJ
ejpam-4643	274	14	vertices	vertex	NOUN
ejpam-4643	274	15	of	of	ADP
ejpam-4643	274	16	g	g	NOUN
ejpam-4643	274	17	with	with	ADP
ejpam-4643	274	18	ng[x	ng[x	PROPN
ejpam-4643	274	19	]	]	X
ejpam-4643	274	20	=	=	PUNCT
ejpam-4643	274	21	ng[y	ng[y	PROPN
ejpam-4643	274	22	]	]	X
ejpam-4643	274	23	;	;	PUNCT
ejpam-4643	274	24	and	and	CCONJ
ejpam-4643	274	25	(	(	PUNCT
ejpam-4643	274	26	iv	iv	X
ejpam-4643	274	27	)	)	PUNCT
ejpam-4643	274	28	tx	tx	NOUN
ejpam-4643	274	29	or	or	CCONJ
ejpam-4643	274	30	ty	ty	INTJ
ejpam-4643	274	31	is	be	AUX
ejpam-4643	274	32	(	(	PUNCT
ejpam-4643	274	33	locating	locate	VERB
ejpam-4643	274	34	)	)	PUNCT
ejpam-4643	274	35	dominating	dominating	NOUN
ejpam-4643	274	36	of	of	ADP
ejpam-4643	274	37	h	h	NOUN
ejpam-4643	274	38	whenever	whenever	SCONJ
ejpam-4643	274	39	x	x	PRON
ejpam-4643	274	40	and	and	CCONJ
ejpam-4643	274	41	y	y	PROPN
ejpam-4643	274	42	are	be	AUX
ejpam-4643	274	43	nonadjacent	nonadjacent	ADJ
ejpam-4643	274	44	vertices	vertex	NOUN
ejpam-4643	274	45	of	of	ADP
ejpam-4643	274	46	g	g	NOUN
ejpam-4643	274	47	with	with	ADP
ejpam-4643	274	48	ng(x	ng(x	NUM
ejpam-4643	274	49	)	)	PUNCT
ejpam-4643	274	50	=	=	PUNCT
ejpam-4643	274	51	ng(y	ng(y	NOUN
ejpam-4643	274	52	)	)	PUNCT
ejpam-4643	274	53	.	.	PUNCT
ejpam-4643	275	1	the	the	DET
ejpam-4643	275	2	following	follow	VERB
ejpam-4643	275	3	is	be	AUX
ejpam-4643	275	4	a	a	DET
ejpam-4643	275	5	direct	direct	ADJ
ejpam-4643	275	6	consquence	consquence	NOUN
ejpam-4643	275	7	of	of	ADP
ejpam-4643	275	8	theorem	theorem	NOUN
ejpam-4643	275	9	15	15	NUM
ejpam-4643	275	10	.	.	PUNCT
ejpam-4643	275	11	corollary	corollary	ADJ
ejpam-4643	275	12	5	5	NUM
ejpam-4643	275	13	.	.	PUNCT
ejpam-4643	276	1	let	let	VERB
ejpam-4643	276	2	g	g	PRON
ejpam-4643	276	3	be	be	AUX
ejpam-4643	276	4	a	a	DET
ejpam-4643	276	5	connected	connected	ADJ
ejpam-4643	276	6	totally	totally	ADV
ejpam-4643	276	7	point	point	NOUN
ejpam-4643	276	8	determining	determine	VERB
ejpam-4643	276	9	graph	graph	NOUN
ejpam-4643	276	10	and	and	CCONJ
ejpam-4643	276	11	let	let	VERB
ejpam-4643	276	12	h	h	NOUN
ejpam-4643	276	13	be	be	AUX
ejpam-4643	276	14	a	a	DET
ejpam-4643	276	15	nontrivial	nontrivial	ADJ
ejpam-4643	276	16	connected	connect	VERB
ejpam-4643	276	17	graph	graph	NOUN
ejpam-4643	276	18	.	.	PUNCT
ejpam-4643	277	1	then	then	ADV
ejpam-4643	277	2	w	w	PROPN
ejpam-4643	277	3	=	=	PUNCT
ejpam-4643	277	4	⋃	⋃	PROPN
ejpam-4643	277	5	x∈s	x∈s	NOUN
ejpam-4643	277	6	[	[	PUNCT
ejpam-4643	277	7	{	{	PUNCT
ejpam-4643	277	8	x	x	NOUN
ejpam-4643	277	9	}	}	PUNCT
ejpam-4643	277	10	×	×	NOUN
ejpam-4643	277	11	tx	tx	PROPN
ejpam-4643	277	12	]	]	PUNCT
ejpam-4643	277	13	is	be	AUX
ejpam-4643	277	14	a	a	DET
ejpam-4643	277	15	minimum	minimum	ADJ
ejpam-4643	277	16	resolving	resolving	NOUN
ejpam-4643	277	17	dominating	dominating	NOUN
ejpam-4643	277	18	set	set	NOUN
ejpam-4643	277	19	of	of	ADP
ejpam-4643	277	20	g[h	g[h	PROPN
ejpam-4643	277	21	]	]	PUNCT
ejpam-4643	278	1	if	if	SCONJ
ejpam-4643	279	1	and	and	CCONJ
ejpam-4643	279	2	only	only	ADV
ejpam-4643	279	3	if	if	SCONJ
ejpam-4643	279	4	s	s	VERB
ejpam-4643	279	5	=	=	SYM
ejpam-4643	279	6	v	v	X
ejpam-4643	279	7	(	(	PUNCT
ejpam-4643	279	8	g	g	NOUN
ejpam-4643	279	9	)	)	PUNCT
ejpam-4643	279	10	and	and	CCONJ
ejpam-4643	279	11	tx	tx	PROPN
ejpam-4643	279	12	is	be	AUX
ejpam-4643	279	13	a	a	DET
ejpam-4643	279	14	minimum	minimum	ADJ
ejpam-4643	279	15	locating	locating	NOUN
ejpam-4643	279	16	set	set	NOUN
ejpam-4643	279	17	of	of	ADP
ejpam-4643	279	18	h	h	NOUN
ejpam-4643	279	19	for	for	ADP
ejpam-4643	279	20	every	every	DET
ejpam-4643	279	21	x	x	SYM
ejpam-4643	279	22	∈	∈	PROPN
ejpam-4643	279	23	v	v	NOUN
ejpam-4643	279	24	(	(	PUNCT
ejpam-4643	279	25	g	g	NOUN
ejpam-4643	279	26	)	)	PUNCT
ejpam-4643	279	27	.	.	PUNCT
ejpam-4643	280	1	corollary	corollary	ADJ
ejpam-4643	280	2	6	6	NUM
ejpam-4643	280	3	.	.	PUNCT
ejpam-4643	281	1	let	let	VERB
ejpam-4643	281	2	g	g	PRON
ejpam-4643	281	3	be	be	AUX
ejpam-4643	281	4	a	a	DET
ejpam-4643	281	5	connected	connected	ADJ
ejpam-4643	281	6	totally	totally	ADV
ejpam-4643	281	7	point	point	NOUN
ejpam-4643	281	8	determining	determine	VERB
ejpam-4643	281	9	graph	graph	NOUN
ejpam-4643	281	10	and	and	CCONJ
ejpam-4643	281	11	let	let	VERB
ejpam-4643	281	12	h	h	NOUN
ejpam-4643	281	13	be	be	AUX
ejpam-4643	281	14	a	a	DET
ejpam-4643	281	15	nontrivial	nontrivial	ADJ
ejpam-4643	281	16	connected	connect	VERB
ejpam-4643	281	17	graph	graph	NOUN
ejpam-4643	281	18	.	.	PUNCT
ejpam-4643	282	1	then	then	ADV
ejpam-4643	282	2	γr	γr	X
ejpam-4643	282	3	(	(	PUNCT
ejpam-4643	282	4	g[h	g[h	PROPN
ejpam-4643	282	5	]	]	PUNCT
ejpam-4643	282	6	)	)	PUNCT
ejpam-4643	282	7	=	=	SYM
ejpam-4643	282	8	|v	|v	PROPN
ejpam-4643	282	9	(	(	PUNCT
ejpam-4643	282	10	g)|	g)|	NOUN
ejpam-4643	282	11	·	·	PUNCT
ejpam-4643	282	12	ln(h	ln(h	NUM
ejpam-4643	282	13	)	)	PUNCT
ejpam-4643	282	14	.	.	PUNCT
ejpam-4643	283	1	proof	proof	NOUN
ejpam-4643	283	2	:	:	PUNCT
ejpam-4643	283	3	let	let	VERB
ejpam-4643	283	4	w	w	NOUN
ejpam-4643	283	5	=	=	PUNCT
ejpam-4643	283	6	⋃	⋃	PROPN
ejpam-4643	283	7	x∈s	x∈s	NOUN
ejpam-4643	283	8	(	(	PUNCT
ejpam-4643	283	9	{	{	PUNCT
ejpam-4643	283	10	x	x	NOUN
ejpam-4643	283	11	}	}	PUNCT
ejpam-4643	283	12	x	x	SYM
ejpam-4643	283	13	tx	tx	PROPN
ejpam-4643	283	14	)	)	PUNCT
ejpam-4643	283	15	be	be	AUX
ejpam-4643	283	16	a	a	DET
ejpam-4643	283	17	minimum	minimum	ADJ
ejpam-4643	283	18	resolving	resolving	NOUN
ejpam-4643	283	19	dominating	dominating	NOUN
ejpam-4643	283	20	set	set	NOUN
ejpam-4643	283	21	of	of	ADP
ejpam-4643	283	22	g[h	g[h	PROPN
ejpam-4643	283	23	]	]	PUNCT
ejpam-4643	283	24	.	.	PUNCT
ejpam-4643	284	1	then	then	ADV
ejpam-4643	284	2	s	s	VERB
ejpam-4643	284	3	=	=	SYM
ejpam-4643	284	4	v	v	PROPN
ejpam-4643	284	5	(	(	PUNCT
ejpam-4643	284	6	g	g	NOUN
ejpam-4643	284	7	)	)	PUNCT
ejpam-4643	284	8	and	and	CCONJ
ejpam-4643	284	9	tx	tx	PROPN
ejpam-4643	284	10	is	be	AUX
ejpam-4643	284	11	a	a	DET
ejpam-4643	284	12	minimum	minimum	ADJ
ejpam-4643	284	13	locating	locating	NOUN
ejpam-4643	284	14	set	set	VERB
ejpam-4643	284	15	in	in	ADP
ejpam-4643	284	16	h	h	NOUN
ejpam-4643	284	17	for	for	ADP
ejpam-4643	284	18	every	every	DET
ejpam-4643	284	19	x	x	SYM
ejpam-4643	284	20	∈	∈	PROPN
ejpam-4643	284	21	v	v	NOUN
ejpam-4643	284	22	(	(	PUNCT
ejpam-4643	284	23	g	g	NOUN
ejpam-4643	284	24	)	)	PUNCT
ejpam-4643	284	25	,	,	PUNCT
ejpam-4643	284	26	by	by	ADP
ejpam-4643	284	27	corollary	corollary	ADJ
ejpam-4643	284	28	5	5	NUM
ejpam-4643	284	29	.	.	PUNCT
ejpam-4643	284	30	therefore	therefore	ADV
ejpam-4643	284	31	,	,	PUNCT
ejpam-4643	284	32	γr(g[h	γr(g[h	ADJ
ejpam-4643	284	33	]	]	X
ejpam-4643	284	34	)	)	PUNCT
ejpam-4643	284	35	=	=	SYM
ejpam-4643	284	36	|v	|v	PROPN
ejpam-4643	284	37	(	(	PUNCT
ejpam-4643	284	38	g)|	g)|	NOUN
ejpam-4643	284	39	·	·	PUNCT
ejpam-4643	284	40	ln(h	ln(h	NUM
ejpam-4643	284	41	)	)	PUNCT
ejpam-4643	284	42	.	.	PUNCT
ejpam-4643	285	1	6	6	X
ejpam-4643	285	2	.	.	X
ejpam-4643	285	3	conclusion	conclusion	NOUN
ejpam-4643	285	4	this	this	DET
ejpam-4643	285	5	study	study	NOUN
ejpam-4643	285	6	did	do	AUX
ejpam-4643	285	7	introduce	introduce	VERB
ejpam-4643	285	8	the	the	DET
ejpam-4643	285	9	concept	concept	NOUN
ejpam-4643	285	10	of	of	ADP
ejpam-4643	285	11	resolving	resolve	VERB
ejpam-4643	285	12	domination	domination	NOUN
ejpam-4643	285	13	under	under	ADP
ejpam-4643	285	14	some	some	DET
ejpam-4643	285	15	binary	binary	ADJ
ejpam-4643	285	16	operations	operation	NOUN
ejpam-4643	285	17	.	.	PUNCT
ejpam-4643	286	1	let	let	VERB
ejpam-4643	286	2	g	g	NOUN
ejpam-4643	286	3	and	and	CCONJ
ejpam-4643	286	4	h	h	PROPN
ejpam-4643	286	5	be	be	VERB
ejpam-4643	286	6	non	non	ADJ
ejpam-4643	286	7	-	-	ADJ
ejpam-4643	286	8	trivial	trivial	ADJ
ejpam-4643	286	9	connected	connected	ADJ
ejpam-4643	286	10	graphs	graph	NOUN
ejpam-4643	286	11	.	.	PUNCT
ejpam-4643	287	1	it	it	PRON
ejpam-4643	287	2	is	be	AUX
ejpam-4643	287	3	shown	show	VERB
ejpam-4643	287	4	that	that	SCONJ
ejpam-4643	287	5	the	the	DET
ejpam-4643	287	6	resolving	resolve	VERB
ejpam-4643	287	7	domination	domination	NOUN
ejpam-4643	287	8	number	number	NOUN
ejpam-4643	287	9	in	in	ADP
ejpam-4643	287	10	the	the	DET
ejpam-4643	287	11	corona	corona	NOUN
ejpam-4643	287	12	of	of	ADP
ejpam-4643	287	13	two	two	NUM
ejpam-4643	287	14	graphs	graph	NOUN
ejpam-4643	287	15	is	be	AUX
ejpam-4643	287	16	n	n	PRON
ejpam-4643	287	17	·	·	PUNCT
ejpam-4643	287	18	γl(h	γl(h	NUM
ejpam-4643	287	19	)	)	PUNCT
ejpam-4643	287	20	,	,	PUNCT
ejpam-4643	287	21	the	the	DET
ejpam-4643	287	22	resolving	resolve	VERB
ejpam-4643	287	23	domination	domination	NOUN
ejpam-4643	287	24	number	number	NOUN
ejpam-4643	287	25	in	in	ADP
ejpam-4643	287	26	the	the	DET
ejpam-4643	287	27	join	join	NOUN
ejpam-4643	287	28	of	of	ADP
ejpam-4643	287	29	two	two	NUM
ejpam-4643	287	30	graphs	graph	NOUN
ejpam-4643	287	31	is	be	AUX
ejpam-4643	287	32	the	the	DET
ejpam-4643	287	33	min	min	PROPN
ejpam-4643	287	34	{	{	PUNCT
ejpam-4643	287	35	sln(h	sln(h	PROPN
ejpam-4643	287	36	)	)	PUNCT
ejpam-4643	287	37	+	+	NUM
ejpam-4643	287	38	ln(g	ln(g	NUM
ejpam-4643	287	39	)	)	PUNCT
ejpam-4643	287	40	,	,	PUNCT
ejpam-4643	287	41	sln(g	sln(g	PROPN
ejpam-4643	287	42	)	)	PUNCT
ejpam-4643	287	43	+	+	NUM
ejpam-4643	287	44	ln(h	ln(h	NUM
ejpam-4643	287	45	)	)	PUNCT
ejpam-4643	287	46	}	}	PUNCT
ejpam-4643	287	47	,	,	PUNCT
ejpam-4643	287	48	and	and	CCONJ
ejpam-4643	287	49	the	the	DET
ejpam-4643	287	50	resolving	resolve	VERB
ejpam-4643	287	51	domination	domination	NOUN
ejpam-4643	287	52	number	number	NOUN
ejpam-4643	287	53	of	of	ADP
ejpam-4643	287	54	the	the	DET
ejpam-4643	287	55	lexicographic	lexicographic	ADJ
ejpam-4643	287	56	product	product	NOUN
ejpam-4643	287	57	of	of	ADP
ejpam-4643	287	58	graphs	graph	NOUN
ejpam-4643	287	59	g	g	NOUN
ejpam-4643	287	60	and	and	CCONJ
ejpam-4643	287	61	h	h	NOUN
ejpam-4643	287	62	is	be	AUX
ejpam-4643	287	63	|v	|v	PROPN
ejpam-4643	287	64	(	(	PUNCT
ejpam-4643	287	65	g)|	g)|	NOUN
ejpam-4643	287	66	·	·	PUNCT
ejpam-4643	287	67	ln(h	ln(h	NUM
ejpam-4643	287	68	)	)	PUNCT
ejpam-4643	287	69	.	.	PUNCT
ejpam-4643	288	1	the	the	DET
ejpam-4643	288	2	parameter	parameter	NOUN
ejpam-4643	288	3	can	can	AUX
ejpam-4643	288	4	be	be	AUX
ejpam-4643	288	5	investigated	investigate	VERB
ejpam-4643	288	6	further	far	ADV
ejpam-4643	288	7	for	for	ADP
ejpam-4643	288	8	graphs	graph	NOUN
ejpam-4643	288	9	under	under	ADP
ejpam-4643	288	10	other	other	ADJ
ejpam-4643	288	11	binary	binary	ADJ
ejpam-4643	288	12	operations	operation	NOUN
ejpam-4643	288	13	.	.	PUNCT
ejpam-4643	289	1	acknowledgements	acknowledgement	NOUN
ejpam-4643	289	2	this	this	DET
ejpam-4643	289	3	research	research	NOUN
ejpam-4643	289	4	is	be	AUX
ejpam-4643	289	5	funded	fund	VERB
ejpam-4643	289	6	by	by	ADP
ejpam-4643	289	7	the	the	DET
ejpam-4643	289	8	commission	commission	NOUN
ejpam-4643	289	9	on	on	ADP
ejpam-4643	289	10	higher	high	ADJ
ejpam-4643	289	11	education	education	NOUN
ejpam-4643	289	12	(	(	PUNCT
ejpam-4643	289	13	ched	che	VERB
ejpam-4643	289	14	)	)	PUNCT
ejpam-4643	289	15	and	and	CCONJ
ejpam-4643	289	16	mindanao	mindanao	PROPN
ejpam-4643	289	17	state	state	PROPN
ejpam-4643	289	18	university	university	PROPN
ejpam-4643	289	19	-	-	PUNCT
ejpam-4643	289	20	iligan	iligan	PROPN
ejpam-4643	289	21	institute	institute	PROPN
ejpam-4643	289	22	of	of	ADP
ejpam-4643	289	23	technology	technology	PROPN
ejpam-4643	289	24	,	,	PUNCT
ejpam-4643	289	25	philippines	philippine	NOUN
ejpam-4643	289	26	.	.	PUNCT
ejpam-4643	290	1	also	also	ADV
ejpam-4643	290	2	,	,	PUNCT
ejpam-4643	290	3	the	the	DET
ejpam-4643	290	4	authors	author	NOUN
ejpam-4643	290	5	would	would	AUX
ejpam-4643	290	6	like	like	VERB
ejpam-4643	290	7	to	to	PART
ejpam-4643	290	8	recognize	recognize	VERB
ejpam-4643	290	9	the	the	DET
ejpam-4643	290	10	efforts	effort	NOUN
ejpam-4643	290	11	of	of	ADP
ejpam-4643	290	12	the	the	DET
ejpam-4643	290	13	anonymous	anonymous	ADJ
ejpam-4643	290	14	reviewers	reviewer	NOUN
ejpam-4643	290	15	whose	whose	DET
ejpam-4643	290	16	suggestions	suggestion	NOUN
ejpam-4643	290	17	and	and	CCONJ
ejpam-4643	290	18	recommendations	recommendation	NOUN
ejpam-4643	290	19	contributed	contribute	VERB
ejpam-4643	290	20	to	to	ADP
ejpam-4643	290	21	the	the	DET
ejpam-4643	290	22	big	big	ADJ
ejpam-4643	290	23	improvement	improvement	NOUN
ejpam-4643	290	24	of	of	ADP
ejpam-4643	290	25	the	the	DET
ejpam-4643	290	26	paper	paper	NOUN
ejpam-4643	290	27	.	.	PUNCT
ejpam-4643	291	1	references	reference	NOUN
ejpam-4643	291	2	[	[	X
ejpam-4643	291	3	1	1	NUM
ejpam-4643	291	4	]	]	X
ejpam-4643	291	5	r.c	r.c	PROPN
ejpam-4643	291	6	.	.	PROPN
ejpam-4643	291	7	brigham	brigham	PROPN
ejpam-4643	291	8	,	,	PUNCT
ejpam-4643	291	9	g.	g.	PROPN
ejpam-4643	291	10	chartrand	chartrand	PROPN
ejpam-4643	291	11	,	,	PUNCT
ejpam-4643	291	12	r.d	r.d	PROPN
ejpam-4643	291	13	.	.	PROPN
ejpam-4643	291	14	dutton	dutton	PROPN
ejpam-4643	291	15	,	,	PUNCT
ejpam-4643	291	16	and	and	CCONJ
ejpam-4643	291	17	p.	p.	PROPN
ejpam-4643	291	18	zhang	zhang	PROPN
ejpam-4643	291	19	.	.	PUNCT
ejpam-4643	291	20	resolving	resolve	VERB
ejpam-4643	291	21	domination	domination	NOUN
ejpam-4643	291	22	in	in	ADP
ejpam-4643	291	23	graphs	graph	NOUN
ejpam-4643	291	24	.	.	PUNCT
ejpam-4643	292	1	mathematica	mathematica	PROPN
ejpam-4643	292	2	bohemica	bohemica	PROPN
ejpam-4643	292	3	,	,	PUNCT
ejpam-4643	292	4	1:25–36	1:25–36	NUM
ejpam-4643	292	5	,	,	PUNCT
ejpam-4643	292	6	2003	2003	NUM
ejpam-4643	292	7	.	.	PUNCT
ejpam-4643	293	1	[	[	X
ejpam-4643	293	2	2	2	NUM
ejpam-4643	293	3	]	]	X
ejpam-4643	293	4	j.m	j.m	PROPN
ejpam-4643	293	5	.	.	PROPN
ejpam-4643	293	6	cabaro	cabaro	PROPN
ejpam-4643	293	7	and	and	CCONJ
ejpam-4643	293	8	h.m	h.m	PROPN
ejpam-4643	293	9	.	.	PROPN
ejpam-4643	293	10	rara	rara	PROPN
ejpam-4643	293	11	.	.	PUNCT
ejpam-4643	294	1	on	on	ADP
ejpam-4643	294	2	2	2	NUM
ejpam-4643	294	3	-	-	PUNCT
ejpam-4643	294	4	resolving	resolve	VERB
ejpam-4643	294	5	sets	set	NOUN
ejpam-4643	294	6	in	in	ADP
ejpam-4643	294	7	the	the	DET
ejpam-4643	294	8	join	join	NOUN
ejpam-4643	294	9	and	and	CCONJ
ejpam-4643	294	10	corona	corona	NOUN
ejpam-4643	294	11	of	of	ADP
ejpam-4643	294	12	graphs	graph	NOUN
ejpam-4643	294	13	.	.	PUNCT
ejpam-4643	295	1	european	european	ADJ
ejpam-4643	295	2	journal	journal	PROPN
ejpam-4643	295	3	of	of	ADP
ejpam-4643	295	4	pure	pure	ADJ
ejpam-4643	295	5	and	and	CCONJ
ejpam-4643	295	6	applied	applied	ADJ
ejpam-4643	295	7	mathematics	mathematic	NOUN
ejpam-4643	295	8	,	,	PUNCT
ejpam-4643	295	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4643	295	10	,	,	PUNCT
ejpam-4643	295	11	2021	2021	NUM
ejpam-4643	295	12	.	.	PUNCT
ejpam-4643	296	1	references	reference	NOUN
ejpam-4643	296	2	28	28	NUM
ejpam-4643	297	1	[	[	X
ejpam-4643	297	2	3	3	NUM
ejpam-4643	297	3	]	]	X
ejpam-4643	297	4	d.	d.	PROPN
ejpam-4643	297	5	geoffrey	geoffrey	PROPN
ejpam-4643	297	6	.	.	PUNCT
ejpam-4643	298	1	nuclei	nuclei	PROPN
ejpam-4643	298	2	for	for	ADP
ejpam-4643	298	3	totally	totally	ADV
ejpam-4643	298	4	point	point	NOUN
ejpam-4643	298	5	determining	determine	VERB
ejpam-4643	298	6	graphs	graph	NOUN
ejpam-4643	298	7	.	.	PUNCT
ejpam-4643	299	1	discrete	discrete	ADJ
ejpam-4643	299	2	mathematics	mathematic	NOUN
ejpam-4643	299	3	,	,	PUNCT
ejpam-4643	299	4	21:145–162	21:145–162	PROPN
ejpam-4643	299	5	,	,	PUNCT
ejpam-4643	299	6	1978	1978	NUM
ejpam-4643	299	7	.	.	PUNCT
ejpam-4643	300	1	[	[	X
ejpam-4643	300	2	4	4	NUM
ejpam-4643	300	3	]	]	X
ejpam-4643	300	4	c.	c.	NOUN
ejpam-4643	300	5	go	go	VERB
ejpam-4643	300	6	and	and	CCONJ
ejpam-4643	300	7	jr	jr	PROPN
ejpam-4643	300	8	.	.	PUNCT
ejpam-4643	301	1	s.r	s.r	PROPN
ejpam-4643	301	2	.	.	PROPN
ejpam-4643	301	3	canoy	canoy	PROPN
ejpam-4643	301	4	.	.	PUNCT
ejpam-4643	302	1	domination	domination	NOUN
ejpam-4643	302	2	in	in	ADP
ejpam-4643	302	3	the	the	DET
ejpam-4643	302	4	corona	corona	NOUN
ejpam-4643	302	5	and	and	CCONJ
ejpam-4643	302	6	join	join	VERB
ejpam-4643	302	7	of	of	ADP
ejpam-4643	302	8	graphs	graph	NOUN
ejpam-4643	302	9	.	.	PUNCT
ejpam-4643	303	1	international	international	ADJ
ejpam-4643	303	2	mathematical	mathematical	PROPN
ejpam-4643	303	3	forum	forum	PROPN
ejpam-4643	303	4	,	,	PUNCT
ejpam-4643	303	5	6(16):763–771	6(16):763–771	NUM
ejpam-4643	303	6	,	,	PUNCT
ejpam-4643	303	7	2011	2011	NUM
ejpam-4643	303	8	.	.	PUNCT
ejpam-4643	304	1	[	[	X
ejpam-4643	304	2	5	5	NUM
ejpam-4643	304	3	]	]	PUNCT
ejpam-4643	304	4	f.	f.	PROPN
ejpam-4643	304	5	harary	harary	PROPN
ejpam-4643	304	6	.	.	PUNCT
ejpam-4643	305	1	graph	graph	NOUN
ejpam-4643	305	2	theory	theory	NOUN
ejpam-4643	305	3	.	.	PUNCT
ejpam-4643	306	1	addison	addison	PROPN
ejpam-4643	306	2	-	-	PUNCT
ejpam-4643	306	3	wesley	wesley	PROPN
ejpam-4643	306	4	publishing	publishing	PROPN
ejpam-4643	306	5	company	company	NOUN
ejpam-4643	306	6	,	,	PUNCT
ejpam-4643	306	7	usa	usa	PROPN
ejpam-4643	306	8	,	,	PUNCT
ejpam-4643	306	9	1969	1969	NUM
ejpam-4643	306	10	.	.	PUNCT
ejpam-4643	307	1	[	[	X
ejpam-4643	307	2	6	6	NUM
ejpam-4643	307	3	]	]	PUNCT
ejpam-4643	307	4	g.	g.	PROPN
ejpam-4643	307	5	monsanto	monsanto	PROPN
ejpam-4643	307	6	and	and	CCONJ
ejpam-4643	307	7	h.	h.	PROPN
ejpam-4643	307	8	rara	rara	PROPN
ejpam-4643	307	9	.	.	PUNCT
ejpam-4643	308	1	on	on	ADP
ejpam-4643	308	2	strong	strong	ADJ
ejpam-4643	308	3	resolving	resolving	NOUN
ejpam-4643	308	4	domination	domination	NOUN
ejpam-4643	308	5	in	in	ADP
ejpam-4643	308	6	the	the	DET
ejpam-4643	308	7	join	join	NOUN
ejpam-4643	308	8	and	and	CCONJ
ejpam-4643	308	9	corona	corona	NOUN
ejpam-4643	308	10	of	of	ADP
ejpam-4643	308	11	graphs	graph	NOUN
ejpam-4643	308	12	.	.	PUNCT
ejpam-4643	309	1	european	european	ADJ
ejpam-4643	309	2	journal	journal	PROPN
ejpam-4643	309	3	of	of	ADP
ejpam-4643	309	4	pure	pure	ADJ
ejpam-4643	309	5	and	and	CCONJ
ejpam-4643	309	6	applied	applied	ADJ
ejpam-4643	309	7	mathematics	mathematic	NOUN
ejpam-4643	309	8	,	,	PUNCT
ejpam-4643	309	9	13(1):170–179	13(1):170–179	NUM
ejpam-4643	309	10	,	,	PUNCT
ejpam-4643	309	11	2020	2020	NUM
ejpam-4643	309	12	.	.	PUNCT
ejpam-4643	310	1	[	[	X
ejpam-4643	310	2	7	7	X
ejpam-4643	310	3	]	]	X
ejpam-4643	310	4	g.	g.	PROPN
ejpam-4643	310	5	monsanto	monsanto	PROPN
ejpam-4643	310	6	and	and	CCONJ
ejpam-4643	310	7	h.	h.	PROPN
ejpam-4643	310	8	rara	rara	PROPN
ejpam-4643	310	9	.	.	PUNCT
ejpam-4643	311	1	resolving	resolve	VERB
ejpam-4643	311	2	restrained	restrained	ADJ
ejpam-4643	311	3	domination	domination	NOUN
ejpam-4643	311	4	in	in	ADP
ejpam-4643	311	5	graphs	graph	NOUN
ejpam-4643	311	6	.	.	PUNCT
ejpam-4643	312	1	european	european	ADJ
ejpam-4643	312	2	journal	journal	PROPN
ejpam-4643	312	3	of	of	ADP
ejpam-4643	312	4	pure	pure	ADJ
ejpam-4643	312	5	and	and	CCONJ
ejpam-4643	312	6	applied	applied	ADJ
ejpam-4643	312	7	mathematics	mathematic	NOUN
ejpam-4643	312	8	,	,	PUNCT
ejpam-4643	312	9	14(3):829–841	14(3):829–841	PROPN
ejpam-4643	312	10	,	,	PUNCT
ejpam-4643	312	11	2021	2021	NUM
ejpam-4643	312	12	.	.	PUNCT
ejpam-4643	313	1	[	[	X
ejpam-4643	313	2	8	8	NUM
ejpam-4643	313	3	]	]	X
ejpam-4643	313	4	g.	g.	PROPN
ejpam-4643	313	5	monsanto	monsanto	PROPN
ejpam-4643	313	6	and	and	CCONJ
ejpam-4643	313	7	h.	h.	PROPN
ejpam-4643	313	8	rara	rara	PROPN
ejpam-4643	313	9	.	.	PUNCT
ejpam-4643	314	1	movable	movable	ADJ
ejpam-4643	314	2	resolving	resolve	VERB
ejpam-4643	314	3	domination	domination	NOUN
ejpam-4643	314	4	in	in	ADP
ejpam-4643	314	5	graphs	graph	NOUN
ejpam-4643	314	6	.	.	PUNCT
ejpam-4643	315	1	discrete	discrete	ADJ
ejpam-4643	315	2	mathematics	mathematic	NOUN
ejpam-4643	315	3	,	,	PUNCT
ejpam-4643	315	4	algorithms	algorithm	NOUN
ejpam-4643	315	5	and	and	CCONJ
ejpam-4643	315	6	applications	application	NOUN
ejpam-4643	315	7	,	,	PUNCT
ejpam-4643	315	8	14(6):2250016	14(6):2250016	NUM
ejpam-4643	315	9	,	,	PUNCT
ejpam-4643	315	10	2022	2022	NUM
ejpam-4643	315	11	.	.	PUNCT
ejpam-4643	316	1	[	[	X
ejpam-4643	316	2	9	9	NUM
ejpam-4643	316	3	]	]	X
ejpam-4643	316	4	g.	g.	PROPN
ejpam-4643	316	5	monsanto	monsanto	PROPN
ejpam-4643	316	6	and	and	CCONJ
ejpam-4643	316	7	h.	h.	PROPN
ejpam-4643	316	8	rara	rara	PROPN
ejpam-4643	316	9	.	.	PUNCT
ejpam-4643	317	1	resolvings	resolving	NOUN
ejpam-4643	317	2	sets	set	VERB
ejpam-4643	317	3	in	in	ADP
ejpam-4643	317	4	graphs	graph	NOUN
ejpam-4643	317	5	.	.	PUNCT
ejpam-4643	318	1	italian	italian	ADJ
ejpam-4643	318	2	journal	journal	NOUN
ejpam-4643	318	3	of	of	ADP
ejpam-4643	318	4	pure	pure	ADJ
ejpam-4643	318	5	and	and	CCONJ
ejpam-4643	318	6	applied	applied	ADJ
ejpam-4643	318	7	mathematics	mathematic	NOUN
ejpam-4643	318	8	,	,	PUNCT
ejpam-4643	318	9	47:862–871	47:862–871	PROPN
ejpam-4643	318	10	,	,	PUNCT
ejpam-4643	318	11	2022	2022	NUM
ejpam-4643	318	12	.	.	PUNCT
ejpam-4643	319	1	[	[	X
ejpam-4643	319	2	10	10	NUM
ejpam-4643	319	3	]	]	X
ejpam-4643	319	4	p.	p.	NOUN
ejpam-4643	319	5	slater	slater	PROPN
ejpam-4643	319	6	.	.	PUNCT
ejpam-4643	320	1	dominating	dominating	NOUN
ejpam-4643	320	2	and	and	CCONJ
ejpam-4643	320	3	reference	reference	NOUN
ejpam-4643	320	4	sets	set	NOUN
ejpam-4643	320	5	in	in	ADP
ejpam-4643	320	6	a	a	DET
ejpam-4643	320	7	graph	graph	NOUN
ejpam-4643	320	8	.	.	PUNCT
ejpam-4643	321	1	journal	journal	NOUN
ejpam-4643	321	2	of	of	ADP
ejpam-4643	321	3	mathematics	mathematics	PROPN
ejpam-4643	321	4	and	and	CCONJ
ejpam-4643	321	5	physical	physical	ADJ
ejpam-4643	321	6	sciences	science	NOUN
ejpam-4643	321	7	,	,	PUNCT
ejpam-4643	321	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4643	321	9	,	,	PUNCT
ejpam-4643	321	10	1988	1988	NUM
ejpam-4643	321	11	.	.	PUNCT
ejpam-4643	322	1	[	[	X
ejpam-4643	322	2	11	11	NUM
ejpam-4643	322	3	]	]	X
ejpam-4643	322	4	jr	jr	PROPN
ejpam-4643	322	5	.	.	PUNCT
ejpam-4643	322	6	s.r	s.r	PROPN
ejpam-4643	322	7	.	.	PROPN
ejpam-4643	322	8	canoy	canoy	PROPN
ejpam-4643	322	9	and	and	CCONJ
ejpam-4643	322	10	g.a	g.a	PROPN
ejpam-4643	322	11	.	.	PROPN
ejpam-4643	322	12	malacas	malacas	PROPN
ejpam-4643	322	13	.	.	PUNCT
ejpam-4643	323	1	locating	locate	VERB
ejpam-4643	323	2	-	-	PUNCT
ejpam-4643	323	3	dominating	dominating	NOUN
ejpam-4643	323	4	sets	set	NOUN
ejpam-4643	323	5	in	in	ADP
ejpam-4643	323	6	a	a	DET
ejpam-4643	323	7	graph	graph	NOUN
ejpam-4643	323	8	.	.	PUNCT
ejpam-4643	324	1	applied	apply	VERB
ejpam-4643	324	2	mathematical	mathematical	ADJ
ejpam-4643	324	3	sciences	science	NOUN
ejpam-4643	324	4	,	,	PUNCT
ejpam-4643	324	5	8(88):4381–4388	8(88):4381–4388	NUM
ejpam-4643	324	6	,	,	PUNCT
ejpam-4643	324	7	2014	2014	NUM
ejpam-4643	324	8	.	.	PUNCT
ejpam-4643	325	1	[	[	X
ejpam-4643	325	2	12	12	NUM
ejpam-4643	325	3	]	]	X
ejpam-4643	325	4	jr	jr	PROPN
ejpam-4643	325	5	.	.	PUNCT
ejpam-4643	325	6	s.r	s.r	PROPN
ejpam-4643	325	7	.	.	PROPN
ejpam-4643	325	8	canoy	canoy	PROPN
ejpam-4643	325	9	and	and	CCONJ
ejpam-4643	325	10	s.a	s.a	PROPN
ejpam-4643	325	11	.	.	PROPN
ejpam-4643	325	12	omega	omega	NOUN
ejpam-4643	325	13	.	.	PUNCT
ejpam-4643	326	1	locating	locate	VERB
ejpam-4643	326	2	sets	set	NOUN
ejpam-4643	326	3	in	in	ADP
ejpam-4643	326	4	a	a	DET
ejpam-4643	326	5	graph	graph	NOUN
ejpam-4643	326	6	.	.	PUNCT
ejpam-4643	327	1	applied	apply	VERB
ejpam-4643	327	2	mathematical	mathematical	ADJ
ejpam-4643	327	3	sciences	science	NOUN
ejpam-4643	327	4	,	,	PUNCT
ejpam-4643	327	5	9(60):2957–2964	9(60):2957–2964	NUM
ejpam-4643	327	6	,	,	PUNCT
ejpam-4643	327	7	2015	2015	NUM
ejpam-4643	327	8	.	.	PUNCT
ejpam-4643	328	1	[	[	X
ejpam-4643	328	2	13	13	NUM
ejpam-4643	328	3	]	]	X
ejpam-4643	328	4	d.p	d.p	PROPN
ejpam-4643	328	5	.	.	PUNCT
ejpam-4643	328	6	summer	summer	NOUN
ejpam-4643	328	7	.	.	PUNCT
ejpam-4643	329	1	point	point	NOUN
ejpam-4643	329	2	determination	determination	NOUN
ejpam-4643	329	3	in	in	ADP
ejpam-4643	329	4	graphs	graph	NOUN
ejpam-4643	329	5	.	.	PUNCT
ejpam-4643	330	1	discrete	discrete	ADJ
ejpam-4643	330	2	mathematics	mathematic	NOUN
ejpam-4643	330	3	,	,	PUNCT
ejpam-4643	330	4	5:1979–1987	5:1979–1987	NUM
ejpam-4643	330	5	,	,	PUNCT
ejpam-4643	330	6	1973	1973	NUM
ejpam-4643	330	7	.	.	PUNCT