id	sid	tid	token	lemma	pos
ejpam-4673	1	1	european	european	PROPN
ejpam-4673	1	2	journal	journal	PROPN
ejpam-4673	1	3	of	of	ADP
ejpam-4673	1	4	pure	pure	ADJ
ejpam-4673	1	5	and	and	CCONJ
ejpam-4673	1	6	applied	apply	VERB
ejpam-4673	1	7	mathematics	mathematic	NOUN
ejpam-4673	1	8	vol	vol	NOUN
ejpam-4673	1	9	.	.	PUNCT
ejpam-4673	2	1	16	16	NUM
ejpam-4673	2	2	,	,	PUNCT
ejpam-4673	2	3	no	no	INTJ
ejpam-4673	2	4	.	.	NOUN
ejpam-4673	2	5	1	1	NUM
ejpam-4673	2	6	,	,	PUNCT
ejpam-4673	2	7	2023	2023	NUM
ejpam-4673	2	8	,	,	PUNCT
ejpam-4673	2	9	440	440	NUM
ejpam-4673	2	10	-	-	SYM
ejpam-4673	2	11	453	453	NUM
ejpam-4673	2	12	issn	issn	PROPN
ejpam-4673	2	13	1307	1307	NUM
ejpam-4673	2	14	-	-	SYM
ejpam-4673	2	15	5543	5543	NUM
ejpam-4673	2	16	–	–	PUNCT
ejpam-4673	2	17	ejpam.com	ejpam.com	X
ejpam-4673	2	18	published	publish	VERB
ejpam-4673	2	19	by	by	ADP
ejpam-4673	2	20	new	new	PROPN
ejpam-4673	2	21	york	york	PROPN
ejpam-4673	2	22	business	business	PROPN
ejpam-4673	2	23	global	global	PROPN
ejpam-4673	2	24	hop	hop	NOUN
ejpam-4673	2	25	differentiating	differentiate	VERB
ejpam-4673	2	26	hop	hop	NOUN
ejpam-4673	2	27	dominating	dominating	NOUN
ejpam-4673	2	28	sets	set	NOUN
ejpam-4673	2	29	in	in	ADP
ejpam-4673	2	30	graphs	graph	NOUN
ejpam-4673	2	31	sergio	sergio	PROPN
ejpam-4673	2	32	r.	r.	PROPN
ejpam-4673	2	33	canoy	canoy	PROPN
ejpam-4673	2	34	,	,	PUNCT
ejpam-4673	2	35	jr.1,∗	jr.1,∗	PROPN
ejpam-4673	2	36	,	,	PUNCT
ejpam-4673	2	37	chrisley	chrisley	PROPN
ejpam-4673	2	38	jade	jade	PROPN
ejpam-4673	2	39	c.	c.	PROPN
ejpam-4673	2	40	saromines1	saromines1	PROPN
ejpam-4673	2	41	1	1	NUM
ejpam-4673	2	42	department	department	NOUN
ejpam-4673	2	43	of	of	ADP
ejpam-4673	2	44	mathematics	mathematic	NOUN
ejpam-4673	2	45	and	and	CCONJ
ejpam-4673	2	46	statistics	statistic	NOUN
ejpam-4673	2	47	,	,	PUNCT
ejpam-4673	2	48	college	college	NOUN
ejpam-4673	2	49	of	of	ADP
ejpam-4673	2	50	science	science	NOUN
ejpam-4673	2	51	and	and	CCONJ
ejpam-4673	2	52	mathematics	mathematic	NOUN
ejpam-4673	2	53	,	,	PUNCT
ejpam-4673	2	54	center	center	NOUN
ejpam-4673	2	55	for	for	ADP
ejpam-4673	2	56	graph	graph	NOUN
ejpam-4673	2	57	theory	theory	NOUN
ejpam-4673	2	58	,	,	PUNCT
ejpam-4673	2	59	premier	premier	PROPN
ejpam-4673	2	60	research	research	PROPN
ejpam-4673	2	61	institute	institute	PROPN
ejpam-4673	2	62	of	of	ADP
ejpam-4673	2	63	science	science	NOUN
ejpam-4673	2	64	and	and	CCONJ
ejpam-4673	2	65	mathematics	mathematic	NOUN
ejpam-4673	2	66	,	,	PUNCT
ejpam-4673	2	67	msu	msu	PROPN
ejpam-4673	2	68	-	-	PUNCT
ejpam-4673	2	69	iligan	iligan	PROPN
ejpam-4673	2	70	institute	institute	PROPN
ejpam-4673	2	71	of	of	ADP
ejpam-4673	2	72	technology	technology	PROPN
ejpam-4673	2	73	,	,	PUNCT
ejpam-4673	2	74	9200	9200	NUM
ejpam-4673	2	75	iligan	iligan	ADJ
ejpam-4673	2	76	city	city	NOUN
ejpam-4673	2	77	,	,	PUNCT
ejpam-4673	2	78	philippines	philippine	NOUN
ejpam-4673	2	79	abstract	abstract	ADJ
ejpam-4673	2	80	.	.	PUNCT
ejpam-4673	3	1	a	a	DET
ejpam-4673	3	2	subset	subset	NOUN
ejpam-4673	3	3	s	s	X
ejpam-4673	3	4	of	of	ADP
ejpam-4673	3	5	v	v	NOUN
ejpam-4673	3	6	(	(	PUNCT
ejpam-4673	3	7	g	g	NOUN
ejpam-4673	3	8	)	)	PUNCT
ejpam-4673	3	9	,	,	PUNCT
ejpam-4673	3	10	where	where	SCONJ
ejpam-4673	3	11	g	g	PROPN
ejpam-4673	3	12	is	be	AUX
ejpam-4673	3	13	a	a	DET
ejpam-4673	3	14	simple	simple	ADJ
ejpam-4673	3	15	undirected	undirected	ADJ
ejpam-4673	3	16	graph	graph	NOUN
ejpam-4673	3	17	,	,	PUNCT
ejpam-4673	3	18	is	be	AUX
ejpam-4673	3	19	hop	hop	NOUN
ejpam-4673	3	20	dominating	dominate	VERB
ejpam-4673	3	21	if	if	SCONJ
ejpam-4673	3	22	for	for	ADP
ejpam-4673	3	23	each	each	PRON
ejpam-4673	3	24	v	v	NUM
ejpam-4673	3	25	∈	∈	PROPN
ejpam-4673	3	26	v	v	NOUN
ejpam-4673	3	27	(	(	PUNCT
ejpam-4673	3	28	g	g	NOUN
ejpam-4673	3	29	)	)	PUNCT
ejpam-4673	3	30	\	\	PROPN
ejpam-4673	4	1	s	s	X
ejpam-4673	4	2	,	,	PUNCT
ejpam-4673	4	3	there	there	PRON
ejpam-4673	4	4	exists	exist	VERB
ejpam-4673	4	5	w	w	PROPN
ejpam-4673	4	6	∈	∈	PROPN
ejpam-4673	4	7	s	s	VERB
ejpam-4673	4	8	such	such	ADJ
ejpam-4673	4	9	that	that	PRON
ejpam-4673	4	10	dg(v	dg(v	ADJ
ejpam-4673	4	11	,	,	PUNCT
ejpam-4673	4	12	w	w	NOUN
ejpam-4673	4	13	)	)	PUNCT
ejpam-4673	4	14	=	=	SYM
ejpam-4673	4	15	2	2	NUM
ejpam-4673	5	1	and	and	CCONJ
ejpam-4673	5	2	it	it	PRON
ejpam-4673	5	3	is	be	AUX
ejpam-4673	5	4	hop	hop	NOUN
ejpam-4673	5	5	differentiating	differentiate	VERB
ejpam-4673	5	6	if	if	SCONJ
ejpam-4673	5	7	n2	n2	ADJ
ejpam-4673	5	8	g[u	g[u	PROPN
ejpam-4673	5	9	]	]	PUNCT
ejpam-4673	5	10	∩	∩	PROPN
ejpam-4673	5	11	s	s	PART
ejpam-4673	5	12	̸=	̸=	PROPN
ejpam-4673	5	13	n2	n2	PROPN
ejpam-4673	5	14	g[v	g[v	PROPN
ejpam-4673	5	15	]	]	PUNCT
ejpam-4673	5	16	∩	∩	X
ejpam-4673	5	17	s	s	PART
ejpam-4673	5	18	for	for	ADP
ejpam-4673	5	19	any	any	DET
ejpam-4673	5	20	two	two	NUM
ejpam-4673	5	21	distinct	distinct	ADJ
ejpam-4673	5	22	vertices	vertex	NOUN
ejpam-4673	5	23	u	u	NOUN
ejpam-4673	5	24	,	,	PUNCT
ejpam-4673	5	25	v	v	NOUN
ejpam-4673	5	26	∈	∈	PROPN
ejpam-4673	5	27	v	v	NOUN
ejpam-4673	5	28	(	(	PUNCT
ejpam-4673	5	29	g	g	NOUN
ejpam-4673	5	30	)	)	PUNCT
ejpam-4673	5	31	.	.	PUNCT
ejpam-4673	6	1	a	a	DET
ejpam-4673	6	2	set	set	NOUN
ejpam-4673	6	3	s	s	NOUN
ejpam-4673	6	4	⊆	⊆	NUM
ejpam-4673	6	5	v	v	NOUN
ejpam-4673	6	6	(	(	PUNCT
ejpam-4673	6	7	g	g	NOUN
ejpam-4673	6	8	)	)	PUNCT
ejpam-4673	6	9	is	be	AUX
ejpam-4673	6	10	hop	hop	NOUN
ejpam-4673	6	11	differentiating	differentiate	VERB
ejpam-4673	6	12	hop	hop	NOUN
ejpam-4673	6	13	dominating	dominating	NOUN
ejpam-4673	6	14	if	if	SCONJ
ejpam-4673	6	15	it	it	PRON
ejpam-4673	6	16	is	be	AUX
ejpam-4673	6	17	both	both	PRON
ejpam-4673	6	18	hop	hop	NOUN
ejpam-4673	6	19	differentiating	differentiating	NOUN
ejpam-4673	6	20	and	and	CCONJ
ejpam-4673	6	21	hop	hop	NOUN
ejpam-4673	6	22	dominating	dominating	NOUN
ejpam-4673	6	23	in	in	ADP
ejpam-4673	6	24	g.	g.	PROPN
ejpam-4673	6	25	the	the	DET
ejpam-4673	6	26	minimum	minimum	ADJ
ejpam-4673	6	27	cardinality	cardinality	NOUN
ejpam-4673	6	28	of	of	ADP
ejpam-4673	6	29	a	a	DET
ejpam-4673	6	30	hop	hop	NOUN
ejpam-4673	6	31	differentiating	differentiate	VERB
ejpam-4673	6	32	hop	hop	NOUN
ejpam-4673	6	33	dominating	dominating	NOUN
ejpam-4673	6	34	set	set	VERB
ejpam-4673	6	35	in	in	ADP
ejpam-4673	6	36	g	g	NOUN
ejpam-4673	6	37	,	,	PUNCT
ejpam-4673	6	38	denoted	denote	VERB
ejpam-4673	6	39	by	by	ADP
ejpam-4673	6	40	γdh(g	γdh(g	NOUN
ejpam-4673	6	41	)	)	PUNCT
ejpam-4673	6	42	,	,	PUNCT
ejpam-4673	6	43	is	be	AUX
ejpam-4673	6	44	called	call	VERB
ejpam-4673	6	45	the	the	DET
ejpam-4673	6	46	hop	hop	NOUN
ejpam-4673	6	47	differentiating	differentiate	VERB
ejpam-4673	6	48	hop	hop	NOUN
ejpam-4673	6	49	domination	domination	NOUN
ejpam-4673	6	50	number	number	NOUN
ejpam-4673	6	51	of	of	ADP
ejpam-4673	6	52	g.	g.	PROPN
ejpam-4673	6	53	in	in	ADP
ejpam-4673	6	54	this	this	DET
ejpam-4673	6	55	paper	paper	NOUN
ejpam-4673	6	56	,	,	PUNCT
ejpam-4673	6	57	we	we	PRON
ejpam-4673	6	58	investigate	investigate	VERB
ejpam-4673	6	59	some	some	DET
ejpam-4673	6	60	properties	property	NOUN
ejpam-4673	6	61	of	of	ADP
ejpam-4673	6	62	this	this	DET
ejpam-4673	6	63	newly	newly	ADV
ejpam-4673	6	64	defined	define	VERB
ejpam-4673	6	65	parameter	parameter	NOUN
ejpam-4673	6	66	.	.	PUNCT
ejpam-4673	7	1	in	in	ADP
ejpam-4673	7	2	particular	particular	ADJ
ejpam-4673	7	3	,	,	PUNCT
ejpam-4673	7	4	we	we	PRON
ejpam-4673	7	5	characterize	characterize	VERB
ejpam-4673	7	6	the	the	DET
ejpam-4673	7	7	hop	hop	NOUN
ejpam-4673	7	8	differentiating	differentiate	VERB
ejpam-4673	7	9	hop	hop	NOUN
ejpam-4673	7	10	dominating	dominating	NOUN
ejpam-4673	7	11	sets	set	NOUN
ejpam-4673	7	12	in	in	ADP
ejpam-4673	7	13	graphs	graph	NOUN
ejpam-4673	7	14	under	under	ADP
ejpam-4673	7	15	some	some	DET
ejpam-4673	7	16	binary	binary	ADJ
ejpam-4673	7	17	operations	operation	NOUN
ejpam-4673	7	18	.	.	PUNCT
ejpam-4673	8	1	2020	2020	NUM
ejpam-4673	8	2	mathematics	mathematic	NOUN
ejpam-4673	8	3	subject	subject	NOUN
ejpam-4673	8	4	classifications	classification	NOUN
ejpam-4673	8	5	:	:	PUNCT
ejpam-4673	8	6	05c69	05c69	X
ejpam-4673	8	7	key	key	ADJ
ejpam-4673	8	8	words	word	NOUN
ejpam-4673	8	9	and	and	CCONJ
ejpam-4673	8	10	phrases	phrase	NOUN
ejpam-4673	8	11	:	:	PUNCT
ejpam-4673	8	12	hop	hop	NOUN
ejpam-4673	8	13	domination	domination	NOUN
ejpam-4673	8	14	,	,	PUNCT
ejpam-4673	8	15	hop	hop	NOUN
ejpam-4673	8	16	differentiating	differentiating	NOUN
ejpam-4673	8	17	,	,	PUNCT
ejpam-4673	8	18	join	join	NOUN
ejpam-4673	8	19	,	,	PUNCT
ejpam-4673	8	20	corona	corona	PROPN
ejpam-4673	8	21	,	,	PUNCT
ejpam-4673	8	22	lexicographic	lexicographic	ADJ
ejpam-4673	8	23	product	product	NOUN
ejpam-4673	8	24	1	1	NUM
ejpam-4673	8	25	.	.	PUNCT
ejpam-4673	8	26	introduction	introduction	NOUN
ejpam-4673	8	27	differentiating	differentiate	VERB
ejpam-4673	8	28	-	-	PUNCT
ejpam-4673	8	29	domination	domination	NOUN
ejpam-4673	8	30	in	in	ADP
ejpam-4673	8	31	a	a	DET
ejpam-4673	8	32	graph	graph	NOUN
ejpam-4673	8	33	,	,	PUNCT
ejpam-4673	8	34	a	a	DET
ejpam-4673	8	35	variation	variation	NOUN
ejpam-4673	8	36	of	of	ADP
ejpam-4673	8	37	the	the	DET
ejpam-4673	8	38	standard	standard	ADJ
ejpam-4673	8	39	domination	domination	NOUN
ejpam-4673	8	40	,	,	PUNCT
ejpam-4673	8	41	was	be	AUX
ejpam-4673	8	42	defined	define	VERB
ejpam-4673	8	43	by	by	ADP
ejpam-4673	8	44	gimbel	gimbel	NOUN
ejpam-4673	8	45	et	et	PROPN
ejpam-4673	8	46	al	al	PROPN
ejpam-4673	8	47	.	.	PUNCT
ejpam-4673	9	1	in	in	ADP
ejpam-4673	9	2	[	[	X
ejpam-4673	9	3	6	6	NUM
ejpam-4673	9	4	]	]	PUNCT
ejpam-4673	9	5	.	.	PUNCT
ejpam-4673	10	1	a	a	DET
ejpam-4673	10	2	differentiating	differentiate	VERB
ejpam-4673	10	3	set	set	NOUN
ejpam-4673	10	4	in	in	ADP
ejpam-4673	10	5	a	a	DET
ejpam-4673	10	6	given	give	VERB
ejpam-4673	10	7	network	network	NOUN
ejpam-4673	10	8	can	can	AUX
ejpam-4673	10	9	be	be	AUX
ejpam-4673	10	10	viewed	view	VERB
ejpam-4673	10	11	as	as	ADP
ejpam-4673	10	12	a	a	DET
ejpam-4673	10	13	set	set	NOUN
ejpam-4673	10	14	of	of	ADP
ejpam-4673	10	15	sensitive	sensitive	ADJ
ejpam-4673	10	16	monitors	monitor	NOUN
ejpam-4673	10	17	used	use	VERB
ejpam-4673	10	18	to	to	PART
ejpam-4673	10	19	safeguard	safeguard	VERB
ejpam-4673	10	20	a	a	DET
ejpam-4673	10	21	given	give	VERB
ejpam-4673	10	22	facility	facility	NOUN
ejpam-4673	10	23	,	,	PUNCT
ejpam-4673	10	24	that	that	ADV
ejpam-4673	10	25	is	is	ADV
ejpam-4673	10	26	,	,	PUNCT
ejpam-4673	10	27	to	to	PART
ejpam-4673	10	28	identify	identify	VERB
ejpam-4673	10	29	the	the	DET
ejpam-4673	10	30	exact	exact	ADJ
ejpam-4673	10	31	location	location	NOUN
ejpam-4673	10	32	of	of	ADP
ejpam-4673	10	33	an	an	DET
ejpam-4673	10	34	intruder	intruder	NOUN
ejpam-4673	10	35	(	(	PUNCT
ejpam-4673	10	36	e.g.	e.g.	ADV
ejpam-4673	10	37	a	a	DET
ejpam-4673	10	38	burglar	burglar	NOUN
ejpam-4673	10	39	,	,	PUNCT
ejpam-4673	10	40	a	a	DET
ejpam-4673	10	41	fire	fire	NOUN
ejpam-4673	10	42	,	,	PUNCT
ejpam-4673	10	43	etc	etc	X
ejpam-4673	10	44	.	.	X
ejpam-4673	10	45	)	)	PUNCT
ejpam-4673	11	1	whenever	whenever	SCONJ
ejpam-4673	11	2	a	a	DET
ejpam-4673	11	3	problem	problem	NOUN
ejpam-4673	11	4	in	in	ADP
ejpam-4673	11	5	a	a	DET
ejpam-4673	11	6	facility	facility	NOUN
ejpam-4673	11	7	arises	arise	VERB
ejpam-4673	11	8	.	.	PUNCT
ejpam-4673	12	1	the	the	DET
ejpam-4673	12	2	requirement	requirement	NOUN
ejpam-4673	12	3	that	that	SCONJ
ejpam-4673	12	4	the	the	DET
ejpam-4673	12	5	set	set	NOUN
ejpam-4673	12	6	have	have	AUX
ejpam-4673	12	7	to	to	PART
ejpam-4673	12	8	be	be	AUX
ejpam-4673	12	9	dominating	dominate	VERB
ejpam-4673	12	10	would	would	AUX
ejpam-4673	12	11	mean	mean	VERB
ejpam-4673	12	12	that	that	SCONJ
ejpam-4673	12	13	every	every	DET
ejpam-4673	12	14	vertex	vertex	NOUN
ejpam-4673	12	15	where	where	SCONJ
ejpam-4673	12	16	there	there	PRON
ejpam-4673	12	17	is	be	VERB
ejpam-4673	12	18	no	no	DET
ejpam-4673	12	19	monitor	monitor	NOUN
ejpam-4673	12	20	on	on	ADP
ejpam-4673	12	21	it	it	PRON
ejpam-4673	12	22	is	be	AUX
ejpam-4673	12	23	connected	connect	VERB
ejpam-4673	12	24	to	to	ADP
ejpam-4673	12	25	at	at	ADV
ejpam-4673	12	26	least	least	ADV
ejpam-4673	12	27	one	one	NUM
ejpam-4673	12	28	monitoring	monitoring	NOUN
ejpam-4673	12	29	device	device	NOUN
ejpam-4673	12	30	.	.	PUNCT
ejpam-4673	13	1	moreover	moreover	ADV
ejpam-4673	13	2	,	,	PUNCT
ejpam-4673	13	3	finding	find	VERB
ejpam-4673	13	4	the	the	DET
ejpam-4673	13	5	differentiating	differentiating	NOUN
ejpam-4673	13	6	-	-	PUNCT
ejpam-4673	13	7	domination	domination	NOUN
ejpam-4673	13	8	number	number	NOUN
ejpam-4673	13	9	of	of	ADP
ejpam-4673	13	10	a	a	DET
ejpam-4673	13	11	graph	graph	NOUN
ejpam-4673	13	12	is	be	AUX
ejpam-4673	13	13	equivalent	equivalent	ADJ
ejpam-4673	13	14	to	to	ADP
ejpam-4673	13	15	finding	find	VERB
ejpam-4673	13	16	the	the	DET
ejpam-4673	13	17	least	least	ADJ
ejpam-4673	13	18	number	number	NOUN
ejpam-4673	13	19	of	of	ADP
ejpam-4673	13	20	monitors	monitor	NOUN
ejpam-4673	13	21	that	that	PRON
ejpam-4673	13	22	can	can	AUX
ejpam-4673	13	23	do	do	VERB
ejpam-4673	13	24	the	the	DET
ejpam-4673	13	25	certain	certain	ADJ
ejpam-4673	13	26	task	task	NOUN
ejpam-4673	13	27	in	in	ADP
ejpam-4673	13	28	a	a	DET
ejpam-4673	13	29	given	give	VERB
ejpam-4673	13	30	network	network	NOUN
ejpam-4673	13	31	.	.	PUNCT
ejpam-4673	14	1	in	in	ADP
ejpam-4673	14	2	other	other	ADJ
ejpam-4673	14	3	studies	study	NOUN
ejpam-4673	14	4	,	,	PUNCT
ejpam-4673	14	5	a	a	DET
ejpam-4673	14	6	differentiating	differentiate	VERB
ejpam-4673	14	7	dominating	dominating	NOUN
ejpam-4673	14	8	set	set	NOUN
ejpam-4673	14	9	is	be	AUX
ejpam-4673	14	10	also	also	ADV
ejpam-4673	14	11	referred	refer	VERB
ejpam-4673	14	12	to	to	ADP
ejpam-4673	14	13	as	as	ADP
ejpam-4673	14	14	an	an	DET
ejpam-4673	14	15	identifying	identify	VERB
ejpam-4673	14	16	code	code	NOUN
ejpam-4673	14	17	(	(	PUNCT
ejpam-4673	14	18	see	see	VERB
ejpam-4673	14	19	[	[	X
ejpam-4673	14	20	14	14	NUM
ejpam-4673	14	21	]	]	SYM
ejpam-4673	14	22	)	)	PUNCT
ejpam-4673	14	23	.	.	PUNCT
ejpam-4673	15	1	differentiating	differentiate	VERB
ejpam-4673	15	2	-	-	PUNCT
ejpam-4673	15	3	domination	domination	NOUN
ejpam-4673	15	4	and	and	CCONJ
ejpam-4673	15	5	some	some	DET
ejpam-4673	15	6	related	relate	VERB
ejpam-4673	15	7	concepts	concept	NOUN
ejpam-4673	15	8	had	have	AUX
ejpam-4673	15	9	been	be	AUX
ejpam-4673	15	10	studied	study	VERB
ejpam-4673	15	11	in	in	ADP
ejpam-4673	15	12	[	[	X
ejpam-4673	15	13	3	3	NUM
ejpam-4673	15	14	]	]	PUNCT
ejpam-4673	15	15	,	,	PUNCT
ejpam-4673	15	16	[	[	X
ejpam-4673	15	17	4	4	NUM
ejpam-4673	15	18	]	]	PUNCT
ejpam-4673	15	19	,	,	PUNCT
ejpam-4673	15	20	[	[	X
ejpam-4673	15	21	9	9	NUM
ejpam-4673	15	22	]	]	PUNCT
ejpam-4673	15	23	,	,	PUNCT
ejpam-4673	15	24	[	[	X
ejpam-4673	15	25	10	10	NUM
ejpam-4673	15	26	]	]	PUNCT
ejpam-4673	15	27	,	,	PUNCT
ejpam-4673	15	28	[	[	X
ejpam-4673	15	29	13	13	NUM
ejpam-4673	15	30	]	]	PUNCT
ejpam-4673	15	31	,	,	PUNCT
ejpam-4673	15	32	[	[	X
ejpam-4673	15	33	15	15	NUM
ejpam-4673	15	34	]	]	PUNCT
ejpam-4673	15	35	,	,	PUNCT
ejpam-4673	15	36	[	[	X
ejpam-4673	15	37	17	17	NUM
ejpam-4673	15	38	]	]	PUNCT
ejpam-4673	15	39	,	,	PUNCT
ejpam-4673	15	40	and	and	CCONJ
ejpam-4673	15	41	[	[	X
ejpam-4673	15	42	18	18	NUM
ejpam-4673	15	43	]	]	PUNCT
ejpam-4673	15	44	.	.	PUNCT
ejpam-4673	16	1	in	in	ADP
ejpam-4673	16	2	2015	2015	NUM
ejpam-4673	16	3	,	,	PUNCT
ejpam-4673	16	4	natarajan	natarajan	PROPN
ejpam-4673	16	5	et	et	PROPN
ejpam-4673	16	6	al	al	PROPN
ejpam-4673	16	7	.	.	PUNCT
ejpam-4673	17	1	(	(	PUNCT
ejpam-4673	17	2	see	see	VERB
ejpam-4673	17	3	[	[	X
ejpam-4673	17	4	16	16	NUM
ejpam-4673	17	5	]	]	PUNCT
ejpam-4673	17	6	)	)	PUNCT
ejpam-4673	17	7	introduced	introduce	VERB
ejpam-4673	17	8	hop	hop	NOUN
ejpam-4673	17	9	domination	domination	NOUN
ejpam-4673	17	10	and	and	CCONJ
ejpam-4673	17	11	made	make	VERB
ejpam-4673	17	12	an	an	DET
ejpam-4673	17	13	initial	initial	ADJ
ejpam-4673	17	14	investigation	investigation	NOUN
ejpam-4673	17	15	of	of	ADP
ejpam-4673	17	16	the	the	DET
ejpam-4673	17	17	concept	concept	NOUN
ejpam-4673	17	18	.	.	PUNCT
ejpam-4673	18	1	the	the	DET
ejpam-4673	18	2	study	study	NOUN
ejpam-4673	18	3	has	have	AUX
ejpam-4673	18	4	led	lead	VERB
ejpam-4673	18	5	other	other	ADJ
ejpam-4673	18	6	researchers	researcher	NOUN
ejpam-4673	18	7	to	to	PART
ejpam-4673	18	8	investigate	investigate	VERB
ejpam-4673	18	9	it	it	PRON
ejpam-4673	18	10	further	far	ADV
ejpam-4673	18	11	∗corresponding	∗corresponde	VERB
ejpam-4673	18	12	author	author	NOUN
ejpam-4673	18	13	.	.	PUNCT
ejpam-4673	19	1	doi	doi	NOUN
ejpam-4673	19	2	:	:	PUNCT
ejpam-4673	19	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4673	https://doi.org/10.29020/nybg.ejpam.v16i1.4673	PROPN
ejpam-4673	19	4	email	email	NOUN
ejpam-4673	19	5	addresses	address	NOUN
ejpam-4673	19	6	:	:	PUNCT
ejpam-4673	19	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4673	19	8	(	(	PUNCT
ejpam-4673	19	9	s.	s.	PROPN
ejpam-4673	19	10	canoy	canoy	PROPN
ejpam-4673	19	11	)	)	PUNCT
ejpam-4673	19	12	,	,	PUNCT
ejpam-4673	19	13	chrisley.saromines@g.msuiit.edu.ph	chrisley.saromines@g.msuiit.edu.ph	PROPN
ejpam-4673	19	14	(	(	PUNCT
ejpam-4673	19	15	c.	c.	PROPN
ejpam-4673	19	16	saromines	saromines	PROPN
ejpam-4673	19	17	)	)	PUNCT
ejpam-4673	19	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4673	19	19	440	440	NUM
ejpam-4673	20	1	©	©	PROPN
ejpam-4673	20	2	2023	2023	NUM
ejpam-4673	20	3	ejpam	ejpam	NOUN
ejpam-4673	20	4	all	all	DET
ejpam-4673	20	5	rights	right	NOUN
ejpam-4673	20	6	reserved	reserve	VERB
ejpam-4673	20	7	.	.	PUNCT
ejpam-4673	21	1	s.	s.	PROPN
ejpam-4673	21	2	canoy	canoy	PROPN
ejpam-4673	21	3	jr	jr	PROPN
ejpam-4673	21	4	.	.	PROPN
ejpam-4673	21	5	,	,	PUNCT
ejpam-4673	21	6	c.	c.	PROPN
ejpam-4673	21	7	saromines	saromine	VERB
ejpam-4673	21	8	/	/	SYM
ejpam-4673	21	9	eur	eur	PROPN
ejpam-4673	21	10	.	.	PUNCT
ejpam-4673	22	1	j.	j.	PROPN
ejpam-4673	22	2	pure	pure	PROPN
ejpam-4673	22	3	appl	appl	PROPN
ejpam-4673	22	4	.	.	PROPN
ejpam-4673	22	5	math	math	PROPN
ejpam-4673	22	6	,	,	PUNCT
ejpam-4673	22	7	16	16	NUM
ejpam-4673	22	8	(	(	PUNCT
ejpam-4673	22	9	1	1	NUM
ejpam-4673	22	10	)	)	PUNCT
ejpam-4673	22	11	(	(	PUNCT
ejpam-4673	22	12	2023	2023	NUM
ejpam-4673	22	13	)	)	PUNCT
ejpam-4673	22	14	,	,	PUNCT
ejpam-4673	22	15	440	440	NUM
ejpam-4673	22	16	-	-	SYM
ejpam-4673	22	17	453	453	NUM
ejpam-4673	22	18	441	441	NUM
ejpam-4673	22	19	and	and	CCONJ
ejpam-4673	22	20	define	define	VERB
ejpam-4673	22	21	some	some	PRON
ejpam-4673	22	22	of	of	ADP
ejpam-4673	22	23	its	its	PRON
ejpam-4673	22	24	variants	variant	NOUN
ejpam-4673	22	25	.	.	PUNCT
ejpam-4673	23	1	in	in	ADP
ejpam-4673	23	2	fact	fact	NOUN
ejpam-4673	23	3	,	,	PUNCT
ejpam-4673	23	4	a	a	DET
ejpam-4673	23	5	number	number	NOUN
ejpam-4673	23	6	of	of	ADP
ejpam-4673	23	7	variations	variation	NOUN
ejpam-4673	23	8	of	of	ADP
ejpam-4673	23	9	hop	hop	NOUN
ejpam-4673	23	10	domination	domination	NOUN
ejpam-4673	23	11	had	have	AUX
ejpam-4673	23	12	already	already	ADV
ejpam-4673	23	13	been	be	AUX
ejpam-4673	23	14	investigated	investigate	VERB
ejpam-4673	23	15	(	(	PUNCT
ejpam-4673	23	16	see	see	VERB
ejpam-4673	23	17	[	[	X
ejpam-4673	23	18	1	1	NUM
ejpam-4673	23	19	]	]	PUNCT
ejpam-4673	23	20	,	,	PUNCT
ejpam-4673	23	21	[	[	X
ejpam-4673	23	22	2	2	NUM
ejpam-4673	23	23	]	]	PUNCT
ejpam-4673	23	24	,	,	PUNCT
ejpam-4673	23	25	[	[	X
ejpam-4673	23	26	7	7	NUM
ejpam-4673	23	27	]	]	PUNCT
ejpam-4673	23	28	,	,	PUNCT
ejpam-4673	23	29	[	[	X
ejpam-4673	23	30	8	8	NUM
ejpam-4673	23	31	]	]	PUNCT
ejpam-4673	23	32	,	,	PUNCT
ejpam-4673	23	33	[	[	X
ejpam-4673	23	34	11	11	NUM
ejpam-4673	23	35	]	]	PUNCT
ejpam-4673	23	36	,	,	PUNCT
ejpam-4673	23	37	[	[	X
ejpam-4673	23	38	12	12	NUM
ejpam-4673	23	39	]	]	PUNCT
ejpam-4673	23	40	,	,	PUNCT
ejpam-4673	23	41	[	[	X
ejpam-4673	23	42	19	19	NUM
ejpam-4673	23	43	]	]	PUNCT
ejpam-4673	23	44	,	,	PUNCT
ejpam-4673	23	45	[	[	X
ejpam-4673	23	46	20	20	NUM
ejpam-4673	23	47	]	]	PUNCT
ejpam-4673	23	48	,	,	PUNCT
ejpam-4673	23	49	[	[	X
ejpam-4673	23	50	21	21	NUM
ejpam-4673	23	51	]	]	PUNCT
ejpam-4673	23	52	,	,	PUNCT
ejpam-4673	23	53	and	and	CCONJ
ejpam-4673	23	54	[	[	X
ejpam-4673	23	55	22	22	NUM
ejpam-4673	23	56	]	]	PUNCT
ejpam-4673	23	57	)	)	PUNCT
ejpam-4673	23	58	.	.	PUNCT
ejpam-4673	24	1	in	in	ADP
ejpam-4673	24	2	this	this	DET
ejpam-4673	24	3	paper	paper	NOUN
ejpam-4673	24	4	,	,	PUNCT
ejpam-4673	24	5	we	we	PRON
ejpam-4673	24	6	define	define	VERB
ejpam-4673	24	7	and	and	CCONJ
ejpam-4673	24	8	do	do	VERB
ejpam-4673	24	9	an	an	DET
ejpam-4673	24	10	initial	initial	ADJ
ejpam-4673	24	11	study	study	NOUN
ejpam-4673	24	12	of	of	ADP
ejpam-4673	24	13	the	the	DET
ejpam-4673	24	14	concept	concept	NOUN
ejpam-4673	24	15	of	of	ADP
ejpam-4673	24	16	hop	hop	NOUN
ejpam-4673	24	17	differentiating	differentiate	VERB
ejpam-4673	24	18	hop	hop	NOUN
ejpam-4673	24	19	dominating	dominating	NOUN
ejpam-4673	24	20	set	set	VERB
ejpam-4673	24	21	in	in	ADP
ejpam-4673	24	22	a	a	DET
ejpam-4673	24	23	graph	graph	NOUN
ejpam-4673	24	24	.	.	PUNCT
ejpam-4673	25	1	it	it	PRON
ejpam-4673	25	2	must	must	AUX
ejpam-4673	25	3	be	be	AUX
ejpam-4673	25	4	pointed	point	VERB
ejpam-4673	25	5	out	out	ADP
ejpam-4673	25	6	that	that	SCONJ
ejpam-4673	25	7	a	a	DET
ejpam-4673	25	8	hop	hop	NOUN
ejpam-4673	25	9	differentiating	differentiate	VERB
ejpam-4673	25	10	set	set	NOUN
ejpam-4673	25	11	is	be	AUX
ejpam-4673	25	12	‘	'	PUNCT
ejpam-4673	25	13	almost	almost	ADV
ejpam-4673	25	14	’	'	PUNCT
ejpam-4673	25	15	a	a	DET
ejpam-4673	25	16	hop	hop	NOUN
ejpam-4673	25	17	dominating	dominating	NOUN
ejpam-4673	25	18	set	set	NOUN
ejpam-4673	25	19	because	because	SCONJ
ejpam-4673	25	20	it	it	PRON
ejpam-4673	25	21	may	may	AUX
ejpam-4673	25	22	allow	allow	VERB
ejpam-4673	25	23	at	at	ADP
ejpam-4673	25	24	most	most	ADV
ejpam-4673	25	25	a	a	DET
ejpam-4673	25	26	vertex	vertex	NOUN
ejpam-4673	25	27	outside	outside	ADP
ejpam-4673	25	28	the	the	DET
ejpam-4673	25	29	set	set	NOUN
ejpam-4673	25	30	to	to	PART
ejpam-4673	25	31	be	be	AUX
ejpam-4673	25	32	‘	'	PUNCT
ejpam-4673	25	33	hop	hop	NOUN
ejpam-4673	25	34	undominated	undominate	VERB
ejpam-4673	25	35	’	'	PUNCT
ejpam-4673	25	36	.	.	PUNCT
ejpam-4673	26	1	a	a	DET
ejpam-4673	26	2	result	result	NOUN
ejpam-4673	26	3	that	that	SCONJ
ejpam-4673	26	4	deals	deal	VERB
ejpam-4673	26	5	with	with	ADP
ejpam-4673	26	6	the	the	DET
ejpam-4673	26	7	concept	concept	NOUN
ejpam-4673	26	8	for	for	ADP
ejpam-4673	26	9	disconnected	disconnected	ADJ
ejpam-4673	26	10	graphs	graph	NOUN
ejpam-4673	26	11	would	would	AUX
ejpam-4673	26	12	show	show	VERB
ejpam-4673	26	13	that	that	SCONJ
ejpam-4673	26	14	the	the	DET
ejpam-4673	26	15	condition	condition	NOUN
ejpam-4673	26	16	‘	'	PUNCT
ejpam-4673	26	17	hop	hop	NOUN
ejpam-4673	26	18	differentiating	differentiate	VERB
ejpam-4673	26	19	hop	hop	NOUN
ejpam-4673	26	20	dominating	dominating	NOUN
ejpam-4673	26	21	’	'	PUNCT
ejpam-4673	26	22	can	can	AUX
ejpam-4673	26	23	not	not	PART
ejpam-4673	26	24	always	always	ADV
ejpam-4673	26	25	be	be	AUX
ejpam-4673	26	26	replaced	replace	VERB
ejpam-4673	26	27	by	by	ADP
ejpam-4673	26	28	‘	'	PUNCT
ejpam-4673	26	29	hop	hop	NOUN
ejpam-4673	26	30	differentiating	differentiating	NOUN
ejpam-4673	26	31	’	'	PUNCT
ejpam-4673	26	32	.	.	PUNCT
ejpam-4673	27	1	this	this	PRON
ejpam-4673	27	2	makes	make	VERB
ejpam-4673	27	3	‘	'	PUNCT
ejpam-4673	27	4	hop	hop	NOUN
ejpam-4673	27	5	differentiating	differentiate	VERB
ejpam-4673	27	6	hop	hop	NOUN
ejpam-4673	27	7	dominating	dominating	NOUN
ejpam-4673	27	8	’	'	PUNCT
ejpam-4673	27	9	an	an	DET
ejpam-4673	27	10	interesting	interesting	ADJ
ejpam-4673	27	11	concept	concept	NOUN
ejpam-4673	27	12	to	to	PART
ejpam-4673	27	13	consider	consider	VERB
ejpam-4673	27	14	.	.	PUNCT
ejpam-4673	28	1	this	this	DET
ejpam-4673	28	2	present	present	ADJ
ejpam-4673	28	3	study	study	NOUN
ejpam-4673	28	4	is	be	AUX
ejpam-4673	28	5	motivated	motivate	VERB
ejpam-4673	28	6	by	by	ADP
ejpam-4673	28	7	the	the	DET
ejpam-4673	28	8	introduction	introduction	NOUN
ejpam-4673	28	9	of	of	ADP
ejpam-4673	28	10	hop	hop	NOUN
ejpam-4673	28	11	domination	domination	NOUN
ejpam-4673	28	12	and	and	CCONJ
ejpam-4673	28	13	differentiating	differentiating	ADJ
ejpam-4673	28	14	-	-	PUNCT
ejpam-4673	28	15	domination	domination	NOUN
ejpam-4673	28	16	concepts	concept	NOUN
ejpam-4673	28	17	.	.	PUNCT
ejpam-4673	29	1	the	the	DET
ejpam-4673	29	2	new	new	ADJ
ejpam-4673	29	3	parameter	parameter	NOUN
ejpam-4673	29	4	,	,	PUNCT
ejpam-4673	29	5	just	just	ADV
ejpam-4673	29	6	like	like	ADP
ejpam-4673	29	7	differentiating	differentiate	VERB
ejpam-4673	29	8	-	-	PUNCT
ejpam-4673	29	9	domination	domination	NOUN
ejpam-4673	29	10	,	,	PUNCT
ejpam-4673	29	11	can	can	AUX
ejpam-4673	29	12	also	also	ADV
ejpam-4673	29	13	be	be	AUX
ejpam-4673	29	14	used	use	VERB
ejpam-4673	29	15	to	to	PART
ejpam-4673	29	16	model	model	VERB
ejpam-4673	29	17	the	the	DET
ejpam-4673	29	18	problem	problem	NOUN
ejpam-4673	29	19	of	of	ADP
ejpam-4673	29	20	determining	determine	VERB
ejpam-4673	29	21	the	the	DET
ejpam-4673	29	22	location	location	NOUN
ejpam-4673	29	23	of	of	ADP
ejpam-4673	29	24	monitoring	monitoring	NOUN
ejpam-4673	29	25	devices	device	NOUN
ejpam-4673	29	26	so	so	SCONJ
ejpam-4673	29	27	as	as	SCONJ
ejpam-4673	29	28	to	to	PART
ejpam-4673	29	29	identify	identify	VERB
ejpam-4673	29	30	the	the	DET
ejpam-4673	29	31	exact	exact	ADJ
ejpam-4673	29	32	location	location	NOUN
ejpam-4673	29	33	of	of	ADP
ejpam-4673	29	34	an	an	DET
ejpam-4673	29	35	intruder	intruder	NOUN
ejpam-4673	29	36	in	in	ADP
ejpam-4673	29	37	a	a	DET
ejpam-4673	29	38	certain	certain	ADJ
ejpam-4673	29	39	facility	facility	NOUN
ejpam-4673	29	40	.	.	PUNCT
ejpam-4673	30	1	2	2	X
ejpam-4673	30	2	.	.	X
ejpam-4673	30	3	terminology	terminology	NOUN
ejpam-4673	30	4	and	and	CCONJ
ejpam-4673	30	5	notation	notation	NOUN
ejpam-4673	30	6	let	let	VERB
ejpam-4673	30	7	g	g	PROPN
ejpam-4673	30	8	=	=	SYM
ejpam-4673	30	9	v	v	PROPN
ejpam-4673	30	10	(	(	PUNCT
ejpam-4673	30	11	g	g	NOUN
ejpam-4673	30	12	)	)	PUNCT
ejpam-4673	30	13	,	,	PUNCT
ejpam-4673	30	14	e(g	e(g	PROPN
ejpam-4673	30	15	)	)	PUNCT
ejpam-4673	30	16	)	)	PUNCT
ejpam-4673	30	17	be	be	AUX
ejpam-4673	30	18	an	an	DET
ejpam-4673	30	19	undirected	undirected	ADJ
ejpam-4673	30	20	graph	graph	NOUN
ejpam-4673	30	21	.	.	PUNCT
ejpam-4673	31	1	for	for	ADP
ejpam-4673	31	2	any	any	DET
ejpam-4673	31	3	two	two	NUM
ejpam-4673	31	4	vertices	vertex	NOUN
ejpam-4673	31	5	u	u	NOUN
ejpam-4673	31	6	and	and	CCONJ
ejpam-4673	31	7	v	v	NOUN
ejpam-4673	31	8	of	of	ADP
ejpam-4673	31	9	g	g	NOUN
ejpam-4673	31	10	,	,	PUNCT
ejpam-4673	31	11	the	the	DET
ejpam-4673	31	12	distance	distance	NOUN
ejpam-4673	31	13	dg(u	dg(u	X
ejpam-4673	31	14	,	,	PUNCT
ejpam-4673	31	15	v	v	NOUN
ejpam-4673	31	16	)	)	PUNCT
ejpam-4673	31	17	is	be	AUX
ejpam-4673	31	18	the	the	DET
ejpam-4673	31	19	length	length	NOUN
ejpam-4673	31	20	of	of	ADP
ejpam-4673	31	21	a	a	DET
ejpam-4673	31	22	shortest	short	ADJ
ejpam-4673	31	23	path	path	NOUN
ejpam-4673	31	24	joining	join	VERB
ejpam-4673	31	25	u	u	NOUN
ejpam-4673	31	26	and	and	CCONJ
ejpam-4673	31	27	v.	v.	ADP
ejpam-4673	31	28	any	any	DET
ejpam-4673	31	29	u	u	NOUN
ejpam-4673	31	30	-	-	NOUN
ejpam-4673	31	31	v	v	ADJ
ejpam-4673	31	32	path	path	NOUN
ejpam-4673	31	33	of	of	ADP
ejpam-4673	31	34	length	length	NOUN
ejpam-4673	31	35	dg(u	dg(u	PROPN
ejpam-4673	31	36	,	,	PUNCT
ejpam-4673	31	37	v	v	NOUN
ejpam-4673	31	38	)	)	PUNCT
ejpam-4673	31	39	is	be	AUX
ejpam-4673	31	40	called	call	VERB
ejpam-4673	31	41	a	a	DET
ejpam-4673	31	42	u	u	NOUN
ejpam-4673	31	43	-	-	NOUN
ejpam-4673	31	44	v	v	ADJ
ejpam-4673	31	45	geodesic	geodesic	NOUN
ejpam-4673	31	46	.	.	PUNCT
ejpam-4673	32	1	the	the	DET
ejpam-4673	32	2	set	set	NOUN
ejpam-4673	32	3	of	of	ADP
ejpam-4673	32	4	neighbors	neighbor	NOUN
ejpam-4673	32	5	of	of	ADP
ejpam-4673	32	6	a	a	DET
ejpam-4673	32	7	vertex	vertex	NOUN
ejpam-4673	32	8	u	u	NOUN
ejpam-4673	32	9	in	in	ADP
ejpam-4673	32	10	g	g	NOUN
ejpam-4673	32	11	,	,	PUNCT
ejpam-4673	32	12	denoted	denote	VERB
ejpam-4673	32	13	by	by	ADP
ejpam-4673	32	14	ng(u	ng(u	NOUN
ejpam-4673	32	15	)	)	PUNCT
ejpam-4673	32	16	,	,	PUNCT
ejpam-4673	32	17	is	be	AUX
ejpam-4673	32	18	called	call	VERB
ejpam-4673	32	19	the	the	DET
ejpam-4673	32	20	open	open	ADJ
ejpam-4673	32	21	neighborhood	neighborhood	NOUN
ejpam-4673	32	22	of	of	ADP
ejpam-4673	32	23	u.	u.	VERB
ejpam-4673	32	24	the	the	DET
ejpam-4673	32	25	closed	closed	ADJ
ejpam-4673	32	26	neighborhood	neighborhood	NOUN
ejpam-4673	32	27	of	of	ADP
ejpam-4673	32	28	u	u	NOUN
ejpam-4673	32	29	is	be	AUX
ejpam-4673	32	30	the	the	DET
ejpam-4673	32	31	set	set	NOUN
ejpam-4673	32	32	ng[u	ng[u	PROPN
ejpam-4673	32	33	]	]	X
ejpam-4673	32	34	=	=	PUNCT
ejpam-4673	32	35	ng(u)∪{u	ng(u)∪{u	VERB
ejpam-4673	32	36	}	}	PUNCT
ejpam-4673	32	37	.	.	PUNCT
ejpam-4673	33	1	the	the	DET
ejpam-4673	33	2	open	open	ADJ
ejpam-4673	33	3	neighborhood	neighborhood	NOUN
ejpam-4673	33	4	ofx	ofx	NOUN
ejpam-4673	33	5	⊆	⊆	NUM
ejpam-4673	33	6	v	v	NOUN
ejpam-4673	33	7	(	(	PUNCT
ejpam-4673	33	8	g	g	NOUN
ejpam-4673	33	9	)	)	PUNCT
ejpam-4673	33	10	is	be	AUX
ejpam-4673	33	11	the	the	DET
ejpam-4673	33	12	setng(x	setng(x	NOUN
ejpam-4673	33	13	)	)	PUNCT
ejpam-4673	33	14	=	=	SYM
ejpam-4673	33	15	⋃	⋃	NOUN
ejpam-4673	33	16	u∈x	u∈x	NOUN
ejpam-4673	33	17	ng(u	ng(u	NOUN
ejpam-4673	33	18	)	)	PUNCT
ejpam-4673	33	19	.	.	PUNCT
ejpam-4673	34	1	the	the	DET
ejpam-4673	34	2	closed	closed	ADJ
ejpam-4673	34	3	neighborhood	neighborhood	NOUN
ejpam-4673	34	4	of	of	ADP
ejpam-4673	34	5	x	x	SYM
ejpam-4673	34	6	is	be	AUX
ejpam-4673	34	7	the	the	DET
ejpam-4673	34	8	set	set	NOUN
ejpam-4673	34	9	ng[x	ng[x	PROPN
ejpam-4673	34	10	]	]	X
ejpam-4673	34	11	=	=	SYM
ejpam-4673	34	12	ng(x)∪x	ng(x)∪x	PROPN
ejpam-4673	34	13	.	.	PUNCT
ejpam-4673	35	1	the	the	DET
ejpam-4673	35	2	minimum	minimum	NOUN
ejpam-4673	35	3	degree	degree	NOUN
ejpam-4673	35	4	of	of	ADP
ejpam-4673	35	5	g	g	NOUN
ejpam-4673	35	6	,	,	PUNCT
ejpam-4673	35	7	denoted	denote	VERB
ejpam-4673	35	8	by	by	ADP
ejpam-4673	35	9	δ(g	δ(g	PROPN
ejpam-4673	35	10	)	)	PUNCT
ejpam-4673	35	11	,	,	PUNCT
ejpam-4673	35	12	is	be	AUX
ejpam-4673	35	13	given	give	VERB
ejpam-4673	35	14	by	by	ADP
ejpam-4673	35	15	δ(g	δ(g	ADV
ejpam-4673	35	16	)	)	PUNCT
ejpam-4673	35	17	=	=	SYM
ejpam-4673	35	18	min{degg(u	min{degg(u	PROPN
ejpam-4673	35	19	)	)	PUNCT
ejpam-4673	35	20	:	:	PUNCT
ejpam-4673	36	1	u	u	PROPN
ejpam-4673	36	2	∈	∈	PROPN
ejpam-4673	36	3	v	v	ADP
ejpam-4673	36	4	(	(	PUNCT
ejpam-4673	36	5	g	g	NOUN
ejpam-4673	36	6	)	)	PUNCT
ejpam-4673	36	7	}	}	PUNCT
ejpam-4673	36	8	,	,	PUNCT
ejpam-4673	36	9	where	where	SCONJ
ejpam-4673	36	10	degg(u	degg(u	X
ejpam-4673	36	11	)	)	PUNCT
ejpam-4673	36	12	=	=	NOUN
ejpam-4673	36	13	|ng(u)|	|ng(u)|	NOUN
ejpam-4673	36	14	.	.	PUNCT
ejpam-4673	37	1	a	a	DET
ejpam-4673	37	2	set	set	NOUN
ejpam-4673	37	3	d	d	NOUN
ejpam-4673	37	4	⊆	⊆	NUM
ejpam-4673	37	5	v	v	ADP
ejpam-4673	37	6	(	(	PUNCT
ejpam-4673	37	7	g	g	NOUN
ejpam-4673	37	8	)	)	PUNCT
ejpam-4673	37	9	is	be	AUX
ejpam-4673	37	10	a	a	DET
ejpam-4673	37	11	dominating	dominating	NOUN
ejpam-4673	37	12	set	set	NOUN
ejpam-4673	37	13	(	(	PUNCT
ejpam-4673	37	14	resp	resp	NOUN
ejpam-4673	37	15	.	.	PUNCT
ejpam-4673	38	1	total	total	ADJ
ejpam-4673	38	2	dominating	dominating	NOUN
ejpam-4673	38	3	set	set	NOUN
ejpam-4673	38	4	)	)	PUNCT
ejpam-4673	38	5	of	of	ADP
ejpam-4673	38	6	g	g	PROPN
ejpam-4673	38	7	if	if	SCONJ
ejpam-4673	38	8	for	for	ADP
ejpam-4673	38	9	every	every	PRON
ejpam-4673	38	10	v	v	NUM
ejpam-4673	38	11	∈	∈	NOUN
ejpam-4673	38	12	v	v	NOUN
ejpam-4673	38	13	(	(	PUNCT
ejpam-4673	38	14	g	g	NOUN
ejpam-4673	38	15	)	)	PUNCT
ejpam-4673	38	16	\	\	PUNCT
ejpam-4673	39	1	d	d	X
ejpam-4673	39	2	(	(	PUNCT
ejpam-4673	39	3	resp	resp	NOUN
ejpam-4673	39	4	.	.	PUNCT
ejpam-4673	40	1	v	v	ADP
ejpam-4673	40	2	∈	∈	PROPN
ejpam-4673	40	3	v	v	NOUN
ejpam-4673	40	4	(	(	PUNCT
ejpam-4673	40	5	g	g	NOUN
ejpam-4673	40	6	)	)	PUNCT
ejpam-4673	40	7	)	)	PUNCT
ejpam-4673	41	1	,	,	PUNCT
ejpam-4673	41	2	there	there	PRON
ejpam-4673	41	3	exists	exist	VERB
ejpam-4673	41	4	u	u	NOUN
ejpam-4673	41	5	∈	∈	PROPN
ejpam-4673	41	6	d	d	ADP
ejpam-4673	41	7	such	such	ADJ
ejpam-4673	41	8	that	that	DET
ejpam-4673	41	9	uv	uv	PROPN
ejpam-4673	41	10	∈	∈	PROPN
ejpam-4673	41	11	e(g	e(g	PROPN
ejpam-4673	41	12	)	)	PUNCT
ejpam-4673	41	13	,	,	PUNCT
ejpam-4673	41	14	that	that	ADV
ejpam-4673	41	15	is	is	ADV
ejpam-4673	41	16	,	,	PUNCT
ejpam-4673	41	17	ng[d	ng[d	PROPN
ejpam-4673	41	18	]	]	PUNCT
ejpam-4673	41	19	=	=	SYM
ejpam-4673	41	20	v	v	X
ejpam-4673	41	21	(	(	PUNCT
ejpam-4673	41	22	g	g	NOUN
ejpam-4673	41	23	)	)	PUNCT
ejpam-4673	41	24	(	(	PUNCT
ejpam-4673	41	25	resp	resp	NOUN
ejpam-4673	41	26	.	.	PUNCT
ejpam-4673	41	27	ng(d	ng(d	PUNCT
ejpam-4673	41	28	)	)	PUNCT
ejpam-4673	41	29	=	=	SYM
ejpam-4673	41	30	v	v	X
ejpam-4673	41	31	(	(	PUNCT
ejpam-4673	41	32	g	g	NOUN
ejpam-4673	41	33	)	)	PUNCT
ejpam-4673	41	34	)	)	PUNCT
ejpam-4673	41	35	.	.	PUNCT
ejpam-4673	42	1	the	the	DET
ejpam-4673	42	2	domination	domination	NOUN
ejpam-4673	42	3	number	number	NOUN
ejpam-4673	42	4	(	(	PUNCT
ejpam-4673	42	5	resp	resp	NOUN
ejpam-4673	42	6	.	.	PUNCT
ejpam-4673	43	1	total	total	ADJ
ejpam-4673	43	2	domination	domination	NOUN
ejpam-4673	43	3	number	number	NOUN
ejpam-4673	43	4	)	)	PUNCT
ejpam-4673	43	5	of	of	ADP
ejpam-4673	43	6	g	g	NOUN
ejpam-4673	43	7	,	,	PUNCT
ejpam-4673	43	8	denoted	denote	VERB
ejpam-4673	43	9	by	by	ADP
ejpam-4673	43	10	γ(g	γ(g	PROPN
ejpam-4673	43	11	)	)	PUNCT
ejpam-4673	43	12	(	(	PUNCT
ejpam-4673	43	13	resp	resp	NOUN
ejpam-4673	43	14	.	.	PUNCT
ejpam-4673	43	15	γt(g	γt(g	PUNCT
ejpam-4673	43	16	)	)	PUNCT
ejpam-4673	43	17	)	)	PUNCT
ejpam-4673	43	18	,	,	PUNCT
ejpam-4673	43	19	is	be	AUX
ejpam-4673	43	20	the	the	DET
ejpam-4673	43	21	minimum	minimum	ADJ
ejpam-4673	43	22	cardinality	cardinality	NOUN
ejpam-4673	43	23	of	of	ADP
ejpam-4673	43	24	a	a	DET
ejpam-4673	43	25	dominating	dominating	NOUN
ejpam-4673	43	26	(	(	PUNCT
ejpam-4673	43	27	resp	resp	NOUN
ejpam-4673	43	28	.	.	PUNCT
ejpam-4673	44	1	total	total	ADJ
ejpam-4673	44	2	dominating	dominating	NOUN
ejpam-4673	44	3	)	)	PUNCT
ejpam-4673	44	4	set	set	VERB
ejpam-4673	44	5	in	in	ADP
ejpam-4673	44	6	g.	g.	PROPN
ejpam-4673	44	7	any	any	DET
ejpam-4673	44	8	dominating	dominating	NOUN
ejpam-4673	44	9	(	(	PUNCT
ejpam-4673	44	10	resp	resp	NOUN
ejpam-4673	44	11	.	.	PUNCT
ejpam-4673	45	1	total	total	ADJ
ejpam-4673	45	2	dominating	dominating	NOUN
ejpam-4673	45	3	)	)	PUNCT
ejpam-4673	45	4	set	set	VERB
ejpam-4673	45	5	in	in	ADP
ejpam-4673	45	6	g	g	PROPN
ejpam-4673	45	7	with	with	ADP
ejpam-4673	45	8	cardinality	cardinality	PROPN
ejpam-4673	45	9	γ(g	γ(g	PROPN
ejpam-4673	45	10	)	)	PUNCT
ejpam-4673	45	11	(	(	PUNCT
ejpam-4673	45	12	resp	resp	NOUN
ejpam-4673	45	13	.	.	PUNCT
ejpam-4673	45	14	γt(g	γt(g	PUNCT
ejpam-4673	45	15	)	)	PUNCT
ejpam-4673	45	16	)	)	PUNCT
ejpam-4673	45	17	,	,	PUNCT
ejpam-4673	45	18	is	be	AUX
ejpam-4673	45	19	called	call	VERB
ejpam-4673	45	20	a	a	DET
ejpam-4673	45	21	γ	γ	NOUN
ejpam-4673	45	22	-	-	PUNCT
ejpam-4673	45	23	set	set	ADJ
ejpam-4673	45	24	(	(	PUNCT
ejpam-4673	45	25	resp	resp	NOUN
ejpam-4673	45	26	.	.	PUNCT
ejpam-4673	46	1	γt	γt	NOUN
ejpam-4673	46	2	-	-	PUNCT
ejpam-4673	46	3	set	set	NOUN
ejpam-4673	46	4	)	)	PUNCT
ejpam-4673	46	5	in	in	ADP
ejpam-4673	46	6	g.	g.	PROPN
ejpam-4673	47	1	if	if	SCONJ
ejpam-4673	47	2	γ(g	γ(g	PROPN
ejpam-4673	47	3	)	)	PUNCT
ejpam-4673	47	4	=	=	SYM
ejpam-4673	47	5	1	1	NUM
ejpam-4673	47	6	and	and	CCONJ
ejpam-4673	47	7	{	{	PUNCT
ejpam-4673	47	8	v	v	NOUN
ejpam-4673	47	9	}	}	PUNCT
ejpam-4673	47	10	is	be	AUX
ejpam-4673	47	11	a	a	DET
ejpam-4673	47	12	dominating	dominating	NOUN
ejpam-4673	47	13	set	set	NOUN
ejpam-4673	47	14	in	in	ADP
ejpam-4673	47	15	g	g	PROPN
ejpam-4673	47	16	,	,	PUNCT
ejpam-4673	47	17	then	then	ADV
ejpam-4673	47	18	we	we	PRON
ejpam-4673	47	19	call	call	VERB
ejpam-4673	47	20	v	v	ADP
ejpam-4673	47	21	a	a	DET
ejpam-4673	47	22	dominating	dominating	NOUN
ejpam-4673	47	23	vertex	vertex	NOUN
ejpam-4673	47	24	in	in	ADP
ejpam-4673	47	25	g.	g.	PROPN
ejpam-4673	47	26	a	a	DET
ejpam-4673	47	27	vertex	vertex	NOUN
ejpam-4673	47	28	v	v	NOUN
ejpam-4673	47	29	in	in	ADP
ejpam-4673	47	30	g	g	PROPN
ejpam-4673	47	31	is	be	AUX
ejpam-4673	47	32	a	a	DET
ejpam-4673	47	33	hop	hop	NOUN
ejpam-4673	47	34	neighbor	neighbor	NOUN
ejpam-4673	47	35	of	of	ADP
ejpam-4673	47	36	vertex	vertex	NOUN
ejpam-4673	47	37	u	u	NOUN
ejpam-4673	47	38	in	in	ADP
ejpam-4673	47	39	g	g	PROPN
ejpam-4673	47	40	if	if	SCONJ
ejpam-4673	47	41	dg(u	dg(u	NOUN
ejpam-4673	47	42	,	,	PUNCT
ejpam-4673	47	43	v	v	NOUN
ejpam-4673	47	44	)	)	PUNCT
ejpam-4673	47	45	=	=	SYM
ejpam-4673	48	1	2	2	X
ejpam-4673	48	2	.	.	X
ejpam-4673	48	3	the	the	DET
ejpam-4673	48	4	set	set	ADJ
ejpam-4673	48	5	n2	n2	ADJ
ejpam-4673	48	6	g(u	g(u	PROPN
ejpam-4673	48	7	)	)	PUNCT
ejpam-4673	48	8	=	=	PRON
ejpam-4673	48	9	{	{	PUNCT
ejpam-4673	48	10	v	v	NUM
ejpam-4673	48	11	∈	∈	NOUN
ejpam-4673	48	12	v	v	NOUN
ejpam-4673	48	13	(	(	PUNCT
ejpam-4673	48	14	g	g	NOUN
ejpam-4673	48	15	)	)	PUNCT
ejpam-4673	48	16	:	:	PUNCT
ejpam-4673	48	17	dg(v	dg(v	X
ejpam-4673	48	18	,	,	PUNCT
ejpam-4673	48	19	u	u	NOUN
ejpam-4673	48	20	)	)	PUNCT
ejpam-4673	48	21	=	=	SYM
ejpam-4673	48	22	2	2	X
ejpam-4673	48	23	}	}	PUNCT
ejpam-4673	48	24	is	be	AUX
ejpam-4673	48	25	called	call	VERB
ejpam-4673	48	26	the	the	DET
ejpam-4673	48	27	open	open	ADJ
ejpam-4673	48	28	hop	hop	NOUN
ejpam-4673	48	29	neighborhood	neighborhood	NOUN
ejpam-4673	48	30	of	of	ADP
ejpam-4673	48	31	u.	u.	PROPN
ejpam-4673	48	32	the	the	DET
ejpam-4673	48	33	closed	closed	ADJ
ejpam-4673	48	34	hop	hop	NOUN
ejpam-4673	48	35	neighborhood	neighborhood	NOUN
ejpam-4673	48	36	of	of	ADP
ejpam-4673	48	37	u	u	NOUN
ejpam-4673	48	38	is	be	AUX
ejpam-4673	48	39	given	give	VERB
ejpam-4673	48	40	by	by	ADP
ejpam-4673	48	41	n2	n2	PROPN
ejpam-4673	48	42	g[u	g[u	PROPN
ejpam-4673	48	43	]	]	X
ejpam-4673	48	44	=	=	SYM
ejpam-4673	48	45	n2	n2	ADJ
ejpam-4673	48	46	g(u	g(u	PROPN
ejpam-4673	48	47	)	)	PUNCT
ejpam-4673	48	48	∪	∪	NOUN
ejpam-4673	48	49	{	{	PUNCT
ejpam-4673	48	50	u	u	NOUN
ejpam-4673	48	51	}	}	PUNCT
ejpam-4673	48	52	.	.	PUNCT
ejpam-4673	49	1	the	the	DET
ejpam-4673	49	2	open	open	ADJ
ejpam-4673	49	3	hop	hop	NOUN
ejpam-4673	49	4	neighborhood	neighborhood	NOUN
ejpam-4673	49	5	of	of	ADP
ejpam-4673	49	6	x	x	PROPN
ejpam-4673	49	7	⊆	⊆	NUM
ejpam-4673	49	8	v	v	ADP
ejpam-4673	49	9	(	(	PUNCT
ejpam-4673	49	10	g	g	NOUN
ejpam-4673	49	11	)	)	PUNCT
ejpam-4673	49	12	is	be	AUX
ejpam-4673	49	13	the	the	DET
ejpam-4673	49	14	set	set	ADJ
ejpam-4673	49	15	n2	n2	ADJ
ejpam-4673	49	16	g(x	g(x	NOUN
ejpam-4673	49	17	)	)	PUNCT
ejpam-4673	50	1	=	=	SYM
ejpam-4673	50	2	⋃	⋃	NOUN
ejpam-4673	50	3	u∈x	u∈x	ADJ
ejpam-4673	50	4	n2	n2	NOUN
ejpam-4673	50	5	g(u	g(u	PROPN
ejpam-4673	50	6	)	)	PUNCT
ejpam-4673	50	7	.	.	PUNCT
ejpam-4673	51	1	the	the	DET
ejpam-4673	51	2	closed	closed	ADJ
ejpam-4673	51	3	hop	hop	NOUN
ejpam-4673	51	4	neighborhood	neighborhood	NOUN
ejpam-4673	51	5	of	of	ADP
ejpam-4673	51	6	x	x	SYM
ejpam-4673	51	7	is	be	AUX
ejpam-4673	51	8	the	the	DET
ejpam-4673	51	9	set	set	ADJ
ejpam-4673	51	10	n2	n2	NOUN
ejpam-4673	51	11	g[x	g[x	PROPN
ejpam-4673	51	12	]	]	X
ejpam-4673	51	13	=	=	SYM
ejpam-4673	51	14	n2	n2	PROPN
ejpam-4673	51	15	g(x	g(x	NOUN
ejpam-4673	51	16	)	)	PUNCT
ejpam-4673	51	17	∪x	∪x	NUM
ejpam-4673	51	18	.	.	PUNCT
ejpam-4673	52	1	a	a	DET
ejpam-4673	52	2	set	set	NOUN
ejpam-4673	52	3	s	s	NOUN
ejpam-4673	52	4	⊆	⊆	NUM
ejpam-4673	52	5	v	v	NOUN
ejpam-4673	52	6	(	(	PUNCT
ejpam-4673	52	7	g	g	NOUN
ejpam-4673	52	8	)	)	PUNCT
ejpam-4673	52	9	is	be	AUX
ejpam-4673	52	10	a	a	DET
ejpam-4673	52	11	hop	hop	NOUN
ejpam-4673	52	12	dominating	dominating	NOUN
ejpam-4673	52	13	set	set	VERB
ejpam-4673	52	14	in	in	ADP
ejpam-4673	52	15	g	g	PROPN
ejpam-4673	52	16	if	if	SCONJ
ejpam-4673	52	17	n2	n2	ADJ
ejpam-4673	52	18	g[s	g[s	PROPN
ejpam-4673	52	19	]	]	X
ejpam-4673	52	20	=	=	SYM
ejpam-4673	52	21	v	v	NOUN
ejpam-4673	52	22	(	(	PUNCT
ejpam-4673	52	23	g	g	NOUN
ejpam-4673	52	24	)	)	PUNCT
ejpam-4673	52	25	,	,	PUNCT
ejpam-4673	52	26	that	that	ADV
ejpam-4673	52	27	is	is	ADV
ejpam-4673	52	28	,	,	PUNCT
ejpam-4673	52	29	for	for	ADP
ejpam-4673	52	30	every	every	DET
ejpam-4673	52	31	v	v	NUM
ejpam-4673	52	32	∈	∈	NOUN
ejpam-4673	52	33	v	v	NOUN
ejpam-4673	52	34	(	(	PUNCT
ejpam-4673	52	35	g)\s	g)\s	NOUN
ejpam-4673	52	36	,	,	PUNCT
ejpam-4673	52	37	there	there	PRON
ejpam-4673	52	38	exists	exist	VERB
ejpam-4673	52	39	u	u	PROPN
ejpam-4673	52	40	∈	∈	PROPN
ejpam-4673	52	41	s	s	VERB
ejpam-4673	52	42	such	such	ADJ
ejpam-4673	52	43	that	that	DET
ejpam-4673	52	44	dg(u	dg(u	ADJ
ejpam-4673	52	45	,	,	PUNCT
ejpam-4673	52	46	v	v	NOUN
ejpam-4673	52	47	)	)	PUNCT
ejpam-4673	53	1	=	=	SYM
ejpam-4673	53	2	2	2	X
ejpam-4673	53	3	.	.	PUNCT
ejpam-4673	54	1	the	the	DET
ejpam-4673	54	2	minimum	minimum	ADJ
ejpam-4673	54	3	cardinality	cardinality	NOUN
ejpam-4673	54	4	among	among	ADP
ejpam-4673	54	5	all	all	DET
ejpam-4673	54	6	hop	hop	NOUN
ejpam-4673	54	7	dominating	dominating	NOUN
ejpam-4673	54	8	sets	set	NOUN
ejpam-4673	54	9	in	in	ADP
ejpam-4673	54	10	g	g	NOUN
ejpam-4673	54	11	,	,	PUNCT
ejpam-4673	54	12	denoted	denote	VERB
ejpam-4673	54	13	by	by	ADP
ejpam-4673	54	14	γh(g	γh(g	NOUN
ejpam-4673	54	15	)	)	PUNCT
ejpam-4673	54	16	,	,	PUNCT
ejpam-4673	54	17	is	be	AUX
ejpam-4673	54	18	called	call	VERB
ejpam-4673	54	19	the	the	DET
ejpam-4673	54	20	hop	hop	NOUN
ejpam-4673	54	21	domination	domination	NOUN
ejpam-4673	54	22	number	number	NOUN
ejpam-4673	54	23	of	of	ADP
ejpam-4673	54	24	g.	g.	PROPN
ejpam-4673	54	25	any	any	DET
ejpam-4673	54	26	hop	hop	NOUN
ejpam-4673	54	27	dominating	dominating	NOUN
ejpam-4673	54	28	set	set	VERB
ejpam-4673	54	29	with	with	ADP
ejpam-4673	54	30	cardinality	cardinality	NOUN
ejpam-4673	54	31	equal	equal	ADJ
ejpam-4673	54	32	to	to	ADP
ejpam-4673	54	33	γh(g	γh(g	NOUN
ejpam-4673	54	34	)	)	PUNCT
ejpam-4673	54	35	is	be	AUX
ejpam-4673	54	36	called	call	VERB
ejpam-4673	54	37	a	a	DET
ejpam-4673	54	38	γh	γh	ADV
ejpam-4673	54	39	-	-	PUNCT
ejpam-4673	54	40	set	set	NOUN
ejpam-4673	54	41	.	.	PUNCT
ejpam-4673	55	1	a	a	DET
ejpam-4673	55	2	set	set	NOUN
ejpam-4673	55	3	s	s	NOUN
ejpam-4673	55	4	⊆	⊆	NUM
ejpam-4673	55	5	v	v	NOUN
ejpam-4673	55	6	(	(	PUNCT
ejpam-4673	55	7	g	g	NOUN
ejpam-4673	55	8	)	)	PUNCT
ejpam-4673	55	9	is	be	AUX
ejpam-4673	55	10	differentiating	differentiate	VERB
ejpam-4673	55	11	in	in	ADP
ejpam-4673	55	12	g	g	PROPN
ejpam-4673	55	13	if	if	SCONJ
ejpam-4673	55	14	for	for	ADP
ejpam-4673	55	15	any	any	DET
ejpam-4673	55	16	two	two	NUM
ejpam-4673	55	17	distinct	distinct	ADJ
ejpam-4673	55	18	vertices	vertex	NOUN
ejpam-4673	55	19	v	v	ADP
ejpam-4673	55	20	,	,	PUNCT
ejpam-4673	55	21	w	w	PROPN
ejpam-4673	55	22	∈	∈	PROPN
ejpam-4673	55	23	v	v	ADP
ejpam-4673	55	24	(	(	PUNCT
ejpam-4673	55	25	g	g	NOUN
ejpam-4673	55	26	)	)	PUNCT
ejpam-4673	55	27	,	,	PUNCT
ejpam-4673	55	28	ng[v	ng[v	X
ejpam-4673	55	29	]	]	PUNCT
ejpam-4673	55	30	∩	∩	PROPN
ejpam-4673	55	31	s	s	PART
ejpam-4673	55	32	̸=	̸=	PROPN
ejpam-4673	55	33	ng[w	ng[w	PROPN
ejpam-4673	55	34	]	]	PUNCT
ejpam-4673	55	35	∩	∩	PROPN
ejpam-4673	55	36	s.	s.	PROPN
ejpam-4673	55	37	a	a	DET
ejpam-4673	55	38	differentiating	differentiate	VERB
ejpam-4673	55	39	set	set	NOUN
ejpam-4673	55	40	s	s	VERB
ejpam-4673	55	41	is	be	AUX
ejpam-4673	55	42	differentiating	differentiate	VERB
ejpam-4673	55	43	-	-	PUNCT
ejpam-4673	55	44	dominating	dominating	NOUN
ejpam-4673	55	45	in	in	ADP
ejpam-4673	55	46	g	g	PROPN
ejpam-4673	55	47	if	if	SCONJ
ejpam-4673	55	48	s.	s.	PROPN
ejpam-4673	55	49	canoy	canoy	PROPN
ejpam-4673	55	50	jr	jr	PROPN
ejpam-4673	55	51	.	.	PROPN
ejpam-4673	55	52	,	,	PUNCT
ejpam-4673	55	53	c.	c.	PROPN
ejpam-4673	55	54	saromines	saromine	VERB
ejpam-4673	55	55	/	/	SYM
ejpam-4673	55	56	eur	eur	PROPN
ejpam-4673	55	57	.	.	PUNCT
ejpam-4673	56	1	j.	j.	PROPN
ejpam-4673	56	2	pure	pure	PROPN
ejpam-4673	56	3	appl	appl	PROPN
ejpam-4673	56	4	.	.	PROPN
ejpam-4673	56	5	math	math	PROPN
ejpam-4673	56	6	,	,	PUNCT
ejpam-4673	56	7	16	16	NUM
ejpam-4673	56	8	(	(	PUNCT
ejpam-4673	56	9	1	1	NUM
ejpam-4673	56	10	)	)	PUNCT
ejpam-4673	56	11	(	(	PUNCT
ejpam-4673	56	12	2023	2023	NUM
ejpam-4673	56	13	)	)	PUNCT
ejpam-4673	56	14	,	,	PUNCT
ejpam-4673	56	15	440	440	NUM
ejpam-4673	56	16	-	-	SYM
ejpam-4673	56	17	453	453	NUM
ejpam-4673	56	18	442	442	NUM
ejpam-4673	56	19	ng(v	ng(v	NOUN
ejpam-4673	56	20	)	)	PUNCT
ejpam-4673	56	21	∩	∩	NOUN
ejpam-4673	56	22	s	s	PART
ejpam-4673	56	23	̸=	̸=	PROPN
ejpam-4673	56	24	∅	∅	NOUN
ejpam-4673	56	25	for	for	ADP
ejpam-4673	56	26	each	each	PRON
ejpam-4673	56	27	v	v	NUM
ejpam-4673	56	28	∈	∈	PROPN
ejpam-4673	56	29	v	v	NOUN
ejpam-4673	56	30	(	(	PUNCT
ejpam-4673	56	31	g	g	NOUN
ejpam-4673	56	32	)	)	PUNCT
ejpam-4673	56	33	\	\	PUNCT
ejpam-4673	57	1	s.	s.	PROPN
ejpam-4673	57	2	the	the	DET
ejpam-4673	57	3	smallest	small	ADJ
ejpam-4673	57	4	cardinality	cardinality	NOUN
ejpam-4673	57	5	of	of	ADP
ejpam-4673	57	6	a	a	DET
ejpam-4673	57	7	differentiating	differentiate	VERB
ejpam-4673	57	8	(	(	PUNCT
ejpam-4673	57	9	resp	resp	NOUN
ejpam-4673	57	10	.	.	PUNCT
ejpam-4673	58	1	differentiating	differentiate	VERB
ejpam-4673	58	2	-	-	PUNCT
ejpam-4673	58	3	dominating	dominating	NOUN
ejpam-4673	58	4	)	)	PUNCT
ejpam-4673	58	5	set	set	VERB
ejpam-4673	58	6	in	in	ADP
ejpam-4673	58	7	g	g	PROPN
ejpam-4673	58	8	is	be	AUX
ejpam-4673	58	9	denoted	denote	VERB
ejpam-4673	58	10	by	by	ADP
ejpam-4673	58	11	dn(g	dn(g	NOUN
ejpam-4673	58	12	)	)	PUNCT
ejpam-4673	58	13	(	(	PUNCT
ejpam-4673	58	14	resp	resp	NOUN
ejpam-4673	58	15	.	.	PUNCT
ejpam-4673	58	16	γd(g	γd(g	NUM
ejpam-4673	58	17	)	)	PUNCT
ejpam-4673	58	18	)	)	PUNCT
ejpam-4673	58	19	.	.	PUNCT
ejpam-4673	59	1	any	any	DET
ejpam-4673	59	2	differentiating	differentiate	VERB
ejpam-4673	59	3	(	(	PUNCT
ejpam-4673	59	4	resp	resp	NOUN
ejpam-4673	59	5	.	.	PUNCT
ejpam-4673	60	1	differentiating	differentiate	VERB
ejpam-4673	60	2	-	-	PUNCT
ejpam-4673	60	3	dominating	dominating	NOUN
ejpam-4673	60	4	)	)	PUNCT
ejpam-4673	60	5	set	set	VERB
ejpam-4673	60	6	in	in	ADP
ejpam-4673	60	7	g	g	PROPN
ejpam-4673	60	8	with	with	ADP
ejpam-4673	60	9	cardinality	cardinality	NOUN
ejpam-4673	60	10	dn(g	dn(g	NUM
ejpam-4673	60	11	)	)	PUNCT
ejpam-4673	60	12	(	(	PUNCT
ejpam-4673	60	13	resp	resp	NOUN
ejpam-4673	60	14	.	.	PUNCT
ejpam-4673	60	15	γd(g	γd(g	NUM
ejpam-4673	60	16	)	)	PUNCT
ejpam-4673	60	17	)	)	PUNCT
ejpam-4673	61	1	is	be	AUX
ejpam-4673	61	2	called	call	VERB
ejpam-4673	61	3	a	a	DET
ejpam-4673	61	4	dn	dn	NOUN
ejpam-4673	61	5	-	-	PUNCT
ejpam-4673	61	6	set	set	ADJ
ejpam-4673	61	7	(	(	PUNCT
ejpam-4673	61	8	resp	resp	NOUN
ejpam-4673	61	9	.	.	PUNCT
ejpam-4673	62	1	γd	γd	ADP
ejpam-4673	62	2	-	-	PUNCT
ejpam-4673	62	3	set	set	NOUN
ejpam-4673	62	4	)	)	PUNCT
ejpam-4673	62	5	.	.	PUNCT
ejpam-4673	63	1	a	a	DET
ejpam-4673	63	2	set	set	NOUN
ejpam-4673	63	3	s	s	NOUN
ejpam-4673	63	4	⊆	⊆	NUM
ejpam-4673	63	5	v	v	NOUN
ejpam-4673	63	6	(	(	PUNCT
ejpam-4673	63	7	g	g	NOUN
ejpam-4673	63	8	)	)	PUNCT
ejpam-4673	63	9	is	be	AUX
ejpam-4673	63	10	hop	hop	NOUN
ejpam-4673	63	11	differentiating	differentiate	VERB
ejpam-4673	63	12	in	in	ADP
ejpam-4673	63	13	g	g	PROPN
ejpam-4673	63	14	if	if	SCONJ
ejpam-4673	63	15	n2	n2	ADJ
ejpam-4673	63	16	g[u]∩s	g[u]∩s	PROPN
ejpam-4673	63	17	̸=	̸=	PROPN
ejpam-4673	63	18	n2	n2	NOUN
ejpam-4673	63	19	g[v]∩s	g[v]∩s	PROPN
ejpam-4673	63	20	for	for	ADP
ejpam-4673	63	21	every	every	DET
ejpam-4673	63	22	two	two	NUM
ejpam-4673	63	23	distinct	distinct	ADJ
ejpam-4673	63	24	vertices	vertex	NOUN
ejpam-4673	63	25	u	u	NOUN
ejpam-4673	63	26	and	and	CCONJ
ejpam-4673	63	27	v	v	NOUN
ejpam-4673	63	28	of	of	ADP
ejpam-4673	63	29	v	v	NOUN
ejpam-4673	63	30	(	(	PUNCT
ejpam-4673	63	31	g	g	NOUN
ejpam-4673	63	32	)	)	PUNCT
ejpam-4673	63	33	.	.	PUNCT
ejpam-4673	64	1	a	a	DET
ejpam-4673	64	2	hop	hop	NOUN
ejpam-4673	64	3	differentiating	differentiate	VERB
ejpam-4673	64	4	set	set	NOUN
ejpam-4673	64	5	in	in	ADP
ejpam-4673	64	6	g	g	NOUN
ejpam-4673	64	7	which	which	PRON
ejpam-4673	64	8	is	be	AUX
ejpam-4673	64	9	also	also	ADV
ejpam-4673	64	10	hop	hop	NOUN
ejpam-4673	64	11	dominating	dominating	NOUN
ejpam-4673	64	12	is	be	AUX
ejpam-4673	64	13	called	call	VERB
ejpam-4673	64	14	a	a	DET
ejpam-4673	64	15	hop	hop	NOUN
ejpam-4673	64	16	differentiating	differentiate	VERB
ejpam-4673	64	17	hop	hop	NOUN
ejpam-4673	64	18	dominating	dominating	NOUN
ejpam-4673	64	19	set	set	NOUN
ejpam-4673	64	20	.	.	PUNCT
ejpam-4673	65	1	the	the	DET
ejpam-4673	65	2	minimum	minimum	ADJ
ejpam-4673	65	3	cardinality	cardinality	NOUN
ejpam-4673	65	4	of	of	ADP
ejpam-4673	65	5	a	a	DET
ejpam-4673	65	6	hop	hop	NOUN
ejpam-4673	65	7	differentiating	differentiate	VERB
ejpam-4673	65	8	(	(	PUNCT
ejpam-4673	65	9	resp	resp	NOUN
ejpam-4673	65	10	.	.	PUNCT
ejpam-4673	66	1	hop	hop	PROPN
ejpam-4673	66	2	differentiating	differentiate	VERB
ejpam-4673	66	3	hop	hop	NOUN
ejpam-4673	66	4	dominating	dominating	NOUN
ejpam-4673	66	5	)	)	PUNCT
ejpam-4673	66	6	set	set	VERB
ejpam-4673	66	7	in	in	ADP
ejpam-4673	66	8	g	g	NOUN
ejpam-4673	66	9	,	,	PUNCT
ejpam-4673	66	10	denoted	denote	VERB
ejpam-4673	66	11	by	by	ADP
ejpam-4673	66	12	hdn(g	hdn(g	PROPN
ejpam-4673	66	13	)	)	PUNCT
ejpam-4673	66	14	(	(	PUNCT
ejpam-4673	66	15	resp	resp	NOUN
ejpam-4673	66	16	.	.	PUNCT
ejpam-4673	66	17	γdh(g	γdh(g	NOUN
ejpam-4673	66	18	)	)	PUNCT
ejpam-4673	66	19	)	)	PUNCT
ejpam-4673	66	20	,	,	PUNCT
ejpam-4673	66	21	is	be	AUX
ejpam-4673	66	22	called	call	VERB
ejpam-4673	66	23	the	the	DET
ejpam-4673	66	24	hop	hop	NOUN
ejpam-4673	66	25	differentiating	differentiate	VERB
ejpam-4673	66	26	number	number	NOUN
ejpam-4673	66	27	(	(	PUNCT
ejpam-4673	66	28	resp	resp	NOUN
ejpam-4673	66	29	.	.	PUNCT
ejpam-4673	67	1	hop	hop	PROPN
ejpam-4673	67	2	differentiating	differentiate	VERB
ejpam-4673	67	3	hop	hop	NOUN
ejpam-4673	67	4	domination	domination	NOUN
ejpam-4673	67	5	number	number	NOUN
ejpam-4673	67	6	)	)	PUNCT
ejpam-4673	67	7	of	of	ADP
ejpam-4673	67	8	g.	g.	PROPN
ejpam-4673	67	9	any	any	DET
ejpam-4673	67	10	hop	hop	NOUN
ejpam-4673	67	11	differentiating	differentiate	VERB
ejpam-4673	67	12	(	(	PUNCT
ejpam-4673	67	13	resp	resp	NOUN
ejpam-4673	67	14	.	.	PUNCT
ejpam-4673	68	1	hop	hop	PROPN
ejpam-4673	68	2	differentiating	differentiate	VERB
ejpam-4673	68	3	hop	hop	NOUN
ejpam-4673	68	4	dominating	dominating	NOUN
ejpam-4673	68	5	)	)	PUNCT
ejpam-4673	68	6	set	set	VERB
ejpam-4673	68	7	in	in	ADP
ejpam-4673	68	8	g	g	NOUN
ejpam-4673	68	9	with	with	ADP
ejpam-4673	68	10	cardinality	cardinality	PROPN
ejpam-4673	68	11	hdn(g	hdn(g	PROPN
ejpam-4673	68	12	)	)	PUNCT
ejpam-4673	68	13	(	(	PUNCT
ejpam-4673	68	14	resp	resp	NOUN
ejpam-4673	68	15	.	.	PUNCT
ejpam-4673	68	16	γdh(g	γdh(g	X
ejpam-4673	68	17	)	)	PUNCT
ejpam-4673	68	18	)	)	PUNCT
ejpam-4673	68	19	is	be	AUX
ejpam-4673	68	20	called	call	VERB
ejpam-4673	68	21	an	an	DET
ejpam-4673	68	22	hdn	hdn	NOUN
ejpam-4673	68	23	-	-	PUNCT
ejpam-4673	68	24	set	set	ADJ
ejpam-4673	68	25	(	(	PUNCT
ejpam-4673	68	26	resp	resp	NOUN
ejpam-4673	68	27	.	.	PUNCT
ejpam-4673	69	1	γdh	γdh	PROPN
ejpam-4673	69	2	-	-	PUNCT
ejpam-4673	69	3	set	set	NOUN
ejpam-4673	69	4	)	)	PUNCT
ejpam-4673	69	5	.	.	PUNCT
ejpam-4673	70	1	suppose	suppose	VERB
ejpam-4673	70	2	g	g	PROPN
ejpam-4673	70	3	is	be	AUX
ejpam-4673	70	4	a	a	DET
ejpam-4673	70	5	non	non	ADJ
ejpam-4673	70	6	-	-	ADJ
ejpam-4673	70	7	trivial	trivial	ADJ
ejpam-4673	70	8	connected	connected	ADJ
ejpam-4673	70	9	graph	graph	NOUN
ejpam-4673	70	10	and	and	CCONJ
ejpam-4673	70	11	suppose	suppose	VERB
ejpam-4673	70	12	that	that	SCONJ
ejpam-4673	70	13	there	there	PRON
ejpam-4673	70	14	exist	exist	VERB
ejpam-4673	70	15	distinct	distinct	ADJ
ejpam-4673	70	16	vertices	vertex	NOUN
ejpam-4673	70	17	u	u	NOUN
ejpam-4673	70	18	and	and	CCONJ
ejpam-4673	70	19	v	v	NOUN
ejpam-4673	70	20	of	of	ADP
ejpam-4673	70	21	g	g	NOUN
ejpam-4673	70	22	such	such	ADJ
ejpam-4673	70	23	that	that	DET
ejpam-4673	70	24	n2	n2	PROPN
ejpam-4673	70	25	g[u	g[u	PROPN
ejpam-4673	70	26	]	]	X
ejpam-4673	70	27	=	=	SYM
ejpam-4673	70	28	n2	n2	PROPN
ejpam-4673	70	29	g[v	g[v	PROPN
ejpam-4673	70	30	]	]	PUNCT
ejpam-4673	70	31	.	.	PUNCT
ejpam-4673	71	1	then	then	ADV
ejpam-4673	71	2	n2	n2	PROPN
ejpam-4673	71	3	g[u	g[u	PROPN
ejpam-4673	71	4	]	]	PUNCT
ejpam-4673	71	5	∩	∩	PROPN
ejpam-4673	71	6	s	s	PART
ejpam-4673	71	7	=	=	PROPN
ejpam-4673	71	8	n2	n2	PROPN
ejpam-4673	71	9	g[v	g[v	PROPN
ejpam-4673	71	10	]	]	PUNCT
ejpam-4673	71	11	∩	∩	X
ejpam-4673	71	12	s	s	PART
ejpam-4673	71	13	for	for	ADP
ejpam-4673	71	14	any	any	DET
ejpam-4673	71	15	set	set	NOUN
ejpam-4673	71	16	s	s	PROPN
ejpam-4673	71	17	⊆	⊆	NUM
ejpam-4673	71	18	v	v	NOUN
ejpam-4673	71	19	(	(	PUNCT
ejpam-4673	71	20	g	g	NOUN
ejpam-4673	71	21	)	)	PUNCT
ejpam-4673	71	22	.	.	PUNCT
ejpam-4673	72	1	this	this	PRON
ejpam-4673	72	2	implies	imply	VERB
ejpam-4673	72	3	that	that	SCONJ
ejpam-4673	72	4	g	g	PROPN
ejpam-4673	72	5	does	do	AUX
ejpam-4673	72	6	not	not	PART
ejpam-4673	72	7	admit	admit	VERB
ejpam-4673	72	8	a	a	DET
ejpam-4673	72	9	hop	hop	NOUN
ejpam-4673	72	10	differentiating	differentiate	VERB
ejpam-4673	72	11	set	set	NOUN
ejpam-4673	72	12	.	.	PUNCT
ejpam-4673	73	1	a	a	DET
ejpam-4673	73	2	connected	connected	ADJ
ejpam-4673	73	3	graph	graph	NOUN
ejpam-4673	73	4	g	g	NOUN
ejpam-4673	73	5	is	be	AUX
ejpam-4673	73	6	point	point	NOUN
ejpam-4673	73	7	determining	determine	VERB
ejpam-4673	73	8	if	if	SCONJ
ejpam-4673	73	9	distinct	distinct	ADJ
ejpam-4673	73	10	vertices	vertex	NOUN
ejpam-4673	73	11	have	have	VERB
ejpam-4673	73	12	distinct	distinct	ADJ
ejpam-4673	73	13	open	open	ADJ
ejpam-4673	73	14	neighborhoods	neighborhood	NOUN
ejpam-4673	73	15	,	,	PUNCT
ejpam-4673	73	16	that	that	ADV
ejpam-4673	73	17	is	is	ADV
ejpam-4673	73	18	,	,	PUNCT
ejpam-4673	73	19	ng(a	ng(a	PRON
ejpam-4673	73	20	)	)	PUNCT
ejpam-4673	73	21	̸=	̸=	PROPN
ejpam-4673	73	22	ng(b	ng(b	CCONJ
ejpam-4673	73	23	)	)	PUNCT
ejpam-4673	73	24	for	for	ADP
ejpam-4673	73	25	distinct	distinct	ADJ
ejpam-4673	73	26	vertices	vertex	NOUN
ejpam-4673	73	27	a	a	PRON
ejpam-4673	73	28	,	,	PUNCT
ejpam-4673	73	29	b	b	PROPN
ejpam-4673	73	30	∈	∈	PROPN
ejpam-4673	73	31	v	v	NOUN
ejpam-4673	73	32	(	(	PUNCT
ejpam-4673	73	33	g	g	NOUN
ejpam-4673	73	34	)	)	PUNCT
ejpam-4673	73	35	.	.	PUNCT
ejpam-4673	74	1	graph	graph	NOUN
ejpam-4673	74	2	g	g	PROPN
ejpam-4673	74	3	is	be	AUX
ejpam-4673	74	4	said	say	VERB
ejpam-4673	74	5	to	to	PART
ejpam-4673	74	6	be	be	AUX
ejpam-4673	74	7	point	point	NOUN
ejpam-4673	74	8	distinguishing	distinguish	VERB
ejpam-4673	74	9	if	if	SCONJ
ejpam-4673	74	10	distinct	distinct	ADJ
ejpam-4673	74	11	vertices	vertex	NOUN
ejpam-4673	74	12	have	have	VERB
ejpam-4673	74	13	distinct	distinct	ADJ
ejpam-4673	74	14	closed	closed	ADJ
ejpam-4673	74	15	neighborhoods	neighborhood	NOUN
ejpam-4673	74	16	,	,	PUNCT
ejpam-4673	74	17	that	that	ADV
ejpam-4673	74	18	is	is	ADV
ejpam-4673	74	19	,	,	PUNCT
ejpam-4673	74	20	ng[a	ng[a	PROPN
ejpam-4673	74	21	]	]	X
ejpam-4673	74	22	̸=	̸=	PROPN
ejpam-4673	74	23	ng[b	ng[b	NOUN
ejpam-4673	74	24	]	]	PUNCT
ejpam-4673	74	25	whenever	whenever	SCONJ
ejpam-4673	74	26	a	a	DET
ejpam-4673	74	27	,	,	PUNCT
ejpam-4673	74	28	b	b	PROPN
ejpam-4673	74	29	∈	∈	PROPN
ejpam-4673	74	30	v	v	NOUN
ejpam-4673	74	31	(	(	PUNCT
ejpam-4673	74	32	g	g	NOUN
ejpam-4673	74	33	)	)	PUNCT
ejpam-4673	74	34	and	and	CCONJ
ejpam-4673	74	35	a	a	DET
ejpam-4673	74	36	̸=	̸=	PROPN
ejpam-4673	74	37	b	b	PROPN
ejpam-4673	74	38	(	(	PUNCT
ejpam-4673	74	39	see	see	VERB
ejpam-4673	74	40	[	[	X
ejpam-4673	74	41	5	5	NUM
ejpam-4673	74	42	]	]	PUNCT
ejpam-4673	74	43	and	and	CCONJ
ejpam-4673	74	44	[	[	X
ejpam-4673	74	45	23	23	NUM
ejpam-4673	74	46	]	]	NUM
ejpam-4673	74	47	)	)	PUNCT
ejpam-4673	74	48	.	.	PUNCT
ejpam-4673	75	1	graph	graph	NOUN
ejpam-4673	75	2	g	g	PROPN
ejpam-4673	75	3	is	be	AUX
ejpam-4673	75	4	distancetwo	distancetwo	ADJ
ejpam-4673	75	5	point	point	NOUN
ejpam-4673	75	6	determining	determine	VERB
ejpam-4673	75	7	(	(	PUNCT
ejpam-4673	75	8	resp	resp	NOUN
ejpam-4673	75	9	.	.	PUNCT
ejpam-4673	76	1	distance	distance	NOUN
ejpam-4673	76	2	-	-	PUNCT
ejpam-4673	76	3	two	two	NUM
ejpam-4673	76	4	point	point	NOUN
ejpam-4673	76	5	distinguishing	distinguishing	NOUN
ejpam-4673	76	6	)	)	PUNCT
ejpam-4673	76	7	if	if	SCONJ
ejpam-4673	76	8	n2	n2	ADJ
ejpam-4673	76	9	g(x	g(x	NOUN
ejpam-4673	76	10	)	)	PUNCT
ejpam-4673	76	11	̸=	̸=	PROPN
ejpam-4673	76	12	n2	n2	PROPN
ejpam-4673	76	13	g(y	g(y	PROPN
ejpam-4673	76	14	)	)	PUNCT
ejpam-4673	76	15	(	(	PUNCT
ejpam-4673	76	16	resp	resp	NOUN
ejpam-4673	76	17	.	.	PUNCT
ejpam-4673	77	1	n2	n2	PROPN
ejpam-4673	77	2	g[x	g[x	PROPN
ejpam-4673	77	3	]	]	X
ejpam-4673	77	4	̸=	̸=	PROPN
ejpam-4673	77	5	n2	n2	PROPN
ejpam-4673	77	6	g[y	g[y	NOUN
ejpam-4673	77	7	]	]	PUNCT
ejpam-4673	77	8	)	)	PUNCT
ejpam-4673	77	9	for	for	ADP
ejpam-4673	77	10	any	any	DET
ejpam-4673	77	11	distinct	distinct	ADJ
ejpam-4673	77	12	vertices	vertex	NOUN
ejpam-4673	77	13	x	x	X
ejpam-4673	77	14	,	,	PUNCT
ejpam-4673	77	15	y	y	PROPN
ejpam-4673	77	16	∈	∈	PROPN
ejpam-4673	77	17	v	v	NOUN
ejpam-4673	77	18	(	(	PUNCT
ejpam-4673	77	19	g	g	NOUN
ejpam-4673	77	20	)	)	PUNCT
ejpam-4673	77	21	.	.	PUNCT
ejpam-4673	78	1	it	it	PRON
ejpam-4673	78	2	is	be	AUX
ejpam-4673	78	3	totally	totally	ADV
ejpam-4673	78	4	distance	distance	NOUN
ejpam-4673	78	5	-	-	PUNCT
ejpam-4673	78	6	two	two	NUM
ejpam-4673	78	7	point	point	NOUN
ejpam-4673	78	8	determining	determine	VERB
ejpam-4673	78	9	if	if	SCONJ
ejpam-4673	78	10	n2	n2	ADJ
ejpam-4673	78	11	g(x	g(x	NOUN
ejpam-4673	78	12	)	)	PUNCT
ejpam-4673	78	13	̸=	̸=	PROPN
ejpam-4673	78	14	n2	n2	PROPN
ejpam-4673	78	15	g(y	g(y	PROPN
ejpam-4673	78	16	)	)	PUNCT
ejpam-4673	78	17	and	and	CCONJ
ejpam-4673	78	18	n2	n2	PROPN
ejpam-4673	78	19	g[x	g[x	PROPN
ejpam-4673	78	20	]	]	X
ejpam-4673	78	21	̸=	̸=	PROPN
ejpam-4673	78	22	n2	n2	PROPN
ejpam-4673	78	23	g[y	g[y	NOUN
ejpam-4673	78	24	]	]	PUNCT
ejpam-4673	78	25	for	for	ADP
ejpam-4673	78	26	any	any	DET
ejpam-4673	78	27	distinct	distinct	ADJ
ejpam-4673	78	28	vertices	vertex	NOUN
ejpam-4673	78	29	x	x	X
ejpam-4673	78	30	,	,	PUNCT
ejpam-4673	78	31	y	y	PROPN
ejpam-4673	78	32	∈	∈	PROPN
ejpam-4673	78	33	v	v	NOUN
ejpam-4673	78	34	(	(	PUNCT
ejpam-4673	78	35	g	g	NOUN
ejpam-4673	78	36	)	)	PUNCT
ejpam-4673	78	37	.	.	PUNCT
ejpam-4673	79	1	g	g	PROPN
ejpam-4673	79	2	is	be	AUX
ejpam-4673	79	3	complement	complement	NOUN
ejpam-4673	79	4	point	point	NOUN
ejpam-4673	79	5	distinguishing	distinguish	VERB
ejpam-4673	79	6	if	if	SCONJ
ejpam-4673	79	7	v	v	NOUN
ejpam-4673	79	8	(	(	PUNCT
ejpam-4673	79	9	g	g	NOUN
ejpam-4673	79	10	)	)	PUNCT
ejpam-4673	79	11	\	\	NOUN
ejpam-4673	79	12	ng(x	ng(x	NUM
ejpam-4673	79	13	)	)	PUNCT
ejpam-4673	79	14	̸=	̸=	PROPN
ejpam-4673	79	15	v	v	NOUN
ejpam-4673	79	16	(	(	PUNCT
ejpam-4673	79	17	g	g	NOUN
ejpam-4673	79	18	)	)	PUNCT
ejpam-4673	79	19	\	\	NOUN
ejpam-4673	79	20	ng(y	ng(y	NOUN
ejpam-4673	79	21	)	)	PUNCT
ejpam-4673	79	22	for	for	ADP
ejpam-4673	79	23	any	any	DET
ejpam-4673	79	24	distinct	distinct	ADJ
ejpam-4673	79	25	vertices	vertex	NOUN
ejpam-4673	79	26	x	x	X
ejpam-4673	79	27	,	,	PUNCT
ejpam-4673	79	28	y	y	PROPN
ejpam-4673	79	29	∈	∈	PROPN
ejpam-4673	79	30	v	v	NOUN
ejpam-4673	79	31	(	(	PUNCT
ejpam-4673	79	32	g	g	NOUN
ejpam-4673	79	33	)	)	PUNCT
ejpam-4673	79	34	.	.	PUNCT
ejpam-4673	80	1	in	in	ADP
ejpam-4673	80	2	other	other	ADJ
ejpam-4673	80	3	words	word	NOUN
ejpam-4673	80	4	,	,	PUNCT
ejpam-4673	80	5	g	g	PROPN
ejpam-4673	80	6	is	be	AUX
ejpam-4673	80	7	complement	complement	NOUN
ejpam-4673	80	8	point	point	NOUN
ejpam-4673	80	9	distinguishing	distinguish	VERB
ejpam-4673	80	10	if	if	SCONJ
ejpam-4673	80	11	g	g	PROPN
ejpam-4673	80	12	is	be	AUX
ejpam-4673	80	13	point	point	NOUN
ejpam-4673	80	14	distinguishing	distinguish	VERB
ejpam-4673	80	15	.	.	PUNCT
ejpam-4673	81	1	a	a	DET
ejpam-4673	81	2	set	set	NOUN
ejpam-4673	81	3	s	s	NOUN
ejpam-4673	81	4	⊆	⊆	NUM
ejpam-4673	81	5	v	v	NOUN
ejpam-4673	81	6	(	(	PUNCT
ejpam-4673	81	7	g	g	NOUN
ejpam-4673	81	8	)	)	PUNCT
ejpam-4673	81	9	is	be	AUX
ejpam-4673	81	10	pointwise	pointwise	VERB
ejpam-4673	81	11	non	non	ADJ
ejpam-4673	81	12	-	-	ADJ
ejpam-4673	81	13	dominating	dominating	ADJ
ejpam-4673	81	14	if	if	SCONJ
ejpam-4673	81	15	for	for	ADP
ejpam-4673	81	16	every	every	PRON
ejpam-4673	81	17	v	v	NUM
ejpam-4673	81	18	∈	∈	NOUN
ejpam-4673	81	19	v	v	NOUN
ejpam-4673	81	20	(	(	PUNCT
ejpam-4673	81	21	g	g	NOUN
ejpam-4673	81	22	)	)	PUNCT
ejpam-4673	81	23	\	\	PROPN
ejpam-4673	82	1	s	s	X
ejpam-4673	82	2	,	,	PUNCT
ejpam-4673	82	3	there	there	PRON
ejpam-4673	82	4	exists	exist	VERB
ejpam-4673	82	5	u	u	PROPN
ejpam-4673	82	6	∈	∈	PROPN
ejpam-4673	82	7	s	s	VERB
ejpam-4673	82	8	such	such	ADJ
ejpam-4673	82	9	that	that	DET
ejpam-4673	82	10	v	v	NOUN
ejpam-4673	82	11	/∈	/∈	PUNCT
ejpam-4673	82	12	ng(u	ng(u	NOUN
ejpam-4673	82	13	)	)	PUNCT
ejpam-4673	82	14	,	,	PUNCT
ejpam-4673	82	15	i.e.	i.e.	X
ejpam-4673	82	16	,	,	PUNCT
ejpam-4673	82	17	[	[	X
ejpam-4673	82	18	v	v	X
ejpam-4673	82	19	(	(	PUNCT
ejpam-4673	82	20	g	g	NOUN
ejpam-4673	82	21	)	)	PUNCT
ejpam-4673	82	22	\	\	NOUN
ejpam-4673	82	23	ng(v	ng(v	PUNCT
ejpam-4673	82	24	)	)	PUNCT
ejpam-4673	82	25	]	]	PUNCT
ejpam-4673	82	26	∩	∩	PROPN
ejpam-4673	82	27	s	s	PART
ejpam-4673	82	28	̸=	̸=	PROPN
ejpam-4673	82	29	∅.	∅.	ADP
ejpam-4673	82	30	the	the	DET
ejpam-4673	82	31	minimum	minimum	ADJ
ejpam-4673	82	32	cardinality	cardinality	NOUN
ejpam-4673	82	33	of	of	ADP
ejpam-4673	82	34	a	a	DET
ejpam-4673	82	35	pointwise	pointwise	ADJ
ejpam-4673	82	36	non	non	ADJ
ejpam-4673	82	37	-	-	ADJ
ejpam-4673	82	38	dominating	dominating	ADJ
ejpam-4673	82	39	set	set	NOUN
ejpam-4673	82	40	in	in	ADP
ejpam-4673	82	41	g	g	NOUN
ejpam-4673	82	42	,	,	PUNCT
ejpam-4673	82	43	denoted	denote	VERB
ejpam-4673	82	44	by	by	ADP
ejpam-4673	82	45	pnd(g	pnd(g	PROPN
ejpam-4673	82	46	)	)	PUNCT
ejpam-4673	82	47	,	,	PUNCT
ejpam-4673	82	48	is	be	AUX
ejpam-4673	82	49	called	call	VERB
ejpam-4673	82	50	a	a	DET
ejpam-4673	82	51	pointwise	pointwise	ADJ
ejpam-4673	82	52	nondomination	nondomination	NOUN
ejpam-4673	82	53	number	number	NOUN
ejpam-4673	82	54	of	of	ADP
ejpam-4673	82	55	g.	g.	PROPN
ejpam-4673	82	56	let	let	VERB
ejpam-4673	82	57	g	g	NOUN
ejpam-4673	82	58	be	be	AUX
ejpam-4673	82	59	a	a	DET
ejpam-4673	82	60	complement	complement	NOUN
ejpam-4673	82	61	point	point	NOUN
ejpam-4673	82	62	distinguishing	distinguish	VERB
ejpam-4673	82	63	graph	graph	NOUN
ejpam-4673	82	64	.	.	PUNCT
ejpam-4673	83	1	a	a	DET
ejpam-4673	83	2	set	set	NOUN
ejpam-4673	83	3	s	s	NOUN
ejpam-4673	83	4	⊆	⊆	NUM
ejpam-4673	83	5	v	v	NOUN
ejpam-4673	83	6	(	(	PUNCT
ejpam-4673	83	7	g	g	NOUN
ejpam-4673	83	8	)	)	PUNCT
ejpam-4673	83	9	is	be	AUX
ejpam-4673	83	10	complement	complement	NOUN
ejpam-4673	83	11	differentiating	differentiate	VERB
ejpam-4673	83	12	in	in	ADP
ejpam-4673	83	13	g	g	PROPN
ejpam-4673	83	14	(	(	PUNCT
ejpam-4673	83	15	or	or	CCONJ
ejpam-4673	83	16	differentiating	differentiate	VERB
ejpam-4673	83	17	in	in	ADP
ejpam-4673	83	18	g	g	NOUN
ejpam-4673	83	19	)	)	PUNCT
ejpam-4673	83	20	if	if	SCONJ
ejpam-4673	83	21	for	for	ADP
ejpam-4673	83	22	any	any	DET
ejpam-4673	83	23	two	two	NUM
ejpam-4673	83	24	distinct	distinct	ADJ
ejpam-4673	83	25	vertices	vertex	NOUN
ejpam-4673	83	26	v	v	ADP
ejpam-4673	83	27	,	,	PUNCT
ejpam-4673	83	28	w	w	PROPN
ejpam-4673	83	29	∈	∈	PROPN
ejpam-4673	83	30	v	v	ADP
ejpam-4673	83	31	(	(	PUNCT
ejpam-4673	83	32	g	g	NOUN
ejpam-4673	83	33	)	)	PUNCT
ejpam-4673	83	34	,	,	PUNCT
ejpam-4673	83	35	ng[v]∩s	ng[v]∩	NOUN
ejpam-4673	83	36	=	=	PUNCT
ejpam-4673	84	1	[	[	X
ejpam-4673	84	2	v	v	X
ejpam-4673	84	3	(	(	PUNCT
ejpam-4673	84	4	g)\ng(v)]∩s	g)\ng(v)]∩	NOUN
ejpam-4673	84	5	̸=	̸=	PROPN
ejpam-4673	84	6	[	[	X
ejpam-4673	84	7	v	v	X
ejpam-4673	84	8	(	(	PUNCT
ejpam-4673	84	9	g)\ng(w)]∩s	g)\ng(w)]∩s	PROPN
ejpam-4673	84	10	=	=	SYM
ejpam-4673	84	11	ng[w]∩s	ng[w]∩s	PROPN
ejpam-4673	84	12	.	.	PUNCT
ejpam-4673	85	1	a	a	DET
ejpam-4673	85	2	complement	complement	NOUN
ejpam-4673	85	3	differentiating	differentiate	VERB
ejpam-4673	85	4	set	set	NOUN
ejpam-4673	85	5	s	s	NOUN
ejpam-4673	85	6	in	in	ADP
ejpam-4673	85	7	g	g	PROPN
ejpam-4673	85	8	is	be	AUX
ejpam-4673	85	9	called	call	VERB
ejpam-4673	85	10	complement	complement	ADJ
ejpam-4673	85	11	differentiating	differentiating	NOUN
ejpam-4673	85	12	-	-	PUNCT
ejpam-4673	85	13	dominating	dominating	NOUN
ejpam-4673	85	14	(	(	PUNCT
ejpam-4673	85	15	or	or	CCONJ
ejpam-4673	85	16	complement	complement	VERB
ejpam-4673	85	17	differentiating	differentiating	NOUN
ejpam-4673	85	18	and	and	CCONJ
ejpam-4673	85	19	pointwise	pointwise	VERB
ejpam-4673	85	20	non	non	ADJ
ejpam-4673	85	21	-	-	ADJ
ejpam-4673	85	22	dominating	dominating	ADJ
ejpam-4673	85	23	or	or	CCONJ
ejpam-4673	85	24	differentiating	differentiating	NOUN
ejpam-4673	85	25	-	-	PUNCT
ejpam-4673	85	26	dominating	dominating	NOUN
ejpam-4673	85	27	in	in	ADP
ejpam-4673	85	28	g	g	NOUN
ejpam-4673	85	29	)	)	PUNCT
ejpam-4673	85	30	if	if	SCONJ
ejpam-4673	85	31	for	for	ADP
ejpam-4673	85	32	each	each	DET
ejpam-4673	85	33	v	v	NUM
ejpam-4673	85	34	∈	∈	NOUN
ejpam-4673	85	35	v	v	NOUN
ejpam-4673	85	36	(	(	PUNCT
ejpam-4673	85	37	g)\s	g)\s	NOUN
ejpam-4673	85	38	,	,	PUNCT
ejpam-4673	86	1	[	[	X
ejpam-4673	86	2	v	v	X
ejpam-4673	86	3	(	(	PUNCT
ejpam-4673	86	4	g)\ng[v]]∩s	g)\ng[v]]∩s	PROPN
ejpam-4673	86	5	=	=	SYM
ejpam-4673	86	6	ng(v)∩s	ng(v)∩s	PROPN
ejpam-4673	86	7	̸=	̸=	PROPN
ejpam-4673	86	8	∅.	∅.	ADP
ejpam-4673	86	9	the	the	DET
ejpam-4673	86	10	smallest	small	ADJ
ejpam-4673	86	11	cardinality	cardinality	NOUN
ejpam-4673	86	12	of	of	ADP
ejpam-4673	86	13	a	a	DET
ejpam-4673	86	14	complement	complement	NOUN
ejpam-4673	86	15	differentiating	differentiate	VERB
ejpam-4673	86	16	(	(	PUNCT
ejpam-4673	86	17	resp	resp	NOUN
ejpam-4673	86	18	.	.	PUNCT
ejpam-4673	87	1	complement	complement	VERB
ejpam-4673	87	2	differentiating	differentiating	NOUN
ejpam-4673	87	3	-	-	PUNCT
ejpam-4673	87	4	dominating	dominating	NOUN
ejpam-4673	87	5	)	)	PUNCT
ejpam-4673	87	6	set	set	VERB
ejpam-4673	87	7	in	in	ADP
ejpam-4673	87	8	g	g	PROPN
ejpam-4673	87	9	is	be	AUX
ejpam-4673	87	10	denoted	denote	VERB
ejpam-4673	87	11	by	by	ADP
ejpam-4673	87	12	cdn(g	cdn(g	PROPN
ejpam-4673	87	13	)	)	PUNCT
ejpam-4673	87	14	(	(	PUNCT
ejpam-4673	87	15	resp	resp	NOUN
ejpam-4673	87	16	.	.	PUNCT
ejpam-4673	88	1	cdpnd(g	cdpnd(g	VERB
ejpam-4673	88	2	)	)	PUNCT
ejpam-4673	88	3	)	)	PUNCT
ejpam-4673	88	4	.	.	PUNCT
ejpam-4673	89	1	any	any	DET
ejpam-4673	89	2	complement	complement	NOUN
ejpam-4673	89	3	-	-	PUNCT
ejpam-4673	89	4	differentiating	differentiate	VERB
ejpam-4673	89	5	(	(	PUNCT
ejpam-4673	89	6	resp	resp	NOUN
ejpam-4673	89	7	.	.	PUNCT
ejpam-4673	90	1	complement	complement	VERB
ejpam-4673	90	2	differentiating	differentiating	NOUN
ejpam-4673	90	3	-	-	PUNCT
ejpam-4673	90	4	dominating	dominating	NOUN
ejpam-4673	90	5	)	)	PUNCT
ejpam-4673	90	6	set	set	VERB
ejpam-4673	90	7	in	in	ADP
ejpam-4673	90	8	g	g	PROPN
ejpam-4673	90	9	with	with	ADP
ejpam-4673	90	10	cardinality	cardinality	PROPN
ejpam-4673	90	11	cdn(g	cdn(g	PROPN
ejpam-4673	90	12	)	)	PUNCT
ejpam-4673	90	13	(	(	PUNCT
ejpam-4673	90	14	resp	resp	NOUN
ejpam-4673	90	15	.	.	PUNCT
ejpam-4673	91	1	cdpnd(g	cdpnd(g	VERB
ejpam-4673	91	2	)	)	PUNCT
ejpam-4673	91	3	)	)	PUNCT
ejpam-4673	92	1	is	be	AUX
ejpam-4673	92	2	called	call	VERB
ejpam-4673	92	3	a	a	DET
ejpam-4673	92	4	cdn	cdn	NOUN
ejpam-4673	92	5	-	-	PUNCT
ejpam-4673	92	6	set	set	VERB
ejpam-4673	92	7	(	(	PUNCT
ejpam-4673	92	8	resp	resp	NOUN
ejpam-4673	92	9	.	.	PUNCT
ejpam-4673	93	1	a	a	DET
ejpam-4673	93	2	cdpnd	cdpnd	NOUN
ejpam-4673	93	3	-	-	PUNCT
ejpam-4673	93	4	set	set	NOUN
ejpam-4673	93	5	)	)	PUNCT
ejpam-4673	93	6	in	in	ADP
ejpam-4673	93	7	g.	g.	PROPN
ejpam-4673	93	8	clearly	clearly	ADV
ejpam-4673	93	9	,	,	PUNCT
ejpam-4673	93	10	cdn(g	cdn(g	PROPN
ejpam-4673	93	11	)	)	PUNCT
ejpam-4673	93	12	=	=	SYM
ejpam-4673	93	13	dn(g	dn(g	X
ejpam-4673	93	14	)	)	PUNCT
ejpam-4673	93	15	and	and	CCONJ
ejpam-4673	93	16	cdpnd(g	cdpnd(g	ADP
ejpam-4673	93	17	)	)	PUNCT
ejpam-4673	93	18	=	=	NOUN
ejpam-4673	93	19	γd(g	γd(g	NUM
ejpam-4673	93	20	)	)	PUNCT
ejpam-4673	93	21	.	.	PUNCT
ejpam-4673	94	1	let	let	VERB
ejpam-4673	94	2	g	g	NOUN
ejpam-4673	94	3	and	and	CCONJ
ejpam-4673	94	4	h	h	NOUN
ejpam-4673	94	5	be	be	VERB
ejpam-4673	94	6	any	any	DET
ejpam-4673	94	7	two	two	NUM
ejpam-4673	94	8	graphs	graph	NOUN
ejpam-4673	94	9	.	.	PUNCT
ejpam-4673	95	1	the	the	DET
ejpam-4673	95	2	join	join	NOUN
ejpam-4673	95	3	g	g	PROPN
ejpam-4673	95	4	+	+	CCONJ
ejpam-4673	95	5	h	h	NOUN
ejpam-4673	95	6	is	be	AUX
ejpam-4673	95	7	the	the	DET
ejpam-4673	95	8	graph	graph	NOUN
ejpam-4673	95	9	with	with	ADP
ejpam-4673	95	10	vertex	vertex	NOUN
ejpam-4673	95	11	set	set	VERB
ejpam-4673	95	12	v	v	NOUN
ejpam-4673	95	13	(	(	PUNCT
ejpam-4673	95	14	g+h	g+h	NOUN
ejpam-4673	95	15	)	)	PUNCT
ejpam-4673	95	16	=	=	SYM
ejpam-4673	95	17	v	v	NOUN
ejpam-4673	95	18	(	(	PUNCT
ejpam-4673	95	19	g)∪	g)∪	VERB
ejpam-4673	95	20	v	v	NUM
ejpam-4673	95	21	(	(	PUNCT
ejpam-4673	95	22	h	h	NOUN
ejpam-4673	95	23	)	)	PUNCT
ejpam-4673	95	24	and	and	CCONJ
ejpam-4673	95	25	edge	edge	NOUN
ejpam-4673	95	26	set	set	VERB
ejpam-4673	95	27	e(g+h	e(g+h	NUM
ejpam-4673	95	28	)	)	PUNCT
ejpam-4673	96	1	=	=	SYM
ejpam-4673	96	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4673	96	3	{	{	PUNCT
ejpam-4673	96	4	uv	uv	NOUN
ejpam-4673	96	5	:	:	PUNCT
ejpam-4673	96	6	u	u	PROPN
ejpam-4673	96	7	∈	∈	PROPN
ejpam-4673	96	8	v	v	ADP
ejpam-4673	96	9	(	(	PUNCT
ejpam-4673	96	10	g	g	NOUN
ejpam-4673	96	11	)	)	PUNCT
ejpam-4673	96	12	,	,	PUNCT
ejpam-4673	96	13	v	v	X
ejpam-4673	96	14	∈	∈	PROPN
ejpam-4673	96	15	v	v	NOUN
ejpam-4673	96	16	(	(	PUNCT
ejpam-4673	96	17	h	h	NOUN
ejpam-4673	96	18	)	)	PUNCT
ejpam-4673	96	19	}	}	PUNCT
ejpam-4673	96	20	.	.	PUNCT
ejpam-4673	97	1	the	the	DET
ejpam-4673	97	2	corona	corona	NOUN
ejpam-4673	97	3	g	g	PROPN
ejpam-4673	97	4	◦	◦	NOUN
ejpam-4673	97	5	h	h	NOUN
ejpam-4673	97	6	is	be	AUX
ejpam-4673	97	7	the	the	DET
ejpam-4673	97	8	graph	graph	NOUN
ejpam-4673	97	9	obtained	obtain	VERB
ejpam-4673	97	10	by	by	ADP
ejpam-4673	97	11	taking	take	VERB
ejpam-4673	97	12	one	one	NUM
ejpam-4673	97	13	copy	copy	NOUN
ejpam-4673	97	14	of	of	ADP
ejpam-4673	97	15	g	g	PROPN
ejpam-4673	97	16	and	and	CCONJ
ejpam-4673	97	17	|v	|v	PROPN
ejpam-4673	97	18	(	(	PUNCT
ejpam-4673	97	19	g)|	g)|	NOUN
ejpam-4673	97	20	copies	copy	NOUN
ejpam-4673	97	21	of	of	ADP
ejpam-4673	97	22	h	h	NOUN
ejpam-4673	97	23	,	,	PUNCT
ejpam-4673	97	24	and	and	CCONJ
ejpam-4673	97	25	then	then	ADV
ejpam-4673	97	26	joining	join	VERB
ejpam-4673	97	27	the	the	DET
ejpam-4673	97	28	ith	ith	PROPN
ejpam-4673	97	29	vertex	vertex	NOUN
ejpam-4673	97	30	of	of	ADP
ejpam-4673	97	31	g	g	NOUN
ejpam-4673	97	32	to	to	ADP
ejpam-4673	97	33	every	every	DET
ejpam-4673	97	34	vertex	vertex	NOUN
ejpam-4673	97	35	of	of	ADP
ejpam-4673	97	36	the	the	DET
ejpam-4673	97	37	ith	ith	PROPN
ejpam-4673	97	38	copy	copy	NOUN
ejpam-4673	97	39	of	of	ADP
ejpam-4673	97	40	h.	h.	PROPN
ejpam-4673	97	41	we	we	PRON
ejpam-4673	97	42	denote	denote	VERB
ejpam-4673	97	43	by	by	ADP
ejpam-4673	97	44	hv	hv	PROPN
ejpam-4673	98	1	the	the	DET
ejpam-4673	98	2	copy	copy	NOUN
ejpam-4673	98	3	of	of	ADP
ejpam-4673	98	4	h	h	NOUN
ejpam-4673	98	5	in	in	ADP
ejpam-4673	98	6	g	g	PROPN
ejpam-4673	98	7	◦	◦	NOUN
ejpam-4673	98	8	h	h	NOUN
ejpam-4673	98	9	corresponding	correspond	VERB
ejpam-4673	98	10	to	to	ADP
ejpam-4673	98	11	the	the	DET
ejpam-4673	98	12	vertex	vertex	NOUN
ejpam-4673	98	13	v	v	ADP
ejpam-4673	98	14	∈	∈	PROPN
ejpam-4673	98	15	g	g	NOUN
ejpam-4673	98	16	and	and	CCONJ
ejpam-4673	98	17	write	write	VERB
ejpam-4673	98	18	v	v	ADP
ejpam-4673	98	19	+	+	CCONJ
ejpam-4673	98	20	hv	hv	NOUN
ejpam-4673	98	21	for	for	ADP
ejpam-4673	98	22	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-4673	98	23	+	+	X
ejpam-4673	98	24	hv	hv	X
ejpam-4673	98	25	.	.	PUNCT
ejpam-4673	99	1	the	the	DET
ejpam-4673	99	2	lexicographic	lexicographic	ADJ
ejpam-4673	99	3	product	product	NOUN
ejpam-4673	99	4	g[h	g[h	PROPN
ejpam-4673	99	5	]	]	PUNCT
ejpam-4673	99	6	is	be	AUX
ejpam-4673	99	7	the	the	DET
ejpam-4673	99	8	graph	graph	NOUN
ejpam-4673	99	9	with	with	ADP
ejpam-4673	99	10	vertex	vertex	NOUN
ejpam-4673	99	11	set	set	VERB
ejpam-4673	99	12	s.	s.	PROPN
ejpam-4673	99	13	canoy	canoy	PROPN
ejpam-4673	99	14	jr	jr	PROPN
ejpam-4673	99	15	.	.	PROPN
ejpam-4673	99	16	,	,	PUNCT
ejpam-4673	99	17	c.	c.	PROPN
ejpam-4673	99	18	saromines	saromine	VERB
ejpam-4673	99	19	/	/	SYM
ejpam-4673	99	20	eur	eur	PROPN
ejpam-4673	99	21	.	.	PUNCT
ejpam-4673	100	1	j.	j.	PROPN
ejpam-4673	100	2	pure	pure	PROPN
ejpam-4673	100	3	appl	appl	PROPN
ejpam-4673	100	4	.	.	PROPN
ejpam-4673	100	5	math	math	PROPN
ejpam-4673	100	6	,	,	PUNCT
ejpam-4673	100	7	16	16	NUM
ejpam-4673	100	8	(	(	PUNCT
ejpam-4673	100	9	1	1	NUM
ejpam-4673	100	10	)	)	PUNCT
ejpam-4673	100	11	(	(	PUNCT
ejpam-4673	100	12	2023	2023	NUM
ejpam-4673	100	13	)	)	PUNCT
ejpam-4673	100	14	,	,	PUNCT
ejpam-4673	100	15	440	440	NUM
ejpam-4673	100	16	-	-	SYM
ejpam-4673	100	17	453	453	NUM
ejpam-4673	100	18	443	443	NUM
ejpam-4673	100	19	v	v	NOUN
ejpam-4673	100	20	(	(	PUNCT
ejpam-4673	100	21	g[h	g[h	PROPN
ejpam-4673	100	22	]	]	PUNCT
ejpam-4673	100	23	)	)	PUNCT
ejpam-4673	101	1	=	=	SYM
ejpam-4673	101	2	v	v	X
ejpam-4673	101	3	(	(	PUNCT
ejpam-4673	101	4	g	g	NOUN
ejpam-4673	101	5	)	)	PUNCT
ejpam-4673	101	6	×	×	NOUN
ejpam-4673	101	7	v	v	NOUN
ejpam-4673	101	8	(	(	PUNCT
ejpam-4673	101	9	h	h	NOUN
ejpam-4673	101	10	)	)	PUNCT
ejpam-4673	101	11	and	and	CCONJ
ejpam-4673	101	12	(	(	PUNCT
ejpam-4673	101	13	v	v	NOUN
ejpam-4673	101	14	,	,	PUNCT
ejpam-4673	101	15	a)(u	a)(u	ADJ
ejpam-4673	101	16	,	,	PUNCT
ejpam-4673	101	17	b	b	X
ejpam-4673	101	18	)	)	PUNCT
ejpam-4673	101	19	∈	∈	NOUN
ejpam-4673	101	20	e(g[h	e(g[h	NOUN
ejpam-4673	101	21	]	]	PUNCT
ejpam-4673	101	22	)	)	PUNCT
ejpam-4673	101	23	if	if	SCONJ
ejpam-4673	101	24	and	and	CCONJ
ejpam-4673	101	25	only	only	ADV
ejpam-4673	101	26	if	if	SCONJ
ejpam-4673	101	27	either	either	DET
ejpam-4673	101	28	uv	uv	PROPN
ejpam-4673	101	29	∈	∈	PROPN
ejpam-4673	101	30	e(g	e(g	PROPN
ejpam-4673	101	31	)	)	PUNCT
ejpam-4673	101	32	or	or	CCONJ
ejpam-4673	101	33	u	u	X
ejpam-4673	101	34	=	=	PROPN
ejpam-4673	101	35	v	v	PROPN
ejpam-4673	101	36	and	and	CCONJ
ejpam-4673	101	37	ab	ab	PROPN
ejpam-4673	101	38	∈	∈	PROPN
ejpam-4673	101	39	e(h	e(h	PROPN
ejpam-4673	101	40	)	)	PUNCT
ejpam-4673	101	41	.	.	PUNCT
ejpam-4673	102	1	any	any	DET
ejpam-4673	102	2	non	non	ADJ
ejpam-4673	102	3	-	-	ADJ
ejpam-4673	102	4	empty	empty	ADJ
ejpam-4673	102	5	set	set	NOUN
ejpam-4673	102	6	c	c	NOUN
ejpam-4673	102	7	⊆	⊆	NUM
ejpam-4673	102	8	v	v	NOUN
ejpam-4673	102	9	(	(	PUNCT
ejpam-4673	102	10	g	g	NOUN
ejpam-4673	102	11	)	)	PUNCT
ejpam-4673	102	12	×	×	NOUN
ejpam-4673	102	13	v	v	NOUN
ejpam-4673	102	14	(	(	PUNCT
ejpam-4673	102	15	h	h	NOUN
ejpam-4673	102	16	)	)	PUNCT
ejpam-4673	102	17	can	can	AUX
ejpam-4673	102	18	be	be	AUX
ejpam-4673	102	19	expressed	express	VERB
ejpam-4673	102	20	as	as	ADP
ejpam-4673	102	21	c	c	NOUN
ejpam-4673	102	22	=	=	PUNCT
ejpam-4673	102	23	⋃	⋃	PROPN
ejpam-4673	102	24	x∈s	x∈s	NOUN
ejpam-4673	103	1	[	[	X
ejpam-4673	103	2	{	{	PUNCT
ejpam-4673	103	3	x	x	NOUN
ejpam-4673	103	4	}	}	PUNCT
ejpam-4673	103	5	×	×	PROPN
ejpam-4673	103	6	tx	tx	PROPN
ejpam-4673	103	7	]	]	X
ejpam-4673	103	8	,	,	PUNCT
ejpam-4673	103	9	where	where	SCONJ
ejpam-4673	103	10	s	s	VERB
ejpam-4673	103	11	⊆	⊆	NUM
ejpam-4673	103	12	v	v	NOUN
ejpam-4673	103	13	(	(	PUNCT
ejpam-4673	103	14	g	g	NOUN
ejpam-4673	103	15	)	)	PUNCT
ejpam-4673	103	16	and	and	CCONJ
ejpam-4673	103	17	tx	tx	VERB
ejpam-4673	103	18	⊆	⊆	NUM
ejpam-4673	103	19	v	v	NOUN
ejpam-4673	103	20	(	(	PUNCT
ejpam-4673	103	21	h	h	NOUN
ejpam-4673	103	22	)	)	PUNCT
ejpam-4673	103	23	for	for	ADP
ejpam-4673	103	24	each	each	DET
ejpam-4673	103	25	x	x	PROPN
ejpam-4673	103	26	∈	∈	PROPN
ejpam-4673	103	27	s.	s.	PROPN
ejpam-4673	103	28	specifically	specifically	ADV
ejpam-4673	103	29	,	,	PUNCT
ejpam-4673	103	30	tx	tx	PROPN
ejpam-4673	103	31	=	=	PUNCT
ejpam-4673	103	32	{	{	PUNCT
ejpam-4673	103	33	a	a	DET
ejpam-4673	103	34	∈	∈	PROPN
ejpam-4673	103	35	v	v	ADP
ejpam-4673	103	36	(	(	PUNCT
ejpam-4673	103	37	h	h	NOUN
ejpam-4673	103	38	)	)	PUNCT
ejpam-4673	103	39	:	:	PUNCT
ejpam-4673	103	40	(	(	PUNCT
ejpam-4673	103	41	x	x	X
ejpam-4673	103	42	,	,	PUNCT
ejpam-4673	103	43	a	a	PRON
ejpam-4673	103	44	)	)	PUNCT
ejpam-4673	103	45	∈	∈	PROPN
ejpam-4673	103	46	c	c	NOUN
ejpam-4673	103	47	}	}	PUNCT
ejpam-4673	103	48	for	for	ADP
ejpam-4673	103	49	each	each	DET
ejpam-4673	103	50	x	x	PROPN
ejpam-4673	103	51	∈	∈	PROPN
ejpam-4673	103	52	s.	s.	PROPN
ejpam-4673	103	53	3	3	X
ejpam-4673	103	54	.	.	NOUN
ejpam-4673	103	55	results	result	NOUN
ejpam-4673	103	56	throughout	throughout	ADP
ejpam-4673	103	57	,	,	PUNCT
ejpam-4673	103	58	a	a	DET
ejpam-4673	103	59	graph	graph	NOUN
ejpam-4673	103	60	is	be	AUX
ejpam-4673	103	61	understood	understand	VERB
ejpam-4673	103	62	to	to	PART
ejpam-4673	103	63	be	be	AUX
ejpam-4673	103	64	distance	distance	NOUN
ejpam-4673	103	65	-	-	PUNCT
ejpam-4673	103	66	two	two	NUM
ejpam-4673	103	67	point	point	NOUN
ejpam-4673	103	68	distinguishing	distinguish	VERB
ejpam-4673	103	69	whenever	whenever	SCONJ
ejpam-4673	103	70	a	a	DET
ejpam-4673	103	71	hop	hop	NOUN
ejpam-4673	103	72	differentiating	differentiate	VERB
ejpam-4673	103	73	set	set	NOUN
ejpam-4673	103	74	is	be	AUX
ejpam-4673	103	75	assumed	assume	VERB
ejpam-4673	103	76	(	(	PUNCT
ejpam-4673	103	77	or	or	CCONJ
ejpam-4673	103	78	mentioned	mention	VERB
ejpam-4673	103	79	)	)	PUNCT
ejpam-4673	103	80	in	in	ADP
ejpam-4673	103	81	it	it	PRON
ejpam-4673	103	82	.	.	PUNCT
ejpam-4673	104	1	lemma	lemma	PROPN
ejpam-4673	104	2	1	1	X
ejpam-4673	104	3	.	.	PUNCT
ejpam-4673	105	1	let	let	VERB
ejpam-4673	105	2	g	g	PRON
ejpam-4673	105	3	be	be	AUX
ejpam-4673	105	4	a	a	DET
ejpam-4673	105	5	graph	graph	NOUN
ejpam-4673	105	6	on	on	ADP
ejpam-4673	105	7	n	n	DET
ejpam-4673	105	8	vertices	vertex	NOUN
ejpam-4673	105	9	.	.	PUNCT
ejpam-4673	106	1	then	then	ADV
ejpam-4673	106	2	γdh(g	γdh(g	PRON
ejpam-4673	106	3	)	)	PUNCT
ejpam-4673	106	4	≥	≥	NOUN
ejpam-4673	106	5	⌈	⌈	NOUN
ejpam-4673	106	6	lnn+	lnn+	PUNCT
ejpam-4673	106	7	ln2	ln2	ADJ
ejpam-4673	106	8	ln2	ln2	ADJ
ejpam-4673	106	9	⌉.	⌉.	ADJ
ejpam-4673	106	10	proof	proof	NOUN
ejpam-4673	106	11	.	.	PUNCT
ejpam-4673	107	1	let	let	VERB
ejpam-4673	107	2	s	s	PRON
ejpam-4673	107	3	be	be	AUX
ejpam-4673	107	4	a	a	DET
ejpam-4673	107	5	hop	hop	NOUN
ejpam-4673	107	6	differentiating	differentiate	VERB
ejpam-4673	107	7	hop	hop	NOUN
ejpam-4673	107	8	dominating	dominating	NOUN
ejpam-4673	107	9	set	set	NOUN
ejpam-4673	107	10	of	of	ADP
ejpam-4673	107	11	g.	g.	PROPN
ejpam-4673	107	12	since	since	SCONJ
ejpam-4673	107	13	s	s	PROPN
ejpam-4673	107	14	is	be	AUX
ejpam-4673	107	15	a	a	DET
ejpam-4673	107	16	hop	hop	NOUN
ejpam-4673	107	17	dominating	dominating	NOUN
ejpam-4673	107	18	set	set	NOUN
ejpam-4673	107	19	,	,	PUNCT
ejpam-4673	107	20	n2	n2	ADJ
ejpam-4673	107	21	g[v]∩s	g[v]∩s	PROPN
ejpam-4673	107	22	̸=	̸=	PROPN
ejpam-4673	107	23	∅	∅	NOUN
ejpam-4673	107	24	for	for	ADP
ejpam-4673	107	25	every	every	DET
ejpam-4673	107	26	v	v	NUM
ejpam-4673	107	27	∈	∈	NOUN
ejpam-4673	107	28	v	v	NOUN
ejpam-4673	107	29	(	(	PUNCT
ejpam-4673	107	30	g	g	NOUN
ejpam-4673	107	31	)	)	PUNCT
ejpam-4673	107	32	.	.	PUNCT
ejpam-4673	108	1	moreover	moreover	ADV
ejpam-4673	108	2	,	,	PUNCT
ejpam-4673	108	3	because	because	SCONJ
ejpam-4673	108	4	it	it	PRON
ejpam-4673	108	5	is	be	AUX
ejpam-4673	108	6	hop	hop	NOUN
ejpam-4673	108	7	differentiating	differentiate	VERB
ejpam-4673	108	8	,	,	PUNCT
ejpam-4673	108	9	it	it	PRON
ejpam-4673	108	10	follows	follow	VERB
ejpam-4673	108	11	that	that	SCONJ
ejpam-4673	108	12	2|s|	2|s|	NUM
ejpam-4673	108	13	>	>	X
ejpam-4673	108	14	n.	n.	NOUN
ejpam-4673	108	15	hence	hence	ADV
ejpam-4673	108	16	,	,	PUNCT
ejpam-4673	108	17	|s|	|s|	X
ejpam-4673	108	18	≥	≥	NOUN
ejpam-4673	108	19	⌈	⌈	NOUN
ejpam-4673	108	20	lnn+ln2	lnn+ln2	X
ejpam-4673	108	21	ln2	ln2	ADJ
ejpam-4673	108	22	⌉.	⌉.	ADV
ejpam-4673	108	23	in	in	ADP
ejpam-4673	108	24	particular	particular	ADJ
ejpam-4673	108	25	,	,	PUNCT
ejpam-4673	108	26	if	if	SCONJ
ejpam-4673	108	27	s	s	VERB
ejpam-4673	108	28	is	be	AUX
ejpam-4673	108	29	a	a	DET
ejpam-4673	108	30	γdh	γdh	NOUN
ejpam-4673	108	31	-	-	PUNCT
ejpam-4673	108	32	set	set	NOUN
ejpam-4673	108	33	of	of	ADP
ejpam-4673	108	34	g	g	NOUN
ejpam-4673	108	35	,	,	PUNCT
ejpam-4673	108	36	then	then	ADV
ejpam-4673	108	37	γdh(g	γdh(g	PRON
ejpam-4673	108	38	)	)	PUNCT
ejpam-4673	108	39	≥	≥	PROPN
ejpam-4673	108	40	⌈	⌈	NOUN
ejpam-4673	108	41	lnn+ln2	lnn+ln2	X
ejpam-4673	108	42	ln2	ln2	ADJ
ejpam-4673	108	43	⌉.	⌉.	ADV
ejpam-4673	108	44	theorem	theorem	ADJ
ejpam-4673	108	45	1	1	NUM
ejpam-4673	108	46	.	.	PUNCT
ejpam-4673	109	1	let	let	VERB
ejpam-4673	109	2	g1	g1	PROPN
ejpam-4673	109	3	,	,	PUNCT
ejpam-4673	109	4	g2	g2	PROPN
ejpam-4673	109	5	,	,	PUNCT
ejpam-4673	109	6	.	.	PUNCT
ejpam-4673	109	7	.	.	PUNCT
ejpam-4673	110	1	.	.	PUNCT
ejpam-4673	111	1	,	,	PUNCT
ejpam-4673	111	2	gk	gk	PROPN
ejpam-4673	111	3	be	be	AUX
ejpam-4673	111	4	the	the	DET
ejpam-4673	111	5	distinct	distinct	ADJ
ejpam-4673	111	6	(	(	PUNCT
ejpam-4673	111	7	distance	distance	NOUN
ejpam-4673	111	8	-	-	PUNCT
ejpam-4673	111	9	two	two	NUM
ejpam-4673	111	10	point	point	NOUN
ejpam-4673	111	11	distinguishing	distinguish	VERB
ejpam-4673	111	12	)	)	PUNCT
ejpam-4673	111	13	components	component	NOUN
ejpam-4673	111	14	of	of	ADP
ejpam-4673	111	15	g	g	NOUN
ejpam-4673	111	16	,	,	PUNCT
ejpam-4673	111	17	where	where	SCONJ
ejpam-4673	111	18	k	k	PROPN
ejpam-4673	111	19	≥	≥	NUM
ejpam-4673	112	1	2	2	NUM
ejpam-4673	112	2	.	.	PUNCT
ejpam-4673	112	3	then	then	ADV
ejpam-4673	112	4	s	s	VERB
ejpam-4673	112	5	is	be	AUX
ejpam-4673	112	6	a	a	DET
ejpam-4673	112	7	hop	hop	NOUN
ejpam-4673	112	8	differentiating	differentiate	VERB
ejpam-4673	112	9	hop	hop	NOUN
ejpam-4673	112	10	dominating	dominating	NOUN
ejpam-4673	112	11	set	set	VERB
ejpam-4673	112	12	in	in	ADP
ejpam-4673	112	13	g	g	PROPN
ejpam-4673	112	14	if	if	SCONJ
ejpam-4673	113	1	and	and	CCONJ
ejpam-4673	113	2	only	only	ADV
ejpam-4673	113	3	if	if	SCONJ
ejpam-4673	113	4	sj	sj	ADP
ejpam-4673	113	5	=	=	NOUN
ejpam-4673	113	6	s	s	PART
ejpam-4673	113	7	∩	∩	ADJ
ejpam-4673	113	8	v	v	NOUN
ejpam-4673	113	9	(	(	PUNCT
ejpam-4673	113	10	gj	gj	NOUN
ejpam-4673	113	11	)	)	PUNCT
ejpam-4673	113	12	is	be	AUX
ejpam-4673	113	13	a	a	DET
ejpam-4673	113	14	hop	hop	NOUN
ejpam-4673	113	15	differentiating	differentiate	VERB
ejpam-4673	113	16	hop	hop	NOUN
ejpam-4673	113	17	dominating	dominating	NOUN
ejpam-4673	113	18	set	set	VERB
ejpam-4673	113	19	in	in	ADP
ejpam-4673	113	20	gj	gj	NOUN
ejpam-4673	113	21	for	for	ADP
ejpam-4673	113	22	each	each	DET
ejpam-4673	113	23	j	j	PROPN
ejpam-4673	113	24	∈	∈	PROPN
ejpam-4673	113	25	{	{	PUNCT
ejpam-4673	113	26	1	1	NUM
ejpam-4673	113	27	,	,	PUNCT
ejpam-4673	113	28	2	2	NUM
ejpam-4673	113	29	,	,	PUNCT
ejpam-4673	113	30	.	.	PUNCT
ejpam-4673	113	31	.	.	PUNCT
ejpam-4673	114	1	.	.	PUNCT
ejpam-4673	115	1	,	,	PUNCT
ejpam-4673	115	2	k	k	X
ejpam-4673	115	3	}	}	PUNCT
ejpam-4673	115	4	.	.	PUNCT
ejpam-4673	116	1	proof	proof	NOUN
ejpam-4673	116	2	.	.	PUNCT
ejpam-4673	117	1	suppose	suppose	VERB
ejpam-4673	117	2	s	s	PRON
ejpam-4673	117	3	is	be	AUX
ejpam-4673	117	4	a	a	DET
ejpam-4673	117	5	hop	hop	NOUN
ejpam-4673	117	6	differentiating	differentiate	VERB
ejpam-4673	117	7	hop	hop	NOUN
ejpam-4673	117	8	dominating	dominating	NOUN
ejpam-4673	117	9	set	set	VERB
ejpam-4673	117	10	in	in	ADP
ejpam-4673	117	11	g	g	NOUN
ejpam-4673	117	12	and	and	CCONJ
ejpam-4673	117	13	let	let	VERB
ejpam-4673	117	14	j	j	PROPN
ejpam-4673	117	15	∈	∈	PROPN
ejpam-4673	117	16	{	{	PUNCT
ejpam-4673	117	17	1	1	NUM
ejpam-4673	117	18	,	,	PUNCT
ejpam-4673	117	19	2	2	NUM
ejpam-4673	117	20	,	,	PUNCT
ejpam-4673	117	21	.	.	PUNCT
ejpam-4673	117	22	.	.	PUNCT
ejpam-4673	118	1	.	.	PUNCT
ejpam-4673	119	1	,	,	PUNCT
ejpam-4673	119	2	k	k	X
ejpam-4673	119	3	}	}	PUNCT
ejpam-4673	119	4	.	.	PUNCT
ejpam-4673	120	1	let	let	VERB
ejpam-4673	120	2	v	v	NUM
ejpam-4673	120	3	∈	∈	PROPN
ejpam-4673	120	4	v	v	NOUN
ejpam-4673	120	5	(	(	PUNCT
ejpam-4673	120	6	gj	gj	NOUN
ejpam-4673	120	7	)	)	PUNCT
ejpam-4673	120	8	\	\	PUNCT
ejpam-4673	121	1	sj	sj	INTJ
ejpam-4673	121	2	.	.	PUNCT
ejpam-4673	122	1	since	since	SCONJ
ejpam-4673	122	2	v	v	NUM
ejpam-4673	122	3	/∈	/∈	PUNCT
ejpam-4673	122	4	s	s	PART
ejpam-4673	122	5	and	and	CCONJ
ejpam-4673	122	6	s	s	VERB
ejpam-4673	122	7	is	be	AUX
ejpam-4673	122	8	a	a	DET
ejpam-4673	122	9	hop	hop	NOUN
ejpam-4673	122	10	dominating	dominating	NOUN
ejpam-4673	122	11	set	set	NOUN
ejpam-4673	122	12	,	,	PUNCT
ejpam-4673	122	13	there	there	PRON
ejpam-4673	122	14	exists	exist	VERB
ejpam-4673	122	15	w	w	PROPN
ejpam-4673	122	16	∈	∈	PROPN
ejpam-4673	122	17	s	s	VERB
ejpam-4673	122	18	such	such	ADJ
ejpam-4673	122	19	that	that	DET
ejpam-4673	122	20	v	v	PROPN
ejpam-4673	122	21	∈	∈	PROPN
ejpam-4673	122	22	n2	n2	NOUN
ejpam-4673	122	23	g(w	g(w	PROPN
ejpam-4673	122	24	)	)	PUNCT
ejpam-4673	122	25	.	.	PUNCT
ejpam-4673	123	1	this	this	PRON
ejpam-4673	123	2	implies	imply	VERB
ejpam-4673	123	3	that	that	SCONJ
ejpam-4673	123	4	w	w	PROPN
ejpam-4673	123	5	∈	∈	PROPN
ejpam-4673	123	6	sj	sj	NOUN
ejpam-4673	123	7	and	and	CCONJ
ejpam-4673	123	8	v	v	ADP
ejpam-4673	123	9	∈	∈	PROPN
ejpam-4673	123	10	n2	n2	ADJ
ejpam-4673	123	11	gj	gj	NOUN
ejpam-4673	123	12	(	(	PUNCT
ejpam-4673	123	13	w	w	NOUN
ejpam-4673	123	14	)	)	PUNCT
ejpam-4673	123	15	.	.	PUNCT
ejpam-4673	124	1	this	this	PRON
ejpam-4673	124	2	shows	show	VERB
ejpam-4673	124	3	that	that	SCONJ
ejpam-4673	124	4	sj	sj	PROPN
ejpam-4673	124	5	is	be	AUX
ejpam-4673	124	6	a	a	DET
ejpam-4673	124	7	hop	hop	NOUN
ejpam-4673	124	8	dominating	dominating	NOUN
ejpam-4673	124	9	set	set	VERB
ejpam-4673	124	10	in	in	ADP
ejpam-4673	124	11	gj	gj	NOUN
ejpam-4673	124	12	.	.	PUNCT
ejpam-4673	125	1	next	next	ADV
ejpam-4673	125	2	,	,	PUNCT
ejpam-4673	125	3	let	let	VERB
ejpam-4673	125	4	a	a	DET
ejpam-4673	125	5	,	,	PUNCT
ejpam-4673	125	6	b	b	PROPN
ejpam-4673	125	7	∈	∈	PROPN
ejpam-4673	125	8	v	v	NOUN
ejpam-4673	125	9	(	(	PUNCT
ejpam-4673	125	10	gj	gj	NOUN
ejpam-4673	125	11	)	)	PUNCT
ejpam-4673	125	12	where	where	SCONJ
ejpam-4673	125	13	a	a	DET
ejpam-4673	125	14	̸=	̸=	PROPN
ejpam-4673	125	15	b.	b.	NOUN
ejpam-4673	125	16	since	since	SCONJ
ejpam-4673	125	17	s	s	PROPN
ejpam-4673	125	18	is	be	AUX
ejpam-4673	125	19	a	a	DET
ejpam-4673	125	20	hop	hop	NOUN
ejpam-4673	125	21	differentiating	differentiate	VERB
ejpam-4673	125	22	set	set	VERB
ejpam-4673	125	23	n2	n2	ADJ
ejpam-4673	125	24	gj	gj	NOUN
ejpam-4673	126	1	[	[	X
ejpam-4673	126	2	a	a	X
ejpam-4673	126	3	]	]	X
ejpam-4673	126	4	∩	∩	ADJ
ejpam-4673	126	5	sj	sj	NOUN
ejpam-4673	126	6	=	=	SYM
ejpam-4673	126	7	n2	n2	ADJ
ejpam-4673	126	8	g[a	g[a	PROPN
ejpam-4673	126	9	]	]	PUNCT
ejpam-4673	126	10	∩	∩	PROPN
ejpam-4673	126	11	s	s	PART
ejpam-4673	126	12	̸=	̸=	PROPN
ejpam-4673	126	13	n2	n2	PROPN
ejpam-4673	126	14	g[b	g[b	PROPN
ejpam-4673	126	15	]	]	PUNCT
ejpam-4673	126	16	∩	∩	PROPN
ejpam-4673	126	17	s	s	PART
ejpam-4673	126	18	=	=	SYM
ejpam-4673	126	19	n2	n2	ADJ
ejpam-4673	126	20	gj	gj	NOUN
ejpam-4673	126	21	[	[	X
ejpam-4673	126	22	b	b	X
ejpam-4673	126	23	]	]	X
ejpam-4673	126	24	∩	∩	ADJ
ejpam-4673	126	25	sj	sj	INTJ
ejpam-4673	126	26	.	.	PUNCT
ejpam-4673	127	1	thus	thus	ADV
ejpam-4673	127	2	,	,	PUNCT
ejpam-4673	127	3	sj	sj	PROPN
ejpam-4673	127	4	is	be	AUX
ejpam-4673	127	5	a	a	DET
ejpam-4673	127	6	hop	hop	NOUN
ejpam-4673	127	7	differentiating	differentiate	VERB
ejpam-4673	127	8	hop	hop	NOUN
ejpam-4673	127	9	dominating	dominating	NOUN
ejpam-4673	127	10	set	set	VERB
ejpam-4673	127	11	in	in	ADP
ejpam-4673	127	12	gj	gj	NOUN
ejpam-4673	127	13	for	for	ADP
ejpam-4673	127	14	each	each	DET
ejpam-4673	127	15	j	j	PROPN
ejpam-4673	127	16	∈	∈	PROPN
ejpam-4673	127	17	{	{	PUNCT
ejpam-4673	127	18	1	1	NUM
ejpam-4673	127	19	,	,	PUNCT
ejpam-4673	127	20	2	2	NUM
ejpam-4673	127	21	,	,	PUNCT
ejpam-4673	127	22	.	.	PUNCT
ejpam-4673	127	23	.	.	PUNCT
ejpam-4673	128	1	.	.	PUNCT
ejpam-4673	129	1	,	,	PUNCT
ejpam-4673	129	2	k	k	X
ejpam-4673	129	3	}	}	PUNCT
ejpam-4673	129	4	.	.	PUNCT
ejpam-4673	130	1	for	for	ADP
ejpam-4673	130	2	the	the	DET
ejpam-4673	130	3	converse	converse	NOUN
ejpam-4673	130	4	,	,	PUNCT
ejpam-4673	130	5	suppose	suppose	VERB
ejpam-4673	130	6	that	that	SCONJ
ejpam-4673	130	7	sj	sj	PROPN
ejpam-4673	130	8	=	=	SYM
ejpam-4673	130	9	s∩v	s∩v	PROPN
ejpam-4673	130	10	(	(	PUNCT
ejpam-4673	130	11	gj	gj	NOUN
ejpam-4673	130	12	)	)	PUNCT
ejpam-4673	130	13	is	be	AUX
ejpam-4673	130	14	a	a	DET
ejpam-4673	130	15	hop	hop	NOUN
ejpam-4673	130	16	differentiating	differentiate	VERB
ejpam-4673	130	17	hop	hop	NOUN
ejpam-4673	130	18	dominating	dominating	NOUN
ejpam-4673	130	19	set	set	VERB
ejpam-4673	130	20	in	in	ADP
ejpam-4673	130	21	gj	gj	NOUN
ejpam-4673	130	22	for	for	ADP
ejpam-4673	130	23	each	each	DET
ejpam-4673	130	24	j	j	PROPN
ejpam-4673	130	25	∈	∈	PROPN
ejpam-4673	130	26	{	{	PUNCT
ejpam-4673	130	27	1	1	NUM
ejpam-4673	130	28	,	,	PUNCT
ejpam-4673	130	29	2	2	NUM
ejpam-4673	130	30	,	,	PUNCT
ejpam-4673	130	31	.	.	PUNCT
ejpam-4673	130	32	.	.	PUNCT
ejpam-4673	131	1	.	.	PUNCT
ejpam-4673	132	1	,	,	PUNCT
ejpam-4673	132	2	k	k	X
ejpam-4673	132	3	}	}	PUNCT
ejpam-4673	132	4	.	.	PUNCT
ejpam-4673	133	1	then	then	ADV
ejpam-4673	133	2	clearly	clearly	ADV
ejpam-4673	133	3	,	,	PUNCT
ejpam-4673	133	4	s	s	VERB
ejpam-4673	133	5	is	be	AUX
ejpam-4673	133	6	a	a	DET
ejpam-4673	133	7	hop	hop	NOUN
ejpam-4673	133	8	dominating	dominating	NOUN
ejpam-4673	133	9	set	set	VERB
ejpam-4673	133	10	in	in	ADP
ejpam-4673	133	11	g.	g.	PROPN
ejpam-4673	133	12	let	let	VERB
ejpam-4673	133	13	v	v	NOUN
ejpam-4673	133	14	,	,	PUNCT
ejpam-4673	133	15	w	w	PROPN
ejpam-4673	133	16	∈	∈	PROPN
ejpam-4673	133	17	v	v	ADP
ejpam-4673	133	18	(	(	PUNCT
ejpam-4673	133	19	g	g	NOUN
ejpam-4673	133	20	)	)	PUNCT
ejpam-4673	133	21	with	with	ADP
ejpam-4673	133	22	v	v	ADP
ejpam-4673	133	23	̸=	̸=	PROPN
ejpam-4673	133	24	w	w	NOUN
ejpam-4673	133	25	and	and	CCONJ
ejpam-4673	133	26	let	let	VERB
ejpam-4673	133	27	gi	gi	VERB
ejpam-4673	133	28	and	and	CCONJ
ejpam-4673	133	29	gj	gj	PROPN
ejpam-4673	133	30	be	be	AUX
ejpam-4673	133	31	the	the	DET
ejpam-4673	133	32	components	component	NOUN
ejpam-4673	133	33	of	of	ADP
ejpam-4673	133	34	g	g	NOUN
ejpam-4673	133	35	with	with	ADP
ejpam-4673	133	36	v	v	NUM
ejpam-4673	133	37	∈	∈	PROPN
ejpam-4673	133	38	v	v	NOUN
ejpam-4673	133	39	(	(	PUNCT
ejpam-4673	133	40	gi	gi	NOUN
ejpam-4673	133	41	)	)	PUNCT
ejpam-4673	133	42	and	and	CCONJ
ejpam-4673	133	43	w	w	PROPN
ejpam-4673	133	44	∈	∈	PROPN
ejpam-4673	133	45	v	v	ADP
ejpam-4673	133	46	(	(	PUNCT
ejpam-4673	133	47	gj	gj	NOUN
ejpam-4673	133	48	)	)	PUNCT
ejpam-4673	133	49	.	.	PUNCT
ejpam-4673	134	1	if	if	SCONJ
ejpam-4673	134	2	i	i	PRON
ejpam-4673	134	3	̸=	̸=	PROPN
ejpam-4673	134	4	j	j	PROPN
ejpam-4673	134	5	,	,	PUNCT
ejpam-4673	134	6	then	then	ADV
ejpam-4673	134	7	n2	n2	PROPN
ejpam-4673	134	8	g[v	g[v	PROPN
ejpam-4673	134	9	]	]	PUNCT
ejpam-4673	134	10	∩	∩	X
ejpam-4673	134	11	s	s	PART
ejpam-4673	134	12	=	=	SYM
ejpam-4673	134	13	n2	n2	ADJ
ejpam-4673	134	14	gi	gi	X
ejpam-4673	135	1	[	[	X
ejpam-4673	135	2	v	v	X
ejpam-4673	135	3	]	]	X
ejpam-4673	135	4	∩	∩	NOUN
ejpam-4673	135	5	si	si	PROPN
ejpam-4673	135	6	̸=	̸=	PROPN
ejpam-4673	135	7	n2	n2	PROPN
ejpam-4673	135	8	gj	gj	NOUN
ejpam-4673	136	1	[	[	X
ejpam-4673	136	2	w	w	X
ejpam-4673	136	3	]	]	X
ejpam-4673	136	4	∩	∩	ADJ
ejpam-4673	136	5	sj	sj	NOUN
ejpam-4673	136	6	=	=	PROPN
ejpam-4673	136	7	n2	n2	PROPN
ejpam-4673	136	8	g[w	g[w	PROPN
ejpam-4673	136	9	]	]	PUNCT
ejpam-4673	136	10	∩	∩	PROPN
ejpam-4673	136	11	s.	s.	PROPN
ejpam-4673	136	12	if	if	SCONJ
ejpam-4673	136	13	i	i	PRON
ejpam-4673	136	14	=	=	SYM
ejpam-4673	136	15	j	j	PROPN
ejpam-4673	136	16	,	,	PUNCT
ejpam-4673	136	17	then	then	ADV
ejpam-4673	136	18	n2	n2	PROPN
ejpam-4673	136	19	g[v	g[v	PROPN
ejpam-4673	136	20	]	]	PUNCT
ejpam-4673	136	21	∩	∩	X
ejpam-4673	136	22	s	s	PART
ejpam-4673	136	23	=	=	SYM
ejpam-4673	136	24	n2	n2	ADJ
ejpam-4673	136	25	gi	gi	X
ejpam-4673	137	1	[	[	X
ejpam-4673	137	2	v	v	X
ejpam-4673	137	3	]	]	X
ejpam-4673	137	4	∩	∩	NOUN
ejpam-4673	137	5	si	si	PROPN
ejpam-4673	137	6	̸=	̸=	PROPN
ejpam-4673	137	7	n2	n2	NOUN
ejpam-4673	137	8	gi	gi	NOUN
ejpam-4673	138	1	[	[	X
ejpam-4673	138	2	w	w	X
ejpam-4673	138	3	]	]	X
ejpam-4673	138	4	∩	∩	ADJ
ejpam-4673	138	5	si	si	PROPN
ejpam-4673	138	6	=	=	SYM
ejpam-4673	138	7	n2	n2	PROPN
ejpam-4673	138	8	g[w	g[w	PROPN
ejpam-4673	138	9	]	]	PUNCT
ejpam-4673	138	10	∩	∩	PROPN
ejpam-4673	138	11	s	s	PART
ejpam-4673	138	12	s.	s.	PROPN
ejpam-4673	138	13	canoy	canoy	PROPN
ejpam-4673	138	14	jr	jr	PROPN
ejpam-4673	138	15	.	.	PROPN
ejpam-4673	138	16	,	,	PUNCT
ejpam-4673	138	17	c.	c.	PROPN
ejpam-4673	138	18	saromines	saromine	VERB
ejpam-4673	138	19	/	/	SYM
ejpam-4673	138	20	eur	eur	PROPN
ejpam-4673	138	21	.	.	PUNCT
ejpam-4673	139	1	j.	j.	PROPN
ejpam-4673	139	2	pure	pure	PROPN
ejpam-4673	139	3	appl	appl	PROPN
ejpam-4673	139	4	.	.	PROPN
ejpam-4673	139	5	math	math	PROPN
ejpam-4673	139	6	,	,	PUNCT
ejpam-4673	139	7	16	16	NUM
ejpam-4673	139	8	(	(	PUNCT
ejpam-4673	139	9	1	1	NUM
ejpam-4673	139	10	)	)	PUNCT
ejpam-4673	139	11	(	(	PUNCT
ejpam-4673	139	12	2023	2023	NUM
ejpam-4673	139	13	)	)	PUNCT
ejpam-4673	139	14	,	,	PUNCT
ejpam-4673	139	15	440	440	NUM
ejpam-4673	139	16	-	-	SYM
ejpam-4673	139	17	453	453	NUM
ejpam-4673	139	18	444	444	NUM
ejpam-4673	139	19	since	since	SCONJ
ejpam-4673	139	20	si	si	PROPN
ejpam-4673	139	21	is	be	AUX
ejpam-4673	139	22	a	a	DET
ejpam-4673	139	23	hop	hop	NOUN
ejpam-4673	139	24	differentiating	differentiate	VERB
ejpam-4673	139	25	set	set	NOUN
ejpam-4673	139	26	in	in	ADP
ejpam-4673	139	27	gi	gi	NOUN
ejpam-4673	139	28	.	.	PUNCT
ejpam-4673	140	1	therefore	therefore	ADV
ejpam-4673	140	2	,	,	PUNCT
ejpam-4673	140	3	s	s	VERB
ejpam-4673	140	4	is	be	AUX
ejpam-4673	140	5	a	a	DET
ejpam-4673	140	6	hop	hop	NOUN
ejpam-4673	140	7	differentiating	differentiate	VERB
ejpam-4673	140	8	hop	hop	NOUN
ejpam-4673	140	9	dominating	dominating	NOUN
ejpam-4673	140	10	set	set	VERB
ejpam-4673	140	11	in	in	ADP
ejpam-4673	140	12	g.	g.	PROPN
ejpam-4673	140	13	it	it	PRON
ejpam-4673	140	14	is	be	AUX
ejpam-4673	140	15	worth	worth	ADJ
ejpam-4673	140	16	mentioning	mention	VERB
ejpam-4673	140	17	that	that	SCONJ
ejpam-4673	140	18	theorem	theorem	NOUN
ejpam-4673	140	19	1	1	NUM
ejpam-4673	140	20	does	do	AUX
ejpam-4673	140	21	not	not	PART
ejpam-4673	140	22	hold	hold	VERB
ejpam-4673	140	23	if	if	SCONJ
ejpam-4673	140	24	‘	'	PUNCT
ejpam-4673	140	25	hop	hop	NOUN
ejpam-4673	140	26	differentiating	differentiate	VERB
ejpam-4673	140	27	hop	hop	NOUN
ejpam-4673	140	28	dominating	dominating	NOUN
ejpam-4673	140	29	’	'	PUNCT
ejpam-4673	140	30	is	be	AUX
ejpam-4673	140	31	replaced	replace	VERB
ejpam-4673	140	32	by	by	ADP
ejpam-4673	140	33	‘	'	PUNCT
ejpam-4673	140	34	hop	hop	NOUN
ejpam-4673	140	35	differentiating	differentiating	NOUN
ejpam-4673	140	36	’	'	PUNCT
ejpam-4673	140	37	.	.	PUNCT
ejpam-4673	141	1	indeed	indeed	ADV
ejpam-4673	141	2	,	,	PUNCT
ejpam-4673	141	3	if	if	SCONJ
ejpam-4673	141	4	there	there	PRON
ejpam-4673	141	5	are	be	VERB
ejpam-4673	141	6	two	two	NUM
ejpam-4673	141	7	distinct	distinct	ADJ
ejpam-4673	141	8	hop	hop	NOUN
ejpam-4673	141	9	differentiating	differentiate	VERB
ejpam-4673	141	10	sets	set	NOUN
ejpam-4673	141	11	sj	sj	INTJ
ejpam-4673	141	12	and	and	CCONJ
ejpam-4673	141	13	sk	sk	INTJ
ejpam-4673	141	14	which	which	PRON
ejpam-4673	141	15	have	have	VERB
ejpam-4673	141	16	each	each	PRON
ejpam-4673	141	17	a	a	DET
ejpam-4673	141	18	single	single	ADJ
ejpam-4673	141	19	vertex	vertex	NOUN
ejpam-4673	141	20	in	in	ADP
ejpam-4673	141	21	v	v	NOUN
ejpam-4673	141	22	(	(	PUNCT
ejpam-4673	141	23	gj	gj	NOUN
ejpam-4673	141	24	)	)	PUNCT
ejpam-4673	141	25	\	\	NOUN
ejpam-4673	141	26	sj	sj	INTJ
ejpam-4673	141	27	and	and	CCONJ
ejpam-4673	141	28	v	v	PROPN
ejpam-4673	141	29	(	(	PUNCT
ejpam-4673	141	30	gk	gk	PROPN
ejpam-4673	141	31	)	)	PUNCT
ejpam-4673	141	32	\	\	PROPN
ejpam-4673	141	33	sk	sk	NOUN
ejpam-4673	141	34	,	,	PUNCT
ejpam-4673	141	35	respectively	respectively	ADV
ejpam-4673	141	36	,	,	PUNCT
ejpam-4673	141	37	such	such	ADJ
ejpam-4673	141	38	that	that	SCONJ
ejpam-4673	141	39	these	these	DET
ejpam-4673	141	40	vertices	vertex	NOUN
ejpam-4673	141	41	are	be	AUX
ejpam-4673	141	42	not	not	PART
ejpam-4673	141	43	hop	hop	ADV
ejpam-4673	141	44	-	-	PUNCT
ejpam-4673	141	45	dominated	dominate	VERB
ejpam-4673	141	46	in	in	ADP
ejpam-4673	141	47	the	the	DET
ejpam-4673	141	48	respective	respective	ADJ
ejpam-4673	141	49	components	component	NOUN
ejpam-4673	141	50	,	,	PUNCT
ejpam-4673	141	51	then	then	ADV
ejpam-4673	141	52	the	the	DET
ejpam-4673	141	53	set	set	NOUN
ejpam-4673	141	54	s	s	VERB
ejpam-4673	141	55	can	can	AUX
ejpam-4673	141	56	not	not	PART
ejpam-4673	141	57	be	be	AUX
ejpam-4673	141	58	a	a	DET
ejpam-4673	141	59	hop	hop	NOUN
ejpam-4673	141	60	differentiating	differentiate	VERB
ejpam-4673	141	61	set	set	NOUN
ejpam-4673	141	62	in	in	ADP
ejpam-4673	141	63	g.	g.	PROPN
ejpam-4673	141	64	the	the	DET
ejpam-4673	141	65	next	next	ADJ
ejpam-4673	141	66	result	result	NOUN
ejpam-4673	141	67	follows	follow	VERB
ejpam-4673	141	68	from	from	ADP
ejpam-4673	141	69	theorem	theorem	ADJ
ejpam-4673	141	70	1	1	NUM
ejpam-4673	141	71	.	.	PUNCT
ejpam-4673	141	72	corollary	corollary	ADJ
ejpam-4673	141	73	1	1	NUM
ejpam-4673	141	74	.	.	PUNCT
ejpam-4673	142	1	let	let	VERB
ejpam-4673	142	2	g1	g1	PROPN
ejpam-4673	142	3	,	,	PUNCT
ejpam-4673	142	4	g2	g2	PROPN
ejpam-4673	142	5	,	,	PUNCT
ejpam-4673	142	6	.	.	PUNCT
ejpam-4673	142	7	.	.	PUNCT
ejpam-4673	143	1	.	.	PUNCT
ejpam-4673	144	1	,	,	PUNCT
ejpam-4673	144	2	gk	gk	PROPN
ejpam-4673	144	3	be	be	AUX
ejpam-4673	144	4	the	the	DET
ejpam-4673	144	5	distinct	distinct	ADJ
ejpam-4673	144	6	components	component	NOUN
ejpam-4673	144	7	of	of	ADP
ejpam-4673	144	8	g.	g.	PROPN
ejpam-4673	144	9	then	then	ADV
ejpam-4673	144	10	γdh(g	γdh(g	PRON
ejpam-4673	144	11	)	)	PUNCT
ejpam-4673	145	1	=	=	SYM
ejpam-4673	145	2	∑k	∑k	PROPN
ejpam-4673	145	3	j=1	j=1	PROPN
ejpam-4673	145	4	γdh(gj	γdh(gj	NUM
ejpam-4673	145	5	)	)	PUNCT
ejpam-4673	145	6	.	.	PUNCT
ejpam-4673	146	1	corollary	corollary	ADJ
ejpam-4673	146	2	2	2	NUM
ejpam-4673	146	3	.	.	PUNCT
ejpam-4673	147	1	let	let	VERB
ejpam-4673	147	2	g1	g1	PROPN
ejpam-4673	147	3	,	,	PUNCT
ejpam-4673	147	4	g2	g2	PROPN
ejpam-4673	147	5	,	,	PUNCT
ejpam-4673	147	6	.	.	PUNCT
ejpam-4673	147	7	.	.	PUNCT
ejpam-4673	148	1	.	.	PUNCT
ejpam-4673	149	1	,	,	PUNCT
ejpam-4673	149	2	gk	gk	PROPN
ejpam-4673	149	3	be	be	AUX
ejpam-4673	149	4	the	the	DET
ejpam-4673	149	5	distinct	distinct	ADJ
ejpam-4673	149	6	components	component	NOUN
ejpam-4673	149	7	of	of	ADP
ejpam-4673	149	8	g.	g.	PROPN
ejpam-4673	149	9	if	if	SCONJ
ejpam-4673	149	10	each	each	PRON
ejpam-4673	149	11	of	of	ADP
ejpam-4673	149	12	these	these	DET
ejpam-4673	149	13	components	component	NOUN
ejpam-4673	149	14	is	be	AUX
ejpam-4673	149	15	complete	complete	ADJ
ejpam-4673	149	16	,	,	PUNCT
ejpam-4673	149	17	then	then	ADV
ejpam-4673	149	18	γdh(g	γdh(g	PRON
ejpam-4673	149	19	)	)	PUNCT
ejpam-4673	149	20	=	=	SYM
ejpam-4673	149	21	|v	|v	PROPN
ejpam-4673	149	22	(	(	PUNCT
ejpam-4673	149	23	g)|	g)|	NOUN
ejpam-4673	149	24	.	.	PUNCT
ejpam-4673	150	1	in	in	ADP
ejpam-4673	150	2	particular	particular	ADJ
ejpam-4673	150	3	,	,	PUNCT
ejpam-4673	150	4	γdh(kn	γdh(kn	NUM
ejpam-4673	150	5	)	)	PUNCT
ejpam-4673	150	6	=	=	SYM
ejpam-4673	150	7	γdh(kn	γdh(kn	NUM
ejpam-4673	150	8	)	)	PUNCT
ejpam-4673	150	9	=	=	SYM
ejpam-4673	151	1	n	n	PROPN
ejpam-4673	151	2	for	for	ADP
ejpam-4673	151	3	all	all	DET
ejpam-4673	151	4	n	n	PRON
ejpam-4673	151	5	≥	≥	NUM
ejpam-4673	151	6	1	1	NUM
ejpam-4673	151	7	.	.	PUNCT
ejpam-4673	151	8	proposition	proposition	NOUN
ejpam-4673	151	9	1	1	NUM
ejpam-4673	151	10	.	.	PUNCT
ejpam-4673	152	1	let	let	VERB
ejpam-4673	152	2	g	g	PRON
ejpam-4673	152	3	be	be	AUX
ejpam-4673	152	4	a	a	DET
ejpam-4673	152	5	graph	graph	NOUN
ejpam-4673	152	6	on	on	ADP
ejpam-4673	152	7	n	n	PRON
ejpam-4673	152	8	≥	≥	NUM
ejpam-4673	152	9	3	3	NUM
ejpam-4673	152	10	vertices	vertex	NOUN
ejpam-4673	152	11	.	.	PUNCT
ejpam-4673	153	1	then	then	ADV
ejpam-4673	153	2	3	3	NUM
ejpam-4673	153	3	≤	≤	NUM
ejpam-4673	153	4	γdh(g	γdh(g	X
ejpam-4673	153	5	)	)	PUNCT
ejpam-4673	153	6	≤	≤	PROPN
ejpam-4673	153	7	n.	n.	NOUN
ejpam-4673	153	8	moreover	moreover	ADV
ejpam-4673	153	9	,	,	PUNCT
ejpam-4673	153	10	the	the	DET
ejpam-4673	153	11	following	follow	VERB
ejpam-4673	153	12	hold	hold	NOUN
ejpam-4673	153	13	:	:	PUNCT
ejpam-4673	153	14	(	(	PUNCT
ejpam-4673	153	15	i	i	NOUN
ejpam-4673	153	16	)	)	PUNCT
ejpam-4673	153	17	if	if	SCONJ
ejpam-4673	153	18	n	n	NUM
ejpam-4673	153	19	=	=	SYM
ejpam-4673	153	20	3	3	NUM
ejpam-4673	153	21	and	and	CCONJ
ejpam-4673	153	22	γdh(g	γdh(g	PRON
ejpam-4673	153	23	)	)	PUNCT
ejpam-4673	153	24	=	=	SYM
ejpam-4673	154	1	3	3	NUM
ejpam-4673	154	2	,	,	PUNCT
ejpam-4673	154	3	then	then	ADV
ejpam-4673	154	4	g	g	PROPN
ejpam-4673	154	5	∈	∈	PROPN
ejpam-4673	154	6	{	{	PUNCT
ejpam-4673	154	7	k3,k3,k1	k3,k3,k1	NOUN
ejpam-4673	154	8	∪k2	∪k2	X
ejpam-4673	154	9	}	}	PUNCT
ejpam-4673	154	10	.	.	PUNCT
ejpam-4673	155	1	(	(	PUNCT
ejpam-4673	155	2	ii	ii	NOUN
ejpam-4673	155	3	)	)	PUNCT
ejpam-4673	155	4	if	if	SCONJ
ejpam-4673	155	5	n	n	NOUN
ejpam-4673	155	6	=	=	SYM
ejpam-4673	155	7	4	4	NUM
ejpam-4673	155	8	,	,	PUNCT
ejpam-4673	155	9	then	then	ADV
ejpam-4673	155	10	γdh(g	γdh(g	PRON
ejpam-4673	155	11	)	)	PUNCT
ejpam-4673	155	12	=	=	SYM
ejpam-4673	155	13	3	3	NUM
ejpam-4673	155	14	if	if	SCONJ
ejpam-4673	155	15	and	and	CCONJ
ejpam-4673	155	16	only	only	ADV
ejpam-4673	155	17	if	if	SCONJ
ejpam-4673	155	18	g	g	PROPN
ejpam-4673	155	19	is	be	AUX
ejpam-4673	155	20	a	a	DET
ejpam-4673	155	21	graph	graph	NOUN
ejpam-4673	155	22	obtained	obtain	VERB
ejpam-4673	155	23	from	from	ADP
ejpam-4673	155	24	k3	k3	VERB
ejpam-4673	155	25	by	by	ADP
ejpam-4673	155	26	attaching	attach	VERB
ejpam-4673	155	27	a	a	DET
ejpam-4673	155	28	pendant	pendant	ADJ
ejpam-4673	155	29	vertex	vertex	NOUN
ejpam-4673	155	30	to	to	ADP
ejpam-4673	155	31	one	one	NUM
ejpam-4673	155	32	of	of	ADP
ejpam-4673	155	33	the	the	DET
ejpam-4673	155	34	vertices	vertex	NOUN
ejpam-4673	155	35	of	of	ADP
ejpam-4673	155	36	k3	k3	VERB
ejpam-4673	155	37	.	.	PUNCT
ejpam-4673	156	1	proof	proof	NOUN
ejpam-4673	156	2	.	.	PUNCT
ejpam-4673	157	1	suppose	suppose	VERB
ejpam-4673	157	2	s	s	NOUN
ejpam-4673	157	3	is	be	AUX
ejpam-4673	157	4	a	a	DET
ejpam-4673	157	5	γdh	γdh	NOUN
ejpam-4673	157	6	-	-	PUNCT
ejpam-4673	157	7	set	set	NOUN
ejpam-4673	157	8	of	of	ADP
ejpam-4673	157	9	g.	g.	PROPN
ejpam-4673	157	10	clearly	clearly	ADV
ejpam-4673	157	11	,	,	PUNCT
ejpam-4673	157	12	γdh(g	γdh(g	X
ejpam-4673	157	13	)	)	PUNCT
ejpam-4673	157	14	≤	≤	NOUN
ejpam-4673	157	15	n.	n.	NOUN
ejpam-4673	157	16	now	now	ADV
ejpam-4673	157	17	,	,	PUNCT
ejpam-4673	157	18	by	by	ADP
ejpam-4673	157	19	lemma	lemma	PROPN
ejpam-4673	157	20	1	1	NUM
ejpam-4673	157	21	,	,	PUNCT
ejpam-4673	157	22	γdh(g	γdh(g	PROPN
ejpam-4673	157	23	)	)	PUNCT
ejpam-4673	157	24	≥	≥	NOUN
ejpam-4673	157	25	⌈	⌈	NOUN
ejpam-4673	157	26	lnn+	lnn+	PUNCT
ejpam-4673	157	27	ln2	ln2	ADJ
ejpam-4673	157	28	ln2	ln2	PROPN
ejpam-4673	157	29	⌉	⌉	X
ejpam-4673	157	30	≥	≥	X
ejpam-4673	157	31	⌈	⌈	X
ejpam-4673	157	32	ln3	ln3	PROPN
ejpam-4673	157	33	+	+	CCONJ
ejpam-4673	157	34	ln2	ln2	ADJ
ejpam-4673	157	35	ln2	ln2	ADJ
ejpam-4673	157	36	⌉	⌉	NOUN
ejpam-4673	157	37	=	=	SYM
ejpam-4673	158	1	3	3	X
ejpam-4673	158	2	.	.	PUNCT
ejpam-4673	159	1	next	next	ADV
ejpam-4673	159	2	,	,	PUNCT
ejpam-4673	159	3	suppose	suppose	VERB
ejpam-4673	159	4	n	n	PROPN
ejpam-4673	159	5	=	=	SYM
ejpam-4673	159	6	3	3	NUM
ejpam-4673	159	7	and	and	CCONJ
ejpam-4673	159	8	γdh(g	γdh(g	PRON
ejpam-4673	159	9	)	)	PUNCT
ejpam-4673	159	10	=	=	SYM
ejpam-4673	160	1	3	3	X
ejpam-4673	160	2	.	.	PUNCT
ejpam-4673	160	3	by	by	ADP
ejpam-4673	160	4	corollary	corollary	ADJ
ejpam-4673	160	5	2	2	NUM
ejpam-4673	160	6	,	,	PUNCT
ejpam-4673	160	7	g	g	PROPN
ejpam-4673	160	8	∈	∈	PROPN
ejpam-4673	160	9	{	{	PUNCT
ejpam-4673	160	10	k3,k3,k1∪k2	k3,k3,k1∪k2	PROPN
ejpam-4673	160	11	}	}	PUNCT
ejpam-4673	160	12	,	,	PUNCT
ejpam-4673	160	13	showing	show	VERB
ejpam-4673	160	14	that	that	SCONJ
ejpam-4673	160	15	(	(	PUNCT
ejpam-4673	160	16	i	i	NOUN
ejpam-4673	160	17	)	)	PUNCT
ejpam-4673	160	18	holds	hold	VERB
ejpam-4673	160	19	.	.	PUNCT
ejpam-4673	160	20	suppose	suppose	VERB
ejpam-4673	160	21	now	now	ADV
ejpam-4673	160	22	that	that	SCONJ
ejpam-4673	160	23	n	n	NOUN
ejpam-4673	160	24	=	=	SYM
ejpam-4673	160	25	4	4	NUM
ejpam-4673	160	26	and	and	CCONJ
ejpam-4673	160	27	γdh(g	γdh(g	PRON
ejpam-4673	160	28	)	)	PUNCT
ejpam-4673	160	29	=	=	SYM
ejpam-4673	160	30	3	3	X
ejpam-4673	160	31	.	.	X
ejpam-4673	160	32	let	let	VERB
ejpam-4673	160	33	s	s	PRON
ejpam-4673	160	34	=	=	X
ejpam-4673	160	35	{	{	PUNCT
ejpam-4673	160	36	a	a	PRON
ejpam-4673	160	37	,	,	PUNCT
ejpam-4673	160	38	b	b	NOUN
ejpam-4673	160	39	,	,	PUNCT
ejpam-4673	160	40	c	c	AUX
ejpam-4673	160	41	}	}	PUNCT
ejpam-4673	160	42	be	be	AUX
ejpam-4673	160	43	a	a	DET
ejpam-4673	160	44	γdh	γdh	NOUN
ejpam-4673	160	45	-	-	PUNCT
ejpam-4673	160	46	set	set	NOUN
ejpam-4673	160	47	of	of	ADP
ejpam-4673	160	48	g	g	NOUN
ejpam-4673	160	49	and	and	CCONJ
ejpam-4673	160	50	let	let	VERB
ejpam-4673	161	1	v	v	NUM
ejpam-4673	161	2	∈	∈	PROPN
ejpam-4673	161	3	v	v	NOUN
ejpam-4673	161	4	(	(	PUNCT
ejpam-4673	161	5	g	g	NOUN
ejpam-4673	161	6	)	)	PUNCT
ejpam-4673	161	7	\	\	PUNCT
ejpam-4673	161	8	s.	s.	PROPN
ejpam-4673	161	9	since	since	SCONJ
ejpam-4673	161	10	γdh(k1	γdh(k1	PROPN
ejpam-4673	161	11	∪k3	∪k3	NOUN
ejpam-4673	161	12	)	)	PUNCT
ejpam-4673	161	13	=	=	SYM
ejpam-4673	161	14	γdh(k2	γdh(k2	NOUN
ejpam-4673	161	15	∪k2	∪k2	X
ejpam-4673	161	16	)	)	PUNCT
ejpam-4673	162	1	=	=	SYM
ejpam-4673	162	2	γdh(k2	γdh(k2	NOUN
ejpam-4673	162	3	∪k2	∪k2	X
ejpam-4673	162	4	)	)	PUNCT
ejpam-4673	163	1	=	=	PUNCT
ejpam-4673	163	2	γdh(k4	γdh(k4	X
ejpam-4673	163	3	)	)	PUNCT
ejpam-4673	163	4	=	=	PUNCT
ejpam-4673	163	5	γdh(k4	γdh(k4	X
ejpam-4673	163	6	)	)	PUNCT
ejpam-4673	163	7	=	=	SYM
ejpam-4673	163	8	4	4	NUM
ejpam-4673	163	9	by	by	ADP
ejpam-4673	163	10	corollary	corollary	ADJ
ejpam-4673	163	11	2	2	NUM
ejpam-4673	163	12	,	,	PUNCT
ejpam-4673	163	13	and	and	CCONJ
ejpam-4673	163	14	because	because	SCONJ
ejpam-4673	163	15	g	g	PROPN
ejpam-4673	163	16	is	be	AUX
ejpam-4673	163	17	distance	distance	NOUN
ejpam-4673	163	18	-	-	PUNCT
ejpam-4673	163	19	two	two	NUM
ejpam-4673	163	20	point	point	NOUN
ejpam-4673	163	21	distinguishing	distinguishing	NOUN
ejpam-4673	163	22	,	,	PUNCT
ejpam-4673	163	23	g	g	PROPN
ejpam-4673	163	24	/∈	/∈	PUNCT
ejpam-4673	163	25	{	{	PUNCT
ejpam-4673	163	26	k1	k1	NOUN
ejpam-4673	163	27	∪k3,k2	∪k3,k2	PROPN
ejpam-4673	163	28	∪k2,k2	∪k2,k2	PROPN
ejpam-4673	163	29	∪k2,k4,k1	∪k2,k4,k1	NOUN
ejpam-4673	163	30	∪	∪	ADJ
ejpam-4673	163	31	p3,k4	p3,k4	PROPN
ejpam-4673	163	32	,	,	PUNCT
ejpam-4673	163	33	p4	p4	ADJ
ejpam-4673	163	34	,	,	PUNCT
ejpam-4673	163	35	c4,k1,3	c4,k1,3	NOUN
ejpam-4673	163	36	,	,	PUNCT
ejpam-4673	163	37	h	h	NOUN
ejpam-4673	163	38	}	}	PUNCT
ejpam-4673	163	39	,	,	PUNCT
ejpam-4673	163	40	where	where	SCONJ
ejpam-4673	163	41	h	h	NOUN
ejpam-4673	163	42	is	be	AUX
ejpam-4673	163	43	obtained	obtain	VERB
ejpam-4673	163	44	from	from	ADP
ejpam-4673	163	45	c4	c4	NOUN
ejpam-4673	163	46	by	by	ADP
ejpam-4673	163	47	adding	add	VERB
ejpam-4673	163	48	an	an	DET
ejpam-4673	163	49	edge	edge	NOUN
ejpam-4673	163	50	connecting	connect	VERB
ejpam-4673	163	51	the	the	DET
ejpam-4673	163	52	non	non	ADJ
ejpam-4673	163	53	-	-	ADJ
ejpam-4673	163	54	adjacent	adjacent	ADJ
ejpam-4673	163	55	vertices	vertex	NOUN
ejpam-4673	163	56	of	of	ADP
ejpam-4673	163	57	c4	c4	NOUN
ejpam-4673	163	58	.	.	PUNCT
ejpam-4673	164	1	since	since	SCONJ
ejpam-4673	164	2	there	there	PRON
ejpam-4673	164	3	are	be	VERB
ejpam-4673	164	4	only	only	ADV
ejpam-4673	164	5	eleven	eleven	NUM
ejpam-4673	164	6	(	(	PUNCT
ejpam-4673	164	7	11	11	NUM
ejpam-4673	164	8	)	)	PUNCT
ejpam-4673	164	9	non	non	ADJ
ejpam-4673	164	10	-	-	ADJ
ejpam-4673	164	11	isomorphic	isomorphic	ADJ
ejpam-4673	164	12	graphs	graph	NOUN
ejpam-4673	164	13	of	of	ADP
ejpam-4673	164	14	order	order	NOUN
ejpam-4673	164	15	four	four	NUM
ejpam-4673	164	16	(	(	PUNCT
ejpam-4673	164	17	4	4	NUM
ejpam-4673	164	18	)	)	PUNCT
ejpam-4673	164	19	,	,	PUNCT
ejpam-4673	164	20	it	it	PRON
ejpam-4673	164	21	follows	follow	VERB
ejpam-4673	164	22	that	that	SCONJ
ejpam-4673	164	23	g	g	PROPN
ejpam-4673	164	24	is	be	AUX
ejpam-4673	164	25	a	a	DET
ejpam-4673	164	26	graph	graph	NOUN
ejpam-4673	164	27	obtained	obtain	VERB
ejpam-4673	164	28	from	from	ADP
ejpam-4673	164	29	k3	k3	VERB
ejpam-4673	164	30	by	by	ADP
ejpam-4673	164	31	attaching	attach	VERB
ejpam-4673	164	32	a	a	DET
ejpam-4673	164	33	pendant	pendant	ADJ
ejpam-4673	164	34	vertex	vertex	NOUN
ejpam-4673	164	35	to	to	ADP
ejpam-4673	164	36	one	one	NUM
ejpam-4673	164	37	of	of	ADP
ejpam-4673	164	38	the	the	DET
ejpam-4673	164	39	vertices	vertex	NOUN
ejpam-4673	164	40	of	of	ADP
ejpam-4673	164	41	k3	k3	PROPN
ejpam-4673	164	42	.	.	PUNCT
ejpam-4673	165	1	for	for	ADP
ejpam-4673	165	2	the	the	DET
ejpam-4673	165	3	converse	converse	NOUN
ejpam-4673	165	4	,	,	PUNCT
ejpam-4673	165	5	suppose	suppose	VERB
ejpam-4673	165	6	that	that	SCONJ
ejpam-4673	165	7	g	g	PROPN
ejpam-4673	165	8	is	be	AUX
ejpam-4673	165	9	a	a	DET
ejpam-4673	165	10	graph	graph	NOUN
ejpam-4673	165	11	obtained	obtain	VERB
ejpam-4673	165	12	from	from	ADP
ejpam-4673	165	13	k3	k3	VERB
ejpam-4673	165	14	by	by	ADP
ejpam-4673	165	15	attaching	attach	VERB
ejpam-4673	165	16	a	a	DET
ejpam-4673	165	17	pendant	pendant	ADJ
ejpam-4673	165	18	vertex	vertex	NOUN
ejpam-4673	165	19	to	to	ADP
ejpam-4673	165	20	one	one	NUM
ejpam-4673	165	21	of	of	ADP
ejpam-4673	165	22	the	the	DET
ejpam-4673	165	23	vertices	vertex	NOUN
ejpam-4673	165	24	of	of	ADP
ejpam-4673	165	25	k3	k3	VERB
ejpam-4673	165	26	.	.	PUNCT
ejpam-4673	166	1	let	let	VERB
ejpam-4673	166	2	v	v	X
ejpam-4673	166	3	(	(	PUNCT
ejpam-4673	166	4	g	g	NOUN
ejpam-4673	166	5	)	)	PUNCT
ejpam-4673	166	6	=	=	NOUN
ejpam-4673	166	7	{	{	PUNCT
ejpam-4673	166	8	a	a	PRON
ejpam-4673	166	9	,	,	PUNCT
ejpam-4673	166	10	b	b	NOUN
ejpam-4673	166	11	,	,	PUNCT
ejpam-4673	166	12	c	c	NOUN
ejpam-4673	166	13	,	,	PUNCT
ejpam-4673	166	14	v	v	NOUN
ejpam-4673	166	15	}	}	PUNCT
ejpam-4673	166	16	such	such	ADJ
ejpam-4673	166	17	that	that	SCONJ
ejpam-4673	166	18	⟨{a	⟨{a	PROPN
ejpam-4673	166	19	,	,	PUNCT
ejpam-4673	166	20	b	b	PROPN
ejpam-4673	166	21	,	,	PUNCT
ejpam-4673	166	22	c}⟩	c}⟩	PROPN
ejpam-4673	166	23	=	=	PRON
ejpam-4673	166	24	k3	k3	PROPN
ejpam-4673	166	25	and	and	CCONJ
ejpam-4673	166	26	s.	s.	PROPN
ejpam-4673	166	27	canoy	canoy	PROPN
ejpam-4673	166	28	jr	jr	PROPN
ejpam-4673	166	29	.	.	PROPN
ejpam-4673	166	30	,	,	PUNCT
ejpam-4673	166	31	c.	c.	PROPN
ejpam-4673	166	32	saromines	saromine	VERB
ejpam-4673	166	33	/	/	SYM
ejpam-4673	166	34	eur	eur	PROPN
ejpam-4673	166	35	.	.	PUNCT
ejpam-4673	167	1	j.	j.	PROPN
ejpam-4673	167	2	pure	pure	PROPN
ejpam-4673	167	3	appl	appl	PROPN
ejpam-4673	167	4	.	.	PROPN
ejpam-4673	167	5	math	math	PROPN
ejpam-4673	167	6	,	,	PUNCT
ejpam-4673	167	7	16	16	NUM
ejpam-4673	167	8	(	(	PUNCT
ejpam-4673	167	9	1	1	NUM
ejpam-4673	167	10	)	)	PUNCT
ejpam-4673	167	11	(	(	PUNCT
ejpam-4673	167	12	2023	2023	NUM
ejpam-4673	167	13	)	)	PUNCT
ejpam-4673	167	14	,	,	PUNCT
ejpam-4673	167	15	440	440	NUM
ejpam-4673	167	16	-	-	SYM
ejpam-4673	167	17	453	453	NUM
ejpam-4673	167	18	445	445	NUM
ejpam-4673	167	19	....................................	....................................	PUNCT
ejpam-4673	167	20	....................................	....................................	PUNCT
ejpam-4673	168	1	....................................	....................................	PUNCT
ejpam-4673	168	2	....................................	....................................	PUNCT
ejpam-4673	169	1	.........	.........	PUNCT
ejpam-4673	169	2	........	........	PUNCT
ejpam-4673	169	3	........	........	PUNCT
ejpam-4673	169	4	........	........	PUNCT
ejpam-4673	169	5	........	........	PUNCT
ejpam-4673	169	6	........	........	PUNCT
ejpam-4673	169	7	........	........	PUNCT
ejpam-4673	169	8	........	........	PUNCT
ejpam-4673	170	1	........	........	PUNCT
ejpam-4673	170	2	...	...	PUNCT
ejpam-4673	171	1	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4673	171	2	...............................................................................................................	...............................................................................................................	PROPN
ejpam-4673	172	1	v	v	ADP
ejpam-4673	172	2	a	a	DET
ejpam-4673	172	3	b	b	NOUN
ejpam-4673	172	4	c	c	NOUN
ejpam-4673	172	5	g	g	NOUN
ejpam-4673	172	6	•	•	NUM
ejpam-4673	172	7	•	•	NOUN
ejpam-4673	172	8	•	•	NUM
ejpam-4673	172	9	figure	figure	NOUN
ejpam-4673	172	10	1	1	NUM
ejpam-4673	172	11	:	:	PUNCT
ejpam-4673	172	12	graph	graph	VERB
ejpam-4673	172	13	g	g	NOUN
ejpam-4673	172	14	on	on	ADP
ejpam-4673	172	15	4	4	NUM
ejpam-4673	172	16	vertices	vertex	NOUN
ejpam-4673	172	17	and	and	CCONJ
ejpam-4673	172	18	γdh(g	γdh(g	PRON
ejpam-4673	172	19	)	)	PUNCT
ejpam-4673	172	20	=	=	SYM
ejpam-4673	172	21	3	3	NUM
ejpam-4673	172	22	va	va	PROPN
ejpam-4673	172	23	∈	∈	PROPN
ejpam-4673	172	24	e(g	e(g	PROPN
ejpam-4673	172	25	)	)	PUNCT
ejpam-4673	172	26	(	(	PUNCT
ejpam-4673	172	27	see	see	VERB
ejpam-4673	172	28	figure	figure	NOUN
ejpam-4673	172	29	1	1	NUM
ejpam-4673	172	30	)	)	PUNCT
ejpam-4673	172	31	.	.	PUNCT
ejpam-4673	173	1	let	let	VERB
ejpam-4673	173	2	s	s	PRON
ejpam-4673	173	3	=	=	X
ejpam-4673	173	4	{	{	PUNCT
ejpam-4673	173	5	a	a	DET
ejpam-4673	173	6	,	,	PUNCT
ejpam-4673	173	7	b	b	NOUN
ejpam-4673	173	8	,	,	PUNCT
ejpam-4673	173	9	c	c	NOUN
ejpam-4673	173	10	}	}	PUNCT
ejpam-4673	173	11	.	.	PUNCT
ejpam-4673	174	1	since	since	SCONJ
ejpam-4673	174	2	dg(v	dg(v	NOUN
ejpam-4673	174	3	,	,	PUNCT
ejpam-4673	174	4	b	b	X
ejpam-4673	174	5	)	)	PUNCT
ejpam-4673	174	6	=	=	SYM
ejpam-4673	174	7	2	2	NUM
ejpam-4673	174	8	,	,	PUNCT
ejpam-4673	174	9	s	s	VERB
ejpam-4673	174	10	is	be	AUX
ejpam-4673	174	11	a	a	DET
ejpam-4673	174	12	hop	hop	NOUN
ejpam-4673	174	13	dominating	dominating	NOUN
ejpam-4673	174	14	set	set	VERB
ejpam-4673	174	15	in	in	ADP
ejpam-4673	174	16	g.	g.	PROPN
ejpam-4673	174	17	moreover	moreover	ADV
ejpam-4673	174	18	,	,	PUNCT
ejpam-4673	174	19	since	since	SCONJ
ejpam-4673	174	20	n2	n2	ADJ
ejpam-4673	174	21	g[v	g[v	PROPN
ejpam-4673	174	22	]	]	PUNCT
ejpam-4673	174	23	∩	∩	X
ejpam-4673	174	24	s	s	PART
ejpam-4673	174	25	=	=	X
ejpam-4673	174	26	{	{	PUNCT
ejpam-4673	174	27	b	b	NOUN
ejpam-4673	174	28	,	,	PUNCT
ejpam-4673	174	29	c	c	NOUN
ejpam-4673	174	30	}	}	PUNCT
ejpam-4673	174	31	,	,	PUNCT
ejpam-4673	174	32	n2	n2	ADJ
ejpam-4673	174	33	g[a	g[a	PROPN
ejpam-4673	174	34	]	]	PUNCT
ejpam-4673	174	35	∩	∩	PROPN
ejpam-4673	174	36	s	s	PART
ejpam-4673	174	37	=	=	X
ejpam-4673	174	38	{	{	PUNCT
ejpam-4673	174	39	a	a	NOUN
ejpam-4673	174	40	}	}	PUNCT
ejpam-4673	174	41	,	,	PUNCT
ejpam-4673	174	42	n2	n2	PROPN
ejpam-4673	174	43	g[b	g[b	PROPN
ejpam-4673	174	44	]	]	PUNCT
ejpam-4673	174	45	∩	∩	X
ejpam-4673	174	46	s	s	PART
ejpam-4673	174	47	=	=	X
ejpam-4673	174	48	{	{	PUNCT
ejpam-4673	174	49	b	b	NOUN
ejpam-4673	174	50	}	}	PUNCT
ejpam-4673	174	51	,	,	PUNCT
ejpam-4673	174	52	and	and	CCONJ
ejpam-4673	174	53	n2	n2	PROPN
ejpam-4673	174	54	g[c	g[c	PROPN
ejpam-4673	174	55	]	]	PUNCT
ejpam-4673	174	56	∩	∩	X
ejpam-4673	174	57	s	s	PART
ejpam-4673	174	58	=	=	X
ejpam-4673	174	59	{	{	PUNCT
ejpam-4673	174	60	c	c	NOUN
ejpam-4673	174	61	}	}	PUNCT
ejpam-4673	174	62	are	be	AUX
ejpam-4673	174	63	all	all	ADV
ejpam-4673	174	64	distinct	distinct	ADJ
ejpam-4673	174	65	,	,	PUNCT
ejpam-4673	174	66	s	s	PART
ejpam-4673	174	67	is	be	AUX
ejpam-4673	174	68	a	a	DET
ejpam-4673	174	69	hop	hop	NOUN
ejpam-4673	174	70	differentiating	differentiate	VERB
ejpam-4673	174	71	set	set	NOUN
ejpam-4673	174	72	.	.	PUNCT
ejpam-4673	175	1	thus	thus	ADV
ejpam-4673	175	2	,	,	PUNCT
ejpam-4673	175	3	by	by	ADP
ejpam-4673	175	4	the	the	DET
ejpam-4673	175	5	first	first	ADJ
ejpam-4673	175	6	part	part	NOUN
ejpam-4673	175	7	,	,	PUNCT
ejpam-4673	175	8	γdh(g	γdh(g	X
ejpam-4673	175	9	)	)	PUNCT
ejpam-4673	175	10	=	=	SYM
ejpam-4673	175	11	3	3	X
ejpam-4673	175	12	.	.	X
ejpam-4673	176	1	this	this	PRON
ejpam-4673	176	2	completes	complete	VERB
ejpam-4673	176	3	the	the	DET
ejpam-4673	176	4	proof	proof	NOUN
ejpam-4673	176	5	of	of	ADP
ejpam-4673	176	6	(	(	PUNCT
ejpam-4673	176	7	ii	ii	NOUN
ejpam-4673	176	8	)	)	PUNCT
ejpam-4673	176	9	.	.	PUNCT
ejpam-4673	177	1	the	the	DET
ejpam-4673	177	2	next	next	ADJ
ejpam-4673	177	3	result	result	NOUN
ejpam-4673	177	4	is	be	AUX
ejpam-4673	177	5	found	find	VERB
ejpam-4673	177	6	in	in	ADP
ejpam-4673	177	7	[	[	X
ejpam-4673	177	8	11	11	NUM
ejpam-4673	177	9	]	]	PUNCT
ejpam-4673	177	10	.	.	PUNCT
ejpam-4673	178	1	theorem	theorem	NOUN
ejpam-4673	178	2	2	2	NUM
ejpam-4673	178	3	.	.	PUNCT
ejpam-4673	179	1	let	let	VERB
ejpam-4673	179	2	g	g	NOUN
ejpam-4673	180	1	and	and	CCONJ
ejpam-4673	180	2	h	h	NOUN
ejpam-4673	180	3	be	be	VERB
ejpam-4673	180	4	any	any	DET
ejpam-4673	180	5	two	two	NUM
ejpam-4673	180	6	graphs	graph	NOUN
ejpam-4673	180	7	.	.	PUNCT
ejpam-4673	181	1	a	a	DET
ejpam-4673	181	2	set	set	NOUN
ejpam-4673	181	3	s	s	NOUN
ejpam-4673	181	4	⊆	⊆	NUM
ejpam-4673	181	5	v	v	NOUN
ejpam-4673	181	6	(	(	PUNCT
ejpam-4673	181	7	g+h	g+h	PROPN
ejpam-4673	181	8	)	)	PUNCT
ejpam-4673	181	9	is	be	AUX
ejpam-4673	181	10	hop	hop	NOUN
ejpam-4673	181	11	dominating	dominate	VERB
ejpam-4673	181	12	in	in	ADP
ejpam-4673	181	13	g+h	g+h	PROPN
ejpam-4673	181	14	if	if	SCONJ
ejpam-4673	181	15	and	and	CCONJ
ejpam-4673	181	16	only	only	ADV
ejpam-4673	181	17	if	if	SCONJ
ejpam-4673	181	18	s	s	VERB
ejpam-4673	181	19	=	=	PUNCT
ejpam-4673	181	20	sg	sg	X
ejpam-4673	181	21	∪	∪	ADJ
ejpam-4673	181	22	sh	sh	PROPN
ejpam-4673	181	23	,	,	PUNCT
ejpam-4673	181	24	where	where	SCONJ
ejpam-4673	181	25	sg	sg	PROPN
ejpam-4673	181	26	and	and	CCONJ
ejpam-4673	181	27	sh	sh	PROPN
ejpam-4673	181	28	are	be	AUX
ejpam-4673	181	29	pointwise	pointwise	PROPN
ejpam-4673	181	30	non	non	ADJ
ejpam-4673	181	31	-	-	ADJ
ejpam-4673	181	32	dominating	dominating	NOUN
ejpam-4673	181	33	in	in	ADP
ejpam-4673	181	34	g	g	PROPN
ejpam-4673	181	35	and	and	CCONJ
ejpam-4673	181	36	h	h	NOUN
ejpam-4673	181	37	,	,	PUNCT
ejpam-4673	181	38	respectively	respectively	ADV
ejpam-4673	181	39	.	.	PUNCT
ejpam-4673	182	1	theorem	theorem	NOUN
ejpam-4673	182	2	3	3	X
ejpam-4673	182	3	.	.	PUNCT
ejpam-4673	183	1	let	let	VERB
ejpam-4673	183	2	g	g	NOUN
ejpam-4673	184	1	and	and	CCONJ
ejpam-4673	184	2	h	h	NOUN
ejpam-4673	184	3	be	be	AUX
ejpam-4673	184	4	any	any	PRON
ejpam-4673	184	5	two	two	NUM
ejpam-4673	184	6	(	(	PUNCT
ejpam-4673	184	7	complement	complement	VERB
ejpam-4673	184	8	distance	distance	NOUN
ejpam-4673	184	9	-	-	PUNCT
ejpam-4673	184	10	two	two	NUM
ejpam-4673	184	11	point	point	NOUN
ejpam-4673	184	12	distinguishing	distinguish	VERB
ejpam-4673	184	13	)	)	PUNCT
ejpam-4673	184	14	graphs	graph	NOUN
ejpam-4673	184	15	.	.	PUNCT
ejpam-4673	185	1	then	then	ADV
ejpam-4673	185	2	s	s	VERB
ejpam-4673	185	3	⊆	⊆	NUM
ejpam-4673	185	4	v	v	NOUN
ejpam-4673	185	5	(	(	PUNCT
ejpam-4673	185	6	g	g	PROPN
ejpam-4673	185	7	+	+	NOUN
ejpam-4673	185	8	h	h	NOUN
ejpam-4673	185	9	)	)	PUNCT
ejpam-4673	185	10	is	be	AUX
ejpam-4673	185	11	hop	hop	NOUN
ejpam-4673	185	12	differentiating	differentiate	VERB
ejpam-4673	185	13	hop	hop	NOUN
ejpam-4673	185	14	dominating	dominating	NOUN
ejpam-4673	185	15	in	in	ADP
ejpam-4673	185	16	g	g	PROPN
ejpam-4673	185	17	+	+	NOUN
ejpam-4673	185	18	h	h	NOUN
ejpam-4673	185	19	if	if	SCONJ
ejpam-4673	186	1	and	and	CCONJ
ejpam-4673	186	2	only	only	ADV
ejpam-4673	186	3	if	if	SCONJ
ejpam-4673	186	4	s	s	VERB
ejpam-4673	186	5	=	=	PUNCT
ejpam-4673	186	6	sg	sg	X
ejpam-4673	186	7	∪	∪	ADJ
ejpam-4673	187	1	sh	sh	PROPN
ejpam-4673	187	2	,	,	PUNCT
ejpam-4673	187	3	where	where	SCONJ
ejpam-4673	187	4	sg	sg	PROPN
ejpam-4673	187	5	and	and	CCONJ
ejpam-4673	187	6	sh	sh	PROPN
ejpam-4673	187	7	are	be	AUX
ejpam-4673	187	8	complement	complement	NOUN
ejpam-4673	187	9	differentiating	differentiating	NOUN
ejpam-4673	187	10	and	and	CCONJ
ejpam-4673	187	11	pointwise	pointwise	VERB
ejpam-4673	187	12	non	non	ADJ
ejpam-4673	187	13	-	-	ADJ
ejpam-4673	187	14	dominating	dominating	ADJ
ejpam-4673	187	15	sets	set	NOUN
ejpam-4673	187	16	in	in	ADP
ejpam-4673	187	17	g	g	PROPN
ejpam-4673	187	18	and	and	CCONJ
ejpam-4673	187	19	h	h	PROPN
ejpam-4673	187	20	(	(	PUNCT
ejpam-4673	187	21	differentiating	differentiate	VERB
ejpam-4673	187	22	-	-	PUNCT
ejpam-4673	187	23	dominating	dominating	NOUN
ejpam-4673	187	24	in	in	ADP
ejpam-4673	187	25	g	g	PROPN
ejpam-4673	187	26	and	and	CCONJ
ejpam-4673	187	27	h	h	NOUN
ejpam-4673	187	28	)	)	PUNCT
ejpam-4673	187	29	,	,	PUNCT
ejpam-4673	188	1	respectively	respectively	ADV
ejpam-4673	188	2	.	.	PUNCT
ejpam-4673	189	1	proof	proof	NOUN
ejpam-4673	189	2	.	.	PUNCT
ejpam-4673	190	1	suppose	suppose	VERB
ejpam-4673	190	2	that	that	SCONJ
ejpam-4673	190	3	s	s	VERB
ejpam-4673	190	4	is	be	AUX
ejpam-4673	190	5	a	a	DET
ejpam-4673	190	6	hop	hop	NOUN
ejpam-4673	190	7	differentiating	differentiate	VERB
ejpam-4673	190	8	hop	hop	NOUN
ejpam-4673	190	9	dominating	dominating	NOUN
ejpam-4673	190	10	set	set	VERB
ejpam-4673	190	11	in	in	ADP
ejpam-4673	190	12	g	g	PROPN
ejpam-4673	190	13	+	+	CCONJ
ejpam-4673	190	14	h.	h.	PROPN
ejpam-4673	190	15	let	let	VERB
ejpam-4673	190	16	sg	sg	PROPN
ejpam-4673	190	17	=	=	SYM
ejpam-4673	190	18	v	v	PROPN
ejpam-4673	190	19	(	(	PUNCT
ejpam-4673	190	20	g	g	NOUN
ejpam-4673	190	21	)	)	PUNCT
ejpam-4673	190	22	∩	∩	NOUN
ejpam-4673	190	23	s	s	NOUN
ejpam-4673	190	24	and	and	CCONJ
ejpam-4673	190	25	sh	sh	PROPN
ejpam-4673	190	26	=	=	SYM
ejpam-4673	190	27	v	v	PROPN
ejpam-4673	190	28	(	(	PUNCT
ejpam-4673	190	29	h	h	NOUN
ejpam-4673	190	30	)	)	PUNCT
ejpam-4673	190	31	∩	∩	NOUN
ejpam-4673	190	32	s.	s.	PROPN
ejpam-4673	190	33	since	since	SCONJ
ejpam-4673	190	34	s	s	PROPN
ejpam-4673	190	35	is	be	AUX
ejpam-4673	190	36	a	a	DET
ejpam-4673	190	37	hop	hop	NOUN
ejpam-4673	190	38	dominating	dominating	NOUN
ejpam-4673	190	39	set	set	VERB
ejpam-4673	190	40	in	in	ADP
ejpam-4673	190	41	g+h	g+h	PROPN
ejpam-4673	190	42	,	,	PUNCT
ejpam-4673	190	43	sg	sg	ADP
ejpam-4673	190	44	̸=	̸=	PROPN
ejpam-4673	190	45	∅	∅	NOUN
ejpam-4673	190	46	and	and	CCONJ
ejpam-4673	190	47	sh	sh	PROPN
ejpam-4673	190	48	̸=	̸=	PROPN
ejpam-4673	190	49	∅.	∅.	ADV
ejpam-4673	190	50	by	by	ADP
ejpam-4673	190	51	theorem	theorem	NOUN
ejpam-4673	190	52	2	2	NUM
ejpam-4673	190	53	,	,	PUNCT
ejpam-4673	190	54	sg	sg	PROPN
ejpam-4673	190	55	and	and	CCONJ
ejpam-4673	190	56	sh	sh	PROPN
ejpam-4673	190	57	are	be	AUX
ejpam-4673	190	58	pointwise	pointwise	PROPN
ejpam-4673	190	59	non	non	ADJ
ejpam-4673	190	60	-	-	ADJ
ejpam-4673	190	61	dominating	dominating	ADJ
ejpam-4673	190	62	sets	set	NOUN
ejpam-4673	190	63	in	in	ADP
ejpam-4673	190	64	g	g	PROPN
ejpam-4673	190	65	and	and	CCONJ
ejpam-4673	190	66	h	h	NOUN
ejpam-4673	190	67	,	,	PUNCT
ejpam-4673	190	68	respectively	respectively	ADV
ejpam-4673	190	69	.	.	PUNCT
ejpam-4673	191	1	if	if	SCONJ
ejpam-4673	191	2	sg	sg	PROPN
ejpam-4673	191	3	=	=	SYM
ejpam-4673	191	4	v	v	NOUN
ejpam-4673	191	5	(	(	PUNCT
ejpam-4673	191	6	g	g	NOUN
ejpam-4673	191	7	)	)	PUNCT
ejpam-4673	191	8	,	,	PUNCT
ejpam-4673	191	9	then	then	ADV
ejpam-4673	191	10	it	it	PRON
ejpam-4673	191	11	is	be	AUX
ejpam-4673	191	12	complement	complement	NOUN
ejpam-4673	191	13	differentiating	differentiate	VERB
ejpam-4673	191	14	in	in	ADP
ejpam-4673	191	15	g.	g.	PROPN
ejpam-4673	191	16	next	next	ADV
ejpam-4673	191	17	,	,	PUNCT
ejpam-4673	191	18	let	let	VERB
ejpam-4673	191	19	x	x	PRON
ejpam-4673	191	20	,	,	PUNCT
ejpam-4673	191	21	y	y	PROPN
ejpam-4673	191	22	∈	∈	PROPN
ejpam-4673	191	23	v	v	ADP
ejpam-4673	191	24	(	(	PUNCT
ejpam-4673	191	25	g	g	NOUN
ejpam-4673	191	26	)	)	PUNCT
ejpam-4673	191	27	where	where	SCONJ
ejpam-4673	191	28	x	x	X
ejpam-4673	191	29	̸=	̸=	PROPN
ejpam-4673	191	30	y.	y.	NOUN
ejpam-4673	191	31	since	since	SCONJ
ejpam-4673	191	32	s	s	PROPN
ejpam-4673	191	33	is	be	AUX
ejpam-4673	191	34	a	a	DET
ejpam-4673	191	35	hop	hop	NOUN
ejpam-4673	191	36	differentiating	differentiate	VERB
ejpam-4673	191	37	set	set	NOUN
ejpam-4673	191	38	,	,	PUNCT
ejpam-4673	191	39	[	[	X
ejpam-4673	191	40	v	v	X
ejpam-4673	191	41	(	(	PUNCT
ejpam-4673	191	42	g	g	NOUN
ejpam-4673	191	43	)	)	PUNCT
ejpam-4673	191	44	\ng(x)]∩sg	\ng(x)]∩sg	NOUN
ejpam-4673	191	45	=	=	PUNCT
ejpam-4673	191	46	n2	n2	PROPN
ejpam-4673	191	47	g+h	g+h	PROPN
ejpam-4673	192	1	[	[	X
ejpam-4673	192	2	x]∩	x]∩	X
ejpam-4673	192	3	s	s	VERB
ejpam-4673	192	4	̸=	̸=	PROPN
ejpam-4673	192	5	n2	n2	NOUN
ejpam-4673	192	6	g+h	g+h	PROPN
ejpam-4673	193	1	[	[	X
ejpam-4673	193	2	y	y	X
ejpam-4673	193	3	]	]	X
ejpam-4673	193	4	∩	∩	X
ejpam-4673	193	5	s	s	PART
ejpam-4673	193	6	=	=	PUNCT
ejpam-4673	194	1	[	[	X
ejpam-4673	194	2	v	v	X
ejpam-4673	194	3	(	(	PUNCT
ejpam-4673	194	4	g	g	NOUN
ejpam-4673	194	5	)	)	PUNCT
ejpam-4673	194	6	\ng(y	\ng(y	NOUN
ejpam-4673	194	7	)	)	PUNCT
ejpam-4673	194	8	]	]	PUNCT
ejpam-4673	194	9	∩	∩	PROPN
ejpam-4673	194	10	sg	sg	ADP
ejpam-4673	194	11	,	,	PUNCT
ejpam-4673	194	12	showing	show	VERB
ejpam-4673	194	13	that	that	SCONJ
ejpam-4673	194	14	sg	sg	PROPN
ejpam-4673	194	15	is	be	AUX
ejpam-4673	194	16	complement	complement	NOUN
ejpam-4673	194	17	differentiating	differentiate	VERB
ejpam-4673	194	18	in	in	ADP
ejpam-4673	194	19	g.	g.	PROPN
ejpam-4673	194	20	thus	thus	ADV
ejpam-4673	194	21	,	,	PUNCT
ejpam-4673	194	22	sg	sg	PROPN
ejpam-4673	194	23	is	be	AUX
ejpam-4673	194	24	a	a	DET
ejpam-4673	194	25	complement	complement	NOUN
ejpam-4673	194	26	differentiating	differentiating	NOUN
ejpam-4673	194	27	and	and	CCONJ
ejpam-4673	194	28	pointwise	pointwise	VERB
ejpam-4673	194	29	non	non	ADJ
ejpam-4673	194	30	-	-	ADJ
ejpam-4673	194	31	dominating	dominating	ADJ
ejpam-4673	194	32	set	set	NOUN
ejpam-4673	194	33	in	in	ADP
ejpam-4673	194	34	g.	g.	PROPN
ejpam-4673	194	35	similarly	similarly	ADV
ejpam-4673	194	36	,	,	PUNCT
ejpam-4673	194	37	sh	sh	PROPN
ejpam-4673	194	38	is	be	AUX
ejpam-4673	194	39	a	a	DET
ejpam-4673	194	40	complement	complement	NOUN
ejpam-4673	194	41	differentiating	differentiating	NOUN
ejpam-4673	194	42	and	and	CCONJ
ejpam-4673	194	43	pointwise	pointwise	VERB
ejpam-4673	194	44	non	non	ADJ
ejpam-4673	194	45	-	-	ADJ
ejpam-4673	194	46	dominating	dominating	ADJ
ejpam-4673	194	47	set	set	NOUN
ejpam-4673	194	48	in	in	ADP
ejpam-4673	194	49	h.	h.	PROPN
ejpam-4673	194	50	for	for	ADP
ejpam-4673	194	51	the	the	DET
ejpam-4673	194	52	converse	converse	NOUN
ejpam-4673	194	53	,	,	PUNCT
ejpam-4673	194	54	suppose	suppose	VERB
ejpam-4673	194	55	that	that	SCONJ
ejpam-4673	194	56	s	s	VERB
ejpam-4673	194	57	=	=	PUNCT
ejpam-4673	194	58	sg	sg	X
ejpam-4673	194	59	∪	∪	NOUN
ejpam-4673	194	60	sh	sh	PROPN
ejpam-4673	194	61	where	where	SCONJ
ejpam-4673	194	62	sg	sg	PROPN
ejpam-4673	194	63	and	and	CCONJ
ejpam-4673	194	64	sh	sh	PROPN
ejpam-4673	194	65	are	be	AUX
ejpam-4673	194	66	complement	complement	NOUN
ejpam-4673	194	67	differentiating	differentiating	NOUN
ejpam-4673	194	68	and	and	CCONJ
ejpam-4673	194	69	pointwise	pointwise	VERB
ejpam-4673	194	70	non	non	ADJ
ejpam-4673	194	71	-	-	ADJ
ejpam-4673	194	72	dominating	dominating	ADJ
ejpam-4673	194	73	sets	set	NOUN
ejpam-4673	194	74	in	in	ADP
ejpam-4673	194	75	g	g	PROPN
ejpam-4673	194	76	and	and	CCONJ
ejpam-4673	194	77	h	h	NOUN
ejpam-4673	194	78	,	,	PUNCT
ejpam-4673	194	79	respectively	respectively	ADV
ejpam-4673	194	80	.	.	PUNCT
ejpam-4673	195	1	then	then	ADV
ejpam-4673	195	2	s	s	VERB
ejpam-4673	195	3	is	be	AUX
ejpam-4673	195	4	a	a	DET
ejpam-4673	195	5	hop	hop	NOUN
ejpam-4673	195	6	dominating	dominating	NOUN
ejpam-4673	195	7	set	set	VERB
ejpam-4673	195	8	in	in	ADP
ejpam-4673	195	9	g	g	PROPN
ejpam-4673	195	10	+	+	CCONJ
ejpam-4673	195	11	h	h	NOUN
ejpam-4673	195	12	by	by	ADP
ejpam-4673	195	13	theorem	theorem	NOUN
ejpam-4673	195	14	2	2	NUM
ejpam-4673	195	15	.	.	PUNCT
ejpam-4673	196	1	next	next	ADV
ejpam-4673	196	2	,	,	PUNCT
ejpam-4673	196	3	let	let	VERB
ejpam-4673	196	4	a	a	DET
ejpam-4673	196	5	,	,	PUNCT
ejpam-4673	196	6	b	b	PROPN
ejpam-4673	196	7	∈	∈	PROPN
ejpam-4673	196	8	v	v	NOUN
ejpam-4673	196	9	(	(	PUNCT
ejpam-4673	196	10	g	g	PROPN
ejpam-4673	196	11	+	+	NOUN
ejpam-4673	196	12	h	h	NOUN
ejpam-4673	196	13	)	)	PUNCT
ejpam-4673	196	14	where	where	SCONJ
ejpam-4673	196	15	a	a	DET
ejpam-4673	196	16	̸=	̸=	PROPN
ejpam-4673	196	17	b.	b.	PROPN
ejpam-4673	196	18	suppose	suppose	VERB
ejpam-4673	196	19	that	that	SCONJ
ejpam-4673	196	20	a	a	DET
ejpam-4673	196	21	,	,	PUNCT
ejpam-4673	196	22	b	b	PROPN
ejpam-4673	196	23	∈	∈	PROPN
ejpam-4673	196	24	v	v	NOUN
ejpam-4673	196	25	(	(	PUNCT
ejpam-4673	196	26	g	g	NOUN
ejpam-4673	196	27	)	)	PUNCT
ejpam-4673	196	28	.	.	PUNCT
ejpam-4673	197	1	since	since	SCONJ
ejpam-4673	197	2	sg	sg	PROPN
ejpam-4673	197	3	is	be	AUX
ejpam-4673	197	4	complement	complement	NOUN
ejpam-4673	197	5	differentiating	differentiate	VERB
ejpam-4673	197	6	in	in	ADP
ejpam-4673	197	7	g	g	PROPN
ejpam-4673	197	8	,	,	PUNCT
ejpam-4673	197	9	n2	n2	NOUN
ejpam-4673	197	10	g+h	g+h	PROPN
ejpam-4673	198	1	[	[	X
ejpam-4673	198	2	a	a	X
ejpam-4673	198	3	]	]	X
ejpam-4673	198	4	∩	∩	X
ejpam-4673	198	5	s	s	PART
ejpam-4673	198	6	=	=	PUNCT
ejpam-4673	199	1	[	[	X
ejpam-4673	199	2	v	v	X
ejpam-4673	199	3	(	(	PUNCT
ejpam-4673	199	4	g	g	NOUN
ejpam-4673	199	5	)	)	PUNCT
ejpam-4673	199	6	\	\	NOUN
ejpam-4673	199	7	ng(a	ng(a	NOUN
ejpam-4673	199	8	)	)	PUNCT
ejpam-4673	199	9	]	]	PUNCT
ejpam-4673	200	1	∩	∩	NOUN
ejpam-4673	200	2	sg	sg	ADP
ejpam-4673	200	3	̸=	̸=	PROPN
ejpam-4673	200	4	[	[	PUNCT
ejpam-4673	200	5	v	v	X
ejpam-4673	200	6	(	(	PUNCT
ejpam-4673	200	7	g	g	NOUN
ejpam-4673	200	8	)	)	PUNCT
ejpam-4673	200	9	\	\	NOUN
ejpam-4673	200	10	ng(b	ng(b	NOUN
ejpam-4673	200	11	)	)	PUNCT
ejpam-4673	200	12	]	]	PUNCT
ejpam-4673	200	13	∩	∩	ADJ
ejpam-4673	200	14	sg	sg	PROPN
ejpam-4673	200	15	=	=	PROPN
ejpam-4673	200	16	n2	n2	PROPN
ejpam-4673	200	17	g+h	g+h	PROPN
ejpam-4673	201	1	[	[	X
ejpam-4673	201	2	b	b	X
ejpam-4673	201	3	]	]	X
ejpam-4673	201	4	∩	∩	PROPN
ejpam-4673	201	5	s.	s.	PROPN
ejpam-4673	201	6	similarly	similarly	ADV
ejpam-4673	201	7	,	,	PUNCT
ejpam-4673	201	8	n2	n2	PROPN
ejpam-4673	201	9	g+h	g+h	PROPN
ejpam-4673	202	1	[	[	X
ejpam-4673	202	2	a	a	X
ejpam-4673	202	3	]	]	X
ejpam-4673	202	4	∩	∩	X
ejpam-4673	202	5	s	s	PART
ejpam-4673	202	6	=	=	PUNCT
ejpam-4673	203	1	[	[	X
ejpam-4673	203	2	v	v	X
ejpam-4673	203	3	(	(	PUNCT
ejpam-4673	203	4	h	h	NOUN
ejpam-4673	203	5	)	)	PUNCT
ejpam-4673	203	6	\nh(a)]∩sh	\nh(a)]∩sh	PUNCT
ejpam-4673	203	7	̸=	̸=	PROPN
ejpam-4673	203	8	[	[	X
ejpam-4673	203	9	v	v	X
ejpam-4673	203	10	(	(	PUNCT
ejpam-4673	203	11	h	h	NOUN
ejpam-4673	203	12	)	)	PUNCT
ejpam-4673	203	13	\nh(b)]∩sh	\nh(b)]∩sh	NOUN
ejpam-4673	203	14	=	=	SYM
ejpam-4673	203	15	n2	n2	NOUN
ejpam-4673	203	16	g+h	g+h	PROPN
ejpam-4673	204	1	[	[	X
ejpam-4673	204	2	b]∩s	b]∩s	X
ejpam-4673	204	3	if	if	SCONJ
ejpam-4673	204	4	a	a	DET
ejpam-4673	204	5	,	,	PUNCT
ejpam-4673	204	6	b	b	PROPN
ejpam-4673	204	7	∈	∈	PROPN
ejpam-4673	204	8	v	v	NOUN
ejpam-4673	204	9	(	(	PUNCT
ejpam-4673	204	10	h	h	NOUN
ejpam-4673	204	11	)	)	PUNCT
ejpam-4673	204	12	.	.	PUNCT
ejpam-4673	205	1	suppose	suppose	VERB
ejpam-4673	205	2	now	now	ADV
ejpam-4673	205	3	that	that	SCONJ
ejpam-4673	205	4	a	a	DET
ejpam-4673	205	5	∈	∈	PROPN
ejpam-4673	205	6	v	v	NOUN
ejpam-4673	205	7	(	(	PUNCT
ejpam-4673	205	8	g	g	NOUN
ejpam-4673	205	9	)	)	PUNCT
ejpam-4673	205	10	and	and	CCONJ
ejpam-4673	205	11	b	b	X
ejpam-4673	205	12	∈	∈	PROPN
ejpam-4673	205	13	v	v	ADP
ejpam-4673	205	14	(	(	PUNCT
ejpam-4673	205	15	h	h	NOUN
ejpam-4673	205	16	)	)	PUNCT
ejpam-4673	205	17	.	.	PUNCT
ejpam-4673	206	1	if	if	SCONJ
ejpam-4673	206	2	a	a	DET
ejpam-4673	206	3	∈	∈	PROPN
ejpam-4673	206	4	sg	sg	NOUN
ejpam-4673	206	5	,	,	PUNCT
ejpam-4673	206	6	then	then	ADV
ejpam-4673	206	7	a	a	DET
ejpam-4673	206	8	∈	∈	PROPN
ejpam-4673	206	9	(	(	PUNCT
ejpam-4673	206	10	n2	n2	NOUN
ejpam-4673	206	11	g+h	g+h	PROPN
ejpam-4673	207	1	[	[	X
ejpam-4673	207	2	a]∩s)\(n2	a]∩s)\(n2	NUM
ejpam-4673	207	3	g+h	g+h	PUNCT
ejpam-4673	208	1	[	[	X
ejpam-4673	208	2	b]∩s	b]∩s	X
ejpam-4673	208	3	)	)	PUNCT
ejpam-4673	208	4	.	.	PUNCT
ejpam-4673	209	1	if	if	SCONJ
ejpam-4673	209	2	a	a	DET
ejpam-4673	209	3	/∈	/∈	INTJ
ejpam-4673	209	4	sg	sg	PROPN
ejpam-4673	209	5	,	,	PUNCT
ejpam-4673	209	6	then	then	ADV
ejpam-4673	209	7	there	there	PRON
ejpam-4673	209	8	exists	exist	VERB
ejpam-4673	209	9	d	d	PROPN
ejpam-4673	209	10	∈	∈	PROPN
ejpam-4673	209	11	sg	sg	ADP
ejpam-4673	209	12	\	\	PROPN
ejpam-4673	209	13	ng(a	ng(a	NOUN
ejpam-4673	209	14	)	)	PUNCT
ejpam-4673	209	15	because	because	SCONJ
ejpam-4673	209	16	sg	sg	PROPN
ejpam-4673	209	17	is	be	AUX
ejpam-4673	209	18	pointwise	pointwise	PROPN
ejpam-4673	209	19	non	non	ADJ
ejpam-4673	209	20	-	-	ADJ
ejpam-4673	209	21	dominating	dominating	NOUN
ejpam-4673	209	22	in	in	ADP
ejpam-4673	209	23	g.	g.	PROPN
ejpam-4673	209	24	hence	hence	ADV
ejpam-4673	209	25	,	,	PUNCT
ejpam-4673	209	26	d	d	PROPN
ejpam-4673	209	27	∈	∈	PROPN
ejpam-4673	209	28	(	(	PUNCT
ejpam-4673	209	29	n2	n2	NOUN
ejpam-4673	209	30	g+h	g+h	PROPN
ejpam-4673	210	1	[	[	X
ejpam-4673	210	2	a	a	X
ejpam-4673	210	3	]	]	X
ejpam-4673	210	4	∩	∩	ADJ
ejpam-4673	210	5	s	s	NOUN
ejpam-4673	210	6	)	)	PUNCT
ejpam-4673	210	7	\	\	NOUN
ejpam-4673	210	8	(	(	PUNCT
ejpam-4673	210	9	n2	n2	NOUN
ejpam-4673	211	1	g+h	g+h	PROPN
ejpam-4673	212	1	[	[	X
ejpam-4673	212	2	b	b	X
ejpam-4673	212	3	]	]	X
ejpam-4673	212	4	∩	∩	X
ejpam-4673	212	5	s	s	PART
ejpam-4673	212	6	)	)	PUNCT
ejpam-4673	212	7	.	.	PUNCT
ejpam-4673	213	1	in	in	ADP
ejpam-4673	213	2	either	either	DET
ejpam-4673	213	3	case	case	NOUN
ejpam-4673	213	4	,	,	PUNCT
ejpam-4673	213	5	we	we	PRON
ejpam-4673	213	6	have	have	VERB
ejpam-4673	213	7	n2	n2	PROPN
ejpam-4673	213	8	g+h	g+h	PROPN
ejpam-4673	214	1	[	[	X
ejpam-4673	214	2	a	a	X
ejpam-4673	214	3	]	]	X
ejpam-4673	214	4	∩	∩	X
ejpam-4673	214	5	s	s	PART
ejpam-4673	214	6	̸=	̸=	PROPN
ejpam-4673	214	7	n2	n2	NOUN
ejpam-4673	214	8	g+h	g+h	PROPN
ejpam-4673	215	1	[	[	X
ejpam-4673	215	2	b	b	X
ejpam-4673	215	3	]	]	X
ejpam-4673	215	4	∩	∩	PROPN
ejpam-4673	215	5	s.	s.	PROPN
ejpam-4673	215	6	therefore	therefore	ADV
ejpam-4673	215	7	,	,	PUNCT
ejpam-4673	215	8	s	s	VERB
ejpam-4673	215	9	is	be	AUX
ejpam-4673	215	10	a	a	DET
ejpam-4673	215	11	hop	hop	NOUN
ejpam-4673	215	12	differentiating	differentiate	VERB
ejpam-4673	215	13	hop	hop	NOUN
ejpam-4673	215	14	dominating	dominating	NOUN
ejpam-4673	215	15	set	set	VERB
ejpam-4673	215	16	in	in	ADP
ejpam-4673	215	17	g+h	g+h	PROPN
ejpam-4673	215	18	.	.	PUNCT
ejpam-4673	216	1	s.	s.	PROPN
ejpam-4673	216	2	canoy	canoy	PROPN
ejpam-4673	216	3	jr	jr	PROPN
ejpam-4673	216	4	.	.	PROPN
ejpam-4673	216	5	,	,	PUNCT
ejpam-4673	216	6	c.	c.	PROPN
ejpam-4673	216	7	saromines	saromine	VERB
ejpam-4673	216	8	/	/	SYM
ejpam-4673	216	9	eur	eur	PROPN
ejpam-4673	216	10	.	.	PUNCT
ejpam-4673	217	1	j.	j.	PROPN
ejpam-4673	217	2	pure	pure	PROPN
ejpam-4673	217	3	appl	appl	PROPN
ejpam-4673	217	4	.	.	PROPN
ejpam-4673	217	5	math	math	PROPN
ejpam-4673	217	6	,	,	PUNCT
ejpam-4673	217	7	16	16	NUM
ejpam-4673	217	8	(	(	PUNCT
ejpam-4673	217	9	1	1	NUM
ejpam-4673	217	10	)	)	PUNCT
ejpam-4673	217	11	(	(	PUNCT
ejpam-4673	217	12	2023	2023	NUM
ejpam-4673	217	13	)	)	PUNCT
ejpam-4673	217	14	,	,	PUNCT
ejpam-4673	217	15	440	440	NUM
ejpam-4673	217	16	-	-	SYM
ejpam-4673	217	17	453	453	NUM
ejpam-4673	217	18	446	446	NUM
ejpam-4673	217	19	corollary	corollary	ADJ
ejpam-4673	217	20	3	3	NUM
ejpam-4673	217	21	.	.	PUNCT
ejpam-4673	218	1	let	let	VERB
ejpam-4673	218	2	g	g	PRON
ejpam-4673	218	3	be	be	AUX
ejpam-4673	218	4	a	a	DET
ejpam-4673	218	5	graph	graph	NOUN
ejpam-4673	218	6	and	and	CCONJ
ejpam-4673	218	7	let	let	VERB
ejpam-4673	218	8	n	n	PRON
ejpam-4673	218	9	be	be	AUX
ejpam-4673	218	10	a	a	DET
ejpam-4673	218	11	positive	positive	ADJ
ejpam-4673	218	12	integer	integer	NOUN
ejpam-4673	218	13	.	.	PUNCT
ejpam-4673	219	1	then	then	ADV
ejpam-4673	219	2	s	s	VERB
ejpam-4673	219	3	⊆	⊆	NUM
ejpam-4673	219	4	v	v	NOUN
ejpam-4673	219	5	(	(	PUNCT
ejpam-4673	219	6	kn	kn	NOUN
ejpam-4673	219	7	+	+	PROPN
ejpam-4673	219	8	g	g	NOUN
ejpam-4673	219	9	)	)	PUNCT
ejpam-4673	219	10	is	be	AUX
ejpam-4673	219	11	a	a	DET
ejpam-4673	219	12	hop	hop	NOUN
ejpam-4673	219	13	differentiating	differentiate	VERB
ejpam-4673	219	14	hop	hop	NOUN
ejpam-4673	219	15	dominating	dominating	NOUN
ejpam-4673	219	16	set	set	VERB
ejpam-4673	219	17	in	in	ADP
ejpam-4673	219	18	kn	kn	PROPN
ejpam-4673	219	19	+	+	CCONJ
ejpam-4673	219	20	g	g	PROPN
ejpam-4673	219	21	if	if	SCONJ
ejpam-4673	220	1	and	and	CCONJ
ejpam-4673	220	2	only	only	ADV
ejpam-4673	220	3	if	if	SCONJ
ejpam-4673	220	4	s	s	VERB
ejpam-4673	220	5	=	=	SYM
ejpam-4673	220	6	v	v	PROPN
ejpam-4673	220	7	(	(	PUNCT
ejpam-4673	220	8	kn	kn	PROPN
ejpam-4673	220	9	)	)	PUNCT
ejpam-4673	220	10	∪	∪	ADP
ejpam-4673	220	11	sg	sg	PROPN
ejpam-4673	220	12	,	,	PUNCT
ejpam-4673	220	13	where	where	SCONJ
ejpam-4673	220	14	sg	sg	PROPN
ejpam-4673	220	15	is	be	AUX
ejpam-4673	220	16	complement	complement	NOUN
ejpam-4673	220	17	differentiating	differentiating	NOUN
ejpam-4673	220	18	and	and	CCONJ
ejpam-4673	220	19	pointwise	pointwise	VERB
ejpam-4673	220	20	non	non	ADJ
ejpam-4673	220	21	-	-	ADJ
ejpam-4673	220	22	dominating	dominating	ADJ
ejpam-4673	220	23	set	set	NOUN
ejpam-4673	220	24	in	in	ADP
ejpam-4673	220	25	g.	g.	PROPN
ejpam-4673	220	26	proof	proof	PROPN
ejpam-4673	220	27	.	.	PUNCT
ejpam-4673	221	1	the	the	DET
ejpam-4673	221	2	only	only	ADJ
ejpam-4673	221	3	pointwise	pointwise	PROPN
ejpam-4673	221	4	non	non	ADJ
ejpam-4673	221	5	-	-	ADJ
ejpam-4673	221	6	dominating	dominating	ADJ
ejpam-4673	221	7	set	set	NOUN
ejpam-4673	221	8	in	in	ADP
ejpam-4673	221	9	kn	kn	PROPN
ejpam-4673	221	10	is	be	AUX
ejpam-4673	221	11	v	v	NOUN
ejpam-4673	221	12	(	(	PUNCT
ejpam-4673	221	13	kn	kn	PROPN
ejpam-4673	221	14	)	)	PUNCT
ejpam-4673	221	15	.	.	PUNCT
ejpam-4673	222	1	thus	thus	ADV
ejpam-4673	222	2	,	,	PUNCT
ejpam-4673	222	3	by	by	ADP
ejpam-4673	222	4	theorem	theorem	NOUN
ejpam-4673	222	5	3	3	NUM
ejpam-4673	222	6	,	,	PUNCT
ejpam-4673	222	7	the	the	DET
ejpam-4673	222	8	result	result	NOUN
ejpam-4673	222	9	follows	follow	VERB
ejpam-4673	222	10	.	.	PUNCT
ejpam-4673	223	1	the	the	DET
ejpam-4673	223	2	next	next	ADJ
ejpam-4673	223	3	results	result	NOUN
ejpam-4673	223	4	follow	follow	VERB
ejpam-4673	223	5	directly	directly	ADV
ejpam-4673	223	6	from	from	ADP
ejpam-4673	223	7	theorem	theorem	ADJ
ejpam-4673	223	8	3	3	NUM
ejpam-4673	223	9	and	and	CCONJ
ejpam-4673	223	10	corollary	corollary	ADJ
ejpam-4673	223	11	3	3	NUM
ejpam-4673	223	12	.	.	PUNCT
ejpam-4673	223	13	corollary	corollary	ADJ
ejpam-4673	223	14	4	4	NUM
ejpam-4673	223	15	.	.	PUNCT
ejpam-4673	224	1	let	let	VERB
ejpam-4673	224	2	g	g	NOUN
ejpam-4673	224	3	and	and	CCONJ
ejpam-4673	224	4	h	h	NOUN
ejpam-4673	224	5	be	be	VERB
ejpam-4673	224	6	any	any	DET
ejpam-4673	224	7	two	two	NUM
ejpam-4673	224	8	graphs	graph	NOUN
ejpam-4673	224	9	.	.	PUNCT
ejpam-4673	225	1	then	then	ADV
ejpam-4673	225	2	γdh(g+h	γdh(g+h	PUNCT
ejpam-4673	225	3	)	)	PUNCT
ejpam-4673	226	1	=	=	SYM
ejpam-4673	226	2	cdpnd(g	cdpnd(g	PROPN
ejpam-4673	226	3	)	)	PUNCT
ejpam-4673	226	4	+	+	NUM
ejpam-4673	226	5	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	226	6	)	)	PUNCT
ejpam-4673	226	7	=	=	SYM
ejpam-4673	226	8	γd(g	γd(g	X
ejpam-4673	226	9	)	)	PUNCT
ejpam-4673	226	10	+	+	CCONJ
ejpam-4673	226	11	γd(h	γd(h	NUM
ejpam-4673	226	12	)	)	PUNCT
ejpam-4673	226	13	.	.	PUNCT
ejpam-4673	227	1	corollary	corollary	ADJ
ejpam-4673	227	2	5	5	NUM
ejpam-4673	227	3	.	.	PUNCT
ejpam-4673	228	1	let	let	VERB
ejpam-4673	228	2	g	g	PRON
ejpam-4673	228	3	be	be	AUX
ejpam-4673	228	4	a	a	DET
ejpam-4673	228	5	graph	graph	NOUN
ejpam-4673	228	6	and	and	CCONJ
ejpam-4673	228	7	let	let	VERB
ejpam-4673	228	8	n	n	PRON
ejpam-4673	228	9	be	be	AUX
ejpam-4673	228	10	a	a	DET
ejpam-4673	228	11	positive	positive	ADJ
ejpam-4673	228	12	integer	integer	NOUN
ejpam-4673	228	13	.	.	PUNCT
ejpam-4673	229	1	then	then	ADV
ejpam-4673	229	2	γdh(kn	γdh(kn	PRON
ejpam-4673	229	3	+	+	CCONJ
ejpam-4673	229	4	g	g	NOUN
ejpam-4673	229	5	)	)	PUNCT
ejpam-4673	229	6	=	=	PUNCT
ejpam-4673	230	1	n+	n+	X
ejpam-4673	230	2	cdpnd(g	cdpnd(g	VERB
ejpam-4673	230	3	)	)	PUNCT
ejpam-4673	230	4	=	=	SYM
ejpam-4673	230	5	n+	n+	X
ejpam-4673	230	6	γd(g	γd(g	NUM
ejpam-4673	230	7	)	)	PUNCT
ejpam-4673	230	8	.	.	PUNCT
ejpam-4673	231	1	the	the	DET
ejpam-4673	231	2	next	next	ADJ
ejpam-4673	231	3	result	result	NOUN
ejpam-4673	231	4	is	be	AUX
ejpam-4673	231	5	a	a	DET
ejpam-4673	231	6	restatement	restatement	NOUN
ejpam-4673	231	7	of	of	ADP
ejpam-4673	231	8	the	the	DET
ejpam-4673	231	9	one	one	NOUN
ejpam-4673	231	10	in	in	ADP
ejpam-4673	231	11	[	[	X
ejpam-4673	231	12	11	11	NUM
ejpam-4673	231	13	]	]	PUNCT
ejpam-4673	231	14	.	.	PUNCT
ejpam-4673	232	1	theorem	theorem	ADJ
ejpam-4673	232	2	4	4	NUM
ejpam-4673	232	3	.	.	PUNCT
ejpam-4673	233	1	let	let	VERB
ejpam-4673	233	2	g	g	NOUN
ejpam-4673	233	3	and	and	CCONJ
ejpam-4673	233	4	h	h	NOUN
ejpam-4673	233	5	be	be	VERB
ejpam-4673	233	6	any	any	DET
ejpam-4673	233	7	two	two	NUM
ejpam-4673	233	8	graphs	graph	NOUN
ejpam-4673	233	9	.	.	PUNCT
ejpam-4673	234	1	a	a	DET
ejpam-4673	234	2	set	set	NOUN
ejpam-4673	234	3	c	c	NOUN
ejpam-4673	234	4	⊆	⊆	NUM
ejpam-4673	234	5	v	v	NOUN
ejpam-4673	234	6	(	(	PUNCT
ejpam-4673	234	7	g	g	NOUN
ejpam-4673	234	8	)	)	PUNCT
ejpam-4673	234	9	is	be	AUX
ejpam-4673	234	10	a	a	DET
ejpam-4673	234	11	hop	hop	NOUN
ejpam-4673	234	12	dominating	dominating	NOUN
ejpam-4673	234	13	set	set	VERB
ejpam-4673	234	14	in	in	ADP
ejpam-4673	234	15	g	g	PROPN
ejpam-4673	234	16	◦	◦	NOUN
ejpam-4673	234	17	h	h	NOUN
ejpam-4673	234	18	if	if	SCONJ
ejpam-4673	235	1	and	and	CCONJ
ejpam-4673	235	2	only	only	ADV
ejpam-4673	235	3	if	if	SCONJ
ejpam-4673	235	4	c	c	PROPN
ejpam-4673	235	5	=	=	SYM
ejpam-4673	235	6	a∪	a∪	PROPN
ejpam-4673	235	7	(	(	PUNCT
ejpam-4673	235	8	∪v∈v	∪v∈v	X
ejpam-4673	235	9	(	(	PUNCT
ejpam-4673	235	10	g)cv	g)cv	PROPN
ejpam-4673	235	11	)	)	PUNCT
ejpam-4673	235	12	,	,	PUNCT
ejpam-4673	235	13	where	where	SCONJ
ejpam-4673	235	14	a	a	DET
ejpam-4673	235	15	⊆	⊆	NUM
ejpam-4673	235	16	v	v	NOUN
ejpam-4673	235	17	(	(	PUNCT
ejpam-4673	235	18	g	g	NOUN
ejpam-4673	235	19	)	)	PUNCT
ejpam-4673	235	20	and	and	CCONJ
ejpam-4673	235	21	cv	cv	PROPN
ejpam-4673	235	22	⊆	⊆	NUM
ejpam-4673	235	23	v	v	PROPN
ejpam-4673	235	24	(	(	PUNCT
ejpam-4673	235	25	hv	hv	PROPN
ejpam-4673	235	26	)	)	PUNCT
ejpam-4673	235	27	for	for	ADP
ejpam-4673	235	28	each	each	DET
ejpam-4673	235	29	v	v	NUM
ejpam-4673	235	30	∈	∈	PROPN
ejpam-4673	235	31	v	v	NOUN
ejpam-4673	235	32	(	(	PUNCT
ejpam-4673	235	33	g	g	NOUN
ejpam-4673	235	34	)	)	PUNCT
ejpam-4673	235	35	,	,	PUNCT
ejpam-4673	235	36	and	and	CCONJ
ejpam-4673	235	37	satisfies	satisfy	VERB
ejpam-4673	235	38	the	the	DET
ejpam-4673	235	39	following	follow	VERB
ejpam-4673	235	40	conditions	condition	NOUN
ejpam-4673	235	41	:	:	PUNCT
ejpam-4673	235	42	(	(	PUNCT
ejpam-4673	235	43	i	i	NOUN
ejpam-4673	235	44	)	)	PUNCT
ejpam-4673	235	45	for	for	ADP
ejpam-4673	235	46	each	each	DET
ejpam-4673	235	47	w	w	PROPN
ejpam-4673	235	48	∈	∈	PROPN
ejpam-4673	235	49	v	v	ADP
ejpam-4673	235	50	(	(	PUNCT
ejpam-4673	235	51	g	g	NOUN
ejpam-4673	235	52	)	)	PUNCT
ejpam-4673	235	53	\	\	PROPN
ejpam-4673	235	54	a	a	PRON
ejpam-4673	235	55	,	,	PUNCT
ejpam-4673	235	56	there	there	PRON
ejpam-4673	235	57	exists	exist	VERB
ejpam-4673	235	58	x	x	X
ejpam-4673	235	59	∈	∈	PROPN
ejpam-4673	235	60	a	a	PRON
ejpam-4673	235	61	with	with	ADP
ejpam-4673	235	62	dg(w	dg(w	NOUN
ejpam-4673	235	63	,	,	PUNCT
ejpam-4673	235	64	x	x	X
ejpam-4673	235	65	)	)	PUNCT
ejpam-4673	235	66	=	=	SYM
ejpam-4673	235	67	2	2	NUM
ejpam-4673	235	68	or	or	CCONJ
ejpam-4673	235	69	there	there	PRON
ejpam-4673	235	70	exists	exist	VERB
ejpam-4673	235	71	y	y	PROPN
ejpam-4673	235	72	∈	∈	PROPN
ejpam-4673	235	73	ng(w	ng(w	NOUN
ejpam-4673	235	74	)	)	PUNCT
ejpam-4673	235	75	with	with	ADP
ejpam-4673	235	76	cy	cy	PROPN
ejpam-4673	235	77	̸=	̸=	PROPN
ejpam-4673	235	78	∅.	∅.	ADP
ejpam-4673	235	79	(	(	PUNCT
ejpam-4673	235	80	ii	ii	NOUN
ejpam-4673	235	81	)	)	PUNCT
ejpam-4673	235	82	cw	cw	NOUN
ejpam-4673	235	83	is	be	AUX
ejpam-4673	235	84	a	a	DET
ejpam-4673	235	85	pointwise	pointwise	ADJ
ejpam-4673	235	86	non	non	ADJ
ejpam-4673	235	87	-	-	ADJ
ejpam-4673	235	88	dominating	dominating	ADJ
ejpam-4673	235	89	set	set	NOUN
ejpam-4673	235	90	in	in	ADP
ejpam-4673	235	91	hw	hw	PRON
ejpam-4673	235	92	for	for	ADP
ejpam-4673	235	93	each	each	DET
ejpam-4673	235	94	w	w	PROPN
ejpam-4673	235	95	∈	∈	PROPN
ejpam-4673	235	96	v	v	ADP
ejpam-4673	235	97	(	(	PUNCT
ejpam-4673	235	98	g	g	NOUN
ejpam-4673	235	99	)	)	PUNCT
ejpam-4673	235	100	\ng(a	\ng(a	PROPN
ejpam-4673	235	101	)	)	PUNCT
ejpam-4673	235	102	.	.	PUNCT
ejpam-4673	236	1	theorem	theorem	NOUN
ejpam-4673	236	2	5	5	NUM
ejpam-4673	236	3	.	.	PUNCT
ejpam-4673	237	1	let	let	VERB
ejpam-4673	237	2	g	g	NOUN
ejpam-4673	237	3	and	and	CCONJ
ejpam-4673	237	4	h	h	PROPN
ejpam-4673	237	5	be	be	VERB
ejpam-4673	237	6	non	non	ADJ
ejpam-4673	237	7	-	-	ADJ
ejpam-4673	237	8	trivial	trivial	ADJ
ejpam-4673	237	9	connected	connected	ADJ
ejpam-4673	237	10	graphs	graph	NOUN
ejpam-4673	237	11	such	such	ADJ
ejpam-4673	237	12	that	that	SCONJ
ejpam-4673	237	13	h	h	NOUN
ejpam-4673	237	14	is	be	AUX
ejpam-4673	237	15	complement	complement	NOUN
ejpam-4673	237	16	point	point	NOUN
ejpam-4673	237	17	distinguishing	distinguishing	NOUN
ejpam-4673	237	18	.	.	PUNCT
ejpam-4673	238	1	then	then	ADV
ejpam-4673	238	2	s	s	VERB
ejpam-4673	238	3	⊆	⊆	NUM
ejpam-4673	238	4	v	v	NOUN
ejpam-4673	238	5	(	(	PUNCT
ejpam-4673	238	6	g	g	PROPN
ejpam-4673	238	7	◦	◦	NOUN
ejpam-4673	238	8	h	h	NOUN
ejpam-4673	238	9	)	)	PUNCT
ejpam-4673	238	10	is	be	AUX
ejpam-4673	238	11	hop	hop	NOUN
ejpam-4673	238	12	differentiating	differentiate	VERB
ejpam-4673	238	13	hop	hop	NOUN
ejpam-4673	238	14	dominating	dominating	NOUN
ejpam-4673	238	15	in	in	ADP
ejpam-4673	238	16	g	g	PROPN
ejpam-4673	238	17	◦	◦	NOUN
ejpam-4673	238	18	h	h	NOUN
ejpam-4673	238	19	if	if	SCONJ
ejpam-4673	239	1	and	and	CCONJ
ejpam-4673	239	2	only	only	ADV
ejpam-4673	239	3	if	if	SCONJ
ejpam-4673	239	4	s	s	VERB
ejpam-4673	239	5	=	=	X
ejpam-4673	239	6	a	a	DET
ejpam-4673	239	7	∪	∪	NOUN
ejpam-4673	239	8	[	[	X
ejpam-4673	239	9	∪v∈v	∪v∈v	X
ejpam-4673	239	10	(	(	PUNCT
ejpam-4673	239	11	g)dv	g)dv	NOUN
ejpam-4673	239	12	]	]	PUNCT
ejpam-4673	239	13	and	and	CCONJ
ejpam-4673	239	14	satisfies	satisfy	VERB
ejpam-4673	239	15	the	the	DET
ejpam-4673	239	16	following	follow	VERB
ejpam-4673	239	17	conditions	condition	NOUN
ejpam-4673	239	18	:	:	PUNCT
ejpam-4673	239	19	(	(	PUNCT
ejpam-4673	239	20	i	i	NOUN
ejpam-4673	239	21	)	)	PUNCT
ejpam-4673	239	22	dw	dw	PROPN
ejpam-4673	239	23	is	be	AUX
ejpam-4673	239	24	a	a	DET
ejpam-4673	239	25	pointwise	pointwise	ADJ
ejpam-4673	239	26	non	non	ADJ
ejpam-4673	239	27	-	-	ADJ
ejpam-4673	239	28	dominating	dominating	ADJ
ejpam-4673	239	29	set	set	NOUN
ejpam-4673	239	30	in	in	ADP
ejpam-4673	239	31	hw	hw	PRON
ejpam-4673	239	32	for	for	ADP
ejpam-4673	239	33	each	each	DET
ejpam-4673	239	34	w	w	PROPN
ejpam-4673	239	35	∈	∈	PROPN
ejpam-4673	239	36	v	v	ADP
ejpam-4673	239	37	(	(	PUNCT
ejpam-4673	239	38	g	g	NOUN
ejpam-4673	239	39	)	)	PUNCT
ejpam-4673	239	40	\ng(a	\ng(a	PROPN
ejpam-4673	239	41	)	)	PUNCT
ejpam-4673	239	42	.	.	PUNCT
ejpam-4673	240	1	(	(	PUNCT
ejpam-4673	240	2	ii	ii	X
ejpam-4673	240	3	)	)	PUNCT
ejpam-4673	240	4	dv	dv	PROPN
ejpam-4673	240	5	is	be	AUX
ejpam-4673	240	6	complement	complement	NOUN
ejpam-4673	240	7	differentiating	differentiate	VERB
ejpam-4673	240	8	in	in	ADP
ejpam-4673	240	9	hv	hv	PROPN
ejpam-4673	240	10	for	for	ADP
ejpam-4673	240	11	each	each	DET
ejpam-4673	240	12	v	v	NUM
ejpam-4673	240	13	∈	∈	PROPN
ejpam-4673	240	14	v	v	NOUN
ejpam-4673	240	15	(	(	PUNCT
ejpam-4673	240	16	g	g	NOUN
ejpam-4673	240	17	)	)	PUNCT
ejpam-4673	240	18	.	.	PUNCT
ejpam-4673	241	1	(	(	PUNCT
ejpam-4673	241	2	iii	iii	X
ejpam-4673	241	3	)	)	PUNCT
ejpam-4673	241	4	for	for	ADP
ejpam-4673	241	5	any	any	DET
ejpam-4673	241	6	two	two	NUM
ejpam-4673	241	7	distinct	distinct	ADJ
ejpam-4673	241	8	vertices	vertex	NOUN
ejpam-4673	241	9	v	v	ADP
ejpam-4673	241	10	,	,	PUNCT
ejpam-4673	241	11	w	w	PROPN
ejpam-4673	241	12	∈	∈	PROPN
ejpam-4673	241	13	v	v	ADP
ejpam-4673	241	14	(	(	PUNCT
ejpam-4673	241	15	g	g	NOUN
ejpam-4673	241	16	)	)	PUNCT
ejpam-4673	241	17	,	,	PUNCT
ejpam-4673	241	18	ng(v	ng(v	PUNCT
ejpam-4673	241	19	)	)	PUNCT
ejpam-4673	241	20	̸=	̸=	PROPN
ejpam-4673	241	21	ng(w	ng(w	NOUN
ejpam-4673	241	22	)	)	PUNCT
ejpam-4673	241	23	or	or	CCONJ
ejpam-4673	241	24	n	n	PRON
ejpam-4673	241	25	2	2	NUM
ejpam-4673	241	26	g[v]∩a	g[v]∩a	PROPN
ejpam-4673	241	27	̸=	̸=	PROPN
ejpam-4673	241	28	n2	n2	NOUN
ejpam-4673	241	29	g[w]∩a	g[w]∩a	PROPN
ejpam-4673	241	30	.	.	PUNCT
ejpam-4673	241	31	(	(	PUNCT
ejpam-4673	241	32	iv	iv	X
ejpam-4673	241	33	)	)	PUNCT
ejpam-4673	241	34	dw	dw	PROPN
ejpam-4673	241	35	is	be	AUX
ejpam-4673	241	36	a	a	DET
ejpam-4673	241	37	total	total	ADJ
ejpam-4673	241	38	dominating	dominating	NOUN
ejpam-4673	241	39	set	set	NOUN
ejpam-4673	241	40	in	in	ADP
ejpam-4673	241	41	hw	hw	NOUN
ejpam-4673	241	42	whenever	whenever	SCONJ
ejpam-4673	241	43	ng(v	ng(v	PUNCT
ejpam-4673	241	44	)	)	PUNCT
ejpam-4673	241	45	=	=	PRON
ejpam-4673	242	1	{	{	PUNCT
ejpam-4673	242	2	w	w	NOUN
ejpam-4673	242	3	}	}	PUNCT
ejpam-4673	242	4	for	for	ADP
ejpam-4673	242	5	some	some	DET
ejpam-4673	242	6	v	v	ADP
ejpam-4673	242	7	∈	∈	NOUN
ejpam-4673	242	8	v	v	NOUN
ejpam-4673	242	9	(	(	PUNCT
ejpam-4673	242	10	g	g	NOUN
ejpam-4673	242	11	)	)	PUNCT
ejpam-4673	242	12	.	.	PUNCT
ejpam-4673	243	1	(	(	PUNCT
ejpam-4673	243	2	v	v	NOUN
ejpam-4673	243	3	)	)	PUNCT
ejpam-4673	243	4	if	if	SCONJ
ejpam-4673	243	5	dv	dv	PROPN
ejpam-4673	243	6	and	and	CCONJ
ejpam-4673	243	7	dw	dw	PROPN
ejpam-4673	243	8	,	,	PUNCT
ejpam-4673	243	9	where	where	SCONJ
ejpam-4673	243	10	v	v	ADP
ejpam-4673	243	11	̸=	̸=	PROPN
ejpam-4673	243	12	w	w	PROPN
ejpam-4673	243	13	,	,	PUNCT
ejpam-4673	243	14	are	be	AUX
ejpam-4673	243	15	not	not	PART
ejpam-4673	243	16	pointwise	pointwise	ADJ
ejpam-4673	243	17	non	non	ADJ
ejpam-4673	243	18	-	-	ADJ
ejpam-4673	243	19	dominating	dominating	NOUN
ejpam-4673	243	20	in	in	ADP
ejpam-4673	243	21	hv	hv	PROPN
ejpam-4673	243	22	and	and	CCONJ
ejpam-4673	243	23	hw	hw	PROPN
ejpam-4673	243	24	,	,	PUNCT
ejpam-4673	243	25	respectively	respectively	ADV
ejpam-4673	243	26	,	,	PUNCT
ejpam-4673	243	27	then	then	ADV
ejpam-4673	243	28	ng(v	ng(v	PUNCT
ejpam-4673	243	29	)	)	PUNCT
ejpam-4673	243	30	∩a	∩a	PROPN
ejpam-4673	243	31	̸=	̸=	PROPN
ejpam-4673	243	32	ng(w	ng(w	PUNCT
ejpam-4673	243	33	)	)	PUNCT
ejpam-4673	244	1	∩a	∩a	PROPN
ejpam-4673	244	2	.	.	PUNCT
ejpam-4673	245	1	proof	proof	NOUN
ejpam-4673	245	2	.	.	PUNCT
ejpam-4673	246	1	suppose	suppose	VERB
ejpam-4673	246	2	s	s	PRON
ejpam-4673	246	3	is	be	AUX
ejpam-4673	246	4	a	a	DET
ejpam-4673	246	5	hop	hop	NOUN
ejpam-4673	246	6	differentiating	differentiate	VERB
ejpam-4673	246	7	hop	hop	NOUN
ejpam-4673	246	8	dominating	dominating	NOUN
ejpam-4673	246	9	set	set	VERB
ejpam-4673	246	10	ing	ing	PROPN
ejpam-4673	246	11	◦	◦	PROPN
ejpam-4673	247	1	h.	h.	PROPN
ejpam-4673	247	2	leta	leta	PROPN
ejpam-4673	247	3	=	=	PUNCT
ejpam-4673	247	4	s∩v	s∩v	NOUN
ejpam-4673	247	5	(	(	PUNCT
ejpam-4673	247	6	g	g	NOUN
ejpam-4673	247	7	)	)	PUNCT
ejpam-4673	247	8	and	and	CCONJ
ejpam-4673	247	9	let	let	VERB
ejpam-4673	247	10	dv	dv	PROPN
ejpam-4673	247	11	=	=	PROPN
ejpam-4673	247	12	s	s	PROPN
ejpam-4673	247	13	∩	∩	ADJ
ejpam-4673	247	14	v	v	X
ejpam-4673	247	15	(	(	PUNCT
ejpam-4673	247	16	hv	hv	PROPN
ejpam-4673	247	17	)	)	PUNCT
ejpam-4673	247	18	for	for	ADP
ejpam-4673	247	19	each	each	DET
ejpam-4673	247	20	v	v	NUM
ejpam-4673	247	21	∈	∈	PROPN
ejpam-4673	247	22	v	v	NOUN
ejpam-4673	247	23	(	(	PUNCT
ejpam-4673	247	24	g	g	NOUN
ejpam-4673	247	25	)	)	PUNCT
ejpam-4673	247	26	.	.	PUNCT
ejpam-4673	248	1	then	then	ADV
ejpam-4673	248	2	s	s	VERB
ejpam-4673	248	3	=	=	PUNCT
ejpam-4673	248	4	a∪	a∪	PROPN
ejpam-4673	249	1	[	[	X
ejpam-4673	249	2	∪v∈v	∪v∈v	X
ejpam-4673	249	3	(	(	PUNCT
ejpam-4673	249	4	g)dv	g)dv	NOUN
ejpam-4673	249	5	]	]	PUNCT
ejpam-4673	249	6	and	and	CCONJ
ejpam-4673	249	7	,	,	PUNCT
ejpam-4673	249	8	by	by	ADP
ejpam-4673	249	9	theorem	theorem	NOUN
ejpam-4673	249	10	4	4	NUM
ejpam-4673	249	11	,	,	PUNCT
ejpam-4673	249	12	(	(	PUNCT
ejpam-4673	249	13	i	i	NOUN
ejpam-4673	249	14	)	)	PUNCT
ejpam-4673	249	15	holds	hold	VERB
ejpam-4673	249	16	.	.	PUNCT
ejpam-4673	250	1	let	let	VERB
ejpam-4673	250	2	v	v	NUM
ejpam-4673	250	3	∈	∈	PROPN
ejpam-4673	250	4	v	v	NOUN
ejpam-4673	250	5	(	(	PUNCT
ejpam-4673	250	6	g	g	NOUN
ejpam-4673	250	7	)	)	PUNCT
ejpam-4673	250	8	and	and	CCONJ
ejpam-4673	250	9	let	let	VERB
ejpam-4673	250	10	a	a	DET
ejpam-4673	250	11	,	,	PUNCT
ejpam-4673	250	12	b	b	PROPN
ejpam-4673	250	13	∈	∈	PROPN
ejpam-4673	250	14	v	v	ADP
ejpam-4673	250	15	(	(	PUNCT
ejpam-4673	250	16	hv	hv	PROPN
ejpam-4673	250	17	)	)	PUNCT
ejpam-4673	250	18	with	with	ADP
ejpam-4673	250	19	a	a	DET
ejpam-4673	250	20	̸=	̸=	PROPN
ejpam-4673	250	21	b.	b.	NOUN
ejpam-4673	250	22	since	since	SCONJ
ejpam-4673	250	23	s	s	PROPN
ejpam-4673	250	24	is	be	AUX
ejpam-4673	250	25	a	a	DET
ejpam-4673	250	26	hop	hop	NOUN
ejpam-4673	250	27	differentiating	differentiate	VERB
ejpam-4673	250	28	set	set	NOUN
ejpam-4673	250	29	,	,	PUNCT
ejpam-4673	250	30	(	(	PUNCT
ejpam-4673	250	31	[	[	X
ejpam-4673	250	32	v	v	X
ejpam-4673	250	33	(	(	PUNCT
ejpam-4673	250	34	hv	hv	NOUN
ejpam-4673	250	35	)	)	PUNCT
ejpam-4673	250	36	\nhv(a	\nhv(a	NOUN
ejpam-4673	250	37	)	)	PUNCT
ejpam-4673	250	38	]	]	PUNCT
ejpam-4673	250	39	∩dv	∩dv	NOUN
ejpam-4673	250	40	)	)	PUNCT
ejpam-4673	250	41	∪	∪	ADP
ejpam-4673	250	42	[	[	X
ejpam-4673	250	43	ng(v	ng(v	X
ejpam-4673	250	44	)	)	PUNCT
ejpam-4673	251	1	∩a	∩a	PROPN
ejpam-4673	251	2	]	]	PUNCT
ejpam-4673	251	3	=	=	PUNCT
ejpam-4673	252	1	n2	n2	PROPN
ejpam-4673	252	2	g	g	PROPN
ejpam-4673	252	3	◦	◦	NOUN
ejpam-4673	252	4	h	h	NOUN
ejpam-4673	253	1	[	[	X
ejpam-4673	253	2	a	a	X
ejpam-4673	253	3	]	]	X
ejpam-4673	253	4	∩	∩	X
ejpam-4673	253	5	s	s	PART
ejpam-4673	253	6	̸=	̸=	PROPN
ejpam-4673	253	7	n2	n2	NOUN
ejpam-4673	253	8	g	g	PROPN
ejpam-4673	253	9	◦	◦	NOUN
ejpam-4673	253	10	h	h	NOUN
ejpam-4673	254	1	[	[	X
ejpam-4673	254	2	b	b	X
ejpam-4673	254	3	]	]	X
ejpam-4673	254	4	∩	∩	X
ejpam-4673	254	5	s	s	X
ejpam-4673	254	6	=	=	X
ejpam-4673	254	7	(	(	PUNCT
ejpam-4673	254	8	[	[	X
ejpam-4673	254	9	v	v	X
ejpam-4673	254	10	(	(	PUNCT
ejpam-4673	254	11	hv	hv	NOUN
ejpam-4673	254	12	)	)	PUNCT
ejpam-4673	254	13	\nhv(b	\nhv(b	PROPN
ejpam-4673	254	14	)	)	PUNCT
ejpam-4673	254	15	]	]	PUNCT
ejpam-4673	254	16	∩dv	∩dv	NOUN
ejpam-4673	254	17	)	)	PUNCT
ejpam-4673	254	18	∪	∪	ADP
ejpam-4673	254	19	[	[	X
ejpam-4673	254	20	ng(v	ng(v	X
ejpam-4673	254	21	)	)	PUNCT
ejpam-4673	255	1	∩a	∩a	PROPN
ejpam-4673	255	2	]	]	PUNCT
ejpam-4673	255	3	.	.	PUNCT
ejpam-4673	256	1	s.	s.	PROPN
ejpam-4673	256	2	canoy	canoy	PROPN
ejpam-4673	256	3	jr	jr	PROPN
ejpam-4673	256	4	.	.	PROPN
ejpam-4673	256	5	,	,	PUNCT
ejpam-4673	256	6	c.	c.	PROPN
ejpam-4673	256	7	saromines	saromine	VERB
ejpam-4673	256	8	/	/	SYM
ejpam-4673	256	9	eur	eur	PROPN
ejpam-4673	256	10	.	.	PUNCT
ejpam-4673	257	1	j.	j.	PROPN
ejpam-4673	257	2	pure	pure	PROPN
ejpam-4673	257	3	appl	appl	PROPN
ejpam-4673	257	4	.	.	PROPN
ejpam-4673	257	5	math	math	PROPN
ejpam-4673	257	6	,	,	PUNCT
ejpam-4673	257	7	16	16	NUM
ejpam-4673	257	8	(	(	PUNCT
ejpam-4673	257	9	1	1	NUM
ejpam-4673	257	10	)	)	PUNCT
ejpam-4673	257	11	(	(	PUNCT
ejpam-4673	257	12	2023	2023	NUM
ejpam-4673	257	13	)	)	PUNCT
ejpam-4673	257	14	,	,	PUNCT
ejpam-4673	257	15	440	440	NUM
ejpam-4673	257	16	-	-	SYM
ejpam-4673	257	17	453	453	NUM
ejpam-4673	257	18	447	447	NUM
ejpam-4673	257	19	hence	hence	ADV
ejpam-4673	257	20	,	,	PUNCT
ejpam-4673	257	21	[	[	X
ejpam-4673	257	22	v	v	X
ejpam-4673	257	23	(	(	PUNCT
ejpam-4673	257	24	hv	hv	NOUN
ejpam-4673	257	25	)	)	PUNCT
ejpam-4673	257	26	\nhv(a	\nhv(a	NOUN
ejpam-4673	257	27	)	)	PUNCT
ejpam-4673	257	28	]	]	PUNCT
ejpam-4673	258	1	∩dv	∩dv	PROPN
ejpam-4673	258	2	̸=	̸=	PROPN
ejpam-4673	258	3	[	[	X
ejpam-4673	258	4	v	v	X
ejpam-4673	258	5	(	(	PUNCT
ejpam-4673	258	6	hv	hv	NOUN
ejpam-4673	258	7	)	)	PUNCT
ejpam-4673	258	8	\nhv(b	\nhv(b	PROPN
ejpam-4673	258	9	)	)	PUNCT
ejpam-4673	258	10	]	]	PUNCT
ejpam-4673	259	1	∩dv	∩dv	NOUN
ejpam-4673	259	2	,	,	PUNCT
ejpam-4673	259	3	showing	show	VERB
ejpam-4673	259	4	that	that	SCONJ
ejpam-4673	259	5	dv	dv	PROPN
ejpam-4673	259	6	is	be	AUX
ejpam-4673	259	7	a	a	DET
ejpam-4673	259	8	complement	complement	NOUN
ejpam-4673	259	9	differentiating	differentiating	NOUN
ejpam-4673	259	10	set	set	NOUN
ejpam-4673	259	11	in	in	ADP
ejpam-4673	259	12	hv	hv	PROPN
ejpam-4673	259	13	.	.	PUNCT
ejpam-4673	260	1	thus	thus	ADV
ejpam-4673	260	2	,	,	PUNCT
ejpam-4673	260	3	(	(	PUNCT
ejpam-4673	260	4	ii	ii	NOUN
ejpam-4673	260	5	)	)	PUNCT
ejpam-4673	260	6	holds	hold	VERB
ejpam-4673	260	7	.	.	PUNCT
ejpam-4673	261	1	next	next	ADV
ejpam-4673	261	2	,	,	PUNCT
ejpam-4673	261	3	let	let	VERB
ejpam-4673	261	4	v	v	ADP
ejpam-4673	261	5	,	,	PUNCT
ejpam-4673	261	6	w	w	PROPN
ejpam-4673	261	7	∈	∈	PROPN
ejpam-4673	261	8	v	v	ADP
ejpam-4673	261	9	(	(	PUNCT
ejpam-4673	261	10	g	g	NOUN
ejpam-4673	261	11	)	)	PUNCT
ejpam-4673	261	12	with	with	ADP
ejpam-4673	261	13	v	v	NOUN
ejpam-4673	261	14	̸=	̸=	PROPN
ejpam-4673	261	15	w.	w.	NOUN
ejpam-4673	261	16	since	since	SCONJ
ejpam-4673	261	17	s	s	PROPN
ejpam-4673	261	18	is	be	AUX
ejpam-4673	261	19	a	a	DET
ejpam-4673	261	20	hop	hop	NOUN
ejpam-4673	261	21	differentiating	differentiate	VERB
ejpam-4673	261	22	set	set	NOUN
ejpam-4673	261	23	,	,	PUNCT
ejpam-4673	262	1	[	[	X
ejpam-4673	262	2	n2	n2	ADJ
ejpam-4673	262	3	g[v	g[v	NOUN
ejpam-4673	262	4	]	]	X
ejpam-4673	263	1	∩a	∩a	X
ejpam-4673	263	2	]	]	PUNCT
ejpam-4673	263	3	∪	∪	ADP
ejpam-4673	263	4	[	[	X
ejpam-4673	263	5	∪x∈ng(v)dx	∪x∈ng(v)dx	X
ejpam-4673	263	6	]	]	PUNCT
ejpam-4673	263	7	=	=	PUNCT
ejpam-4673	263	8	n2	n2	PROPN
ejpam-4673	263	9	g	g	PROPN
ejpam-4673	263	10	◦	◦	NOUN
ejpam-4673	263	11	h	h	NOUN
ejpam-4673	263	12	[	[	X
ejpam-4673	263	13	v	v	X
ejpam-4673	263	14	]	]	X
ejpam-4673	263	15	∩	∩	PROPN
ejpam-4673	263	16	s	s	PART
ejpam-4673	263	17	̸=	̸=	PROPN
ejpam-4673	263	18	n2	n2	NOUN
ejpam-4673	263	19	g	g	PROPN
ejpam-4673	263	20	◦	◦	NOUN
ejpam-4673	263	21	h	h	NOUN
ejpam-4673	264	1	[	[	X
ejpam-4673	264	2	w	w	X
ejpam-4673	264	3	]	]	X
ejpam-4673	264	4	∩	∩	X
ejpam-4673	264	5	s	s	PART
ejpam-4673	264	6	=	=	PUNCT
ejpam-4673	264	7	[	[	X
ejpam-4673	264	8	n2	n2	ADJ
ejpam-4673	264	9	g[w	g[w	PROPN
ejpam-4673	264	10	]	]	X
ejpam-4673	265	1	∩a	∩a	X
ejpam-4673	265	2	]	]	PUNCT
ejpam-4673	265	3	∪	∪	ADP
ejpam-4673	265	4	[	[	PUNCT
ejpam-4673	265	5	∪y∈ng(w)dy	∪y∈ng(w)dy	NOUN
ejpam-4673	265	6	]	]	PUNCT
ejpam-4673	265	7	.	.	PUNCT
ejpam-4673	266	1	this	this	PRON
ejpam-4673	266	2	implies	imply	VERB
ejpam-4673	266	3	that	that	DET
ejpam-4673	266	4	n2	n2	ADJ
ejpam-4673	266	5	g[v	g[v	PROPN
ejpam-4673	266	6	]	]	PUNCT
ejpam-4673	266	7	∩	∩	NOUN
ejpam-4673	266	8	a	a	DET
ejpam-4673	266	9	̸=	̸=	PROPN
ejpam-4673	266	10	n2	n2	ADJ
ejpam-4673	266	11	g[w	g[w	PROPN
ejpam-4673	266	12	]	]	PUNCT
ejpam-4673	266	13	∩	∩	NOUN
ejpam-4673	266	14	a	a	PRON
ejpam-4673	266	15	or	or	CCONJ
ejpam-4673	266	16	ng(v	ng(v	NUM
ejpam-4673	266	17	)	)	PUNCT
ejpam-4673	266	18	̸=	̸=	PROPN
ejpam-4673	266	19	ng(w	ng(w	NOUN
ejpam-4673	266	20	)	)	PUNCT
ejpam-4673	266	21	,	,	PUNCT
ejpam-4673	266	22	showing	show	VERB
ejpam-4673	266	23	that	that	SCONJ
ejpam-4673	266	24	(	(	PUNCT
ejpam-4673	266	25	iii	iii	NOUN
ejpam-4673	266	26	)	)	PUNCT
ejpam-4673	266	27	holds	hold	VERB
ejpam-4673	266	28	.	.	PUNCT
ejpam-4673	267	1	to	to	PART
ejpam-4673	267	2	show	show	VERB
ejpam-4673	267	3	(	(	PUNCT
ejpam-4673	267	4	iv	iv	NUM
ejpam-4673	267	5	)	)	PUNCT
ejpam-4673	267	6	,	,	PUNCT
ejpam-4673	267	7	let	let	VERB
ejpam-4673	267	8	w	w	NOUN
ejpam-4673	267	9	∈	∈	PROPN
ejpam-4673	267	10	v	v	ADP
ejpam-4673	267	11	(	(	PUNCT
ejpam-4673	267	12	g	g	NOUN
ejpam-4673	267	13	)	)	PUNCT
ejpam-4673	267	14	such	such	ADJ
ejpam-4673	267	15	that	that	SCONJ
ejpam-4673	267	16	ng(v	ng(v	PUNCT
ejpam-4673	267	17	)	)	PUNCT
ejpam-4673	268	1	=	=	SYM
ejpam-4673	268	2	{	{	PUNCT
ejpam-4673	268	3	w	w	NOUN
ejpam-4673	268	4	}	}	PUNCT
ejpam-4673	268	5	for	for	ADP
ejpam-4673	268	6	some	some	DET
ejpam-4673	268	7	v	v	ADP
ejpam-4673	268	8	∈	∈	NOUN
ejpam-4673	268	9	v	v	NOUN
ejpam-4673	268	10	(	(	PUNCT
ejpam-4673	268	11	g	g	NOUN
ejpam-4673	268	12	)	)	PUNCT
ejpam-4673	268	13	.	.	PUNCT
ejpam-4673	269	1	suppose	suppose	VERB
ejpam-4673	269	2	dw	dw	NOUN
ejpam-4673	269	3	is	be	AUX
ejpam-4673	269	4	not	not	PART
ejpam-4673	269	5	a	a	DET
ejpam-4673	269	6	total	total	ADJ
ejpam-4673	269	7	dominating	dominating	NOUN
ejpam-4673	269	8	set	set	VERB
ejpam-4673	269	9	in	in	ADP
ejpam-4673	269	10	hw	hw	PRON
ejpam-4673	269	11	.	.	PUNCT
ejpam-4673	270	1	then	then	ADV
ejpam-4673	270	2	there	there	PRON
ejpam-4673	270	3	exists	exist	VERB
ejpam-4673	270	4	p	p	PROPN
ejpam-4673	270	5	∈	∈	PROPN
ejpam-4673	270	6	v	v	ADP
ejpam-4673	270	7	(	(	PUNCT
ejpam-4673	270	8	hw	hw	NOUN
ejpam-4673	270	9	)	)	PUNCT
ejpam-4673	270	10	such	such	ADJ
ejpam-4673	270	11	that	that	SCONJ
ejpam-4673	270	12	p	p	PROPN
ejpam-4673	270	13	/∈	/∈	PROPN
ejpam-4673	270	14	nhw(dw	nhw(dw	PRON
ejpam-4673	270	15	)	)	PUNCT
ejpam-4673	270	16	.	.	PUNCT
ejpam-4673	271	1	it	it	PRON
ejpam-4673	271	2	follows	follow	VERB
ejpam-4673	271	3	that	that	DET
ejpam-4673	271	4	n2	n2	NOUN
ejpam-4673	271	5	g	g	PROPN
ejpam-4673	271	6	◦	◦	NOUN
ejpam-4673	271	7	h	h	NOUN
ejpam-4673	272	1	[	[	X
ejpam-4673	272	2	p]∩s	p]∩s	X
ejpam-4673	272	3	=	=	SYM
ejpam-4673	272	4	(	(	PUNCT
ejpam-4673	272	5	ng(w)∩a)∪[(v	ng(w)∩a)∪[(v	PROPN
ejpam-4673	272	6	(	(	PUNCT
ejpam-4673	272	7	hw)\nhw(p))∩dw	hw)\nhw(p))∩dw	X
ejpam-4673	272	8	]	]	X
ejpam-4673	272	9	=	=	SYM
ejpam-4673	272	10	(	(	PUNCT
ejpam-4673	272	11	ng(w)∩a)∪dw	ng(w)∩a)∪dw	NOUN
ejpam-4673	272	12	=	=	NOUN
ejpam-4673	272	13	n2	n2	PROPN
ejpam-4673	272	14	g	g	PROPN
ejpam-4673	272	15	◦	◦	NOUN
ejpam-4673	272	16	h	h	NOUN
ejpam-4673	273	1	[	[	X
ejpam-4673	273	2	v]∩s	v]∩s	PROPN
ejpam-4673	273	3	,	,	PUNCT
ejpam-4673	273	4	a	a	DET
ejpam-4673	273	5	contradiction	contradiction	NOUN
ejpam-4673	273	6	to	to	ADP
ejpam-4673	273	7	the	the	DET
ejpam-4673	273	8	assumption	assumption	NOUN
ejpam-4673	273	9	that	that	SCONJ
ejpam-4673	273	10	s	s	VERB
ejpam-4673	273	11	is	be	AUX
ejpam-4673	273	12	a	a	DET
ejpam-4673	273	13	hop	hop	NOUN
ejpam-4673	273	14	differentiating	differentiate	VERB
ejpam-4673	273	15	set	set	NOUN
ejpam-4673	273	16	.	.	PUNCT
ejpam-4673	274	1	therefore	therefore	ADV
ejpam-4673	274	2	,	,	PUNCT
ejpam-4673	274	3	dw	dw	PROPN
ejpam-4673	274	4	is	be	AUX
ejpam-4673	274	5	a	a	DET
ejpam-4673	274	6	total	total	ADJ
ejpam-4673	274	7	dominating	dominating	NOUN
ejpam-4673	274	8	set	set	NOUN
ejpam-4673	274	9	in	in	ADP
ejpam-4673	274	10	hw	hw	NOUN
ejpam-4673	274	11	,	,	PUNCT
ejpam-4673	274	12	showing	show	VERB
ejpam-4673	274	13	that	that	SCONJ
ejpam-4673	274	14	(	(	PUNCT
ejpam-4673	274	15	iv	iv	X
ejpam-4673	274	16	)	)	PUNCT
ejpam-4673	274	17	holds	hold	NOUN
ejpam-4673	274	18	.	.	PUNCT
ejpam-4673	275	1	finally	finally	ADV
ejpam-4673	275	2	,	,	PUNCT
ejpam-4673	275	3	suppose	suppose	VERB
ejpam-4673	275	4	dv	dv	PROPN
ejpam-4673	275	5	and	and	CCONJ
ejpam-4673	275	6	dw	dw	PROPN
ejpam-4673	275	7	,	,	PUNCT
ejpam-4673	275	8	where	where	SCONJ
ejpam-4673	275	9	v	v	ADP
ejpam-4673	275	10	̸=	̸=	PROPN
ejpam-4673	275	11	w	w	PROPN
ejpam-4673	275	12	,	,	PUNCT
ejpam-4673	275	13	are	be	AUX
ejpam-4673	275	14	not	not	PART
ejpam-4673	275	15	pointwise	pointwise	ADJ
ejpam-4673	275	16	non	non	ADJ
ejpam-4673	275	17	-	-	ADJ
ejpam-4673	275	18	dominating	dominating	ADJ
ejpam-4673	275	19	sets	set	NOUN
ejpam-4673	275	20	in	in	ADP
ejpam-4673	275	21	hv	hv	PROPN
ejpam-4673	275	22	.	.	PUNCT
ejpam-4673	276	1	then	then	ADV
ejpam-4673	276	2	there	there	PRON
ejpam-4673	276	3	exist	exist	VERB
ejpam-4673	276	4	p	p	PROPN
ejpam-4673	276	5	∈	∈	PROPN
ejpam-4673	276	6	v	v	NOUN
ejpam-4673	276	7	(	(	PUNCT
ejpam-4673	276	8	hv)\dv	hv)\dv	NOUN
ejpam-4673	276	9	and	and	CCONJ
ejpam-4673	276	10	q	q	PROPN
ejpam-4673	276	11	∈	∈	PROPN
ejpam-4673	276	12	v	v	ADP
ejpam-4673	276	13	(	(	PUNCT
ejpam-4673	276	14	hw	hw	NOUN
ejpam-4673	276	15	)	)	PUNCT
ejpam-4673	276	16	\dw	\dw	NOUN
ejpam-4673	276	17	such	such	ADJ
ejpam-4673	276	18	that	that	SCONJ
ejpam-4673	276	19	(	(	PUNCT
ejpam-4673	276	20	v	v	NOUN
ejpam-4673	276	21	(	(	PUNCT
ejpam-4673	276	22	hv	hv	NOUN
ejpam-4673	276	23	)	)	PUNCT
ejpam-4673	276	24	\nhv(p))∩dv	\nhv(p))∩dv	VERB
ejpam-4673	276	25	=	=	NOUN
ejpam-4673	276	26	∅	∅	NOUN
ejpam-4673	276	27	and	and	CCONJ
ejpam-4673	276	28	(	(	PUNCT
ejpam-4673	276	29	v	v	NOUN
ejpam-4673	276	30	(	(	PUNCT
ejpam-4673	276	31	hw	hw	NOUN
ejpam-4673	276	32	)	)	PUNCT
ejpam-4673	276	33	\nhw(q))∩dw	\nhw(q))∩dw	NUM
ejpam-4673	276	34	=	=	PUNCT
ejpam-4673	276	35	∅.	∅.	NOUN
ejpam-4673	276	36	since	since	SCONJ
ejpam-4673	276	37	s	s	PROPN
ejpam-4673	276	38	is	be	AUX
ejpam-4673	276	39	hop	hop	NOUN
ejpam-4673	276	40	differentiating	differentiating	NOUN
ejpam-4673	276	41	,	,	PUNCT
ejpam-4673	276	42	ng(v	ng(v	PUNCT
ejpam-4673	276	43	)	)	PUNCT
ejpam-4673	276	44	∩a	∩a	PROPN
ejpam-4673	276	45	̸=	̸=	PROPN
ejpam-4673	276	46	ng(w	ng(w	PUNCT
ejpam-4673	276	47	)	)	PUNCT
ejpam-4673	277	1	∩a	∩a	PROPN
ejpam-4673	277	2	.	.	PUNCT
ejpam-4673	278	1	this	this	PRON
ejpam-4673	278	2	shows	show	VERB
ejpam-4673	278	3	that	that	SCONJ
ejpam-4673	278	4	(	(	PUNCT
ejpam-4673	278	5	v	v	NOUN
ejpam-4673	278	6	)	)	PUNCT
ejpam-4673	278	7	holds	hold	NOUN
ejpam-4673	278	8	.	.	PUNCT
ejpam-4673	279	1	for	for	ADP
ejpam-4673	279	2	the	the	DET
ejpam-4673	279	3	converse	converse	NOUN
ejpam-4673	279	4	,	,	PUNCT
ejpam-4673	279	5	suppose	suppose	VERB
ejpam-4673	279	6	that	that	SCONJ
ejpam-4673	279	7	s	s	VERB
ejpam-4673	279	8	is	be	AUX
ejpam-4673	279	9	as	as	SCONJ
ejpam-4673	279	10	described	describe	VERB
ejpam-4673	279	11	and	and	CCONJ
ejpam-4673	279	12	satisfies	satisfie	NOUN
ejpam-4673	279	13	properties	property	NOUN
ejpam-4673	279	14	(	(	PUNCT
ejpam-4673	279	15	i)-(v	i)-(v	PROPN
ejpam-4673	279	16	)	)	PUNCT
ejpam-4673	279	17	.	.	PUNCT
ejpam-4673	280	1	let	let	VERB
ejpam-4673	280	2	v	v	NUM
ejpam-4673	280	3	∈	∈	PROPN
ejpam-4673	280	4	v	v	NOUN
ejpam-4673	280	5	(	(	PUNCT
ejpam-4673	280	6	g	g	NOUN
ejpam-4673	280	7	)	)	PUNCT
ejpam-4673	280	8	\	\	PROPN
ejpam-4673	281	1	a	a	PRON
ejpam-4673	282	1	and	and	CCONJ
ejpam-4673	282	2	choose	choose	VERB
ejpam-4673	282	3	any	any	DET
ejpam-4673	282	4	u	u	NOUN
ejpam-4673	282	5	∈	∈	PROPN
ejpam-4673	282	6	ng(v	ng(v	PUNCT
ejpam-4673	282	7	)	)	PUNCT
ejpam-4673	282	8	.	.	PUNCT
ejpam-4673	283	1	by	by	ADP
ejpam-4673	283	2	(	(	PUNCT
ejpam-4673	283	3	ii	ii	NOUN
ejpam-4673	283	4	)	)	PUNCT
ejpam-4673	283	5	,	,	PUNCT
ejpam-4673	283	6	du	du	PROPN
ejpam-4673	283	7	is	be	AUX
ejpam-4673	283	8	complement	complement	NOUN
ejpam-4673	283	9	differentiating	differentiating	NOUN
ejpam-4673	283	10	and	and	CCONJ
ejpam-4673	283	11	so	so	ADV
ejpam-4673	283	12	du	du	PROPN
ejpam-4673	283	13	̸=	̸=	PROPN
ejpam-4673	283	14	∅.	∅.	ADV
ejpam-4673	283	15	thus	thus	ADV
ejpam-4673	283	16	,	,	PUNCT
ejpam-4673	283	17	s	s	PART
ejpam-4673	283	18	satisfies	satisfie	NOUN
ejpam-4673	283	19	(	(	PUNCT
ejpam-4673	283	20	i	i	NOUN
ejpam-4673	283	21	)	)	PUNCT
ejpam-4673	283	22	and	and	CCONJ
ejpam-4673	283	23	(	(	PUNCT
ejpam-4673	283	24	ii	ii	NOUN
ejpam-4673	283	25	)	)	PUNCT
ejpam-4673	283	26	of	of	ADP
ejpam-4673	283	27	theorem	theorem	NOUN
ejpam-4673	283	28	4	4	NUM
ejpam-4673	283	29	,	,	PUNCT
ejpam-4673	283	30	showing	show	VERB
ejpam-4673	283	31	that	that	SCONJ
ejpam-4673	283	32	it	it	PRON
ejpam-4673	283	33	is	be	AUX
ejpam-4673	283	34	a	a	DET
ejpam-4673	283	35	hop	hop	NOUN
ejpam-4673	283	36	dominating	dominating	NOUN
ejpam-4673	283	37	set	set	VERB
ejpam-4673	283	38	in	in	ADP
ejpam-4673	283	39	g	g	PROPN
ejpam-4673	283	40	◦	◦	NOUN
ejpam-4673	283	41	h.	h.	PROPN
ejpam-4673	283	42	now	now	ADV
ejpam-4673	283	43	let	let	VERB
ejpam-4673	283	44	a	a	DET
ejpam-4673	283	45	,	,	PUNCT
ejpam-4673	283	46	b	b	PROPN
ejpam-4673	283	47	∈	∈	PROPN
ejpam-4673	283	48	v	v	NOUN
ejpam-4673	283	49	(	(	PUNCT
ejpam-4673	283	50	g	g	PROPN
ejpam-4673	283	51	◦	◦	NOUN
ejpam-4673	283	52	h	h	NOUN
ejpam-4673	283	53	)	)	PUNCT
ejpam-4673	283	54	with	with	ADP
ejpam-4673	283	55	a	a	DET
ejpam-4673	283	56	̸=	̸=	PROPN
ejpam-4673	283	57	b	b	PROPN
ejpam-4673	283	58	and	and	CCONJ
ejpam-4673	283	59	let	let	VERB
ejpam-4673	283	60	v	v	NOUN
ejpam-4673	283	61	,	,	PUNCT
ejpam-4673	283	62	w	w	PROPN
ejpam-4673	283	63	∈	∈	PROPN
ejpam-4673	283	64	v	v	ADP
ejpam-4673	283	65	(	(	PUNCT
ejpam-4673	283	66	g	g	NOUN
ejpam-4673	283	67	)	)	PUNCT
ejpam-4673	283	68	such	such	ADJ
ejpam-4673	283	69	that	that	SCONJ
ejpam-4673	283	70	a	a	DET
ejpam-4673	283	71	∈	∈	PROPN
ejpam-4673	283	72	v	v	NOUN
ejpam-4673	283	73	(	(	PUNCT
ejpam-4673	283	74	v	v	PROPN
ejpam-4673	283	75	+	+	NOUN
ejpam-4673	283	76	hv	hv	NOUN
ejpam-4673	283	77	)	)	PUNCT
ejpam-4673	283	78	and	and	CCONJ
ejpam-4673	283	79	b	b	X
ejpam-4673	283	80	∈	∈	PROPN
ejpam-4673	283	81	v	v	NOUN
ejpam-4673	283	82	(	(	PUNCT
ejpam-4673	283	83	w	w	NOUN
ejpam-4673	283	84	+	+	NOUN
ejpam-4673	283	85	hw	hw	NOUN
ejpam-4673	283	86	)	)	PUNCT
ejpam-4673	283	87	.	.	PUNCT
ejpam-4673	284	1	consider	consider	VERB
ejpam-4673	284	2	the	the	DET
ejpam-4673	284	3	following	follow	VERB
ejpam-4673	284	4	cases	case	NOUN
ejpam-4673	284	5	:	:	PUNCT
ejpam-4673	284	6	case	case	NOUN
ejpam-4673	284	7	1	1	NUM
ejpam-4673	284	8	:	:	SYM
ejpam-4673	284	9	v	v	NOUN
ejpam-4673	284	10	=	=	SYM
ejpam-4673	284	11	w	w	NOUN
ejpam-4673	284	12	suppose	suppose	VERB
ejpam-4673	284	13	a	a	DET
ejpam-4673	284	14	,	,	PUNCT
ejpam-4673	284	15	b	b	PROPN
ejpam-4673	284	16	∈	∈	PROPN
ejpam-4673	284	17	v	v	ADP
ejpam-4673	284	18	(	(	PUNCT
ejpam-4673	284	19	hv	hv	PROPN
ejpam-4673	284	20	)	)	PUNCT
ejpam-4673	284	21	.	.	PUNCT
ejpam-4673	285	1	since	since	SCONJ
ejpam-4673	285	2	dv	dv	PROPN
ejpam-4673	285	3	is	be	AUX
ejpam-4673	285	4	a	a	DET
ejpam-4673	285	5	complement	complement	NOUN
ejpam-4673	285	6	differentiating	differentiating	NOUN
ejpam-4673	285	7	set	set	NOUN
ejpam-4673	285	8	in	in	ADP
ejpam-4673	285	9	hv	hv	PROPN
ejpam-4673	285	10	(	(	PUNCT
ejpam-4673	285	11	by	by	ADP
ejpam-4673	285	12	(	(	PUNCT
ejpam-4673	285	13	ii	ii	NOUN
ejpam-4673	285	14	)	)	PUNCT
ejpam-4673	285	15	)	)	PUNCT
ejpam-4673	285	16	,	,	PUNCT
ejpam-4673	285	17	n2	n2	ADJ
ejpam-4673	285	18	g	g	PROPN
ejpam-4673	285	19	◦	◦	NOUN
ejpam-4673	285	20	h	h	NOUN
ejpam-4673	286	1	[	[	X
ejpam-4673	286	2	a	a	X
ejpam-4673	286	3	]	]	X
ejpam-4673	286	4	∩	∩	X
ejpam-4673	286	5	s	s	PART
ejpam-4673	286	6	̸=	̸=	PROPN
ejpam-4673	286	7	n2	n2	NOUN
ejpam-4673	286	8	g	g	PROPN
ejpam-4673	286	9	◦	◦	NOUN
ejpam-4673	286	10	h	h	NOUN
ejpam-4673	287	1	[	[	X
ejpam-4673	287	2	b	b	X
ejpam-4673	287	3	]	]	X
ejpam-4673	287	4	∩	∩	PROPN
ejpam-4673	287	5	s.	s.	PROPN
ejpam-4673	287	6	suppose	suppose	VERB
ejpam-4673	287	7	a	a	DET
ejpam-4673	287	8	=	=	X
ejpam-4673	287	9	v	v	NOUN
ejpam-4673	287	10	and	and	CCONJ
ejpam-4673	287	11	b	b	NOUN
ejpam-4673	287	12	∈	∈	PROPN
ejpam-4673	287	13	v	v	ADP
ejpam-4673	287	14	(	(	PUNCT
ejpam-4673	287	15	hv	hv	PROPN
ejpam-4673	287	16	)	)	PUNCT
ejpam-4673	287	17	.	.	PUNCT
ejpam-4673	288	1	pick	pick	VERB
ejpam-4673	288	2	any	any	DET
ejpam-4673	288	3	z	z	NOUN
ejpam-4673	288	4	∈	∈	PROPN
ejpam-4673	288	5	ng(v	ng(v	NOUN
ejpam-4673	288	6	)	)	PUNCT
ejpam-4673	288	7	.	.	PUNCT
ejpam-4673	289	1	since	since	SCONJ
ejpam-4673	289	2	dz	dz	PRON
ejpam-4673	289	3	⊆	⊆	NUM
ejpam-4673	289	4	n2	n2	NOUN
ejpam-4673	289	5	g	g	PROPN
ejpam-4673	289	6	◦	◦	NOUN
ejpam-4673	289	7	h	h	NOUN
ejpam-4673	289	8	[	[	X
ejpam-4673	289	9	a	a	X
ejpam-4673	289	10	]	]	X
ejpam-4673	289	11	\n2	\n2	PROPN
ejpam-4673	289	12	g	g	PROPN
ejpam-4673	289	13	◦	◦	NOUN
ejpam-4673	289	14	h	h	NOUN
ejpam-4673	289	15	[	[	X
ejpam-4673	289	16	b	b	X
ejpam-4673	289	17	]	]	X
ejpam-4673	289	18	,	,	PUNCT
ejpam-4673	289	19	it	it	PRON
ejpam-4673	289	20	follows	follow	VERB
ejpam-4673	289	21	that	that	DET
ejpam-4673	289	22	n2	n2	NOUN
ejpam-4673	289	23	g	g	PROPN
ejpam-4673	289	24	◦	◦	NOUN
ejpam-4673	289	25	h	h	NOUN
ejpam-4673	290	1	[	[	X
ejpam-4673	290	2	a	a	X
ejpam-4673	290	3	]	]	X
ejpam-4673	290	4	∩	∩	X
ejpam-4673	290	5	s	s	PART
ejpam-4673	290	6	̸=	̸=	PROPN
ejpam-4673	290	7	n2	n2	NOUN
ejpam-4673	290	8	g	g	PROPN
ejpam-4673	290	9	◦	◦	NOUN
ejpam-4673	290	10	h	h	NOUN
ejpam-4673	291	1	[	[	X
ejpam-4673	291	2	b	b	X
ejpam-4673	291	3	]	]	X
ejpam-4673	291	4	∩	∩	ADJ
ejpam-4673	291	5	s.	s.	PROPN
ejpam-4673	291	6	case	case	NOUN
ejpam-4673	291	7	2	2	NUM
ejpam-4673	291	8	:	:	PUNCT
ejpam-4673	291	9	v	v	ADP
ejpam-4673	291	10	̸=	̸=	PROPN
ejpam-4673	291	11	w	w	NOUN
ejpam-4673	291	12	suppose	suppose	VERB
ejpam-4673	291	13	a	a	DET
ejpam-4673	291	14	=	=	X
ejpam-4673	291	15	v	v	NOUN
ejpam-4673	291	16	and	and	CCONJ
ejpam-4673	291	17	b	b	NOUN
ejpam-4673	291	18	=	=	SYM
ejpam-4673	291	19	w.	w.	PROPN
ejpam-4673	291	20	then	then	ADV
ejpam-4673	291	21	v	v	NOUN
ejpam-4673	291	22	,	,	PUNCT
ejpam-4673	291	23	w	w	PROPN
ejpam-4673	291	24	∈	∈	PROPN
ejpam-4673	291	25	v	v	ADP
ejpam-4673	291	26	(	(	PUNCT
ejpam-4673	291	27	g	g	NOUN
ejpam-4673	291	28	)	)	PUNCT
ejpam-4673	291	29	.	.	PUNCT
ejpam-4673	292	1	by	by	ADP
ejpam-4673	292	2	property	property	NOUN
ejpam-4673	292	3	(	(	PUNCT
ejpam-4673	292	4	iii	iii	NOUN
ejpam-4673	292	5	)	)	PUNCT
ejpam-4673	292	6	,	,	PUNCT
ejpam-4673	292	7	ng(v	ng(v	PUNCT
ejpam-4673	292	8	)	)	PUNCT
ejpam-4673	292	9	̸=	̸=	PROPN
ejpam-4673	292	10	ng(w	ng(w	NOUN
ejpam-4673	292	11	)	)	PUNCT
ejpam-4673	292	12	or	or	CCONJ
ejpam-4673	292	13	n2	n2	ADJ
ejpam-4673	292	14	g[v	g[v	PROPN
ejpam-4673	292	15	]	]	PUNCT
ejpam-4673	292	16	∩	∩	NOUN
ejpam-4673	292	17	a	a	DET
ejpam-4673	292	18	̸=	̸=	PROPN
ejpam-4673	292	19	n2	n2	ADJ
ejpam-4673	292	20	g[w	g[w	PROPN
ejpam-4673	292	21	]	]	PUNCT
ejpam-4673	292	22	∩	∩	ADJ
ejpam-4673	292	23	a.	a.	NOUN
ejpam-4673	292	24	if	if	SCONJ
ejpam-4673	292	25	n2	n2	PROPN
ejpam-4673	292	26	g[v	g[v	PROPN
ejpam-4673	292	27	]	]	PUNCT
ejpam-4673	292	28	∩	∩	NOUN
ejpam-4673	292	29	a	a	DET
ejpam-4673	292	30	̸=	̸=	PROPN
ejpam-4673	292	31	n2	n2	ADJ
ejpam-4673	292	32	g[w	g[w	PROPN
ejpam-4673	292	33	]	]	PUNCT
ejpam-4673	292	34	∩	∩	PROPN
ejpam-4673	292	35	a	a	X
ejpam-4673	292	36	,	,	PUNCT
ejpam-4673	292	37	then	then	ADV
ejpam-4673	292	38	n2	n2	PROPN
ejpam-4673	292	39	g	g	PROPN
ejpam-4673	292	40	◦	◦	NOUN
ejpam-4673	292	41	h	h	NOUN
ejpam-4673	293	1	[	[	X
ejpam-4673	293	2	a	a	X
ejpam-4673	293	3	]	]	X
ejpam-4673	293	4	∩	∩	X
ejpam-4673	293	5	s	s	PART
ejpam-4673	293	6	̸=	̸=	PROPN
ejpam-4673	293	7	n2	n2	NOUN
ejpam-4673	293	8	g	g	PROPN
ejpam-4673	293	9	◦	◦	NOUN
ejpam-4673	293	10	h	h	NOUN
ejpam-4673	294	1	[	[	X
ejpam-4673	294	2	b	b	X
ejpam-4673	294	3	]	]	X
ejpam-4673	294	4	∩	∩	PROPN
ejpam-4673	294	5	s.	s.	PROPN
ejpam-4673	294	6	suppose	suppose	VERB
ejpam-4673	294	7	ng(v	ng(v	NOUN
ejpam-4673	294	8	)	)	PUNCT
ejpam-4673	294	9	̸=	̸=	PROPN
ejpam-4673	294	10	ng(w	ng(w	NOUN
ejpam-4673	294	11	)	)	PUNCT
ejpam-4673	294	12	.	.	PUNCT
ejpam-4673	295	1	we	we	PRON
ejpam-4673	295	2	may	may	AUX
ejpam-4673	295	3	assume	assume	VERB
ejpam-4673	295	4	that	that	SCONJ
ejpam-4673	295	5	there	there	PRON
ejpam-4673	295	6	exists	exist	VERB
ejpam-4673	295	7	p	p	PROPN
ejpam-4673	295	8	∈	∈	PROPN
ejpam-4673	295	9	ng(v	ng(v	NOUN
ejpam-4673	295	10	)	)	PUNCT
ejpam-4673	295	11	\	\	NOUN
ejpam-4673	295	12	ng(w	ng(w	NOUN
ejpam-4673	295	13	)	)	PUNCT
ejpam-4673	295	14	.	.	PUNCT
ejpam-4673	296	1	then	then	ADV
ejpam-4673	296	2	dp	dp	VERB
ejpam-4673	296	3	⊆	⊆	NUM
ejpam-4673	296	4	n2	n2	NOUN
ejpam-4673	296	5	g	g	PROPN
ejpam-4673	296	6	◦	◦	NOUN
ejpam-4673	296	7	h	h	NOUN
ejpam-4673	297	1	[	[	X
ejpam-4673	297	2	a	a	X
ejpam-4673	297	3	]	]	X
ejpam-4673	297	4	\n2	\n2	PROPN
ejpam-4673	297	5	g	g	PROPN
ejpam-4673	297	6	◦	◦	NOUN
ejpam-4673	297	7	h	h	NOUN
ejpam-4673	298	1	[	[	X
ejpam-4673	298	2	b	b	X
ejpam-4673	298	3	]	]	X
ejpam-4673	298	4	.	.	PUNCT
ejpam-4673	299	1	hence	hence	ADV
ejpam-4673	299	2	,	,	PUNCT
ejpam-4673	299	3	n2	n2	ADJ
ejpam-4673	299	4	g	g	PROPN
ejpam-4673	299	5	◦	◦	NOUN
ejpam-4673	299	6	h	h	NOUN
ejpam-4673	300	1	[	[	X
ejpam-4673	300	2	a	a	X
ejpam-4673	300	3	]	]	X
ejpam-4673	300	4	∩	∩	X
ejpam-4673	300	5	s	s	PART
ejpam-4673	300	6	̸=	̸=	PROPN
ejpam-4673	300	7	n2	n2	NOUN
ejpam-4673	300	8	g	g	PROPN
ejpam-4673	300	9	◦	◦	NOUN
ejpam-4673	300	10	h	h	NOUN
ejpam-4673	301	1	[	[	X
ejpam-4673	301	2	b	b	X
ejpam-4673	301	3	]	]	X
ejpam-4673	301	4	∩	∩	ADJ
ejpam-4673	301	5	s.	s.	PROPN
ejpam-4673	301	6	next	next	ADV
ejpam-4673	301	7	,	,	PUNCT
ejpam-4673	301	8	suppose	suppose	VERB
ejpam-4673	301	9	that	that	SCONJ
ejpam-4673	301	10	a	a	DET
ejpam-4673	301	11	=	=	SYM
ejpam-4673	301	12	v	v	NOUN
ejpam-4673	301	13	and	and	CCONJ
ejpam-4673	301	14	b	b	NOUN
ejpam-4673	301	15	∈	∈	PROPN
ejpam-4673	301	16	v	v	NOUN
ejpam-4673	301	17	(	(	PUNCT
ejpam-4673	301	18	hw	hw	NOUN
ejpam-4673	301	19	)	)	PUNCT
ejpam-4673	301	20	(	(	PUNCT
ejpam-4673	301	21	or	or	CCONJ
ejpam-4673	301	22	b	b	X
ejpam-4673	301	23	=	=	SYM
ejpam-4673	301	24	w	w	PROPN
ejpam-4673	301	25	and	and	CCONJ
ejpam-4673	301	26	a	a	DET
ejpam-4673	301	27	∈	∈	PROPN
ejpam-4673	301	28	v	v	ADP
ejpam-4673	301	29	(	(	PUNCT
ejpam-4673	301	30	hv	hv	NOUN
ejpam-4673	301	31	)	)	PUNCT
ejpam-4673	301	32	)	)	PUNCT
ejpam-4673	301	33	.	.	PUNCT
ejpam-4673	302	1	if	if	SCONJ
ejpam-4673	302	2	|ng(v)|	|ng(v)|	NOUN
ejpam-4673	302	3	>	>	X
ejpam-4673	302	4	1	1	NUM
ejpam-4673	302	5	or	or	CCONJ
ejpam-4673	302	6	vw	vw	PRON
ejpam-4673	302	7	/∈	/∈	PUNCT
ejpam-4673	302	8	e(g	e(g	PROPN
ejpam-4673	302	9	)	)	PUNCT
ejpam-4673	302	10	,	,	PUNCT
ejpam-4673	302	11	pick	pick	VERB
ejpam-4673	302	12	any	any	DET
ejpam-4673	302	13	z	z	NOUN
ejpam-4673	302	14	∈	∈	PROPN
ejpam-4673	302	15	ng(v	ng(v	PUNCT
ejpam-4673	302	16	)	)	PUNCT
ejpam-4673	302	17	\	\	NOUN
ejpam-4673	302	18	{	{	PUNCT
ejpam-4673	302	19	w	w	NOUN
ejpam-4673	302	20	}	}	PUNCT
ejpam-4673	302	21	.	.	PUNCT
ejpam-4673	303	1	then	then	ADV
ejpam-4673	303	2	dz	dz	VERB
ejpam-4673	303	3	⊆	⊆	NUM
ejpam-4673	303	4	n2	n2	NOUN
ejpam-4673	303	5	g	g	PROPN
ejpam-4673	303	6	◦	◦	NOUN
ejpam-4673	303	7	h	h	NOUN
ejpam-4673	304	1	[	[	X
ejpam-4673	304	2	a	a	X
ejpam-4673	304	3	]	]	PUNCT
ejpam-4673	304	4	\	\	PROPN
ejpam-4673	304	5	n2	n2	PROPN
ejpam-4673	304	6	g	g	PROPN
ejpam-4673	304	7	◦	◦	NOUN
ejpam-4673	304	8	h	h	NOUN
ejpam-4673	305	1	[	[	X
ejpam-4673	305	2	b	b	X
ejpam-4673	305	3	]	]	X
ejpam-4673	305	4	.	.	PUNCT
ejpam-4673	306	1	it	it	PRON
ejpam-4673	306	2	follows	follow	VERB
ejpam-4673	306	3	that	that	DET
ejpam-4673	306	4	n2	n2	NOUN
ejpam-4673	306	5	g	g	PROPN
ejpam-4673	306	6	◦	◦	NOUN
ejpam-4673	306	7	h	h	NOUN
ejpam-4673	307	1	[	[	X
ejpam-4673	307	2	a	a	X
ejpam-4673	307	3	]	]	X
ejpam-4673	307	4	∩	∩	X
ejpam-4673	307	5	s	s	PART
ejpam-4673	307	6	̸=	̸=	PROPN
ejpam-4673	307	7	n2	n2	NOUN
ejpam-4673	307	8	g	g	PROPN
ejpam-4673	307	9	◦	◦	NOUN
ejpam-4673	307	10	h	h	NOUN
ejpam-4673	308	1	[	[	X
ejpam-4673	308	2	b	b	X
ejpam-4673	308	3	]	]	X
ejpam-4673	308	4	∩	∩	PROPN
ejpam-4673	308	5	s.	s.	PROPN
ejpam-4673	308	6	suppose	suppose	VERB
ejpam-4673	308	7	that	that	SCONJ
ejpam-4673	308	8	ng(v	ng(v	NOUN
ejpam-4673	308	9	)	)	PUNCT
ejpam-4673	308	10	=	=	SYM
ejpam-4673	308	11	{	{	PUNCT
ejpam-4673	308	12	w	w	NOUN
ejpam-4673	308	13	}	}	PUNCT
ejpam-4673	308	14	.	.	PUNCT
ejpam-4673	309	1	by	by	ADP
ejpam-4673	309	2	(	(	PUNCT
ejpam-4673	309	3	iv	iv	X
ejpam-4673	309	4	)	)	PUNCT
ejpam-4673	309	5	,	,	PUNCT
ejpam-4673	309	6	dw	dw	PROPN
ejpam-4673	309	7	is	be	AUX
ejpam-4673	309	8	a	a	DET
ejpam-4673	309	9	total	total	ADJ
ejpam-4673	309	10	dominating	dominating	NOUN
ejpam-4673	309	11	set	set	NOUN
ejpam-4673	309	12	of	of	ADP
ejpam-4673	309	13	hw	hw	PRON
ejpam-4673	309	14	.	.	PUNCT
ejpam-4673	310	1	hence	hence	ADV
ejpam-4673	310	2	,	,	PUNCT
ejpam-4673	310	3	(	(	PUNCT
ejpam-4673	310	4	v	v	X
ejpam-4673	310	5	(	(	PUNCT
ejpam-4673	310	6	hw	hw	NOUN
ejpam-4673	310	7	)	)	PUNCT
ejpam-4673	310	8	\	\	PROPN
ejpam-4673	310	9	nhw(b	nhw(b	PROPN
ejpam-4673	310	10	)	)	PUNCT
ejpam-4673	310	11	)	)	PUNCT
ejpam-4673	310	12	∩	∩	PROPN
ejpam-4673	310	13	dw	dw	PROPN
ejpam-4673	310	14	̸=	̸=	PROPN
ejpam-4673	310	15	dw	dw	PROPN
ejpam-4673	310	16	.	.	PUNCT
ejpam-4673	311	1	this	this	PRON
ejpam-4673	311	2	would	would	AUX
ejpam-4673	311	3	imply	imply	VERB
ejpam-4673	311	4	that	that	DET
ejpam-4673	311	5	n2	n2	NOUN
ejpam-4673	311	6	g	g	PROPN
ejpam-4673	311	7	◦	◦	NOUN
ejpam-4673	311	8	h	h	NOUN
ejpam-4673	312	1	[	[	X
ejpam-4673	312	2	a	a	X
ejpam-4673	312	3	]	]	X
ejpam-4673	312	4	∩	∩	X
ejpam-4673	312	5	s	s	PART
ejpam-4673	312	6	̸=	̸=	PROPN
ejpam-4673	312	7	n2	n2	NOUN
ejpam-4673	312	8	g	g	PROPN
ejpam-4673	312	9	◦	◦	NOUN
ejpam-4673	312	10	h	h	NOUN
ejpam-4673	313	1	[	[	X
ejpam-4673	313	2	b	b	X
ejpam-4673	313	3	]	]	X
ejpam-4673	313	4	∩	∩	PROPN
ejpam-4673	313	5	s.	s.	PROPN
ejpam-4673	313	6	finally	finally	ADV
ejpam-4673	313	7	,	,	PUNCT
ejpam-4673	313	8	suppose	suppose	VERB
ejpam-4673	313	9	that	that	SCONJ
ejpam-4673	313	10	a	a	DET
ejpam-4673	313	11	∈	∈	PROPN
ejpam-4673	313	12	v	v	ADP
ejpam-4673	313	13	(	(	PUNCT
ejpam-4673	313	14	hv	hv	PROPN
ejpam-4673	313	15	)	)	PUNCT
ejpam-4673	313	16	and	and	CCONJ
ejpam-4673	313	17	b	b	X
ejpam-4673	313	18	∈	∈	PROPN
ejpam-4673	313	19	v	v	NOUN
ejpam-4673	313	20	(	(	PUNCT
ejpam-4673	313	21	hw	hw	NOUN
ejpam-4673	313	22	)	)	PUNCT
ejpam-4673	313	23	.	.	PUNCT
ejpam-4673	314	1	if	if	SCONJ
ejpam-4673	314	2	[	[	X
ejpam-4673	314	3	v	v	X
ejpam-4673	314	4	(	(	PUNCT
ejpam-4673	314	5	hv)\nhw(a)]∩dv	hv)\nhw(a)]∩dv	NOUN
ejpam-4673	314	6	̸=	̸=	PROPN
ejpam-4673	314	7	∅	∅	NOUN
ejpam-4673	314	8	or	or	CCONJ
ejpam-4673	314	9	[	[	X
ejpam-4673	314	10	v	v	X
ejpam-4673	314	11	(	(	PUNCT
ejpam-4673	314	12	hw)\nhw(b)]∩dw	hw)\nhw(b)]∩dw	VERB
ejpam-4673	314	13	̸=	̸=	PROPN
ejpam-4673	314	14	∅	∅	NOUN
ejpam-4673	314	15	,	,	PUNCT
ejpam-4673	314	16	thenn2	thenn2	NOUN
ejpam-4673	314	17	g	g	ADP
ejpam-4673	314	18	◦	◦	NOUN
ejpam-4673	314	19	h	h	NOUN
ejpam-4673	315	1	[	[	X
ejpam-4673	315	2	a]∩s	a]∩s	DET
ejpam-4673	315	3	̸=	̸=	PROPN
ejpam-4673	315	4	n2	n2	NOUN
ejpam-4673	315	5	g	g	PROPN
ejpam-4673	315	6	◦	◦	NOUN
ejpam-4673	315	7	h	h	NOUN
ejpam-4673	316	1	[	[	X
ejpam-4673	316	2	b]∩s	b]∩s	X
ejpam-4673	316	3	.	.	PROPN
ejpam-4673	316	4	suppose	suppose	VERB
ejpam-4673	316	5	both	both	DET
ejpam-4673	316	6	sets	set	NOUN
ejpam-4673	316	7	are	be	AUX
ejpam-4673	316	8	empty	empty	ADJ
ejpam-4673	316	9	.	.	PUNCT
ejpam-4673	317	1	then	then	ADV
ejpam-4673	317	2	ng(v	ng(v	PUNCT
ejpam-4673	317	3	)	)	PUNCT
ejpam-4673	317	4	∩	∩	NOUN
ejpam-4673	317	5	a	a	DET
ejpam-4673	317	6	̸=	̸=	PROPN
ejpam-4673	317	7	ng(w	ng(w	NOUN
ejpam-4673	317	8	)	)	PUNCT
ejpam-4673	317	9	∩	∩	NOUN
ejpam-4673	317	10	a	a	X
ejpam-4673	317	11	by	by	ADP
ejpam-4673	317	12	(	(	PUNCT
ejpam-4673	317	13	v	v	NOUN
ejpam-4673	317	14	)	)	PUNCT
ejpam-4673	317	15	.	.	PUNCT
ejpam-4673	318	1	it	it	PRON
ejpam-4673	318	2	follows	follow	VERB
ejpam-4673	318	3	that	that	DET
ejpam-4673	318	4	n2	n2	NOUN
ejpam-4673	318	5	g	g	PROPN
ejpam-4673	318	6	◦	◦	NOUN
ejpam-4673	318	7	h	h	NOUN
ejpam-4673	319	1	[	[	X
ejpam-4673	319	2	a	a	X
ejpam-4673	319	3	]	]	X
ejpam-4673	319	4	∩	∩	X
ejpam-4673	319	5	s	s	PART
ejpam-4673	319	6	̸=	̸=	PROPN
ejpam-4673	319	7	n2	n2	NOUN
ejpam-4673	319	8	g	g	PROPN
ejpam-4673	319	9	◦	◦	NOUN
ejpam-4673	319	10	h	h	NOUN
ejpam-4673	320	1	[	[	X
ejpam-4673	320	2	b	b	X
ejpam-4673	320	3	]	]	X
ejpam-4673	320	4	∩	∩	PROPN
ejpam-4673	320	5	s.	s.	PROPN
ejpam-4673	320	6	s.	s.	PROPN
ejpam-4673	320	7	canoy	canoy	PROPN
ejpam-4673	320	8	jr	jr	PROPN
ejpam-4673	320	9	.	.	PROPN
ejpam-4673	320	10	,	,	PUNCT
ejpam-4673	320	11	c.	c.	PROPN
ejpam-4673	320	12	saromines	saromine	VERB
ejpam-4673	320	13	/	/	SYM
ejpam-4673	320	14	eur	eur	PROPN
ejpam-4673	320	15	.	.	PUNCT
ejpam-4673	321	1	j.	j.	PROPN
ejpam-4673	321	2	pure	pure	PROPN
ejpam-4673	321	3	appl	appl	PROPN
ejpam-4673	321	4	.	.	PROPN
ejpam-4673	321	5	math	math	PROPN
ejpam-4673	321	6	,	,	PUNCT
ejpam-4673	321	7	16	16	NUM
ejpam-4673	321	8	(	(	PUNCT
ejpam-4673	321	9	1	1	NUM
ejpam-4673	321	10	)	)	PUNCT
ejpam-4673	321	11	(	(	PUNCT
ejpam-4673	321	12	2023	2023	NUM
ejpam-4673	321	13	)	)	PUNCT
ejpam-4673	321	14	,	,	PUNCT
ejpam-4673	321	15	440	440	NUM
ejpam-4673	321	16	-	-	SYM
ejpam-4673	321	17	453	453	NUM
ejpam-4673	321	18	448	448	NUM
ejpam-4673	321	19	accordingly	accordingly	ADV
ejpam-4673	321	20	,	,	PUNCT
ejpam-4673	321	21	s	s	VERB
ejpam-4673	321	22	is	be	AUX
ejpam-4673	321	23	a	a	DET
ejpam-4673	321	24	hop	hop	NOUN
ejpam-4673	321	25	differentiating	differentiate	VERB
ejpam-4673	321	26	hop	hop	NOUN
ejpam-4673	321	27	dominating	dominating	NOUN
ejpam-4673	321	28	set	set	NOUN
ejpam-4673	321	29	of	of	ADP
ejpam-4673	321	30	g	g	PROPN
ejpam-4673	321	31	◦	◦	NOUN
ejpam-4673	321	32	h.	h.	PROPN
ejpam-4673	321	33	corollary	corollary	ADJ
ejpam-4673	321	34	6	6	NUM
ejpam-4673	321	35	.	.	PUNCT
ejpam-4673	322	1	let	let	VERB
ejpam-4673	322	2	g	g	NOUN
ejpam-4673	322	3	and	and	CCONJ
ejpam-4673	322	4	h	h	PROPN
ejpam-4673	322	5	be	be	VERB
ejpam-4673	322	6	non	non	ADJ
ejpam-4673	322	7	-	-	ADJ
ejpam-4673	322	8	trivial	trivial	ADJ
ejpam-4673	322	9	connected	connected	ADJ
ejpam-4673	322	10	graphs	graph	NOUN
ejpam-4673	322	11	such	such	ADJ
ejpam-4673	322	12	that	that	PRON
ejpam-4673	322	13	δ(g	δ(g	PROPN
ejpam-4673	322	14	)	)	PUNCT
ejpam-4673	322	15	≥	≥	NOUN
ejpam-4673	322	16	2	2	NUM
ejpam-4673	322	17	and	and	CCONJ
ejpam-4673	322	18	g	g	PROPN
ejpam-4673	322	19	and	and	CCONJ
ejpam-4673	322	20	h	h	NOUN
ejpam-4673	322	21	are	be	AUX
ejpam-4673	322	22	point	point	NOUN
ejpam-4673	322	23	determining	determine	VERB
ejpam-4673	322	24	and	and	CCONJ
ejpam-4673	322	25	complement	complement	VERB
ejpam-4673	322	26	point	point	NOUN
ejpam-4673	322	27	distinguishing	distinguishing	NOUN
ejpam-4673	322	28	,	,	PUNCT
ejpam-4673	322	29	respectively	respectively	ADV
ejpam-4673	322	30	.	.	PUNCT
ejpam-4673	323	1	then	then	ADV
ejpam-4673	323	2	γdh(g	γdh(g	VERB
ejpam-4673	323	3	◦	◦	NOUN
ejpam-4673	323	4	h	h	NOUN
ejpam-4673	323	5	)	)	PUNCT
ejpam-4673	323	6	≤	≤	NOUN
ejpam-4673	323	7	cdpnd(h)|v	cdpnd(h)|v	PROPN
ejpam-4673	323	8	(	(	PUNCT
ejpam-4673	323	9	g)|	g)|	NOUN
ejpam-4673	323	10	.	.	PUNCT
ejpam-4673	324	1	proof	proof	NOUN
ejpam-4673	324	2	.	.	PUNCT
ejpam-4673	325	1	let	let	VERB
ejpam-4673	325	2	a	a	DET
ejpam-4673	325	3	=	=	NOUN
ejpam-4673	325	4	∅	∅	NOUN
ejpam-4673	325	5	and	and	CCONJ
ejpam-4673	325	6	let	let	VERB
ejpam-4673	325	7	dv	dv	PROPN
ejpam-4673	325	8	be	be	AUX
ejpam-4673	325	9	a	a	DET
ejpam-4673	325	10	cdpnd	cdpnd	NOUN
ejpam-4673	325	11	-	-	PUNCT
ejpam-4673	325	12	set	set	NOUN
ejpam-4673	325	13	of	of	ADP
ejpam-4673	325	14	h	h	NOUN
ejpam-4673	325	15	for	for	ADP
ejpam-4673	325	16	each	each	DET
ejpam-4673	325	17	v	v	NUM
ejpam-4673	325	18	∈	∈	PROPN
ejpam-4673	325	19	v	v	NOUN
ejpam-4673	325	20	(	(	PUNCT
ejpam-4673	325	21	g	g	NOUN
ejpam-4673	325	22	)	)	PUNCT
ejpam-4673	325	23	.	.	PUNCT
ejpam-4673	326	1	then	then	ADV
ejpam-4673	326	2	s	s	VERB
ejpam-4673	326	3	=	=	PUNCT
ejpam-4673	326	4	a	a	DET
ejpam-4673	326	5	∪	∪	ADJ
ejpam-4673	326	6	[	[	X
ejpam-4673	326	7	∪v∈v	∪v∈v	X
ejpam-4673	326	8	(	(	PUNCT
ejpam-4673	326	9	g)dv	g)dv	NOUN
ejpam-4673	326	10	]	]	X
ejpam-4673	326	11	=	=	SYM
ejpam-4673	326	12	∪v∈v	∪v∈v	X
ejpam-4673	326	13	(	(	PUNCT
ejpam-4673	326	14	g)dv	g)dv	PROPN
ejpam-4673	326	15	is	be	AUX
ejpam-4673	326	16	a	a	DET
ejpam-4673	326	17	hop	hop	NOUN
ejpam-4673	326	18	differentiating	differentiate	VERB
ejpam-4673	326	19	hop	hop	NOUN
ejpam-4673	326	20	dominating	dominating	NOUN
ejpam-4673	326	21	set	set	VERB
ejpam-4673	326	22	in	in	ADP
ejpam-4673	326	23	g	g	PROPN
ejpam-4673	326	24	◦	◦	NOUN
ejpam-4673	326	25	h	h	NOUN
ejpam-4673	326	26	by	by	ADP
ejpam-4673	326	27	theorem	theorem	NOUN
ejpam-4673	326	28	5	5	NUM
ejpam-4673	326	29	.	.	PUNCT
ejpam-4673	326	30	thus	thus	ADV
ejpam-4673	326	31	,	,	PUNCT
ejpam-4673	326	32	γdh(g	γdh(g	PROPN
ejpam-4673	326	33	◦	◦	NOUN
ejpam-4673	326	34	h	h	NOUN
ejpam-4673	326	35	)	)	PUNCT
ejpam-4673	326	36	≤	≤	NOUN
ejpam-4673	326	37	|c|	|c|	PROPN
ejpam-4673	326	38	=	=	SYM
ejpam-4673	326	39	cdpnd(h)|v	cdpnd(h)|v	PROPN
ejpam-4673	326	40	(	(	PUNCT
ejpam-4673	326	41	g)|	g)|	PROPN
ejpam-4673	326	42	.	.	PUNCT
ejpam-4673	327	1	this	this	PRON
ejpam-4673	327	2	proves	prove	VERB
ejpam-4673	327	3	the	the	DET
ejpam-4673	327	4	assertion	assertion	NOUN
ejpam-4673	327	5	.	.	PUNCT
ejpam-4673	328	1	we	we	PRON
ejpam-4673	328	2	note	note	VERB
ejpam-4673	328	3	that	that	SCONJ
ejpam-4673	328	4	the	the	DET
ejpam-4673	328	5	bound	bind	VERB
ejpam-4673	328	6	given	give	VERB
ejpam-4673	328	7	in	in	ADP
ejpam-4673	328	8	corollary	corollary	ADJ
ejpam-4673	328	9	6	6	NUM
ejpam-4673	328	10	is	be	AUX
ejpam-4673	328	11	tight	tight	ADJ
ejpam-4673	328	12	.	.	PUNCT
ejpam-4673	329	1	indeed	indeed	ADV
ejpam-4673	329	2	,	,	PUNCT
ejpam-4673	329	3	if	if	SCONJ
ejpam-4673	329	4	g	g	NOUN
ejpam-4673	329	5	=	=	NOUN
ejpam-4673	329	6	h	h	NOUN
ejpam-4673	329	7	=	=	SYM
ejpam-4673	329	8	k2	k2	PROPN
ejpam-4673	329	9	,	,	PUNCT
ejpam-4673	329	10	then	then	ADV
ejpam-4673	329	11	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	329	12	)	)	PUNCT
ejpam-4673	329	13	=	=	SYM
ejpam-4673	329	14	2	2	NUM
ejpam-4673	329	15	and	and	CCONJ
ejpam-4673	329	16	γdh(g	γdh(g	PRON
ejpam-4673	329	17	◦	◦	NOUN
ejpam-4673	329	18	h	h	NOUN
ejpam-4673	329	19	)	)	PUNCT
ejpam-4673	329	20	=	=	SYM
ejpam-4673	329	21	4	4	NUM
ejpam-4673	329	22	=	=	SYM
ejpam-4673	329	23	cdpnd(h)|v	cdpnd(h)|v	PROPN
ejpam-4673	329	24	(	(	PUNCT
ejpam-4673	329	25	g)|	g)|	PROPN
ejpam-4673	329	26	.	.	PUNCT
ejpam-4673	330	1	the	the	DET
ejpam-4673	330	2	next	next	ADJ
ejpam-4673	330	3	result	result	NOUN
ejpam-4673	330	4	is	be	AUX
ejpam-4673	330	5	found	find	VERB
ejpam-4673	330	6	in	in	ADP
ejpam-4673	330	7	[	[	X
ejpam-4673	330	8	11	11	NUM
ejpam-4673	330	9	]	]	PUNCT
ejpam-4673	330	10	.	.	PUNCT
ejpam-4673	331	1	theorem	theorem	ADJ
ejpam-4673	331	2	6	6	NUM
ejpam-4673	331	3	.	.	PUNCT
ejpam-4673	332	1	let	let	VERB
ejpam-4673	332	2	g	g	NOUN
ejpam-4673	333	1	and	and	CCONJ
ejpam-4673	333	2	h	h	NOUN
ejpam-4673	333	3	be	be	AUX
ejpam-4673	333	4	connected	connect	VERB
ejpam-4673	333	5	non	non	ADJ
ejpam-4673	333	6	-	-	ADJ
ejpam-4673	333	7	trivial	trivial	ADJ
ejpam-4673	333	8	graphs	graph	NOUN
ejpam-4673	333	9	.	.	PUNCT
ejpam-4673	334	1	a	a	DET
ejpam-4673	334	2	subset	subset	NOUN
ejpam-4673	334	3	c	c	NOUN
ejpam-4673	334	4	=	=	PUNCT
ejpam-4673	334	5	⋃	⋃	PROPN
ejpam-4673	334	6	x∈s	x∈s	NOUN
ejpam-4673	335	1	[	[	X
ejpam-4673	335	2	{	{	PUNCT
ejpam-4673	335	3	x}×tx	x}×tx	X
ejpam-4673	335	4	]	]	X
ejpam-4673	335	5	of	of	ADP
ejpam-4673	335	6	v	v	NOUN
ejpam-4673	335	7	(	(	PUNCT
ejpam-4673	335	8	g[h	g[h	PROPN
ejpam-4673	335	9	]	]	PUNCT
ejpam-4673	335	10	is	be	AUX
ejpam-4673	335	11	a	a	DET
ejpam-4673	335	12	hop	hop	NOUN
ejpam-4673	335	13	dominating	dominating	NOUN
ejpam-4673	335	14	set	set	VERB
ejpam-4673	335	15	in	in	ADP
ejpam-4673	335	16	g[h	g[h	PROPN
ejpam-4673	335	17	]	]	PUNCT
ejpam-4673	335	18	if	if	SCONJ
ejpam-4673	335	19	and	and	CCONJ
ejpam-4673	335	20	only	only	ADV
ejpam-4673	335	21	if	if	SCONJ
ejpam-4673	335	22	the	the	DET
ejpam-4673	335	23	following	follow	VERB
ejpam-4673	335	24	conditions	condition	NOUN
ejpam-4673	335	25	hold	hold	VERB
ejpam-4673	335	26	.	.	PUNCT
ejpam-4673	336	1	(	(	PUNCT
ejpam-4673	336	2	i	i	NOUN
ejpam-4673	336	3	)	)	PUNCT
ejpam-4673	336	4	s	s	VERB
ejpam-4673	336	5	is	be	AUX
ejpam-4673	336	6	a	a	DET
ejpam-4673	336	7	hop	hop	NOUN
ejpam-4673	336	8	dominating	dominating	NOUN
ejpam-4673	336	9	set	set	VERB
ejpam-4673	336	10	in	in	ADP
ejpam-4673	336	11	g.	g.	PROPN
ejpam-4673	336	12	(	(	PUNCT
ejpam-4673	336	13	ii	ii	PROPN
ejpam-4673	336	14	)	)	PUNCT
ejpam-4673	336	15	tx	tx	PROPN
ejpam-4673	336	16	is	be	AUX
ejpam-4673	336	17	a	a	DET
ejpam-4673	336	18	pointwise	pointwise	ADJ
ejpam-4673	336	19	non	non	ADJ
ejpam-4673	336	20	-	-	ADJ
ejpam-4673	336	21	dominating	dominating	ADJ
ejpam-4673	336	22	set	set	NOUN
ejpam-4673	336	23	in	in	ADP
ejpam-4673	336	24	h	h	NOUN
ejpam-4673	336	25	for	for	ADP
ejpam-4673	336	26	each	each	DET
ejpam-4673	336	27	x	x	SYM
ejpam-4673	336	28	∈	∈	PROPN
ejpam-4673	336	29	s	s	PART
ejpam-4673	336	30	\n2	\n2	ADJ
ejpam-4673	336	31	g(s	g(	NOUN
ejpam-4673	336	32	)	)	PUNCT
ejpam-4673	336	33	.	.	PUNCT
ejpam-4673	337	1	theorem	theorem	ADJ
ejpam-4673	337	2	7	7	NUM
ejpam-4673	337	3	.	.	PUNCT
ejpam-4673	338	1	let	let	VERB
ejpam-4673	338	2	g	g	NOUN
ejpam-4673	338	3	and	and	CCONJ
ejpam-4673	338	4	h	h	PROPN
ejpam-4673	338	5	be	be	VERB
ejpam-4673	338	6	non	non	ADJ
ejpam-4673	338	7	-	-	ADJ
ejpam-4673	338	8	trivial	trivial	ADJ
ejpam-4673	338	9	connected	connected	ADJ
ejpam-4673	338	10	graphs	graph	NOUN
ejpam-4673	338	11	such	such	ADJ
ejpam-4673	338	12	that	that	SCONJ
ejpam-4673	338	13	g	g	PROPN
ejpam-4673	338	14	and	and	CCONJ
ejpam-4673	338	15	h	h	NOUN
ejpam-4673	338	16	are	be	AUX
ejpam-4673	338	17	,	,	PUNCT
ejpam-4673	338	18	respectively	respectively	ADV
ejpam-4673	338	19	,	,	PUNCT
ejpam-4673	338	20	distance	distance	NOUN
ejpam-4673	338	21	-	-	PUNCT
ejpam-4673	338	22	two	two	NUM
ejpam-4673	338	23	point	point	NOUN
ejpam-4673	338	24	distinguishing	distinguish	VERB
ejpam-4673	338	25	and	and	CCONJ
ejpam-4673	338	26	complement	complement	VERB
ejpam-4673	338	27	point	point	NOUN
ejpam-4673	338	28	distinguishing	distinguishing	NOUN
ejpam-4673	338	29	.	.	PUNCT
ejpam-4673	339	1	then	then	ADV
ejpam-4673	339	2	c	c	X
ejpam-4673	339	3	=	=	PUNCT
ejpam-4673	339	4	⋃	⋃	PROPN
ejpam-4673	339	5	x∈s	x∈s	NOUN
ejpam-4673	340	1	[	[	X
ejpam-4673	340	2	{	{	PUNCT
ejpam-4673	340	3	x	x	NOUN
ejpam-4673	340	4	}	}	PUNCT
ejpam-4673	340	5	×	×	PROPN
ejpam-4673	340	6	tx	tx	PROPN
ejpam-4673	340	7	]	]	X
ejpam-4673	340	8	,	,	PUNCT
ejpam-4673	340	9	where	where	SCONJ
ejpam-4673	340	10	s	s	VERB
ejpam-4673	340	11	⊆	⊆	NUM
ejpam-4673	340	12	v	v	NOUN
ejpam-4673	340	13	(	(	PUNCT
ejpam-4673	340	14	g	g	NOUN
ejpam-4673	340	15	)	)	PUNCT
ejpam-4673	340	16	and	and	CCONJ
ejpam-4673	340	17	tx	tx	VERB
ejpam-4673	340	18	⊆	⊆	NUM
ejpam-4673	340	19	v	v	NOUN
ejpam-4673	340	20	(	(	PUNCT
ejpam-4673	340	21	h	h	NOUN
ejpam-4673	340	22	)	)	PUNCT
ejpam-4673	340	23	for	for	ADP
ejpam-4673	340	24	each	each	DET
ejpam-4673	340	25	x	x	SYM
ejpam-4673	340	26	∈	∈	PROPN
ejpam-4673	340	27	s	s	NOUN
ejpam-4673	340	28	,	,	PUNCT
ejpam-4673	340	29	is	be	AUX
ejpam-4673	340	30	a	a	DET
ejpam-4673	340	31	hop	hop	NOUN
ejpam-4673	340	32	differentiating	differentiate	VERB
ejpam-4673	340	33	hop	hop	NOUN
ejpam-4673	340	34	dominating	dominating	NOUN
ejpam-4673	340	35	set	set	VERB
ejpam-4673	340	36	in	in	ADP
ejpam-4673	340	37	g[h	g[h	PROPN
ejpam-4673	340	38	]	]	PUNCT
ejpam-4673	340	39	if	if	SCONJ
ejpam-4673	340	40	and	and	CCONJ
ejpam-4673	340	41	only	only	ADV
ejpam-4673	340	42	if	if	SCONJ
ejpam-4673	340	43	the	the	DET
ejpam-4673	340	44	following	follow	VERB
ejpam-4673	340	45	conditions	condition	NOUN
ejpam-4673	340	46	hold	hold	VERB
ejpam-4673	340	47	:	:	PUNCT
ejpam-4673	340	48	(	(	PUNCT
ejpam-4673	340	49	i	i	NOUN
ejpam-4673	340	50	)	)	PUNCT
ejpam-4673	340	51	s	s	PART
ejpam-4673	340	52	=	=	SYM
ejpam-4673	340	53	v	v	X
ejpam-4673	340	54	(	(	PUNCT
ejpam-4673	340	55	g	g	NOUN
ejpam-4673	340	56	)	)	PUNCT
ejpam-4673	340	57	(	(	PUNCT
ejpam-4673	340	58	ii	ii	NOUN
ejpam-4673	340	59	)	)	PUNCT
ejpam-4673	340	60	tx	tx	PROPN
ejpam-4673	340	61	is	be	AUX
ejpam-4673	340	62	a	a	DET
ejpam-4673	340	63	pointwise	pointwise	ADJ
ejpam-4673	340	64	non	non	ADJ
ejpam-4673	340	65	-	-	ADJ
ejpam-4673	340	66	dominating	dominating	ADJ
ejpam-4673	340	67	set	set	NOUN
ejpam-4673	340	68	in	in	ADP
ejpam-4673	340	69	h	h	NOUN
ejpam-4673	340	70	for	for	ADP
ejpam-4673	340	71	each	each	DET
ejpam-4673	340	72	x	x	SYM
ejpam-4673	340	73	∈	∈	PROPN
ejpam-4673	340	74	s	s	PART
ejpam-4673	340	75	\n2	\n2	ADJ
ejpam-4673	340	76	g(s	g(	NOUN
ejpam-4673	340	77	)	)	PUNCT
ejpam-4673	340	78	.	.	PUNCT
ejpam-4673	341	1	(	(	PUNCT
ejpam-4673	341	2	iii	iii	X
ejpam-4673	341	3	)	)	PUNCT
ejpam-4673	341	4	tx	tx	PROPN
ejpam-4673	341	5	is	be	AUX
ejpam-4673	341	6	a	a	DET
ejpam-4673	341	7	complement	complement	NOUN
ejpam-4673	341	8	differentiating	differentiating	NOUN
ejpam-4673	341	9	set	set	NOUN
ejpam-4673	341	10	in	in	ADP
ejpam-4673	341	11	h	h	NOUN
ejpam-4673	341	12	for	for	ADP
ejpam-4673	341	13	all	all	DET
ejpam-4673	341	14	x	x	SYM
ejpam-4673	341	15	∈	∈	PROPN
ejpam-4673	341	16	s.	s.	PROPN
ejpam-4673	341	17	(	(	PUNCT
ejpam-4673	341	18	iv	iv	X
ejpam-4673	341	19	)	)	PUNCT
ejpam-4673	341	20	if	if	SCONJ
ejpam-4673	341	21	n2	n2	ADJ
ejpam-4673	341	22	g(x	g(x	NOUN
ejpam-4673	341	23	)	)	PUNCT
ejpam-4673	342	1	=	=	SYM
ejpam-4673	342	2	n2	n2	PROPN
ejpam-4673	342	3	g(y	g(y	PROPN
ejpam-4673	342	4	)	)	PUNCT
ejpam-4673	342	5	for	for	ADP
ejpam-4673	342	6	distinct	distinct	ADJ
ejpam-4673	342	7	vertices	vertex	NOUN
ejpam-4673	342	8	x	x	PUNCT
ejpam-4673	342	9	and	and	CCONJ
ejpam-4673	342	10	y	y	PROPN
ejpam-4673	342	11	,	,	PUNCT
ejpam-4673	342	12	then	then	ADV
ejpam-4673	342	13	tx	tx	PROPN
ejpam-4673	342	14	or	or	CCONJ
ejpam-4673	342	15	ty	ty	INTJ
ejpam-4673	342	16	is	be	AUX
ejpam-4673	342	17	pointwise	pointwise	PRON
ejpam-4673	342	18	nondominating	nondominate	VERB
ejpam-4673	342	19	in	in	ADP
ejpam-4673	342	20	h.	h.	PROPN
ejpam-4673	342	21	proof	proof	NOUN
ejpam-4673	342	22	.	.	PUNCT
ejpam-4673	343	1	suppose	suppose	VERB
ejpam-4673	343	2	c	c	NOUN
ejpam-4673	343	3	is	be	AUX
ejpam-4673	343	4	a	a	DET
ejpam-4673	343	5	hop	hop	NOUN
ejpam-4673	343	6	differentiating	differentiate	VERB
ejpam-4673	343	7	hop	hop	NOUN
ejpam-4673	343	8	dominating	dominating	NOUN
ejpam-4673	343	9	set	set	VERB
ejpam-4673	343	10	in	in	ADP
ejpam-4673	343	11	g[h	g[h	PROPN
ejpam-4673	343	12	]	]	PUNCT
ejpam-4673	343	13	.	.	PUNCT
ejpam-4673	344	1	then	then	ADV
ejpam-4673	344	2	,	,	PUNCT
ejpam-4673	344	3	by	by	ADP
ejpam-4673	344	4	theorem	theorem	NOUN
ejpam-4673	344	5	6	6	NUM
ejpam-4673	344	6	,	,	PUNCT
ejpam-4673	344	7	(	(	PUNCT
ejpam-4673	344	8	ii	ii	NOUN
ejpam-4673	344	9	)	)	PUNCT
ejpam-4673	344	10	holds	hold	VERB
ejpam-4673	344	11	.	.	PUNCT
ejpam-4673	344	12	suppose	suppose	VERB
ejpam-4673	344	13	there	there	PRON
ejpam-4673	344	14	exists	exist	VERB
ejpam-4673	344	15	z	z	PROPN
ejpam-4673	344	16	∈	∈	PROPN
ejpam-4673	344	17	v	v	ADP
ejpam-4673	344	18	(	(	PUNCT
ejpam-4673	344	19	g	g	NOUN
ejpam-4673	344	20	)	)	PUNCT
ejpam-4673	344	21	\	\	PUNCT
ejpam-4673	345	1	s.	s.	PROPN
ejpam-4673	345	2	pick	pick	VERB
ejpam-4673	345	3	distinct	distinct	ADJ
ejpam-4673	345	4	vertices	vertex	NOUN
ejpam-4673	345	5	a	a	PRON
ejpam-4673	345	6	,	,	PUNCT
ejpam-4673	345	7	b	b	PROPN
ejpam-4673	345	8	∈	∈	PROPN
ejpam-4673	345	9	v	v	NOUN
ejpam-4673	345	10	(	(	PUNCT
ejpam-4673	345	11	h	h	NOUN
ejpam-4673	345	12	)	)	PUNCT
ejpam-4673	345	13	.	.	PUNCT
ejpam-4673	346	1	then	then	ADV
ejpam-4673	346	2	(	(	PUNCT
ejpam-4673	346	3	z	z	NOUN
ejpam-4673	346	4	,	,	PUNCT
ejpam-4673	346	5	a	a	NOUN
ejpam-4673	346	6	)	)	PUNCT
ejpam-4673	346	7	,	,	PUNCT
ejpam-4673	346	8	(	(	PUNCT
ejpam-4673	346	9	z	z	X
ejpam-4673	346	10	,	,	PUNCT
ejpam-4673	346	11	b	b	NOUN
ejpam-4673	346	12	)	)	PUNCT
ejpam-4673	346	13	∈	∈	NOUN
ejpam-4673	346	14	v	v	NOUN
ejpam-4673	346	15	(	(	PUNCT
ejpam-4673	346	16	g[h	g[h	PROPN
ejpam-4673	346	17	]	]	PUNCT
ejpam-4673	346	18	)	)	PUNCT
ejpam-4673	346	19	\	\	PROPN
ejpam-4673	347	1	c	c	NOUN
ejpam-4673	347	2	and	and	CCONJ
ejpam-4673	347	3	so	so	ADV
ejpam-4673	347	4	n2	n2	ADJ
ejpam-4673	347	5	g[h][(z	g[h][(z	NOUN
ejpam-4673	347	6	,	,	PUNCT
ejpam-4673	347	7	a	a	NOUN
ejpam-4673	347	8	)	)	PUNCT
ejpam-4673	347	9	]	]	PUNCT
ejpam-4673	347	10	∩	∩	NOUN
ejpam-4673	347	11	c	c	NOUN
ejpam-4673	347	12	=	=	PUNCT
ejpam-4673	347	13	⋃	⋃	NOUN
ejpam-4673	347	14	x∈n2	x∈n2	NOUN
ejpam-4673	347	15	g(z)∩s	g(z)∩s	PROPN
ejpam-4673	348	1	[	[	X
ejpam-4673	348	2	{	{	PUNCT
ejpam-4673	348	3	x	x	NOUN
ejpam-4673	348	4	}	}	PUNCT
ejpam-4673	348	5	×	×	NOUN
ejpam-4673	348	6	tx	tx	PROPN
ejpam-4673	348	7	]	]	X
ejpam-4673	348	8	=	=	SYM
ejpam-4673	348	9	n2	n2	ADJ
ejpam-4673	348	10	g[h][(z	g[h][(z	PROPN
ejpam-4673	348	11	,	,	PUNCT
ejpam-4673	348	12	b	b	NOUN
ejpam-4673	348	13	)	)	PUNCT
ejpam-4673	348	14	]	]	PUNCT
ejpam-4673	348	15	∩	∩	PROPN
ejpam-4673	348	16	c.	c.	PROPN
ejpam-4673	348	17	s.	s.	PROPN
ejpam-4673	348	18	canoy	canoy	PROPN
ejpam-4673	348	19	jr	jr	PROPN
ejpam-4673	348	20	.	.	PROPN
ejpam-4673	348	21	,	,	PUNCT
ejpam-4673	348	22	c.	c.	PROPN
ejpam-4673	348	23	saromines	saromine	VERB
ejpam-4673	348	24	/	/	SYM
ejpam-4673	348	25	eur	eur	PROPN
ejpam-4673	348	26	.	.	PUNCT
ejpam-4673	349	1	j.	j.	PROPN
ejpam-4673	349	2	pure	pure	PROPN
ejpam-4673	349	3	appl	appl	PROPN
ejpam-4673	349	4	.	.	PROPN
ejpam-4673	349	5	math	math	PROPN
ejpam-4673	349	6	,	,	PUNCT
ejpam-4673	349	7	16	16	NUM
ejpam-4673	349	8	(	(	PUNCT
ejpam-4673	349	9	1	1	NUM
ejpam-4673	349	10	)	)	PUNCT
ejpam-4673	349	11	(	(	PUNCT
ejpam-4673	349	12	2023	2023	NUM
ejpam-4673	349	13	)	)	PUNCT
ejpam-4673	349	14	,	,	PUNCT
ejpam-4673	349	15	440	440	NUM
ejpam-4673	349	16	-	-	SYM
ejpam-4673	349	17	453	453	NUM
ejpam-4673	349	18	449	449	NUM
ejpam-4673	350	1	this	this	PRON
ejpam-4673	350	2	implies	imply	VERB
ejpam-4673	350	3	that	that	SCONJ
ejpam-4673	350	4	c	c	PROPN
ejpam-4673	350	5	is	be	AUX
ejpam-4673	350	6	not	not	PART
ejpam-4673	350	7	a	a	DET
ejpam-4673	350	8	hop	hop	NOUN
ejpam-4673	350	9	differentiating	differentiate	VERB
ejpam-4673	350	10	set	set	NOUN
ejpam-4673	350	11	,	,	PUNCT
ejpam-4673	350	12	contrary	contrary	ADV
ejpam-4673	350	13	to	to	ADP
ejpam-4673	350	14	our	our	PRON
ejpam-4673	350	15	assumption	assumption	NOUN
ejpam-4673	350	16	.	.	PUNCT
ejpam-4673	351	1	thus	thus	ADV
ejpam-4673	351	2	,	,	PUNCT
ejpam-4673	351	3	s	s	VERB
ejpam-4673	351	4	=	=	SYM
ejpam-4673	351	5	v	v	X
ejpam-4673	351	6	(	(	PUNCT
ejpam-4673	351	7	g	g	NOUN
ejpam-4673	351	8	)	)	PUNCT
ejpam-4673	351	9	,	,	PUNCT
ejpam-4673	351	10	showing	show	VERB
ejpam-4673	351	11	that	that	SCONJ
ejpam-4673	351	12	(	(	PUNCT
ejpam-4673	351	13	i	i	NOUN
ejpam-4673	351	14	)	)	PUNCT
ejpam-4673	351	15	holds	hold	VERB
ejpam-4673	351	16	.	.	PUNCT
ejpam-4673	352	1	now	now	ADV
ejpam-4673	352	2	let	let	VERB
ejpam-4673	352	3	x	x	PUNCT
ejpam-4673	352	4	∈	∈	PROPN
ejpam-4673	352	5	s	s	X
ejpam-4673	352	6	and	and	CCONJ
ejpam-4673	352	7	p	p	X
ejpam-4673	352	8	,	,	PUNCT
ejpam-4673	352	9	q	q	PROPN
ejpam-4673	352	10	∈	∈	PROPN
ejpam-4673	352	11	v	v	ADP
ejpam-4673	352	12	(	(	PUNCT
ejpam-4673	352	13	h	h	NOUN
ejpam-4673	352	14	)	)	PUNCT
ejpam-4673	352	15	with	with	ADP
ejpam-4673	352	16	p	p	PROPN
ejpam-4673	352	17	̸=	̸=	PROPN
ejpam-4673	352	18	q.	q.	NOUN
ejpam-4673	352	19	then	then	ADV
ejpam-4673	352	20	(	(	PUNCT
ejpam-4673	352	21	x	x	X
ejpam-4673	352	22	,	,	PUNCT
ejpam-4673	352	23	p	p	NOUN
ejpam-4673	352	24	)	)	PUNCT
ejpam-4673	352	25	,	,	PUNCT
ejpam-4673	352	26	(	(	PUNCT
ejpam-4673	352	27	x	x	X
ejpam-4673	352	28	,	,	PUNCT
ejpam-4673	352	29	q	q	NOUN
ejpam-4673	352	30	)	)	PUNCT
ejpam-4673	352	31	∈	∈	NOUN
ejpam-4673	352	32	v	v	NOUN
ejpam-4673	352	33	(	(	PUNCT
ejpam-4673	352	34	g[h	g[h	PROPN
ejpam-4673	352	35	]	]	PUNCT
ejpam-4673	352	36	)	)	PUNCT
ejpam-4673	352	37	and	and	CCONJ
ejpam-4673	352	38	n2	n2	PROPN
ejpam-4673	352	39	g[h][(x	g[h][(x	PROPN
ejpam-4673	352	40	,	,	PUNCT
ejpam-4673	352	41	p	p	NOUN
ejpam-4673	352	42	)	)	PUNCT
ejpam-4673	352	43	]	]	PUNCT
ejpam-4673	352	44	∩	∩	NOUN
ejpam-4673	352	45	c	c	NOUN
ejpam-4673	353	1	=	=	PUNCT
ejpam-4673	354	1	[	[	X
ejpam-4673	354	2	{	{	PUNCT
ejpam-4673	354	3	x	x	NOUN
ejpam-4673	354	4	}	}	PUNCT
ejpam-4673	354	5	×	×	NOUN
ejpam-4673	354	6	[	[	X
ejpam-4673	354	7	(	(	PUNCT
ejpam-4673	354	8	v	v	NOUN
ejpam-4673	354	9	(	(	PUNCT
ejpam-4673	354	10	h	h	NOUN
ejpam-4673	354	11	)	)	PUNCT
ejpam-4673	354	12	\nh(p	\nh(p	NOUN
ejpam-4673	354	13	)	)	PUNCT
ejpam-4673	354	14	)	)	PUNCT
ejpam-4673	355	1	∩	∩	PROPN
ejpam-4673	355	2	tx	tx	ADP
ejpam-4673	355	3	]	]	X
ejpam-4673	355	4	]	]	PUNCT
ejpam-4673	355	5	∪	∪	ADP
ejpam-4673	355	6	[	[	X
ejpam-4673	355	7	∪w∈n2	∪w∈n2	X
ejpam-4673	355	8	g(x)∩s({w	g(x)∩s({w	ADJ
ejpam-4673	355	9	}	}	PUNCT
ejpam-4673	355	10	×	×	PROPN
ejpam-4673	355	11	tw	tw	NOUN
ejpam-4673	355	12	)	)	PUNCT
ejpam-4673	355	13	]	]	PUNCT
ejpam-4673	355	14	and	and	CCONJ
ejpam-4673	355	15	n2	n2	PROPN
ejpam-4673	355	16	g[h][(x	g[h][(x	PROPN
ejpam-4673	355	17	,	,	PUNCT
ejpam-4673	355	18	q	q	NOUN
ejpam-4673	355	19	)	)	PUNCT
ejpam-4673	355	20	]	]	PUNCT
ejpam-4673	356	1	∩	∩	NOUN
ejpam-4673	356	2	c	c	NOUN
ejpam-4673	356	3	=	=	PUNCT
ejpam-4673	357	1	[	[	X
ejpam-4673	357	2	{	{	PUNCT
ejpam-4673	357	3	x	x	NOUN
ejpam-4673	357	4	}	}	PUNCT
ejpam-4673	357	5	×	×	NOUN
ejpam-4673	357	6	[	[	X
ejpam-4673	357	7	(	(	PUNCT
ejpam-4673	357	8	v	v	NOUN
ejpam-4673	357	9	(	(	PUNCT
ejpam-4673	357	10	h	h	NOUN
ejpam-4673	357	11	)	)	PUNCT
ejpam-4673	357	12	\nh(q	\nh(q	ADV
ejpam-4673	357	13	)	)	PUNCT
ejpam-4673	357	14	)	)	PUNCT
ejpam-4673	357	15	∩	∩	PROPN
ejpam-4673	357	16	tx	tx	ADP
ejpam-4673	357	17	]	]	X
ejpam-4673	357	18	]	]	PUNCT
ejpam-4673	357	19	∪	∪	ADP
ejpam-4673	357	20	[	[	X
ejpam-4673	357	21	∪w∈n2	∪w∈n2	X
ejpam-4673	357	22	g(x)∩s({w	g(x)∩s({w	ADJ
ejpam-4673	357	23	}	}	PUNCT
ejpam-4673	357	24	×	×	PROPN
ejpam-4673	357	25	tw	tw	NOUN
ejpam-4673	357	26	)	)	PUNCT
ejpam-4673	357	27	]	]	PUNCT
ejpam-4673	357	28	.	.	PUNCT
ejpam-4673	358	1	since	since	SCONJ
ejpam-4673	358	2	c	c	PROPN
ejpam-4673	358	3	is	be	AUX
ejpam-4673	358	4	a	a	DET
ejpam-4673	358	5	hop	hop	NOUN
ejpam-4673	358	6	differentiating	differentiate	VERB
ejpam-4673	358	7	set	set	NOUN
ejpam-4673	358	8	,	,	PUNCT
ejpam-4673	358	9	(	(	PUNCT
ejpam-4673	358	10	v	v	NOUN
ejpam-4673	358	11	(	(	PUNCT
ejpam-4673	358	12	h	h	NOUN
ejpam-4673	358	13	)	)	PUNCT
ejpam-4673	358	14	\nh(p	\nh(p	NOUN
ejpam-4673	358	15	)	)	PUNCT
ejpam-4673	358	16	)	)	PUNCT
ejpam-4673	358	17	∩	∩	PROPN
ejpam-4673	358	18	tx	tx	PROPN
ejpam-4673	358	19	̸=	̸=	PROPN
ejpam-4673	358	20	(	(	PUNCT
ejpam-4673	358	21	v	v	PROPN
ejpam-4673	358	22	(	(	PUNCT
ejpam-4673	358	23	h	h	NOUN
ejpam-4673	358	24	)	)	PUNCT
ejpam-4673	358	25	\nh(q	\nh(q	ADV
ejpam-4673	358	26	)	)	PUNCT
ejpam-4673	358	27	)	)	PUNCT
ejpam-4673	358	28	∩	∩	PROPN
ejpam-4673	358	29	tx	tx	PROPN
ejpam-4673	358	30	.	.	PUNCT
ejpam-4673	359	1	hence	hence	ADV
ejpam-4673	359	2	,	,	PUNCT
ejpam-4673	359	3	tx	tx	PROPN
ejpam-4673	359	4	is	be	AUX
ejpam-4673	359	5	a	a	DET
ejpam-4673	359	6	complement	complement	NOUN
ejpam-4673	359	7	-	-	PUNCT
ejpam-4673	359	8	differentiating	differentiate	VERB
ejpam-4673	359	9	set	set	VERB
ejpam-4673	359	10	inh	inh	NOUN
ejpam-4673	359	11	,	,	PUNCT
ejpam-4673	359	12	showing	show	VERB
ejpam-4673	359	13	that	that	SCONJ
ejpam-4673	359	14	(	(	PUNCT
ejpam-4673	359	15	iii	iii	NOUN
ejpam-4673	359	16	)	)	PUNCT
ejpam-4673	359	17	holds	hold	VERB
ejpam-4673	359	18	.	.	PUNCT
ejpam-4673	360	1	next	next	ADV
ejpam-4673	360	2	,	,	PUNCT
ejpam-4673	360	3	suppose	suppose	VERB
ejpam-4673	360	4	that	that	SCONJ
ejpam-4673	360	5	x	x	PROPN
ejpam-4673	360	6	and	and	CCONJ
ejpam-4673	360	7	y	y	PROPN
ejpam-4673	360	8	are	be	AUX
ejpam-4673	360	9	distinct	distinct	ADJ
ejpam-4673	360	10	vertices	vertex	NOUN
ejpam-4673	360	11	of	of	ADP
ejpam-4673	360	12	g	g	NOUN
ejpam-4673	360	13	with	with	ADP
ejpam-4673	360	14	n2	n2	ADJ
ejpam-4673	360	15	g(x	g(x	NOUN
ejpam-4673	360	16	)	)	PUNCT
ejpam-4673	360	17	=	=	SYM
ejpam-4673	360	18	n2	n2	PROPN
ejpam-4673	360	19	g(y	g(y	PROPN
ejpam-4673	360	20	)	)	PUNCT
ejpam-4673	360	21	.	.	PUNCT
ejpam-4673	361	1	suppose	suppose	VERB
ejpam-4673	361	2	tx	tx	PROPN
ejpam-4673	361	3	and	and	CCONJ
ejpam-4673	361	4	ty	ty	INTJ
ejpam-4673	361	5	are	be	AUX
ejpam-4673	361	6	not	not	PART
ejpam-4673	361	7	pointwise	pointwise	ADJ
ejpam-4673	361	8	non	non	ADJ
ejpam-4673	361	9	-	-	ADJ
ejpam-4673	361	10	dominating	dominating	ADJ
ejpam-4673	361	11	sets	set	NOUN
ejpam-4673	361	12	.	.	PUNCT
ejpam-4673	362	1	then	then	ADV
ejpam-4673	362	2	there	there	PRON
ejpam-4673	362	3	exist	exist	VERB
ejpam-4673	362	4	p	p	PROPN
ejpam-4673	362	5	∈	∈	PROPN
ejpam-4673	362	6	v	v	ADP
ejpam-4673	362	7	(	(	PUNCT
ejpam-4673	362	8	h	h	NOUN
ejpam-4673	362	9	)	)	PUNCT
ejpam-4673	362	10	\	\	PROPN
ejpam-4673	362	11	tx	tx	PROPN
ejpam-4673	362	12	and	and	CCONJ
ejpam-4673	362	13	q	q	PROPN
ejpam-4673	362	14	∈	∈	PROPN
ejpam-4673	362	15	v	v	ADP
ejpam-4673	362	16	(	(	PUNCT
ejpam-4673	362	17	h	h	NOUN
ejpam-4673	362	18	)	)	PUNCT
ejpam-4673	362	19	\	\	NOUN
ejpam-4673	363	1	ty	ty	INTJ
ejpam-4673	363	2	such	such	ADJ
ejpam-4673	363	3	that	that	SCONJ
ejpam-4673	363	4	[	[	X
ejpam-4673	363	5	v	v	X
ejpam-4673	363	6	(	(	PUNCT
ejpam-4673	363	7	h	h	NOUN
ejpam-4673	363	8	)	)	PUNCT
ejpam-4673	363	9	\	\	NOUN
ejpam-4673	363	10	nh(p	nh(p	PROPN
ejpam-4673	363	11	)	)	PUNCT
ejpam-4673	363	12	]	]	PUNCT
ejpam-4673	363	13	∩	∩	PROPN
ejpam-4673	363	14	tx	tx	NOUN
ejpam-4673	363	15	=	=	SYM
ejpam-4673	363	16	∅	∅	NOUN
ejpam-4673	363	17	and	and	CCONJ
ejpam-4673	363	18	[	[	X
ejpam-4673	363	19	v	v	X
ejpam-4673	363	20	(	(	PUNCT
ejpam-4673	363	21	h	h	NOUN
ejpam-4673	363	22	)	)	PUNCT
ejpam-4673	363	23	\	\	NOUN
ejpam-4673	363	24	nh(q	nh(q	PROPN
ejpam-4673	363	25	)	)	PUNCT
ejpam-4673	363	26	]	]	PUNCT
ejpam-4673	363	27	∩	∩	NOUN
ejpam-4673	363	28	ty	ty	X
ejpam-4673	363	29	=	=	PUNCT
ejpam-4673	363	30	∅.	∅.	NOUN
ejpam-4673	363	31	since	since	SCONJ
ejpam-4673	363	32	n2	n2	ADJ
ejpam-4673	363	33	g(x	g(x	NOUN
ejpam-4673	363	34	)	)	PUNCT
ejpam-4673	363	35	=	=	SYM
ejpam-4673	363	36	n2	n2	PROPN
ejpam-4673	363	37	g(y	g(y	PROPN
ejpam-4673	363	38	)	)	PUNCT
ejpam-4673	363	39	,	,	PUNCT
ejpam-4673	363	40	it	it	PRON
ejpam-4673	363	41	follows	follow	VERB
ejpam-4673	363	42	that	that	DET
ejpam-4673	363	43	n2	n2	PROPN
ejpam-4673	363	44	g[h][(x	g[h][(x	PROPN
ejpam-4673	363	45	,	,	PUNCT
ejpam-4673	363	46	p	p	NOUN
ejpam-4673	363	47	)	)	PUNCT
ejpam-4673	363	48	]	]	PUNCT
ejpam-4673	363	49	∩	∩	PROPN
ejpam-4673	363	50	c	c	NOUN
ejpam-4673	363	51	=	=	SYM
ejpam-4673	363	52	n2	n2	PROPN
ejpam-4673	363	53	g[h][(y	g[h][(y	NOUN
ejpam-4673	363	54	,	,	PUNCT
ejpam-4673	363	55	q	q	NOUN
ejpam-4673	363	56	)	)	PUNCT
ejpam-4673	363	57	]	]	PUNCT
ejpam-4673	364	1	∩	∩	PROPN
ejpam-4673	364	2	c	c	X
ejpam-4673	364	3	,	,	PUNCT
ejpam-4673	364	4	contradicting	contradict	VERB
ejpam-4673	364	5	the	the	DET
ejpam-4673	364	6	assumption	assumption	NOUN
ejpam-4673	364	7	that	that	SCONJ
ejpam-4673	364	8	c	c	PROPN
ejpam-4673	364	9	is	be	AUX
ejpam-4673	364	10	a	a	DET
ejpam-4673	364	11	hop	hop	NOUN
ejpam-4673	364	12	differentiating	differentiating	NOUN
ejpam-4673	364	13	set	set	NOUN
ejpam-4673	364	14	in	in	ADP
ejpam-4673	364	15	g[h	g[h	PROPN
ejpam-4673	364	16	]	]	PUNCT
ejpam-4673	364	17	.	.	PUNCT
ejpam-4673	365	1	thus	thus	ADV
ejpam-4673	365	2	,	,	PUNCT
ejpam-4673	365	3	tx	tx	PROPN
ejpam-4673	365	4	or	or	CCONJ
ejpam-4673	365	5	ty	ty	INTJ
ejpam-4673	365	6	is	be	AUX
ejpam-4673	365	7	pointwise	pointwise	ADJ
ejpam-4673	365	8	non	non	ADJ
ejpam-4673	365	9	-	-	ADJ
ejpam-4673	365	10	dominating	dominating	NOUN
ejpam-4673	365	11	in	in	ADP
ejpam-4673	365	12	h	h	NOUN
ejpam-4673	365	13	,	,	PUNCT
ejpam-4673	365	14	showing	show	VERB
ejpam-4673	365	15	that	that	SCONJ
ejpam-4673	365	16	(	(	PUNCT
ejpam-4673	365	17	iv	iv	X
ejpam-4673	365	18	)	)	PUNCT
ejpam-4673	365	19	holds	hold	NOUN
ejpam-4673	365	20	.	.	PUNCT
ejpam-4673	366	1	for	for	ADP
ejpam-4673	366	2	the	the	DET
ejpam-4673	366	3	converse	converse	NOUN
ejpam-4673	366	4	,	,	PUNCT
ejpam-4673	366	5	suppose	suppose	VERB
ejpam-4673	366	6	that	that	SCONJ
ejpam-4673	366	7	c	c	PROPN
ejpam-4673	366	8	satisfies	satisfy	VERB
ejpam-4673	366	9	properties	property	NOUN
ejpam-4673	366	10	(	(	PUNCT
ejpam-4673	366	11	i)-(iv	i)-(iv	ADJ
ejpam-4673	366	12	)	)	PUNCT
ejpam-4673	366	13	.	.	PUNCT
ejpam-4673	367	1	since	since	SCONJ
ejpam-4673	367	2	(	(	PUNCT
ejpam-4673	367	3	i	i	NOUN
ejpam-4673	367	4	)	)	PUNCT
ejpam-4673	367	5	and	and	CCONJ
ejpam-4673	367	6	(	(	PUNCT
ejpam-4673	367	7	ii	ii	NOUN
ejpam-4673	367	8	)	)	PUNCT
ejpam-4673	367	9	hold	hold	VERB
ejpam-4673	367	10	,	,	PUNCT
ejpam-4673	367	11	c	c	PROPN
ejpam-4673	367	12	is	be	AUX
ejpam-4673	367	13	a	a	DET
ejpam-4673	367	14	hop	hop	NOUN
ejpam-4673	367	15	dominating	dominating	NOUN
ejpam-4673	367	16	set	set	VERB
ejpam-4673	367	17	by	by	ADP
ejpam-4673	367	18	theorem	theorem	NOUN
ejpam-4673	367	19	6	6	NUM
ejpam-4673	367	20	.	.	PUNCT
ejpam-4673	368	1	next	next	ADV
ejpam-4673	368	2	,	,	PUNCT
ejpam-4673	368	3	let	let	VERB
ejpam-4673	368	4	(	(	PUNCT
ejpam-4673	368	5	v	v	NOUN
ejpam-4673	368	6	,	,	PUNCT
ejpam-4673	368	7	q	q	NOUN
ejpam-4673	368	8	)	)	PUNCT
ejpam-4673	368	9	,	,	PUNCT
ejpam-4673	368	10	(	(	PUNCT
ejpam-4673	368	11	w	w	PROPN
ejpam-4673	368	12	,	,	PUNCT
ejpam-4673	368	13	s	s	PART
ejpam-4673	368	14	)	)	PUNCT
ejpam-4673	368	15	∈	∈	NOUN
ejpam-4673	368	16	v	v	NOUN
ejpam-4673	368	17	(	(	PUNCT
ejpam-4673	368	18	g[h	g[h	PROPN
ejpam-4673	368	19	]	]	PUNCT
ejpam-4673	368	20	)	)	PUNCT
ejpam-4673	368	21	with	with	ADP
ejpam-4673	368	22	(	(	PUNCT
ejpam-4673	368	23	v	v	NOUN
ejpam-4673	368	24	,	,	PUNCT
ejpam-4673	368	25	q	q	NOUN
ejpam-4673	368	26	)	)	PUNCT
ejpam-4673	368	27	̸=	̸=	PROPN
ejpam-4673	368	28	(	(	PUNCT
ejpam-4673	368	29	w	w	PROPN
ejpam-4673	368	30	,	,	PUNCT
ejpam-4673	368	31	s	s	NOUN
ejpam-4673	368	32	)	)	PUNCT
ejpam-4673	368	33	.	.	PUNCT
ejpam-4673	369	1	then	then	ADV
ejpam-4673	369	2	n2	n2	PROPN
ejpam-4673	369	3	g[h][(v	g[h][(v	PROPN
ejpam-4673	369	4	,	,	PUNCT
ejpam-4673	369	5	q	q	NOUN
ejpam-4673	369	6	)	)	PUNCT
ejpam-4673	369	7	]	]	PUNCT
ejpam-4673	370	1	∩	∩	NOUN
ejpam-4673	370	2	c	c	NOUN
ejpam-4673	370	3	=	=	PUNCT
ejpam-4673	371	1	[	[	X
ejpam-4673	371	2	{	{	PUNCT
ejpam-4673	371	3	v	v	NOUN
ejpam-4673	371	4	}	}	PUNCT
ejpam-4673	371	5	×	×	NOUN
ejpam-4673	371	6	[	[	X
ejpam-4673	371	7	(	(	PUNCT
ejpam-4673	371	8	v	v	NOUN
ejpam-4673	371	9	(	(	PUNCT
ejpam-4673	371	10	h	h	NOUN
ejpam-4673	371	11	)	)	PUNCT
ejpam-4673	371	12	\nh(q	\nh(q	ADV
ejpam-4673	371	13	)	)	PUNCT
ejpam-4673	371	14	)	)	PUNCT
ejpam-4673	371	15	∩	∩	ADJ
ejpam-4673	371	16	tv	tv	NOUN
ejpam-4673	371	17	]	]	PUNCT
ejpam-4673	371	18	∪	∪	ADP
ejpam-4673	371	19	[	[	PUNCT
ejpam-4673	371	20	⋃	⋃	NOUN
ejpam-4673	371	21	z∈n2	z∈n2	ADJ
ejpam-4673	371	22	g(v	g(v	NOUN
ejpam-4673	371	23	)	)	PUNCT
ejpam-4673	372	1	[	[	X
ejpam-4673	372	2	{	{	PUNCT
ejpam-4673	372	3	z	z	NOUN
ejpam-4673	372	4	}	}	PUNCT
ejpam-4673	372	5	×	×	PROPN
ejpam-4673	372	6	tz	tz	NOUN
ejpam-4673	372	7	]	]	X
ejpam-4673	372	8	,	,	PUNCT
ejpam-4673	372	9	and	and	CCONJ
ejpam-4673	372	10	n2	n2	PROPN
ejpam-4673	372	11	g[h][(w	g[h][(w	PROPN
ejpam-4673	372	12	,	,	PUNCT
ejpam-4673	372	13	s	s	PART
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ejpam-4673	372	15	]	]	PUNCT
ejpam-4673	372	16	∩	∩	NOUN
ejpam-4673	372	17	c	c	NOUN
ejpam-4673	372	18	=	=	PUNCT
ejpam-4673	373	1	[	[	X
ejpam-4673	373	2	{	{	PUNCT
ejpam-4673	373	3	w	w	NOUN
ejpam-4673	373	4	}	}	PUNCT
ejpam-4673	373	5	×	×	NOUN
ejpam-4673	373	6	(	(	PUNCT
ejpam-4673	373	7	v	v	NOUN
ejpam-4673	373	8	(	(	PUNCT
ejpam-4673	373	9	h	h	NOUN
ejpam-4673	373	10	)	)	PUNCT
ejpam-4673	373	11	\nh(s	\nh(	NOUN
ejpam-4673	373	12	)	)	PUNCT
ejpam-4673	373	13	)	)	PUNCT
ejpam-4673	373	14	∩	∩	PROPN
ejpam-4673	373	15	tw	tw	SYM
ejpam-4673	373	16	]	]	X
ejpam-4673	373	17	∪	∪	ADP
ejpam-4673	373	18	[	[	PUNCT
ejpam-4673	373	19	⋃	⋃	NOUN
ejpam-4673	373	20	y∈n2	y∈n2	NOUN
ejpam-4673	373	21	g(w	g(w	NOUN
ejpam-4673	373	22	)	)	PUNCT
ejpam-4673	374	1	[	[	X
ejpam-4673	374	2	{	{	PUNCT
ejpam-4673	374	3	y	y	NOUN
ejpam-4673	374	4	}	}	PUNCT
ejpam-4673	374	5	×	×	NOUN
ejpam-4673	374	6	ty	ty	PRON
ejpam-4673	374	7	]	]	PUNCT
ejpam-4673	374	8	.	.	PUNCT
ejpam-4673	375	1	consider	consider	VERB
ejpam-4673	375	2	the	the	DET
ejpam-4673	375	3	following	follow	VERB
ejpam-4673	375	4	cases	case	NOUN
ejpam-4673	375	5	:	:	PUNCT
ejpam-4673	375	6	case	case	NOUN
ejpam-4673	375	7	1	1	NUM
ejpam-4673	375	8	:	:	SYM
ejpam-4673	375	9	v	v	NOUN
ejpam-4673	375	10	=	=	SYM
ejpam-4673	375	11	w	w	NOUN
ejpam-4673	375	12	then	then	ADV
ejpam-4673	375	13	q	q	X
ejpam-4673	375	14	,	,	PUNCT
ejpam-4673	375	15	s	s	NOUN
ejpam-4673	375	16	∈	∈	PROPN
ejpam-4673	375	17	v	v	ADP
ejpam-4673	375	18	(	(	PUNCT
ejpam-4673	375	19	h	h	NOUN
ejpam-4673	375	20	)	)	PUNCT
ejpam-4673	375	21	with	with	ADP
ejpam-4673	375	22	q	q	PROPN
ejpam-4673	375	23	̸=	̸=	PROPN
ejpam-4673	375	24	s.	s.	PROPN
ejpam-4673	375	25	by	by	ADP
ejpam-4673	375	26	(	(	PUNCT
ejpam-4673	375	27	iii	iii	NOUN
ejpam-4673	375	28	)	)	PUNCT
ejpam-4673	375	29	,	,	PUNCT
ejpam-4673	375	30	tv	tv	NOUN
ejpam-4673	375	31	is	be	AUX
ejpam-4673	375	32	a	a	DET
ejpam-4673	375	33	complement	complement	NOUN
ejpam-4673	375	34	-	-	PUNCT
ejpam-4673	375	35	differentiating	differentiate	VERB
ejpam-4673	375	36	set	set	NOUN
ejpam-4673	375	37	;	;	PUNCT
ejpam-4673	375	38	hence	hence	ADV
ejpam-4673	375	39	,	,	PUNCT
ejpam-4673	375	40	[	[	X
ejpam-4673	375	41	v	v	X
ejpam-4673	375	42	(	(	PUNCT
ejpam-4673	375	43	h)\nh(q)]∩tv	h)\nh(q)]∩tv	ADV
ejpam-4673	375	44	̸=	̸=	PROPN
ejpam-4673	375	45	[	[	X
ejpam-4673	375	46	v	v	X
ejpam-4673	375	47	(	(	PUNCT
ejpam-4673	375	48	h)\nh(s)]∩tv	h)\nh(s)]∩tv	NOUN
ejpam-4673	375	49	.	.	PUNCT
ejpam-4673	376	1	it	it	PRON
ejpam-4673	376	2	follows	follow	VERB
ejpam-4673	376	3	that	that	SCONJ
ejpam-4673	376	4	n	n	ADJ
ejpam-4673	376	5	2	2	NUM
ejpam-4673	376	6	g[h][(v	g[h][(v	ADJ
ejpam-4673	376	7	,	,	PUNCT
ejpam-4673	376	8	q)]∩c	q)]∩c	PROPN
ejpam-4673	376	9	̸=	̸=	PROPN
ejpam-4673	376	10	n2	n2	NOUN
ejpam-4673	376	11	g[h][(v	g[h][(v	NOUN
ejpam-4673	376	12	,	,	PUNCT
ejpam-4673	376	13	s)]∩	s)]∩	PROPN
ejpam-4673	376	14	c.	c.	NOUN
ejpam-4673	376	15	case	case	NOUN
ejpam-4673	376	16	2	2	NUM
ejpam-4673	376	17	:	:	PUNCT
ejpam-4673	376	18	v	v	ADP
ejpam-4673	376	19	̸=	̸=	PROPN
ejpam-4673	376	20	w	w	NOUN
ejpam-4673	376	21	suppose	suppose	VERB
ejpam-4673	376	22	first	first	ADV
ejpam-4673	376	23	that	that	PRON
ejpam-4673	376	24	dg(v	dg(v	NOUN
ejpam-4673	376	25	,	,	PUNCT
ejpam-4673	376	26	w	w	NOUN
ejpam-4673	376	27	)	)	PUNCT
ejpam-4673	376	28	̸=	̸=	PROPN
ejpam-4673	376	29	2	2	NUM
ejpam-4673	376	30	.	.	PUNCT
ejpam-4673	377	1	if	if	SCONJ
ejpam-4673	377	2	n2	n2	ADJ
ejpam-4673	377	3	g(v	g(v	X
ejpam-4673	377	4	)	)	PUNCT
ejpam-4673	377	5	̸=	̸=	PROPN
ejpam-4673	377	6	n2	n2	NOUN
ejpam-4673	377	7	g(w	g(w	PROPN
ejpam-4673	377	8	)	)	PUNCT
ejpam-4673	377	9	,	,	PUNCT
ejpam-4673	377	10	then	then	ADV
ejpam-4673	377	11	clearly	clearly	ADV
ejpam-4673	377	12	,	,	PUNCT
ejpam-4673	377	13	n2	n2	PROPN
ejpam-4673	377	14	g[h][(v	g[h][(v	NOUN
ejpam-4673	377	15	,	,	PUNCT
ejpam-4673	377	16	q	q	NOUN
ejpam-4673	377	17	)	)	PUNCT
ejpam-4673	377	18	]	]	PUNCT
ejpam-4673	377	19	∩	∩	PROPN
ejpam-4673	377	20	c	c	PROPN
ejpam-4673	377	21	̸=	̸=	PROPN
ejpam-4673	377	22	n2	n2	PROPN
ejpam-4673	377	23	g[h][(w	g[h][(w	PROPN
ejpam-4673	377	24	,	,	PUNCT
ejpam-4673	377	25	s)]∩c	s)]∩c	PROPN
ejpam-4673	377	26	.	.	PUNCT
ejpam-4673	378	1	if	if	SCONJ
ejpam-4673	378	2	n2	n2	ADJ
ejpam-4673	378	3	g(v	g(v	X
ejpam-4673	378	4	)	)	PUNCT
ejpam-4673	378	5	=	=	SYM
ejpam-4673	378	6	n2	n2	PROPN
ejpam-4673	378	7	g(w	g(w	PROPN
ejpam-4673	378	8	)	)	PUNCT
ejpam-4673	378	9	,	,	PUNCT
ejpam-4673	378	10	then	then	ADV
ejpam-4673	378	11	tv	tv	NOUN
ejpam-4673	378	12	or	or	CCONJ
ejpam-4673	378	13	tw	tw	PROPN
ejpam-4673	378	14	is	be	AUX
ejpam-4673	378	15	pointwise	pointwise	ADJ
ejpam-4673	378	16	non	non	ADJ
ejpam-4673	378	17	-	-	ADJ
ejpam-4673	378	18	dominating	dominating	NOUN
ejpam-4673	378	19	in	in	ADP
ejpam-4673	378	20	h	h	NOUN
ejpam-4673	378	21	by	by	X
ejpam-4673	378	22	(	(	PUNCT
ejpam-4673	378	23	iv	iv	NOUN
ejpam-4673	378	24	)	)	PUNCT
ejpam-4673	378	25	.	.	PUNCT
ejpam-4673	379	1	hence	hence	ADV
ejpam-4673	379	2	,	,	PUNCT
ejpam-4673	379	3	n2	n2	NOUN
ejpam-4673	379	4	g[h][(v	g[h][(v	NOUN
ejpam-4673	379	5	,	,	PUNCT
ejpam-4673	379	6	q)]∩c	q)]∩c	PROPN
ejpam-4673	379	7	̸=	̸=	PROPN
ejpam-4673	379	8	n2	n2	PROPN
ejpam-4673	379	9	g[h][(w	g[h][(w	PROPN
ejpam-4673	379	10	,	,	PUNCT
ejpam-4673	379	11	s)]∩c	s)]∩c	PROPN
ejpam-4673	379	12	.	.	PUNCT
ejpam-4673	380	1	next	next	ADV
ejpam-4673	380	2	,	,	PUNCT
ejpam-4673	380	3	suppose	suppose	VERB
ejpam-4673	380	4	that	that	SCONJ
ejpam-4673	380	5	dg(v	dg(v	NOUN
ejpam-4673	380	6	,	,	PUNCT
ejpam-4673	380	7	w	w	NOUN
ejpam-4673	380	8	)	)	PUNCT
ejpam-4673	380	9	=	=	SYM
ejpam-4673	380	10	2	2	X
ejpam-4673	380	11	.	.	PUNCT
ejpam-4673	380	12	since	since	SCONJ
ejpam-4673	380	13	g	g	PROPN
ejpam-4673	380	14	is	be	AUX
ejpam-4673	380	15	distance	distance	NOUN
ejpam-4673	380	16	-	-	PUNCT
ejpam-4673	380	17	two	two	NUM
ejpam-4673	380	18	point	point	NOUN
ejpam-4673	380	19	distinguishing	distinguishing	NOUN
ejpam-4673	380	20	,	,	PUNCT
ejpam-4673	380	21	n2	n2	ADJ
ejpam-4673	380	22	g[v	g[v	PROPN
ejpam-4673	380	23	]	]	PUNCT
ejpam-4673	380	24	̸=	̸=	PROPN
ejpam-4673	380	25	n2	n2	NOUN
ejpam-4673	380	26	g[w	g[w	PROPN
ejpam-4673	380	27	]	]	PUNCT
ejpam-4673	380	28	.	.	PUNCT
ejpam-4673	381	1	it	it	PRON
ejpam-4673	381	2	follows	follow	VERB
ejpam-4673	381	3	that	that	SCONJ
ejpam-4673	381	4	n	n	ADJ
ejpam-4673	381	5	2	2	NUM
ejpam-4673	381	6	g[h][(v	g[h][(v	ADJ
ejpam-4673	381	7	,	,	PUNCT
ejpam-4673	381	8	q)]∩c	q)]∩c	PROPN
ejpam-4673	381	9	̸=	̸=	PROPN
ejpam-4673	381	10	n2	n2	PROPN
ejpam-4673	381	11	g[h][(w	g[h][(w	PROPN
ejpam-4673	381	12	,	,	PUNCT
ejpam-4673	381	13	s	s	PART
ejpam-4673	381	14	)	)	PUNCT
ejpam-4673	381	15	]	]	PUNCT
ejpam-4673	381	16	∩	∩	PROPN
ejpam-4673	381	17	c.	c.	PROPN
ejpam-4673	381	18	accordingly	accordingly	ADV
ejpam-4673	381	19	,	,	PUNCT
ejpam-4673	381	20	c	c	PROPN
ejpam-4673	381	21	is	be	AUX
ejpam-4673	381	22	a	a	DET
ejpam-4673	381	23	hop	hop	NOUN
ejpam-4673	381	24	differentiating	differentiate	VERB
ejpam-4673	381	25	hop	hop	NOUN
ejpam-4673	381	26	dominating	dominating	NOUN
ejpam-4673	381	27	set	set	VERB
ejpam-4673	381	28	in	in	ADP
ejpam-4673	381	29	g[h	g[h	PROPN
ejpam-4673	381	30	]	]	PUNCT
ejpam-4673	381	31	.	.	PUNCT
ejpam-4673	382	1	s.	s.	PROPN
ejpam-4673	382	2	canoy	canoy	PROPN
ejpam-4673	382	3	jr	jr	PROPN
ejpam-4673	382	4	.	.	PROPN
ejpam-4673	382	5	,	,	PUNCT
ejpam-4673	382	6	c.	c.	PROPN
ejpam-4673	382	7	saromines	saromine	VERB
ejpam-4673	382	8	/	/	SYM
ejpam-4673	382	9	eur	eur	PROPN
ejpam-4673	382	10	.	.	PUNCT
ejpam-4673	383	1	j.	j.	PROPN
ejpam-4673	383	2	pure	pure	PROPN
ejpam-4673	383	3	appl	appl	PROPN
ejpam-4673	383	4	.	.	PROPN
ejpam-4673	383	5	math	math	PROPN
ejpam-4673	383	6	,	,	PUNCT
ejpam-4673	383	7	16	16	NUM
ejpam-4673	383	8	(	(	PUNCT
ejpam-4673	383	9	1	1	NUM
ejpam-4673	383	10	)	)	PUNCT
ejpam-4673	383	11	(	(	PUNCT
ejpam-4673	383	12	2023	2023	NUM
ejpam-4673	383	13	)	)	PUNCT
ejpam-4673	383	14	,	,	PUNCT
ejpam-4673	383	15	440	440	NUM
ejpam-4673	383	16	-	-	SYM
ejpam-4673	383	17	453	453	NUM
ejpam-4673	383	18	450	450	NUM
ejpam-4673	383	19	corollary	corollary	NOUN
ejpam-4673	383	20	7	7	NUM
ejpam-4673	383	21	.	.	PUNCT
ejpam-4673	384	1	let	let	VERB
ejpam-4673	384	2	g	g	NOUN
ejpam-4673	384	3	and	and	CCONJ
ejpam-4673	384	4	h	h	PROPN
ejpam-4673	384	5	be	be	VERB
ejpam-4673	384	6	non	non	ADJ
ejpam-4673	384	7	-	-	ADJ
ejpam-4673	384	8	trivial	trivial	ADJ
ejpam-4673	384	9	connected	connected	ADJ
ejpam-4673	384	10	graphs	graph	NOUN
ejpam-4673	384	11	such	such	ADJ
ejpam-4673	384	12	that	that	SCONJ
ejpam-4673	384	13	g	g	PROPN
ejpam-4673	384	14	and	and	CCONJ
ejpam-4673	384	15	h	h	NOUN
ejpam-4673	384	16	are	be	AUX
ejpam-4673	384	17	,	,	PUNCT
ejpam-4673	384	18	respectively	respectively	ADV
ejpam-4673	384	19	,	,	PUNCT
ejpam-4673	384	20	distance	distance	NOUN
ejpam-4673	384	21	-	-	PUNCT
ejpam-4673	384	22	two	two	NUM
ejpam-4673	384	23	point	point	NOUN
ejpam-4673	384	24	distinguishing	distinguish	VERB
ejpam-4673	384	25	and	and	CCONJ
ejpam-4673	384	26	complement	complement	VERB
ejpam-4673	384	27	point	point	NOUN
ejpam-4673	384	28	distinguishing	distinguishing	NOUN
ejpam-4673	384	29	.	.	PUNCT
ejpam-4673	385	1	then	then	ADV
ejpam-4673	385	2	γdh(g[h	γdh(g[h	NUM
ejpam-4673	385	3	]	]	PUNCT
ejpam-4673	385	4	)	)	PUNCT
ejpam-4673	385	5	≤	≤	NUM
ejpam-4673	385	6	|v	|v	X
ejpam-4673	385	7	(	(	PUNCT
ejpam-4673	385	8	g)|cdpnd(h	g)|cdpnd(h	NOUN
ejpam-4673	385	9	)	)	PUNCT
ejpam-4673	385	10	=	=	SYM
ejpam-4673	385	11	|v	|v	PROPN
ejpam-4673	385	12	(	(	PUNCT
ejpam-4673	385	13	g)|γd(h	g)|γd(h	PROPN
ejpam-4673	385	14	)	)	PUNCT
ejpam-4673	385	15	.	.	PUNCT
ejpam-4673	386	1	if	if	SCONJ
ejpam-4673	386	2	,	,	PUNCT
ejpam-4673	386	3	in	in	ADP
ejpam-4673	386	4	addition	addition	NOUN
ejpam-4673	386	5	,	,	PUNCT
ejpam-4673	386	6	g	g	PROPN
ejpam-4673	386	7	is	be	AUX
ejpam-4673	386	8	also	also	ADV
ejpam-4673	386	9	distance	distance	NOUN
ejpam-4673	386	10	-	-	PUNCT
ejpam-4673	386	11	two	two	NUM
ejpam-4673	386	12	point	point	NOUN
ejpam-4673	386	13	determining	determine	VERB
ejpam-4673	386	14	and	and	CCONJ
ejpam-4673	386	15	γ(g	γ(g	NOUN
ejpam-4673	386	16	)	)	PUNCT
ejpam-4673	387	1	̸=	̸=	PROPN
ejpam-4673	387	2	1	1	NUM
ejpam-4673	387	3	,	,	PUNCT
ejpam-4673	387	4	then	then	ADV
ejpam-4673	387	5	γdh(g[h	γdh(g[h	NUM
ejpam-4673	387	6	]	]	PUNCT
ejpam-4673	387	7	)	)	PUNCT
ejpam-4673	387	8	=	=	SYM
ejpam-4673	387	9	|v	|v	PROPN
ejpam-4673	387	10	(	(	PUNCT
ejpam-4673	387	11	g)|cdn(h	g)|cdn(h	NOUN
ejpam-4673	387	12	)	)	PUNCT
ejpam-4673	387	13	=	=	SYM
ejpam-4673	387	14	|v	|v	PROPN
ejpam-4673	387	15	(	(	PUNCT
ejpam-4673	387	16	g)|dn(h	g)|dn(h	PROPN
ejpam-4673	387	17	)	)	PUNCT
ejpam-4673	387	18	.	.	PUNCT
ejpam-4673	388	1	proof	proof	NOUN
ejpam-4673	388	2	.	.	PUNCT
ejpam-4673	389	1	let	let	VERB
ejpam-4673	389	2	s	s	PRON
ejpam-4673	389	3	=	=	X
ejpam-4673	389	4	v	v	ADJ
ejpam-4673	389	5	(	(	PUNCT
ejpam-4673	389	6	g	g	NOUN
ejpam-4673	389	7	)	)	PUNCT
ejpam-4673	389	8	and	and	CCONJ
ejpam-4673	389	9	let	let	VERB
ejpam-4673	389	10	tx	tx	PART
ejpam-4673	389	11	be	be	AUX
ejpam-4673	389	12	a	a	DET
ejpam-4673	389	13	cdpnd	cdpnd	NOUN
ejpam-4673	389	14	-	-	PUNCT
ejpam-4673	389	15	set	set	VERB
ejpam-4673	389	16	in	in	ADP
ejpam-4673	389	17	h	h	NOUN
ejpam-4673	389	18	for	for	ADP
ejpam-4673	389	19	each	each	DET
ejpam-4673	389	20	x	x	SYM
ejpam-4673	389	21	∈	∈	PROPN
ejpam-4673	389	22	v	v	NOUN
ejpam-4673	389	23	(	(	PUNCT
ejpam-4673	389	24	g	g	NOUN
ejpam-4673	389	25	)	)	PUNCT
ejpam-4673	389	26	.	.	PUNCT
ejpam-4673	390	1	by	by	ADP
ejpam-4673	390	2	theorem	theorem	NOUN
ejpam-4673	390	3	7	7	NUM
ejpam-4673	390	4	,	,	PUNCT
ejpam-4673	390	5	c	c	NOUN
ejpam-4673	390	6	=	=	PUNCT
ejpam-4673	390	7	⋃	⋃	PROPN
ejpam-4673	390	8	x∈s	x∈s	NOUN
ejpam-4673	391	1	[	[	X
ejpam-4673	391	2	{	{	PUNCT
ejpam-4673	391	3	x}×tx	x}×tx	X
ejpam-4673	391	4	]	]	X
ejpam-4673	391	5	is	be	AUX
ejpam-4673	391	6	a	a	DET
ejpam-4673	391	7	hop	hop	NOUN
ejpam-4673	391	8	differentiating	differentiate	VERB
ejpam-4673	391	9	hop	hop	NOUN
ejpam-4673	391	10	dominating	dominating	NOUN
ejpam-4673	391	11	set	set	VERB
ejpam-4673	391	12	in	in	ADP
ejpam-4673	391	13	g[h	g[h	PROPN
ejpam-4673	391	14	]	]	PUNCT
ejpam-4673	391	15	.	.	PUNCT
ejpam-4673	392	1	it	it	PRON
ejpam-4673	392	2	follows	follow	VERB
ejpam-4673	392	3	that	that	SCONJ
ejpam-4673	392	4	γdh(g[h	γdh(g[h	NUM
ejpam-4673	392	5	]	]	PUNCT
ejpam-4673	392	6	)	)	PUNCT
ejpam-4673	392	7	≤	≤	PROPN
ejpam-4673	392	8	|c|	|c|	PROPN
ejpam-4673	392	9	=	=	SYM
ejpam-4673	392	10	|v	|v	PROPN
ejpam-4673	392	11	(	(	PUNCT
ejpam-4673	392	12	g)|cdpnd(h	g)|cdpnd(h	NOUN
ejpam-4673	392	13	)	)	PUNCT
ejpam-4673	392	14	.	.	PUNCT
ejpam-4673	393	1	next	next	ADV
ejpam-4673	393	2	,	,	PUNCT
ejpam-4673	393	3	suppose	suppose	VERB
ejpam-4673	393	4	that	that	SCONJ
ejpam-4673	393	5	γ(g	γ(g	PROPN
ejpam-4673	393	6	)	)	PUNCT
ejpam-4673	393	7	̸=	̸=	PROPN
ejpam-4673	393	8	1	1	NUM
ejpam-4673	393	9	.	.	PUNCT
ejpam-4673	394	1	let	let	VERB
ejpam-4673	394	2	s′	s′	ADJ
ejpam-4673	394	3	=	=	SYM
ejpam-4673	394	4	v	v	ADJ
ejpam-4673	394	5	(	(	PUNCT
ejpam-4673	394	6	g	g	NOUN
ejpam-4673	394	7	)	)	PUNCT
ejpam-4673	394	8	and	and	CCONJ
ejpam-4673	394	9	let	let	VERB
ejpam-4673	394	10	rx	rx	AUX
ejpam-4673	394	11	be	be	AUX
ejpam-4673	394	12	a	a	DET
ejpam-4673	394	13	cdn	cdn	NOUN
ejpam-4673	394	14	-	-	PUNCT
ejpam-4673	394	15	set	set	VERB
ejpam-4673	394	16	in	in	ADP
ejpam-4673	394	17	h	h	NOUN
ejpam-4673	394	18	for	for	ADP
ejpam-4673	394	19	each	each	DET
ejpam-4673	394	20	x	x	SYM
ejpam-4673	394	21	∈	∈	PROPN
ejpam-4673	394	22	s′.	s′.	PROPN
ejpam-4673	394	23	since	since	SCONJ
ejpam-4673	394	24	γ(g	γ(g	PROPN
ejpam-4673	394	25	)	)	PUNCT
ejpam-4673	394	26	̸=	̸=	PROPN
ejpam-4673	394	27	1	1	NUM
ejpam-4673	394	28	,	,	PUNCT
ejpam-4673	394	29	x	x	SYM
ejpam-4673	394	30	∈	∈	PROPN
ejpam-4673	394	31	n2	n2	ADJ
ejpam-4673	394	32	g(s	g(s	PROPN
ejpam-4673	394	33	′	′	NUM
ejpam-4673	394	34	)	)	PUNCT
ejpam-4673	394	35	for	for	ADP
ejpam-4673	394	36	each	each	DET
ejpam-4673	394	37	x	x	SYM
ejpam-4673	394	38	∈	∈	PROPN
ejpam-4673	394	39	s′.	s′.	X
ejpam-4673	394	40	thus	thus	ADV
ejpam-4673	394	41	,	,	PUNCT
ejpam-4673	394	42	by	by	ADP
ejpam-4673	394	43	theorem	theorem	NOUN
ejpam-4673	394	44	7	7	NUM
ejpam-4673	394	45	,	,	PUNCT
ejpam-4673	394	46	c	c	NOUN
ejpam-4673	394	47	=	=	PUNCT
ejpam-4673	394	48	⋃	⋃	NOUN
ejpam-4673	394	49	x∈s′	x∈s′	PRON
ejpam-4673	395	1	[	[	X
ejpam-4673	395	2	{	{	PUNCT
ejpam-4673	395	3	x	x	ADJ
ejpam-4673	395	4	}	}	PUNCT
ejpam-4673	395	5	×rx	×rx	PROPN
ejpam-4673	395	6	]	]	PUNCT
ejpam-4673	395	7	is	be	AUX
ejpam-4673	395	8	a	a	DET
ejpam-4673	395	9	hop	hop	NOUN
ejpam-4673	395	10	differentiating	differentiate	VERB
ejpam-4673	395	11	hop	hop	NOUN
ejpam-4673	395	12	dominating	dominating	NOUN
ejpam-4673	395	13	set	set	VERB
ejpam-4673	395	14	in	in	ADP
ejpam-4673	395	15	g[h	g[h	PROPN
ejpam-4673	395	16	]	]	PUNCT
ejpam-4673	395	17	.	.	PUNCT
ejpam-4673	396	1	it	it	PRON
ejpam-4673	396	2	follows	follow	VERB
ejpam-4673	396	3	that	that	SCONJ
ejpam-4673	396	4	γdh(g[h	γdh(g[h	NUM
ejpam-4673	396	5	]	]	PUNCT
ejpam-4673	396	6	)	)	PUNCT
ejpam-4673	396	7	≤	≤	PROPN
ejpam-4673	396	8	|c|	|c|	PROPN
ejpam-4673	396	9	=	=	SYM
ejpam-4673	396	10	|v	|v	PROPN
ejpam-4673	396	11	(	(	PUNCT
ejpam-4673	396	12	g)|cdn(h	g)|cdn(h	NOUN
ejpam-4673	396	13	)	)	PUNCT
ejpam-4673	396	14	.	.	PUNCT
ejpam-4673	397	1	now	now	ADV
ejpam-4673	397	2	,	,	PUNCT
ejpam-4673	397	3	if	if	SCONJ
ejpam-4673	397	4	c0	c0	PROPN
ejpam-4673	397	5	=	=	PUNCT
ejpam-4673	397	6	⋃	⋃	PROPN
ejpam-4673	397	7	x∈s0	x∈s0	NOUN
ejpam-4673	398	1	[	[	X
ejpam-4673	398	2	{	{	PUNCT
ejpam-4673	398	3	x	x	NOUN
ejpam-4673	398	4	}	}	PUNCT
ejpam-4673	398	5	×	×	PROPN
ejpam-4673	398	6	tx	tx	PROPN
ejpam-4673	398	7	]	]	PUNCT
ejpam-4673	398	8	is	be	AUX
ejpam-4673	398	9	a	a	DET
ejpam-4673	398	10	γdh	γdh	NOUN
ejpam-4673	398	11	-	-	PUNCT
ejpam-4673	398	12	set	set	NOUN
ejpam-4673	398	13	in	in	ADP
ejpam-4673	398	14	g[h	g[h	PROPN
ejpam-4673	398	15	]	]	PUNCT
ejpam-4673	398	16	,	,	PUNCT
ejpam-4673	398	17	then	then	ADV
ejpam-4673	398	18	s0	s0	PROPN
ejpam-4673	398	19	=	=	SYM
ejpam-4673	398	20	v	v	PROPN
ejpam-4673	398	21	(	(	PUNCT
ejpam-4673	398	22	g	g	NOUN
ejpam-4673	398	23	)	)	PUNCT
ejpam-4673	398	24	and	and	CCONJ
ejpam-4673	398	25	tx	tx	PROPN
ejpam-4673	398	26	is	be	AUX
ejpam-4673	398	27	a	a	DET
ejpam-4673	398	28	complement	complement	NOUN
ejpam-4673	398	29	-	-	PUNCT
ejpam-4673	398	30	differentiating	differentiate	VERB
ejpam-4673	398	31	set	set	NOUN
ejpam-4673	398	32	in	in	ADP
ejpam-4673	398	33	h	h	NOUN
ejpam-4673	398	34	for	for	ADP
ejpam-4673	398	35	each	each	DET
ejpam-4673	398	36	x	x	SYM
ejpam-4673	398	37	∈	∈	PROPN
ejpam-4673	398	38	v	v	NOUN
ejpam-4673	398	39	(	(	PUNCT
ejpam-4673	398	40	g	g	NOUN
ejpam-4673	398	41	)	)	PUNCT
ejpam-4673	398	42	,	,	PUNCT
ejpam-4673	398	43	by	by	ADP
ejpam-4673	398	44	theorem	theorem	NOUN
ejpam-4673	398	45	7	7	NUM
ejpam-4673	398	46	.	.	PUNCT
ejpam-4673	398	47	hence	hence	ADV
ejpam-4673	398	48	,	,	PUNCT
ejpam-4673	398	49	γdh(g[h	γdh(g[h	PROPN
ejpam-4673	398	50	]	]	PUNCT
ejpam-4673	398	51	)	)	PUNCT
ejpam-4673	398	52	=	=	SYM
ejpam-4673	398	53	|c0|	|c0|	NOUN
ejpam-4673	398	54	=	=	SYM
ejpam-4673	398	55	∑	∑	PUNCT
ejpam-4673	398	56	x∈s0	x∈s0	PROPN
ejpam-4673	398	57	|tx|	|tx|	PROPN
ejpam-4673	398	58	≥	≥	NUM
ejpam-4673	398	59	|v	|v	PROPN
ejpam-4673	398	60	(	(	PUNCT
ejpam-4673	398	61	g)|cdn(h	g)|cdn(h	NOUN
ejpam-4673	398	62	)	)	PUNCT
ejpam-4673	398	63	.	.	PUNCT
ejpam-4673	399	1	therefore	therefore	ADV
ejpam-4673	399	2	,	,	PUNCT
ejpam-4673	399	3	γlh(g[h	γlh(g[h	NUM
ejpam-4673	399	4	]	]	PUNCT
ejpam-4673	399	5	)	)	PUNCT
ejpam-4673	399	6	=	=	SYM
ejpam-4673	399	7	|v	|v	PROPN
ejpam-4673	399	8	(	(	PUNCT
ejpam-4673	399	9	g)|cdn(h	g)|cdn(h	NOUN
ejpam-4673	399	10	)	)	PUNCT
ejpam-4673	399	11	.	.	PUNCT
ejpam-4673	400	1	corollary	corollary	ADJ
ejpam-4673	400	2	8	8	NUM
ejpam-4673	400	3	.	.	PUNCT
ejpam-4673	401	1	let	let	VERB
ejpam-4673	401	2	g	g	NOUN
ejpam-4673	401	3	and	and	CCONJ
ejpam-4673	401	4	h	h	PROPN
ejpam-4673	401	5	be	be	VERB
ejpam-4673	401	6	non	non	ADJ
ejpam-4673	401	7	-	-	ADJ
ejpam-4673	401	8	trivial	trivial	ADJ
ejpam-4673	401	9	connected	connected	ADJ
ejpam-4673	401	10	graphs	graph	NOUN
ejpam-4673	401	11	such	such	ADJ
ejpam-4673	401	12	that	that	SCONJ
ejpam-4673	401	13	g	g	PROPN
ejpam-4673	401	14	and	and	CCONJ
ejpam-4673	401	15	h	h	NOUN
ejpam-4673	401	16	are	be	AUX
ejpam-4673	401	17	,	,	PUNCT
ejpam-4673	401	18	respectively	respectively	ADV
ejpam-4673	401	19	,	,	PUNCT
ejpam-4673	401	20	totally	totally	ADV
ejpam-4673	401	21	distance	distance	NOUN
ejpam-4673	401	22	-	-	PUNCT
ejpam-4673	401	23	two	two	NUM
ejpam-4673	401	24	point	point	NOUN
ejpam-4673	401	25	determining	determine	VERB
ejpam-4673	401	26	and	and	CCONJ
ejpam-4673	401	27	complement	complement	VERB
ejpam-4673	401	28	point	point	NOUN
ejpam-4673	401	29	distinguishing	distinguishing	NOUN
ejpam-4673	401	30	.	.	PUNCT
ejpam-4673	402	1	if	if	SCONJ
ejpam-4673	402	2	γ(g	γ(g	PROPN
ejpam-4673	402	3	)	)	PUNCT
ejpam-4673	402	4	=	=	SYM
ejpam-4673	402	5	1	1	NUM
ejpam-4673	402	6	,	,	PUNCT
ejpam-4673	402	7	then	then	ADV
ejpam-4673	402	8	γdh(g[h	γdh(g[h	NUM
ejpam-4673	402	9	]	]	PUNCT
ejpam-4673	402	10	)	)	PUNCT
ejpam-4673	402	11	=	=	SYM
ejpam-4673	402	12	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	402	13	)	)	PUNCT
ejpam-4673	402	14	+	+	CCONJ
ejpam-4673	402	15	(	(	PUNCT
ejpam-4673	402	16	|v	|v	X
ejpam-4673	402	17	(	(	PUNCT
ejpam-4673	402	18	g)|	g)|	NOUN
ejpam-4673	402	19	−	−	PROPN
ejpam-4673	402	20	1)cdn(h	1)cdn(h	NUM
ejpam-4673	402	21	)	)	PUNCT
ejpam-4673	402	22	.	.	PUNCT
ejpam-4673	403	1	proof	proof	NOUN
ejpam-4673	403	2	.	.	PUNCT
ejpam-4673	404	1	let	let	VERB
ejpam-4673	404	2	dg	dg	VERB
ejpam-4673	404	3	=	=	PUNCT
ejpam-4673	404	4	{	{	PUNCT
ejpam-4673	404	5	v	v	NUM
ejpam-4673	404	6	∈	∈	NOUN
ejpam-4673	404	7	v	v	NOUN
ejpam-4673	404	8	(	(	PUNCT
ejpam-4673	404	9	g	g	NOUN
ejpam-4673	404	10	)	)	PUNCT
ejpam-4673	404	11	:	:	PUNCT
ejpam-4673	404	12	{	{	PUNCT
ejpam-4673	404	13	v	v	NOUN
ejpam-4673	404	14	}	}	PUNCT
ejpam-4673	404	15	is	be	AUX
ejpam-4673	404	16	a	a	DET
ejpam-4673	404	17	dominating	dominating	NOUN
ejpam-4673	404	18	set	set	NOUN
ejpam-4673	404	19	of	of	ADP
ejpam-4673	404	20	g	g	NOUN
ejpam-4673	404	21	}	}	PUNCT
ejpam-4673	404	22	.	.	PUNCT
ejpam-4673	405	1	since	since	SCONJ
ejpam-4673	405	2	g	g	PROPN
ejpam-4673	405	3	is	be	AUX
ejpam-4673	405	4	distance	distance	NOUN
ejpam-4673	405	5	-	-	PUNCT
ejpam-4673	405	6	two	two	NUM
ejpam-4673	405	7	point	point	NOUN
ejpam-4673	405	8	distinguishing	distinguishing	NOUN
ejpam-4673	405	9	,	,	PUNCT
ejpam-4673	405	10	it	it	PRON
ejpam-4673	405	11	follows	follow	VERB
ejpam-4673	405	12	that	that	SCONJ
ejpam-4673	405	13	|dg|	|dg|	PROPN
ejpam-4673	405	14	=	=	SYM
ejpam-4673	405	15	1	1	X
ejpam-4673	405	16	.	.	X
ejpam-4673	406	1	set	set	VERB
ejpam-4673	406	2	s	s	PART
ejpam-4673	406	3	=	=	X
ejpam-4673	406	4	v	v	ADJ
ejpam-4673	406	5	(	(	PUNCT
ejpam-4673	406	6	g	g	NOUN
ejpam-4673	406	7	)	)	PUNCT
ejpam-4673	406	8	.	.	PUNCT
ejpam-4673	407	1	let	let	VERB
ejpam-4673	407	2	tv	tv	NOUN
ejpam-4673	407	3	be	be	AUX
ejpam-4673	407	4	a	a	DET
ejpam-4673	407	5	cdpnd	cdpnd	NOUN
ejpam-4673	407	6	-	-	PUNCT
ejpam-4673	407	7	set	set	VERB
ejpam-4673	407	8	in	in	ADP
ejpam-4673	407	9	h	h	NOUN
ejpam-4673	407	10	for	for	ADP
ejpam-4673	407	11	v	v	NOUN
ejpam-4673	407	12	∈	∈	NOUN
ejpam-4673	407	13	dg	dg	NOUN
ejpam-4673	407	14	and	and	CCONJ
ejpam-4673	407	15	let	let	VERB
ejpam-4673	407	16	tx	tx	PART
ejpam-4673	407	17	be	be	AUX
ejpam-4673	407	18	a	a	DET
ejpam-4673	407	19	cdn	cdn	NOUN
ejpam-4673	407	20	-	-	PUNCT
ejpam-4673	407	21	set	set	VERB
ejpam-4673	407	22	in	in	ADP
ejpam-4673	407	23	h	h	NOUN
ejpam-4673	407	24	for	for	ADP
ejpam-4673	407	25	each	each	DET
ejpam-4673	407	26	x	x	SYM
ejpam-4673	407	27	∈	∈	PROPN
ejpam-4673	407	28	v	v	ADP
ejpam-4673	407	29	(	(	PUNCT
ejpam-4673	407	30	g	g	NOUN
ejpam-4673	407	31	)	)	PUNCT
ejpam-4673	407	32	\	\	NOUN
ejpam-4673	407	33	{	{	PUNCT
ejpam-4673	407	34	v	v	NOUN
ejpam-4673	407	35	}	}	PUNCT
ejpam-4673	407	36	.	.	PUNCT
ejpam-4673	408	1	then	then	ADV
ejpam-4673	408	2	,	,	PUNCT
ejpam-4673	408	3	by	by	ADP
ejpam-4673	408	4	theorem	theorem	NOUN
ejpam-4673	408	5	7	7	NUM
ejpam-4673	408	6	,	,	PUNCT
ejpam-4673	408	7	c	c	NOUN
ejpam-4673	408	8	=	=	PUNCT
ejpam-4673	408	9	[	[	PUNCT
ejpam-4673	408	10	⋃	⋃	NOUN
ejpam-4673	408	11	x∈s\{v}({x	x∈s\{v}({x	PROPN
ejpam-4673	408	12	}	}	PUNCT
ejpam-4673	408	13	×	×	PROPN
ejpam-4673	408	14	tx	tx	PROPN
ejpam-4673	408	15	)	)	PUNCT
ejpam-4673	408	16	]	]	PUNCT
ejpam-4673	408	17	∪	∪	X
ejpam-4673	408	18	(	(	PUNCT
ejpam-4673	408	19	{	{	PUNCT
ejpam-4673	408	20	v	v	NOUN
ejpam-4673	408	21	}	}	PUNCT
ejpam-4673	408	22	×	×	NOUN
ejpam-4673	408	23	tv	tv	NOUN
ejpam-4673	408	24	)	)	PUNCT
ejpam-4673	408	25	is	be	AUX
ejpam-4673	408	26	a	a	DET
ejpam-4673	408	27	hop	hop	NOUN
ejpam-4673	408	28	differentiating	differentiate	VERB
ejpam-4673	408	29	hop	hop	NOUN
ejpam-4673	408	30	dominating	dominating	NOUN
ejpam-4673	408	31	set	set	VERB
ejpam-4673	408	32	in	in	ADP
ejpam-4673	408	33	g[h	g[h	PROPN
ejpam-4673	408	34	]	]	PUNCT
ejpam-4673	408	35	.	.	PUNCT
ejpam-4673	409	1	hence	hence	ADV
ejpam-4673	409	2	,	,	PUNCT
ejpam-4673	409	3	γdh(g[h	γdh(g[h	PROPN
ejpam-4673	409	4	]	]	PUNCT
ejpam-4673	409	5	)	)	PUNCT
ejpam-4673	409	6	≤	≤	NUM
ejpam-4673	409	7	|c|	|c|	PROPN
ejpam-4673	409	8	=	=	SYM
ejpam-4673	409	9	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	409	10	)	)	PUNCT
ejpam-4673	410	1	+	+	CCONJ
ejpam-4673	410	2	(	(	PUNCT
ejpam-4673	410	3	|v	|v	X
ejpam-4673	410	4	(	(	PUNCT
ejpam-4673	410	5	g)|	g)|	NOUN
ejpam-4673	410	6	−	−	PROPN
ejpam-4673	410	7	1)cdn(h	1)cdn(h	NUM
ejpam-4673	410	8	)	)	PUNCT
ejpam-4673	410	9	.	.	PUNCT
ejpam-4673	410	10	suppose	suppose	VERB
ejpam-4673	410	11	now	now	ADV
ejpam-4673	410	12	that	that	SCONJ
ejpam-4673	410	13	c∗	c∗	NOUN
ejpam-4673	410	14	=	=	PUNCT
ejpam-4673	410	15	[	[	PUNCT
ejpam-4673	410	16	⋃	⋃	NOUN
ejpam-4673	410	17	x∈s∗({x}×rx	x∈s∗({x}×rx	NOUN
ejpam-4673	410	18	)	)	PUNCT
ejpam-4673	410	19	]	]	PUNCT
ejpam-4673	410	20	is	be	AUX
ejpam-4673	410	21	a	a	DET
ejpam-4673	410	22	γdh	γdh	NOUN
ejpam-4673	410	23	-	-	PUNCT
ejpam-4673	410	24	set	set	NOUN
ejpam-4673	410	25	in	in	ADP
ejpam-4673	410	26	g[h	g[h	PROPN
ejpam-4673	410	27	]	]	PUNCT
ejpam-4673	410	28	and	and	CCONJ
ejpam-4673	410	29	let	let	VERB
ejpam-4673	410	30	dg	dg	VERB
ejpam-4673	410	31	=	=	PUNCT
ejpam-4673	410	32	{	{	PUNCT
ejpam-4673	410	33	v	v	NOUN
ejpam-4673	410	34	}	}	PUNCT
ejpam-4673	410	35	.	.	PUNCT
ejpam-4673	411	1	by	by	ADP
ejpam-4673	411	2	theorem	theorem	NOUN
ejpam-4673	411	3	7	7	NUM
ejpam-4673	411	4	,	,	PUNCT
ejpam-4673	411	5	s∗	s∗	PROPN
ejpam-4673	411	6	=	=	SYM
ejpam-4673	411	7	v	v	PROPN
ejpam-4673	411	8	(	(	PUNCT
ejpam-4673	411	9	g	g	NOUN
ejpam-4673	411	10	)	)	PUNCT
ejpam-4673	411	11	,	,	PUNCT
ejpam-4673	411	12	rv	rv	PROPN
ejpam-4673	411	13	is	be	AUX
ejpam-4673	411	14	complement	complement	NOUN
ejpam-4673	411	15	-	-	PUNCT
ejpam-4673	411	16	differentiating	differentiate	VERB
ejpam-4673	411	17	and	and	CCONJ
ejpam-4673	411	18	pointwise	pointwise	VERB
ejpam-4673	411	19	non	non	ADJ
ejpam-4673	411	20	-	-	ADJ
ejpam-4673	411	21	dominating	dominating	ADJ
ejpam-4673	411	22	and	and	CCONJ
ejpam-4673	411	23	rx	rx	NOUN
ejpam-4673	411	24	is	be	AUX
ejpam-4673	411	25	complement	complement	NOUN
ejpam-4673	411	26	-	-	PUNCT
ejpam-4673	411	27	differentiating	differentiate	VERB
ejpam-4673	411	28	in	in	ADP
ejpam-4673	411	29	h	h	NOUN
ejpam-4673	411	30	for	for	ADP
ejpam-4673	411	31	each	each	PRON
ejpam-4673	411	32	x	x	SYM
ejpam-4673	411	33	∈	∈	PROPN
ejpam-4673	411	34	v	v	ADP
ejpam-4673	411	35	(	(	PUNCT
ejpam-4673	411	36	g	g	NOUN
ejpam-4673	411	37	)	)	PUNCT
ejpam-4673	411	38	\	\	NOUN
ejpam-4673	411	39	{	{	PUNCT
ejpam-4673	411	40	v	v	NOUN
ejpam-4673	411	41	}	}	PUNCT
ejpam-4673	411	42	.	.	PUNCT
ejpam-4673	412	1	thus	thus	ADV
ejpam-4673	412	2	,	,	PUNCT
ejpam-4673	412	3	γdh(g[h	γdh(g[h	PROPN
ejpam-4673	412	4	]	]	X
ejpam-4673	412	5	)	)	PUNCT
ejpam-4673	412	6	=	=	SYM
ejpam-4673	413	1	|c∗|	|c∗|	VERB
ejpam-4673	413	2	=	=	NOUN
ejpam-4673	413	3	|rv|+	|rv|+	PRON
ejpam-4673	413	4	∑	∑	ADJ
ejpam-4673	413	5	x∈s∗\{v	x∈s∗\{v	PROPN
ejpam-4673	413	6	}	}	PUNCT
ejpam-4673	413	7	|rx|	|rx|	NOUN
ejpam-4673	413	8	≥	≥	NUM
ejpam-4673	413	9	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	413	10	)	)	PUNCT
ejpam-4673	414	1	+	+	CCONJ
ejpam-4673	414	2	(	(	PUNCT
ejpam-4673	414	3	|v	|v	X
ejpam-4673	414	4	(	(	PUNCT
ejpam-4673	414	5	g)|	g)|	NOUN
ejpam-4673	414	6	−	−	PROPN
ejpam-4673	414	7	1)cdn(h	1)cdn(h	NUM
ejpam-4673	414	8	)	)	PUNCT
ejpam-4673	414	9	.	.	PUNCT
ejpam-4673	415	1	therefore	therefore	ADV
ejpam-4673	415	2	,	,	PUNCT
ejpam-4673	415	3	γdh(g[h	γdh(g[h	PROPN
ejpam-4673	415	4	]	]	PUNCT
ejpam-4673	415	5	)	)	PUNCT
ejpam-4673	415	6	=	=	SYM
ejpam-4673	415	7	cdpnd(h	cdpnd(h	NOUN
ejpam-4673	415	8	)	)	PUNCT
ejpam-4673	416	1	+	+	CCONJ
ejpam-4673	416	2	(	(	PUNCT
ejpam-4673	416	3	|v	|v	X
ejpam-4673	416	4	(	(	PUNCT
ejpam-4673	416	5	g)|	g)|	NOUN
ejpam-4673	416	6	−	−	PROPN
ejpam-4673	416	7	1)cdn(h	1)cdn(h	NUM
ejpam-4673	416	8	)	)	PUNCT
ejpam-4673	416	9	as	as	SCONJ
ejpam-4673	416	10	asserted	assert	VERB
ejpam-4673	416	11	.	.	PUNCT
ejpam-4673	417	1	corollary	corollary	ADJ
ejpam-4673	417	2	9	9	NUM
ejpam-4673	417	3	.	.	PUNCT
ejpam-4673	418	1	let	let	VERB
ejpam-4673	418	2	g	g	PRON
ejpam-4673	418	3	be	be	AUX
ejpam-4673	418	4	a	a	DET
ejpam-4673	418	5	non	non	ADJ
ejpam-4673	418	6	-	-	ADJ
ejpam-4673	418	7	trivial	trivial	ADJ
ejpam-4673	418	8	connected	connect	VERB
ejpam-4673	418	9	totally	totally	ADV
ejpam-4673	418	10	distance	distance	NOUN
ejpam-4673	418	11	-	-	PUNCT
ejpam-4673	418	12	two	two	NUM
ejpam-4673	418	13	point	point	NOUN
ejpam-4673	418	14	determining	determine	VERB
ejpam-4673	418	15	graph	graph	NOUN
ejpam-4673	418	16	and	and	CCONJ
ejpam-4673	418	17	let	let	VERB
ejpam-4673	418	18	p	p	PRON
ejpam-4673	418	19	≥	≥	NUM
ejpam-4673	418	20	2	2	NUM
ejpam-4673	418	21	be	be	AUX
ejpam-4673	418	22	a	a	DET
ejpam-4673	418	23	positive	positive	ADJ
ejpam-4673	418	24	integer	integer	NOUN
ejpam-4673	418	25	.	.	PUNCT
ejpam-4673	419	1	then	then	ADV
ejpam-4673	419	2	γdh(g[kp	γdh(g[kp	PROPN
ejpam-4673	419	3	]	]	PUNCT
ejpam-4673	419	4	)	)	PUNCT
ejpam-4673	420	1	=	=	PRON
ejpam-4673	420	2	{	{	PUNCT
ejpam-4673	420	3	(	(	PUNCT
ejpam-4673	420	4	p−	p−	NOUN
ejpam-4673	420	5	1)|v	1)|v	NUM
ejpam-4673	420	6	(	(	PUNCT
ejpam-4673	420	7	g)|	g)|	VERB
ejpam-4673	420	8	if	if	SCONJ
ejpam-4673	420	9	γ(g	γ(g	NOUN
ejpam-4673	420	10	)	)	PUNCT
ejpam-4673	420	11	̸=	̸=	PROPN
ejpam-4673	420	12	1	1	NUM
ejpam-4673	420	13	(	(	PUNCT
ejpam-4673	420	14	p−	p−	NOUN
ejpam-4673	420	15	1)|v	1)|v	NUM
ejpam-4673	420	16	(	(	PUNCT
ejpam-4673	420	17	g)|+	g)|+	PROPN
ejpam-4673	420	18	1	1	NUM
ejpam-4673	420	19	if	if	SCONJ
ejpam-4673	420	20	γ(g	γ(g	NOUN
ejpam-4673	420	21	)	)	PUNCT
ejpam-4673	420	22	=	=	SYM
ejpam-4673	420	23	1	1	X
ejpam-4673	420	24	.	.	PUNCT
ejpam-4673	420	25	references	reference	NOUN
ejpam-4673	420	26	451	451	NUM
ejpam-4673	420	27	proof	proof	NOUN
ejpam-4673	420	28	.	.	PUNCT
ejpam-4673	421	1	suppose	suppose	VERB
ejpam-4673	421	2	first	first	ADV
ejpam-4673	421	3	that	that	PRON
ejpam-4673	421	4	γ(g	γ(g	PROPN
ejpam-4673	421	5	)	)	PUNCT
ejpam-4673	421	6	̸=	̸=	PROPN
ejpam-4673	421	7	1	1	NUM
ejpam-4673	421	8	.	.	PUNCT
ejpam-4673	421	9	by	by	ADP
ejpam-4673	421	10	corollary	corollary	ADJ
ejpam-4673	421	11	7	7	NUM
ejpam-4673	421	12	and	and	CCONJ
ejpam-4673	421	13	the	the	DET
ejpam-4673	421	14	fact	fact	NOUN
ejpam-4673	421	15	that	that	SCONJ
ejpam-4673	421	16	cdn(kp	cdn(kp	NOUN
ejpam-4673	421	17	)	)	PUNCT
ejpam-4673	421	18	=	=	SYM
ejpam-4673	421	19	dn(kp	dn(kp	PROPN
ejpam-4673	421	20	)	)	PUNCT
ejpam-4673	422	1	=	=	PUNCT
ejpam-4673	423	1	p−	p−	NOUN
ejpam-4673	423	2	1	1	NUM
ejpam-4673	423	3	,	,	PUNCT
ejpam-4673	423	4	it	it	PRON
ejpam-4673	423	5	follows	follow	VERB
ejpam-4673	423	6	that	that	SCONJ
ejpam-4673	423	7	γdh(g[kp	γdh(g[kp	PROPN
ejpam-4673	423	8	]	]	PUNCT
ejpam-4673	423	9	)	)	PUNCT
ejpam-4673	423	10	=	=	SYM
ejpam-4673	424	1	(	(	PUNCT
ejpam-4673	424	2	p−	p−	NOUN
ejpam-4673	424	3	1)|v	1)|v	NUM
ejpam-4673	424	4	(	(	PUNCT
ejpam-4673	424	5	g)|	g)|	PROPN
ejpam-4673	424	6	.	.	PUNCT
ejpam-4673	425	1	next	next	ADV
ejpam-4673	425	2	,	,	PUNCT
ejpam-4673	425	3	suppose	suppose	VERB
ejpam-4673	425	4	that	that	SCONJ
ejpam-4673	425	5	γ(g	γ(g	PROPN
ejpam-4673	425	6	)	)	PUNCT
ejpam-4673	425	7	=	=	PUNCT
ejpam-4673	426	1	1	1	X
ejpam-4673	426	2	.	.	PUNCT
ejpam-4673	426	3	by	by	ADP
ejpam-4673	426	4	corollary	corollary	ADJ
ejpam-4673	426	5	8	8	NUM
ejpam-4673	426	6	and	and	CCONJ
ejpam-4673	426	7	the	the	DET
ejpam-4673	426	8	fact	fact	NOUN
ejpam-4673	426	9	that	that	SCONJ
ejpam-4673	426	10	cdpnd(kp	cdpnd(kp	NOUN
ejpam-4673	426	11	)	)	PUNCT
ejpam-4673	426	12	=	=	SYM
ejpam-4673	426	13	γd(kp	γd(kp	NOUN
ejpam-4673	426	14	)	)	PUNCT
ejpam-4673	426	15	=	=	SYM
ejpam-4673	427	1	p	p	X
ejpam-4673	427	2	,	,	PUNCT
ejpam-4673	427	3	we	we	PRON
ejpam-4673	427	4	have	have	AUX
ejpam-4673	427	5	γdh(g[kp	γdh(g[kp	PROPN
ejpam-4673	427	6	]	]	PUNCT
ejpam-4673	427	7	)	)	PUNCT
ejpam-4673	428	1	=	=	SYM
ejpam-4673	428	2	p+	p+	X
ejpam-4673	428	3	(	(	PUNCT
ejpam-4673	428	4	p−	p−	NOUN
ejpam-4673	428	5	1)(|v	1)(|v	NUM
ejpam-4673	428	6	(	(	PUNCT
ejpam-4673	428	7	g)|	g)|	NOUN
ejpam-4673	428	8	−	−	NOUN
ejpam-4673	428	9	1	1	NUM
ejpam-4673	428	10	)	)	PUNCT
ejpam-4673	428	11	=	=	NOUN
ejpam-4673	428	12	(	(	PUNCT
ejpam-4673	428	13	p−	p−	NOUN
ejpam-4673	428	14	1)|v	1)|v	NUM
ejpam-4673	428	15	(	(	PUNCT
ejpam-4673	428	16	g)|+	g)|+	PROPN
ejpam-4673	428	17	1	1	NUM
ejpam-4673	428	18	.	.	PUNCT
ejpam-4673	428	19	corollary	corollary	ADJ
ejpam-4673	428	20	10	10	NUM
ejpam-4673	428	21	.	.	PUNCT
ejpam-4673	429	1	let	let	VERB
ejpam-4673	429	2	h	h	PRON
ejpam-4673	429	3	be	be	AUX
ejpam-4673	429	4	a	a	DET
ejpam-4673	429	5	non	non	ADJ
ejpam-4673	429	6	-	-	ADJ
ejpam-4673	429	7	trivial	trivial	ADJ
ejpam-4673	429	8	connected	connected	ADJ
ejpam-4673	429	9	complement	complement	NOUN
ejpam-4673	429	10	point	point	NOUN
ejpam-4673	429	11	distinguishing	distinguish	VERB
ejpam-4673	429	12	graph	graph	NOUN
ejpam-4673	429	13	and	and	CCONJ
ejpam-4673	429	14	let	let	VERB
ejpam-4673	429	15	p	p	PRON
ejpam-4673	429	16	≥	≥	NUM
ejpam-4673	429	17	2	2	NUM
ejpam-4673	429	18	be	be	AUX
ejpam-4673	429	19	a	a	DET
ejpam-4673	429	20	positive	positive	ADJ
ejpam-4673	429	21	integer	integer	NOUN
ejpam-4673	429	22	.	.	PUNCT
ejpam-4673	430	1	then	then	ADV
ejpam-4673	430	2	γdh(kp[h	γdh(kp[h	PROPN
ejpam-4673	430	3	]	]	PUNCT
ejpam-4673	430	4	)	)	PUNCT
ejpam-4673	430	5	=	=	PUNCT
ejpam-4673	430	6	p[cdpnd(h	p[cdpnd(h	NOUN
ejpam-4673	430	7	)	)	PUNCT
ejpam-4673	430	8	]	]	PUNCT
ejpam-4673	430	9	.	.	PUNCT
ejpam-4673	431	1	proof	proof	NOUN
ejpam-4673	431	2	.	.	PUNCT
ejpam-4673	432	1	let	let	VERB
ejpam-4673	432	2	g	g	NOUN
ejpam-4673	432	3	=	=	SYM
ejpam-4673	432	4	kp	kp	PROPN
ejpam-4673	432	5	.	.	PUNCT
ejpam-4673	433	1	then	then	ADV
ejpam-4673	433	2	v	v	NOUN
ejpam-4673	433	3	is	be	AUX
ejpam-4673	433	4	a	a	DET
ejpam-4673	433	5	dominating	dominating	NOUN
ejpam-4673	433	6	vertex	vertex	NOUN
ejpam-4673	433	7	of	of	ADP
ejpam-4673	433	8	g	g	NOUN
ejpam-4673	433	9	for	for	ADP
ejpam-4673	433	10	each	each	DET
ejpam-4673	433	11	v	v	NUM
ejpam-4673	433	12	∈	∈	PROPN
ejpam-4673	433	13	v	v	NOUN
ejpam-4673	433	14	(	(	PUNCT
ejpam-4673	433	15	g	g	NOUN
ejpam-4673	433	16	)	)	PUNCT
ejpam-4673	433	17	.	.	PUNCT
ejpam-4673	434	1	thus	thus	ADV
ejpam-4673	434	2	,	,	PUNCT
ejpam-4673	434	3	if	if	SCONJ
ejpam-4673	434	4	c0	c0	PROPN
ejpam-4673	434	5	=	=	PUNCT
ejpam-4673	434	6	⋃	⋃	VERB
ejpam-4673	434	7	z∈s0	z∈s0	NOUN
ejpam-4673	434	8	[	[	X
ejpam-4673	434	9	{	{	PUNCT
ejpam-4673	434	10	z	z	NOUN
ejpam-4673	434	11	}	}	PUNCT
ejpam-4673	434	12	×	×	PROPN
ejpam-4673	434	13	tz	tz	NOUN
ejpam-4673	434	14	]	]	X
ejpam-4673	434	15	is	be	AUX
ejpam-4673	434	16	a	a	DET
ejpam-4673	434	17	γdh	γdh	NOUN
ejpam-4673	434	18	-	-	PUNCT
ejpam-4673	434	19	set	set	NOUN
ejpam-4673	434	20	of	of	ADP
ejpam-4673	434	21	g[h	g[h	PROPN
ejpam-4673	434	22	]	]	PUNCT
ejpam-4673	434	23	,	,	PUNCT
ejpam-4673	434	24	then	then	ADV
ejpam-4673	434	25	s0	s0	PROPN
ejpam-4673	434	26	=	=	SYM
ejpam-4673	434	27	v	v	PROPN
ejpam-4673	434	28	(	(	PUNCT
ejpam-4673	434	29	g	g	NOUN
ejpam-4673	434	30	)	)	PUNCT
ejpam-4673	434	31	and	and	CCONJ
ejpam-4673	434	32	each	each	DET
ejpam-4673	434	33	tz	tz	NOUN
ejpam-4673	434	34	is	be	AUX
ejpam-4673	434	35	a	a	DET
ejpam-4673	434	36	cdpnd	cdpnd	NOUN
ejpam-4673	434	37	-	-	PUNCT
ejpam-4673	434	38	set	set	NOUN
ejpam-4673	434	39	of	of	ADP
ejpam-4673	434	40	h	h	NOUN
ejpam-4673	434	41	by	by	ADP
ejpam-4673	434	42	theorem	theorem	NOUN
ejpam-4673	434	43	7	7	NUM
ejpam-4673	434	44	.	.	PUNCT
ejpam-4673	434	45	consequently	consequently	ADV
ejpam-4673	434	46	,	,	PUNCT
ejpam-4673	434	47	γdh(kp[h	γdh(kp[h	PROPN
ejpam-4673	434	48	]	]	PUNCT
ejpam-4673	434	49	)	)	PUNCT
ejpam-4673	434	50	=	=	PUNCT
ejpam-4673	434	51	p[cdpnd(h	p[cdpnd(h	NOUN
ejpam-4673	434	52	)	)	PUNCT
ejpam-4673	434	53	]	]	PUNCT
ejpam-4673	434	54	.	.	PUNCT
ejpam-4673	435	1	4	4	X
ejpam-4673	435	2	.	.	X
ejpam-4673	435	3	conclusion	conclusion	VERB
ejpam-4673	435	4	hop	hop	NOUN
ejpam-4673	435	5	differentiating	differentiate	VERB
ejpam-4673	435	6	hop	hop	NOUN
ejpam-4673	435	7	domination	domination	NOUN
ejpam-4673	435	8	is	be	AUX
ejpam-4673	435	9	introduced	introduce	VERB
ejpam-4673	435	10	and	and	CCONJ
ejpam-4673	435	11	studied	study	VERB
ejpam-4673	435	12	for	for	ADP
ejpam-4673	435	13	some	some	DET
ejpam-4673	435	14	graphs	graph	NOUN
ejpam-4673	435	15	.	.	PUNCT
ejpam-4673	436	1	in	in	ADP
ejpam-4673	436	2	particular	particular	ADJ
ejpam-4673	436	3	,	,	PUNCT
ejpam-4673	436	4	characterizations	characterization	NOUN
ejpam-4673	436	5	of	of	ADP
ejpam-4673	436	6	the	the	DET
ejpam-4673	436	7	hop	hop	NOUN
ejpam-4673	436	8	differentiating	differentiate	VERB
ejpam-4673	436	9	hop	hop	NOUN
ejpam-4673	436	10	dominating	dominating	NOUN
ejpam-4673	436	11	sets	set	NOUN
ejpam-4673	436	12	in	in	ADP
ejpam-4673	436	13	the	the	DET
ejpam-4673	436	14	join	join	NOUN
ejpam-4673	436	15	,	,	PUNCT
ejpam-4673	436	16	corona	corona	PROPN
ejpam-4673	436	17	,	,	PUNCT
ejpam-4673	436	18	and	and	CCONJ
ejpam-4673	436	19	lexicographic	lexicographic	ADJ
ejpam-4673	436	20	product	product	NOUN
ejpam-4673	436	21	of	of	ADP
ejpam-4673	436	22	two	two	NUM
ejpam-4673	436	23	graphs	graph	NOUN
ejpam-4673	436	24	are	be	AUX
ejpam-4673	436	25	given	give	VERB
ejpam-4673	436	26	.	.	PUNCT
ejpam-4673	437	1	these	these	DET
ejpam-4673	437	2	characterizations	characterization	NOUN
ejpam-4673	437	3	are	be	AUX
ejpam-4673	437	4	used	use	VERB
ejpam-4673	437	5	to	to	PART
ejpam-4673	437	6	obtain	obtain	VERB
ejpam-4673	437	7	either	either	CCONJ
ejpam-4673	437	8	an	an	DET
ejpam-4673	437	9	upper	upper	ADJ
ejpam-4673	437	10	bound	bind	VERB
ejpam-4673	437	11	or	or	CCONJ
ejpam-4673	437	12	the	the	DET
ejpam-4673	437	13	exact	exact	ADJ
ejpam-4673	437	14	value	value	NOUN
ejpam-4673	437	15	of	of	ADP
ejpam-4673	437	16	the	the	DET
ejpam-4673	437	17	hop	hop	NOUN
ejpam-4673	437	18	differentiating	differentiate	VERB
ejpam-4673	437	19	hop	hop	NOUN
ejpam-4673	437	20	domination	domination	NOUN
ejpam-4673	437	21	number	number	NOUN
ejpam-4673	437	22	of	of	ADP
ejpam-4673	437	23	the	the	DET
ejpam-4673	437	24	graph	graph	NOUN
ejpam-4673	437	25	.	.	PUNCT
ejpam-4673	438	1	the	the	DET
ejpam-4673	438	2	concept	concept	NOUN
ejpam-4673	438	3	can	can	AUX
ejpam-4673	438	4	be	be	AUX
ejpam-4673	438	5	studied	study	VERB
ejpam-4673	438	6	further	far	ADV
ejpam-4673	438	7	for	for	ADP
ejpam-4673	438	8	other	other	ADJ
ejpam-4673	438	9	interesting	interesting	ADJ
ejpam-4673	438	10	graphs	graph	NOUN
ejpam-4673	438	11	and	and	CCONJ
ejpam-4673	438	12	the	the	DET
ejpam-4673	438	13	complexity	complexity	NOUN
ejpam-4673	438	14	of	of	ADP
ejpam-4673	438	15	the	the	DET
ejpam-4673	438	16	hop	hop	NOUN
ejpam-4673	438	17	differentiating	differentiate	VERB
ejpam-4673	438	18	hop	hop	NOUN
ejpam-4673	438	19	dominating	dominating	NOUN
ejpam-4673	438	20	decision	decision	NOUN
ejpam-4673	438	21	problem	problem	NOUN
ejpam-4673	438	22	can	can	AUX
ejpam-4673	438	23	likewise	likewise	ADV
ejpam-4673	438	24	be	be	AUX
ejpam-4673	438	25	investigated	investigate	VERB
ejpam-4673	438	26	.	.	PUNCT
ejpam-4673	439	1	5	5	X
ejpam-4673	439	2	.	.	X
ejpam-4673	439	3	acknowledgements	acknowledgement	NOUN
ejpam-4673	439	4	the	the	DET
ejpam-4673	439	5	authors	author	NOUN
ejpam-4673	439	6	would	would	AUX
ejpam-4673	439	7	like	like	VERB
ejpam-4673	439	8	to	to	PART
ejpam-4673	439	9	thank	thank	VERB
ejpam-4673	439	10	the	the	DET
ejpam-4673	439	11	referees	referee	NOUN
ejpam-4673	439	12	for	for	ADP
ejpam-4673	439	13	the	the	DET
ejpam-4673	439	14	invaluable	invaluable	ADJ
ejpam-4673	439	15	assistance	assistance	NOUN
ejpam-4673	439	16	they	they	PRON
ejpam-4673	439	17	gave	give	VERB
ejpam-4673	439	18	us	we	PRON
ejpam-4673	439	19	through	through	ADP
ejpam-4673	439	20	their	their	PRON
ejpam-4673	439	21	comments	comment	NOUN
ejpam-4673	439	22	and	and	CCONJ
ejpam-4673	439	23	suggestions	suggestion	NOUN
ejpam-4673	439	24	which	which	PRON
ejpam-4673	439	25	contributed	contribute	VERB
ejpam-4673	439	26	to	to	ADP
ejpam-4673	439	27	the	the	DET
ejpam-4673	439	28	improvement	improvement	NOUN
ejpam-4673	439	29	of	of	ADP
ejpam-4673	439	30	the	the	DET
ejpam-4673	439	31	paper	paper	NOUN
ejpam-4673	439	32	.	.	PUNCT
ejpam-4673	440	1	the	the	DET
ejpam-4673	440	2	authors	author	NOUN
ejpam-4673	440	3	would	would	AUX
ejpam-4673	440	4	like	like	VERB
ejpam-4673	440	5	to	to	PART
ejpam-4673	440	6	thank	thank	VERB
ejpam-4673	440	7	the	the	DET
ejpam-4673	440	8	department	department	NOUN
ejpam-4673	440	9	of	of	ADP
ejpam-4673	440	10	science	science	NOUN
ejpam-4673	440	11	and	and	CCONJ
ejpam-4673	440	12	technology	technology	NOUN
ejpam-4673	440	13	accelerated	accelerate	VERB
ejpam-4673	440	14	science	science	NOUN
ejpam-4673	440	15	and	and	CCONJ
ejpam-4673	440	16	technology	technology	NOUN
ejpam-4673	440	17	human	human	ADJ
ejpam-4673	440	18	resource	resource	NOUN
ejpam-4673	440	19	development	development	NOUN
ejpam-4673	440	20	program	program	NOUN
ejpam-4673	440	21	(	(	PUNCT
ejpam-4673	440	22	dostasthrdp)-philippines	dostasthrdp)-philippine	NOUN
ejpam-4673	440	23	and	and	CCONJ
ejpam-4673	440	24	msu	msu	PROPN
ejpam-4673	440	25	-	-	PUNCT
ejpam-4673	440	26	iligan	iligan	PROPN
ejpam-4673	440	27	institute	institute	PROPN
ejpam-4673	440	28	of	of	ADP
ejpam-4673	440	29	technology	technology	NOUN
ejpam-4673	440	30	for	for	ADP
ejpam-4673	440	31	funding	fund	VERB
ejpam-4673	440	32	this	this	DET
ejpam-4673	440	33	research	research	NOUN
ejpam-4673	440	34	.	.	PUNCT
ejpam-4673	441	1	references	reference	NOUN
ejpam-4673	441	2	[	[	X
ejpam-4673	441	3	1	1	NUM
ejpam-4673	441	4	]	]	PUNCT
ejpam-4673	441	5	s.	s.	PROPN
ejpam-4673	441	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4673	441	7	,	,	PUNCT
ejpam-4673	441	8	b.	b.	PROPN
ejpam-4673	441	9	krishnakumari	krishnakumari	PROPN
ejpam-4673	441	10	,	,	PUNCT
ejpam-4673	441	11	b.	b.	PROPN
ejpam-4673	441	12	natarjan	natarjan	PROPN
ejpam-4673	441	13	,	,	PUNCT
ejpam-4673	441	14	and	and	CCONJ
ejpam-4673	441	15	y.	y.	PROPN
ejpam-4673	441	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4673	441	17	.	.	PUNCT
ejpam-4673	442	1	bounds	bound	NOUN
ejpam-4673	442	2	on	on	ADP
ejpam-4673	442	3	the	the	DET
ejpam-4673	442	4	hop	hop	NOUN
ejpam-4673	442	5	domination	domination	NOUN
ejpam-4673	442	6	number	number	NOUN
ejpam-4673	442	7	of	of	ADP
ejpam-4673	442	8	a	a	DET
ejpam-4673	442	9	tree	tree	NOUN
ejpam-4673	442	10	.	.	PUNCT
ejpam-4673	443	1	proceedings	proceeding	NOUN
ejpam-4673	443	2	-	-	PUNCT
ejpam-4673	443	3	mathematical	mathematical	ADJ
ejpam-4673	443	4	sciences	science	NOUN
ejpam-4673	443	5	.	.	PUNCT
ejpam-4673	443	6	,	,	PUNCT
ejpam-4673	443	7	125(4):449–455	125(4):449–455	ADP
ejpam-4673	443	8	,	,	PUNCT
ejpam-4673	443	9	2015	2015	NUM
ejpam-4673	443	10	.	.	PUNCT
ejpam-4673	444	1	[	[	X
ejpam-4673	444	2	2	2	NUM
ejpam-4673	444	3	]	]	PUNCT
ejpam-4673	444	4	s.	s.	PROPN
ejpam-4673	444	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4673	444	6	,	,	PUNCT
ejpam-4673	444	7	c.	c.	PROPN
ejpam-4673	444	8	natarajan	natarajan	PROPN
ejpam-4673	444	9	,	,	PUNCT
ejpam-4673	444	10	and	and	CCONJ
ejpam-4673	444	11	g.	g.	PROPN
ejpam-4673	444	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4673	444	13	.	.	PUNCT
ejpam-4673	445	1	a	a	DET
ejpam-4673	445	2	note	note	NOUN
ejpam-4673	445	3	on	on	ADP
ejpam-4673	445	4	hop	hop	NOUN
ejpam-4673	445	5	domination	domination	NOUN
ejpam-4673	445	6	number	number	NOUN
ejpam-4673	445	7	of	of	ADP
ejpam-4673	445	8	some	some	DET
ejpam-4673	445	9	special	special	ADJ
ejpam-4673	445	10	families	family	NOUN
ejpam-4673	445	11	of	of	ADP
ejpam-4673	445	12	graphs	graph	NOUN
ejpam-4673	445	13	.	.	PUNCT
ejpam-4673	446	1	international	international	ADJ
ejpam-4673	446	2	journal	journal	NOUN
ejpam-4673	446	3	of	of	ADP
ejpam-4673	446	4	pure	pure	ADJ
ejpam-4673	446	5	and	and	CCONJ
ejpam-4673	446	6	applied	applied	ADJ
ejpam-4673	446	7	mathematics	mathematic	NOUN
ejpam-4673	446	8	.	.	PUNCT
ejpam-4673	446	9	,	,	PUNCT
ejpam-4673	446	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4673	446	11	,	,	PUNCT
ejpam-4673	446	12	2018	2018	NUM
ejpam-4673	446	13	.	.	PUNCT
ejpam-4673	447	1	[	[	X
ejpam-4673	447	2	3	3	X
ejpam-4673	447	3	]	]	X
ejpam-4673	447	4	c.	c.	NOUN
ejpam-4673	447	5	colbourn	colbourn	NOUN
ejpam-4673	447	6	,	,	PUNCT
ejpam-4673	447	7	p.	p.	PROPN
ejpam-4673	447	8	slater	slater	PROPN
ejpam-4673	447	9	,	,	PUNCT
ejpam-4673	447	10	and	and	CCONJ
ejpam-4673	447	11	l.	l.	PROPN
ejpam-4673	447	12	stewart	stewart	PROPN
ejpam-4673	447	13	.	.	PUNCT
ejpam-4673	448	1	locating	locate	VERB
ejpam-4673	448	2	-	-	PUNCT
ejpam-4673	448	3	dominating	dominating	NOUN
ejpam-4673	448	4	sets	set	NOUN
ejpam-4673	448	5	in	in	ADP
ejpam-4673	448	6	seriesparallel	seriesparallel	NOUN
ejpam-4673	448	7	networks	network	NOUN
ejpam-4673	448	8	.	.	PUNCT
ejpam-4673	449	1	congr	congr	NOUN
ejpam-4673	449	2	.	.	PUNCT
ejpam-4673	450	1	numer	numer	PROPN
ejpam-4673	450	2	.	.	PROPN
ejpam-4673	450	3	,	,	PUNCT
ejpam-4673	451	1	56:135–162	56:135–162	NUM
ejpam-4673	451	2	,	,	PUNCT
ejpam-4673	451	3	1987	1987	NUM
ejpam-4673	451	4	.	.	PUNCT
ejpam-4673	452	1	references	reference	NOUN
ejpam-4673	452	2	452	452	NUM
ejpam-4673	452	3	[	[	SYM
ejpam-4673	452	4	4	4	NUM
ejpam-4673	452	5	]	]	PUNCT
ejpam-4673	452	6	a.	a.	NOUN
ejpam-4673	452	7	finbow	finbow	NOUN
ejpam-4673	452	8	and	and	CCONJ
ejpam-4673	452	9	b.	b.	PROPN
ejpam-4673	452	10	hartnell	hartnell	PROPN
ejpam-4673	452	11	.	.	PUNCT
ejpam-4673	453	1	locating	locate	VERB
ejpam-4673	453	2	-	-	PUNCT
ejpam-4673	453	3	dominating	dominating	NOUN
ejpam-4673	453	4	sets	set	NOUN
ejpam-4673	453	5	in	in	ADP
ejpam-4673	453	6	seriesparallel	seriesparallel	NOUN
ejpam-4673	453	7	networks	network	NOUN
ejpam-4673	453	8	.	.	PUNCT
ejpam-4673	454	1	congr	congr	NOUN
ejpam-4673	454	2	.	.	PUNCT
ejpam-4673	455	1	numer	numer	PROPN
ejpam-4673	455	2	.	.	PROPN
ejpam-4673	455	3	,	,	PUNCT
ejpam-4673	456	1	65:191–200	65:191–200	NUM
ejpam-4673	456	2	,	,	PUNCT
ejpam-4673	456	3	1988	1988	NUM
ejpam-4673	456	4	.	.	PUNCT
ejpam-4673	457	1	[	[	X
ejpam-4673	457	2	5	5	X
ejpam-4673	457	3	]	]	PUNCT
ejpam-4673	457	4	d.	d.	PROPN
ejpam-4673	457	5	geoffrey	geoffrey	PROPN
ejpam-4673	457	6	.	.	PUNCT
ejpam-4673	458	1	nuclei	nuclei	PROPN
ejpam-4673	458	2	for	for	ADP
ejpam-4673	458	3	totally	totally	ADV
ejpam-4673	458	4	point	point	NOUN
ejpam-4673	458	5	determining	determine	VERB
ejpam-4673	458	6	graphs	graph	NOUN
ejpam-4673	458	7	.	.	PUNCT
ejpam-4673	459	1	discrete	discrete	ADJ
ejpam-4673	459	2	mathematics	mathematic	NOUN
ejpam-4673	459	3	,	,	PUNCT
ejpam-4673	459	4	21:145–162	21:145–162	PROPN
ejpam-4673	459	5	,	,	PUNCT
ejpam-4673	459	6	1978	1978	NUM
ejpam-4673	459	7	.	.	PUNCT
ejpam-4673	460	1	[	[	X
ejpam-4673	460	2	6	6	NUM
ejpam-4673	460	3	]	]	PUNCT
ejpam-4673	460	4	j.	j.	PROPN
ejpam-4673	460	5	gimbel	gimbel	PROPN
ejpam-4673	460	6	,	,	PUNCT
ejpam-4673	460	7	b.	b.	PROPN
ejpam-4673	460	8	van	van	PROPN
ejpam-4673	460	9	gorden	gorden	PROPN
ejpam-4673	460	10	,	,	PUNCT
ejpam-4673	460	11	m.	m.	NOUN
ejpam-4673	460	12	nicolescu	nicolescu	PROPN
ejpam-4673	460	13	,	,	PUNCT
ejpam-4673	460	14	c.	c.	PROPN
ejpam-4673	460	15	umstead	umstead	PROPN
ejpam-4673	460	16	,	,	PUNCT
ejpam-4673	460	17	and	and	CCONJ
ejpam-4673	460	18	n.	n.	PROPN
ejpam-4673	460	19	vaianna	vaianna	PROPN
ejpam-4673	460	20	.	.	PUNCT
ejpam-4673	461	1	location	location	NOUN
ejpam-4673	461	2	with	with	ADP
ejpam-4673	461	3	dominating	dominating	NOUN
ejpam-4673	461	4	sets	set	NOUN
ejpam-4673	461	5	.	.	PUNCT
ejpam-4673	462	1	congress	congress	PROPN
ejpam-4673	462	2	numer	numer	PROPN
ejpam-4673	462	3	.	.	PROPN
ejpam-4673	462	4	,	,	PUNCT
ejpam-4673	462	5	151:129–144	151:129–144	NUM
ejpam-4673	462	6	,	,	PUNCT
ejpam-4673	462	7	2001	2001	NUM
ejpam-4673	462	8	.	.	PUNCT
ejpam-4673	463	1	[	[	X
ejpam-4673	463	2	7	7	X
ejpam-4673	463	3	]	]	PUNCT
ejpam-4673	463	4	j.	j.	PROPN
ejpam-4673	463	5	hassan	hassan	PROPN
ejpam-4673	463	6	and	and	CCONJ
ejpam-4673	463	7	s.	s.	PROPN
ejpam-4673	463	8	canoy	canoy	PROPN
ejpam-4673	463	9	jr	jr	PROPN
ejpam-4673	463	10	.	.	PROPN
ejpam-4673	463	11	hop	hop	PROPN
ejpam-4673	463	12	independent	independent	ADJ
ejpam-4673	463	13	hop	hop	NOUN
ejpam-4673	463	14	domination	domination	NOUN
ejpam-4673	463	15	in	in	ADP
ejpam-4673	463	16	graphs	graph	NOUN
ejpam-4673	463	17	.	.	PUNCT
ejpam-4673	464	1	eur	eur	PROPN
ejpam-4673	464	2	.	.	PUNCT
ejpam-4673	465	1	j.	j.	PROPN
ejpam-4673	465	2	pure	pure	PROPN
ejpam-4673	465	3	appl	appl	PROPN
ejpam-4673	465	4	.	.	PUNCT
ejpam-4673	465	5	math	math	PROPN
ejpam-4673	465	6	.	.	PUNCT
ejpam-4673	465	7	,	,	PUNCT
ejpam-4673	465	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4673	465	9	,	,	PUNCT
ejpam-4673	465	10	2022	2022	NUM
ejpam-4673	465	11	.	.	PUNCT
ejpam-4673	466	1	[	[	X
ejpam-4673	466	2	8	8	NUM
ejpam-4673	466	3	]	]	X
ejpam-4673	466	4	m.	m.	NOUN
ejpam-4673	466	5	henning	henning	PROPN
ejpam-4673	466	6	and	and	CCONJ
ejpam-4673	466	7	n.	n.	PROPN
ejpam-4673	466	8	rad	rad	PROPN
ejpam-4673	466	9	.	.	PROPN
ejpam-4673	467	1	on	on	ADP
ejpam-4673	467	2	2	2	NUM
ejpam-4673	467	3	-	-	PUNCT
ejpam-4673	467	4	step	step	NOUN
ejpam-4673	467	5	and	and	CCONJ
ejpam-4673	467	6	hop	hop	NOUN
ejpam-4673	467	7	dominating	dominating	NOUN
ejpam-4673	467	8	sets	set	NOUN
ejpam-4673	467	9	in	in	ADP
ejpam-4673	467	10	graphs	graph	NOUN
ejpam-4673	467	11	.	.	PUNCT
ejpam-4673	468	1	graphs	graph	NOUN
ejpam-4673	468	2	and	and	CCONJ
ejpam-4673	468	3	combinatorics	combinatoric	NOUN
ejpam-4673	468	4	.	.	PUNCT
ejpam-4673	468	5	,	,	PUNCT
ejpam-4673	468	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4673	468	7	,	,	PUNCT
ejpam-4673	468	8	2017	2017	NUM
ejpam-4673	468	9	.	.	PUNCT
ejpam-4673	469	1	[	[	X
ejpam-4673	469	2	9	9	NUM
ejpam-4673	469	3	]	]	PUNCT
ejpam-4673	469	4	s.	s.	PROPN
ejpam-4673	469	5	canoy	canoy	PROPN
ejpam-4673	469	6	jr	jr	PROPN
ejpam-4673	469	7	.	.	PROPN
ejpam-4673	469	8	and	and	CCONJ
ejpam-4673	469	9	g.	g.	PROPN
ejpam-4673	469	10	malacas	malacas	PROPN
ejpam-4673	469	11	.	.	PUNCT
ejpam-4673	470	1	determining	determine	VERB
ejpam-4673	470	2	the	the	DET
ejpam-4673	470	3	intruder	intruder	NOUN
ejpam-4673	470	4	’s	’s	PART
ejpam-4673	470	5	location	location	NOUN
ejpam-4673	470	6	in	in	ADP
ejpam-4673	470	7	a	a	DET
ejpam-4673	470	8	given	give	VERB
ejpam-4673	470	9	network	network	NOUN
ejpam-4673	470	10	:	:	PUNCT
ejpam-4673	470	11	locating	locate	VERB
ejpam-4673	470	12	-	-	PUNCT
ejpam-4673	470	13	dominating	dominating	NOUN
ejpam-4673	470	14	sets	set	NOUN
ejpam-4673	470	15	in	in	ADP
ejpam-4673	470	16	a	a	DET
ejpam-4673	470	17	graph	graph	NOUN
ejpam-4673	470	18	.	.	PUNCT
ejpam-4673	471	1	nrcp	nrcp	PROPN
ejpam-4673	471	2	research	research	PROPN
ejpam-4673	471	3	journal	journal	PROPN
ejpam-4673	471	4	,	,	PUNCT
ejpam-4673	471	5	13(1):1–8	13(1):1–8	NUM
ejpam-4673	471	6	,	,	PUNCT
ejpam-4673	471	7	2013	2013	NUM
ejpam-4673	471	8	.	.	PUNCT
ejpam-4673	472	1	[	[	X
ejpam-4673	472	2	10	10	NUM
ejpam-4673	472	3	]	]	X
ejpam-4673	472	4	s.	s.	PROPN
ejpam-4673	472	5	canoy	canoy	PROPN
ejpam-4673	472	6	jr	jr	PROPN
ejpam-4673	472	7	.	.	PROPN
ejpam-4673	472	8	and	and	CCONJ
ejpam-4673	472	9	g.	g.	PROPN
ejpam-4673	472	10	malacas	malacas	PROPN
ejpam-4673	472	11	.	.	PUNCT
ejpam-4673	473	1	differentiating	differentiate	VERB
ejpam-4673	473	2	-	-	PUNCT
ejpam-4673	473	3	dominating	dominating	NOUN
ejpam-4673	473	4	sets	set	NOUN
ejpam-4673	473	5	in	in	ADP
ejpam-4673	473	6	graphs	graph	NOUN
ejpam-4673	473	7	under	under	ADP
ejpam-4673	473	8	binary	binary	ADJ
ejpam-4673	473	9	operations	operation	NOUN
ejpam-4673	473	10	.	.	PUNCT
ejpam-4673	474	1	tamkang	tamkang	PROPN
ejpam-4673	474	2	journal	journal	PROPN
ejpam-4673	474	3	of	of	ADP
ejpam-4673	474	4	mathematics	mathematic	NOUN
ejpam-4673	474	5	,	,	PUNCT
ejpam-4673	474	6	46(1):51–60	46(1):51–60	NOUN
ejpam-4673	474	7	,	,	PUNCT
ejpam-4673	474	8	2015	2015	NUM
ejpam-4673	474	9	.	.	PUNCT
ejpam-4673	475	1	[	[	X
ejpam-4673	475	2	11	11	NUM
ejpam-4673	475	3	]	]	X
ejpam-4673	475	4	s.	s.	PROPN
ejpam-4673	475	5	canoy	canoy	PROPN
ejpam-4673	475	6	jr	jr	PROPN
ejpam-4673	475	7	.	.	PROPN
ejpam-4673	475	8	,	,	PUNCT
ejpam-4673	475	9	r.	r.	PROPN
ejpam-4673	475	10	mollejon	mollejon	NOUN
ejpam-4673	475	11	,	,	PUNCT
ejpam-4673	475	12	and	and	CCONJ
ejpam-4673	475	13	j.	j.	PROPN
ejpam-4673	475	14	g.	g.	PROPN
ejpam-4673	475	15	canoy	canoy	PROPN
ejpam-4673	475	16	.	.	PUNCT
ejpam-4673	476	1	hop	hop	PROPN
ejpam-4673	476	2	dominating	dominating	NOUN
ejpam-4673	476	3	sets	set	NOUN
ejpam-4673	476	4	in	in	ADP
ejpam-4673	476	5	graphs	graph	NOUN
ejpam-4673	476	6	under	under	ADP
ejpam-4673	476	7	binary	binary	ADJ
ejpam-4673	476	8	operations	operation	NOUN
ejpam-4673	476	9	.	.	PUNCT
ejpam-4673	477	1	eur	eur	PROPN
ejpam-4673	477	2	.	.	PUNCT
ejpam-4673	478	1	j.	j.	PROPN
ejpam-4673	478	2	pure	pure	PROPN
ejpam-4673	478	3	appl	appl	PROPN
ejpam-4673	478	4	.	.	PUNCT
ejpam-4673	478	5	math	math	PROPN
ejpam-4673	478	6	.	.	PUNCT
ejpam-4673	478	7	,	,	PUNCT
ejpam-4673	479	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4673	479	2	,	,	PUNCT
ejpam-4673	479	3	2019	2019	NUM
ejpam-4673	479	4	.	.	PUNCT
ejpam-4673	480	1	[	[	X
ejpam-4673	480	2	12	12	NUM
ejpam-4673	480	3	]	]	X
ejpam-4673	480	4	s.	s.	PROPN
ejpam-4673	480	5	canoy	canoy	PROPN
ejpam-4673	480	6	jr	jr	PROPN
ejpam-4673	480	7	.	.	PROPN
ejpam-4673	480	8	and	and	CCONJ
ejpam-4673	480	9	g.	g.	PROPN
ejpam-4673	480	10	salasalan	salasalan	NOUN
ejpam-4673	480	11	.	.	PUNCT
ejpam-4673	481	1	a	a	DET
ejpam-4673	481	2	variant	variant	NOUN
ejpam-4673	481	3	of	of	ADP
ejpam-4673	481	4	hop	hop	NOUN
ejpam-4673	481	5	dominationin	dominationin	NOUN
ejpam-4673	481	6	graphs	graph	NOUN
ejpam-4673	481	7	.	.	PUNCT
ejpam-4673	482	1	eur	eur	PROPN
ejpam-4673	482	2	.	.	PUNCT
ejpam-4673	483	1	j.	j.	PROPN
ejpam-4673	483	2	pure	pure	PROPN
ejpam-4673	483	3	appl	appl	PROPN
ejpam-4673	483	4	.	.	PUNCT
ejpam-4673	483	5	math	math	PROPN
ejpam-4673	483	6	.	.	PUNCT
ejpam-4673	483	7	,	,	PUNCT
ejpam-4673	483	8	15(2):342–353	15(2):342–353	NUM
ejpam-4673	483	9	,	,	PUNCT
ejpam-4673	483	10	2021	2021	NUM
ejpam-4673	483	11	.	.	PUNCT
ejpam-4673	484	1	[	[	X
ejpam-4673	484	2	13	13	NUM
ejpam-4673	484	3	]	]	PUNCT
ejpam-4673	484	4	s.	s.	PROPN
ejpam-4673	484	5	canoy	canoy	PROPN
ejpam-4673	484	6	jr	jr	PROPN
ejpam-4673	484	7	.	.	PROPN
ejpam-4673	484	8	and	and	CCONJ
ejpam-4673	484	9	g.	g.	PROPN
ejpam-4673	484	10	salasalan	salasalan	NOUN
ejpam-4673	484	11	.	.	PUNCT
ejpam-4673	485	1	locating	locate	VERB
ejpam-4673	485	2	-	-	PUNCT
ejpam-4673	485	3	hop	hop	NOUN
ejpam-4673	485	4	domination	domination	NOUN
ejpam-4673	485	5	in	in	ADP
ejpam-4673	485	6	graphs	graph	NOUN
ejpam-4673	485	7	.	.	PUNCT
ejpam-4673	486	1	kyungpook	kyungpook	PROPN
ejpam-4673	486	2	mathematical	mathematical	PROPN
ejpam-4673	486	3	journal	journal	PROPN
ejpam-4673	486	4	,	,	PUNCT
ejpam-4673	486	5	62:193–204	62:193–204	PROPN
ejpam-4673	486	6	,	,	PUNCT
ejpam-4673	486	7	2022	2022	NUM
ejpam-4673	486	8	.	.	PUNCT
ejpam-4673	487	1	[	[	X
ejpam-4673	487	2	14	14	NUM
ejpam-4673	487	3	]	]	X
ejpam-4673	487	4	m.	m.	NOUN
ejpam-4673	487	5	karpovsky	karpovsky	PROPN
ejpam-4673	487	6	,	,	PUNCT
ejpam-4673	487	7	k.	k.	PROPN
ejpam-4673	487	8	chakrabarty	chakrabarty	PROPN
ejpam-4673	487	9	,	,	PUNCT
ejpam-4673	487	10	and	and	CCONJ
ejpam-4673	487	11	l.	l.	PROPN
ejpam-4673	487	12	levitin	levitin	PROPN
ejpam-4673	487	13	.	.	PUNCT
ejpam-4673	488	1	on	on	ADP
ejpam-4673	488	2	a	a	DET
ejpam-4673	488	3	new	new	ADJ
ejpam-4673	488	4	class	class	NOUN
ejpam-4673	488	5	of	of	ADP
ejpam-4673	488	6	codes	code	NOUN
ejpam-4673	488	7	for	for	ADP
ejpam-4673	488	8	identifying	identify	VERB
ejpam-4673	488	9	vertices	vertex	NOUN
ejpam-4673	488	10	in	in	ADP
ejpam-4673	488	11	graphs	graph	NOUN
ejpam-4673	488	12	.	.	PUNCT
ejpam-4673	489	1	ieee	ieee	PROPN
ejpam-4673	489	2	trans	trans	PROPN
ejpam-4673	489	3	.	.	PUNCT
ejpam-4673	490	1	inform	inform	NOUN
ejpam-4673	490	2	.	.	PUNCT
ejpam-4673	491	1	theory	theory	NOUN
ejpam-4673	491	2	,	,	PUNCT
ejpam-4673	491	3	44(2):599–611	44(2):599–611	PROPN
ejpam-4673	491	4	,	,	PUNCT
ejpam-4673	491	5	1998	1998	NUM
ejpam-4673	491	6	.	.	PUNCT
ejpam-4673	492	1	[	[	X
ejpam-4673	492	2	15	15	NUM
ejpam-4673	492	3	]	]	X
ejpam-4673	492	4	s.	s.	PROPN
ejpam-4673	492	5	canoy	canoy	PROPN
ejpam-4673	492	6	jr	jr	PROPN
ejpam-4673	492	7	.	.	PROPN
ejpam-4673	492	8	,	,	PUNCT
ejpam-4673	492	9	g.	g.	PROPN
ejpam-4673	492	10	malacas	malacas	PROPN
ejpam-4673	492	11	and	and	CCONJ
ejpam-4673	492	12	d.	d.	PROPN
ejpam-4673	492	13	tarepe	tarepe	PROPN
ejpam-4673	492	14	.	.	PUNCT
ejpam-4673	493	1	locating	locate	VERB
ejpam-4673	493	2	-	-	PUNCT
ejpam-4673	493	3	dominating	dominating	NOUN
ejpam-4673	493	4	sets	set	NOUN
ejpam-4673	493	5	in	in	ADP
ejpam-4673	493	6	graphs	graph	NOUN
ejpam-4673	493	7	.	.	PUNCT
ejpam-4673	494	1	applied	apply	VERB
ejpam-4673	494	2	mathematical	mathematical	ADJ
ejpam-4673	494	3	sciences	sciences	PROPN
ejpam-4673	494	4	,	,	PUNCT
ejpam-4673	494	5	8:4381–4388	8:4381–4388	NUM
ejpam-4673	494	6	,	,	PUNCT
ejpam-4673	494	7	2014	2014	NUM
ejpam-4673	494	8	.	.	PUNCT
ejpam-4673	495	1	[	[	X
ejpam-4673	495	2	16	16	NUM
ejpam-4673	495	3	]	]	X
ejpam-4673	495	4	c.	c.	PROPN
ejpam-4673	495	5	natarajan	natarajan	PROPN
ejpam-4673	495	6	and	and	CCONJ
ejpam-4673	495	7	s.	s.	PROPN
ejpam-4673	495	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4673	495	9	.	.	PUNCT
ejpam-4673	496	1	hop	hop	PROPN
ejpam-4673	496	2	domination	domination	NOUN
ejpam-4673	496	3	in	in	ADP
ejpam-4673	496	4	graphs	graphs	PROPN
ejpam-4673	496	5	ii	ii	PROPN
ejpam-4673	496	6	.	.	PUNCT
ejpam-4673	496	7	versita	versita	PROPN
ejpam-4673	496	8	,	,	PUNCT
ejpam-4673	496	9	23(2):187	23(2):187	NUM
ejpam-4673	496	10	–	–	PUNCT
ejpam-4673	496	11	199	199	NUM
ejpam-4673	496	12	,	,	PUNCT
ejpam-4673	496	13	2015	2015	NUM
ejpam-4673	496	14	.	.	PUNCT
ejpam-4673	497	1	[	[	X
ejpam-4673	497	2	17	17	NUM
ejpam-4673	497	3	]	]	PUNCT
ejpam-4673	497	4	b.	b.	PROPN
ejpam-4673	497	5	omamalin	omamalin	PROPN
ejpam-4673	497	6	,	,	PUNCT
ejpam-4673	497	7	s.	s.	PROPN
ejpam-4673	497	8	canoy	canoy	PROPN
ejpam-4673	497	9	jr	jr	PROPN
ejpam-4673	497	10	.	.	PROPN
ejpam-4673	497	11	,	,	PUNCT
ejpam-4673	497	12	and	and	CCONJ
ejpam-4673	497	13	h	h	PROPN
ejpam-4673	497	14	rara	rara	NOUN
ejpam-4673	497	15	.	.	PUNCT
ejpam-4673	498	1	locating	locate	VERB
ejpam-4673	498	2	total	total	ADJ
ejpam-4673	498	3	dominating	dominating	NOUN
ejpam-4673	498	4	sets	set	NOUN
ejpam-4673	498	5	in	in	ADP
ejpam-4673	498	6	the	the	DET
ejpam-4673	498	7	join	join	NOUN
ejpam-4673	498	8	,	,	PUNCT
ejpam-4673	498	9	corona	corona	NOUN
ejpam-4673	498	10	and	and	CCONJ
ejpam-4673	498	11	composition	composition	NOUN
ejpam-4673	498	12	of	of	ADP
ejpam-4673	498	13	graphs	graph	NOUN
ejpam-4673	498	14	.	.	PUNCT
ejpam-4673	499	1	applied	apply	VERB
ejpam-4673	499	2	mathematical	mathematical	ADJ
ejpam-4673	499	3	sciences	science	NOUN
ejpam-4673	499	4	,	,	PUNCT
ejpam-4673	499	5	8:2363–2374	8:2363–2374	NUM
ejpam-4673	499	6	,	,	PUNCT
ejpam-4673	499	7	2014	2014	NUM
ejpam-4673	499	8	.	.	PUNCT
ejpam-4673	500	1	[	[	X
ejpam-4673	500	2	18	18	NUM
ejpam-4673	500	3	]	]	X
ejpam-4673	500	4	s.	s.	PROPN
ejpam-4673	500	5	omega	omega	PROPN
ejpam-4673	500	6	and	and	CCONJ
ejpam-4673	500	7	s.	s.	PROPN
ejpam-4673	500	8	canoy	canoy	PROPN
ejpam-4673	500	9	jr	jr	PROPN
ejpam-4673	500	10	.	.	PUNCT
ejpam-4673	500	11	locating	locate	VERB
ejpam-4673	500	12	sets	set	NOUN
ejpam-4673	500	13	in	in	ADP
ejpam-4673	500	14	a	a	DET
ejpam-4673	500	15	graph	graph	NOUN
ejpam-4673	500	16	.	.	PUNCT
ejpam-4673	501	1	applied	apply	VERB
ejpam-4673	501	2	mathematical	mathematical	ADJ
ejpam-4673	501	3	sciences	science	NOUN
ejpam-4673	501	4	,	,	PUNCT
ejpam-4673	501	5	9:2957–2964	9:2957–2964	NUM
ejpam-4673	501	6	,	,	PUNCT
ejpam-4673	501	7	2015	2015	NUM
ejpam-4673	501	8	.	.	PUNCT
ejpam-4673	502	1	[	[	X
ejpam-4673	502	2	19	19	NUM
ejpam-4673	502	3	]	]	X
ejpam-4673	502	4	y.	y.	PROPN
ejpam-4673	502	5	pabilona	pabilona	PROPN
ejpam-4673	502	6	and	and	CCONJ
ejpam-4673	502	7	h.	h.	PROPN
ejpam-4673	502	8	rara	rara	PROPN
ejpam-4673	502	9	.	.	PUNCT
ejpam-4673	503	1	connected	connect	VERB
ejpam-4673	503	2	hop	hop	NOUN
ejpam-4673	503	3	domination	domination	NOUN
ejpam-4673	503	4	in	in	ADP
ejpam-4673	503	5	graphs	graph	NOUN
ejpam-4673	503	6	under	under	ADP
ejpam-4673	503	7	some	some	DET
ejpam-4673	503	8	binary	binary	ADJ
ejpam-4673	503	9	operations	operation	NOUN
ejpam-4673	503	10	.	.	PUNCT
ejpam-4673	504	1	asian	asian	ADJ
ejpam-4673	504	2	-	-	PUNCT
ejpam-4673	504	3	eur	eur	NOUN
ejpam-4673	504	4	.	.	PUNCT
ejpam-4673	505	1	j.	j.	PROPN
ejpam-4673	505	2	math	math	PROPN
ejpam-4673	505	3	.	.	PROPN
ejpam-4673	505	4	,	,	PUNCT
ejpam-4673	505	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4673	505	6	,	,	PUNCT
ejpam-4673	505	7	2018	2018	NUM
ejpam-4673	505	8	.	.	PUNCT
ejpam-4673	505	9	references	reference	NOUN
ejpam-4673	505	10	453	453	NUM
ejpam-4673	505	11	[	[	SYM
ejpam-4673	505	12	20	20	NUM
ejpam-4673	505	13	]	]	PUNCT
ejpam-4673	505	14	r.	r.	PROPN
ejpam-4673	505	15	rakim	rakim	PROPN
ejpam-4673	505	16	,	,	PUNCT
ejpam-4673	505	17	h.	h.	PROPN
ejpam-4673	505	18	rara	rara	PROPN
ejpam-4673	505	19	,	,	PUNCT
ejpam-4673	505	20	and	and	CCONJ
ejpam-4673	505	21	c.j	c.j	PROPN
ejpam-4673	505	22	.	.	PROPN
ejpam-4673	505	23	saromines	saromine	NOUN
ejpam-4673	505	24	.	.	PUNCT
ejpam-4673	506	1	perfect	perfect	ADJ
ejpam-4673	506	2	hop	hop	NOUN
ejpam-4673	506	3	domination	domination	NOUN
ejpam-4673	506	4	in	in	ADP
ejpam-4673	506	5	graphs	graph	NOUN
ejpam-4673	506	6	.	.	PUNCT
ejpam-4673	507	1	applied	apply	VERB
ejpam-4673	507	2	mathematical	mathematical	ADJ
ejpam-4673	507	3	sciences	science	NOUN
ejpam-4673	507	4	,	,	PUNCT
ejpam-4673	507	5	1(13):635–649	1(13):635–649	NUM
ejpam-4673	507	6	,	,	PUNCT
ejpam-4673	507	7	2018	2018	NUM
ejpam-4673	507	8	.	.	PUNCT
ejpam-4673	508	1	[	[	X
ejpam-4673	508	2	21	21	NUM
ejpam-4673	508	3	]	]	X
ejpam-4673	508	4	g.	g.	PROPN
ejpam-4673	508	5	salasalan	salasalan	NOUN
ejpam-4673	508	6	and	and	CCONJ
ejpam-4673	508	7	s.	s.	PROPN
ejpam-4673	508	8	canoy	canoy	PROPN
ejpam-4673	508	9	jr	jr	PROPN
ejpam-4673	508	10	.	.	PROPN
ejpam-4673	508	11	global	global	PROPN
ejpam-4673	508	12	hop	hop	PROPN
ejpam-4673	508	13	domination	domination	PROPN
ejpam-4673	508	14	numbers	number	NOUN
ejpam-4673	508	15	of	of	ADP
ejpam-4673	508	16	graphs	graph	NOUN
ejpam-4673	508	17	.	.	PUNCT
ejpam-4673	509	1	eur	eur	PROPN
ejpam-4673	509	2	.	.	PUNCT
ejpam-4673	510	1	j.	j.	PROPN
ejpam-4673	510	2	pure	pure	PROPN
ejpam-4673	510	3	appl	appl	PROPN
ejpam-4673	510	4	.	.	PUNCT
ejpam-4673	510	5	math	math	PROPN
ejpam-4673	510	6	.	.	PUNCT
ejpam-4673	510	7	,	,	PUNCT
ejpam-4673	510	8	14(1):112–125	14(1):112–125	NUM
ejpam-4673	510	9	,	,	PUNCT
ejpam-4673	510	10	2021	2021	NUM
ejpam-4673	510	11	.	.	PUNCT
ejpam-4673	511	1	[	[	X
ejpam-4673	511	2	22	22	NUM
ejpam-4673	511	3	]	]	X
ejpam-4673	511	4	g.	g.	NOUN
ejpam-4673	511	5	salasalan	salasalan	NOUN
ejpam-4673	511	6	and	and	CCONJ
ejpam-4673	511	7	s.	s.	PROPN
ejpam-4673	511	8	canoy	canoy	PROPN
ejpam-4673	511	9	jr	jr	PROPN
ejpam-4673	511	10	.	.	PUNCT
ejpam-4673	511	11	revisiting	revisit	VERB
ejpam-4673	511	12	domination	domination	NOUN
ejpam-4673	511	13	,	,	PUNCT
ejpam-4673	511	14	hop	hop	NOUN
ejpam-4673	511	15	domination	domination	NOUN
ejpam-4673	511	16	,	,	PUNCT
ejpam-4673	511	17	and	and	CCONJ
ejpam-4673	511	18	global	global	ADJ
ejpam-4673	511	19	hop	hop	NOUN
ejpam-4673	511	20	domination	domination	NOUN
ejpam-4673	511	21	in	in	ADP
ejpam-4673	511	22	graphs	graph	NOUN
ejpam-4673	511	23	.	.	PUNCT
ejpam-4673	512	1	eur	eur	PROPN
ejpam-4673	512	2	.	.	PUNCT
ejpam-4673	513	1	j.	j.	PROPN
ejpam-4673	513	2	pure	pure	PROPN
ejpam-4673	513	3	appl	appl	PROPN
ejpam-4673	513	4	.	.	PUNCT
ejpam-4673	513	5	math	math	PROPN
ejpam-4673	513	6	.	.	PUNCT
ejpam-4673	513	7	,	,	PUNCT
ejpam-4673	514	1	14(4):1415–1428	14(4):1415–1428	NUM
ejpam-4673	514	2	,	,	PUNCT
ejpam-4673	514	3	2021	2021	NUM
ejpam-4673	514	4	.	.	PUNCT
ejpam-4673	515	1	[	[	X
ejpam-4673	515	2	23	23	NUM
ejpam-4673	515	3	]	]	X
ejpam-4673	515	4	d.p	d.p	PROPN
ejpam-4673	515	5	.	.	PUNCT
ejpam-4673	515	6	summer	summer	NOUN
ejpam-4673	515	7	.	.	PUNCT
ejpam-4673	516	1	point	point	NOUN
ejpam-4673	516	2	determination	determination	NOUN
ejpam-4673	516	3	in	in	ADP
ejpam-4673	516	4	graphs∗.	graphs∗.	PROPN
ejpam-4673	516	5	discrete	discrete	ADJ
ejpam-4673	516	6	mathematics	mathematic	NOUN
ejpam-4673	516	7	,	,	PUNCT
ejpam-4673	516	8	north	north	NOUN
ejpam-4673	516	9	-	-	PUNCT
ejpam-4673	516	10	holland	holland	PROPN
ejpam-4673	516	11	publishing	publishing	PROPN
ejpam-4673	516	12	company	company	NOUN
ejpam-4673	516	13	,	,	PUNCT
ejpam-4673	516	14	pages	page	NOUN
ejpam-4673	516	15	179–187	179–187	NUM
ejpam-4673	516	16	,	,	PUNCT
ejpam-4673	516	17	1973	1973	NUM
ejpam-4673	516	18	.	.	PUNCT