id	sid	tid	token	lemma	pos
ejpam-5918	1	1	european	european	PROPN
ejpam-5918	1	2	journal	journal	PROPN
ejpam-5918	1	3	of	of	ADP
ejpam-5918	1	4	pure	pure	ADJ
ejpam-5918	1	5	and	and	CCONJ
ejpam-5918	1	6	applied	applied	ADJ
ejpam-5918	1	7	mathematics	mathematic	NOUN
ejpam-5918	1	8	2025	2025	NUM
ejpam-5918	1	9	,	,	PUNCT
ejpam-5918	1	10	vol	vol	NOUN
ejpam-5918	1	11	.	.	PROPN
ejpam-5918	1	12	18	18	NUM
ejpam-5918	1	13	,	,	PUNCT
ejpam-5918	1	14	issue	issue	NOUN
ejpam-5918	1	15	2	2	NUM
ejpam-5918	1	16	,	,	PUNCT
ejpam-5918	1	17	article	article	NOUN
ejpam-5918	1	18	number	number	NOUN
ejpam-5918	1	19	5918	5918	NUM
ejpam-5918	1	20	issn	issn	VERB
ejpam-5918	1	21	1307	1307	NUM
ejpam-5918	1	22	-	-	SYM
ejpam-5918	1	23	5543	5543	NUM
ejpam-5918	1	24	–	–	PUNCT
ejpam-5918	1	25	ejpam.com	ejpam.com	X
ejpam-5918	1	26	published	publish	VERB
ejpam-5918	1	27	by	by	ADP
ejpam-5918	1	28	new	new	PROPN
ejpam-5918	1	29	york	york	PROPN
ejpam-5918	1	30	business	business	PROPN
ejpam-5918	1	31	global	global	PROPN
ejpam-5918	1	32	internally	internally	ADV
ejpam-5918	1	33	-	-	PUNCT
ejpam-5918	1	34	locating	locate	VERB
ejpam-5918	1	35	dominating	dominating	NOUN
ejpam-5918	1	36	sets	set	NOUN
ejpam-5918	1	37	in	in	ADP
ejpam-5918	1	38	graphs	graph	NOUN
ejpam-5918	1	39	irish	irish	PROPN
ejpam-5918	1	40	s.	s.	PROPN
ejpam-5918	1	41	tropico1,∗	tropico1,∗	PROPN
ejpam-5918	1	42	,	,	PUNCT
ejpam-5918	1	43	isagani	isagani	PROPN
ejpam-5918	1	44	s.	s.	PROPN
ejpam-5918	1	45	cabahug	cabahug	PROPN
ejpam-5918	1	46	,	,	PUNCT
ejpam-5918	1	47	jr.1	jr.1	PROPN
ejpam-5918	1	48	1	1	NUM
ejpam-5918	1	49	department	department	NOUN
ejpam-5918	1	50	of	of	ADP
ejpam-5918	1	51	mathematics	mathematic	NOUN
ejpam-5918	1	52	,	,	PUNCT
ejpam-5918	1	53	college	college	NOUN
ejpam-5918	1	54	of	of	ADP
ejpam-5918	1	55	arts	art	NOUN
ejpam-5918	1	56	and	and	CCONJ
ejpam-5918	1	57	sciences	science	NOUN
ejpam-5918	1	58	,	,	PUNCT
ejpam-5918	1	59	central	central	ADJ
ejpam-5918	1	60	mindanao	mindanao	PROPN
ejpam-5918	1	61	university	university	PROPN
ejpam-5918	1	62	,	,	PUNCT
ejpam-5918	1	63	musuan	musuan	PROPN
ejpam-5918	1	64	,	,	PUNCT
ejpam-5918	1	65	maramag	maramag	NOUN
ejpam-5918	1	66	,	,	PUNCT
ejpam-5918	1	67	bukidnon	bukidnon	NOUN
ejpam-5918	1	68	,	,	PUNCT
ejpam-5918	1	69	8714	8714	NUM
ejpam-5918	1	70	philippines	philippine	NOUN
ejpam-5918	1	71	abstract	abstract	ADJ
ejpam-5918	1	72	.	.	PUNCT
ejpam-5918	2	1	for	for	ADP
ejpam-5918	2	2	a	a	DET
ejpam-5918	2	3	connected	connected	ADJ
ejpam-5918	2	4	graph	graph	NOUN
ejpam-5918	2	5	g	g	NOUN
ejpam-5918	2	6	,	,	PUNCT
ejpam-5918	2	7	a	a	DET
ejpam-5918	2	8	subset	subset	NOUN
ejpam-5918	2	9	i	i	PRON
ejpam-5918	2	10	⊆	⊆	PROPN
ejpam-5918	2	11	v	v	ADP
ejpam-5918	2	12	(	(	PUNCT
ejpam-5918	2	13	g	g	NOUN
ejpam-5918	2	14	)	)	PUNCT
ejpam-5918	2	15	is	be	AUX
ejpam-5918	2	16	a	a	DET
ejpam-5918	2	17	locating	locate	VERB
ejpam-5918	2	18	-	-	PUNCT
ejpam-5918	2	19	dominating	dominating	NOUN
ejpam-5918	2	20	set	set	NOUN
ejpam-5918	2	21	if	if	SCONJ
ejpam-5918	2	22	it	it	PRON
ejpam-5918	2	23	is	be	AUX
ejpam-5918	2	24	a	a	DET
ejpam-5918	2	25	dominating	dominating	NOUN
ejpam-5918	2	26	set	set	NOUN
ejpam-5918	2	27	and	and	CCONJ
ejpam-5918	2	28	for	for	ADP
ejpam-5918	2	29	every	every	DET
ejpam-5918	2	30	two	two	NUM
ejpam-5918	2	31	distinct	distinct	ADJ
ejpam-5918	2	32	vertices	vertex	NOUN
ejpam-5918	2	33	x	x	X
ejpam-5918	2	34	,	,	PUNCT
ejpam-5918	2	35	y	y	PROPN
ejpam-5918	2	36	∈	∈	PROPN
ejpam-5918	2	37	v	v	ADP
ejpam-5918	2	38	(	(	PUNCT
ejpam-5918	2	39	g	g	NOUN
ejpam-5918	2	40	)	)	PUNCT
ejpam-5918	2	41	\	\	PROPN
ejpam-5918	3	1	i	i	PRON
ejpam-5918	3	2	,	,	PUNCT
ejpam-5918	3	3	n(x	n(x	PROPN
ejpam-5918	3	4	)	)	PUNCT
ejpam-5918	3	5	∩	∩	NOUN
ejpam-5918	3	6	i	i	PRON
ejpam-5918	3	7	̸=	̸=	PROPN
ejpam-5918	3	8	n(y	n(y	PROPN
ejpam-5918	3	9	)	)	PUNCT
ejpam-5918	3	10	∩	∩	PROPN
ejpam-5918	3	11	i.	i.	NOUN
ejpam-5918	3	12	this	this	DET
ejpam-5918	3	13	paper	paper	NOUN
ejpam-5918	3	14	introduces	introduce	VERB
ejpam-5918	3	15	the	the	DET
ejpam-5918	3	16	concept	concept	NOUN
ejpam-5918	3	17	of	of	ADP
ejpam-5918	3	18	an	an	DET
ejpam-5918	3	19	internally	internally	ADV
ejpam-5918	3	20	-	-	PUNCT
ejpam-5918	3	21	locating	locate	VERB
ejpam-5918	3	22	dominating	dominating	NOUN
ejpam-5918	3	23	set	set	NOUN
ejpam-5918	3	24	.	.	PUNCT
ejpam-5918	4	1	specifically	specifically	ADV
ejpam-5918	4	2	,	,	PUNCT
ejpam-5918	4	3	a	a	DET
ejpam-5918	4	4	nonempty	nonempty	NOUN
ejpam-5918	4	5	set	set	VERB
ejpam-5918	4	6	i	i	PRON
ejpam-5918	4	7	⊆	⊆	NUM
ejpam-5918	4	8	v	v	ADP
ejpam-5918	4	9	(	(	PUNCT
ejpam-5918	4	10	g	g	NOUN
ejpam-5918	4	11	)	)	PUNCT
ejpam-5918	4	12	with	with	ADP
ejpam-5918	4	13	|i|	|i|	PRON
ejpam-5918	4	14	≥	≥	NOUN
ejpam-5918	4	15	2	2	NUM
ejpam-5918	4	16	is	be	AUX
ejpam-5918	4	17	an	an	DET
ejpam-5918	4	18	internally	internally	ADV
ejpam-5918	4	19	-	-	PUNCT
ejpam-5918	4	20	locating	locate	VERB
ejpam-5918	4	21	set	set	NOUN
ejpam-5918	4	22	in	in	ADP
ejpam-5918	4	23	a	a	DET
ejpam-5918	4	24	nontrivial	nontrivial	ADJ
ejpam-5918	4	25	connected	connect	VERB
ejpam-5918	4	26	graph	graph	NOUN
ejpam-5918	4	27	g	g	PROPN
ejpam-5918	4	28	if	if	SCONJ
ejpam-5918	5	1	and	and	CCONJ
ejpam-5918	5	2	only	only	ADV
ejpam-5918	5	3	if	if	SCONJ
ejpam-5918	5	4	,	,	PUNCT
ejpam-5918	5	5	for	for	ADP
ejpam-5918	5	6	every	every	DET
ejpam-5918	5	7	u	u	NOUN
ejpam-5918	5	8	,	,	PUNCT
ejpam-5918	5	9	v	v	NOUN
ejpam-5918	5	10	∈	∈	PROPN
ejpam-5918	6	1	i	i	PRON
ejpam-5918	6	2	,	,	PUNCT
ejpam-5918	6	3	n(u)∩	n(u)∩	ADV
ejpam-5918	6	4	i	i	PRON
ejpam-5918	6	5	̸=	̸=	PROPN
ejpam-5918	6	6	n(v)∩	n(v)∩	PROPN
ejpam-5918	6	7	i.	i.	NOUN
ejpam-5918	6	8	thus	thus	ADV
ejpam-5918	6	9	,	,	PUNCT
ejpam-5918	6	10	i	i	PRON
ejpam-5918	6	11	is	be	AUX
ejpam-5918	6	12	an	an	DET
ejpam-5918	6	13	internally	internally	ADV
ejpam-5918	6	14	-	-	PUNCT
ejpam-5918	6	15	locating	locate	VERB
ejpam-5918	6	16	dominating	dominating	NOUN
ejpam-5918	6	17	set	set	NOUN
ejpam-5918	6	18	if	if	SCONJ
ejpam-5918	6	19	it	it	PRON
ejpam-5918	6	20	is	be	AUX
ejpam-5918	6	21	both	both	CCONJ
ejpam-5918	6	22	an	an	DET
ejpam-5918	6	23	internally	internally	ADV
ejpam-5918	6	24	-	-	PUNCT
ejpam-5918	6	25	locating	locate	VERB
ejpam-5918	6	26	set	set	NOUN
ejpam-5918	6	27	and	and	CCONJ
ejpam-5918	6	28	a	a	DET
ejpam-5918	6	29	dominating	dominating	NOUN
ejpam-5918	6	30	set	set	NOUN
ejpam-5918	6	31	.	.	PUNCT
ejpam-5918	7	1	in	in	ADP
ejpam-5918	7	2	addition	addition	NOUN
ejpam-5918	7	3	,	,	PUNCT
ejpam-5918	7	4	this	this	DET
ejpam-5918	7	5	paper	paper	NOUN
ejpam-5918	7	6	identifies	identify	VERB
ejpam-5918	7	7	some	some	DET
ejpam-5918	7	8	properties	property	NOUN
ejpam-5918	7	9	of	of	ADP
ejpam-5918	7	10	this	this	DET
ejpam-5918	7	11	concept	concept	NOUN
ejpam-5918	7	12	,	,	PUNCT
ejpam-5918	7	13	provides	provide	VERB
ejpam-5918	7	14	characterizations	characterization	NOUN
ejpam-5918	7	15	of	of	ADP
ejpam-5918	7	16	certain	certain	ADJ
ejpam-5918	7	17	special	special	ADJ
ejpam-5918	7	18	classes	class	NOUN
ejpam-5918	7	19	of	of	ADP
ejpam-5918	7	20	graphs	graph	NOUN
ejpam-5918	7	21	,	,	PUNCT
ejpam-5918	7	22	including	include	VERB
ejpam-5918	7	23	total	total	ADJ
ejpam-5918	7	24	graphs	graph	NOUN
ejpam-5918	7	25	and	and	CCONJ
ejpam-5918	7	26	shadow	shadow	NOUN
ejpam-5918	7	27	graphs	graph	NOUN
ejpam-5918	7	28	with	with	ADP
ejpam-5918	7	29	∆(g	∆(g	NOUN
ejpam-5918	7	30	)	)	PUNCT
ejpam-5918	7	31	=	=	SYM
ejpam-5918	7	32	2	2	NUM
ejpam-5918	7	33	,	,	PUNCT
ejpam-5918	7	34	with	with	ADP
ejpam-5918	7	35	their	their	PRON
ejpam-5918	7	36	corresponding	corresponding	ADJ
ejpam-5918	7	37	internally	internally	ADV
ejpam-5918	7	38	-	-	PUNCT
ejpam-5918	7	39	locating	locate	VERB
ejpam-5918	7	40	domination	domination	NOUN
ejpam-5918	7	41	number	number	NOUN
ejpam-5918	7	42	,	,	PUNCT
ejpam-5918	7	43	and	and	CCONJ
ejpam-5918	7	44	cases	case	NOUN
ejpam-5918	7	45	where	where	SCONJ
ejpam-5918	7	46	γli(g	γli(g	VERB
ejpam-5918	7	47	)	)	PUNCT
ejpam-5918	7	48	=	=	SYM
ejpam-5918	8	1	2	2	X
ejpam-5918	8	2	.	.	PUNCT
ejpam-5918	8	3	moreover	moreover	ADV
ejpam-5918	8	4	,	,	PUNCT
ejpam-5918	8	5	it	it	PRON
ejpam-5918	8	6	provides	provide	VERB
ejpam-5918	8	7	a	a	DET
ejpam-5918	8	8	sufficient	sufficient	ADJ
ejpam-5918	8	9	condition	condition	NOUN
ejpam-5918	8	10	for	for	ADP
ejpam-5918	8	11	γ(g	γ(g	PROPN
ejpam-5918	8	12	)	)	PUNCT
ejpam-5918	8	13	=	=	SYM
ejpam-5918	8	14	γli(g	γli(g	PROPN
ejpam-5918	8	15	)	)	PUNCT
ejpam-5918	8	16	,	,	PUNCT
ejpam-5918	8	17	specifically	specifically	ADV
ejpam-5918	8	18	when	when	SCONJ
ejpam-5918	8	19	g	g	PROPN
ejpam-5918	8	20	is	be	AUX
ejpam-5918	8	21	a	a	DET
ejpam-5918	8	22	corona	corona	NOUN
ejpam-5918	8	23	product	product	NOUN
ejpam-5918	8	24	.	.	PUNCT
ejpam-5918	9	1	2020	2020	NUM
ejpam-5918	9	2	mathematics	mathematic	NOUN
ejpam-5918	9	3	subject	subject	NOUN
ejpam-5918	9	4	classifications	classification	NOUN
ejpam-5918	9	5	:	:	PUNCT
ejpam-5918	9	6	05c69	05c69	X
ejpam-5918	9	7	key	key	ADJ
ejpam-5918	9	8	words	word	NOUN
ejpam-5918	9	9	and	and	CCONJ
ejpam-5918	9	10	phrases	phrase	NOUN
ejpam-5918	9	11	:	:	PUNCT
ejpam-5918	9	12	internally	internally	ADV
ejpam-5918	9	13	-	-	PUNCT
ejpam-5918	9	14	locating	locate	VERB
ejpam-5918	9	15	set	set	NOUN
ejpam-5918	9	16	,	,	PUNCT
ejpam-5918	9	17	internally	internally	ADV
ejpam-5918	9	18	-	-	PUNCT
ejpam-5918	9	19	locating	locate	VERB
ejpam-5918	9	20	dominating	dominating	NOUN
ejpam-5918	9	21	set	set	NOUN
ejpam-5918	9	22	,	,	PUNCT
ejpam-5918	9	23	internallylocating	internallylocate	VERB
ejpam-5918	9	24	domination	domination	NOUN
ejpam-5918	9	25	number	number	NOUN
ejpam-5918	9	26	,	,	PUNCT
ejpam-5918	9	27	total	total	ADJ
ejpam-5918	9	28	graph	graph	NOUN
ejpam-5918	9	29	,	,	PUNCT
ejpam-5918	9	30	shadow	shadow	NOUN
ejpam-5918	9	31	graph	graph	NOUN
ejpam-5918	9	32	,	,	PUNCT
ejpam-5918	9	33	corona	corona	NOUN
ejpam-5918	9	34	of	of	ADP
ejpam-5918	9	35	graph	graph	NOUN
ejpam-5918	9	36	1	1	NUM
ejpam-5918	9	37	.	.	PUNCT
ejpam-5918	9	38	introduction	introduction	NOUN
ejpam-5918	9	39	over	over	ADP
ejpam-5918	9	40	time	time	NOUN
ejpam-5918	9	41	,	,	PUNCT
ejpam-5918	9	42	graph	graph	NOUN
ejpam-5918	9	43	theory	theory	NOUN
ejpam-5918	9	44	has	have	AUX
ejpam-5918	9	45	evolved	evolve	VERB
ejpam-5918	9	46	into	into	ADP
ejpam-5918	9	47	a	a	DET
ejpam-5918	9	48	powerful	powerful	ADJ
ejpam-5918	9	49	tool	tool	NOUN
ejpam-5918	9	50	for	for	ADP
ejpam-5918	9	51	analyzing	analyze	VERB
ejpam-5918	9	52	networks	network	NOUN
ejpam-5918	9	53	and	and	CCONJ
ejpam-5918	9	54	solving	solve	VERB
ejpam-5918	9	55	optimization	optimization	NOUN
ejpam-5918	9	56	problems	problem	NOUN
ejpam-5918	9	57	.	.	PUNCT
ejpam-5918	10	1	two	two	NUM
ejpam-5918	10	2	fundamental	fundamental	ADJ
ejpam-5918	10	3	concepts	concept	NOUN
ejpam-5918	10	4	in	in	ADP
ejpam-5918	10	5	this	this	DET
ejpam-5918	10	6	field	field	NOUN
ejpam-5918	10	7	are	be	AUX
ejpam-5918	10	8	dominating	dominate	VERB
ejpam-5918	10	9	sets	set	NOUN
ejpam-5918	10	10	and	and	CCONJ
ejpam-5918	10	11	locating	locating	NOUN
ejpam-5918	10	12	sets	set	NOUN
ejpam-5918	10	13	.	.	PUNCT
ejpam-5918	11	1	domination	domination	NOUN
ejpam-5918	11	2	theory	theory	NOUN
ejpam-5918	11	3	,	,	PUNCT
ejpam-5918	11	4	introduced	introduce	VERB
ejpam-5918	11	5	by	by	ADP
ejpam-5918	11	6	berge	berge	NOUN
ejpam-5918	11	7	and	and	CCONJ
ejpam-5918	11	8	ore	ore	NOUN
ejpam-5918	11	9	in	in	ADP
ejpam-5918	11	10	the	the	DET
ejpam-5918	11	11	1960s	1960	NOUN
ejpam-5918	11	12	[	[	X
ejpam-5918	11	13	1	1	NUM
ejpam-5918	11	14	]	]	PUNCT
ejpam-5918	11	15	,	,	PUNCT
ejpam-5918	11	16	has	have	VERB
ejpam-5918	11	17	its	its	PRON
ejpam-5918	11	18	applications	application	NOUN
ejpam-5918	11	19	in	in	ADP
ejpam-5918	11	20	various	various	ADJ
ejpam-5918	11	21	areas	area	NOUN
ejpam-5918	11	22	,	,	PUNCT
ejpam-5918	11	23	including	include	VERB
ejpam-5918	11	24	facility	facility	NOUN
ejpam-5918	11	25	location	location	NOUN
ejpam-5918	11	26	problems	problem	NOUN
ejpam-5918	11	27	(	(	PUNCT
ejpam-5918	11	28	flps	flps	PROPN
ejpam-5918	11	29	)	)	PUNCT
ejpam-5918	12	1	[	[	X
ejpam-5918	12	2	2	2	NUM
ejpam-5918	12	3	]	]	PUNCT
ejpam-5918	12	4	.	.	PUNCT
ejpam-5918	13	1	flps	flp	NOUN
ejpam-5918	13	2	focus	focus	VERB
ejpam-5918	13	3	on	on	ADP
ejpam-5918	13	4	optimizing	optimize	VERB
ejpam-5918	13	5	factors	factor	NOUN
ejpam-5918	13	6	such	such	ADJ
ejpam-5918	13	7	as	as	ADP
ejpam-5918	13	8	transportation	transportation	NOUN
ejpam-5918	13	9	costs	cost	NOUN
ejpam-5918	13	10	and	and	CCONJ
ejpam-5918	13	11	market	market	NOUN
ejpam-5918	13	12	share	share	NOUN
ejpam-5918	13	13	[	[	X
ejpam-5918	13	14	2	2	NUM
ejpam-5918	13	15	]	]	PUNCT
ejpam-5918	13	16	.	.	PUNCT
ejpam-5918	14	1	locating	locate	VERB
ejpam-5918	14	2	sets	set	NOUN
ejpam-5918	14	3	,	,	PUNCT
ejpam-5918	14	4	introduced	introduce	VERB
ejpam-5918	14	5	by	by	ADP
ejpam-5918	14	6	slater	slater	NOUN
ejpam-5918	15	1	[	[	X
ejpam-5918	15	2	3	3	NUM
ejpam-5918	15	3	]	]	PUNCT
ejpam-5918	15	4	,	,	PUNCT
ejpam-5918	15	5	are	be	AUX
ejpam-5918	15	6	also	also	ADV
ejpam-5918	15	7	important	important	ADJ
ejpam-5918	15	8	,	,	PUNCT
ejpam-5918	15	9	with	with	ADP
ejpam-5918	15	10	applications	application	NOUN
ejpam-5918	15	11	in	in	ADP
ejpam-5918	15	12	systems	system	NOUN
ejpam-5918	15	13	like	like	ADP
ejpam-5918	15	14	sonar	sonar	NOUN
ejpam-5918	15	15	and	and	CCONJ
ejpam-5918	15	16	long	long	ADJ
ejpam-5918	15	17	-	-	PUNCT
ejpam-5918	15	18	range	range	NOUN
ejpam-5918	15	19	navigation	navigation	NOUN
ejpam-5918	15	20	(	(	PUNCT
ejpam-5918	15	21	loran	loran	NOUN
ejpam-5918	15	22	)	)	PUNCT
ejpam-5918	15	23	stations	station	NOUN
ejpam-5918	15	24	[	[	X
ejpam-5918	15	25	4	4	NUM
ejpam-5918	15	26	]	]	PUNCT
ejpam-5918	15	27	.	.	PUNCT
ejpam-5918	16	1	in	in	ADP
ejpam-5918	16	2	1998	1998	NUM
ejpam-5918	16	3	,	,	PUNCT
ejpam-5918	16	4	slater	slater	NOUN
ejpam-5918	16	5	combined	combine	VERB
ejpam-5918	16	6	the	the	DET
ejpam-5918	16	7	ideas	idea	NOUN
ejpam-5918	16	8	of	of	ADP
ejpam-5918	16	9	domination	domination	NOUN
ejpam-5918	16	10	and	and	CCONJ
ejpam-5918	16	11	location	location	NOUN
ejpam-5918	16	12	to	to	PART
ejpam-5918	16	13	introduce	introduce	VERB
ejpam-5918	16	14	locatingdominating	locatingdominating	NOUN
ejpam-5918	16	15	sets	set	NOUN
ejpam-5918	16	16	[	[	X
ejpam-5918	16	17	5	5	NUM
ejpam-5918	16	18	]	]	PUNCT
ejpam-5918	16	19	,	,	PUNCT
ejpam-5918	16	20	which	which	PRON
ejpam-5918	16	21	help	help	AUX
ejpam-5918	16	22	identify	identify	VERB
ejpam-5918	16	23	vertices	vertex	NOUN
ejpam-5918	16	24	while	while	SCONJ
ejpam-5918	16	25	also	also	ADV
ejpam-5918	16	26	dominating	dominate	VERB
ejpam-5918	16	27	the	the	DET
ejpam-5918	16	28	graph	graph	NOUN
ejpam-5918	16	29	.	.	PUNCT
ejpam-5918	17	1	these	these	DET
ejpam-5918	17	2	sets	set	NOUN
ejpam-5918	17	3	have	have	VERB
ejpam-5918	17	4	applications	application	NOUN
ejpam-5918	17	5	in	in	ADP
ejpam-5918	17	6	fields	field	NOUN
ejpam-5918	17	7	such	such	ADJ
ejpam-5918	17	8	as	as	ADP
ejpam-5918	17	9	fire	fire	NOUN
ejpam-5918	17	10	location	location	NOUN
ejpam-5918	17	11	detection	detection	NOUN
ejpam-5918	17	12	and	and	CCONJ
ejpam-5918	17	13	multiprocessor	multiprocessor	NOUN
ejpam-5918	17	14	error	error	NOUN
ejpam-5918	17	15	diagnosis	diagnosis	NOUN
ejpam-5918	17	16	[	[	X
ejpam-5918	17	17	6	6	NUM
ejpam-5918	17	18	]	]	PUNCT
ejpam-5918	17	19	.	.	PUNCT
ejpam-5918	18	1	slater	slater	PROPN
ejpam-5918	18	2	’s	’s	PART
ejpam-5918	18	3	work	work	NOUN
ejpam-5918	18	4	,	,	PUNCT
ejpam-5918	18	5	along	along	ADP
ejpam-5918	18	6	with	with	ADP
ejpam-5918	18	7	subsequent	subsequent	ADJ
ejpam-5918	18	8	studies	study	NOUN
ejpam-5918	18	9	by	by	ADP
ejpam-5918	18	10	canoy	canoy	NOUN
ejpam-5918	18	11	and	and	CCONJ
ejpam-5918	18	12	omega	omega	NOUN
ejpam-5918	18	13	,	,	PUNCT
ejpam-5918	18	14	expanded	expand	VERB
ejpam-5918	18	15	∗corresponding	∗corresponding	NOUN
ejpam-5918	18	16	author	author	NOUN
ejpam-5918	18	17	.	.	PUNCT
ejpam-5918	19	1	doi	doi	NOUN
ejpam-5918	19	2	:	:	PUNCT
ejpam-5918	19	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5918	https://doi.org/10.29020/nybg.ejpam.v18i2.5918	PROPN
ejpam-5918	19	4	email	email	NOUN
ejpam-5918	19	5	addresses	address	NOUN
ejpam-5918	19	6	:	:	PUNCT
ejpam-5918	19	7	irish.tropico17@gmail.com	irish.tropico17@gmail.com	PROPN
ejpam-5918	19	8	(	(	PUNCT
ejpam-5918	19	9	i.	i.	PROPN
ejpam-5918	19	10	tropico	tropico	PROPN
ejpam-5918	19	11	)	)	PUNCT
ejpam-5918	19	12	,	,	PUNCT
ejpam-5918	19	13	isaganicabahugjr@cmu.edu.ph	isaganicabahugjr@cmu.edu.ph	PROPN
ejpam-5918	19	14	(	(	PUNCT
ejpam-5918	19	15	i.	i.	PROPN
ejpam-5918	19	16	cabahug	cabahug	PROPN
ejpam-5918	19	17	,	,	PUNCT
ejpam-5918	19	18	jr	jr	PROPN
ejpam-5918	19	19	.	.	PUNCT
ejpam-5918	19	20	)	)	PUNCT
ejpam-5918	19	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5918	20	1	1	1	NUM
ejpam-5918	20	2	copyright	copyright	NOUN
ejpam-5918	20	3	:	:	PUNCT
ejpam-5918	20	4	©	©	PROPN
ejpam-5918	20	5	2025	2025	NUM
ejpam-5918	20	6	the	the	DET
ejpam-5918	20	7	author(s	author(s	NOUN
ejpam-5918	20	8	)	)	PUNCT
ejpam-5918	20	9	.	.	PUNCT
ejpam-5918	21	1	(	(	PUNCT
ejpam-5918	21	2	cc	cc	NOUN
ejpam-5918	21	3	by	by	ADP
ejpam-5918	21	4	-	-	PUNCT
ejpam-5918	21	5	nc	nc	PROPN
ejpam-5918	21	6	4.0	4.0	NUM
ejpam-5918	21	7	)	)	PUNCT
ejpam-5918	21	8	i.	i.	NOUN
ejpam-5918	21	9	tropico	tropico	PROPN
ejpam-5918	21	10	,	,	PUNCT
ejpam-5918	21	11	i.	i.	PROPN
ejpam-5918	21	12	cabahug	cabahug	PROPN
ejpam-5918	21	13	,	,	PUNCT
ejpam-5918	21	14	jr	jr	PROPN
ejpam-5918	21	15	.	.	PROPN
ejpam-5918	21	16	/	/	SYM
ejpam-5918	21	17	eur	eur	PROPN
ejpam-5918	21	18	.	.	PUNCT
ejpam-5918	22	1	j.	j.	PROPN
ejpam-5918	22	2	pure	pure	PROPN
ejpam-5918	22	3	appl	appl	PROPN
ejpam-5918	22	4	.	.	PROPN
ejpam-5918	22	5	math	math	PROPN
ejpam-5918	22	6	,	,	PUNCT
ejpam-5918	22	7	18	18	NUM
ejpam-5918	22	8	(	(	PUNCT
ejpam-5918	22	9	2	2	NUM
ejpam-5918	22	10	)	)	PUNCT
ejpam-5918	22	11	(	(	PUNCT
ejpam-5918	22	12	2025	2025	NUM
ejpam-5918	22	13	)	)	PUNCT
ejpam-5918	22	14	,	,	PUNCT
ejpam-5918	22	15	5918	5918	NUM
ejpam-5918	22	16	2	2	NUM
ejpam-5918	22	17	of	of	ADP
ejpam-5918	22	18	21	21	NUM
ejpam-5918	22	19	the	the	DET
ejpam-5918	22	20	theory	theory	NOUN
ejpam-5918	22	21	by	by	ADP
ejpam-5918	22	22	exploring	explore	VERB
ejpam-5918	22	23	locating	locate	VERB
ejpam-5918	22	24	sets	set	NOUN
ejpam-5918	22	25	in	in	ADP
ejpam-5918	22	26	complex	complex	ADJ
ejpam-5918	22	27	graph	graph	NOUN
ejpam-5918	22	28	operations	operation	NOUN
ejpam-5918	22	29	,	,	PUNCT
ejpam-5918	22	30	such	such	ADJ
ejpam-5918	22	31	as	as	ADP
ejpam-5918	22	32	the	the	DET
ejpam-5918	22	33	join	join	NOUN
ejpam-5918	22	34	and	and	CCONJ
ejpam-5918	22	35	corona	corona	NOUN
ejpam-5918	22	36	of	of	ADP
ejpam-5918	22	37	graphs	graph	NOUN
ejpam-5918	22	38	[	[	X
ejpam-5918	22	39	7	7	NUM
ejpam-5918	22	40	]	]	PUNCT
ejpam-5918	22	41	.	.	PUNCT
ejpam-5918	23	1	canoy	canoy	PROPN
ejpam-5918	23	2	and	and	CCONJ
ejpam-5918	23	3	malacas	malacas	NOUN
ejpam-5918	23	4	further	far	ADV
ejpam-5918	23	5	characterized	characterize	VERB
ejpam-5918	23	6	locating	locate	VERB
ejpam-5918	23	7	-	-	PUNCT
ejpam-5918	23	8	dominating	dominating	NOUN
ejpam-5918	23	9	sets	set	NOUN
ejpam-5918	23	10	in	in	ADP
ejpam-5918	23	11	graph	graph	NOUN
ejpam-5918	23	12	compositions	composition	NOUN
ejpam-5918	23	13	and	and	CCONJ
ejpam-5918	23	14	corona	corona	NOUN
ejpam-5918	23	15	graphs	graph	NOUN
ejpam-5918	23	16	[	[	X
ejpam-5918	23	17	8	8	NUM
ejpam-5918	23	18	]	]	PUNCT
ejpam-5918	23	19	.	.	PUNCT
ejpam-5918	24	1	although	although	SCONJ
ejpam-5918	24	2	much	much	ADJ
ejpam-5918	24	3	progress	progress	NOUN
ejpam-5918	24	4	has	have	AUX
ejpam-5918	24	5	been	be	AUX
ejpam-5918	24	6	made	make	VERB
ejpam-5918	24	7	in	in	ADP
ejpam-5918	24	8	understanding	understanding	NOUN
ejpam-5918	24	9	dominating	dominating	NOUN
ejpam-5918	24	10	and	and	CCONJ
ejpam-5918	24	11	locating	locating	NOUN
ejpam-5918	24	12	sets	set	NOUN
ejpam-5918	24	13	,	,	PUNCT
ejpam-5918	24	14	there	there	PRON
ejpam-5918	24	15	are	be	VERB
ejpam-5918	24	16	still	still	ADV
ejpam-5918	24	17	unexplored	unexplored	ADJ
ejpam-5918	24	18	concepts	concept	NOUN
ejpam-5918	24	19	.	.	PUNCT
ejpam-5918	25	1	this	this	PRON
ejpam-5918	25	2	led	lead	VERB
ejpam-5918	25	3	to	to	ADP
ejpam-5918	25	4	a	a	DET
ejpam-5918	25	5	question	question	NOUN
ejpam-5918	25	6	about	about	ADP
ejpam-5918	25	7	the	the	DET
ejpam-5918	25	8	distinctness	distinctness	NOUN
ejpam-5918	25	9	within	within	ADP
ejpam-5918	25	10	the	the	DET
ejpam-5918	25	11	set	set	NOUN
ejpam-5918	25	12	.	.	PUNCT
ejpam-5918	26	1	this	this	DET
ejpam-5918	26	2	study	study	NOUN
ejpam-5918	26	3	introduces	introduce	VERB
ejpam-5918	26	4	internally	internally	ADV
ejpam-5918	26	5	-	-	PUNCT
ejpam-5918	26	6	locating	locate	VERB
ejpam-5918	26	7	dominating	dominating	NOUN
ejpam-5918	26	8	sets	set	NOUN
ejpam-5918	26	9	and	and	CCONJ
ejpam-5918	26	10	explores	explore	VERB
ejpam-5918	26	11	their	their	PRON
ejpam-5918	26	12	properties	property	NOUN
ejpam-5918	26	13	in	in	ADP
ejpam-5918	26	14	special	special	ADJ
ejpam-5918	26	15	graphs	graph	NOUN
ejpam-5918	26	16	,	,	PUNCT
ejpam-5918	26	17	particularly	particularly	ADV
ejpam-5918	26	18	focusing	focus	VERB
ejpam-5918	26	19	on	on	ADP
ejpam-5918	26	20	unary	unary	ADJ
ejpam-5918	26	21	operations	operation	NOUN
ejpam-5918	26	22	such	such	ADJ
ejpam-5918	26	23	as	as	ADP
ejpam-5918	26	24	total	total	ADJ
ejpam-5918	26	25	and	and	CCONJ
ejpam-5918	26	26	shadow	shadow	VERB
ejpam-5918	26	27	graphs	graph	NOUN
ejpam-5918	26	28	with	with	ADP
ejpam-5918	26	29	∆(g	∆(g	NOUN
ejpam-5918	26	30	)	)	PUNCT
ejpam-5918	26	31	=	=	SYM
ejpam-5918	26	32	2	2	NUM
ejpam-5918	26	33	,	,	PUNCT
ejpam-5918	26	34	along	along	ADP
ejpam-5918	26	35	with	with	ADP
ejpam-5918	26	36	their	their	PRON
ejpam-5918	26	37	internally	internally	ADV
ejpam-5918	26	38	-	-	PUNCT
ejpam-5918	26	39	locating	locate	VERB
ejpam-5918	26	40	domination	domination	NOUN
ejpam-5918	26	41	numbers	number	NOUN
ejpam-5918	26	42	,	,	PUNCT
ejpam-5918	26	43	and	and	CCONJ
ejpam-5918	26	44	binary	binary	ADJ
ejpam-5918	26	45	operations	operation	NOUN
ejpam-5918	26	46	such	such	ADJ
ejpam-5918	26	47	as	as	ADP
ejpam-5918	26	48	the	the	DET
ejpam-5918	26	49	corona	corona	NOUN
ejpam-5918	26	50	of	of	ADP
ejpam-5918	26	51	graphs	graph	NOUN
ejpam-5918	26	52	.	.	PUNCT
ejpam-5918	27	1	some	some	DET
ejpam-5918	27	2	aspects	aspect	NOUN
ejpam-5918	27	3	of	of	ADP
ejpam-5918	27	4	the	the	DET
ejpam-5918	27	5	proofs	proof	NOUN
ejpam-5918	27	6	in	in	ADP
ejpam-5918	27	7	this	this	DET
ejpam-5918	27	8	study	study	NOUN
ejpam-5918	27	9	were	be	AUX
ejpam-5918	27	10	inspired	inspire	VERB
ejpam-5918	27	11	by	by	ADP
ejpam-5918	27	12	[	[	PUNCT
ejpam-5918	27	13	9	9	NUM
ejpam-5918	27	14	]	]	SYM
ejpam-5918	27	15	.	.	PUNCT
ejpam-5918	28	1	2	2	X
ejpam-5918	28	2	.	.	X
ejpam-5918	28	3	terminology	terminology	NOUN
ejpam-5918	28	4	and	and	CCONJ
ejpam-5918	28	5	notation	notation	NOUN
ejpam-5918	28	6	this	this	DET
ejpam-5918	28	7	study	study	NOUN
ejpam-5918	28	8	considers	consider	VERB
ejpam-5918	28	9	finite	finite	ADJ
ejpam-5918	28	10	,	,	PUNCT
ejpam-5918	28	11	simple	simple	ADJ
ejpam-5918	28	12	,	,	PUNCT
ejpam-5918	28	13	nontrivial	nontrivial	NOUN
ejpam-5918	28	14	,	,	PUNCT
ejpam-5918	28	15	connected	connect	VERB
ejpam-5918	28	16	,	,	PUNCT
ejpam-5918	28	17	and	and	CCONJ
ejpam-5918	28	18	undirected	undirected	ADJ
ejpam-5918	28	19	graphs	graph	NOUN
ejpam-5918	28	20	.	.	PUNCT
ejpam-5918	29	1	some	some	DET
ejpam-5918	29	2	definitions	definition	NOUN
ejpam-5918	29	3	of	of	ADP
ejpam-5918	29	4	the	the	DET
ejpam-5918	29	5	concepts	concept	NOUN
ejpam-5918	29	6	covered	cover	VERB
ejpam-5918	29	7	in	in	ADP
ejpam-5918	29	8	this	this	DET
ejpam-5918	29	9	study	study	NOUN
ejpam-5918	29	10	is	be	AUX
ejpam-5918	29	11	included	include	VERB
ejpam-5918	29	12	within	within	ADP
ejpam-5918	29	13	.	.	PUNCT
ejpam-5918	30	1	for	for	ADP
ejpam-5918	30	2	fundamental	fundamental	ADJ
ejpam-5918	30	3	graphtheoretic	graphtheoretic	ADJ
ejpam-5918	30	4	concepts	concept	NOUN
ejpam-5918	30	5	and	and	CCONJ
ejpam-5918	30	6	additional	additional	ADJ
ejpam-5918	30	7	terms	term	NOUN
ejpam-5918	30	8	,	,	PUNCT
ejpam-5918	30	9	the	the	DET
ejpam-5918	30	10	readers	reader	NOUN
ejpam-5918	30	11	may	may	AUX
ejpam-5918	30	12	refer	refer	VERB
ejpam-5918	30	13	to	to	ADP
ejpam-5918	30	14	[	[	X
ejpam-5918	30	15	10	10	NUM
ejpam-5918	30	16	]	]	PUNCT
ejpam-5918	30	17	,	,	PUNCT
ejpam-5918	30	18	[	[	X
ejpam-5918	30	19	11	11	NUM
ejpam-5918	30	20	]	]	PUNCT
ejpam-5918	30	21	,	,	PUNCT
ejpam-5918	30	22	[	[	X
ejpam-5918	30	23	4	4	NUM
ejpam-5918	30	24	]	]	PUNCT
ejpam-5918	30	25	,	,	PUNCT
ejpam-5918	30	26	[	[	X
ejpam-5918	30	27	12	12	NUM
ejpam-5918	30	28	]	]	PUNCT
ejpam-5918	30	29	,	,	PUNCT
ejpam-5918	30	30	[	[	X
ejpam-5918	30	31	13	13	NUM
ejpam-5918	30	32	]	]	PUNCT
ejpam-5918	30	33	,	,	PUNCT
ejpam-5918	30	34	[	[	X
ejpam-5918	30	35	14	14	NUM
ejpam-5918	30	36	]	]	PUNCT
ejpam-5918	30	37	,	,	PUNCT
ejpam-5918	30	38	[	[	X
ejpam-5918	30	39	7	7	NUM
ejpam-5918	30	40	]	]	PUNCT
ejpam-5918	30	41	,	,	PUNCT
ejpam-5918	30	42	[	[	X
ejpam-5918	30	43	15	15	NUM
ejpam-5918	30	44	]	]	PUNCT
ejpam-5918	30	45	,	,	PUNCT
ejpam-5918	30	46	[	[	X
ejpam-5918	30	47	16	16	NUM
ejpam-5918	30	48	]	]	PUNCT
ejpam-5918	30	49	.	.	PUNCT
ejpam-5918	31	1	let	let	VERB
ejpam-5918	31	2	g	g	PROPN
ejpam-5918	31	3	=	=	SYM
ejpam-5918	31	4	(	(	PUNCT
ejpam-5918	31	5	v	v	NOUN
ejpam-5918	31	6	,	,	PUNCT
ejpam-5918	31	7	e	e	NOUN
ejpam-5918	31	8	)	)	PUNCT
ejpam-5918	31	9	be	be	AUX
ejpam-5918	31	10	a	a	DET
ejpam-5918	31	11	graph	graph	NOUN
ejpam-5918	31	12	.	.	PUNCT
ejpam-5918	32	1	if	if	SCONJ
ejpam-5918	32	2	the	the	DET
ejpam-5918	32	3	pair	pair	NOUN
ejpam-5918	32	4	u	u	NOUN
ejpam-5918	32	5	and	and	CCONJ
ejpam-5918	32	6	v	v	NOUN
ejpam-5918	32	7	is	be	AUX
ejpam-5918	32	8	in	in	ADP
ejpam-5918	32	9	e	e	NOUN
ejpam-5918	32	10	,	,	PUNCT
ejpam-5918	32	11	then	then	ADV
ejpam-5918	32	12	e	e	X
ejpam-5918	32	13	=	=	NOUN
ejpam-5918	32	14	uv	uv	NOUN
ejpam-5918	32	15	is	be	AUX
ejpam-5918	32	16	an	an	DET
ejpam-5918	32	17	edge	edge	NOUN
ejpam-5918	32	18	of	of	ADP
ejpam-5918	32	19	g	g	NOUN
ejpam-5918	32	20	and	and	CCONJ
ejpam-5918	32	21	the	the	DET
ejpam-5918	32	22	vertices	vertex	NOUN
ejpam-5918	32	23	u	u	NOUN
ejpam-5918	32	24	and	and	CCONJ
ejpam-5918	32	25	v	v	NOUN
ejpam-5918	32	26	are	be	AUX
ejpam-5918	32	27	adjacent	adjacent	ADJ
ejpam-5918	32	28	in	in	ADP
ejpam-5918	32	29	g.	g.	PROPN
ejpam-5918	32	30	two	two	NUM
ejpam-5918	32	31	adjacent	adjacent	ADJ
ejpam-5918	32	32	vertices	vertex	NOUN
ejpam-5918	32	33	in	in	ADP
ejpam-5918	32	34	g	g	PROPN
ejpam-5918	32	35	are	be	AUX
ejpam-5918	32	36	referred	refer	VERB
ejpam-5918	32	37	to	to	ADP
ejpam-5918	32	38	as	as	ADP
ejpam-5918	32	39	neighbors	neighbor	NOUN
ejpam-5918	32	40	of	of	ADP
ejpam-5918	32	41	each	each	DET
ejpam-5918	32	42	other	other	ADJ
ejpam-5918	32	43	.	.	PUNCT
ejpam-5918	33	1	the	the	DET
ejpam-5918	33	2	set	set	NOUN
ejpam-5918	33	3	of	of	ADP
ejpam-5918	33	4	neighbors	neighbor	NOUN
ejpam-5918	33	5	of	of	ADP
ejpam-5918	33	6	a	a	DET
ejpam-5918	33	7	vertex	vertex	NOUN
ejpam-5918	33	8	v	v	NOUN
ejpam-5918	33	9	is	be	AUX
ejpam-5918	33	10	called	call	VERB
ejpam-5918	33	11	the	the	DET
ejpam-5918	33	12	open	open	ADJ
ejpam-5918	33	13	neighborhood	neighborhood	NOUN
ejpam-5918	33	14	of	of	ADP
ejpam-5918	33	15	v	v	NOUN
ejpam-5918	33	16	denoted	denote	VERB
ejpam-5918	33	17	by	by	ADP
ejpam-5918	33	18	ng(v	ng(v	NOUN
ejpam-5918	33	19	)	)	PUNCT
ejpam-5918	33	20	=	=	SYM
ejpam-5918	33	21	n(v	n(v	PROPN
ejpam-5918	33	22	)	)	PUNCT
ejpam-5918	34	1	[	[	X
ejpam-5918	34	2	4	4	NUM
ejpam-5918	34	3	]	]	PUNCT
ejpam-5918	34	4	.	.	PUNCT
ejpam-5918	35	1	the	the	DET
ejpam-5918	35	2	degree	degree	NOUN
ejpam-5918	35	3	of	of	ADP
ejpam-5918	35	4	a	a	DET
ejpam-5918	35	5	vertex	vertex	NOUN
ejpam-5918	35	6	v	v	NOUN
ejpam-5918	35	7	in	in	ADP
ejpam-5918	35	8	a	a	DET
ejpam-5918	35	9	graph	graph	NOUN
ejpam-5918	35	10	g	g	NOUN
ejpam-5918	35	11	is	be	AUX
ejpam-5918	35	12	the	the	DET
ejpam-5918	35	13	number	number	NOUN
ejpam-5918	35	14	of	of	ADP
ejpam-5918	35	15	vertices	vertex	NOUN
ejpam-5918	35	16	that	that	PRON
ejpam-5918	35	17	are	be	AUX
ejpam-5918	35	18	adjacent	adjacent	ADJ
ejpam-5918	35	19	to	to	ADP
ejpam-5918	35	20	v	v	NOUN
ejpam-5918	35	21	,	,	PUNCT
ejpam-5918	35	22	denoted	denote	VERB
ejpam-5918	35	23	by	by	ADP
ejpam-5918	35	24	degg(v	degg(v	PROPN
ejpam-5918	35	25	)	)	PUNCT
ejpam-5918	35	26	or	or	CCONJ
ejpam-5918	35	27	simply	simply	ADV
ejpam-5918	35	28	deg(v	deg(v	PROPN
ejpam-5918	35	29	)	)	PUNCT
ejpam-5918	35	30	.	.	PUNCT
ejpam-5918	36	1	a	a	DET
ejpam-5918	36	2	vertex	vertex	NOUN
ejpam-5918	36	3	of	of	ADP
ejpam-5918	36	4	degree	degree	NOUN
ejpam-5918	36	5	0	0	PUNCT
ejpam-5918	36	6	is	be	AUX
ejpam-5918	36	7	referred	refer	VERB
ejpam-5918	36	8	to	to	ADP
ejpam-5918	36	9	as	as	ADP
ejpam-5918	36	10	an	an	DET
ejpam-5918	36	11	isolated	isolated	ADJ
ejpam-5918	36	12	vertex	vertex	NOUN
ejpam-5918	36	13	and	and	CCONJ
ejpam-5918	36	14	a	a	DET
ejpam-5918	36	15	vertex	vertex	NOUN
ejpam-5918	36	16	of	of	ADP
ejpam-5918	36	17	degree	degree	NOUN
ejpam-5918	36	18	1	1	NUM
ejpam-5918	36	19	is	be	AUX
ejpam-5918	36	20	an	an	DET
ejpam-5918	36	21	end	end	NOUN
ejpam-5918	36	22	-	-	PUNCT
ejpam-5918	36	23	vertex	vertex	NOUN
ejpam-5918	36	24	or	or	CCONJ
ejpam-5918	36	25	leaf	leaf	NOUN
ejpam-5918	36	26	.	.	PUNCT
ejpam-5918	37	1	the	the	DET
ejpam-5918	37	2	largest	large	ADJ
ejpam-5918	37	3	degree	degree	NOUN
ejpam-5918	37	4	among	among	ADP
ejpam-5918	37	5	the	the	DET
ejpam-5918	37	6	vertices	vertex	NOUN
ejpam-5918	37	7	of	of	ADP
ejpam-5918	37	8	g	g	PROPN
ejpam-5918	37	9	is	be	AUX
ejpam-5918	37	10	called	call	VERB
ejpam-5918	37	11	the	the	DET
ejpam-5918	37	12	maximum	maximum	ADJ
ejpam-5918	37	13	degree	degree	NOUN
ejpam-5918	37	14	of	of	ADP
ejpam-5918	37	15	g	g	NOUN
ejpam-5918	37	16	,	,	PUNCT
ejpam-5918	37	17	denoted	denote	VERB
ejpam-5918	37	18	by	by	ADP
ejpam-5918	37	19	∆(g	∆(g	PROPN
ejpam-5918	37	20	)	)	PUNCT
ejpam-5918	38	1	[	[	X
ejpam-5918	38	2	4	4	NUM
ejpam-5918	38	3	]	]	PUNCT
ejpam-5918	38	4	.	.	PUNCT
ejpam-5918	39	1	a	a	DET
ejpam-5918	39	2	set	set	NOUN
ejpam-5918	39	3	s	s	NOUN
ejpam-5918	39	4	⊆	⊆	NUM
ejpam-5918	39	5	v	v	NOUN
ejpam-5918	39	6	(	(	PUNCT
ejpam-5918	39	7	g	g	NOUN
ejpam-5918	39	8	)	)	PUNCT
ejpam-5918	39	9	is	be	AUX
ejpam-5918	39	10	a	a	DET
ejpam-5918	39	11	dominating	dominating	NOUN
ejpam-5918	39	12	set	set	NOUN
ejpam-5918	39	13	of	of	ADP
ejpam-5918	39	14	g	g	NOUN
ejpam-5918	39	15	,	,	PUNCT
ejpam-5918	39	16	if	if	SCONJ
ejpam-5918	39	17	every	every	DET
ejpam-5918	39	18	vertex	vertex	NOUN
ejpam-5918	39	19	in	in	ADP
ejpam-5918	39	20	v	v	NOUN
ejpam-5918	39	21	(	(	PUNCT
ejpam-5918	39	22	g	g	NOUN
ejpam-5918	39	23	)	)	PUNCT
ejpam-5918	39	24	\	\	PROPN
ejpam-5918	40	1	s	s	PART
ejpam-5918	40	2	is	be	AUX
ejpam-5918	40	3	adjacent	adjacent	ADJ
ejpam-5918	40	4	to	to	ADP
ejpam-5918	40	5	at	at	ADV
ejpam-5918	40	6	least	least	ADV
ejpam-5918	40	7	one	one	NUM
ejpam-5918	40	8	vertex	vertex	NOUN
ejpam-5918	40	9	in	in	ADP
ejpam-5918	40	10	s.	s.	PROPN
ejpam-5918	40	11	the	the	DET
ejpam-5918	40	12	domination	domination	NOUN
ejpam-5918	40	13	number	number	PROPN
ejpam-5918	40	14	γ(g	γ(g	PROPN
ejpam-5918	40	15	)	)	PUNCT
ejpam-5918	40	16	is	be	AUX
ejpam-5918	40	17	the	the	DET
ejpam-5918	40	18	minimum	minimum	ADJ
ejpam-5918	40	19	cardinality	cardinality	NOUN
ejpam-5918	40	20	of	of	ADP
ejpam-5918	40	21	dominating	dominating	NOUN
ejpam-5918	40	22	set	set	NOUN
ejpam-5918	40	23	[	[	X
ejpam-5918	40	24	10	10	NUM
ejpam-5918	40	25	]	]	PUNCT
ejpam-5918	40	26	.	.	PUNCT
ejpam-5918	41	1	a	a	DET
ejpam-5918	41	2	subset	subset	NOUN
ejpam-5918	41	3	s	s	X
ejpam-5918	41	4	of	of	ADP
ejpam-5918	41	5	v	v	NOUN
ejpam-5918	41	6	(	(	PUNCT
ejpam-5918	41	7	g	g	NOUN
ejpam-5918	41	8	)	)	PUNCT
ejpam-5918	41	9	is	be	AUX
ejpam-5918	41	10	a	a	DET
ejpam-5918	41	11	locating	locating	NOUN
ejpam-5918	41	12	set	set	VERB
ejpam-5918	41	13	in	in	ADP
ejpam-5918	41	14	a	a	DET
ejpam-5918	41	15	connected	connected	ADJ
ejpam-5918	41	16	graph	graph	NOUN
ejpam-5918	41	17	g	g	NOUN
ejpam-5918	41	18	if	if	SCONJ
ejpam-5918	41	19	for	for	ADP
ejpam-5918	41	20	any	any	DET
ejpam-5918	41	21	two	two	NUM
ejpam-5918	41	22	distinct	distinct	ADJ
ejpam-5918	41	23	vertices	vertex	NOUN
ejpam-5918	41	24	u	u	NOUN
ejpam-5918	41	25	and	and	CCONJ
ejpam-5918	41	26	v	v	NOUN
ejpam-5918	41	27	in	in	ADP
ejpam-5918	41	28	v	v	NUM
ejpam-5918	41	29	(	(	PUNCT
ejpam-5918	41	30	g	g	NOUN
ejpam-5918	41	31	)	)	PUNCT
ejpam-5918	41	32	\	\	PROPN
ejpam-5918	42	1	s	s	PROPN
ejpam-5918	42	2	,	,	PUNCT
ejpam-5918	42	3	ng(u	ng(u	NOUN
ejpam-5918	42	4	)	)	PUNCT
ejpam-5918	42	5	∩	∩	NOUN
ejpam-5918	42	6	s	s	PART
ejpam-5918	42	7	̸=	̸=	PROPN
ejpam-5918	42	8	ng(v	ng(v	NUM
ejpam-5918	42	9	)	)	PUNCT
ejpam-5918	42	10	∩	∩	NOUN
ejpam-5918	42	11	s	s	PART
ejpam-5918	42	12	[	[	X
ejpam-5918	42	13	7	7	NUM
ejpam-5918	42	14	]	]	PUNCT
ejpam-5918	42	15	.	.	PUNCT
ejpam-5918	43	1	a	a	DET
ejpam-5918	43	2	set	set	NOUN
ejpam-5918	43	3	d	d	NOUN
ejpam-5918	43	4	⊆	⊆	NUM
ejpam-5918	43	5	v	v	NOUN
ejpam-5918	43	6	is	be	AUX
ejpam-5918	43	7	a	a	DET
ejpam-5918	43	8	locating	locate	VERB
ejpam-5918	43	9	-	-	PUNCT
ejpam-5918	43	10	dominating	dominating	NOUN
ejpam-5918	43	11	set	set	NOUN
ejpam-5918	43	12	if	if	SCONJ
ejpam-5918	43	13	it	it	PRON
ejpam-5918	43	14	is	be	AUX
ejpam-5918	43	15	dominating	dominate	VERB
ejpam-5918	43	16	and	and	CCONJ
ejpam-5918	43	17	every	every	DET
ejpam-5918	43	18	two	two	NUM
ejpam-5918	43	19	vertices	vertex	NOUN
ejpam-5918	43	20	x	x	X
ejpam-5918	43	21	,	,	PUNCT
ejpam-5918	43	22	y	y	PROPN
ejpam-5918	43	23	∈	∈	PROPN
ejpam-5918	43	24	v	v	ADP
ejpam-5918	43	25	(	(	PUNCT
ejpam-5918	43	26	g	g	NOUN
ejpam-5918	43	27	)	)	PUNCT
ejpam-5918	43	28	\	\	PROPN
ejpam-5918	44	1	s	s	PROPN
ejpam-5918	44	2	,	,	PUNCT
ejpam-5918	44	3	n(x	n(x	ADJ
ejpam-5918	44	4	)	)	PUNCT
ejpam-5918	44	5	∩	∩	NOUN
ejpam-5918	44	6	d	d	PROPN
ejpam-5918	44	7	̸=	̸=	PROPN
ejpam-5918	44	8	n(y	n(y	PROPN
ejpam-5918	44	9	)	)	PUNCT
ejpam-5918	44	10	∩	∩	PROPN
ejpam-5918	44	11	d.	d.	PROPN
ejpam-5918	44	12	the	the	DET
ejpam-5918	44	13	locating	locate	VERB
ejpam-5918	44	14	-	-	PUNCT
ejpam-5918	44	15	domination	domination	NOUN
ejpam-5918	44	16	number	number	NOUN
ejpam-5918	44	17	,	,	PUNCT
ejpam-5918	44	18	denoted	denote	VERB
ejpam-5918	44	19	by	by	ADP
ejpam-5918	44	20	γl(g	γl(g	NUM
ejpam-5918	44	21	)	)	PUNCT
ejpam-5918	44	22	is	be	AUX
ejpam-5918	44	23	the	the	DET
ejpam-5918	44	24	minimum	minimum	ADJ
ejpam-5918	44	25	cardinality	cardinality	NOUN
ejpam-5918	44	26	of	of	ADP
ejpam-5918	44	27	an	an	DET
ejpam-5918	44	28	locating	locate	VERB
ejpam-5918	44	29	-	-	PUNCT
ejpam-5918	44	30	dominating	dominate	VERB
ejpam-5918	44	31	set	set	NOUN
ejpam-5918	44	32	of	of	ADP
ejpam-5918	44	33	g	g	PROPN
ejpam-5918	44	34	[	[	X
ejpam-5918	44	35	12	12	NUM
ejpam-5918	44	36	]	]	PUNCT
ejpam-5918	44	37	.	.	PUNCT
ejpam-5918	45	1	a	a	DET
ejpam-5918	45	2	gear	gear	NOUN
ejpam-5918	45	3	graph	graph	NOUN
ejpam-5918	45	4	,	,	PUNCT
ejpam-5918	45	5	denoted	denote	VERB
ejpam-5918	45	6	by	by	ADP
ejpam-5918	45	7	gn	gn	PROPN
ejpam-5918	45	8	,	,	PUNCT
ejpam-5918	45	9	is	be	AUX
ejpam-5918	45	10	obtained	obtain	VERB
ejpam-5918	45	11	from	from	ADP
ejpam-5918	45	12	the	the	DET
ejpam-5918	45	13	wheel	wheel	NOUN
ejpam-5918	45	14	graph	graph	NOUN
ejpam-5918	45	15	by	by	ADP
ejpam-5918	45	16	adding	add	VERB
ejpam-5918	45	17	a	a	DET
ejpam-5918	45	18	vertex	vertex	NOUN
ejpam-5918	45	19	between	between	ADP
ejpam-5918	45	20	every	every	DET
ejpam-5918	45	21	pair	pair	NOUN
ejpam-5918	45	22	of	of	ADP
ejpam-5918	45	23	adjacent	adjacent	ADJ
ejpam-5918	45	24	vertices	vertex	NOUN
ejpam-5918	45	25	of	of	ADP
ejpam-5918	45	26	the	the	DET
ejpam-5918	45	27	cycle	cycle	NOUN
ejpam-5918	45	28	[	[	X
ejpam-5918	45	29	16	16	NUM
ejpam-5918	45	30	]	]	PUNCT
ejpam-5918	45	31	.	.	PUNCT
ejpam-5918	46	1	example	example	NOUN
ejpam-5918	47	1	1	1	X
ejpam-5918	47	2	.	.	X
ejpam-5918	47	3	consider	consider	VERB
ejpam-5918	47	4	the	the	DET
ejpam-5918	47	5	wheel	wheel	NOUN
ejpam-5918	47	6	graph	graph	NOUN
ejpam-5918	47	7	w4	w4	NOUN
ejpam-5918	47	8	with	with	ADP
ejpam-5918	47	9	v	v	PROPN
ejpam-5918	47	10	(	(	PUNCT
ejpam-5918	47	11	w4	w4	NOUN
ejpam-5918	47	12	)	)	PUNCT
ejpam-5918	47	13	=	=	PRON
ejpam-5918	47	14	{	{	PUNCT
ejpam-5918	47	15	u}∪{v1	u}∪{v1	ADP
ejpam-5918	47	16	,	,	PUNCT
ejpam-5918	47	17	v2	v2	PROPN
ejpam-5918	47	18	,	,	PUNCT
ejpam-5918	47	19	v3	v3	PROPN
ejpam-5918	47	20	,	,	PUNCT
ejpam-5918	47	21	v4	v4	NOUN
ejpam-5918	47	22	}	}	PUNCT
ejpam-5918	47	23	and	and	CCONJ
ejpam-5918	47	24	e(w4	e(w4	NOUN
ejpam-5918	47	25	)	)	PUNCT
ejpam-5918	48	1	=	=	PRON
ejpam-5918	48	2	{	{	PUNCT
ejpam-5918	48	3	uvi|1	uvi|1	X
ejpam-5918	48	4	≤	≤	NUM
ejpam-5918	48	5	i	i	PRON
ejpam-5918	48	6	≤	≤	ADJ
ejpam-5918	48	7	4	4	NUM
ejpam-5918	48	8	}	}	PUNCT
ejpam-5918	48	9	∪	∪	X
ejpam-5918	48	10	{	{	PUNCT
ejpam-5918	48	11	v1v2	v1v2	NOUN
ejpam-5918	48	12	,	,	PUNCT
ejpam-5918	48	13	v2v3	v2v3	PROPN
ejpam-5918	48	14	,	,	PUNCT
ejpam-5918	48	15	v3	v3	PROPN
ejpam-5918	48	16	,	,	PUNCT
ejpam-5918	48	17	v4	v4	PROPN
ejpam-5918	48	18	,	,	PUNCT
ejpam-5918	48	19	v1v4	v1v4	X
ejpam-5918	48	20	}	}	PUNCT
ejpam-5918	48	21	.	.	PUNCT
ejpam-5918	49	1	the	the	DET
ejpam-5918	49	2	gear	gear	NOUN
ejpam-5918	49	3	graph	graph	NOUN
ejpam-5918	49	4	g4	g4	NOUN
ejpam-5918	49	5	in	in	ADP
ejpam-5918	49	6	figure	figure	NOUN
ejpam-5918	49	7	1	1	NUM
ejpam-5918	49	8	,	,	PUNCT
ejpam-5918	49	9	is	be	AUX
ejpam-5918	49	10	obtained	obtain	VERB
ejpam-5918	49	11	by	by	ADP
ejpam-5918	49	12	adding	add	VERB
ejpam-5918	49	13	vertices	vertex	NOUN
ejpam-5918	49	14	a0	a0	PROPN
ejpam-5918	49	15	,	,	PUNCT
ejpam-5918	49	16	a1	a1	PROPN
ejpam-5918	49	17	,	,	PUNCT
ejpam-5918	49	18	a2	a2	PROPN
ejpam-5918	49	19	,	,	PUNCT
ejpam-5918	49	20	and	and	CCONJ
ejpam-5918	49	21	a3	a3	NOUN
ejpam-5918	49	22	between	between	ADP
ejpam-5918	49	23	the	the	DET
ejpam-5918	49	24	vertices	vertex	NOUN
ejpam-5918	49	25	v1	v1	VERB
ejpam-5918	49	26	and	and	CCONJ
ejpam-5918	49	27	v2	v2	NOUN
ejpam-5918	49	28	,	,	PUNCT
ejpam-5918	49	29	v2	v2	PROPN
ejpam-5918	49	30	and	and	CCONJ
ejpam-5918	49	31	v3	v3	PROPN
ejpam-5918	49	32	,	,	PUNCT
ejpam-5918	49	33	v3	v3	PROPN
ejpam-5918	49	34	and	and	CCONJ
ejpam-5918	49	35	v4	v4	NOUN
ejpam-5918	49	36	,	,	PUNCT
ejpam-5918	49	37	and	and	CCONJ
ejpam-5918	49	38	v4	v4	NOUN
ejpam-5918	49	39	and	and	CCONJ
ejpam-5918	49	40	v1	v1	NOUN
ejpam-5918	49	41	,	,	PUNCT
ejpam-5918	49	42	respectively	respectively	ADV
ejpam-5918	49	43	.	.	PUNCT
ejpam-5918	50	1	i.	i.	PROPN
ejpam-5918	50	2	tropico	tropico	PROPN
ejpam-5918	50	3	,	,	PUNCT
ejpam-5918	50	4	i.	i.	PROPN
ejpam-5918	50	5	cabahug	cabahug	PROPN
ejpam-5918	50	6	,	,	PUNCT
ejpam-5918	50	7	jr	jr	PROPN
ejpam-5918	50	8	.	.	PROPN
ejpam-5918	50	9	/	/	SYM
ejpam-5918	50	10	eur	eur	PROPN
ejpam-5918	50	11	.	.	PUNCT
ejpam-5918	51	1	j.	j.	PROPN
ejpam-5918	51	2	pure	pure	PROPN
ejpam-5918	51	3	appl	appl	PROPN
ejpam-5918	51	4	.	.	PROPN
ejpam-5918	51	5	math	math	PROPN
ejpam-5918	51	6	,	,	PUNCT
ejpam-5918	51	7	18	18	NUM
ejpam-5918	51	8	(	(	PUNCT
ejpam-5918	51	9	2	2	NUM
ejpam-5918	51	10	)	)	PUNCT
ejpam-5918	51	11	(	(	PUNCT
ejpam-5918	51	12	2025	2025	NUM
ejpam-5918	51	13	)	)	PUNCT
ejpam-5918	51	14	,	,	PUNCT
ejpam-5918	51	15	5918	5918	NUM
ejpam-5918	51	16	3	3	NUM
ejpam-5918	51	17	of	of	ADP
ejpam-5918	51	18	21	21	NUM
ejpam-5918	51	19	v1	v1	NOUN
ejpam-5918	51	20	v3	v3	PROPN
ejpam-5918	51	21	v2	v2	PROPN
ejpam-5918	51	22	v4	v4	PROPN
ejpam-5918	51	23	u	u	PROPN
ejpam-5918	51	24	a0	a0	PROPN
ejpam-5918	51	25	a2	a2	PROPN
ejpam-5918	51	26	a1	a1	PROPN
ejpam-5918	51	27	a3	a3	NOUN
ejpam-5918	51	28	figure	figure	NOUN
ejpam-5918	51	29	1	1	NUM
ejpam-5918	51	30	:	:	PUNCT
ejpam-5918	51	31	the	the	DET
ejpam-5918	51	32	gear	gear	NOUN
ejpam-5918	51	33	graph	graph	NOUN
ejpam-5918	51	34	g4	g4	VERB
ejpam-5918	51	35	an	an	DET
ejpam-5918	51	36	banana	banana	NOUN
ejpam-5918	51	37	tree	tree	NOUN
ejpam-5918	51	38	graph	graph	NOUN
ejpam-5918	51	39	is	be	AUX
ejpam-5918	51	40	a	a	DET
ejpam-5918	51	41	graph	graph	NOUN
ejpam-5918	51	42	obtained	obtain	VERB
ejpam-5918	51	43	by	by	ADP
ejpam-5918	51	44	connecting	connect	VERB
ejpam-5918	51	45	one	one	NUM
ejpam-5918	51	46	leaf	leaf	NOUN
ejpam-5918	51	47	to	to	ADP
ejpam-5918	51	48	each	each	PRON
ejpam-5918	51	49	of	of	ADP
ejpam-5918	51	50	n	n	NOUN
ejpam-5918	51	51	copies	copy	NOUN
ejpam-5918	51	52	of	of	ADP
ejpam-5918	51	53	a	a	DET
ejpam-5918	51	54	star	star	NOUN
ejpam-5918	51	55	graph	graph	NOUN
ejpam-5918	51	56	k1,k	k1,k	PROPN
ejpam-5918	51	57	with	with	ADP
ejpam-5918	51	58	a	a	DET
ejpam-5918	51	59	single	single	ADJ
ejpam-5918	51	60	root	root	NOUN
ejpam-5918	51	61	vertex	vertex	NOUN
ejpam-5918	51	62	that	that	PRON
ejpam-5918	51	63	is	be	AUX
ejpam-5918	51	64	distinct	distinct	ADJ
ejpam-5918	51	65	from	from	ADP
ejpam-5918	51	66	all	all	DET
ejpam-5918	51	67	the	the	DET
ejpam-5918	51	68	stars	star	NOUN
ejpam-5918	51	69	,	,	PUNCT
ejpam-5918	51	70	denoted	denote	VERB
ejpam-5918	51	71	by	by	ADP
ejpam-5918	51	72	bn	bn	PROPN
ejpam-5918	51	73	,	,	PUNCT
ejpam-5918	51	74	k+1	k+1	X
ejpam-5918	52	1	[	[	X
ejpam-5918	52	2	17	17	NUM
ejpam-5918	52	3	]	]	PUNCT
ejpam-5918	52	4	.	.	PUNCT
ejpam-5918	52	5	example	example	NOUN
ejpam-5918	53	1	2	2	NUM
ejpam-5918	53	2	.	.	X
ejpam-5918	53	3	consider	consider	VERB
ejpam-5918	53	4	the	the	DET
ejpam-5918	53	5	star	star	NOUN
ejpam-5918	53	6	graph	graph	NOUN
ejpam-5918	53	7	k1,3	k1,3	X
ejpam-5918	53	8	with	with	ADP
ejpam-5918	53	9	v	v	PROPN
ejpam-5918	53	10	(	(	PUNCT
ejpam-5918	53	11	k1,3	k1,3	PROPN
ejpam-5918	53	12	)	)	PUNCT
ejpam-5918	53	13	=	=	PRON
ejpam-5918	53	14	{	{	PUNCT
ejpam-5918	53	15	x1	x1	PROPN
ejpam-5918	53	16	,	,	PUNCT
ejpam-5918	53	17	y1	y1	PROPN
ejpam-5918	53	18	,	,	PUNCT
ejpam-5918	53	19	y2	y2	PROPN
ejpam-5918	53	20	,	,	PUNCT
ejpam-5918	53	21	y3	y3	PROPN
ejpam-5918	53	22	}	}	PUNCT
ejpam-5918	53	23	.	.	PUNCT
ejpam-5918	54	1	then	then	ADV
ejpam-5918	54	2	in	in	ADP
ejpam-5918	54	3	figure	figure	NOUN
ejpam-5918	54	4	2	2	NUM
ejpam-5918	54	5	is	be	AUX
ejpam-5918	54	6	a	a	DET
ejpam-5918	54	7	banana	banana	NOUN
ejpam-5918	54	8	tree	tree	NOUN
ejpam-5918	54	9	graph	graph	NOUN
ejpam-5918	54	10	b3,4	b3,4	ADJ
ejpam-5918	54	11	obtained	obtain	VERB
ejpam-5918	54	12	by	by	ADP
ejpam-5918	54	13	connecting	connect	VERB
ejpam-5918	54	14	one	one	NUM
ejpam-5918	54	15	leaf	leaf	NOUN
ejpam-5918	54	16	of	of	ADP
ejpam-5918	54	17	three	three	NUM
ejpam-5918	54	18	copies	copy	NOUN
ejpam-5918	54	19	of	of	ADP
ejpam-5918	54	20	star	star	NOUN
ejpam-5918	54	21	k1,3	k1,3	PROPN
ejpam-5918	54	22	with	with	ADP
ejpam-5918	54	23	a	a	DET
ejpam-5918	54	24	single	single	ADJ
ejpam-5918	54	25	root	root	NOUN
ejpam-5918	54	26	vertex	vertex	NOUN
ejpam-5918	54	27	u.	u.	PROPN
ejpam-5918	54	28	x1,1	x1,1	PROPN
ejpam-5918	54	29	x1,3x1,2	x1,3x1,2	NUM
ejpam-5918	55	1	u	u	NOUN
ejpam-5918	55	2	y2,1	y2,1	PROPN
ejpam-5918	55	3	y1,1	y1,1	PROPN
ejpam-5918	55	4	y3,1	y3,1	PROPN
ejpam-5918	56	1	y2,2	y2,2	PROPN
ejpam-5918	56	2	y1,2	y1,2	PROPN
ejpam-5918	56	3	y3,2	y3,2	NOUN
ejpam-5918	57	1	y2,3	y2,3	NOUN
ejpam-5918	57	2	y1,3	y1,3	VERB
ejpam-5918	57	3	y3,3	y3,3	NOUN
ejpam-5918	57	4	figure	figure	NOUN
ejpam-5918	57	5	2	2	NUM
ejpam-5918	57	6	:	:	PUNCT
ejpam-5918	57	7	the	the	DET
ejpam-5918	57	8	banana	banana	NOUN
ejpam-5918	57	9	tree	tree	NOUN
ejpam-5918	57	10	graph	graph	NOUN
ejpam-5918	57	11	b3,4	b3,4	VERB
ejpam-5918	57	12	a	a	DET
ejpam-5918	57	13	lollipop	lollipop	NOUN
ejpam-5918	57	14	graph	graph	NOUN
ejpam-5918	57	15	is	be	AUX
ejpam-5918	57	16	the	the	DET
ejpam-5918	57	17	graph	graph	NOUN
ejpam-5918	57	18	obtained	obtain	VERB
ejpam-5918	57	19	by	by	ADP
ejpam-5918	57	20	joining	join	VERB
ejpam-5918	57	21	a	a	DET
ejpam-5918	57	22	complete	complete	ADJ
ejpam-5918	57	23	graph	graph	NOUN
ejpam-5918	57	24	km	km	NOUN
ejpam-5918	57	25	to	to	ADP
ejpam-5918	57	26	path	path	NOUN
ejpam-5918	57	27	graph	graph	NOUN
ejpam-5918	57	28	pn	pn	PROPN
ejpam-5918	57	29	with	with	ADP
ejpam-5918	57	30	a	a	DET
ejpam-5918	57	31	bridge	bridge	NOUN
ejpam-5918	57	32	,	,	PUNCT
ejpam-5918	57	33	denoted	denote	VERB
ejpam-5918	57	34	by	by	ADP
ejpam-5918	57	35	lm	lm	NOUN
ejpam-5918	57	36	,	,	PUNCT
ejpam-5918	57	37	n	n	PROPN
ejpam-5918	57	38	[	[	X
ejpam-5918	57	39	17	17	NUM
ejpam-5918	57	40	]	]	PUNCT
ejpam-5918	57	41	.	.	PUNCT
ejpam-5918	58	1	example	example	NOUN
ejpam-5918	59	1	3	3	X
ejpam-5918	59	2	.	.	X
ejpam-5918	59	3	consider	consider	VERB
ejpam-5918	59	4	the	the	DET
ejpam-5918	59	5	complete	complete	ADJ
ejpam-5918	59	6	graph	graph	NOUN
ejpam-5918	59	7	k3	k3	VERB
ejpam-5918	59	8	with	with	ADP
ejpam-5918	59	9	v	v	NOUN
ejpam-5918	59	10	(	(	PUNCT
ejpam-5918	59	11	k3	k3	PROPN
ejpam-5918	59	12	)	)	PUNCT
ejpam-5918	59	13	=	=	SYM
ejpam-5918	59	14	{	{	PUNCT
ejpam-5918	59	15	v1	v1	PROPN
ejpam-5918	59	16	,	,	PUNCT
ejpam-5918	59	17	v2	v2	PROPN
ejpam-5918	59	18	,	,	PUNCT
ejpam-5918	59	19	v3	v3	PROPN
ejpam-5918	59	20	}	}	PUNCT
ejpam-5918	59	21	and	and	CCONJ
ejpam-5918	59	22	a	a	DET
ejpam-5918	59	23	path	path	NOUN
ejpam-5918	59	24	graph	graph	NOUN
ejpam-5918	59	25	p4	p4	ADJ
ejpam-5918	59	26	with	with	ADP
ejpam-5918	59	27	v	v	NOUN
ejpam-5918	59	28	(	(	PUNCT
ejpam-5918	59	29	p4	p4	ADJ
ejpam-5918	59	30	)	)	PUNCT
ejpam-5918	59	31	=	=	PUNCT
ejpam-5918	59	32	{	{	PUNCT
ejpam-5918	59	33	x1	x1	PROPN
ejpam-5918	59	34	,	,	PUNCT
ejpam-5918	59	35	x2	x2	PROPN
ejpam-5918	59	36	,	,	PUNCT
ejpam-5918	59	37	x3	x3	ADJ
ejpam-5918	59	38	,	,	PUNCT
ejpam-5918	59	39	x4	x4	PROPN
ejpam-5918	59	40	}	}	PUNCT
ejpam-5918	59	41	.	.	PUNCT
ejpam-5918	60	1	then	then	ADV
ejpam-5918	60	2	in	in	ADP
ejpam-5918	60	3	figure	figure	NOUN
ejpam-5918	60	4	3	3	NUM
ejpam-5918	60	5	is	be	AUX
ejpam-5918	60	6	a	a	DET
ejpam-5918	60	7	lollipop	lollipop	NOUN
ejpam-5918	60	8	graph	graph	NOUN
ejpam-5918	60	9	l3,4	l3,4	PROPN
ejpam-5918	60	10	obtained	obtain	VERB
ejpam-5918	60	11	from	from	ADP
ejpam-5918	60	12	joining	join	VERB
ejpam-5918	60	13	the	the	DET
ejpam-5918	60	14	vertex	vertex	NOUN
ejpam-5918	60	15	v3	v3	PROPN
ejpam-5918	60	16	and	and	CCONJ
ejpam-5918	60	17	x1	x1	PROPN
ejpam-5918	60	18	.	.	PUNCT
ejpam-5918	61	1	v1	v1	PROPN
ejpam-5918	61	2	v2	v2	PROPN
ejpam-5918	61	3	v3	v3	PROPN
ejpam-5918	61	4	x1	x1	PROPN
ejpam-5918	62	1	x2	x2	PROPN
ejpam-5918	62	2	x3	x3	PROPN
ejpam-5918	62	3	x4	x4	PROPN
ejpam-5918	62	4	figure	figure	NOUN
ejpam-5918	62	5	3	3	NUM
ejpam-5918	62	6	:	:	PUNCT
ejpam-5918	62	7	the	the	DET
ejpam-5918	62	8	lollipop	lollipop	NOUN
ejpam-5918	62	9	graph	graph	NOUN
ejpam-5918	62	10	l3,4	l3,4	PROPN
ejpam-5918	62	11	i.	i.	PROPN
ejpam-5918	62	12	tropico	tropico	PROPN
ejpam-5918	62	13	,	,	PUNCT
ejpam-5918	62	14	i.	i.	PROPN
ejpam-5918	62	15	cabahug	cabahug	PROPN
ejpam-5918	62	16	,	,	PUNCT
ejpam-5918	62	17	jr	jr	PROPN
ejpam-5918	62	18	.	.	PROPN
ejpam-5918	62	19	/	/	SYM
ejpam-5918	62	20	eur	eur	PROPN
ejpam-5918	62	21	.	.	PUNCT
ejpam-5918	63	1	j.	j.	PROPN
ejpam-5918	63	2	pure	pure	PROPN
ejpam-5918	63	3	appl	appl	PROPN
ejpam-5918	63	4	.	.	PROPN
ejpam-5918	63	5	math	math	PROPN
ejpam-5918	63	6	,	,	PUNCT
ejpam-5918	63	7	18	18	NUM
ejpam-5918	63	8	(	(	PUNCT
ejpam-5918	63	9	2	2	NUM
ejpam-5918	63	10	)	)	PUNCT
ejpam-5918	63	11	(	(	PUNCT
ejpam-5918	63	12	2025	2025	NUM
ejpam-5918	63	13	)	)	PUNCT
ejpam-5918	63	14	,	,	PUNCT
ejpam-5918	63	15	5918	5918	NUM
ejpam-5918	63	16	4	4	NUM
ejpam-5918	63	17	of	of	ADP
ejpam-5918	63	18	21	21	NUM
ejpam-5918	63	19	the	the	DET
ejpam-5918	63	20	total	total	ADJ
ejpam-5918	63	21	graph	graph	NOUN
ejpam-5918	63	22	t	t	PROPN
ejpam-5918	63	23	(	(	PUNCT
ejpam-5918	63	24	g	g	NOUN
ejpam-5918	63	25	)	)	PUNCT
ejpam-5918	63	26	of	of	ADP
ejpam-5918	63	27	a	a	DET
ejpam-5918	63	28	graph	graph	NOUN
ejpam-5918	63	29	g	g	NOUN
ejpam-5918	63	30	,	,	PUNCT
ejpam-5918	63	31	is	be	AUX
ejpam-5918	63	32	a	a	DET
ejpam-5918	63	33	graph	graph	NOUN
ejpam-5918	63	34	g	g	ADP
ejpam-5918	63	35	such	such	ADJ
ejpam-5918	63	36	that	that	SCONJ
ejpam-5918	63	37	the	the	DET
ejpam-5918	63	38	vertices	vertex	NOUN
ejpam-5918	63	39	set	set	VERB
ejpam-5918	63	40	of	of	ADP
ejpam-5918	63	41	t	t	PROPN
ejpam-5918	63	42	(	(	PUNCT
ejpam-5918	63	43	g	g	NOUN
ejpam-5918	63	44	)	)	PUNCT
ejpam-5918	63	45	corresponds	correspond	VERB
ejpam-5918	63	46	to	to	ADP
ejpam-5918	63	47	the	the	DET
ejpam-5918	63	48	vertices	vertex	NOUN
ejpam-5918	63	49	and	and	CCONJ
ejpam-5918	63	50	edges	edge	NOUN
ejpam-5918	63	51	of	of	ADP
ejpam-5918	63	52	g	g	NOUN
ejpam-5918	63	53	and	and	CCONJ
ejpam-5918	63	54	two	two	NUM
ejpam-5918	63	55	vertices	vertex	NOUN
ejpam-5918	63	56	are	be	AUX
ejpam-5918	63	57	adjacent	adjacent	ADJ
ejpam-5918	63	58	in	in	ADP
ejpam-5918	63	59	t	t	PROPN
ejpam-5918	63	60	(	(	PUNCT
ejpam-5918	63	61	g	g	NOUN
ejpam-5918	63	62	)	)	PUNCT
ejpam-5918	64	1	if	if	SCONJ
ejpam-5918	64	2	and	and	CCONJ
ejpam-5918	64	3	only	only	ADV
ejpam-5918	64	4	if	if	SCONJ
ejpam-5918	64	5	their	their	PRON
ejpam-5918	64	6	corresponding	correspond	VERB
ejpam-5918	64	7	elements	element	NOUN
ejpam-5918	64	8	are	be	AUX
ejpam-5918	64	9	either	either	CCONJ
ejpam-5918	64	10	adjacent	adjacent	ADJ
ejpam-5918	64	11	or	or	CCONJ
ejpam-5918	64	12	incident	incident	NOUN
ejpam-5918	64	13	in	in	ADP
ejpam-5918	64	14	g.	g.	PROPN
ejpam-5918	64	15	the	the	DET
ejpam-5918	64	16	total	total	ADJ
ejpam-5918	64	17	graph	graph	NOUN
ejpam-5918	64	18	has	have	VERB
ejpam-5918	64	19	a	a	DET
ejpam-5918	64	20	vertex	vertex	NOUN
ejpam-5918	64	21	set	set	VERB
ejpam-5918	64	22	v	v	NOUN
ejpam-5918	64	23	(	(	PUNCT
ejpam-5918	64	24	t	t	PROPN
ejpam-5918	64	25	(	(	PUNCT
ejpam-5918	64	26	g	g	NOUN
ejpam-5918	64	27	)	)	PUNCT
ejpam-5918	64	28	)	)	PUNCT
ejpam-5918	65	1	=	=	SYM
ejpam-5918	65	2	v	v	X
ejpam-5918	65	3	(	(	PUNCT
ejpam-5918	65	4	g	g	NOUN
ejpam-5918	65	5	)	)	PUNCT
ejpam-5918	65	6	∪	∪	ADP
ejpam-5918	65	7	e(g	e(g	PROPN
ejpam-5918	65	8	)	)	PUNCT
ejpam-5918	66	1	[	[	X
ejpam-5918	66	2	18	18	NUM
ejpam-5918	66	3	]	]	PUNCT
ejpam-5918	66	4	.	.	PUNCT
ejpam-5918	66	5	example	example	NOUN
ejpam-5918	66	6	4	4	X
ejpam-5918	66	7	.	.	PUNCT
ejpam-5918	67	1	consider	consider	VERB
ejpam-5918	67	2	the	the	DET
ejpam-5918	67	3	path	path	NOUN
ejpam-5918	67	4	graph	graph	NOUN
ejpam-5918	67	5	p4	p4	ADJ
ejpam-5918	67	6	,	,	PUNCT
ejpam-5918	67	7	v	v	NOUN
ejpam-5918	67	8	(	(	PUNCT
ejpam-5918	67	9	p4	p4	ADJ
ejpam-5918	67	10	)	)	PUNCT
ejpam-5918	67	11	=	=	SYM
ejpam-5918	67	12	{	{	PUNCT
ejpam-5918	67	13	v1	v1	PROPN
ejpam-5918	67	14	,	,	PUNCT
ejpam-5918	67	15	v2	v2	PROPN
ejpam-5918	67	16	,	,	PUNCT
ejpam-5918	67	17	v3	v3	PROPN
ejpam-5918	67	18	,	,	PUNCT
ejpam-5918	67	19	v4	v4	PROPN
ejpam-5918	67	20	}	}	PUNCT
ejpam-5918	67	21	and	and	CCONJ
ejpam-5918	67	22	e(p4	e(p4	NOUN
ejpam-5918	67	23	)	)	PUNCT
ejpam-5918	68	1	=	=	PRON
ejpam-5918	68	2	{	{	PUNCT
ejpam-5918	68	3	e1	e1	PROPN
ejpam-5918	68	4	,	,	PUNCT
ejpam-5918	68	5	e2	e2	PROPN
ejpam-5918	68	6	,	,	PUNCT
ejpam-5918	68	7	e3	e3	NOUN
ejpam-5918	68	8	}	}	PUNCT
ejpam-5918	68	9	such	such	ADJ
ejpam-5918	68	10	that	that	DET
ejpam-5918	68	11	e1	e1	NOUN
ejpam-5918	68	12	=	=	SYM
ejpam-5918	68	13	v1v2	v1v2	X
ejpam-5918	68	14	,	,	PUNCT
ejpam-5918	68	15	e2	e2	PROPN
ejpam-5918	68	16	=	=	SYM
ejpam-5918	68	17	v2v3	v2v3	PROPN
ejpam-5918	68	18	,	,	PUNCT
ejpam-5918	68	19	and	and	CCONJ
ejpam-5918	68	20	e3	e3	NOUN
ejpam-5918	68	21	=	=	SYM
ejpam-5918	68	22	v3v4	v3v4	PROPN
ejpam-5918	68	23	.	.	PUNCT
ejpam-5918	69	1	then	then	ADV
ejpam-5918	69	2	in	in	ADP
ejpam-5918	69	3	figure	figure	NOUN
ejpam-5918	69	4	4	4	NUM
ejpam-5918	69	5	is	be	AUX
ejpam-5918	69	6	the	the	DET
ejpam-5918	69	7	total	total	ADJ
ejpam-5918	69	8	graph	graph	NOUN
ejpam-5918	69	9	of	of	ADP
ejpam-5918	69	10	path	path	NOUN
ejpam-5918	69	11	graph	graph	NOUN
ejpam-5918	69	12	p4	p4	ADJ
ejpam-5918	69	13	,	,	PUNCT
ejpam-5918	69	14	denoted	denote	VERB
ejpam-5918	69	15	by	by	ADP
ejpam-5918	69	16	t	t	PROPN
ejpam-5918	69	17	(	(	PUNCT
ejpam-5918	69	18	p4	p4	ADJ
ejpam-5918	69	19	)	)	PUNCT
ejpam-5918	69	20	has	have	VERB
ejpam-5918	69	21	v	v	X
ejpam-5918	69	22	(	(	PUNCT
ejpam-5918	69	23	t	t	PROPN
ejpam-5918	69	24	(	(	PUNCT
ejpam-5918	69	25	p4	p4	ADJ
ejpam-5918	69	26	)	)	PUNCT
ejpam-5918	69	27	)	)	PUNCT
ejpam-5918	70	1	=	=	PRON
ejpam-5918	70	2	{	{	PUNCT
ejpam-5918	70	3	v1	v1	PROPN
ejpam-5918	70	4	,	,	PUNCT
ejpam-5918	70	5	v2	v2	PROPN
ejpam-5918	70	6	,	,	PUNCT
ejpam-5918	70	7	v3	v3	PROPN
ejpam-5918	70	8	,	,	PUNCT
ejpam-5918	70	9	v4	v4	PROPN
ejpam-5918	70	10	,	,	PUNCT
ejpam-5918	70	11	e1	e1	PROPN
ejpam-5918	70	12	,	,	PUNCT
ejpam-5918	70	13	e2	e2	PROPN
ejpam-5918	70	14	,	,	PUNCT
ejpam-5918	70	15	e3	e3	NOUN
ejpam-5918	70	16	}	}	PUNCT
ejpam-5918	70	17	with	with	ADP
ejpam-5918	70	18	each	each	PRON
ejpam-5918	70	19	of	of	ADP
ejpam-5918	70	20	the	the	DET
ejpam-5918	70	21	vertices	vertex	NOUN
ejpam-5918	70	22	in	in	ADP
ejpam-5918	70	23	the	the	DET
ejpam-5918	70	24	vertex	vertex	NOUN
ejpam-5918	70	25	set	set	NOUN
ejpam-5918	70	26	of	of	ADP
ejpam-5918	70	27	t	t	PROPN
ejpam-5918	70	28	(	(	PUNCT
ejpam-5918	70	29	p4	p4	ADJ
ejpam-5918	70	30	)	)	PUNCT
ejpam-5918	70	31	is	be	AUX
ejpam-5918	70	32	joined	join	VERB
ejpam-5918	70	33	by	by	ADP
ejpam-5918	70	34	an	an	DET
ejpam-5918	70	35	edge	edge	NOUN
ejpam-5918	70	36	if	if	SCONJ
ejpam-5918	70	37	it	it	PRON
ejpam-5918	70	38	is	be	AUX
ejpam-5918	70	39	adjacent	adjacent	ADJ
ejpam-5918	70	40	or	or	CCONJ
ejpam-5918	70	41	incident	incident	NOUN
ejpam-5918	70	42	in	in	ADP
ejpam-5918	70	43	p4	p4	ADJ
ejpam-5918	70	44	.	.	PUNCT
ejpam-5918	71	1	v1	v1	PROPN
ejpam-5918	71	2	v2	v2	PROPN
ejpam-5918	71	3	v3	v3	PROPN
ejpam-5918	71	4	v4	v4	PROPN
ejpam-5918	71	5	e1	e1	PROPN
ejpam-5918	71	6	e2	e2	PROPN
ejpam-5918	71	7	e3	e3	NOUN
ejpam-5918	71	8	figure	figure	NOUN
ejpam-5918	71	9	4	4	NUM
ejpam-5918	71	10	:	:	PUNCT
ejpam-5918	71	11	the	the	DET
ejpam-5918	71	12	total	total	ADJ
ejpam-5918	71	13	graph	graph	NOUN
ejpam-5918	71	14	of	of	ADP
ejpam-5918	71	15	path	path	NOUN
ejpam-5918	71	16	graph	graph	NOUN
ejpam-5918	71	17	p4	p4	ADJ
ejpam-5918	71	18	the	the	DET
ejpam-5918	71	19	shadow	shadow	NOUN
ejpam-5918	71	20	graph	graph	NOUN
ejpam-5918	71	21	s(g	s(g	PROPN
ejpam-5918	71	22	)	)	PUNCT
ejpam-5918	71	23	of	of	ADP
ejpam-5918	71	24	a	a	DET
ejpam-5918	71	25	graph	graph	NOUN
ejpam-5918	71	26	g	g	NOUN
ejpam-5918	71	27	is	be	AUX
ejpam-5918	71	28	obtained	obtain	VERB
ejpam-5918	71	29	from	from	ADP
ejpam-5918	71	30	g	g	NOUN
ejpam-5918	71	31	by	by	ADP
ejpam-5918	71	32	adding	add	VERB
ejpam-5918	71	33	,	,	PUNCT
ejpam-5918	71	34	for	for	ADP
ejpam-5918	71	35	each	each	DET
ejpam-5918	71	36	vertex	vertex	NOUN
ejpam-5918	71	37	v	v	NOUN
ejpam-5918	71	38	of	of	ADP
ejpam-5918	71	39	g	g	NOUN
ejpam-5918	71	40	,	,	PUNCT
ejpam-5918	71	41	a	a	DET
ejpam-5918	71	42	new	new	ADJ
ejpam-5918	71	43	vertex	vertex	NOUN
ejpam-5918	71	44	v′	v′	NOUN
ejpam-5918	71	45	,	,	PUNCT
ejpam-5918	71	46	called	call	VERB
ejpam-5918	71	47	the	the	DET
ejpam-5918	71	48	shadow	shadow	NOUN
ejpam-5918	71	49	vertex	vertex	NOUN
ejpam-5918	71	50	of	of	ADP
ejpam-5918	71	51	v	v	NOUN
ejpam-5918	71	52	,	,	PUNCT
ejpam-5918	71	53	and	and	CCONJ
ejpam-5918	71	54	joining	join	VERB
ejpam-5918	71	55	v′	v′	NOUN
ejpam-5918	71	56	to	to	ADP
ejpam-5918	71	57	the	the	DET
ejpam-5918	71	58	neighbors	neighbor	NOUN
ejpam-5918	71	59	of	of	ADP
ejpam-5918	71	60	v	v	NUM
ejpam-5918	71	61	in	in	ADP
ejpam-5918	71	62	g.	g.	PROPN
ejpam-5918	71	63	the	the	DET
ejpam-5918	71	64	set	set	NOUN
ejpam-5918	71	65	of	of	ADP
ejpam-5918	71	66	all	all	DET
ejpam-5918	71	67	shadow	shadow	NOUN
ejpam-5918	71	68	vertices	vertex	NOUN
ejpam-5918	71	69	is	be	AUX
ejpam-5918	71	70	denoted	denote	VERB
ejpam-5918	71	71	by	by	ADP
ejpam-5918	71	72	v	v	NOUN
ejpam-5918	71	73	′(g	′(g	NOUN
ejpam-5918	71	74	)	)	PUNCT
ejpam-5918	72	1	[	[	X
ejpam-5918	72	2	4	4	NUM
ejpam-5918	72	3	]	]	PUNCT
ejpam-5918	72	4	.	.	PUNCT
ejpam-5918	72	5	example	example	NOUN
ejpam-5918	72	6	5	5	NUM
ejpam-5918	72	7	.	.	PUNCT
ejpam-5918	73	1	consider	consider	VERB
ejpam-5918	73	2	the	the	DET
ejpam-5918	73	3	path	path	NOUN
ejpam-5918	73	4	graph	graph	NOUN
ejpam-5918	73	5	p4	p4	ADJ
ejpam-5918	73	6	in	in	ADP
ejpam-5918	73	7	figure	figure	NOUN
ejpam-5918	73	8	4	4	NUM
ejpam-5918	73	9	with	with	ADP
ejpam-5918	73	10	v	v	NOUN
ejpam-5918	73	11	(	(	PUNCT
ejpam-5918	73	12	p4	p4	ADJ
ejpam-5918	73	13	)	)	PUNCT
ejpam-5918	73	14	=	=	SYM
ejpam-5918	73	15	{	{	PUNCT
ejpam-5918	73	16	v1	v1	PROPN
ejpam-5918	73	17	,	,	PUNCT
ejpam-5918	73	18	v2	v2	PROPN
ejpam-5918	73	19	,	,	PUNCT
ejpam-5918	73	20	v3	v3	PROPN
ejpam-5918	73	21	,	,	PUNCT
ejpam-5918	73	22	v4	v4	PROPN
ejpam-5918	73	23	}	}	PUNCT
ejpam-5918	73	24	.	.	PUNCT
ejpam-5918	74	1	then	then	ADV
ejpam-5918	74	2	the	the	DET
ejpam-5918	74	3	shadow	shadow	NOUN
ejpam-5918	74	4	graph	graph	NOUN
ejpam-5918	74	5	of	of	ADP
ejpam-5918	74	6	path	path	NOUN
ejpam-5918	74	7	graph	graph	NOUN
ejpam-5918	74	8	p4	p4	NOUN
ejpam-5918	74	9	is	be	AUX
ejpam-5918	74	10	shown	show	VERB
ejpam-5918	74	11	in	in	ADP
ejpam-5918	74	12	figure	figure	NOUN
ejpam-5918	74	13	5	5	NUM
ejpam-5918	74	14	with	with	ADP
ejpam-5918	74	15	v	v	NOUN
ejpam-5918	74	16	′(p4	′(p4	NOUN
ejpam-5918	74	17	)	)	PUNCT
ejpam-5918	75	1	=	=	PRON
ejpam-5918	75	2	{	{	PUNCT
ejpam-5918	75	3	v′1	v′1	ADJ
ejpam-5918	75	4	,	,	PUNCT
ejpam-5918	75	5	v′2	v′2	ADJ
ejpam-5918	75	6	,	,	PUNCT
ejpam-5918	75	7	v′3	v′3	NOUN
ejpam-5918	75	8	,	,	PUNCT
ejpam-5918	75	9	v′4	v′4	NOUN
ejpam-5918	75	10	}	}	PUNCT
ejpam-5918	75	11	.	.	PUNCT
ejpam-5918	76	1	v1	v1	PROPN
ejpam-5918	76	2	v2	v2	PROPN
ejpam-5918	76	3	v3	v3	PROPN
ejpam-5918	76	4	v4	v4	PROPN
ejpam-5918	76	5	v′1	v′1	PROPN
ejpam-5918	76	6	v′2	v′2	PROPN
ejpam-5918	76	7	v′3	v′3	PROPN
ejpam-5918	76	8	v′4	v′4	NOUN
ejpam-5918	76	9	figure	figure	NOUN
ejpam-5918	76	10	5	5	NUM
ejpam-5918	76	11	:	:	PUNCT
ejpam-5918	76	12	the	the	DET
ejpam-5918	76	13	shadow	shadow	NOUN
ejpam-5918	76	14	graph	graph	NOUN
ejpam-5918	76	15	of	of	ADP
ejpam-5918	76	16	path	path	NOUN
ejpam-5918	76	17	graph	graph	NOUN
ejpam-5918	76	18	p4	p4	ADJ
ejpam-5918	76	19	3	3	NUM
ejpam-5918	76	20	.	.	PUNCT
ejpam-5918	76	21	known	know	VERB
ejpam-5918	76	22	result	result	NOUN
ejpam-5918	76	23	corollary	corollary	NOUN
ejpam-5918	76	24	1	1	NUM
ejpam-5918	76	25	.	.	PUNCT
ejpam-5918	77	1	[	[	X
ejpam-5918	77	2	19	19	NUM
ejpam-5918	77	3	]	]	PUNCT
ejpam-5918	77	4	let	let	VERB
ejpam-5918	77	5	g	g	PRON
ejpam-5918	77	6	be	be	AUX
ejpam-5918	77	7	a	a	DET
ejpam-5918	77	8	connected	connected	ADJ
ejpam-5918	77	9	graph	graph	NOUN
ejpam-5918	77	10	of	of	ADP
ejpam-5918	77	11	order	order	NOUN
ejpam-5918	77	12	m	m	ADV
ejpam-5918	77	13	,	,	PUNCT
ejpam-5918	77	14	and	and	CCONJ
ejpam-5918	77	15	let	let	VERB
ejpam-5918	77	16	h	h	NOUN
ejpam-5918	77	17	be	be	AUX
ejpam-5918	77	18	any	any	DET
ejpam-5918	77	19	graph	graph	NOUN
ejpam-5918	77	20	of	of	ADP
ejpam-5918	77	21	order	order	NOUN
ejpam-5918	77	22	n.	n.	NOUN
ejpam-5918	77	23	then	then	ADV
ejpam-5918	77	24	,	,	PUNCT
ejpam-5918	77	25	γ(g	γ(g	PROPN
ejpam-5918	77	26	◦	◦	NOUN
ejpam-5918	77	27	h	h	NOUN
ejpam-5918	77	28	)	)	PUNCT
ejpam-5918	77	29	=	=	NUM
ejpam-5918	77	30	m	m	PROPN
ejpam-5918	77	31	,	,	PUNCT
ejpam-5918	77	32	where	where	SCONJ
ejpam-5918	77	33	γ(g	γ(g	PROPN
ejpam-5918	77	34	◦	◦	NOUN
ejpam-5918	77	35	h	h	NOUN
ejpam-5918	77	36	)	)	PUNCT
ejpam-5918	77	37	represents	represent	VERB
ejpam-5918	77	38	the	the	DET
ejpam-5918	77	39	domination	domination	NOUN
ejpam-5918	77	40	number	number	NOUN
ejpam-5918	77	41	of	of	ADP
ejpam-5918	77	42	the	the	DET
ejpam-5918	77	43	corona	corona	NOUN
ejpam-5918	77	44	product	product	NOUN
ejpam-5918	77	45	g	g	PROPN
ejpam-5918	77	46	◦	◦	PROPN
ejpam-5918	77	47	h.	h.	PROPN
ejpam-5918	77	48	i.	i.	PROPN
ejpam-5918	77	49	tropico	tropico	PROPN
ejpam-5918	77	50	,	,	PUNCT
ejpam-5918	77	51	i.	i.	PROPN
ejpam-5918	77	52	cabahug	cabahug	PROPN
ejpam-5918	77	53	,	,	PUNCT
ejpam-5918	77	54	jr	jr	PROPN
ejpam-5918	77	55	.	.	PROPN
ejpam-5918	77	56	/	/	SYM
ejpam-5918	77	57	eur	eur	PROPN
ejpam-5918	77	58	.	.	PUNCT
ejpam-5918	78	1	j.	j.	PROPN
ejpam-5918	78	2	pure	pure	PROPN
ejpam-5918	78	3	appl	appl	PROPN
ejpam-5918	78	4	.	.	PROPN
ejpam-5918	78	5	math	math	PROPN
ejpam-5918	78	6	,	,	PUNCT
ejpam-5918	78	7	18	18	NUM
ejpam-5918	78	8	(	(	PUNCT
ejpam-5918	78	9	2	2	NUM
ejpam-5918	78	10	)	)	PUNCT
ejpam-5918	78	11	(	(	PUNCT
ejpam-5918	78	12	2025	2025	NUM
ejpam-5918	78	13	)	)	PUNCT
ejpam-5918	78	14	,	,	PUNCT
ejpam-5918	78	15	5918	5918	NUM
ejpam-5918	78	16	5	5	NUM
ejpam-5918	78	17	of	of	ADP
ejpam-5918	78	18	21	21	NUM
ejpam-5918	78	19	4	4	NUM
ejpam-5918	78	20	.	.	PUNCT
ejpam-5918	78	21	results	result	VERB
ejpam-5918	78	22	this	this	DET
ejpam-5918	78	23	paper	paper	NOUN
ejpam-5918	78	24	uses	use	VERB
ejpam-5918	78	25	the	the	DET
ejpam-5918	78	26	following	follow	VERB
ejpam-5918	78	27	terms	term	NOUN
ejpam-5918	78	28	to	to	PART
ejpam-5918	78	29	denote	denote	VERB
ejpam-5918	78	30	specific	specific	ADJ
ejpam-5918	78	31	concepts	concept	NOUN
ejpam-5918	78	32	:	:	PUNCT
ejpam-5918	78	33	degi(v	degi(v	NOUN
ejpam-5918	78	34	)	)	PUNCT
ejpam-5918	78	35	represents	represent	VERB
ejpam-5918	78	36	the	the	DET
ejpam-5918	78	37	degree	degree	NOUN
ejpam-5918	78	38	of	of	ADP
ejpam-5918	78	39	vertex	vertex	NOUN
ejpam-5918	78	40	v	v	NOUN
ejpam-5918	78	41	within	within	ADP
ejpam-5918	78	42	the	the	DET
ejpam-5918	78	43	set	set	NOUN
ejpam-5918	78	44	i	i	PROPN
ejpam-5918	78	45	,	,	PUNCT
ejpam-5918	78	46	ni(v	ni(v	NOUN
ejpam-5918	78	47	)	)	PUNCT
ejpam-5918	78	48	signifies	signify	VERB
ejpam-5918	78	49	the	the	DET
ejpam-5918	78	50	neighborhood	neighborhood	NOUN
ejpam-5918	78	51	of	of	ADP
ejpam-5918	78	52	vertex	vertex	NOUN
ejpam-5918	78	53	v	v	NOUN
ejpam-5918	78	54	within	within	ADP
ejpam-5918	78	55	the	the	DET
ejpam-5918	78	56	set	set	NOUN
ejpam-5918	79	1	i	i	PRON
ejpam-5918	79	2	,	,	PUNCT
ejpam-5918	79	3	γ	γ	PROPN
ejpam-5918	79	4	−	−	PROPN
ejpam-5918	79	5	set	set	NOUN
ejpam-5918	79	6	refers	refer	VERB
ejpam-5918	79	7	to	to	ADP
ejpam-5918	79	8	the	the	DET
ejpam-5918	79	9	minimum	minimum	ADJ
ejpam-5918	79	10	dominating	dominating	NOUN
ejpam-5918	79	11	set	set	NOUN
ejpam-5918	79	12	,	,	PUNCT
ejpam-5918	79	13	ils	ils	X
ejpam-5918	79	14	signifies	signify	VERB
ejpam-5918	79	15	an	an	DET
ejpam-5918	79	16	internally	internally	ADV
ejpam-5918	79	17	-	-	PUNCT
ejpam-5918	79	18	locating	locate	VERB
ejpam-5918	79	19	set	set	NOUN
ejpam-5918	79	20	,	,	PUNCT
ejpam-5918	79	21	ilds	ilds	PROPN
ejpam-5918	79	22	denotes	denote	VERB
ejpam-5918	79	23	an	an	DET
ejpam-5918	79	24	internally	internally	ADV
ejpam-5918	79	25	-	-	PUNCT
ejpam-5918	79	26	locating	locate	VERB
ejpam-5918	79	27	dominating	dominating	NOUN
ejpam-5918	79	28	set	set	NOUN
ejpam-5918	79	29	,	,	PUNCT
ejpam-5918	79	30	and	and	CCONJ
ejpam-5918	79	31	the	the	DET
ejpam-5918	79	32	γli	γli	NOUN
ejpam-5918	79	33	−	−	PROPN
ejpam-5918	79	34	set	set	NOUN
ejpam-5918	79	35	represents	represent	VERB
ejpam-5918	79	36	the	the	DET
ejpam-5918	79	37	minimum	minimum	NOUN
ejpam-5918	79	38	internally	internally	ADV
ejpam-5918	79	39	-	-	PUNCT
ejpam-5918	79	40	locating	locate	VERB
ejpam-5918	79	41	dominating	dominating	NOUN
ejpam-5918	79	42	set	set	NOUN
ejpam-5918	79	43	.	.	PUNCT
ejpam-5918	80	1	definition	definition	NOUN
ejpam-5918	80	2	1	1	NUM
ejpam-5918	80	3	.	.	PUNCT
ejpam-5918	81	1	a	a	DET
ejpam-5918	81	2	non	non	ADJ
ejpam-5918	81	3	-	-	ADJ
ejpam-5918	81	4	empty	empty	ADJ
ejpam-5918	81	5	set	set	NOUN
ejpam-5918	81	6	s	s	PROPN
ejpam-5918	81	7	⊆	⊆	NUM
ejpam-5918	81	8	v	v	NOUN
ejpam-5918	81	9	(	(	PUNCT
ejpam-5918	81	10	g	g	NOUN
ejpam-5918	81	11	)	)	PUNCT
ejpam-5918	81	12	with	with	ADP
ejpam-5918	81	13	|s|	|s|	NOUN
ejpam-5918	81	14	≥	≥	PROPN
ejpam-5918	81	15	2	2	NUM
ejpam-5918	81	16	is	be	AUX
ejpam-5918	81	17	an	an	DET
ejpam-5918	81	18	internally	internally	ADV
ejpam-5918	81	19	-	-	PUNCT
ejpam-5918	81	20	locating	locate	VERB
ejpam-5918	81	21	set	set	NOUN
ejpam-5918	81	22	in	in	ADP
ejpam-5918	81	23	a	a	DET
ejpam-5918	81	24	connected	connected	ADJ
ejpam-5918	81	25	graph	graph	NOUN
ejpam-5918	81	26	g	g	NOUN
ejpam-5918	81	27	if	if	SCONJ
ejpam-5918	82	1	and	and	CCONJ
ejpam-5918	82	2	only	only	ADV
ejpam-5918	82	3	if	if	SCONJ
ejpam-5918	82	4	for	for	ADP
ejpam-5918	82	5	every	every	DET
ejpam-5918	82	6	u	u	NOUN
ejpam-5918	82	7	,	,	PUNCT
ejpam-5918	82	8	v	v	ADP
ejpam-5918	82	9	∈	∈	PROPN
ejpam-5918	82	10	s	s	NOUN
ejpam-5918	82	11	,	,	PUNCT
ejpam-5918	82	12	the	the	DET
ejpam-5918	82	13	n(u	n(u	PROPN
ejpam-5918	82	14	)	)	PUNCT
ejpam-5918	82	15	∩	∩	PROPN
ejpam-5918	82	16	s	s	PART
ejpam-5918	82	17	̸=	̸=	PROPN
ejpam-5918	82	18	n(v	n(v	PROPN
ejpam-5918	82	19	)	)	PUNCT
ejpam-5918	82	20	∩	∩	PROPN
ejpam-5918	82	21	s.	s.	PROPN
ejpam-5918	82	22	example	example	VERB
ejpam-5918	82	23	6	6	NUM
ejpam-5918	82	24	.	.	PUNCT
ejpam-5918	82	25	consider	consider	VERB
ejpam-5918	82	26	the	the	DET
ejpam-5918	82	27	graph	graph	NOUN
ejpam-5918	82	28	g	g	NOUN
ejpam-5918	82	29	in	in	ADP
ejpam-5918	82	30	figure	figure	NOUN
ejpam-5918	82	31	6	6	NUM
ejpam-5918	82	32	,	,	PUNCT
ejpam-5918	82	33	and	and	CCONJ
ejpam-5918	82	34	a	a	DET
ejpam-5918	82	35	set	set	NOUN
ejpam-5918	82	36	i	i	PRON
ejpam-5918	82	37	=	=	PUNCT
ejpam-5918	82	38	{	{	PUNCT
ejpam-5918	82	39	v2	v2	PROPN
ejpam-5918	82	40	,	,	PUNCT
ejpam-5918	82	41	v3	v3	PROPN
ejpam-5918	82	42	,	,	PUNCT
ejpam-5918	82	43	v5	v5	PROPN
ejpam-5918	82	44	}	}	PUNCT
ejpam-5918	82	45	⊂	⊂	PROPN
ejpam-5918	82	46	v	v	X
ejpam-5918	82	47	(	(	PUNCT
ejpam-5918	82	48	g	g	NOUN
ejpam-5918	82	49	)	)	PUNCT
ejpam-5918	82	50	.	.	PUNCT
ejpam-5918	83	1	note	note	VERB
ejpam-5918	83	2	that	that	SCONJ
ejpam-5918	83	3	n(v2	n(v2	NOUN
ejpam-5918	83	4	)	)	PUNCT
ejpam-5918	83	5	∩	∩	NOUN
ejpam-5918	83	6	i	i	PRON
ejpam-5918	83	7	=	=	SYM
ejpam-5918	83	8	{	{	PUNCT
ejpam-5918	83	9	v3	v3	PROPN
ejpam-5918	83	10	,	,	PUNCT
ejpam-5918	83	11	v5	v5	PROPN
ejpam-5918	83	12	}	}	PUNCT
ejpam-5918	83	13	,	,	PUNCT
ejpam-5918	83	14	n(v3	n(v3	NOUN
ejpam-5918	83	15	)	)	PUNCT
ejpam-5918	83	16	∩	∩	NOUN
ejpam-5918	83	17	i	i	PRON
ejpam-5918	83	18	=	=	SYM
ejpam-5918	83	19	{	{	PUNCT
ejpam-5918	83	20	v2	v2	PROPN
ejpam-5918	83	21	,	,	PUNCT
ejpam-5918	83	22	v5	v5	NOUN
ejpam-5918	83	23	}	}	PUNCT
ejpam-5918	83	24	,	,	PUNCT
ejpam-5918	83	25	and	and	CCONJ
ejpam-5918	83	26	n(v5	n(v5	NOUN
ejpam-5918	83	27	)	)	PUNCT
ejpam-5918	83	28	∩	∩	NOUN
ejpam-5918	84	1	i	i	PRON
ejpam-5918	84	2	=	=	SYM
ejpam-5918	84	3	{	{	PUNCT
ejpam-5918	84	4	v2	v2	PROPN
ejpam-5918	84	5	,	,	PUNCT
ejpam-5918	84	6	v3	v3	PROPN
ejpam-5918	84	7	}	}	PUNCT
ejpam-5918	84	8	.	.	PUNCT
ejpam-5918	85	1	by	by	ADP
ejpam-5918	85	2	definition	definition	NOUN
ejpam-5918	85	3	1	1	NUM
ejpam-5918	85	4	,	,	PUNCT
ejpam-5918	85	5	i	i	PRON
ejpam-5918	85	6	is	be	AUX
ejpam-5918	85	7	an	an	DET
ejpam-5918	85	8	internally	internally	ADV
ejpam-5918	85	9	-	-	PUNCT
ejpam-5918	85	10	locating	locate	VERB
ejpam-5918	85	11	set	set	NOUN
ejpam-5918	85	12	in	in	ADP
ejpam-5918	85	13	g.	g.	PROPN
ejpam-5918	85	14	v1	v1	PROPN
ejpam-5918	85	15	v2	v2	PROPN
ejpam-5918	85	16	v3	v3	PROPN
ejpam-5918	85	17	v4	v4	PROPN
ejpam-5918	85	18	v5	v5	PROPN
ejpam-5918	85	19	v6	v6	PROPN
ejpam-5918	85	20	figure	figure	NOUN
ejpam-5918	85	21	6	6	NUM
ejpam-5918	85	22	:	:	PUNCT
ejpam-5918	85	23	a	a	DET
ejpam-5918	85	24	graph	graph	NOUN
ejpam-5918	85	25	g	g	NOUN
ejpam-5918	85	26	definition	definition	NOUN
ejpam-5918	85	27	2	2	NUM
ejpam-5918	85	28	.	.	PUNCT
ejpam-5918	86	1	a	a	DET
ejpam-5918	86	2	set	set	NOUN
ejpam-5918	86	3	i	i	PRON
ejpam-5918	86	4	⊆	⊆	NUM
ejpam-5918	86	5	v	v	ADP
ejpam-5918	86	6	(	(	PUNCT
ejpam-5918	86	7	g	g	NOUN
ejpam-5918	86	8	)	)	PUNCT
ejpam-5918	86	9	such	such	ADJ
ejpam-5918	86	10	that	that	SCONJ
ejpam-5918	86	11	|i|	|i|	ADP
ejpam-5918	86	12	≥	≥	NOUN
ejpam-5918	86	13	2	2	NUM
ejpam-5918	86	14	is	be	AUX
ejpam-5918	86	15	an	an	DET
ejpam-5918	86	16	internally	internally	ADV
ejpam-5918	86	17	-	-	PUNCT
ejpam-5918	86	18	locating	locate	VERB
ejpam-5918	86	19	dominating	dominating	NOUN
ejpam-5918	86	20	set	set	VERB
ejpam-5918	86	21	if	if	SCONJ
ejpam-5918	86	22	and	and	CCONJ
ejpam-5918	86	23	only	only	ADV
ejpam-5918	86	24	if	if	SCONJ
ejpam-5918	86	25	i	i	PRON
ejpam-5918	86	26	is	be	AUX
ejpam-5918	86	27	a	a	DET
ejpam-5918	86	28	dominating	dominating	NOUN
ejpam-5918	86	29	set	set	NOUN
ejpam-5918	86	30	and	and	CCONJ
ejpam-5918	86	31	an	an	DET
ejpam-5918	86	32	internally	internally	ADV
ejpam-5918	86	33	-	-	PUNCT
ejpam-5918	86	34	locating	locate	VERB
ejpam-5918	86	35	set	set	NOUN
ejpam-5918	86	36	in	in	ADP
ejpam-5918	86	37	g.	g.	PROPN
ejpam-5918	86	38	moreover	moreover	ADV
ejpam-5918	86	39	,	,	PUNCT
ejpam-5918	86	40	the	the	DET
ejpam-5918	86	41	minimum	minimum	ADJ
ejpam-5918	86	42	cardinality	cardinality	NOUN
ejpam-5918	86	43	of	of	ADP
ejpam-5918	86	44	internally	internally	ADV
ejpam-5918	86	45	-	-	PUNCT
ejpam-5918	86	46	locating	locate	VERB
ejpam-5918	86	47	dominating	dominating	NOUN
ejpam-5918	86	48	set	set	NOUN
ejpam-5918	86	49	,	,	PUNCT
ejpam-5918	86	50	denoted	denote	VERB
ejpam-5918	86	51	by	by	ADP
ejpam-5918	86	52	γli(g	γli(g	PROPN
ejpam-5918	86	53	)	)	PUNCT
ejpam-5918	86	54	is	be	AUX
ejpam-5918	86	55	called	call	VERB
ejpam-5918	86	56	an	an	DET
ejpam-5918	86	57	internally	internally	ADV
ejpam-5918	86	58	-	-	PUNCT
ejpam-5918	86	59	locating	locate	VERB
ejpam-5918	86	60	domination	domination	NOUN
ejpam-5918	86	61	number	number	NOUN
ejpam-5918	86	62	of	of	ADP
ejpam-5918	86	63	g.	g.	PROPN
ejpam-5918	86	64	example	example	PROPN
ejpam-5918	87	1	7	7	X
ejpam-5918	87	2	.	.	X
ejpam-5918	87	3	consider	consider	VERB
ejpam-5918	87	4	the	the	DET
ejpam-5918	87	5	graph	graph	NOUN
ejpam-5918	87	6	g	g	NOUN
ejpam-5918	87	7	in	in	ADP
ejpam-5918	87	8	figure	figure	NOUN
ejpam-5918	87	9	6	6	NUM
ejpam-5918	87	10	,	,	PUNCT
ejpam-5918	87	11	and	and	CCONJ
ejpam-5918	87	12	a	a	DET
ejpam-5918	87	13	set	set	NOUN
ejpam-5918	87	14	i	i	PRON
ejpam-5918	87	15	=	=	PUNCT
ejpam-5918	87	16	{	{	PUNCT
ejpam-5918	87	17	v2	v2	PROPN
ejpam-5918	87	18	,	,	PUNCT
ejpam-5918	87	19	v5	v5	PROPN
ejpam-5918	87	20	}	}	PUNCT
ejpam-5918	87	21	⊂	⊂	PROPN
ejpam-5918	87	22	v	v	X
ejpam-5918	87	23	(	(	PUNCT
ejpam-5918	87	24	g	g	NOUN
ejpam-5918	87	25	)	)	PUNCT
ejpam-5918	87	26	.	.	PUNCT
ejpam-5918	88	1	note	note	VERB
ejpam-5918	88	2	that	that	DET
ejpam-5918	88	3	n(v2)∩	n(v2)∩	NOUN
ejpam-5918	89	1	i	i	NOUN
ejpam-5918	89	2	=	=	SYM
ejpam-5918	89	3	{	{	PUNCT
ejpam-5918	89	4	v5	v5	PROPN
ejpam-5918	89	5	}	}	PUNCT
ejpam-5918	89	6	=	=	NOUN
ejpam-5918	89	7	̸	̸	NUM
ejpam-5918	89	8	{	{	PUNCT
ejpam-5918	89	9	v2	v2	NOUN
ejpam-5918	89	10	}	}	PUNCT
ejpam-5918	89	11	=	=	SYM
ejpam-5918	89	12	n(v5)∩	n(v5)∩	ADJ
ejpam-5918	89	13	i.	i.	NOUN
ejpam-5918	89	14	by	by	ADP
ejpam-5918	89	15	definition	definition	NOUN
ejpam-5918	89	16	1	1	NUM
ejpam-5918	89	17	,	,	PUNCT
ejpam-5918	89	18	i	i	PRON
ejpam-5918	89	19	is	be	AUX
ejpam-5918	89	20	an	an	DET
ejpam-5918	89	21	internally	internally	ADV
ejpam-5918	89	22	-	-	PUNCT
ejpam-5918	89	23	locating	locate	VERB
ejpam-5918	89	24	set	set	NOUN
ejpam-5918	89	25	in	in	ADP
ejpam-5918	89	26	g.	g.	PROPN
ejpam-5918	89	27	note	note	VERB
ejpam-5918	89	28	that	that	SCONJ
ejpam-5918	89	29	i	i	PRON
ejpam-5918	89	30	is	be	AUX
ejpam-5918	89	31	a	a	DET
ejpam-5918	89	32	dominating	dominating	NOUN
ejpam-5918	89	33	set	set	NOUN
ejpam-5918	89	34	in	in	ADP
ejpam-5918	89	35	g	g	PROPN
ejpam-5918	89	36	and	and	CCONJ
ejpam-5918	89	37	also	also	ADV
ejpam-5918	90	1	a	a	DET
ejpam-5918	90	2	γ	γ	NOUN
ejpam-5918	90	3	−	−	PROPN
ejpam-5918	90	4	set	set	NOUN
ejpam-5918	90	5	.	.	PUNCT
ejpam-5918	91	1	by	by	ADP
ejpam-5918	91	2	definition	definition	NOUN
ejpam-5918	91	3	2	2	NUM
ejpam-5918	91	4	,	,	PUNCT
ejpam-5918	91	5	i	i	PRON
ejpam-5918	91	6	is	be	AUX
ejpam-5918	91	7	an	an	DET
ejpam-5918	91	8	internally	internally	ADV
ejpam-5918	91	9	-	-	PUNCT
ejpam-5918	91	10	locating	locate	VERB
ejpam-5918	91	11	dominating	dominating	NOUN
ejpam-5918	91	12	set	set	NOUN
ejpam-5918	91	13	and	and	CCONJ
ejpam-5918	91	14	also	also	ADV
ejpam-5918	91	15	a	a	DET
ejpam-5918	91	16	γli	γli	ADJ
ejpam-5918	91	17	−	−	NOUN
ejpam-5918	91	18	set	set	VERB
ejpam-5918	91	19	in	in	ADP
ejpam-5918	91	20	g.	g.	PROPN
ejpam-5918	91	21	therefore	therefore	ADV
ejpam-5918	91	22	,	,	PUNCT
ejpam-5918	91	23	γli(g	γli(g	PROPN
ejpam-5918	91	24	)	)	PUNCT
ejpam-5918	92	1	=	=	SYM
ejpam-5918	92	2	2	2	X
ejpam-5918	92	3	.	.	X
ejpam-5918	92	4	theorem	theorem	NOUN
ejpam-5918	92	5	1	1	NUM
ejpam-5918	92	6	.	.	PUNCT
ejpam-5918	93	1	let	let	VERB
ejpam-5918	93	2	g	g	PRON
ejpam-5918	93	3	be	be	AUX
ejpam-5918	93	4	a	a	DET
ejpam-5918	93	5	graph	graph	NOUN
ejpam-5918	93	6	and	and	CCONJ
ejpam-5918	93	7	i	i	PRON
ejpam-5918	93	8	⊆	⊆	NUM
ejpam-5918	93	9	v	v	ADP
ejpam-5918	93	10	(	(	PUNCT
ejpam-5918	93	11	g	g	NOUN
ejpam-5918	93	12	)	)	PUNCT
ejpam-5918	93	13	such	such	ADJ
ejpam-5918	93	14	that	that	PRON
ejpam-5918	93	15	|i|	|i|	VERB
ejpam-5918	93	16	≥	≥	NOUN
ejpam-5918	93	17	2	2	NUM
ejpam-5918	94	1	and	and	CCONJ
ejpam-5918	94	2	i	i	PRON
ejpam-5918	94	3	is	be	AUX
ejpam-5918	94	4	a	a	DET
ejpam-5918	94	5	dominating	dominating	NOUN
ejpam-5918	94	6	set	set	NOUN
ejpam-5918	94	7	.	.	PUNCT
ejpam-5918	95	1	then	then	ADV
ejpam-5918	95	2	i	i	PRON
ejpam-5918	95	3	is	be	AUX
ejpam-5918	95	4	not	not	PART
ejpam-5918	95	5	an	an	DET
ejpam-5918	95	6	internally	internally	ADV
ejpam-5918	95	7	-	-	PUNCT
ejpam-5918	95	8	locating	locate	VERB
ejpam-5918	95	9	dominating	dominating	NOUN
ejpam-5918	95	10	set	set	VERB
ejpam-5918	95	11	in	in	ADP
ejpam-5918	95	12	g	g	PROPN
ejpam-5918	95	13	if	if	SCONJ
ejpam-5918	95	14	one	one	NUM
ejpam-5918	95	15	of	of	ADP
ejpam-5918	95	16	the	the	DET
ejpam-5918	95	17	following	follow	VERB
ejpam-5918	95	18	holds	hold	VERB
ejpam-5918	95	19	:	:	PUNCT
ejpam-5918	95	20	(	(	PUNCT
ejpam-5918	95	21	i	i	NOUN
ejpam-5918	95	22	)	)	PUNCT
ejpam-5918	95	23	h	h	PROPN
ejpam-5918	95	24	is	be	AUX
ejpam-5918	95	25	a	a	DET
ejpam-5918	95	26	component	component	NOUN
ejpam-5918	95	27	of	of	ADP
ejpam-5918	95	28	g[i	g[i	NOUN
ejpam-5918	95	29	]	]	X
ejpam-5918	95	30	such	such	ADJ
ejpam-5918	95	31	that	that	SCONJ
ejpam-5918	95	32	h	h	NOUN
ejpam-5918	95	33	=	=	SYM
ejpam-5918	95	34	p3	p3	PROPN
ejpam-5918	95	35	or	or	CCONJ
ejpam-5918	95	36	c4	c4	NOUN
ejpam-5918	95	37	;	;	PUNCT
ejpam-5918	95	38	(	(	PUNCT
ejpam-5918	95	39	ii	ii	X
ejpam-5918	95	40	)	)	PUNCT
ejpam-5918	96	1	i	i	PRON
ejpam-5918	96	2	induced	induce	VERB
ejpam-5918	96	3	more	more	ADJ
ejpam-5918	96	4	than	than	ADP
ejpam-5918	96	5	one	one	NUM
ejpam-5918	96	6	isolated	isolate	VERB
ejpam-5918	96	7	vertex	vertex	NOUN
ejpam-5918	96	8	or	or	CCONJ
ejpam-5918	96	9	an	an	DET
ejpam-5918	96	10	empty	empty	ADJ
ejpam-5918	96	11	graph	graph	NOUN
ejpam-5918	96	12	of	of	ADP
ejpam-5918	96	13	order	order	NOUN
ejpam-5918	96	14	n	n	PRON
ejpam-5918	96	15	≥	≥	NOUN
ejpam-5918	96	16	2	2	NUM
ejpam-5918	96	17	;	;	PUNCT
ejpam-5918	96	18	(	(	PUNCT
ejpam-5918	96	19	iii	iii	X
ejpam-5918	96	20	)	)	PUNCT
ejpam-5918	96	21	the	the	DET
ejpam-5918	96	22	component	component	NOUN
ejpam-5918	96	23	of	of	ADP
ejpam-5918	96	24	g[i	g[i	ADJ
ejpam-5918	96	25	]	]	X
ejpam-5918	96	26	=	=	SYM
ejpam-5918	96	27	km	km	PROPN
ejpam-5918	96	28	,	,	PUNCT
ejpam-5918	96	29	n	n	CCONJ
ejpam-5918	96	30	,	,	PUNCT
ejpam-5918	96	31	where	where	SCONJ
ejpam-5918	96	32	m	m	PROPN
ejpam-5918	96	33	≥	≥	VERB
ejpam-5918	96	34	1	1	NUM
ejpam-5918	96	35	and	and	CCONJ
ejpam-5918	96	36	n	n	PRON
ejpam-5918	96	37	≥	≥	NOUN
ejpam-5918	96	38	3	3	NUM
ejpam-5918	96	39	;	;	PUNCT
ejpam-5918	96	40	or	or	CCONJ
ejpam-5918	96	41	(	(	PUNCT
ejpam-5918	96	42	iv	iv	X
ejpam-5918	96	43	)	)	PUNCT
ejpam-5918	96	44	the	the	DET
ejpam-5918	96	45	component	component	NOUN
ejpam-5918	96	46	of	of	ADP
ejpam-5918	96	47	g[i	g[i	ADJ
ejpam-5918	96	48	]	]	X
ejpam-5918	96	49	=	=	SYM
ejpam-5918	96	50	d4	d4	PROPN
ejpam-5918	96	51	.	.	PUNCT
ejpam-5918	96	52	i.	i.	PROPN
ejpam-5918	96	53	tropico	tropico	PROPN
ejpam-5918	96	54	,	,	PUNCT
ejpam-5918	96	55	i.	i.	PROPN
ejpam-5918	96	56	cabahug	cabahug	PROPN
ejpam-5918	96	57	,	,	PUNCT
ejpam-5918	96	58	jr	jr	PROPN
ejpam-5918	96	59	.	.	PROPN
ejpam-5918	96	60	/	/	SYM
ejpam-5918	96	61	eur	eur	PROPN
ejpam-5918	96	62	.	.	PUNCT
ejpam-5918	97	1	j.	j.	PROPN
ejpam-5918	97	2	pure	pure	PROPN
ejpam-5918	97	3	appl	appl	PROPN
ejpam-5918	97	4	.	.	PROPN
ejpam-5918	97	5	math	math	PROPN
ejpam-5918	97	6	,	,	PUNCT
ejpam-5918	97	7	18	18	NUM
ejpam-5918	97	8	(	(	PUNCT
ejpam-5918	97	9	2	2	NUM
ejpam-5918	97	10	)	)	PUNCT
ejpam-5918	97	11	(	(	PUNCT
ejpam-5918	97	12	2025	2025	NUM
ejpam-5918	97	13	)	)	PUNCT
ejpam-5918	97	14	,	,	PUNCT
ejpam-5918	97	15	5918	5918	NUM
ejpam-5918	97	16	6	6	NUM
ejpam-5918	97	17	of	of	ADP
ejpam-5918	97	18	21	21	NUM
ejpam-5918	97	19	proof	proof	NOUN
ejpam-5918	97	20	.	.	PUNCT
ejpam-5918	98	1	let	let	VERB
ejpam-5918	98	2	g	g	PRON
ejpam-5918	98	3	be	be	AUX
ejpam-5918	98	4	a	a	DET
ejpam-5918	98	5	graph	graph	NOUN
ejpam-5918	98	6	and	and	CCONJ
ejpam-5918	98	7	i	i	PRON
ejpam-5918	98	8	⊆	⊆	NUM
ejpam-5918	98	9	v	v	ADP
ejpam-5918	98	10	(	(	PUNCT
ejpam-5918	98	11	g	g	NOUN
ejpam-5918	98	12	)	)	PUNCT
ejpam-5918	98	13	such	such	ADJ
ejpam-5918	98	14	that	that	PRON
ejpam-5918	98	15	|i|	|i|	VERB
ejpam-5918	98	16	≥	≥	NOUN
ejpam-5918	98	17	2	2	NUM
ejpam-5918	98	18	.	.	PUNCT
ejpam-5918	98	19	assume	assume	VERB
ejpam-5918	98	20	that	that	SCONJ
ejpam-5918	98	21	(	(	PUNCT
ejpam-5918	98	22	i)−	i)−	PROPN
ejpam-5918	98	23	(	(	PUNCT
ejpam-5918	98	24	iv	iv	NOUN
ejpam-5918	98	25	)	)	PUNCT
ejpam-5918	98	26	hold	hold	NOUN
ejpam-5918	98	27	.	.	PUNCT
ejpam-5918	99	1	if	if	SCONJ
ejpam-5918	99	2	h	h	NOUN
ejpam-5918	99	3	=	=	SYM
ejpam-5918	99	4	p3	p3	PROPN
ejpam-5918	99	5	,	,	PUNCT
ejpam-5918	99	6	consider	consider	VERB
ejpam-5918	99	7	v	v	NOUN
ejpam-5918	99	8	(	(	PUNCT
ejpam-5918	99	9	h	h	NOUN
ejpam-5918	99	10	)	)	PUNCT
ejpam-5918	99	11	=	=	NOUN
ejpam-5918	99	12	v	v	X
ejpam-5918	99	13	(	(	PUNCT
ejpam-5918	99	14	p3	p3	PROPN
ejpam-5918	99	15	)	)	PUNCT
ejpam-5918	99	16	=	=	PRON
ejpam-5918	99	17	{	{	PUNCT
ejpam-5918	99	18	v1	v1	PROPN
ejpam-5918	99	19	,	,	PUNCT
ejpam-5918	99	20	v2	v2	PROPN
ejpam-5918	99	21	,	,	PUNCT
ejpam-5918	99	22	v3	v3	PROPN
ejpam-5918	99	23	}	}	PUNCT
ejpam-5918	99	24	and	and	CCONJ
ejpam-5918	99	25	e(h	e(h	PROPN
ejpam-5918	99	26	)	)	PUNCT
ejpam-5918	99	27	=	=	SYM
ejpam-5918	99	28	e(p3	e(p3	NOUN
ejpam-5918	99	29	)	)	PUNCT
ejpam-5918	100	1	=	=	PRON
ejpam-5918	100	2	{	{	PUNCT
ejpam-5918	100	3	v1v2	v1v2	PROPN
ejpam-5918	100	4	,	,	PUNCT
ejpam-5918	100	5	v2v3	v2v3	NOUN
ejpam-5918	100	6	}	}	PUNCT
ejpam-5918	100	7	.	.	PUNCT
ejpam-5918	101	1	note	note	VERB
ejpam-5918	101	2	that	that	SCONJ
ejpam-5918	101	3	h	h	NOUN
ejpam-5918	101	4	⊆	⊆	NUM
ejpam-5918	101	5	g[i	g[i	X
ejpam-5918	101	6	]	]	X
ejpam-5918	101	7	,	,	PUNCT
ejpam-5918	101	8	thus	thus	ADV
ejpam-5918	101	9	v	v	ADJ
ejpam-5918	101	10	(	(	PUNCT
ejpam-5918	101	11	h	h	NOUN
ejpam-5918	101	12	)	)	PUNCT
ejpam-5918	101	13	⊆	⊆	NUM
ejpam-5918	101	14	i.	i.	NOUN
ejpam-5918	101	15	observe	observe	VERB
ejpam-5918	101	16	that	that	SCONJ
ejpam-5918	101	17	n(v1	n(v1	NOUN
ejpam-5918	101	18	)	)	PUNCT
ejpam-5918	101	19	∩	∩	NOUN
ejpam-5918	102	1	i	i	PRON
ejpam-5918	102	2	=	=	SYM
ejpam-5918	102	3	{	{	PUNCT
ejpam-5918	102	4	v2	v2	NOUN
ejpam-5918	102	5	}	}	PUNCT
ejpam-5918	102	6	=	=	SYM
ejpam-5918	102	7	n(v3	n(v3	NOUN
ejpam-5918	102	8	)	)	PUNCT
ejpam-5918	102	9	∩	∩	PROPN
ejpam-5918	102	10	i.	i.	PROPN
ejpam-5918	102	11	thus	thus	ADV
ejpam-5918	102	12	,	,	PUNCT
ejpam-5918	102	13	i	i	PRON
ejpam-5918	102	14	is	be	AUX
ejpam-5918	102	15	neither	neither	CCONJ
ejpam-5918	102	16	an	an	DET
ejpam-5918	102	17	ils	ils	NOUN
ejpam-5918	102	18	nor	nor	CCONJ
ejpam-5918	102	19	ilds	ild	NOUN
ejpam-5918	102	20	.	.	PUNCT
ejpam-5918	103	1	similarly	similarly	ADV
ejpam-5918	103	2	,	,	PUNCT
ejpam-5918	103	3	if	if	SCONJ
ejpam-5918	103	4	h	h	NOUN
ejpam-5918	103	5	=	=	SYM
ejpam-5918	103	6	c4	c4	NOUN
ejpam-5918	103	7	,	,	PUNCT
ejpam-5918	103	8	let	let	VERB
ejpam-5918	103	9	v	v	X
ejpam-5918	103	10	(	(	PUNCT
ejpam-5918	103	11	h	h	NOUN
ejpam-5918	103	12	)	)	PUNCT
ejpam-5918	103	13	=	=	NOUN
ejpam-5918	103	14	v	v	X
ejpam-5918	103	15	(	(	PUNCT
ejpam-5918	103	16	c4	c4	NOUN
ejpam-5918	103	17	)	)	PUNCT
ejpam-5918	103	18	=	=	SYM
ejpam-5918	103	19	{	{	PUNCT
ejpam-5918	103	20	c1	c1	PROPN
ejpam-5918	103	21	,	,	PUNCT
ejpam-5918	103	22	c2	c2	PROPN
ejpam-5918	103	23	,	,	PUNCT
ejpam-5918	103	24	c3	c3	PROPN
ejpam-5918	103	25	,	,	PUNCT
ejpam-5918	103	26	c4	c4	NOUN
ejpam-5918	103	27	}	}	PUNCT
ejpam-5918	103	28	and	and	CCONJ
ejpam-5918	103	29	e(h	e(h	PROPN
ejpam-5918	103	30	)	)	PUNCT
ejpam-5918	103	31	=	=	SYM
ejpam-5918	104	1	e(c4	e(c4	NOUN
ejpam-5918	104	2	)	)	PUNCT
ejpam-5918	105	1	=	=	PRON
ejpam-5918	105	2	{	{	PUNCT
ejpam-5918	105	3	c1c2	c1c2	NOUN
ejpam-5918	105	4	,	,	PUNCT
ejpam-5918	105	5	c2c3	c2c3	ADJ
ejpam-5918	105	6	,	,	PUNCT
ejpam-5918	105	7	c3c4	c3c4	ADJ
ejpam-5918	105	8	,	,	PUNCT
ejpam-5918	105	9	c4c1	c4c1	NOUN
ejpam-5918	105	10	}	}	PUNCT
ejpam-5918	105	11	.	.	PUNCT
ejpam-5918	106	1	note	note	VERB
ejpam-5918	106	2	that	that	SCONJ
ejpam-5918	106	3	h	h	NOUN
ejpam-5918	106	4	⊆	⊆	NUM
ejpam-5918	106	5	g[i	g[i	X
ejpam-5918	106	6	]	]	X
ejpam-5918	106	7	,	,	PUNCT
ejpam-5918	106	8	thus	thus	ADV
ejpam-5918	106	9	v	v	ADJ
ejpam-5918	106	10	(	(	PUNCT
ejpam-5918	106	11	h	h	NOUN
ejpam-5918	106	12	)	)	PUNCT
ejpam-5918	106	13	⊆	⊆	NUM
ejpam-5918	106	14	i.	i.	NOUN
ejpam-5918	106	15	observe	observe	VERB
ejpam-5918	106	16	that	that	SCONJ
ejpam-5918	106	17	n(c1	n(c1	NOUN
ejpam-5918	106	18	)	)	PUNCT
ejpam-5918	106	19	∩	∩	NOUN
ejpam-5918	106	20	i	i	PRON
ejpam-5918	106	21	=	=	SYM
ejpam-5918	106	22	{	{	PUNCT
ejpam-5918	106	23	c2	c2	PROPN
ejpam-5918	106	24	,	,	PUNCT
ejpam-5918	106	25	c4	c4	NOUN
ejpam-5918	106	26	}	}	PUNCT
ejpam-5918	106	27	=	=	SYM
ejpam-5918	106	28	n(c3	n(c3	ADJ
ejpam-5918	106	29	)	)	PUNCT
ejpam-5918	106	30	∩	∩	ADJ
ejpam-5918	106	31	i.	i.	NOUN
ejpam-5918	106	32	thus	thus	ADV
ejpam-5918	106	33	,	,	PUNCT
ejpam-5918	106	34	i	i	PRON
ejpam-5918	106	35	is	be	AUX
ejpam-5918	106	36	neither	neither	CCONJ
ejpam-5918	106	37	an	an	DET
ejpam-5918	106	38	ils	ils	NOUN
ejpam-5918	106	39	nor	nor	CCONJ
ejpam-5918	106	40	ilds	ild	NOUN
ejpam-5918	106	41	.	.	PUNCT
ejpam-5918	107	1	now	now	ADV
ejpam-5918	107	2	,	,	PUNCT
ejpam-5918	107	3	if	if	SCONJ
ejpam-5918	107	4	i	i	PRON
ejpam-5918	107	5	induces	induce	VERB
ejpam-5918	107	6	an	an	DET
ejpam-5918	107	7	isolated	isolated	ADJ
ejpam-5918	107	8	vertex	vertex	NOUN
ejpam-5918	107	9	v	v	NOUN
ejpam-5918	107	10	,	,	PUNCT
ejpam-5918	107	11	then	then	ADV
ejpam-5918	107	12	n(v	n(v	PROPN
ejpam-5918	107	13	)	)	PUNCT
ejpam-5918	107	14	∩	∩	NOUN
ejpam-5918	107	15	i	i	PRON
ejpam-5918	107	16	=	=	PUNCT
ejpam-5918	107	17	∅.	∅.	VERB
ejpam-5918	107	18	by	by	ADP
ejpam-5918	107	19	(	(	PUNCT
ejpam-5918	107	20	ii	ii	NOUN
ejpam-5918	107	21	)	)	PUNCT
ejpam-5918	107	22	,	,	PUNCT
ejpam-5918	107	23	there	there	PRON
ejpam-5918	107	24	exists	exist	VERB
ejpam-5918	107	25	u	u	PROPN
ejpam-5918	107	26	∈	∈	PROPN
ejpam-5918	107	27	i	i	PRON
ejpam-5918	107	28	,	,	PUNCT
ejpam-5918	107	29	u	u	PROPN
ejpam-5918	107	30	̸=	̸=	PROPN
ejpam-5918	107	31	v	v	NOUN
ejpam-5918	107	32	,	,	PUNCT
ejpam-5918	107	33	such	such	ADJ
ejpam-5918	107	34	that	that	DET
ejpam-5918	107	35	n(u	n(u	PROPN
ejpam-5918	107	36	)	)	PUNCT
ejpam-5918	107	37	∩	∩	NOUN
ejpam-5918	107	38	i	i	PRON
ejpam-5918	107	39	=	=	PUNCT
ejpam-5918	107	40	∅.	∅.	VERB
ejpam-5918	107	41	thus	thus	ADV
ejpam-5918	107	42	,	,	PUNCT
ejpam-5918	107	43	n(v	n(v	PROPN
ejpam-5918	107	44	)	)	PUNCT
ejpam-5918	107	45	∩	∩	NOUN
ejpam-5918	107	46	i	i	NOUN
ejpam-5918	107	47	=	=	NOUN
ejpam-5918	107	48	∅	∅	NOUN
ejpam-5918	107	49	=	=	SYM
ejpam-5918	107	50	n(u	n(u	PROPN
ejpam-5918	107	51	)	)	PUNCT
ejpam-5918	107	52	∩	∩	PROPN
ejpam-5918	107	53	i.	i.	NOUN
ejpam-5918	107	54	hence	hence	ADV
ejpam-5918	107	55	,	,	PUNCT
ejpam-5918	107	56	i	i	PRON
ejpam-5918	107	57	is	be	AUX
ejpam-5918	107	58	neither	neither	CCONJ
ejpam-5918	107	59	an	an	DET
ejpam-5918	107	60	ils	ils	NOUN
ejpam-5918	107	61	nor	nor	CCONJ
ejpam-5918	107	62	ilds	ild	NOUN
ejpam-5918	107	63	.	.	PUNCT
ejpam-5918	108	1	by	by	ADP
ejpam-5918	108	2	the	the	DET
ejpam-5918	108	3	definition	definition	NOUN
ejpam-5918	108	4	of	of	ADP
ejpam-5918	108	5	an	an	DET
ejpam-5918	108	6	empty	empty	ADJ
ejpam-5918	108	7	graph	graph	NOUN
ejpam-5918	108	8	,	,	PUNCT
ejpam-5918	108	9	this	this	PRON
ejpam-5918	108	10	generally	generally	ADV
ejpam-5918	108	11	holds	hold	VERB
ejpam-5918	108	12	if	if	SCONJ
ejpam-5918	108	13	i	i	PRON
ejpam-5918	108	14	induces	induce	VERB
ejpam-5918	108	15	an	an	DET
ejpam-5918	108	16	empty	empty	ADJ
ejpam-5918	108	17	graph	graph	NOUN
ejpam-5918	108	18	of	of	ADP
ejpam-5918	108	19	order	order	NOUN
ejpam-5918	108	20	n	n	PRON
ejpam-5918	108	21	≥	≥	NOUN
ejpam-5918	108	22	2	2	NUM
ejpam-5918	108	23	.	.	PUNCT
ejpam-5918	109	1	by	by	ADP
ejpam-5918	109	2	(	(	PUNCT
ejpam-5918	109	3	iii	iii	NOUN
ejpam-5918	109	4	)	)	PUNCT
ejpam-5918	109	5	,	,	PUNCT
ejpam-5918	109	6	let	let	VERB
ejpam-5918	109	7	h	h	NOUN
ejpam-5918	109	8	=	=	PUNCT
ejpam-5918	109	9	km	km	PROPN
ejpam-5918	109	10	,	,	PUNCT
ejpam-5918	109	11	n	n	CCONJ
ejpam-5918	109	12	,	,	PUNCT
ejpam-5918	109	13	m	m	VERB
ejpam-5918	109	14	≥	≥	NOUN
ejpam-5918	109	15	1	1	NUM
ejpam-5918	109	16	and	and	CCONJ
ejpam-5918	109	17	n	n	PRON
ejpam-5918	109	18	≥	≥	NOUN
ejpam-5918	109	19	3	3	NUM
ejpam-5918	109	20	.	.	PUNCT
ejpam-5918	110	1	by	by	ADP
ejpam-5918	110	2	the	the	DET
ejpam-5918	110	3	definition	definition	NOUN
ejpam-5918	110	4	of	of	ADP
ejpam-5918	110	5	km	km	PROPN
ejpam-5918	110	6	,	,	PUNCT
ejpam-5918	110	7	n	n	CCONJ
ejpam-5918	110	8	,	,	PUNCT
ejpam-5918	110	9	v	v	PROPN
ejpam-5918	110	10	(	(	PUNCT
ejpam-5918	110	11	h	h	NOUN
ejpam-5918	110	12	)	)	PUNCT
ejpam-5918	110	13	=	=	NOUN
ejpam-5918	110	14	v	v	X
ejpam-5918	110	15	(	(	PUNCT
ejpam-5918	110	16	km	km	PROPN
ejpam-5918	110	17	,	,	PUNCT
ejpam-5918	110	18	n	n	CCONJ
ejpam-5918	110	19	)	)	PUNCT
ejpam-5918	110	20	=	=	PRON
ejpam-5918	110	21	{	{	PUNCT
ejpam-5918	110	22	x1	x1	PROPN
ejpam-5918	110	23	,	,	PUNCT
ejpam-5918	110	24	x2	x2	PROPN
ejpam-5918	110	25	,	,	PUNCT
ejpam-5918	110	26	.	.	PUNCT
ejpam-5918	110	27	.	.	PUNCT
ejpam-5918	110	28	.	.	PUNCT
ejpam-5918	111	1	,	,	PUNCT
ejpam-5918	111	2	xm}∪	xm}∪	PROPN
ejpam-5918	112	1	{	{	PUNCT
ejpam-5918	112	2	y1	y1	PROPN
ejpam-5918	112	3	,	,	PUNCT
ejpam-5918	112	4	y2	y2	PROPN
ejpam-5918	112	5	,	,	PUNCT
ejpam-5918	112	6	.	.	PUNCT
ejpam-5918	112	7	.	.	PUNCT
ejpam-5918	112	8	.	.	PUNCT
ejpam-5918	113	1	,	,	PUNCT
ejpam-5918	113	2	yn	yn	PRON
ejpam-5918	113	3	}	}	PUNCT
ejpam-5918	113	4	and	and	CCONJ
ejpam-5918	113	5	e(km	e(km	NOUN
ejpam-5918	113	6	,	,	PUNCT
ejpam-5918	113	7	n	n	CCONJ
ejpam-5918	113	8	)	)	PUNCT
ejpam-5918	113	9	=	=	NOUN
ejpam-5918	113	10	{	{	PUNCT
ejpam-5918	113	11	xiyj	xiyj	NOUN
ejpam-5918	113	12	|1	|1	NUM
ejpam-5918	113	13	≤	≤	NUM
ejpam-5918	113	14	i	i	NOUN
ejpam-5918	113	15	≤	≤	NOUN
ejpam-5918	113	16	m	m	ADP
ejpam-5918	113	17	,	,	PUNCT
ejpam-5918	113	18	1	1	NUM
ejpam-5918	113	19	≤	≤	NUM
ejpam-5918	113	20	j	j	PROPN
ejpam-5918	113	21	≤	≤	PROPN
ejpam-5918	113	22	n	n	CCONJ
ejpam-5918	113	23	}	}	PUNCT
ejpam-5918	113	24	.	.	PUNCT
ejpam-5918	114	1	note	note	VERB
ejpam-5918	114	2	that	that	SCONJ
ejpam-5918	114	3	h	h	NOUN
ejpam-5918	114	4	⊆	⊆	NUM
ejpam-5918	114	5	g[i	g[i	X
ejpam-5918	114	6	]	]	X
ejpam-5918	114	7	,	,	PUNCT
ejpam-5918	114	8	thus	thus	ADV
ejpam-5918	114	9	v	v	ADJ
ejpam-5918	114	10	(	(	PUNCT
ejpam-5918	114	11	h	h	NOUN
ejpam-5918	114	12	)	)	PUNCT
ejpam-5918	114	13	⊆	⊆	NUM
ejpam-5918	114	14	i.	i.	NOUN
ejpam-5918	114	15	wlog	wlog	NOUN
ejpam-5918	114	16	,	,	PUNCT
ejpam-5918	114	17	consider	consider	VERB
ejpam-5918	114	18	x1	x1	PROPN
ejpam-5918	114	19	and	and	CCONJ
ejpam-5918	114	20	x2	x2	PROPN
ejpam-5918	114	21	∈	∈	PROPN
ejpam-5918	114	22	v	v	X
ejpam-5918	114	23	(	(	PUNCT
ejpam-5918	114	24	km	km	PROPN
ejpam-5918	114	25	,	,	PUNCT
ejpam-5918	114	26	n	n	CCONJ
ejpam-5918	114	27	)	)	PUNCT
ejpam-5918	114	28	.	.	PUNCT
ejpam-5918	115	1	this	this	PRON
ejpam-5918	115	2	implies	imply	VERB
ejpam-5918	115	3	n(x1)∩i	n(x1)∩i	PROPN
ejpam-5918	115	4	=	=	SYM
ejpam-5918	115	5	{	{	PUNCT
ejpam-5918	115	6	y1	y1	PROPN
ejpam-5918	115	7	,	,	PUNCT
ejpam-5918	115	8	y2	y2	PROPN
ejpam-5918	115	9	,	,	PUNCT
ejpam-5918	115	10	.	.	PUNCT
ejpam-5918	115	11	.	.	PUNCT
ejpam-5918	115	12	.	.	PUNCT
ejpam-5918	116	1	,	,	PUNCT
ejpam-5918	116	2	yn	yn	PROPN
ejpam-5918	116	3	}	}	PUNCT
ejpam-5918	116	4	,	,	PUNCT
ejpam-5918	116	5	and	and	CCONJ
ejpam-5918	116	6	n(x2)∩i	n(x2)∩i	PROPN
ejpam-5918	116	7	=	=	PROPN
ejpam-5918	116	8	{	{	PUNCT
ejpam-5918	116	9	y1	y1	PROPN
ejpam-5918	116	10	,	,	PUNCT
ejpam-5918	116	11	y2	y2	PROPN
ejpam-5918	116	12	,	,	PUNCT
ejpam-5918	116	13	.	.	PUNCT
ejpam-5918	116	14	.	.	PUNCT
ejpam-5918	117	1	.	.	PUNCT
ejpam-5918	118	1	,	,	PUNCT
ejpam-5918	118	2	yn	yn	PROPN
ejpam-5918	118	3	}	}	PUNCT
ejpam-5918	118	4	.	.	PUNCT
ejpam-5918	119	1	thus	thus	ADV
ejpam-5918	119	2	,	,	PUNCT
ejpam-5918	119	3	n(x1)∩i	n(x1)∩i	PROPN
ejpam-5918	119	4	=	=	SYM
ejpam-5918	119	5	n(x2)∩i	n(x2)∩i	NOUN
ejpam-5918	119	6	.	.	PUNCT
ejpam-5918	120	1	hence	hence	ADV
ejpam-5918	120	2	,	,	PUNCT
ejpam-5918	120	3	i	i	PRON
ejpam-5918	120	4	is	be	AUX
ejpam-5918	120	5	neither	neither	CCONJ
ejpam-5918	120	6	an	an	DET
ejpam-5918	120	7	ils	ils	NOUN
ejpam-5918	120	8	nor	nor	CCONJ
ejpam-5918	120	9	ilds	ild	NOUN
ejpam-5918	120	10	.	.	PUNCT
ejpam-5918	121	1	this	this	PRON
ejpam-5918	121	2	is	be	AUX
ejpam-5918	121	3	also	also	ADV
ejpam-5918	121	4	true	true	ADJ
ejpam-5918	121	5	for	for	ADP
ejpam-5918	121	6	h	h	NOUN
ejpam-5918	121	7	=	=	SYM
ejpam-5918	121	8	k1,n	k1,n	PROPN
ejpam-5918	121	9	,	,	PUNCT
ejpam-5918	121	10	n	n	PRON
ejpam-5918	121	11	≥	≥	NOUN
ejpam-5918	121	12	3	3	NUM
ejpam-5918	121	13	.	.	PUNCT
ejpam-5918	122	1	finally	finally	ADV
ejpam-5918	122	2	,	,	PUNCT
ejpam-5918	122	3	by	by	ADP
ejpam-5918	122	4	(	(	PUNCT
ejpam-5918	122	5	iv	iv	X
ejpam-5918	122	6	)	)	PUNCT
ejpam-5918	122	7	,	,	PUNCT
ejpam-5918	122	8	if	if	SCONJ
ejpam-5918	122	9	h	h	NOUN
ejpam-5918	122	10	=	=	SYM
ejpam-5918	122	11	d4	d4	PROPN
ejpam-5918	122	12	,	,	PUNCT
ejpam-5918	122	13	let	let	VERB
ejpam-5918	122	14	v	v	X
ejpam-5918	122	15	(	(	PUNCT
ejpam-5918	122	16	h	h	NOUN
ejpam-5918	122	17	)	)	PUNCT
ejpam-5918	122	18	=	=	NOUN
ejpam-5918	122	19	v	v	X
ejpam-5918	122	20	(	(	PUNCT
ejpam-5918	122	21	d4	d4	PROPN
ejpam-5918	122	22	)	)	PUNCT
ejpam-5918	122	23	=	=	PRON
ejpam-5918	122	24	{	{	PUNCT
ejpam-5918	122	25	d1	d1	PROPN
ejpam-5918	122	26	,	,	PUNCT
ejpam-5918	122	27	d2	d2	PROPN
ejpam-5918	122	28	,	,	PUNCT
ejpam-5918	122	29	d3	d3	PROPN
ejpam-5918	122	30	,	,	PUNCT
ejpam-5918	122	31	d4	d4	PROPN
ejpam-5918	122	32	}	}	PUNCT
ejpam-5918	122	33	and	and	CCONJ
ejpam-5918	122	34	e(h	e(h	PROPN
ejpam-5918	122	35	)	)	PUNCT
ejpam-5918	122	36	=	=	SYM
ejpam-5918	122	37	e(d4	e(d4	NOUN
ejpam-5918	122	38	)	)	PUNCT
ejpam-5918	122	39	=	=	SYM
ejpam-5918	122	40	{	{	PUNCT
ejpam-5918	122	41	d1d2	d1d2	X
ejpam-5918	122	42	,	,	PUNCT
ejpam-5918	122	43	d2d3	d2d3	PROPN
ejpam-5918	122	44	,	,	PUNCT
ejpam-5918	122	45	d3d4	d3d4	PROPN
ejpam-5918	122	46	,	,	PUNCT
ejpam-5918	122	47	d4d1	d4d1	X
ejpam-5918	122	48	,	,	PUNCT
ejpam-5918	122	49	d1d3	d1d3	NOUN
ejpam-5918	122	50	}	}	PUNCT
ejpam-5918	122	51	.	.	PUNCT
ejpam-5918	123	1	note	note	VERB
ejpam-5918	123	2	that	that	SCONJ
ejpam-5918	123	3	h	h	NOUN
ejpam-5918	123	4	⊆	⊆	NUM
ejpam-5918	123	5	g[i	g[i	X
ejpam-5918	123	6	]	]	X
ejpam-5918	123	7	,	,	PUNCT
ejpam-5918	123	8	thus	thus	ADV
ejpam-5918	123	9	v	v	ADJ
ejpam-5918	123	10	(	(	PUNCT
ejpam-5918	123	11	h	h	NOUN
ejpam-5918	123	12	)	)	PUNCT
ejpam-5918	123	13	⊆	⊆	NUM
ejpam-5918	123	14	i.	i.	NOUN
ejpam-5918	123	15	observe	observe	VERB
ejpam-5918	123	16	that	that	SCONJ
ejpam-5918	123	17	n(d2)∩	n(d2)∩	NOUN
ejpam-5918	123	18	i	i	PRON
ejpam-5918	123	19	=	=	SYM
ejpam-5918	123	20	{	{	PUNCT
ejpam-5918	123	21	d1	d1	PROPN
ejpam-5918	123	22	,	,	PUNCT
ejpam-5918	123	23	d3	d3	PROPN
ejpam-5918	123	24	}	}	PUNCT
ejpam-5918	123	25	=	=	SYM
ejpam-5918	123	26	n(d4	n(d4	ADJ
ejpam-5918	123	27	)	)	PUNCT
ejpam-5918	123	28	∩	∩	PROPN
ejpam-5918	123	29	i.	i.	NOUN
ejpam-5918	123	30	thus	thus	ADV
ejpam-5918	123	31	,	,	PUNCT
ejpam-5918	123	32	i	i	PRON
ejpam-5918	123	33	is	be	AUX
ejpam-5918	123	34	neither	neither	CCONJ
ejpam-5918	123	35	an	an	DET
ejpam-5918	123	36	ils	ils	NOUN
ejpam-5918	123	37	nor	nor	CCONJ
ejpam-5918	123	38	ilds	ild	NOUN
ejpam-5918	123	39	.	.	PUNCT
ejpam-5918	124	1	theorem	theorem	NOUN
ejpam-5918	124	2	2	2	NUM
ejpam-5918	124	3	.	.	PUNCT
ejpam-5918	125	1	let	let	VERB
ejpam-5918	125	2	g	g	PRON
ejpam-5918	125	3	be	be	AUX
ejpam-5918	125	4	a	a	DET
ejpam-5918	125	5	graph	graph	NOUN
ejpam-5918	125	6	.	.	PUNCT
ejpam-5918	126	1	then	then	ADV
ejpam-5918	126	2	γli(g	γli(g	PROPN
ejpam-5918	126	3	)	)	PUNCT
ejpam-5918	127	1	=	=	SYM
ejpam-5918	127	2	2	2	NUM
ejpam-5918	127	3	if	if	SCONJ
ejpam-5918	127	4	one	one	NUM
ejpam-5918	127	5	of	of	ADP
ejpam-5918	127	6	the	the	DET
ejpam-5918	127	7	following	follow	VERB
ejpam-5918	127	8	hold	hold	NOUN
ejpam-5918	127	9	:	:	PUNCT
ejpam-5918	127	10	(	(	PUNCT
ejpam-5918	127	11	i	i	NOUN
ejpam-5918	127	12	)	)	PUNCT
ejpam-5918	127	13	γ(g	γ(g	PROPN
ejpam-5918	127	14	)	)	PUNCT
ejpam-5918	127	15	=	=	SYM
ejpam-5918	127	16	1	1	NUM
ejpam-5918	127	17	(	(	PUNCT
ejpam-5918	127	18	ii	ii	NOUN
ejpam-5918	127	19	)	)	PUNCT
ejpam-5918	127	20	γ(g	γ(g	PROPN
ejpam-5918	127	21	)	)	PUNCT
ejpam-5918	128	1	=	=	SYM
ejpam-5918	128	2	2	2	NUM
ejpam-5918	128	3	,	,	PUNCT
ejpam-5918	128	4	where	where	SCONJ
ejpam-5918	128	5	{	{	PUNCT
ejpam-5918	128	6	u	u	NOUN
ejpam-5918	128	7	,	,	PUNCT
ejpam-5918	128	8	v	v	NOUN
ejpam-5918	128	9	}	}	PUNCT
ejpam-5918	128	10	is	be	AUX
ejpam-5918	128	11	the	the	DET
ejpam-5918	128	12	γ	γ	X
ejpam-5918	128	13	−	−	NOUN
ejpam-5918	128	14	set	set	NOUN
ejpam-5918	128	15	and	and	CCONJ
ejpam-5918	128	16	u	u	NOUN
ejpam-5918	128	17	,	,	PUNCT
ejpam-5918	128	18	v	v	NOUN
ejpam-5918	128	19	are	be	AUX
ejpam-5918	128	20	adjacent	adjacent	ADJ
ejpam-5918	128	21	.	.	PUNCT
ejpam-5918	129	1	proof	proof	NOUN
ejpam-5918	129	2	.	.	PUNCT
ejpam-5918	130	1	let	let	VERB
ejpam-5918	130	2	g	g	PRON
ejpam-5918	130	3	be	be	AUX
ejpam-5918	130	4	a	a	DET
ejpam-5918	130	5	graph	graph	NOUN
ejpam-5918	130	6	.	.	PUNCT
ejpam-5918	131	1	case	case	NOUN
ejpam-5918	131	2	1	1	NUM
ejpam-5918	131	3	:	:	PUNCT
ejpam-5918	131	4	if	if	SCONJ
ejpam-5918	131	5	γ(g	γ(g	PROPN
ejpam-5918	131	6	)	)	PUNCT
ejpam-5918	131	7	=	=	SYM
ejpam-5918	132	1	1	1	NUM
ejpam-5918	132	2	,	,	PUNCT
ejpam-5918	132	3	this	this	PRON
ejpam-5918	132	4	means	mean	VERB
ejpam-5918	132	5	that	that	SCONJ
ejpam-5918	132	6	there	there	PRON
ejpam-5918	132	7	exists	exist	VERB
ejpam-5918	132	8	a	a	DET
ejpam-5918	132	9	single	single	ADJ
ejpam-5918	132	10	vertex	vertex	NOUN
ejpam-5918	132	11	v	v	ADP
ejpam-5918	132	12	∈	∈	PROPN
ejpam-5918	132	13	v	v	NOUN
ejpam-5918	132	14	(	(	PUNCT
ejpam-5918	132	15	g	g	NOUN
ejpam-5918	132	16	)	)	PUNCT
ejpam-5918	132	17	such	such	ADJ
ejpam-5918	132	18	that	that	SCONJ
ejpam-5918	132	19	n(v	n(v	PROPN
ejpam-5918	132	20	)	)	PUNCT
ejpam-5918	132	21	=	=	SYM
ejpam-5918	132	22	v	v	X
ejpam-5918	132	23	(	(	PUNCT
ejpam-5918	132	24	g	g	NOUN
ejpam-5918	132	25	)	)	PUNCT
ejpam-5918	132	26	\	\	NOUN
ejpam-5918	132	27	{	{	PUNCT
ejpam-5918	132	28	v	v	NOUN
ejpam-5918	132	29	}	}	PUNCT
ejpam-5918	132	30	.	.	PUNCT
ejpam-5918	133	1	in	in	ADP
ejpam-5918	133	2	this	this	DET
ejpam-5918	133	3	case	case	NOUN
ejpam-5918	133	4	,	,	PUNCT
ejpam-5918	133	5	{	{	PUNCT
ejpam-5918	133	6	v	v	NOUN
ejpam-5918	133	7	}	}	PUNCT
ejpam-5918	133	8	is	be	AUX
ejpam-5918	133	9	the	the	DET
ejpam-5918	133	10	γ	γ	NOUN
ejpam-5918	133	11	-	-	PUNCT
ejpam-5918	133	12	set	set	NOUN
ejpam-5918	133	13	.	.	PUNCT
ejpam-5918	134	1	this	this	PRON
ejpam-5918	134	2	implies	imply	VERB
ejpam-5918	134	3	that	that	SCONJ
ejpam-5918	134	4	for	for	ADP
ejpam-5918	134	5	any	any	DET
ejpam-5918	134	6	u	u	PROPN
ejpam-5918	134	7	∈	∈	PROPN
ejpam-5918	134	8	v	v	NOUN
ejpam-5918	134	9	(	(	PUNCT
ejpam-5918	134	10	g	g	NOUN
ejpam-5918	134	11	)	)	PUNCT
ejpam-5918	134	12	,	,	PUNCT
ejpam-5918	134	13	u	u	PROPN
ejpam-5918	134	14	̸=	̸=	PROPN
ejpam-5918	134	15	v	v	NOUN
ejpam-5918	134	16	,	,	PUNCT
ejpam-5918	134	17	{	{	PUNCT
ejpam-5918	134	18	u	u	NOUN
ejpam-5918	134	19	,	,	PUNCT
ejpam-5918	134	20	v	v	NOUN
ejpam-5918	134	21	}	}	PUNCT
ejpam-5918	134	22	is	be	AUX
ejpam-5918	134	23	a	a	DET
ejpam-5918	134	24	dominating	dominating	NOUN
ejpam-5918	134	25	set	set	NOUN
ejpam-5918	134	26	.	.	PUNCT
ejpam-5918	135	1	since	since	SCONJ
ejpam-5918	135	2	n(v	n(v	PROPN
ejpam-5918	135	3	)	)	PUNCT
ejpam-5918	135	4	=	=	SYM
ejpam-5918	135	5	v	v	X
ejpam-5918	135	6	(	(	PUNCT
ejpam-5918	135	7	g	g	NOUN
ejpam-5918	135	8	)	)	PUNCT
ejpam-5918	135	9	\	\	NOUN
ejpam-5918	135	10	{	{	PUNCT
ejpam-5918	135	11	v	v	NOUN
ejpam-5918	135	12	}	}	PUNCT
ejpam-5918	135	13	,	,	PUNCT
ejpam-5918	135	14	and	and	CCONJ
ejpam-5918	135	15	u	u	NOUN
ejpam-5918	135	16	is	be	AUX
ejpam-5918	135	17	dominated	dominate	VERB
ejpam-5918	135	18	by	by	ADP
ejpam-5918	135	19	v	v	NOUN
ejpam-5918	135	20	,	,	PUNCT
ejpam-5918	135	21	this	this	PRON
ejpam-5918	135	22	implies	imply	VERB
ejpam-5918	135	23	n(u	n(u	PROPN
ejpam-5918	135	24	)	)	PUNCT
ejpam-5918	135	25	∩	∩	NOUN
ejpam-5918	135	26	{	{	PUNCT
ejpam-5918	135	27	u	u	NOUN
ejpam-5918	135	28	,	,	PUNCT
ejpam-5918	135	29	v	v	NOUN
ejpam-5918	135	30	}	}	PUNCT
ejpam-5918	135	31	=	=	SYM
ejpam-5918	135	32	{	{	PUNCT
ejpam-5918	135	33	v	v	NOUN
ejpam-5918	135	34	}	}	PUNCT
ejpam-5918	135	35	and	and	CCONJ
ejpam-5918	135	36	n(v	n(v	PROPN
ejpam-5918	135	37	)	)	PUNCT
ejpam-5918	135	38	∩	∩	NOUN
ejpam-5918	135	39	{	{	PUNCT
ejpam-5918	135	40	u	u	NOUN
ejpam-5918	135	41	,	,	PUNCT
ejpam-5918	135	42	v	v	NOUN
ejpam-5918	135	43	}	}	PUNCT
ejpam-5918	135	44	=	=	PUNCT
ejpam-5918	135	45	{	{	PUNCT
ejpam-5918	135	46	u	u	NOUN
ejpam-5918	135	47	}	}	PUNCT
ejpam-5918	135	48	.	.	PUNCT
ejpam-5918	136	1	thus	thus	ADV
ejpam-5918	136	2	,	,	PUNCT
ejpam-5918	136	3	n(u	n(u	PROPN
ejpam-5918	136	4	)	)	PUNCT
ejpam-5918	136	5	∩	∩	NOUN
ejpam-5918	136	6	{	{	PUNCT
ejpam-5918	136	7	u	u	NOUN
ejpam-5918	136	8	,	,	PUNCT
ejpam-5918	136	9	v	v	NOUN
ejpam-5918	136	10	}	}	PUNCT
ejpam-5918	136	11	̸=	̸=	PROPN
ejpam-5918	136	12	n(v	n(v	PROPN
ejpam-5918	136	13	)	)	PUNCT
ejpam-5918	136	14	∩	∩	NOUN
ejpam-5918	136	15	{	{	PUNCT
ejpam-5918	136	16	u	u	NOUN
ejpam-5918	136	17	,	,	PUNCT
ejpam-5918	136	18	v	v	NOUN
ejpam-5918	136	19	}	}	PUNCT
ejpam-5918	136	20	,	,	PUNCT
ejpam-5918	136	21	which	which	PRON
ejpam-5918	136	22	confirms	confirm	VERB
ejpam-5918	136	23	that	that	SCONJ
ejpam-5918	136	24	{	{	PUNCT
ejpam-5918	136	25	u	u	NOUN
ejpam-5918	136	26	,	,	PUNCT
ejpam-5918	136	27	v	v	NOUN
ejpam-5918	136	28	}	}	PUNCT
ejpam-5918	136	29	is	be	AUX
ejpam-5918	136	30	an	an	DET
ejpam-5918	136	31	internally	internally	ADV
ejpam-5918	136	32	-	-	PUNCT
ejpam-5918	136	33	locating	locate	VERB
ejpam-5918	136	34	set	set	NOUN
ejpam-5918	136	35	.	.	PUNCT
ejpam-5918	137	1	by	by	ADP
ejpam-5918	137	2	definition	definition	NOUN
ejpam-5918	137	3	of	of	ADP
ejpam-5918	137	4	γli	γli	PROPN
ejpam-5918	137	5	−	−	PROPN
ejpam-5918	137	6	set	set	NOUN
ejpam-5918	137	7	,	,	PUNCT
ejpam-5918	137	8	this	this	PRON
ejpam-5918	137	9	follows	follow	VERB
ejpam-5918	137	10	that	that	PRON
ejpam-5918	137	11	γli(g	γli(g	ADV
ejpam-5918	137	12	)	)	PUNCT
ejpam-5918	137	13	=	=	SYM
ejpam-5918	137	14	2	2	NUM
ejpam-5918	137	15	in	in	ADP
ejpam-5918	137	16	this	this	DET
ejpam-5918	137	17	case	case	NOUN
ejpam-5918	137	18	.	.	PUNCT
ejpam-5918	138	1	case	case	NOUN
ejpam-5918	138	2	2	2	NUM
ejpam-5918	138	3	:	:	PUNCT
ejpam-5918	138	4	if	if	SCONJ
ejpam-5918	138	5	γ(g	γ(g	PROPN
ejpam-5918	138	6	)	)	PUNCT
ejpam-5918	138	7	=	=	SYM
ejpam-5918	139	1	2	2	NUM
ejpam-5918	139	2	,	,	PUNCT
ejpam-5918	139	3	where	where	SCONJ
ejpam-5918	139	4	{	{	PUNCT
ejpam-5918	139	5	u	u	NOUN
ejpam-5918	139	6	,	,	PUNCT
ejpam-5918	139	7	v	v	NOUN
ejpam-5918	139	8	}	}	PUNCT
ejpam-5918	139	9	is	be	AUX
ejpam-5918	139	10	the	the	DET
ejpam-5918	139	11	γ	γ	X
ejpam-5918	139	12	−	−	NOUN
ejpam-5918	139	13	set	set	NOUN
ejpam-5918	139	14	and	and	CCONJ
ejpam-5918	139	15	u	u	NOUN
ejpam-5918	139	16	,	,	PUNCT
ejpam-5918	139	17	v	v	NOUN
ejpam-5918	139	18	are	be	AUX
ejpam-5918	139	19	adjacent	adjacent	ADJ
ejpam-5918	139	20	.	.	PUNCT
ejpam-5918	140	1	clearly	clearly	ADV
ejpam-5918	140	2	,	,	PUNCT
ejpam-5918	140	3	{	{	PUNCT
ejpam-5918	140	4	u	u	NOUN
ejpam-5918	140	5	,	,	PUNCT
ejpam-5918	140	6	v	v	NOUN
ejpam-5918	140	7	}	}	PUNCT
ejpam-5918	140	8	is	be	AUX
ejpam-5918	140	9	γli	γli	ADJ
ejpam-5918	140	10	−	−	PROPN
ejpam-5918	140	11	set	set	NOUN
ejpam-5918	140	12	.	.	PUNCT
ejpam-5918	141	1	hence	hence	ADV
ejpam-5918	141	2	,	,	PUNCT
ejpam-5918	141	3	γli(g	γli(g	PROPN
ejpam-5918	141	4	)	)	PUNCT
ejpam-5918	141	5	=	=	SYM
ejpam-5918	141	6	2	2	NUM
ejpam-5918	141	7	in	in	ADP
ejpam-5918	141	8	this	this	DET
ejpam-5918	141	9	case	case	NOUN
ejpam-5918	141	10	.	.	PUNCT
ejpam-5918	142	1	corollary	corollary	ADJ
ejpam-5918	142	2	2	2	NUM
ejpam-5918	142	3	.	.	PUNCT
ejpam-5918	143	1	the	the	DET
ejpam-5918	143	2	γli(g	γli(g	PROPN
ejpam-5918	143	3	)	)	PUNCT
ejpam-5918	143	4	=	=	SYM
ejpam-5918	143	5	2	2	NUM
ejpam-5918	143	6	if	if	SCONJ
ejpam-5918	143	7	(	(	PUNCT
ejpam-5918	143	8	i	i	NOUN
ejpam-5918	143	9	)	)	PUNCT
ejpam-5918	143	10	g	g	PROPN
ejpam-5918	143	11	=	=	PUNCT
ejpam-5918	143	12	pn	pn	PROPN
ejpam-5918	143	13	=	=	SYM
ejpam-5918	143	14	cn	cn	PROPN
ejpam-5918	143	15	,	,	PUNCT
ejpam-5918	143	16	2	2	NUM
ejpam-5918	143	17	≤	≤	NUM
ejpam-5918	143	18	n	n	CCONJ
ejpam-5918	143	19	≤	≤	NOUN
ejpam-5918	143	20	3	3	NUM
ejpam-5918	143	21	;	;	PUNCT
ejpam-5918	143	22	(	(	PUNCT
ejpam-5918	143	23	ii	ii	NOUN
ejpam-5918	143	24	)	)	PUNCT
ejpam-5918	143	25	g	g	PROPN
ejpam-5918	143	26	=	=	SYM
ejpam-5918	143	27	kn	kn	PROPN
ejpam-5918	143	28	,	,	PUNCT
ejpam-5918	143	29	n	n	PROPN
ejpam-5918	143	30	≥	≥	NOUN
ejpam-5918	143	31	2	2	NUM
ejpam-5918	143	32	i.	i.	NOUN
ejpam-5918	143	33	tropico	tropico	PROPN
ejpam-5918	143	34	,	,	PUNCT
ejpam-5918	143	35	i.	i.	PROPN
ejpam-5918	143	36	cabahug	cabahug	PROPN
ejpam-5918	143	37	,	,	PUNCT
ejpam-5918	143	38	jr	jr	PROPN
ejpam-5918	143	39	.	.	PROPN
ejpam-5918	143	40	/	/	SYM
ejpam-5918	143	41	eur	eur	PROPN
ejpam-5918	143	42	.	.	PUNCT
ejpam-5918	144	1	j.	j.	PROPN
ejpam-5918	144	2	pure	pure	PROPN
ejpam-5918	144	3	appl	appl	PROPN
ejpam-5918	144	4	.	.	PROPN
ejpam-5918	144	5	math	math	PROPN
ejpam-5918	144	6	,	,	PUNCT
ejpam-5918	144	7	18	18	NUM
ejpam-5918	144	8	(	(	PUNCT
ejpam-5918	144	9	2	2	NUM
ejpam-5918	144	10	)	)	PUNCT
ejpam-5918	144	11	(	(	PUNCT
ejpam-5918	144	12	2025	2025	NUM
ejpam-5918	144	13	)	)	PUNCT
ejpam-5918	144	14	,	,	PUNCT
ejpam-5918	144	15	5918	5918	NUM
ejpam-5918	144	16	7	7	NUM
ejpam-5918	144	17	of	of	ADP
ejpam-5918	144	18	21	21	NUM
ejpam-5918	144	19	(	(	PUNCT
ejpam-5918	144	20	iii	iii	NOUN
ejpam-5918	144	21	)	)	PUNCT
ejpam-5918	144	22	g	g	NOUN
ejpam-5918	144	23	=	=	SYM
ejpam-5918	144	24	k1,n	k1,n	PROPN
ejpam-5918	144	25	,	,	PUNCT
ejpam-5918	144	26	n	n	PRON
ejpam-5918	144	27	≥	≥	NOUN
ejpam-5918	144	28	2	2	NUM
ejpam-5918	144	29	;	;	PUNCT
ejpam-5918	144	30	(	(	PUNCT
ejpam-5918	144	31	iv	iv	X
ejpam-5918	144	32	)	)	PUNCT
ejpam-5918	144	33	g	g	NOUN
ejpam-5918	144	34	=	=	SYM
ejpam-5918	144	35	fn	fn	PROPN
ejpam-5918	144	36	,	,	PUNCT
ejpam-5918	144	37	n	n	PRON
ejpam-5918	144	38	≥	≥	NOUN
ejpam-5918	144	39	2	2	NUM
ejpam-5918	144	40	;	;	PUNCT
ejpam-5918	144	41	and	and	CCONJ
ejpam-5918	144	42	(	(	PUNCT
ejpam-5918	144	43	v	v	NOUN
ejpam-5918	144	44	)	)	PUNCT
ejpam-5918	144	45	g	g	PROPN
ejpam-5918	144	46	=	=	SYM
ejpam-5918	144	47	wn	wn	PROPN
ejpam-5918	144	48	,	,	PUNCT
ejpam-5918	144	49	n	n	PRON
ejpam-5918	144	50	≥	≥	NOUN
ejpam-5918	144	51	4	4	NUM
ejpam-5918	144	52	.	.	PUNCT
ejpam-5918	145	1	proof	proof	NOUN
ejpam-5918	145	2	.	.	PUNCT
ejpam-5918	146	1	this	this	PRON
ejpam-5918	146	2	follows	follow	VERB
ejpam-5918	146	3	from	from	ADP
ejpam-5918	146	4	the	the	DET
ejpam-5918	146	5	definition	definition	NOUN
ejpam-5918	146	6	of	of	ADP
ejpam-5918	146	7	dominating	dominate	VERB
ejpam-5918	146	8	set	set	NOUN
ejpam-5918	146	9	and	and	CCONJ
ejpam-5918	146	10	theorem	theorem	VERB
ejpam-5918	146	11	2	2	NUM
ejpam-5918	146	12	(	(	PUNCT
ejpam-5918	146	13	i	i	NOUN
ejpam-5918	146	14	)	)	PUNCT
ejpam-5918	146	15	.	.	PUNCT
ejpam-5918	147	1	theorem	theorem	NOUN
ejpam-5918	147	2	3	3	X
ejpam-5918	147	3	.	.	PUNCT
ejpam-5918	148	1	let	let	VERB
ejpam-5918	148	2	g	g	PRON
ejpam-5918	148	3	be	be	AUX
ejpam-5918	148	4	a	a	DET
ejpam-5918	148	5	graph	graph	NOUN
ejpam-5918	148	6	with	with	ADP
ejpam-5918	148	7	n	n	PRON
ejpam-5918	148	8	≥	≥	NUM
ejpam-5918	148	9	4	4	NUM
ejpam-5918	148	10	.	.	PUNCT
ejpam-5918	148	11	then	then	ADV
ejpam-5918	148	12	γ(g	γ(g	PROPN
ejpam-5918	148	13	)	)	PUNCT
ejpam-5918	149	1	=	=	PUNCT
ejpam-5918	149	2	γli(g	γli(g	PROPN
ejpam-5918	149	3	)	)	PUNCT
ejpam-5918	149	4	if	if	SCONJ
ejpam-5918	149	5	g	g	PROPN
ejpam-5918	149	6	=	=	SYM
ejpam-5918	149	7	pn	pn	PROPN
ejpam-5918	149	8	◦	◦	PROPN
ejpam-5918	149	9	h	h	PROPN
ejpam-5918	149	10	,	,	PUNCT
ejpam-5918	149	11	for	for	ADP
ejpam-5918	149	12	any	any	DET
ejpam-5918	149	13	graph	graph	NOUN
ejpam-5918	149	14	variation	variation	NOUN
ejpam-5918	149	15	of	of	ADP
ejpam-5918	149	16	h.	h.	NOUN
ejpam-5918	149	17	proof	proof	NOUN
ejpam-5918	149	18	.	.	PUNCT
ejpam-5918	150	1	let	let	VERB
ejpam-5918	150	2	g	g	PRON
ejpam-5918	150	3	be	be	AUX
ejpam-5918	150	4	a	a	DET
ejpam-5918	150	5	graph	graph	NOUN
ejpam-5918	150	6	with	with	ADP
ejpam-5918	150	7	n	n	NUM
ejpam-5918	150	8	≥	≥	NOUN
ejpam-5918	150	9	4	4	NUM
ejpam-5918	150	10	and	and	CCONJ
ejpam-5918	150	11	g	g	NOUN
ejpam-5918	150	12	=	=	SYM
ejpam-5918	150	13	pn	pn	PROPN
ejpam-5918	150	14	◦	◦	PROPN
ejpam-5918	150	15	h	h	NOUN
ejpam-5918	150	16	,	,	PUNCT
ejpam-5918	150	17	for	for	ADP
ejpam-5918	150	18	any	any	DET
ejpam-5918	150	19	graph	graph	NOUN
ejpam-5918	150	20	variation	variation	NOUN
ejpam-5918	150	21	of	of	ADP
ejpam-5918	150	22	h.	h.	NOUN
ejpam-5918	150	23	by	by	ADP
ejpam-5918	150	24	corollary	corollary	ADJ
ejpam-5918	150	25	1	1	NUM
ejpam-5918	150	26	,	,	PUNCT
ejpam-5918	150	27	γ(g	γ(g	PROPN
ejpam-5918	150	28	)	)	PUNCT
ejpam-5918	151	1	=	=	VERB
ejpam-5918	151	2	n.	n.	NOUN
ejpam-5918	151	3	by	by	ADP
ejpam-5918	151	4	definition	definition	NOUN
ejpam-5918	151	5	of	of	ADP
ejpam-5918	151	6	path	path	NOUN
ejpam-5918	151	7	graph	graph	NOUN
ejpam-5918	151	8	pn	pn	PROPN
ejpam-5918	151	9	and	and	CCONJ
ejpam-5918	151	10	since	since	SCONJ
ejpam-5918	151	11	g	g	PROPN
ejpam-5918	151	12	=	=	SYM
ejpam-5918	151	13	pn	pn	PROPN
ejpam-5918	151	14	◦	◦	PROPN
ejpam-5918	151	15	h	h	PROPN
ejpam-5918	151	16	,	,	PUNCT
ejpam-5918	151	17	v	v	PROPN
ejpam-5918	151	18	(	(	PUNCT
ejpam-5918	151	19	pn	pn	NOUN
ejpam-5918	151	20	)	)	PUNCT
ejpam-5918	151	21	=	=	SYM
ejpam-5918	151	22	{	{	PUNCT
ejpam-5918	151	23	v1	v1	PROPN
ejpam-5918	151	24	,	,	PUNCT
ejpam-5918	151	25	v2	v2	PROPN
ejpam-5918	151	26	,	,	PUNCT
ejpam-5918	151	27	.	.	PUNCT
ejpam-5918	151	28	.	.	PUNCT
ejpam-5918	151	29	.	.	PUNCT
ejpam-5918	152	1	,	,	PUNCT
ejpam-5918	152	2	vn	vn	PROPN
ejpam-5918	152	3	}	}	PUNCT
ejpam-5918	152	4	is	be	AUX
ejpam-5918	152	5	a	a	DET
ejpam-5918	152	6	γ	γ	NOUN
ejpam-5918	152	7	−	−	NOUN
ejpam-5918	152	8	set	set	NOUN
ejpam-5918	152	9	.	.	PUNCT
ejpam-5918	153	1	now	now	ADV
ejpam-5918	153	2	,	,	PUNCT
ejpam-5918	153	3	observe	observe	VERB
ejpam-5918	153	4	that	that	SCONJ
ejpam-5918	153	5	n(v1	n(v1	NOUN
ejpam-5918	153	6	)	)	PUNCT
ejpam-5918	153	7	∩	∩	ADJ
ejpam-5918	153	8	v	v	X
ejpam-5918	153	9	(	(	PUNCT
ejpam-5918	153	10	pn	pn	NOUN
ejpam-5918	153	11	)	)	PUNCT
ejpam-5918	153	12	=	=	PRON
ejpam-5918	153	13	{	{	PUNCT
ejpam-5918	153	14	v2	v2	NOUN
ejpam-5918	153	15	}	}	PUNCT
ejpam-5918	153	16	,	,	PUNCT
ejpam-5918	153	17	n(vi	n(vi	NUM
ejpam-5918	153	18	)	)	PUNCT
ejpam-5918	153	19	∩	∩	NOUN
ejpam-5918	153	20	v	v	X
ejpam-5918	153	21	(	(	PUNCT
ejpam-5918	153	22	pn	pn	NOUN
ejpam-5918	153	23	)	)	PUNCT
ejpam-5918	153	24	=	=	PRON
ejpam-5918	153	25	{	{	PUNCT
ejpam-5918	153	26	vi−1	vi−1	PROPN
ejpam-5918	153	27	,	,	PUNCT
ejpam-5918	153	28	vi+1	vi+1	NOUN
ejpam-5918	153	29	}	}	PUNCT
ejpam-5918	153	30	,	,	PUNCT
ejpam-5918	153	31	2	2	NUM
ejpam-5918	153	32	≤	≤	NUM
ejpam-5918	153	33	i	i	PRON
ejpam-5918	153	34	≤	≤	ADJ
ejpam-5918	153	35	n−	n−	PROPN
ejpam-5918	153	36	1	1	NUM
ejpam-5918	153	37	n(vn	n(vn	NOUN
ejpam-5918	153	38	)	)	PUNCT
ejpam-5918	153	39	∩	∩	ADJ
ejpam-5918	153	40	v	v	X
ejpam-5918	153	41	(	(	PUNCT
ejpam-5918	153	42	pn	pn	NOUN
ejpam-5918	153	43	)	)	PUNCT
ejpam-5918	153	44	=	=	PUNCT
ejpam-5918	153	45	{	{	PUNCT
ejpam-5918	153	46	vn−1	vn−1	PROPN
ejpam-5918	153	47	}	}	PUNCT
ejpam-5918	153	48	.	.	PUNCT
ejpam-5918	154	1	thus	thus	ADV
ejpam-5918	154	2	,	,	PUNCT
ejpam-5918	154	3	v	v	INTJ
ejpam-5918	154	4	(	(	PUNCT
ejpam-5918	154	5	pn	pn	NOUN
ejpam-5918	154	6	)	)	PUNCT
ejpam-5918	154	7	is	be	AUX
ejpam-5918	154	8	an	an	DET
ejpam-5918	154	9	ils	ils	NOUN
ejpam-5918	154	10	and	and	CCONJ
ejpam-5918	154	11	γli	γli	ADJ
ejpam-5918	154	12	−	−	PROPN
ejpam-5918	154	13	set	set	NOUN
ejpam-5918	154	14	.	.	PUNCT
ejpam-5918	155	1	hence	hence	ADV
ejpam-5918	155	2	γli(g	γli(g	PROPN
ejpam-5918	155	3	)	)	PUNCT
ejpam-5918	156	1	=	=	SYM
ejpam-5918	156	2	n.	n.	PROPN
ejpam-5918	156	3	therefore	therefore	ADV
ejpam-5918	156	4	,	,	PUNCT
ejpam-5918	156	5	γ(g	γ(g	PROPN
ejpam-5918	156	6	)	)	PUNCT
ejpam-5918	156	7	=	=	SYM
ejpam-5918	156	8	γli(g	γli(g	PROPN
ejpam-5918	156	9	)	)	PUNCT
ejpam-5918	156	10	.	.	PUNCT
ejpam-5918	157	1	theorem	theorem	ADJ
ejpam-5918	157	2	4	4	NUM
ejpam-5918	157	3	.	.	PUNCT
ejpam-5918	158	1	let	let	VERB
ejpam-5918	158	2	g	g	PRON
ejpam-5918	158	3	be	be	AUX
ejpam-5918	158	4	a	a	DET
ejpam-5918	158	5	graph	graph	NOUN
ejpam-5918	158	6	with	with	ADP
ejpam-5918	158	7	∆(g	∆(g	NOUN
ejpam-5918	158	8	)	)	PUNCT
ejpam-5918	158	9	=	=	SYM
ejpam-5918	158	10	2	2	NUM
ejpam-5918	158	11	and	and	CCONJ
ejpam-5918	158	12	i	i	PRON
ejpam-5918	159	1	⊆	⊆	NUM
ejpam-5918	159	2	v	v	X
ejpam-5918	159	3	(	(	PUNCT
ejpam-5918	159	4	g	g	NOUN
ejpam-5918	159	5	)	)	PUNCT
ejpam-5918	159	6	such	such	ADJ
ejpam-5918	159	7	that	that	PRON
ejpam-5918	159	8	|i|	|i|	VERB
ejpam-5918	159	9	≥	≥	NOUN
ejpam-5918	159	10	2	2	NUM
ejpam-5918	159	11	.	.	PUNCT
ejpam-5918	160	1	then	then	ADV
ejpam-5918	160	2	i	i	PRON
ejpam-5918	160	3	is	be	AUX
ejpam-5918	160	4	the	the	DET
ejpam-5918	160	5	minimum	minimum	NOUN
ejpam-5918	160	6	internally	internally	ADV
ejpam-5918	160	7	-	-	PUNCT
ejpam-5918	160	8	locating	locate	VERB
ejpam-5918	160	9	dominating	dominating	NOUN
ejpam-5918	160	10	set	set	VERB
ejpam-5918	160	11	in	in	ADP
ejpam-5918	160	12	g	g	PROPN
ejpam-5918	160	13	if	if	SCONJ
ejpam-5918	161	1	and	and	CCONJ
ejpam-5918	161	2	only	only	ADV
ejpam-5918	161	3	if	if	SCONJ
ejpam-5918	161	4	the	the	DET
ejpam-5918	161	5	following	follow	VERB
ejpam-5918	161	6	holds	hold	VERB
ejpam-5918	161	7	:	:	PUNCT
ejpam-5918	161	8	(	(	PUNCT
ejpam-5918	161	9	i	i	NOUN
ejpam-5918	161	10	)	)	PUNCT
ejpam-5918	161	11	if	if	SCONJ
ejpam-5918	161	12	degi(v	degi(v	NOUN
ejpam-5918	161	13	)	)	PUNCT
ejpam-5918	161	14	=	=	SYM
ejpam-5918	161	15	1	1	NUM
ejpam-5918	161	16	,	,	PUNCT
ejpam-5918	161	17	then	then	ADV
ejpam-5918	161	18	degv	degv	NOUN
ejpam-5918	161	19	(	(	PUNCT
ejpam-5918	161	20	g)\i(v	g)\i(v	PROPN
ejpam-5918	161	21	)	)	PUNCT
ejpam-5918	161	22	=	=	SYM
ejpam-5918	162	1	1	1	NUM
ejpam-5918	162	2	;	;	PUNCT
ejpam-5918	162	3	(	(	PUNCT
ejpam-5918	162	4	ii	ii	NOUN
ejpam-5918	162	5	)	)	PUNCT
ejpam-5918	162	6	if	if	SCONJ
ejpam-5918	162	7	degi(v	degi(v	NOUN
ejpam-5918	162	8	)	)	PUNCT
ejpam-5918	162	9	=	=	SYM
ejpam-5918	162	10	0	0	NUM
ejpam-5918	162	11	,	,	PUNCT
ejpam-5918	162	12	then	then	ADV
ejpam-5918	162	13	v	v	NOUN
ejpam-5918	162	14	is	be	AUX
ejpam-5918	162	15	unique	unique	ADJ
ejpam-5918	162	16	in	in	ADP
ejpam-5918	162	17	i	i	PRON
ejpam-5918	162	18	;	;	PUNCT
ejpam-5918	162	19	(	(	PUNCT
ejpam-5918	162	20	iii	iii	X
ejpam-5918	162	21	)	)	PUNCT
ejpam-5918	162	22	if	if	SCONJ
ejpam-5918	162	23	degi(v	degi(v	NOUN
ejpam-5918	162	24	)	)	PUNCT
ejpam-5918	162	25	=	=	SYM
ejpam-5918	162	26	0	0	NUM
ejpam-5918	162	27	and	and	CCONJ
ejpam-5918	162	28	deg(v	deg(v	PROPN
ejpam-5918	162	29	)	)	PUNCT
ejpam-5918	162	30	=	=	SYM
ejpam-5918	162	31	1	1	NUM
ejpam-5918	162	32	or	or	CCONJ
ejpam-5918	162	33	2	2	NUM
ejpam-5918	162	34	,	,	PUNCT
ejpam-5918	162	35	then	then	ADV
ejpam-5918	162	36	degv	degv	NOUN
ejpam-5918	162	37	(	(	PUNCT
ejpam-5918	162	38	g)\i(v	g)\i(v	NOUN
ejpam-5918	162	39	)	)	PUNCT
ejpam-5918	162	40	=	=	SYM
ejpam-5918	162	41	deg(v	deg(v	PROPN
ejpam-5918	162	42	)	)	PUNCT
ejpam-5918	162	43	;	;	PUNCT
ejpam-5918	162	44	and	and	CCONJ
ejpam-5918	162	45	(	(	PUNCT
ejpam-5918	162	46	iv	iv	X
ejpam-5918	162	47	)	)	PUNCT
ejpam-5918	162	48	for	for	ADP
ejpam-5918	162	49	all	all	PRON
ejpam-5918	162	50	u	u	PROPN
ejpam-5918	162	51	∈	∈	PROPN
ejpam-5918	162	52	v	v	NOUN
ejpam-5918	162	53	(	(	PUNCT
ejpam-5918	162	54	g	g	NOUN
ejpam-5918	162	55	)	)	PUNCT
ejpam-5918	162	56	\	\	PUNCT
ejpam-5918	163	1	i	i	PRON
ejpam-5918	163	2	,	,	PUNCT
ejpam-5918	163	3	u	u	PROPN
ejpam-5918	163	4	∈	∈	PROPN
ejpam-5918	163	5	n(v	n(v	PROPN
ejpam-5918	163	6	)	)	PUNCT
ejpam-5918	163	7	for	for	ADP
ejpam-5918	163	8	some	some	DET
ejpam-5918	163	9	v	v	ADP
ejpam-5918	163	10	∈	∈	PROPN
ejpam-5918	163	11	i.	i.	NOUN
ejpam-5918	163	12	proof	proof	NOUN
ejpam-5918	163	13	.	.	PUNCT
ejpam-5918	164	1	let	let	VERB
ejpam-5918	164	2	g	g	PRON
ejpam-5918	164	3	be	be	AUX
ejpam-5918	164	4	a	a	DET
ejpam-5918	164	5	graph	graph	NOUN
ejpam-5918	164	6	with	with	ADP
ejpam-5918	164	7	∆(g	∆(g	NOUN
ejpam-5918	164	8	)	)	PUNCT
ejpam-5918	164	9	=	=	SYM
ejpam-5918	164	10	2	2	NUM
ejpam-5918	164	11	and	and	CCONJ
ejpam-5918	164	12	i	i	PRON
ejpam-5918	165	1	⊆	⊆	NUM
ejpam-5918	165	2	v	v	X
ejpam-5918	165	3	(	(	PUNCT
ejpam-5918	165	4	g	g	NOUN
ejpam-5918	165	5	)	)	PUNCT
ejpam-5918	165	6	such	such	ADJ
ejpam-5918	165	7	that	that	PRON
ejpam-5918	165	8	|i|	|i|	VERB
ejpam-5918	165	9	≥	≥	NOUN
ejpam-5918	165	10	2	2	NUM
ejpam-5918	165	11	.	.	PUNCT
ejpam-5918	165	12	assume	assume	VERB
ejpam-5918	165	13	i	i	PRON
ejpam-5918	165	14	is	be	AUX
ejpam-5918	165	15	the	the	DET
ejpam-5918	165	16	γli−	γli−	PROPN
ejpam-5918	165	17	set	set	VERB
ejpam-5918	165	18	in	in	ADP
ejpam-5918	165	19	g.	g.	PROPN
ejpam-5918	165	20	now	now	ADV
ejpam-5918	165	21	,	,	PUNCT
ejpam-5918	165	22	if	if	SCONJ
ejpam-5918	165	23	degi(v	degi(v	NOUN
ejpam-5918	165	24	)	)	PUNCT
ejpam-5918	165	25	=	=	SYM
ejpam-5918	165	26	1	1	NUM
ejpam-5918	165	27	,	,	PUNCT
ejpam-5918	165	28	v	v	NOUN
ejpam-5918	165	29	has	have	VERB
ejpam-5918	165	30	one	one	NUM
ejpam-5918	165	31	neighbor	neighbor	NOUN
ejpam-5918	165	32	in	in	ADP
ejpam-5918	165	33	i.	i.	PROPN
ejpam-5918	165	34	since	since	SCONJ
ejpam-5918	165	35	i	i	PRON
ejpam-5918	165	36	is	be	AUX
ejpam-5918	165	37	dominating	dominate	VERB
ejpam-5918	165	38	and	and	CCONJ
ejpam-5918	165	39	∆(g	∆(g	NOUN
ejpam-5918	165	40	)	)	PUNCT
ejpam-5918	165	41	=	=	SYM
ejpam-5918	165	42	2	2	NUM
ejpam-5918	165	43	,	,	PUNCT
ejpam-5918	165	44	v	v	X
ejpam-5918	165	45	must	must	AUX
ejpam-5918	165	46	have	have	VERB
ejpam-5918	165	47	one	one	NUM
ejpam-5918	165	48	neighbor	neighbor	NOUN
ejpam-5918	165	49	in	in	ADP
ejpam-5918	165	50	v	v	PROPN
ejpam-5918	165	51	(	(	PUNCT
ejpam-5918	165	52	g	g	NOUN
ejpam-5918	165	53	)	)	PUNCT
ejpam-5918	165	54	\	\	PUNCT
ejpam-5918	166	1	i	i	PRON
ejpam-5918	166	2	,	,	PUNCT
ejpam-5918	166	3	i.e.	i.e.	X
ejpam-5918	166	4	,	,	PUNCT
ejpam-5918	166	5	degv	degv	NOUN
ejpam-5918	166	6	(	(	PUNCT
ejpam-5918	166	7	g)\i(v	g)\i(v	NOUN
ejpam-5918	166	8	)	)	PUNCT
ejpam-5918	166	9	=	=	SYM
ejpam-5918	166	10	1	1	X
ejpam-5918	166	11	.	.	PUNCT
ejpam-5918	166	12	thus	thus	ADV
ejpam-5918	166	13	,	,	PUNCT
ejpam-5918	166	14	(	(	PUNCT
ejpam-5918	166	15	i	i	NOUN
ejpam-5918	166	16	)	)	PUNCT
ejpam-5918	166	17	holds	hold	VERB
ejpam-5918	166	18	.	.	PUNCT
ejpam-5918	167	1	for	for	ADP
ejpam-5918	167	2	(	(	PUNCT
ejpam-5918	167	3	ii	ii	NOUN
ejpam-5918	167	4	)	)	PUNCT
ejpam-5918	167	5	,	,	PUNCT
ejpam-5918	167	6	since	since	SCONJ
ejpam-5918	167	7	i	i	PRON
ejpam-5918	167	8	is	be	AUX
ejpam-5918	167	9	an	an	DET
ejpam-5918	167	10	ilds	ild	NOUN
ejpam-5918	167	11	,	,	PUNCT
ejpam-5918	167	12	we	we	PRON
ejpam-5918	167	13	have	have	AUX
ejpam-5918	167	14	n(v)∩i	n(v)∩i	NOUN
ejpam-5918	167	15	=	=	SYM
ejpam-5918	167	16	∅	∅	NOUN
ejpam-5918	167	17	if	if	SCONJ
ejpam-5918	167	18	degi(v	degi(v	NOUN
ejpam-5918	167	19	)	)	PUNCT
ejpam-5918	167	20	=	=	SYM
ejpam-5918	167	21	0	0	X
ejpam-5918	167	22	.	.	PUNCT
ejpam-5918	167	23	suppose	suppose	VERB
ejpam-5918	167	24	that	that	SCONJ
ejpam-5918	167	25	v	v	NOUN
ejpam-5918	167	26	is	be	AUX
ejpam-5918	167	27	not	not	PART
ejpam-5918	167	28	unique	unique	ADJ
ejpam-5918	167	29	in	in	ADP
ejpam-5918	167	30	i	i	PRON
ejpam-5918	167	31	,	,	PUNCT
ejpam-5918	167	32	this	this	PRON
ejpam-5918	167	33	implies	imply	VERB
ejpam-5918	167	34	that	that	SCONJ
ejpam-5918	167	35	there	there	PRON
ejpam-5918	167	36	exists	exist	VERB
ejpam-5918	167	37	u	u	NOUN
ejpam-5918	167	38	∈	∈	PROPN
ejpam-5918	167	39	i	i	PRON
ejpam-5918	167	40	where	where	SCONJ
ejpam-5918	167	41	u	u	NOUN
ejpam-5918	167	42	̸=	̸=	PROPN
ejpam-5918	167	43	v	v	ADP
ejpam-5918	167	44	such	such	DET
ejpam-5918	167	45	that	that	DET
ejpam-5918	167	46	degi(u	degi(u	NOUN
ejpam-5918	167	47	)	)	PUNCT
ejpam-5918	167	48	=	=	SYM
ejpam-5918	168	1	0	0	X
ejpam-5918	168	2	.	.	PUNCT
ejpam-5918	169	1	thus	thus	ADV
ejpam-5918	169	2	,	,	PUNCT
ejpam-5918	169	3	n(u	n(u	PROPN
ejpam-5918	169	4	)	)	PUNCT
ejpam-5918	169	5	∩	∩	NOUN
ejpam-5918	169	6	i	i	NOUN
ejpam-5918	169	7	=	=	NOUN
ejpam-5918	169	8	∅	∅	NOUN
ejpam-5918	169	9	=	=	PUNCT
ejpam-5918	169	10	n(v	n(v	PROPN
ejpam-5918	169	11	)	)	PUNCT
ejpam-5918	169	12	∩	∩	PROPN
ejpam-5918	169	13	i.	i.	NOUN
ejpam-5918	169	14	a	a	DET
ejpam-5918	169	15	contradiction	contradiction	NOUN
ejpam-5918	169	16	,	,	PUNCT
ejpam-5918	169	17	since	since	SCONJ
ejpam-5918	169	18	i	i	PRON
ejpam-5918	169	19	is	be	AUX
ejpam-5918	169	20	an	an	DET
ejpam-5918	169	21	ils	ils	NOUN
ejpam-5918	169	22	.	.	PUNCT
ejpam-5918	169	23	thus	thus	ADV
ejpam-5918	169	24	,	,	PUNCT
ejpam-5918	169	25	v	v	NOUN
ejpam-5918	169	26	with	with	ADP
ejpam-5918	169	27	degi(v	degi(v	NOUN
ejpam-5918	169	28	)	)	PUNCT
ejpam-5918	169	29	=	=	SYM
ejpam-5918	169	30	0	0	PUNCT
ejpam-5918	169	31	is	be	AUX
ejpam-5918	169	32	unique	unique	ADJ
ejpam-5918	169	33	in	in	ADP
ejpam-5918	169	34	i.	i.	NOUN
ejpam-5918	169	35	if	if	SCONJ
ejpam-5918	169	36	degi(v	degi(v	NOUN
ejpam-5918	169	37	)	)	PUNCT
ejpam-5918	169	38	=	=	SYM
ejpam-5918	169	39	0	0	NUM
ejpam-5918	169	40	and	and	CCONJ
ejpam-5918	169	41	deg(v	deg(v	PROPN
ejpam-5918	169	42	)	)	PUNCT
ejpam-5918	169	43	=	=	SYM
ejpam-5918	169	44	1	1	NUM
ejpam-5918	169	45	or	or	CCONJ
ejpam-5918	169	46	2	2	NUM
ejpam-5918	169	47	,	,	PUNCT
ejpam-5918	169	48	degv	degv	NOUN
ejpam-5918	169	49	(	(	PUNCT
ejpam-5918	169	50	g)\i(v	g)\i(v	NOUN
ejpam-5918	169	51	)	)	PUNCT
ejpam-5918	169	52	=	=	SYM
ejpam-5918	169	53	deg(v	deg(v	PROPN
ejpam-5918	169	54	)	)	PUNCT
ejpam-5918	169	55	,	,	PUNCT
ejpam-5918	169	56	since	since	SCONJ
ejpam-5918	169	57	all	all	DET
ejpam-5918	169	58	neighbors	neighbor	NOUN
ejpam-5918	169	59	of	of	ADP
ejpam-5918	169	60	v	v	NUM
ejpam-5918	169	61	must	must	AUX
ejpam-5918	169	62	lie	lie	VERB
ejpam-5918	169	63	in	in	ADP
ejpam-5918	169	64	v	v	NOUN
ejpam-5918	169	65	(	(	PUNCT
ejpam-5918	169	66	g	g	NOUN
ejpam-5918	169	67	)	)	PUNCT
ejpam-5918	169	68	\	\	PROPN
ejpam-5918	169	69	i.	i.	NOUN
ejpam-5918	169	70	hence	hence	ADV
ejpam-5918	169	71	,	,	PUNCT
ejpam-5918	169	72	(	(	PUNCT
ejpam-5918	169	73	iii	iii	NOUN
ejpam-5918	169	74	)	)	PUNCT
ejpam-5918	169	75	holds	hold	VERB
ejpam-5918	169	76	.	.	PUNCT
ejpam-5918	170	1	lastly	lastly	ADV
ejpam-5918	170	2	,	,	PUNCT
ejpam-5918	170	3	by	by	ADP
ejpam-5918	170	4	definition	definition	NOUN
ejpam-5918	170	5	of	of	ADP
ejpam-5918	170	6	dominating	dominating	NOUN
ejpam-5918	170	7	set	set	NOUN
ejpam-5918	170	8	,	,	PUNCT
ejpam-5918	170	9	then	then	ADV
ejpam-5918	170	10	for	for	ADP
ejpam-5918	170	11	all	all	DET
ejpam-5918	170	12	u	u	NOUN
ejpam-5918	170	13	∈	∈	PROPN
ejpam-5918	170	14	v	v	NOUN
ejpam-5918	170	15	(	(	PUNCT
ejpam-5918	170	16	g	g	NOUN
ejpam-5918	170	17	)	)	PUNCT
ejpam-5918	170	18	\	\	PUNCT
ejpam-5918	171	1	i	i	PRON
ejpam-5918	171	2	,	,	PUNCT
ejpam-5918	171	3	u	u	NOUN
ejpam-5918	171	4	is	be	AUX
ejpam-5918	171	5	adjacent	adjacent	ADJ
ejpam-5918	171	6	to	to	ADP
ejpam-5918	171	7	at	at	ADV
ejpam-5918	171	8	least	least	ADV
ejpam-5918	171	9	one	one	NUM
ejpam-5918	171	10	v	v	ADP
ejpam-5918	171	11	∈	∈	NOUN
ejpam-5918	172	1	i	i	PRON
ejpam-5918	172	2	,	,	PUNCT
ejpam-5918	172	3	as	as	SCONJ
ejpam-5918	172	4	i	i	PRON
ejpam-5918	172	5	is	be	AUX
ejpam-5918	172	6	dominating	dominate	VERB
ejpam-5918	172	7	.	.	PUNCT
ejpam-5918	173	1	thus	thus	ADV
ejpam-5918	173	2	,	,	PUNCT
ejpam-5918	173	3	(	(	PUNCT
ejpam-5918	173	4	iv	iv	X
ejpam-5918	173	5	)	)	PUNCT
ejpam-5918	173	6	holds	hold	NOUN
ejpam-5918	173	7	.	.	PUNCT
ejpam-5918	174	1	i.	i.	PROPN
ejpam-5918	174	2	tropico	tropico	PROPN
ejpam-5918	174	3	,	,	PUNCT
ejpam-5918	174	4	i.	i.	PROPN
ejpam-5918	174	5	cabahug	cabahug	PROPN
ejpam-5918	174	6	,	,	PUNCT
ejpam-5918	174	7	jr	jr	PROPN
ejpam-5918	174	8	.	.	PROPN
ejpam-5918	174	9	/	/	SYM
ejpam-5918	174	10	eur	eur	PROPN
ejpam-5918	174	11	.	.	PUNCT
ejpam-5918	175	1	j.	j.	PROPN
ejpam-5918	175	2	pure	pure	PROPN
ejpam-5918	175	3	appl	appl	PROPN
ejpam-5918	175	4	.	.	PROPN
ejpam-5918	175	5	math	math	PROPN
ejpam-5918	175	6	,	,	PUNCT
ejpam-5918	175	7	18	18	NUM
ejpam-5918	175	8	(	(	PUNCT
ejpam-5918	175	9	2	2	NUM
ejpam-5918	175	10	)	)	PUNCT
ejpam-5918	175	11	(	(	PUNCT
ejpam-5918	175	12	2025	2025	NUM
ejpam-5918	175	13	)	)	PUNCT
ejpam-5918	175	14	,	,	PUNCT
ejpam-5918	175	15	5918	5918	NUM
ejpam-5918	175	16	8	8	NUM
ejpam-5918	175	17	of	of	ADP
ejpam-5918	175	18	21	21	NUM
ejpam-5918	175	19	conversely	conversely	ADV
ejpam-5918	175	20	,	,	PUNCT
ejpam-5918	175	21	assume	assume	VERB
ejpam-5918	175	22	i	i	PRON
ejpam-5918	175	23	satisfies	satisfy	VERB
ejpam-5918	175	24	(	(	PUNCT
ejpam-5918	175	25	i)-(iv	i)-(iv	NOUN
ejpam-5918	175	26	)	)	PUNCT
ejpam-5918	175	27	.	.	PUNCT
ejpam-5918	176	1	by	by	ADP
ejpam-5918	176	2	(	(	PUNCT
ejpam-5918	176	3	iv	iv	X
ejpam-5918	176	4	)	)	PUNCT
ejpam-5918	176	5	,	,	PUNCT
ejpam-5918	176	6	clearly	clearly	ADV
ejpam-5918	176	7	,	,	PUNCT
ejpam-5918	176	8	i	i	PRON
ejpam-5918	176	9	is	be	AUX
ejpam-5918	176	10	a	a	DET
ejpam-5918	176	11	dominating	dominating	NOUN
ejpam-5918	176	12	set	set	NOUN
ejpam-5918	176	13	.	.	PUNCT
ejpam-5918	177	1	by	by	ADP
ejpam-5918	177	2	(	(	PUNCT
ejpam-5918	177	3	i	i	NOUN
ejpam-5918	177	4	)	)	PUNCT
ejpam-5918	177	5	,	,	PUNCT
ejpam-5918	177	6	it	it	PRON
ejpam-5918	177	7	follows	follow	VERB
ejpam-5918	177	8	that	that	SCONJ
ejpam-5918	177	9	for	for	ADP
ejpam-5918	177	10	every	every	DET
ejpam-5918	177	11	v	v	NOUN
ejpam-5918	177	12	∈	∈	NOUN
ejpam-5918	177	13	i	i	PRON
ejpam-5918	177	14	,	,	PUNCT
ejpam-5918	177	15	there	there	PRON
ejpam-5918	177	16	exist	exist	VERB
ejpam-5918	177	17	a	a	DET
ejpam-5918	177	18	unique	unique	ADJ
ejpam-5918	177	19	u	u	NOUN
ejpam-5918	177	20	∈	∈	NOUN
ejpam-5918	177	21	i	i	PRON
ejpam-5918	177	22	such	such	ADJ
ejpam-5918	177	23	that	that	SCONJ
ejpam-5918	177	24	n(v	n(v	PROPN
ejpam-5918	177	25	)	)	PUNCT
ejpam-5918	177	26	∩	∩	NOUN
ejpam-5918	177	27	i	i	PRON
ejpam-5918	177	28	=	=	PUNCT
ejpam-5918	177	29	u.	u.	VERB
ejpam-5918	177	30	by	by	ADP
ejpam-5918	177	31	(	(	PUNCT
ejpam-5918	177	32	ii	ii	NOUN
ejpam-5918	177	33	)	)	PUNCT
ejpam-5918	177	34	and	and	CCONJ
ejpam-5918	177	35	(	(	PUNCT
ejpam-5918	177	36	iii	iii	NOUN
ejpam-5918	177	37	)	)	PUNCT
ejpam-5918	177	38	,	,	PUNCT
ejpam-5918	177	39	there	there	PRON
ejpam-5918	177	40	exist	exist	VERB
ejpam-5918	177	41	no	no	DET
ejpam-5918	177	42	u	u	NOUN
ejpam-5918	177	43	,	,	PUNCT
ejpam-5918	177	44	v	v	NOUN
ejpam-5918	177	45	∈	∈	NOUN
ejpam-5918	177	46	i	i	PRON
ejpam-5918	177	47	such	such	ADJ
ejpam-5918	177	48	that	that	DET
ejpam-5918	177	49	n(u	n(u	PROPN
ejpam-5918	177	50	)	)	PUNCT
ejpam-5918	177	51	∩	∩	NOUN
ejpam-5918	177	52	i	i	NOUN
ejpam-5918	177	53	=	=	NOUN
ejpam-5918	177	54	∅	∅	NOUN
ejpam-5918	177	55	=	=	PUNCT
ejpam-5918	177	56	n(v	n(v	PROPN
ejpam-5918	177	57	)	)	PUNCT
ejpam-5918	177	58	∩	∩	PROPN
ejpam-5918	177	59	i.	i.	NOUN
ejpam-5918	177	60	thus	thus	ADV
ejpam-5918	177	61	,	,	PUNCT
ejpam-5918	177	62	i	i	PRON
ejpam-5918	177	63	is	be	AUX
ejpam-5918	177	64	an	an	DET
ejpam-5918	177	65	ils	ils	NOUN
ejpam-5918	177	66	.	.	PUNCT
ejpam-5918	177	67	now	now	ADV
ejpam-5918	177	68	,	,	PUNCT
ejpam-5918	177	69	by	by	ADP
ejpam-5918	177	70	removing	remove	VERB
ejpam-5918	177	71	any	any	DET
ejpam-5918	177	72	vertex	vertex	NOUN
ejpam-5918	177	73	in	in	ADP
ejpam-5918	177	74	i	i	PRON
ejpam-5918	177	75	,	,	PUNCT
ejpam-5918	177	76	then	then	ADV
ejpam-5918	177	77	it	it	PRON
ejpam-5918	177	78	contradicts	contradict	VERB
ejpam-5918	177	79	(	(	PUNCT
ejpam-5918	177	80	iv	iv	NUM
ejpam-5918	177	81	)	)	PUNCT
ejpam-5918	177	82	.	.	PUNCT
ejpam-5918	178	1	hence	hence	ADV
ejpam-5918	178	2	,	,	PUNCT
ejpam-5918	178	3	i	i	PRON
ejpam-5918	178	4	is	be	AUX
ejpam-5918	178	5	the	the	DET
ejpam-5918	178	6	γli	γli	ADJ
ejpam-5918	178	7	−	−	PROPN
ejpam-5918	178	8	set	set	NOUN
ejpam-5918	178	9	.	.	PUNCT
ejpam-5918	179	1	corollary	corollary	ADJ
ejpam-5918	179	2	3	3	X
ejpam-5918	179	3	.	.	PUNCT
ejpam-5918	180	1	let	let	VERB
ejpam-5918	180	2	g	g	PRON
ejpam-5918	180	3	be	be	AUX
ejpam-5918	180	4	a	a	DET
ejpam-5918	180	5	path	path	NOUN
ejpam-5918	180	6	graph	graph	NOUN
ejpam-5918	180	7	pn	pn	NOUN
ejpam-5918	180	8	or	or	CCONJ
ejpam-5918	180	9	a	a	DET
ejpam-5918	180	10	cycle	cycle	NOUN
ejpam-5918	180	11	graph	graph	NOUN
ejpam-5918	180	12	cn	cn	VERB
ejpam-5918	180	13	with	with	ADP
ejpam-5918	180	14	n	n	NUM
ejpam-5918	180	15	≥	≥	NUM
ejpam-5918	180	16	4	4	NUM
ejpam-5918	180	17	.	.	PUNCT
ejpam-5918	181	1	then	then	ADV
ejpam-5918	181	2	,	,	PUNCT
ejpam-5918	181	3	γli(g	γli(g	PROPN
ejpam-5918	181	4	)	)	PUNCT
ejpam-5918	181	5	=	=	SYM
ejpam-5918	181	6	γli(pn	γli(pn	NOUN
ejpam-5918	181	7	)	)	PUNCT
ejpam-5918	181	8	=	=	SYM
ejpam-5918	181	9	γli(cn	γli(cn	NOUN
ejpam-5918	181	10	)	)	PUNCT
ejpam-5918	181	11	=	=	PUNCT
ejpam-5918	181	12			PROPN
ejpam-5918	181	13	n	n	PRON
ejpam-5918	181	14	2	2	NUM
ejpam-5918	181	15	if	if	SCONJ
ejpam-5918	181	16	n	n	PRON
ejpam-5918	181	17	≡	≡	PROPN
ejpam-5918	181	18	0	0	NUM
ejpam-5918	181	19	,	,	PUNCT
ejpam-5918	181	20	2	2	NUM
ejpam-5918	181	21	(	(	PUNCT
ejpam-5918	181	22	mod	mod	NOUN
ejpam-5918	181	23	4	4	NUM
ejpam-5918	181	24	)	)	PUNCT
ejpam-5918	181	25	n+1	n+1	NUM
ejpam-5918	181	26	2	2	NUM
ejpam-5918	181	27	if	if	SCONJ
ejpam-5918	181	28	n	n	PRON
ejpam-5918	181	29	≡	≡	PROPN
ejpam-5918	181	30	1	1	NUM
ejpam-5918	181	31	(	(	PUNCT
ejpam-5918	181	32	mod	mod	NOUN
ejpam-5918	181	33	4	4	NUM
ejpam-5918	181	34	)	)	PUNCT
ejpam-5918	181	35	n−1	n−1	PROPN
ejpam-5918	181	36	2	2	NUM
ejpam-5918	181	37	if	if	SCONJ
ejpam-5918	181	38	n	n	PRON
ejpam-5918	181	39	≡	≡	PROPN
ejpam-5918	181	40	3	3	NUM
ejpam-5918	181	41	(	(	PUNCT
ejpam-5918	181	42	mod	mod	NOUN
ejpam-5918	181	43	4	4	NUM
ejpam-5918	181	44	)	)	PUNCT
ejpam-5918	181	45	proof	proof	NOUN
ejpam-5918	181	46	.	.	PUNCT
ejpam-5918	182	1	let	let	VERB
ejpam-5918	182	2	g	g	PRON
ejpam-5918	182	3	be	be	AUX
ejpam-5918	182	4	a	a	DET
ejpam-5918	182	5	path	path	NOUN
ejpam-5918	182	6	graph	graph	NOUN
ejpam-5918	182	7	pn	pn	NOUN
ejpam-5918	182	8	or	or	CCONJ
ejpam-5918	182	9	a	a	DET
ejpam-5918	182	10	cycle	cycle	NOUN
ejpam-5918	182	11	graph	graph	NOUN
ejpam-5918	182	12	cn	cn	VERB
ejpam-5918	182	13	with	with	ADP
ejpam-5918	182	14	n	n	NUM
ejpam-5918	182	15	≥	≥	NUM
ejpam-5918	182	16	4	4	NUM
ejpam-5918	182	17	.	.	X
ejpam-5918	183	1	for	for	ADP
ejpam-5918	183	2	convenience	convenience	NOUN
ejpam-5918	183	3	,	,	PUNCT
ejpam-5918	183	4	let	let	VERB
ejpam-5918	183	5	v	v	X
ejpam-5918	183	6	(	(	PUNCT
ejpam-5918	183	7	pn	pn	NOUN
ejpam-5918	183	8	)	)	PUNCT
ejpam-5918	183	9	=	=	NOUN
ejpam-5918	183	10	v	v	X
ejpam-5918	183	11	(	(	PUNCT
ejpam-5918	183	12	cn	cn	PROPN
ejpam-5918	183	13	)	)	PUNCT
ejpam-5918	183	14	=	=	SYM
ejpam-5918	183	15	{	{	PUNCT
ejpam-5918	183	16	v1	v1	PROPN
ejpam-5918	183	17	,	,	PUNCT
ejpam-5918	183	18	v2	v2	PROPN
ejpam-5918	183	19	,	,	PUNCT
ejpam-5918	183	20	v3	v3	PROPN
ejpam-5918	183	21	,	,	PUNCT
ejpam-5918	183	22	.	.	PUNCT
ejpam-5918	183	23	.	.	PUNCT
ejpam-5918	184	1	.	.	PUNCT
ejpam-5918	185	1	,	,	PUNCT
ejpam-5918	185	2	vn−1	vn−1	PROPN
ejpam-5918	185	3	,	,	PUNCT
ejpam-5918	185	4	vn	vn	NOUN
ejpam-5918	185	5	}	}	PUNCT
ejpam-5918	185	6	,	,	PUNCT
ejpam-5918	185	7	e(pn	e(pn	NOUN
ejpam-5918	185	8	)	)	PUNCT
ejpam-5918	185	9	=	=	PRON
ejpam-5918	185	10	{	{	PUNCT
ejpam-5918	185	11	v1v2	v1v2	PROPN
ejpam-5918	185	12	,	,	PUNCT
ejpam-5918	185	13	v2v3	v2v3	PROPN
ejpam-5918	185	14	,	,	PUNCT
ejpam-5918	185	15	.	.	PUNCT
ejpam-5918	185	16	.	.	PUNCT
ejpam-5918	185	17	.	.	PUNCT
ejpam-5918	186	1	,	,	PUNCT
ejpam-5918	186	2	vn−1vn	vn−1vn	NUM
ejpam-5918	186	3	}	}	PUNCT
ejpam-5918	186	4	and	and	CCONJ
ejpam-5918	186	5	e(cn	e(cn	NOUN
ejpam-5918	186	6	)	)	PUNCT
ejpam-5918	186	7	=	=	PRON
ejpam-5918	186	8	{	{	PUNCT
ejpam-5918	186	9	v1v2	v1v2	PROPN
ejpam-5918	186	10	,	,	PUNCT
ejpam-5918	186	11	v2v3	v2v3	PROPN
ejpam-5918	186	12	,	,	PUNCT
ejpam-5918	186	13	.	.	PUNCT
ejpam-5918	186	14	.	.	PUNCT
ejpam-5918	187	1	.	.	PUNCT
ejpam-5918	188	1	,	,	PUNCT
ejpam-5918	188	2	vn−1vn	vn−1vn	NUM
ejpam-5918	188	3	,	,	PUNCT
ejpam-5918	188	4	vnv1	vnv1	NOUN
ejpam-5918	188	5	}	}	PUNCT
ejpam-5918	188	6	.	.	PUNCT
ejpam-5918	189	1	if	if	SCONJ
ejpam-5918	189	2	g	g	PROPN
ejpam-5918	189	3	=	=	SYM
ejpam-5918	189	4	pn	pn	PROPN
ejpam-5918	189	5	,	,	PUNCT
ejpam-5918	189	6	consider	consider	VERB
ejpam-5918	189	7	the	the	DET
ejpam-5918	189	8	following	follow	VERB
ejpam-5918	189	9	cases	case	NOUN
ejpam-5918	189	10	:	:	PUNCT
ejpam-5918	189	11	case	case	NOUN
ejpam-5918	189	12	1	1	NUM
ejpam-5918	189	13	:	:	PUNCT
ejpam-5918	189	14	n	n	NUM
ejpam-5918	189	15	≡	≡	PROPN
ejpam-5918	189	16	0	0	PUNCT
ejpam-5918	190	1	(	(	PUNCT
ejpam-5918	190	2	mod	mod	PROPN
ejpam-5918	190	3	4	4	X
ejpam-5918	190	4	)	)	PUNCT
ejpam-5918	190	5	let	let	VERB
ejpam-5918	190	6	i	i	PRON
ejpam-5918	190	7	⊆	⊆	NUM
ejpam-5918	190	8	v	v	NOUN
ejpam-5918	190	9	(	(	PUNCT
ejpam-5918	190	10	pn	pn	NOUN
ejpam-5918	190	11	)	)	PUNCT
ejpam-5918	190	12	with	with	ADP
ejpam-5918	190	13	i	i	PRON
ejpam-5918	190	14	=	=	PUNCT
ejpam-5918	190	15	{	{	PUNCT
ejpam-5918	190	16	v2	v2	PROPN
ejpam-5918	190	17	,	,	PUNCT
ejpam-5918	190	18	v3	v3	PROPN
ejpam-5918	190	19	,	,	PUNCT
ejpam-5918	190	20	v6	v6	NOUN
ejpam-5918	190	21	,	,	PUNCT
ejpam-5918	190	22	v7	v7	NOUN
ejpam-5918	190	23	,	,	PUNCT
ejpam-5918	190	24	.	.	PUNCT
ejpam-5918	190	25	.	.	PUNCT
ejpam-5918	191	1	.	.	PUNCT
ejpam-5918	192	1	,	,	PUNCT
ejpam-5918	192	2	vn−2	vn−2	PROPN
ejpam-5918	192	3	,	,	PUNCT
ejpam-5918	192	4	vn−1	vn−1	ADJ
ejpam-5918	192	5	}	}	PUNCT
ejpam-5918	192	6	.	.	PUNCT
ejpam-5918	193	1	observe	observe	VERB
ejpam-5918	193	2	that	that	SCONJ
ejpam-5918	193	3	|i|	|i|	VERB
ejpam-5918	193	4	=	=	SYM
ejpam-5918	193	5	n	n	PRON
ejpam-5918	193	6	2	2	NUM
ejpam-5918	193	7	.	.	PUNCT
ejpam-5918	194	1	by	by	ADP
ejpam-5918	194	2	theorem	theorem	NOUN
ejpam-5918	194	3	4	4	NUM
ejpam-5918	194	4	,	,	PUNCT
ejpam-5918	194	5	i	i	PRON
ejpam-5918	194	6	is	be	AUX
ejpam-5918	194	7	a	a	DET
ejpam-5918	194	8	γli	γli	ADJ
ejpam-5918	194	9	−	−	PROPN
ejpam-5918	194	10	set	set	NOUN
ejpam-5918	194	11	.	.	PUNCT
ejpam-5918	195	1	therefore	therefore	ADV
ejpam-5918	195	2	,	,	PUNCT
ejpam-5918	195	3	γli(pn	γli(pn	ADJ
ejpam-5918	195	4	)	)	PUNCT
ejpam-5918	195	5	=	=	SYM
ejpam-5918	195	6	|i|	|i|	PROPN
ejpam-5918	195	7	=	=	SYM
ejpam-5918	195	8	n	n	PRON
ejpam-5918	195	9	2	2	NUM
ejpam-5918	195	10	.	.	PUNCT
ejpam-5918	195	11	case	case	NOUN
ejpam-5918	195	12	2	2	NUM
ejpam-5918	195	13	:	:	PUNCT
ejpam-5918	195	14	n	n	NUM
ejpam-5918	195	15	≡	≡	PROPN
ejpam-5918	195	16	1	1	NUM
ejpam-5918	195	17	(	(	PUNCT
ejpam-5918	195	18	mod	mod	NOUN
ejpam-5918	195	19	4	4	X
ejpam-5918	195	20	)	)	PUNCT
ejpam-5918	195	21	let	let	VERB
ejpam-5918	195	22	i	i	PRON
ejpam-5918	195	23	⊆	⊆	NUM
ejpam-5918	195	24	v	v	NOUN
ejpam-5918	195	25	(	(	PUNCT
ejpam-5918	195	26	pn	pn	NOUN
ejpam-5918	195	27	)	)	PUNCT
ejpam-5918	195	28	with	with	ADP
ejpam-5918	195	29	i	i	PRON
ejpam-5918	195	30	=	=	PUNCT
ejpam-5918	195	31	{	{	PUNCT
ejpam-5918	195	32	v2	v2	PROPN
ejpam-5918	195	33	,	,	PUNCT
ejpam-5918	195	34	v3	v3	PROPN
ejpam-5918	195	35	,	,	PUNCT
ejpam-5918	195	36	v6	v6	NOUN
ejpam-5918	195	37	,	,	PUNCT
ejpam-5918	195	38	v7	v7	NOUN
ejpam-5918	195	39	,	,	PUNCT
ejpam-5918	195	40	.	.	PUNCT
ejpam-5918	195	41	.	.	PUNCT
ejpam-5918	196	1	.	.	PUNCT
ejpam-5918	197	1	,	,	PUNCT
ejpam-5918	197	2	vn−3	vn−3	PROPN
ejpam-5918	197	3	,	,	PUNCT
ejpam-5918	197	4	vn−2	vn−2	PROPN
ejpam-5918	197	5	,	,	PUNCT
ejpam-5918	197	6	vn	vn	PROPN
ejpam-5918	197	7	}	}	PUNCT
ejpam-5918	197	8	.	.	PUNCT
ejpam-5918	198	1	observe	observe	VERB
ejpam-5918	198	2	that	that	SCONJ
ejpam-5918	198	3	|i|	|i|	VERB
ejpam-5918	198	4	=	=	SYM
ejpam-5918	198	5	n+1	n+1	PROPN
ejpam-5918	198	6	2	2	NUM
ejpam-5918	198	7	.	.	PUNCT
ejpam-5918	199	1	by	by	ADP
ejpam-5918	199	2	theorem	theorem	NOUN
ejpam-5918	199	3	4	4	NUM
ejpam-5918	199	4	,	,	PUNCT
ejpam-5918	199	5	i	i	PRON
ejpam-5918	199	6	is	be	AUX
ejpam-5918	199	7	a	a	DET
ejpam-5918	199	8	γli	γli	ADJ
ejpam-5918	199	9	−	−	PROPN
ejpam-5918	199	10	set	set	NOUN
ejpam-5918	199	11	.	.	PUNCT
ejpam-5918	200	1	therefore	therefore	ADV
ejpam-5918	200	2	,	,	PUNCT
ejpam-5918	200	3	γli(pn	γli(pn	ADJ
ejpam-5918	200	4	)	)	PUNCT
ejpam-5918	200	5	=	=	SYM
ejpam-5918	200	6	|i|	|i|	PROPN
ejpam-5918	200	7	=	=	SYM
ejpam-5918	200	8	n+1	n+1	PROPN
ejpam-5918	200	9	2	2	NUM
ejpam-5918	200	10	.	.	PUNCT
ejpam-5918	201	1	case	case	NOUN
ejpam-5918	201	2	3	3	NUM
ejpam-5918	201	3	:	:	PUNCT
ejpam-5918	201	4	n	n	NUM
ejpam-5918	201	5	≡	≡	PROPN
ejpam-5918	201	6	2	2	NUM
ejpam-5918	201	7	(	(	PUNCT
ejpam-5918	201	8	mod	mod	NOUN
ejpam-5918	201	9	4	4	X
ejpam-5918	201	10	)	)	PUNCT
ejpam-5918	201	11	let	let	VERB
ejpam-5918	201	12	i	i	PRON
ejpam-5918	201	13	⊆	⊆	NUM
ejpam-5918	201	14	v	v	NOUN
ejpam-5918	201	15	(	(	PUNCT
ejpam-5918	201	16	pn	pn	NOUN
ejpam-5918	201	17	)	)	PUNCT
ejpam-5918	201	18	with	with	ADP
ejpam-5918	201	19	i	i	PRON
ejpam-5918	201	20	=	=	PUNCT
ejpam-5918	201	21	{	{	PUNCT
ejpam-5918	201	22	v2	v2	PROPN
ejpam-5918	201	23	,	,	PUNCT
ejpam-5918	201	24	v3	v3	PROPN
ejpam-5918	201	25	,	,	PUNCT
ejpam-5918	201	26	v6	v6	NOUN
ejpam-5918	201	27	,	,	PUNCT
ejpam-5918	201	28	v7	v7	NOUN
ejpam-5918	201	29	,	,	PUNCT
ejpam-5918	201	30	.	.	PUNCT
ejpam-5918	201	31	.	.	PUNCT
ejpam-5918	202	1	.	.	PUNCT
ejpam-5918	203	1	,	,	PUNCT
ejpam-5918	203	2	vn−2	vn−2	PROPN
ejpam-5918	203	3	,	,	PUNCT
ejpam-5918	203	4	vn−1	vn−1	ADJ
ejpam-5918	203	5	}	}	PUNCT
ejpam-5918	203	6	.	.	PUNCT
ejpam-5918	204	1	observe	observe	VERB
ejpam-5918	204	2	that	that	SCONJ
ejpam-5918	204	3	|i|	|i|	VERB
ejpam-5918	204	4	=	=	SYM
ejpam-5918	204	5	n	n	PRON
ejpam-5918	204	6	2	2	NUM
ejpam-5918	204	7	.	.	PUNCT
ejpam-5918	205	1	by	by	ADP
ejpam-5918	205	2	theorem	theorem	NOUN
ejpam-5918	205	3	4	4	NUM
ejpam-5918	205	4	,	,	PUNCT
ejpam-5918	205	5	i	i	PRON
ejpam-5918	205	6	is	be	AUX
ejpam-5918	205	7	a	a	DET
ejpam-5918	205	8	γli	γli	ADJ
ejpam-5918	205	9	−	−	PROPN
ejpam-5918	205	10	set	set	NOUN
ejpam-5918	205	11	.	.	PUNCT
ejpam-5918	206	1	therefore	therefore	ADV
ejpam-5918	206	2	,	,	PUNCT
ejpam-5918	206	3	γli(pn	γli(pn	ADJ
ejpam-5918	206	4	)	)	PUNCT
ejpam-5918	206	5	=	=	SYM
ejpam-5918	206	6	|i|	|i|	PROPN
ejpam-5918	206	7	=	=	SYM
ejpam-5918	206	8	n	n	PRON
ejpam-5918	206	9	2	2	NUM
ejpam-5918	206	10	.	.	PUNCT
ejpam-5918	206	11	case	case	NOUN
ejpam-5918	206	12	4	4	NUM
ejpam-5918	206	13	:	:	PUNCT
ejpam-5918	206	14	n	n	NUM
ejpam-5918	206	15	≡	≡	PROPN
ejpam-5918	206	16	3	3	NUM
ejpam-5918	206	17	(	(	PUNCT
ejpam-5918	206	18	mod	mod	NOUN
ejpam-5918	206	19	4	4	X
ejpam-5918	206	20	)	)	PUNCT
ejpam-5918	206	21	let	let	VERB
ejpam-5918	206	22	i	i	PRON
ejpam-5918	206	23	⊆	⊆	NUM
ejpam-5918	206	24	v	v	NOUN
ejpam-5918	206	25	(	(	PUNCT
ejpam-5918	206	26	pn	pn	NOUN
ejpam-5918	206	27	)	)	PUNCT
ejpam-5918	206	28	with	with	ADP
ejpam-5918	206	29	i	i	PRON
ejpam-5918	206	30	=	=	PUNCT
ejpam-5918	206	31	{	{	PUNCT
ejpam-5918	206	32	v2	v2	PROPN
ejpam-5918	206	33	,	,	PUNCT
ejpam-5918	206	34	v3	v3	PROPN
ejpam-5918	206	35	,	,	PUNCT
ejpam-5918	206	36	v6	v6	NOUN
ejpam-5918	206	37	,	,	PUNCT
ejpam-5918	206	38	v7	v7	NOUN
ejpam-5918	206	39	,	,	PUNCT
ejpam-5918	206	40	.	.	PUNCT
ejpam-5918	206	41	.	.	PUNCT
ejpam-5918	207	1	.	.	PUNCT
ejpam-5918	208	1	,	,	PUNCT
ejpam-5918	208	2	vn−5	vn−5	PROPN
ejpam-5918	208	3	,	,	PUNCT
ejpam-5918	208	4	vn−4	vn−4	NOUN
ejpam-5918	208	5	,	,	PUNCT
ejpam-5918	208	6	vn−1	vn−1	ADJ
ejpam-5918	208	7	}	}	PUNCT
ejpam-5918	208	8	.	.	PUNCT
ejpam-5918	209	1	observe	observe	VERB
ejpam-5918	209	2	that	that	SCONJ
ejpam-5918	209	3	|i|	|i|	VERB
ejpam-5918	209	4	=	=	SYM
ejpam-5918	209	5	n−1	n−1	PROPN
ejpam-5918	209	6	2	2	NUM
ejpam-5918	209	7	.	.	PUNCT
ejpam-5918	210	1	by	by	ADP
ejpam-5918	210	2	theorem	theorem	NOUN
ejpam-5918	210	3	4	4	NUM
ejpam-5918	210	4	,	,	PUNCT
ejpam-5918	210	5	i	i	PRON
ejpam-5918	210	6	is	be	AUX
ejpam-5918	210	7	a	a	DET
ejpam-5918	210	8	γli	γli	ADJ
ejpam-5918	210	9	−	−	PROPN
ejpam-5918	210	10	set	set	NOUN
ejpam-5918	210	11	.	.	PUNCT
ejpam-5918	211	1	therefore	therefore	ADV
ejpam-5918	211	2	,	,	PUNCT
ejpam-5918	211	3	γli(pn	γli(pn	ADJ
ejpam-5918	211	4	)	)	PUNCT
ejpam-5918	211	5	=	=	SYM
ejpam-5918	211	6	|i|	|i|	PROPN
ejpam-5918	211	7	=	=	SYM
ejpam-5918	211	8	n−1	n−1	PROPN
ejpam-5918	211	9	2	2	NUM
ejpam-5918	211	10	.	.	PUNCT
ejpam-5918	212	1	a	a	DET
ejpam-5918	212	2	similar	similar	ADJ
ejpam-5918	212	3	argument	argument	NOUN
ejpam-5918	212	4	follows	follow	VERB
ejpam-5918	212	5	for	for	ADP
ejpam-5918	212	6	g	g	PROPN
ejpam-5918	212	7	=	=	SYM
ejpam-5918	212	8	cn	cn	PROPN
ejpam-5918	212	9	,	,	PUNCT
ejpam-5918	212	10	as	as	SCONJ
ejpam-5918	212	11	the	the	DET
ejpam-5918	212	12	number	number	NOUN
ejpam-5918	212	13	of	of	ADP
ejpam-5918	212	14	vertices	vertex	NOUN
ejpam-5918	212	15	is	be	AUX
ejpam-5918	212	16	the	the	DET
ejpam-5918	212	17	same	same	ADJ
ejpam-5918	212	18	as	as	ADP
ejpam-5918	212	19	in	in	ADP
ejpam-5918	212	20	the	the	DET
ejpam-5918	212	21	path	path	NOUN
ejpam-5918	212	22	graph	graph	NOUN
ejpam-5918	212	23	pn	pn	PROPN
ejpam-5918	212	24	,	,	PUNCT
ejpam-5918	212	25	resulting	result	VERB
ejpam-5918	212	26	the	the	DET
ejpam-5918	212	27	same	same	ADJ
ejpam-5918	212	28	values	value	NOUN
ejpam-5918	212	29	for	for	ADP
ejpam-5918	212	30	γli(g	γli(g	PROPN
ejpam-5918	212	31	)	)	PUNCT
ejpam-5918	212	32	in	in	ADP
ejpam-5918	212	33	all	all	DET
ejpam-5918	212	34	cases	case	NOUN
ejpam-5918	212	35	.	.	PUNCT
ejpam-5918	213	1	theorem	theorem	NOUN
ejpam-5918	213	2	5	5	NUM
ejpam-5918	213	3	.	.	PUNCT
ejpam-5918	214	1	let	let	VERB
ejpam-5918	214	2	g	g	PRON
ejpam-5918	214	3	be	be	AUX
ejpam-5918	214	4	a	a	DET
ejpam-5918	214	5	banana	banana	NOUN
ejpam-5918	214	6	tree	tree	NOUN
ejpam-5918	214	7	graph	graph	NOUN
ejpam-5918	214	8	bn	bn	PROPN
ejpam-5918	214	9	,	,	PUNCT
ejpam-5918	214	10	k+1	k+1	X
ejpam-5918	214	11	with	with	ADP
ejpam-5918	214	12	n	n	PRON
ejpam-5918	214	13	≥	≥	NUM
ejpam-5918	214	14	2	2	NUM
ejpam-5918	214	15	and	and	CCONJ
ejpam-5918	214	16	k	k	PROPN
ejpam-5918	214	17	≥	≥	NUM
ejpam-5918	214	18	3	3	NUM
ejpam-5918	214	19	,	,	PUNCT
ejpam-5918	214	20	and	and	CCONJ
ejpam-5918	214	21	i	i	PRON
ejpam-5918	214	22	⊆	⊆	NUM
ejpam-5918	214	23	v	v	X
ejpam-5918	214	24	(	(	PUNCT
ejpam-5918	214	25	g	g	NOUN
ejpam-5918	214	26	)	)	PUNCT
ejpam-5918	214	27	with	with	ADP
ejpam-5918	214	28	|i|	|i|	PRON
ejpam-5918	214	29	≥	≥	NOUN
ejpam-5918	214	30	2	2	NUM
ejpam-5918	214	31	.	.	PUNCT
ejpam-5918	215	1	then	then	ADV
ejpam-5918	215	2	,	,	PUNCT
ejpam-5918	215	3	i	i	PRON
ejpam-5918	215	4	is	be	AUX
ejpam-5918	215	5	the	the	DET
ejpam-5918	215	6	minimum	minimum	NOUN
ejpam-5918	215	7	internally	internally	ADV
ejpam-5918	215	8	-	-	PUNCT
ejpam-5918	215	9	locating	locate	VERB
ejpam-5918	215	10	dominating	dominating	NOUN
ejpam-5918	215	11	set	set	NOUN
ejpam-5918	215	12	of	of	ADP
ejpam-5918	215	13	g	g	PROPN
ejpam-5918	215	14	if	if	SCONJ
ejpam-5918	216	1	and	and	CCONJ
ejpam-5918	216	2	only	only	ADV
ejpam-5918	216	3	if	if	SCONJ
ejpam-5918	216	4	the	the	DET
ejpam-5918	216	5	following	follow	VERB
ejpam-5918	216	6	holds	hold	VERB
ejpam-5918	216	7	:	:	PUNCT
ejpam-5918	216	8	(	(	PUNCT
ejpam-5918	216	9	i	i	NOUN
ejpam-5918	216	10	)	)	PUNCT
ejpam-5918	216	11	for	for	ADP
ejpam-5918	216	12	every	every	DET
ejpam-5918	216	13	ui	ui	PROPN
ejpam-5918	216	14	∈	∈	PROPN
ejpam-5918	216	15	v	v	NOUN
ejpam-5918	216	16	(	(	PUNCT
ejpam-5918	216	17	k1i	k1i	PROPN
ejpam-5918	216	18	,	,	PUNCT
ejpam-5918	216	19	ki	ki	PROPN
ejpam-5918	216	20	)	)	PUNCT
ejpam-5918	216	21	,	,	PUNCT
ejpam-5918	216	22	then	then	ADV
ejpam-5918	216	23	ui	ui	PROPN
ejpam-5918	216	24	∈	∈	PROPN
ejpam-5918	217	1	i	i	PRON
ejpam-5918	217	2	;	;	PUNCT
ejpam-5918	217	3	(	(	PUNCT
ejpam-5918	217	4	ii	ii	NOUN
ejpam-5918	217	5	)	)	PUNCT
ejpam-5918	217	6	there	there	PRON
ejpam-5918	217	7	exists	exist	VERB
ejpam-5918	217	8	exactly	exactly	ADV
ejpam-5918	217	9	one	one	NUM
ejpam-5918	217	10	ui	ui	NOUN
ejpam-5918	217	11	∈	∈	PROPN
ejpam-5918	217	12	v	v	NOUN
ejpam-5918	217	13	(	(	PUNCT
ejpam-5918	217	14	k1i	k1i	PROPN
ejpam-5918	217	15	,	,	PUNCT
ejpam-5918	217	16	ki	ki	PROPN
ejpam-5918	217	17	)	)	PUNCT
ejpam-5918	217	18	such	such	ADJ
ejpam-5918	217	19	that	that	SCONJ
ejpam-5918	217	20	degi(ui	degi(ui	NOUN
ejpam-5918	217	21	)	)	PUNCT
ejpam-5918	217	22	=	=	SYM
ejpam-5918	217	23	0	0	NUM
ejpam-5918	217	24	;	;	PUNCT
ejpam-5918	217	25	i.	i.	PROPN
ejpam-5918	217	26	tropico	tropico	PROPN
ejpam-5918	217	27	,	,	PUNCT
ejpam-5918	217	28	i.	i.	PROPN
ejpam-5918	217	29	cabahug	cabahug	PROPN
ejpam-5918	217	30	,	,	PUNCT
ejpam-5918	217	31	jr	jr	PROPN
ejpam-5918	217	32	.	.	PROPN
ejpam-5918	217	33	/	/	SYM
ejpam-5918	217	34	eur	eur	PROPN
ejpam-5918	217	35	.	.	PUNCT
ejpam-5918	218	1	j.	j.	PROPN
ejpam-5918	218	2	pure	pure	PROPN
ejpam-5918	218	3	appl	appl	PROPN
ejpam-5918	218	4	.	.	PROPN
ejpam-5918	218	5	math	math	PROPN
ejpam-5918	218	6	,	,	PUNCT
ejpam-5918	218	7	18	18	NUM
ejpam-5918	218	8	(	(	PUNCT
ejpam-5918	218	9	2	2	NUM
ejpam-5918	218	10	)	)	PUNCT
ejpam-5918	218	11	(	(	PUNCT
ejpam-5918	218	12	2025	2025	NUM
ejpam-5918	218	13	)	)	PUNCT
ejpam-5918	218	14	,	,	PUNCT
ejpam-5918	218	15	5918	5918	NUM
ejpam-5918	218	16	9	9	NUM
ejpam-5918	218	17	of	of	ADP
ejpam-5918	218	18	21	21	NUM
ejpam-5918	218	19	(	(	PUNCT
ejpam-5918	218	20	iii	iii	NOUN
ejpam-5918	218	21	)	)	PUNCT
ejpam-5918	218	22	if	if	SCONJ
ejpam-5918	218	23	degi(ui	degi(ui	NOUN
ejpam-5918	218	24	)	)	PUNCT
ejpam-5918	218	25	̸=	̸=	PROPN
ejpam-5918	218	26	0	0	NUM
ejpam-5918	218	27	,	,	PUNCT
ejpam-5918	218	28	then	then	ADV
ejpam-5918	218	29	degi(uj	degi(uj	VERB
ejpam-5918	218	30	)	)	PUNCT
ejpam-5918	218	31	=	=	SYM
ejpam-5918	219	1	1	1	NUM
ejpam-5918	219	2	,	,	PUNCT
ejpam-5918	219	3	i	i	PRON
ejpam-5918	219	4	̸=	̸=	PROPN
ejpam-5918	219	5	j	j	PROPN
ejpam-5918	219	6	;	;	PUNCT
ejpam-5918	219	7	and	and	CCONJ
ejpam-5918	219	8	(	(	PUNCT
ejpam-5918	219	9	iv	iv	X
ejpam-5918	219	10	)	)	PUNCT
ejpam-5918	219	11	there	there	PRON
ejpam-5918	219	12	exist	exist	VERB
ejpam-5918	219	13	v	v	ADP
ejpam-5918	219	14	∈	∈	PROPN
ejpam-5918	220	1	i	i	PRON
ejpam-5918	220	2	,	,	PUNCT
ejpam-5918	220	3	such	such	ADJ
ejpam-5918	220	4	that	that	SCONJ
ejpam-5918	220	5	r	r	PROPN
ejpam-5918	220	6	∈	∈	PROPN
ejpam-5918	220	7	n(v	n(v	PROPN
ejpam-5918	220	8	)	)	PUNCT
ejpam-5918	220	9	.	.	PUNCT
ejpam-5918	221	1	where	where	SCONJ
ejpam-5918	221	2	ui	ui	PROPN
ejpam-5918	221	3	∈	∈	PROPN
ejpam-5918	221	4	v	v	PROPN
ejpam-5918	221	5	(	(	PUNCT
ejpam-5918	221	6	k1i	k1i	PROPN
ejpam-5918	221	7	,	,	PUNCT
ejpam-5918	221	8	ki	ki	PROPN
ejpam-5918	221	9	)	)	PUNCT
ejpam-5918	221	10	is	be	AUX
ejpam-5918	221	11	the	the	DET
ejpam-5918	221	12	central	central	ADJ
ejpam-5918	221	13	vertex	vertex	NOUN
ejpam-5918	221	14	of	of	ADP
ejpam-5918	221	15	the	the	DET
ejpam-5918	221	16	ith	ith	PROPN
ejpam-5918	221	17	copy	copy	NOUN
ejpam-5918	221	18	of	of	ADP
ejpam-5918	221	19	a	a	DET
ejpam-5918	221	20	star	star	NOUN
ejpam-5918	221	21	graph	graph	NOUN
ejpam-5918	221	22	k1i	k1i	PROPN
ejpam-5918	221	23	,	,	PUNCT
ejpam-5918	221	24	ki	ki	PROPN
ejpam-5918	221	25	,	,	PUNCT
ejpam-5918	221	26	1	1	NUM
ejpam-5918	221	27	≤	≤	NUM
ejpam-5918	221	28	i	i	PRON
ejpam-5918	221	29	≤	≤	ADJ
ejpam-5918	221	30	n	n	CCONJ
ejpam-5918	221	31	and	and	CCONJ
ejpam-5918	221	32	r	r	X
ejpam-5918	221	33	a	a	DET
ejpam-5918	221	34	single	single	ADJ
ejpam-5918	221	35	root	root	NOUN
ejpam-5918	221	36	vertex	vertex	NOUN
ejpam-5918	221	37	of	of	ADP
ejpam-5918	221	38	g.	g.	PROPN
ejpam-5918	221	39	proof	proof	NOUN
ejpam-5918	221	40	.	.	PUNCT
ejpam-5918	222	1	let	let	VERB
ejpam-5918	222	2	g	g	NOUN
ejpam-5918	222	3	=	=	SYM
ejpam-5918	222	4	bn	bn	PROPN
ejpam-5918	222	5	,	,	PUNCT
ejpam-5918	222	6	k+1	k+1	X
ejpam-5918	222	7	be	be	VERB
ejpam-5918	222	8	a	a	DET
ejpam-5918	222	9	banana	banana	NOUN
ejpam-5918	222	10	tree	tree	NOUN
ejpam-5918	222	11	graph	graph	NOUN
ejpam-5918	222	12	,	,	PUNCT
ejpam-5918	222	13	where	where	SCONJ
ejpam-5918	222	14	n	n	PRON
ejpam-5918	222	15	≥	≥	X
ejpam-5918	222	16	2	2	NUM
ejpam-5918	222	17	and	and	CCONJ
ejpam-5918	222	18	k	k	PROPN
ejpam-5918	222	19	≥	≥	NUM
ejpam-5918	222	20	3	3	NUM
ejpam-5918	222	21	,	,	PUNCT
ejpam-5918	222	22	and	and	CCONJ
ejpam-5918	222	23	let	let	VERB
ejpam-5918	222	24	i	i	PRON
ejpam-5918	222	25	⊆	⊆	NUM
ejpam-5918	222	26	v	v	X
ejpam-5918	222	27	(	(	PUNCT
ejpam-5918	222	28	g	g	NOUN
ejpam-5918	222	29	)	)	PUNCT
ejpam-5918	222	30	with	with	ADP
ejpam-5918	222	31	|i|	|i|	PRON
ejpam-5918	222	32	≥	≥	NOUN
ejpam-5918	222	33	2	2	NUM
ejpam-5918	222	34	.	.	PUNCT
ejpam-5918	222	35	suppose	suppose	VERB
ejpam-5918	222	36	that	that	SCONJ
ejpam-5918	222	37	ui	ui	PROPN
ejpam-5918	222	38	∈	∈	PROPN
ejpam-5918	222	39	v	v	PROPN
ejpam-5918	222	40	(	(	PUNCT
ejpam-5918	222	41	k1i	k1i	PROPN
ejpam-5918	222	42	,	,	PUNCT
ejpam-5918	222	43	ki	ki	PROPN
ejpam-5918	222	44	)	)	PUNCT
ejpam-5918	222	45	be	be	AUX
ejpam-5918	222	46	a	a	DET
ejpam-5918	222	47	central	central	ADJ
ejpam-5918	222	48	vertex	vertex	NOUN
ejpam-5918	222	49	of	of	ADP
ejpam-5918	222	50	the	the	DET
ejpam-5918	222	51	ith	ith	PROPN
ejpam-5918	222	52	copy	copy	NOUN
ejpam-5918	222	53	of	of	ADP
ejpam-5918	222	54	a	a	DET
ejpam-5918	222	55	star	star	NOUN
ejpam-5918	222	56	graph	graph	NOUN
ejpam-5918	222	57	k1i	k1i	PROPN
ejpam-5918	222	58	,	,	PUNCT
ejpam-5918	222	59	ki	ki	PROPN
ejpam-5918	222	60	,	,	PUNCT
ejpam-5918	222	61	1	1	NUM
ejpam-5918	222	62	≤	≤	NUM
ejpam-5918	222	63	i	i	PRON
ejpam-5918	222	64	≤	≤	ADJ
ejpam-5918	222	65	n	n	CCONJ
ejpam-5918	222	66	and	and	CCONJ
ejpam-5918	222	67	r	r	X
ejpam-5918	222	68	a	a	DET
ejpam-5918	222	69	single	single	ADJ
ejpam-5918	222	70	root	root	NOUN
ejpam-5918	222	71	vertex	vertex	NOUN
ejpam-5918	222	72	of	of	ADP
ejpam-5918	222	73	g.	g.	PROPN
ejpam-5918	222	74	assume	assume	VERB
ejpam-5918	222	75	i	i	PRON
ejpam-5918	222	76	is	be	AUX
ejpam-5918	222	77	the	the	DET
ejpam-5918	222	78	γli	γli	NOUN
ejpam-5918	222	79	−	−	PROPN
ejpam-5918	222	80	set	set	NOUN
ejpam-5918	222	81	of	of	ADP
ejpam-5918	222	82	g.	g.	PROPN
ejpam-5918	222	83	then	then	ADV
ejpam-5918	222	84	,	,	PUNCT
ejpam-5918	222	85	i	i	PRON
ejpam-5918	222	86	is	be	AUX
ejpam-5918	222	87	a	a	DET
ejpam-5918	222	88	dominating	dominating	NOUN
ejpam-5918	222	89	set	set	NOUN
ejpam-5918	222	90	,	,	PUNCT
ejpam-5918	222	91	so	so	CCONJ
ejpam-5918	222	92	every	every	DET
ejpam-5918	222	93	vertex	vertex	NOUN
ejpam-5918	222	94	in	in	ADP
ejpam-5918	222	95	g	g	PROPN
ejpam-5918	222	96	must	must	AUX
ejpam-5918	222	97	be	be	AUX
ejpam-5918	222	98	adjacent	adjacent	ADJ
ejpam-5918	222	99	to	to	ADP
ejpam-5918	222	100	at	at	ADV
ejpam-5918	222	101	least	least	ADV
ejpam-5918	222	102	one	one	NUM
ejpam-5918	222	103	vertex	vertex	NOUN
ejpam-5918	222	104	in	in	ADP
ejpam-5918	222	105	i.	i.	NOUN
ejpam-5918	222	106	in	in	ADP
ejpam-5918	222	107	k1i	k1i	PROPN
ejpam-5918	222	108	,	,	PUNCT
ejpam-5918	222	109	ki	ki	PROPN
ejpam-5918	222	110	,	,	PUNCT
ejpam-5918	222	111	the	the	DET
ejpam-5918	222	112	central	central	ADJ
ejpam-5918	222	113	vertex	vertex	NOUN
ejpam-5918	222	114	ui	ui	NOUN
ejpam-5918	222	115	is	be	AUX
ejpam-5918	222	116	connected	connect	VERB
ejpam-5918	222	117	to	to	ADP
ejpam-5918	222	118	all	all	DET
ejpam-5918	222	119	ki	ki	PROPN
ejpam-5918	222	120	leaves	leave	VERB
ejpam-5918	222	121	.	.	PUNCT
ejpam-5918	223	1	to	to	PART
ejpam-5918	223	2	dominate	dominate	VERB
ejpam-5918	223	3	the	the	DET
ejpam-5918	223	4	leaves	leave	NOUN
ejpam-5918	223	5	of	of	ADP
ejpam-5918	223	6	k1i	k1i	PROPN
ejpam-5918	223	7	,	,	PUNCT
ejpam-5918	223	8	ki	ki	PROPN
ejpam-5918	223	9	,	,	PUNCT
ejpam-5918	223	10	ui	ui	PROPN
ejpam-5918	223	11	must	must	AUX
ejpam-5918	223	12	belong	belong	VERB
ejpam-5918	223	13	to	to	ADP
ejpam-5918	223	14	i.	i.	PROPN
ejpam-5918	223	15	thus	thus	ADV
ejpam-5918	223	16	,	,	PUNCT
ejpam-5918	223	17	(	(	PUNCT
ejpam-5918	223	18	i	i	NOUN
ejpam-5918	223	19	)	)	PUNCT
ejpam-5918	223	20	holds	hold	VERB
ejpam-5918	223	21	.	.	PUNCT
ejpam-5918	224	1	by	by	ADP
ejpam-5918	224	2	definition	definition	NOUN
ejpam-5918	224	3	of	of	ADP
ejpam-5918	224	4	ilds	ild	NOUN
ejpam-5918	224	5	,	,	PUNCT
ejpam-5918	224	6	for	for	ADP
ejpam-5918	224	7	any	any	DET
ejpam-5918	224	8	u	u	NOUN
ejpam-5918	224	9	,	,	PUNCT
ejpam-5918	224	10	v	v	NOUN
ejpam-5918	224	11	∈	∈	X
ejpam-5918	225	1	i	i	PRON
ejpam-5918	225	2	,	,	PUNCT
ejpam-5918	225	3	their	their	PRON
ejpam-5918	225	4	neighborhoods	neighborhood	NOUN
ejpam-5918	225	5	within	within	ADP
ejpam-5918	225	6	i	i	PRON
ejpam-5918	225	7	must	must	AUX
ejpam-5918	225	8	satisfy	satisfy	VERB
ejpam-5918	225	9	n(u)∩	n(u)∩	ADV
ejpam-5918	225	10	i	i	PRON
ejpam-5918	225	11	̸=	̸=	PROPN
ejpam-5918	225	12	n(v)∩	n(v)∩	PROPN
ejpam-5918	225	13	i.	i.	NOUN
ejpam-5918	225	14	to	to	PART
ejpam-5918	225	15	minimize	minimize	VERB
ejpam-5918	225	16	|i|	|i|	NOUN
ejpam-5918	225	17	,	,	PUNCT
ejpam-5918	225	18	exactly	exactly	ADV
ejpam-5918	225	19	one	one	NUM
ejpam-5918	225	20	ui	ui	NOUN
ejpam-5918	225	21	in	in	ADP
ejpam-5918	225	22	v	v	NOUN
ejpam-5918	225	23	(	(	PUNCT
ejpam-5918	225	24	k1i	k1i	X
ejpam-5918	225	25	,	,	PUNCT
ejpam-5918	225	26	k	k	NOUN
ejpam-5918	225	27	)	)	PUNCT
ejpam-5918	225	28	must	must	AUX
ejpam-5918	225	29	have	have	VERB
ejpam-5918	225	30	degi(ui	degi(ui	NOUN
ejpam-5918	225	31	)	)	PUNCT
ejpam-5918	225	32	=	=	SYM
ejpam-5918	226	1	0	0	X
ejpam-5918	226	2	.	.	PUNCT
ejpam-5918	227	1	hence	hence	ADV
ejpam-5918	227	2	,	,	PUNCT
ejpam-5918	227	3	(	(	PUNCT
ejpam-5918	227	4	ii	ii	NOUN
ejpam-5918	227	5	)	)	PUNCT
ejpam-5918	227	6	holds	hold	VERB
ejpam-5918	227	7	.	.	PUNCT
ejpam-5918	228	1	now	now	ADV
ejpam-5918	228	2	,	,	PUNCT
ejpam-5918	228	3	if	if	SCONJ
ejpam-5918	228	4	degi(ui	degi(ui	NOUN
ejpam-5918	228	5	)	)	PUNCT
ejpam-5918	228	6	=	=	SYM
ejpam-5918	228	7	0	0	NUM
ejpam-5918	228	8	,	,	PUNCT
ejpam-5918	228	9	since	since	SCONJ
ejpam-5918	228	10	(	(	PUNCT
ejpam-5918	228	11	ii	ii	NOUN
ejpam-5918	228	12	)	)	PUNCT
ejpam-5918	228	13	holds	hold	VERB
ejpam-5918	228	14	,	,	PUNCT
ejpam-5918	228	15	degi(uj	degi(uj	PROPN
ejpam-5918	228	16	)	)	PUNCT
ejpam-5918	228	17	≥	≥	NOUN
ejpam-5918	228	18	1	1	NUM
ejpam-5918	228	19	,	,	PUNCT
ejpam-5918	228	20	i	i	PRON
ejpam-5918	228	21	̸=	̸=	PROPN
ejpam-5918	228	22	j.	j.	PROPN
ejpam-5918	228	23	then	then	ADV
ejpam-5918	228	24	,	,	PUNCT
ejpam-5918	228	25	by	by	ADP
ejpam-5918	228	26	theorem	theorem	NOUN
ejpam-5918	228	27	1	1	NUM
ejpam-5918	228	28	(	(	PUNCT
ejpam-5918	228	29	i	i	NOUN
ejpam-5918	228	30	)	)	PUNCT
ejpam-5918	228	31	and	and	CCONJ
ejpam-5918	228	32	(	(	PUNCT
ejpam-5918	228	33	iii	iii	NOUN
ejpam-5918	228	34	)	)	PUNCT
ejpam-5918	228	35	,	,	PUNCT
ejpam-5918	228	36	this	this	PRON
ejpam-5918	228	37	follows	follow	VERB
ejpam-5918	228	38	degi(uj	degi(uj	PROPN
ejpam-5918	228	39	)	)	PUNCT
ejpam-5918	228	40	≤	≤	NOUN
ejpam-5918	228	41	1	1	NUM
ejpam-5918	228	42	.	.	PUNCT
ejpam-5918	229	1	thus	thus	ADV
ejpam-5918	229	2	,	,	PUNCT
ejpam-5918	229	3	degi(uj	degi(uj	PROPN
ejpam-5918	229	4	)	)	PUNCT
ejpam-5918	229	5	=	=	SYM
ejpam-5918	230	1	1	1	NUM
ejpam-5918	230	2	,	,	PUNCT
ejpam-5918	230	3	i	i	PRON
ejpam-5918	230	4	̸=	̸=	PROPN
ejpam-5918	230	5	j.	j.	PROPN
ejpam-5918	230	6	lastly	lastly	ADV
ejpam-5918	230	7	,	,	PUNCT
ejpam-5918	230	8	by	by	ADP
ejpam-5918	230	9	i	i	PRON
ejpam-5918	230	10	as	as	ADP
ejpam-5918	230	11	an	an	DET
ejpam-5918	230	12	ilds	ild	NOUN
ejpam-5918	230	13	,	,	PUNCT
ejpam-5918	230	14	and	and	CCONJ
ejpam-5918	230	15	since	since	SCONJ
ejpam-5918	230	16	(	(	PUNCT
ejpam-5918	230	17	iii	iii	NOUN
ejpam-5918	230	18	)	)	PUNCT
ejpam-5918	230	19	holds	hold	VERB
ejpam-5918	230	20	,	,	PUNCT
ejpam-5918	230	21	to	to	PART
ejpam-5918	230	22	dominate	dominate	VERB
ejpam-5918	230	23	r	r	NOUN
ejpam-5918	230	24	,	,	PUNCT
ejpam-5918	230	25	there	there	PRON
ejpam-5918	230	26	must	must	AUX
ejpam-5918	230	27	exist	exist	VERB
ejpam-5918	230	28	v	v	ADP
ejpam-5918	230	29	∈	∈	NOUN
ejpam-5918	230	30	i	i	PRON
ejpam-5918	230	31	such	such	ADJ
ejpam-5918	230	32	that	that	SCONJ
ejpam-5918	230	33	r	r	PROPN
ejpam-5918	230	34	∈	∈	PROPN
ejpam-5918	230	35	n(v	n(v	PROPN
ejpam-5918	230	36	)	)	PUNCT
ejpam-5918	230	37	.	.	PUNCT
ejpam-5918	231	1	conversely	conversely	ADV
ejpam-5918	231	2	,	,	PUNCT
ejpam-5918	231	3	assume	assume	VERB
ejpam-5918	231	4	that	that	SCONJ
ejpam-5918	231	5	i	i	PRON
ejpam-5918	231	6	⊆	⊆	NUM
ejpam-5918	231	7	v	v	ADP
ejpam-5918	231	8	(	(	PUNCT
ejpam-5918	231	9	g	g	NOUN
ejpam-5918	231	10	)	)	PUNCT
ejpam-5918	231	11	satisfies	satisfy	VERB
ejpam-5918	231	12	conditions	condition	NOUN
ejpam-5918	231	13	(	(	PUNCT
ejpam-5918	231	14	i)−	i)−	PROPN
ejpam-5918	231	15	(	(	PUNCT
ejpam-5918	231	16	iv	iv	NOUN
ejpam-5918	231	17	)	)	PUNCT
ejpam-5918	231	18	.	.	PUNCT
ejpam-5918	232	1	by	by	ADP
ejpam-5918	232	2	(	(	PUNCT
ejpam-5918	232	3	i	i	NOUN
ejpam-5918	232	4	)	)	PUNCT
ejpam-5918	232	5	and	and	CCONJ
ejpam-5918	232	6	(	(	PUNCT
ejpam-5918	232	7	iv	iv	X
ejpam-5918	232	8	)	)	PUNCT
ejpam-5918	232	9	,	,	PUNCT
ejpam-5918	232	10	every	every	DET
ejpam-5918	232	11	vertex	vertex	NOUN
ejpam-5918	232	12	in	in	ADP
ejpam-5918	232	13	g	g	PROPN
ejpam-5918	232	14	is	be	AUX
ejpam-5918	232	15	dominated	dominate	VERB
ejpam-5918	232	16	by	by	ADP
ejpam-5918	232	17	i.	i.	PROPN
ejpam-5918	232	18	by	by	ADP
ejpam-5918	232	19	(	(	PUNCT
ejpam-5918	232	20	ii	ii	NOUN
ejpam-5918	232	21	)	)	PUNCT
ejpam-5918	232	22	,	,	PUNCT
ejpam-5918	232	23	there	there	PRON
ejpam-5918	232	24	exists	exist	VERB
ejpam-5918	232	25	ui	ui	PROPN
ejpam-5918	232	26	∈	∈	PROPN
ejpam-5918	232	27	i	i	PRON
ejpam-5918	232	28	such	such	ADJ
ejpam-5918	232	29	that	that	SCONJ
ejpam-5918	232	30	ni(ui	ni(ui	NOUN
ejpam-5918	232	31	)	)	PUNCT
ejpam-5918	233	1	=	=	NOUN
ejpam-5918	233	2	∅	∅	NOUN
ejpam-5918	233	3	,	,	PUNCT
ejpam-5918	233	4	and	and	CCONJ
ejpam-5918	233	5	by	by	ADP
ejpam-5918	233	6	(	(	PUNCT
ejpam-5918	233	7	iii	iii	NOUN
ejpam-5918	233	8	)	)	PUNCT
ejpam-5918	233	9	,	,	PUNCT
ejpam-5918	233	10	for	for	ADP
ejpam-5918	233	11	all	all	PRON
ejpam-5918	233	12	uj	uj	PROPN
ejpam-5918	233	13	∈	∈	PROPN
ejpam-5918	233	14	i	i	PRON
ejpam-5918	233	15	,	,	PUNCT
ejpam-5918	233	16	i	i	PROPN
ejpam-5918	233	17	̸=	̸=	PROPN
ejpam-5918	233	18	j	j	PROPN
ejpam-5918	233	19	,	,	PUNCT
ejpam-5918	233	20	ni(uj	ni(uj	PROPN
ejpam-5918	233	21	)	)	PUNCT
ejpam-5918	233	22	is	be	AUX
ejpam-5918	233	23	a	a	DET
ejpam-5918	233	24	singleton	singleton	NOUN
ejpam-5918	233	25	set	set	NOUN
ejpam-5918	233	26	.	.	PUNCT
ejpam-5918	234	1	since	since	SCONJ
ejpam-5918	234	2	degi(uj	degi(uj	PROPN
ejpam-5918	234	3	)	)	PUNCT
ejpam-5918	234	4	=	=	SYM
ejpam-5918	234	5	1	1	NUM
ejpam-5918	234	6	,	,	PUNCT
ejpam-5918	234	7	i	i	PRON
ejpam-5918	234	8	̸=	̸=	PROPN
ejpam-5918	234	9	j	j	PROPN
ejpam-5918	234	10	,	,	PUNCT
ejpam-5918	234	11	it	it	PRON
ejpam-5918	234	12	follows	follow	VERB
ejpam-5918	234	13	that	that	SCONJ
ejpam-5918	234	14	uj	uj	PROPN
ejpam-5918	234	15	is	be	AUX
ejpam-5918	234	16	adjacent	adjacent	ADJ
ejpam-5918	234	17	to	to	ADP
ejpam-5918	234	18	one	one	NUM
ejpam-5918	234	19	of	of	ADP
ejpam-5918	234	20	the	the	DET
ejpam-5918	234	21	leaves	leave	NOUN
ejpam-5918	234	22	of	of	ADP
ejpam-5918	234	23	the	the	DET
ejpam-5918	234	24	star	star	NOUN
ejpam-5918	234	25	graph	graph	NOUN
ejpam-5918	234	26	k1j	k1j	NOUN
ejpam-5918	234	27	,	,	PUNCT
ejpam-5918	234	28	kj	kj	PROPN
ejpam-5918	234	29	.	.	PUNCT
ejpam-5918	235	1	note	note	VERB
ejpam-5918	235	2	that	that	SCONJ
ejpam-5918	235	3	for	for	ADP
ejpam-5918	235	4	all	all	DET
ejpam-5918	235	5	vi	vi	NOUN
ejpam-5918	235	6	∈	∈	NOUN
ejpam-5918	235	7	v	v	NOUN
ejpam-5918	235	8	(	(	PUNCT
ejpam-5918	235	9	k1i	k1i	PROPN
ejpam-5918	235	10	,	,	PUNCT
ejpam-5918	235	11	ki	ki	PROPN
ejpam-5918	235	12	)	)	PUNCT
ejpam-5918	235	13	,	,	PUNCT
ejpam-5918	235	14	n(vi	n(vi	NUM
ejpam-5918	235	15	)	)	PUNCT
ejpam-5918	235	16	̸=	̸=	PROPN
ejpam-5918	235	17	vj	vj	INTJ
ejpam-5918	235	18	,	,	PUNCT
ejpam-5918	235	19	for	for	ADP
ejpam-5918	235	20	all	all	PRON
ejpam-5918	235	21	vj	vj	PRON
ejpam-5918	235	22	∈	∈	PROPN
ejpam-5918	235	23	v	v	PROPN
ejpam-5918	235	24	(	(	PUNCT
ejpam-5918	235	25	k1j	k1j	X
ejpam-5918	235	26	,	,	PUNCT
ejpam-5918	235	27	kj	kj	PROPN
ejpam-5918	235	28	)	)	PUNCT
ejpam-5918	235	29	,	,	PUNCT
ejpam-5918	235	30	i	i	PRON
ejpam-5918	235	31	̸=	̸=	PROPN
ejpam-5918	235	32	j.	j.	PROPN
ejpam-5918	235	33	consequently	consequently	ADV
ejpam-5918	235	34	,	,	PUNCT
ejpam-5918	235	35	for	for	ADP
ejpam-5918	235	36	all	all	DET
ejpam-5918	235	37	u	u	NOUN
ejpam-5918	235	38	,	,	PUNCT
ejpam-5918	235	39	v	v	NOUN
ejpam-5918	235	40	∈	∈	PROPN
ejpam-5918	235	41	i	i	PRON
ejpam-5918	235	42	,	,	PUNCT
ejpam-5918	235	43	n(u	n(u	PROPN
ejpam-5918	235	44	)	)	PUNCT
ejpam-5918	235	45	∩	∩	NOUN
ejpam-5918	235	46	i	i	PRON
ejpam-5918	235	47	̸=	̸=	PROPN
ejpam-5918	235	48	n(v	n(v	PROPN
ejpam-5918	235	49	)	)	PUNCT
ejpam-5918	235	50	∩	∩	PROPN
ejpam-5918	235	51	i.	i.	NOUN
ejpam-5918	235	52	thus	thus	ADV
ejpam-5918	235	53	,	,	PUNCT
ejpam-5918	235	54	i	i	PRON
ejpam-5918	235	55	is	be	AUX
ejpam-5918	235	56	an	an	DET
ejpam-5918	235	57	ilds	ild	NOUN
ejpam-5918	235	58	.	.	PUNCT
ejpam-5918	236	1	now	now	ADV
ejpam-5918	236	2	,	,	PUNCT
ejpam-5918	236	3	by	by	ADP
ejpam-5918	236	4	removing	remove	VERB
ejpam-5918	236	5	any	any	DET
ejpam-5918	236	6	vertex	vertex	NOUN
ejpam-5918	236	7	v	v	ADP
ejpam-5918	236	8	∈	∈	NOUN
ejpam-5918	237	1	i	i	PRON
ejpam-5918	237	2	,	,	PUNCT
ejpam-5918	237	3	it	it	PRON
ejpam-5918	237	4	violates	violate	VERB
ejpam-5918	237	5	either	either	CCONJ
ejpam-5918	237	6	domination	domination	NOUN
ejpam-5918	237	7	or	or	CCONJ
ejpam-5918	237	8	ils	ils	NOUN
ejpam-5918	237	9	property	property	NOUN
ejpam-5918	237	10	.	.	PUNCT
ejpam-5918	238	1	hence	hence	ADV
ejpam-5918	238	2	,	,	PUNCT
ejpam-5918	238	3	i	i	PRON
ejpam-5918	238	4	is	be	AUX
ejpam-5918	238	5	a	a	DET
ejpam-5918	238	6	γli	γli	ADJ
ejpam-5918	238	7	−	−	NOUN
ejpam-5918	238	8	set	set	NOUN
ejpam-5918	238	9	.	.	PUNCT
ejpam-5918	239	1	corollary	corollary	ADJ
ejpam-5918	239	2	4	4	NUM
ejpam-5918	239	3	.	.	PUNCT
ejpam-5918	240	1	let	let	VERB
ejpam-5918	240	2	g	g	PRON
ejpam-5918	240	3	be	be	AUX
ejpam-5918	240	4	a	a	DET
ejpam-5918	240	5	banana	banana	NOUN
ejpam-5918	240	6	tree	tree	NOUN
ejpam-5918	240	7	graph	graph	NOUN
ejpam-5918	240	8	bn	bn	PROPN
ejpam-5918	240	9	,	,	PUNCT
ejpam-5918	240	10	k+1	k+1	X
ejpam-5918	240	11	with	with	ADP
ejpam-5918	240	12	n	n	PRON
ejpam-5918	240	13	≥	≥	NUM
ejpam-5918	240	14	2	2	NUM
ejpam-5918	240	15	and	and	CCONJ
ejpam-5918	240	16	k	k	PROPN
ejpam-5918	240	17	≥	≥	NUM
ejpam-5918	240	18	3	3	NUM
ejpam-5918	240	19	.	.	PUNCT
ejpam-5918	241	1	then	then	ADV
ejpam-5918	241	2	,	,	PUNCT
ejpam-5918	241	3	γli(g	γli(g	PROPN
ejpam-5918	241	4	)	)	PUNCT
ejpam-5918	242	1	=	=	PUNCT
ejpam-5918	243	1	2n−	2n−	NUM
ejpam-5918	243	2	1	1	NUM
ejpam-5918	243	3	.	.	PUNCT
ejpam-5918	243	4	proof	proof	NOUN
ejpam-5918	243	5	.	.	PUNCT
ejpam-5918	244	1	by	by	ADP
ejpam-5918	244	2	theorem	theorem	NOUN
ejpam-5918	244	3	5	5	NUM
ejpam-5918	244	4	(	(	PUNCT
ejpam-5918	244	5	i)-(iii	i)-(iii	NOUN
ejpam-5918	244	6	)	)	PUNCT
ejpam-5918	244	7	,	,	PUNCT
ejpam-5918	244	8	|i|	|i|	VERB
ejpam-5918	244	9	=	=	PUNCT
ejpam-5918	245	1	2n−	2n−	NUM
ejpam-5918	245	2	1	1	NUM
ejpam-5918	245	3	.	.	PUNCT
ejpam-5918	246	1	hence	hence	ADV
ejpam-5918	246	2	,	,	PUNCT
ejpam-5918	246	3	γli(g	γli(g	PROPN
ejpam-5918	246	4	)	)	PUNCT
ejpam-5918	247	1	=	=	PUNCT
ejpam-5918	248	1	2n−	2n−	NUM
ejpam-5918	248	2	1	1	NUM
ejpam-5918	248	3	.	.	PUNCT
ejpam-5918	248	4	theorem	theorem	NOUN
ejpam-5918	248	5	6	6	NUM
ejpam-5918	248	6	.	.	PUNCT
ejpam-5918	249	1	let	let	VERB
ejpam-5918	249	2	g	g	PRON
ejpam-5918	249	3	be	be	AUX
ejpam-5918	249	4	a	a	DET
ejpam-5918	249	5	gear	gear	NOUN
ejpam-5918	249	6	graph	graph	NOUN
ejpam-5918	249	7	gn	gn	PROPN
ejpam-5918	249	8	with	with	ADP
ejpam-5918	249	9	n	n	PRON
ejpam-5918	249	10	≥	≥	NUM
ejpam-5918	249	11	3	3	NUM
ejpam-5918	249	12	,	,	PUNCT
ejpam-5918	249	13	and	and	CCONJ
ejpam-5918	249	14	i	i	PRON
ejpam-5918	249	15	⊆	⊆	NUM
ejpam-5918	249	16	v	v	X
ejpam-5918	249	17	(	(	PUNCT
ejpam-5918	249	18	g	g	NOUN
ejpam-5918	249	19	)	)	PUNCT
ejpam-5918	249	20	such	such	ADJ
ejpam-5918	249	21	that	that	PRON
ejpam-5918	249	22	|i|	|i|	VERB
ejpam-5918	249	23	≥	≥	NOUN
ejpam-5918	249	24	2	2	NUM
ejpam-5918	249	25	.	.	PUNCT
ejpam-5918	250	1	then	then	ADV
ejpam-5918	250	2	i	i	PRON
ejpam-5918	250	3	is	be	AUX
ejpam-5918	250	4	a	a	DET
ejpam-5918	250	5	minimum	minimum	NOUN
ejpam-5918	250	6	internally	internally	ADV
ejpam-5918	250	7	-	-	PUNCT
ejpam-5918	250	8	locating	locate	VERB
ejpam-5918	250	9	dominating	dominating	NOUN
ejpam-5918	250	10	set	set	VERB
ejpam-5918	250	11	in	in	ADP
ejpam-5918	250	12	g	g	PROPN
ejpam-5918	250	13	if	if	SCONJ
ejpam-5918	251	1	and	and	CCONJ
ejpam-5918	251	2	only	only	ADV
ejpam-5918	251	3	if	if	SCONJ
ejpam-5918	251	4	the	the	DET
ejpam-5918	251	5	following	follow	VERB
ejpam-5918	251	6	holds	hold	VERB
ejpam-5918	251	7	:	:	PUNCT
ejpam-5918	251	8	(	(	PUNCT
ejpam-5918	251	9	i	i	NOUN
ejpam-5918	251	10	)	)	PUNCT
ejpam-5918	251	11	u	u	NOUN
ejpam-5918	251	12	/∈	/∈	PUNCT
ejpam-5918	252	1	i	i	PRON
ejpam-5918	252	2	,	,	PUNCT
ejpam-5918	252	3	where	where	SCONJ
ejpam-5918	252	4	u	u	PROPN
ejpam-5918	252	5	∈	∈	PROPN
ejpam-5918	252	6	v	v	ADP
ejpam-5918	252	7	(	(	PUNCT
ejpam-5918	252	8	g	g	NOUN
ejpam-5918	252	9	)	)	PUNCT
ejpam-5918	252	10	be	be	AUX
ejpam-5918	252	11	a	a	DET
ejpam-5918	252	12	central	central	ADJ
ejpam-5918	252	13	vertex	vertex	NOUN
ejpam-5918	252	14	in	in	ADP
ejpam-5918	252	15	g	g	NOUN
ejpam-5918	252	16	;	;	PUNCT
ejpam-5918	252	17	(	(	PUNCT
ejpam-5918	252	18	ii	ii	X
ejpam-5918	252	19	)	)	PUNCT
ejpam-5918	253	1	i	i	PRON
ejpam-5918	253	2	is	be	AUX
ejpam-5918	253	3	a	a	DET
ejpam-5918	253	4	minimum	minimum	NOUN
ejpam-5918	253	5	internally	internally	ADV
ejpam-5918	253	6	-	-	PUNCT
ejpam-5918	253	7	locating	locate	VERB
ejpam-5918	253	8	dominating	dominating	NOUN
ejpam-5918	253	9	set	set	NOUN
ejpam-5918	253	10	of	of	ADP
ejpam-5918	253	11	c2n	c2n	NOUN
ejpam-5918	253	12	.	.	PUNCT
ejpam-5918	254	1	proof	proof	NOUN
ejpam-5918	254	2	.	.	PUNCT
ejpam-5918	255	1	let	let	VERB
ejpam-5918	255	2	g	g	PROPN
ejpam-5918	255	3	=	=	PUNCT
ejpam-5918	255	4	gn	gn	PROPN
ejpam-5918	255	5	be	be	AUX
ejpam-5918	255	6	a	a	DET
ejpam-5918	255	7	gear	gear	NOUN
ejpam-5918	255	8	graph	graph	NOUN
ejpam-5918	255	9	with	with	ADP
ejpam-5918	255	10	n	n	NUM
ejpam-5918	255	11	≥	≥	NUM
ejpam-5918	255	12	3	3	NUM
ejpam-5918	255	13	,	,	PUNCT
ejpam-5918	255	14	vertex	vertex	NOUN
ejpam-5918	255	15	set	set	VERB
ejpam-5918	255	16	v	v	NOUN
ejpam-5918	255	17	(	(	PUNCT
ejpam-5918	255	18	gn	gn	PROPN
ejpam-5918	255	19	)	)	PUNCT
ejpam-5918	255	20	=	=	PRON
ejpam-5918	255	21	{	{	PUNCT
ejpam-5918	255	22	u	u	NOUN
ejpam-5918	255	23	}	}	PUNCT
ejpam-5918	255	24	∪	∪	X
ejpam-5918	255	25	{	{	PUNCT
ejpam-5918	255	26	vi	vi	NOUN
ejpam-5918	255	27	|	|	NOUN
ejpam-5918	255	28	1	1	NUM
ejpam-5918	255	29	≤	≤	NUM
ejpam-5918	255	30	i	i	PRON
ejpam-5918	255	31	≤	≤	NOUN
ejpam-5918	255	32	n	n	CCONJ
ejpam-5918	255	33	}	}	PUNCT
ejpam-5918	255	34	∪	∪	ADJ
ejpam-5918	255	35	{	{	PUNCT
ejpam-5918	255	36	vi	vi	NOUN
ejpam-5918	255	37	,	,	PUNCT
ejpam-5918	255	38	i+1	i+1	PUNCT
ejpam-5918	255	39	|	|	ADV
ejpam-5918	255	40	1	1	NUM
ejpam-5918	255	41	≤	≤	NUM
ejpam-5918	255	42	i	i	PRON
ejpam-5918	255	43	≤	≤	ADJ
ejpam-5918	255	44	n	n	CCONJ
ejpam-5918	255	45	}	}	PUNCT
ejpam-5918	255	46	i.	i.	PROPN
ejpam-5918	255	47	tropico	tropico	PROPN
ejpam-5918	255	48	,	,	PUNCT
ejpam-5918	255	49	i.	i.	PROPN
ejpam-5918	255	50	cabahug	cabahug	PROPN
ejpam-5918	255	51	,	,	PUNCT
ejpam-5918	255	52	jr	jr	PROPN
ejpam-5918	255	53	.	.	PROPN
ejpam-5918	255	54	/	/	SYM
ejpam-5918	255	55	eur	eur	PROPN
ejpam-5918	255	56	.	.	PUNCT
ejpam-5918	256	1	j.	j.	PROPN
ejpam-5918	256	2	pure	pure	PROPN
ejpam-5918	256	3	appl	appl	PROPN
ejpam-5918	256	4	.	.	PROPN
ejpam-5918	256	5	math	math	PROPN
ejpam-5918	256	6	,	,	PUNCT
ejpam-5918	256	7	18	18	NUM
ejpam-5918	256	8	(	(	PUNCT
ejpam-5918	256	9	2	2	NUM
ejpam-5918	256	10	)	)	PUNCT
ejpam-5918	256	11	(	(	PUNCT
ejpam-5918	256	12	2025	2025	NUM
ejpam-5918	256	13	)	)	PUNCT
ejpam-5918	256	14	,	,	PUNCT
ejpam-5918	256	15	5918	5918	NUM
ejpam-5918	256	16	10	10	NUM
ejpam-5918	256	17	of	of	ADP
ejpam-5918	256	18	21	21	NUM
ejpam-5918	256	19	and	and	CCONJ
ejpam-5918	256	20	edge	edge	VERB
ejpam-5918	256	21	set	set	VERB
ejpam-5918	256	22	e(gn	e(gn	NOUN
ejpam-5918	256	23	)	)	PUNCT
ejpam-5918	256	24	=	=	SYM
ejpam-5918	256	25	e(c2n	e(c2n	NOUN
ejpam-5918	256	26	)	)	PUNCT
ejpam-5918	256	27	∪	∪	NOUN
ejpam-5918	256	28	{	{	PUNCT
ejpam-5918	256	29	uvi	uvi	PROPN
ejpam-5918	256	30	|	|	ADV
ejpam-5918	256	31	1	1	NUM
ejpam-5918	256	32	≤	≤	NUM
ejpam-5918	256	33	i	i	PRON
ejpam-5918	256	34	≤	≤	NOUN
ejpam-5918	256	35	n	n	CCONJ
ejpam-5918	256	36	}	}	PUNCT
ejpam-5918	256	37	,	,	PUNCT
ejpam-5918	256	38	where	where	SCONJ
ejpam-5918	256	39	u	u	NOUN
ejpam-5918	256	40	is	be	AUX
ejpam-5918	256	41	the	the	DET
ejpam-5918	256	42	central	central	ADJ
ejpam-5918	256	43	vertex	vertex	NOUN
ejpam-5918	256	44	of	of	ADP
ejpam-5918	256	45	gn	gn	PROPN
ejpam-5918	256	46	and	and	CCONJ
ejpam-5918	256	47	c2n	c2n	NOUN
ejpam-5918	256	48	is	be	AUX
ejpam-5918	256	49	a	a	DET
ejpam-5918	256	50	cycle	cycle	NOUN
ejpam-5918	256	51	graph	graph	NOUN
ejpam-5918	256	52	of	of	ADP
ejpam-5918	256	53	order	order	NOUN
ejpam-5918	256	54	2n	2n	NUM
ejpam-5918	256	55	.	.	PUNCT
ejpam-5918	257	1	assume	assume	VERB
ejpam-5918	257	2	i	i	PRON
ejpam-5918	257	3	⊆	⊆	NUM
ejpam-5918	257	4	v	v	ADP
ejpam-5918	257	5	(	(	PUNCT
ejpam-5918	257	6	g	g	NOUN
ejpam-5918	257	7	)	)	PUNCT
ejpam-5918	257	8	is	be	AUX
ejpam-5918	257	9	a	a	DET
ejpam-5918	257	10	γli	γli	ADV
ejpam-5918	257	11	-	-	PUNCT
ejpam-5918	257	12	set	set	NOUN
ejpam-5918	257	13	of	of	ADP
ejpam-5918	257	14	g.	g.	PROPN
ejpam-5918	257	15	then	then	ADV
ejpam-5918	257	16	,	,	PUNCT
ejpam-5918	257	17	the	the	DET
ejpam-5918	257	18	central	central	ADJ
ejpam-5918	257	19	vertex	vertex	NOUN
ejpam-5918	257	20	u	u	NOUN
ejpam-5918	257	21	is	be	AUX
ejpam-5918	257	22	adjacent	adjacent	ADJ
ejpam-5918	257	23	to	to	ADP
ejpam-5918	257	24	all	all	DET
ejpam-5918	257	25	vi	vi	PROPN
ejpam-5918	257	26	,	,	PUNCT
ejpam-5918	257	27	1	1	NUM
ejpam-5918	257	28	≤	≤	NUM
ejpam-5918	257	29	i	i	PRON
ejpam-5918	257	30	≤	≤	NOUN
ejpam-5918	258	1	n	n	CCONJ
ejpam-5918	259	1	but	but	CCONJ
ejpam-5918	259	2	is	be	AUX
ejpam-5918	259	3	not	not	PART
ejpam-5918	259	4	adjacent	adjacent	ADJ
ejpam-5918	259	5	to	to	ADP
ejpam-5918	259	6	any	any	DET
ejpam-5918	259	7	vi	vi	NOUN
ejpam-5918	259	8	,	,	PUNCT
ejpam-5918	259	9	i+1	i+1	PRON
ejpam-5918	259	10	.	.	PUNCT
ejpam-5918	260	1	suppose	suppose	VERB
ejpam-5918	260	2	u	u	PROPN
ejpam-5918	260	3	∈	∈	PROPN
ejpam-5918	260	4	i.	i.	NOUN
ejpam-5918	260	5	then	then	ADV
ejpam-5918	260	6	,	,	PUNCT
ejpam-5918	260	7	u	u	PRON
ejpam-5918	260	8	dominates	dominate	VERB
ejpam-5918	260	9	all	all	DET
ejpam-5918	260	10	vi	vi	NOUN
ejpam-5918	260	11	,	,	PUNCT
ejpam-5918	260	12	but	but	CCONJ
ejpam-5918	260	13	it	it	PRON
ejpam-5918	260	14	does	do	AUX
ejpam-5918	260	15	not	not	PART
ejpam-5918	260	16	dominate	dominate	VERB
ejpam-5918	260	17	vi	vi	NOUN
ejpam-5918	260	18	,	,	PUNCT
ejpam-5918	260	19	i+1	i+1	NUM
ejpam-5918	260	20	,	,	PUNCT
ejpam-5918	260	21	which	which	PRON
ejpam-5918	260	22	must	must	AUX
ejpam-5918	260	23	still	still	ADV
ejpam-5918	260	24	be	be	AUX
ejpam-5918	260	25	dominated	dominate	VERB
ejpam-5918	260	26	by	by	ADP
ejpam-5918	260	27	other	other	ADJ
ejpam-5918	260	28	vertices	vertex	NOUN
ejpam-5918	260	29	in	in	ADP
ejpam-5918	260	30	i.	i.	NOUN
ejpam-5918	260	31	removing	remove	VERB
ejpam-5918	260	32	u	u	NOUN
ejpam-5918	260	33	from	from	ADP
ejpam-5918	260	34	i	i	PRON
ejpam-5918	260	35	does	do	AUX
ejpam-5918	260	36	not	not	PART
ejpam-5918	260	37	violate	violate	VERB
ejpam-5918	260	38	the	the	DET
ejpam-5918	260	39	domination	domination	NOUN
ejpam-5918	260	40	or	or	CCONJ
ejpam-5918	260	41	ilds	ild	VERB
ejpam-5918	260	42	conditions	condition	NOUN
ejpam-5918	260	43	.	.	PUNCT
ejpam-5918	261	1	thus	thus	ADV
ejpam-5918	261	2	,	,	PUNCT
ejpam-5918	261	3	u	u	NOUN
ejpam-5918	261	4	/∈	/∈	PUNCT
ejpam-5918	262	1	i	i	PRON
ejpam-5918	262	2	,	,	PUNCT
ejpam-5918	262	3	as	as	SCONJ
ejpam-5918	262	4	its	its	PRON
ejpam-5918	262	5	inclusion	inclusion	NOUN
ejpam-5918	262	6	would	would	AUX
ejpam-5918	262	7	violate	violate	VERB
ejpam-5918	262	8	the	the	DET
ejpam-5918	262	9	minimality	minimality	NOUN
ejpam-5918	262	10	of	of	ADP
ejpam-5918	262	11	i.	i.	PROPN
ejpam-5918	262	12	now	now	ADV
ejpam-5918	262	13	,	,	PUNCT
ejpam-5918	262	14	by	by	ADP
ejpam-5918	262	15	definition	definition	NOUN
ejpam-5918	262	16	of	of	ADP
ejpam-5918	262	17	g	g	PROPN
ejpam-5918	262	18	,	,	PUNCT
ejpam-5918	262	19	v	v	NOUN
ejpam-5918	262	20	(	(	PUNCT
ejpam-5918	262	21	g	g	NOUN
ejpam-5918	262	22	)	)	PUNCT
ejpam-5918	262	23	\	\	NOUN
ejpam-5918	262	24	{	{	PUNCT
ejpam-5918	262	25	u	u	NOUN
ejpam-5918	262	26	}	}	PUNCT
ejpam-5918	262	27	is	be	AUX
ejpam-5918	262	28	a	a	DET
ejpam-5918	262	29	c2n	c2n	NOUN
ejpam-5918	262	30	.	.	PUNCT
ejpam-5918	263	1	since	since	SCONJ
ejpam-5918	263	2	(	(	PUNCT
ejpam-5918	263	3	i	i	NOUN
ejpam-5918	263	4	)	)	PUNCT
ejpam-5918	263	5	holds	hold	VERB
ejpam-5918	263	6	,	,	PUNCT
ejpam-5918	263	7	and	and	CCONJ
ejpam-5918	263	8	by	by	ADP
ejpam-5918	263	9	theorem	theorem	NOUN
ejpam-5918	263	10	4	4	NUM
ejpam-5918	263	11	,	,	PUNCT
ejpam-5918	263	12	i	i	PRON
ejpam-5918	263	13	is	be	AUX
ejpam-5918	263	14	a	a	DET
ejpam-5918	263	15	γli	γli	ADV
ejpam-5918	263	16	-	-	PUNCT
ejpam-5918	263	17	set	set	NOUN
ejpam-5918	263	18	of	of	ADP
ejpam-5918	263	19	c2n	c2n	NOUN
ejpam-5918	263	20	.	.	PUNCT
ejpam-5918	264	1	conversely	conversely	ADV
ejpam-5918	264	2	,	,	PUNCT
ejpam-5918	264	3	assume	assume	VERB
ejpam-5918	264	4	that	that	SCONJ
ejpam-5918	264	5	u	u	PROPN
ejpam-5918	264	6	/∈	/∈	PUNCT
ejpam-5918	265	1	i	i	PRON
ejpam-5918	265	2	and	and	CCONJ
ejpam-5918	265	3	i	i	PRON
ejpam-5918	265	4	is	be	AUX
ejpam-5918	265	5	a	a	DET
ejpam-5918	265	6	γli	γli	ADJ
ejpam-5918	265	7	−	−	NOUN
ejpam-5918	265	8	set	set	NOUN
ejpam-5918	265	9	of	of	ADP
ejpam-5918	265	10	c2n	c2n	NOUN
ejpam-5918	265	11	.	.	PUNCT
ejpam-5918	266	1	clearly	clearly	ADV
ejpam-5918	266	2	,	,	PUNCT
ejpam-5918	266	3	by	by	ADP
ejpam-5918	266	4	theorem	theorem	NOUN
ejpam-5918	266	5	4	4	NUM
ejpam-5918	266	6	,	,	PUNCT
ejpam-5918	266	7	i	i	PRON
ejpam-5918	266	8	is	be	AUX
ejpam-5918	266	9	the	the	DET
ejpam-5918	266	10	γli	γli	NOUN
ejpam-5918	266	11	−	−	PROPN
ejpam-5918	266	12	set	set	NOUN
ejpam-5918	266	13	of	of	ADP
ejpam-5918	266	14	g.	g.	PROPN
ejpam-5918	266	15	corollary	corollary	PROPN
ejpam-5918	266	16	5	5	NUM
ejpam-5918	266	17	.	.	PUNCT
ejpam-5918	267	1	let	let	VERB
ejpam-5918	267	2	g	g	PRON
ejpam-5918	267	3	be	be	AUX
ejpam-5918	267	4	a	a	DET
ejpam-5918	267	5	gear	gear	NOUN
ejpam-5918	267	6	graph	graph	NOUN
ejpam-5918	267	7	gn	gn	PROPN
ejpam-5918	267	8	with	with	ADP
ejpam-5918	267	9	n	n	PRON
ejpam-5918	267	10	≥	≥	NUM
ejpam-5918	267	11	3	3	NUM
ejpam-5918	267	12	.	.	PUNCT
ejpam-5918	268	1	then	then	ADV
ejpam-5918	268	2	,	,	PUNCT
ejpam-5918	268	3	γli(g	γli(g	PROPN
ejpam-5918	268	4	)	)	PUNCT
ejpam-5918	268	5	=	=	SYM
ejpam-5918	269	1	n.	n.	NOUN
ejpam-5918	269	2	proof	proof	NOUN
ejpam-5918	269	3	.	.	PUNCT
ejpam-5918	270	1	note	note	VERB
ejpam-5918	270	2	that	that	SCONJ
ejpam-5918	270	3	|v	|v	PROPN
ejpam-5918	270	4	(	(	PUNCT
ejpam-5918	270	5	gn)|	gn)|	PROPN
ejpam-5918	270	6	−	−	PROPN
ejpam-5918	270	7	1	1	NUM
ejpam-5918	270	8	=	=	SYM
ejpam-5918	270	9	|v	|v	X
ejpam-5918	270	10	(	(	PUNCT
ejpam-5918	270	11	c2n)|	c2n)|	PROPN
ejpam-5918	270	12	=	=	SYM
ejpam-5918	270	13	2n	2n	NUM
ejpam-5918	270	14	,	,	PUNCT
ejpam-5918	270	15	and	and	CCONJ
ejpam-5918	270	16	also	also	ADV
ejpam-5918	270	17	by	by	ADP
ejpam-5918	270	18	theorem	theorem	NOUN
ejpam-5918	270	19	6	6	NUM
ejpam-5918	270	20	,	,	PUNCT
ejpam-5918	270	21	|i|	|i|	ADP
ejpam-5918	270	22	=	=	SYM
ejpam-5918	270	23	2n	2n	NUM
ejpam-5918	270	24	,	,	PUNCT
ejpam-5918	270	25	where	where	SCONJ
ejpam-5918	270	26	i	i	PRON
ejpam-5918	270	27	is	be	AUX
ejpam-5918	270	28	the	the	DET
ejpam-5918	270	29	γli	γli	NOUN
ejpam-5918	270	30	−	−	PROPN
ejpam-5918	270	31	set	set	NOUN
ejpam-5918	270	32	of	of	ADP
ejpam-5918	270	33	gn	gn	PROPN
ejpam-5918	270	34	.	.	PUNCT
ejpam-5918	271	1	this	this	PRON
ejpam-5918	271	2	implies	imply	VERB
ejpam-5918	271	3	,	,	PUNCT
ejpam-5918	271	4	2n	2n	NUM
ejpam-5918	271	5	≡	≡	PROPN
ejpam-5918	271	6	0	0	NUM
ejpam-5918	271	7	,	,	PUNCT
ejpam-5918	271	8	2	2	NUM
ejpam-5918	271	9	(	(	PUNCT
ejpam-5918	271	10	mod	mod	NOUN
ejpam-5918	271	11	4	4	NUM
ejpam-5918	271	12	)	)	PUNCT
ejpam-5918	271	13	.	.	PUNCT
ejpam-5918	272	1	by	by	ADP
ejpam-5918	272	2	corollary	corollary	ADJ
ejpam-5918	272	3	3	3	NUM
ejpam-5918	272	4	,	,	PUNCT
ejpam-5918	272	5	if	if	SCONJ
ejpam-5918	272	6	n	n	PRON
ejpam-5918	272	7	≡	≡	PROPN
ejpam-5918	272	8	0	0	NUM
ejpam-5918	272	9	,	,	PUNCT
ejpam-5918	272	10	2	2	NUM
ejpam-5918	272	11	(	(	PUNCT
ejpam-5918	272	12	mod	mod	NOUN
ejpam-5918	272	13	4	4	NUM
ejpam-5918	272	14	)	)	PUNCT
ejpam-5918	272	15	,	,	PUNCT
ejpam-5918	272	16	then	then	ADV
ejpam-5918	272	17	γli(c2n	γli(c2n	PUNCT
ejpam-5918	272	18	)	)	PUNCT
ejpam-5918	272	19	=	=	SYM
ejpam-5918	272	20	n	n	PRON
ejpam-5918	272	21	2	2	NUM
ejpam-5918	272	22	.	.	PUNCT
ejpam-5918	272	23	let	let	VERB
ejpam-5918	272	24	l	l	NOUN
ejpam-5918	272	25	∈	∈	PROPN
ejpam-5918	272	26	z	z	NOUN
ejpam-5918	272	27	such	such	ADJ
ejpam-5918	272	28	that	that	DET
ejpam-5918	272	29	l	l	NOUN
ejpam-5918	272	30	=	=	SYM
ejpam-5918	272	31	2n	2n	NUM
ejpam-5918	272	32	.	.	PUNCT
ejpam-5918	273	1	with	with	ADP
ejpam-5918	273	2	this	this	PRON
ejpam-5918	273	3	,	,	PUNCT
ejpam-5918	273	4	γli(gn	γli(gn	NOUN
ejpam-5918	273	5	)	)	PUNCT
ejpam-5918	273	6	=	=	SYM
ejpam-5918	273	7	l	l	NOUN
ejpam-5918	273	8	2	2	NUM
ejpam-5918	273	9	=	=	SYM
ejpam-5918	273	10	2n	2n	NUM
ejpam-5918	273	11	2	2	NUM
ejpam-5918	273	12	=	=	SYM
ejpam-5918	273	13	n.	n.	NOUN
ejpam-5918	273	14	hence	hence	ADV
ejpam-5918	273	15	,	,	PUNCT
ejpam-5918	273	16	γli(g	γli(g	PROPN
ejpam-5918	273	17	)	)	PUNCT
ejpam-5918	273	18	=	=	SYM
ejpam-5918	273	19	n.	n.	NOUN
ejpam-5918	273	20	theorem	theorem	VERB
ejpam-5918	273	21	7	7	NUM
ejpam-5918	273	22	.	.	PUNCT
ejpam-5918	274	1	let	let	VERB
ejpam-5918	274	2	g	g	PRON
ejpam-5918	274	3	be	be	AUX
ejpam-5918	274	4	a	a	DET
ejpam-5918	274	5	lollipop	lollipop	NOUN
ejpam-5918	274	6	graph	graph	NOUN
ejpam-5918	274	7	lm	lm	PROPN
ejpam-5918	274	8	,	,	PUNCT
ejpam-5918	274	9	n	n	PROPN
ejpam-5918	274	10	with	with	ADP
ejpam-5918	274	11	m	m	PROPN
ejpam-5918	274	12	≥	≥	NUM
ejpam-5918	274	13	3	3	NUM
ejpam-5918	274	14	and	and	CCONJ
ejpam-5918	274	15	n	n	PRON
ejpam-5918	274	16	≥	≥	NOUN
ejpam-5918	274	17	4	4	NUM
ejpam-5918	274	18	,	,	PUNCT
ejpam-5918	274	19	and	and	CCONJ
ejpam-5918	274	20	i	i	PRON
ejpam-5918	274	21	⊆	⊆	NUM
ejpam-5918	274	22	v	v	X
ejpam-5918	274	23	(	(	PUNCT
ejpam-5918	274	24	g	g	NOUN
ejpam-5918	274	25	)	)	PUNCT
ejpam-5918	274	26	such	such	ADJ
ejpam-5918	274	27	that	that	PRON
ejpam-5918	274	28	|i|	|i|	VERB
ejpam-5918	274	29	≥	≥	NOUN
ejpam-5918	274	30	2	2	NUM
ejpam-5918	274	31	.	.	PUNCT
ejpam-5918	275	1	then	then	ADV
ejpam-5918	275	2	i	i	PRON
ejpam-5918	275	3	is	be	AUX
ejpam-5918	275	4	a	a	DET
ejpam-5918	275	5	minimum	minimum	NOUN
ejpam-5918	275	6	internally	internally	ADV
ejpam-5918	275	7	-	-	PUNCT
ejpam-5918	275	8	locating	locate	VERB
ejpam-5918	275	9	dominating	dominating	NOUN
ejpam-5918	275	10	set	set	VERB
ejpam-5918	275	11	in	in	ADP
ejpam-5918	275	12	g	g	PROPN
ejpam-5918	275	13	if	if	SCONJ
ejpam-5918	276	1	and	and	CCONJ
ejpam-5918	276	2	only	only	ADV
ejpam-5918	276	3	if	if	SCONJ
ejpam-5918	276	4	the	the	DET
ejpam-5918	276	5	following	follow	VERB
ejpam-5918	276	6	holds	hold	VERB
ejpam-5918	276	7	:	:	PUNCT
ejpam-5918	276	8	(	(	PUNCT
ejpam-5918	276	9	i	i	NOUN
ejpam-5918	276	10	)	)	PUNCT
ejpam-5918	276	11	u	u	NOUN
ejpam-5918	276	12	∈	∈	PROPN
ejpam-5918	276	13	i	i	PRON
ejpam-5918	276	14	and	and	CCONJ
ejpam-5918	276	15	degi(u	degi(u	VERB
ejpam-5918	276	16	)	)	PUNCT
ejpam-5918	276	17	=	=	SYM
ejpam-5918	276	18	0	0	NUM
ejpam-5918	276	19	or	or	CCONJ
ejpam-5918	276	20	degi(u	degi(u	NOUN
ejpam-5918	276	21	)	)	PUNCT
ejpam-5918	276	22	=	=	SYM
ejpam-5918	277	1	1	1	NUM
ejpam-5918	277	2	;	;	PUNCT
ejpam-5918	277	3	(	(	PUNCT
ejpam-5918	277	4	ii	ii	NOUN
ejpam-5918	277	5	)	)	PUNCT
ejpam-5918	277	6	for	for	ADP
ejpam-5918	277	7	every	every	DET
ejpam-5918	277	8	v	v	NOUN
ejpam-5918	277	9	∈	∈	NOUN
ejpam-5918	277	10	i	i	PRON
ejpam-5918	277	11	,	,	PUNCT
ejpam-5918	277	12	if	if	SCONJ
ejpam-5918	277	13	degi(v	degi(v	NOUN
ejpam-5918	277	14	)	)	PUNCT
ejpam-5918	277	15	=	=	SYM
ejpam-5918	277	16	0	0	NUM
ejpam-5918	277	17	or	or	CCONJ
ejpam-5918	277	18	1	1	NUM
ejpam-5918	277	19	,	,	PUNCT
ejpam-5918	277	20	then	then	ADV
ejpam-5918	277	21	degv	degv	NOUN
ejpam-5918	277	22	(	(	PUNCT
ejpam-5918	277	23	g)\i(v	g)\i(v	PROPN
ejpam-5918	277	24	)	)	PUNCT
ejpam-5918	277	25	=	=	PUNCT
ejpam-5918	278	1	1	1	NUM
ejpam-5918	278	2	;	;	PUNCT
ejpam-5918	278	3	(	(	PUNCT
ejpam-5918	278	4	iii	iii	X
ejpam-5918	278	5	)	)	PUNCT
ejpam-5918	278	6	if	if	SCONJ
ejpam-5918	278	7	degi(v	degi(v	NOUN
ejpam-5918	278	8	)	)	PUNCT
ejpam-5918	278	9	=	=	SYM
ejpam-5918	278	10	0	0	NUM
ejpam-5918	278	11	,	,	PUNCT
ejpam-5918	278	12	then	then	ADV
ejpam-5918	278	13	v	v	NOUN
ejpam-5918	278	14	is	be	AUX
ejpam-5918	278	15	unique	unique	ADJ
ejpam-5918	278	16	in	in	ADP
ejpam-5918	278	17	i	i	PRON
ejpam-5918	278	18	;	;	PUNCT
ejpam-5918	278	19	and	and	CCONJ
ejpam-5918	278	20	(	(	PUNCT
ejpam-5918	278	21	iv	iv	X
ejpam-5918	278	22	)	)	PUNCT
ejpam-5918	278	23	for	for	ADP
ejpam-5918	278	24	all	all	PRON
ejpam-5918	278	25	x	x	SYM
ejpam-5918	278	26	∈	∈	PROPN
ejpam-5918	278	27	v	v	NOUN
ejpam-5918	278	28	(	(	PUNCT
ejpam-5918	278	29	g	g	NOUN
ejpam-5918	278	30	)	)	PUNCT
ejpam-5918	278	31	\	\	PUNCT
ejpam-5918	279	1	i	i	PRON
ejpam-5918	279	2	,	,	PUNCT
ejpam-5918	279	3	x	x	PROPN
ejpam-5918	279	4	∈	∈	PROPN
ejpam-5918	279	5	n(y	n(y	PROPN
ejpam-5918	279	6	)	)	PUNCT
ejpam-5918	279	7	for	for	ADP
ejpam-5918	279	8	some	some	DET
ejpam-5918	279	9	y	y	PROPN
ejpam-5918	279	10	∈	∈	PROPN
ejpam-5918	279	11	i.	i.	NOUN
ejpam-5918	279	12	where	where	SCONJ
ejpam-5918	279	13	,	,	PUNCT
ejpam-5918	279	14	u	u	PROPN
ejpam-5918	279	15	∈	∈	PROPN
ejpam-5918	279	16	v	v	NOUN
ejpam-5918	279	17	(	(	PUNCT
ejpam-5918	279	18	km	km	NOUN
ejpam-5918	279	19	)	)	PUNCT
ejpam-5918	279	20	and	and	CCONJ
ejpam-5918	279	21	incident	incident	NOUN
ejpam-5918	279	22	to	to	ADP
ejpam-5918	279	23	a	a	DET
ejpam-5918	279	24	bridge	bridge	NOUN
ejpam-5918	279	25	and	and	CCONJ
ejpam-5918	279	26	v	v	NOUN
ejpam-5918	279	27	∈	∈	NOUN
ejpam-5918	279	28	v	v	NOUN
ejpam-5918	279	29	(	(	PUNCT
ejpam-5918	279	30	pn	pn	NOUN
ejpam-5918	279	31	)	)	PUNCT
ejpam-5918	279	32	.	.	PUNCT
ejpam-5918	280	1	proof	proof	NOUN
ejpam-5918	280	2	.	.	PUNCT
ejpam-5918	281	1	let	let	VERB
ejpam-5918	281	2	g	g	NOUN
ejpam-5918	281	3	=	=	SYM
ejpam-5918	281	4	lm	lm	PROPN
ejpam-5918	281	5	,	,	PUNCT
ejpam-5918	281	6	n	n	PRON
ejpam-5918	281	7	be	be	VERB
ejpam-5918	281	8	a	a	DET
ejpam-5918	281	9	lollipop	lollipop	NOUN
ejpam-5918	281	10	graph	graph	NOUN
ejpam-5918	281	11	with	with	ADP
ejpam-5918	281	12	m	m	PROPN
ejpam-5918	281	13	≥	≥	NUM
ejpam-5918	281	14	3	3	NUM
ejpam-5918	281	15	and	and	CCONJ
ejpam-5918	281	16	n	n	PRON
ejpam-5918	281	17	≥	≥	NOUN
ejpam-5918	281	18	4	4	NUM
ejpam-5918	281	19	,	,	PUNCT
ejpam-5918	281	20	and	and	CCONJ
ejpam-5918	281	21	i	i	PRON
ejpam-5918	281	22	⊆	⊆	NUM
ejpam-5918	281	23	v	v	X
ejpam-5918	281	24	(	(	PUNCT
ejpam-5918	281	25	g	g	NOUN
ejpam-5918	281	26	)	)	PUNCT
ejpam-5918	281	27	such	such	ADJ
ejpam-5918	281	28	that	that	PRON
ejpam-5918	281	29	|i|	|i|	VERB
ejpam-5918	281	30	≥	≥	NOUN
ejpam-5918	281	31	2	2	NUM
ejpam-5918	281	32	.	.	PUNCT
ejpam-5918	281	33	assume	assume	VERB
ejpam-5918	281	34	i	i	PRON
ejpam-5918	281	35	is	be	AUX
ejpam-5918	281	36	a	a	DET
ejpam-5918	281	37	γli	γli	ADJ
ejpam-5918	281	38	−	−	NOUN
ejpam-5918	281	39	set	set	VERB
ejpam-5918	281	40	in	in	ADP
ejpam-5918	281	41	g.	g.	PROPN
ejpam-5918	281	42	let	let	VERB
ejpam-5918	281	43	u	u	PRON
ejpam-5918	281	44	∈	∈	PROPN
ejpam-5918	281	45	v	v	X
ejpam-5918	281	46	(	(	PUNCT
ejpam-5918	281	47	km	km	NOUN
ejpam-5918	281	48	)	)	PUNCT
ejpam-5918	281	49	be	be	VERB
ejpam-5918	281	50	incident	incident	NOUN
ejpam-5918	281	51	to	to	ADP
ejpam-5918	281	52	the	the	DET
ejpam-5918	281	53	bridge	bridge	NOUN
ejpam-5918	281	54	.	.	PUNCT
ejpam-5918	282	1	since	since	SCONJ
ejpam-5918	282	2	i	i	PRON
ejpam-5918	282	3	is	be	AUX
ejpam-5918	282	4	a	a	DET
ejpam-5918	282	5	γli	γli	ADJ
ejpam-5918	282	6	−	−	NOUN
ejpam-5918	282	7	set	set	NOUN
ejpam-5918	282	8	,	,	PUNCT
ejpam-5918	282	9	u	u	NOUN
ejpam-5918	282	10	∈	∈	PROPN
ejpam-5918	282	11	i	i	PRON
ejpam-5918	282	12	to	to	PART
ejpam-5918	282	13	dominate	dominate	VERB
ejpam-5918	282	14	a	a	DET
ejpam-5918	282	15	vertex	vertex	NOUN
ejpam-5918	282	16	in	in	ADP
ejpam-5918	282	17	pn	pn	PROPN
ejpam-5918	282	18	.	.	PUNCT
ejpam-5918	283	1	if	if	SCONJ
ejpam-5918	283	2	degi(u	degi(u	PROPN
ejpam-5918	283	3	)	)	PUNCT
ejpam-5918	283	4	>	>	X
ejpam-5918	284	1	1	1	NUM
ejpam-5918	284	2	,	,	PUNCT
ejpam-5918	284	3	then	then	ADV
ejpam-5918	284	4	multiple	multiple	ADJ
ejpam-5918	284	5	vertices	vertex	NOUN
ejpam-5918	284	6	in	in	ADP
ejpam-5918	284	7	i	i	PRON
ejpam-5918	284	8	are	be	AUX
ejpam-5918	284	9	unnecessarily	unnecessarily	ADV
ejpam-5918	284	10	dominated	dominate	VERB
ejpam-5918	284	11	,	,	PUNCT
ejpam-5918	284	12	contradicting	contradict	VERB
ejpam-5918	284	13	the	the	DET
ejpam-5918	284	14	minimality	minimality	NOUN
ejpam-5918	284	15	of	of	ADP
ejpam-5918	284	16	i.	i.	PROPN
ejpam-5918	284	17	hence	hence	ADV
ejpam-5918	284	18	,	,	PUNCT
ejpam-5918	284	19	degi(u	degi(u	PROPN
ejpam-5918	284	20	)	)	PUNCT
ejpam-5918	284	21	=	=	SYM
ejpam-5918	284	22	0	0	NUM
ejpam-5918	284	23	or	or	CCONJ
ejpam-5918	284	24	degi(u	degi(u	NOUN
ejpam-5918	284	25	)	)	PUNCT
ejpam-5918	284	26	=	=	SYM
ejpam-5918	285	1	1	1	X
ejpam-5918	285	2	.	.	X
ejpam-5918	285	3	note	note	VERB
ejpam-5918	285	4	that	that	SCONJ
ejpam-5918	285	5	v	v	INTJ
ejpam-5918	285	6	(	(	PUNCT
ejpam-5918	285	7	lm	lm	INTJ
ejpam-5918	285	8	,	,	PUNCT
ejpam-5918	285	9	n	n	CCONJ
ejpam-5918	285	10	)	)	PUNCT
ejpam-5918	285	11	\	\	PROPN
ejpam-5918	285	12	v	v	X
ejpam-5918	285	13	(	(	PUNCT
ejpam-5918	285	14	km	km	NOUN
ejpam-5918	285	15	)	)	PUNCT
ejpam-5918	285	16	induces	induce	VERB
ejpam-5918	285	17	a	a	DET
ejpam-5918	285	18	path	path	NOUN
ejpam-5918	285	19	graph	graph	NOUN
ejpam-5918	285	20	pn	pn	PROPN
ejpam-5918	285	21	.	.	PUNCT
ejpam-5918	285	22	thus	thus	ADV
ejpam-5918	285	23	,	,	PUNCT
ejpam-5918	285	24	by	by	ADP
ejpam-5918	285	25	theorem	theorem	NOUN
ejpam-5918	285	26	4	4	NUM
ejpam-5918	285	27	,	,	PUNCT
ejpam-5918	285	28	(	(	PUNCT
ejpam-5918	285	29	ii	ii	NOUN
ejpam-5918	285	30	)	)	PUNCT
ejpam-5918	285	31	,	,	PUNCT
ejpam-5918	285	32	(	(	PUNCT
ejpam-5918	285	33	iii	iii	NOUN
ejpam-5918	285	34	)	)	PUNCT
ejpam-5918	285	35	and	and	CCONJ
ejpam-5918	285	36	(	(	PUNCT
ejpam-5918	285	37	iv	iv	X
ejpam-5918	285	38	)	)	PUNCT
ejpam-5918	285	39	holds	hold	NOUN
ejpam-5918	285	40	.	.	PUNCT
ejpam-5918	286	1	i.	i.	PROPN
ejpam-5918	286	2	tropico	tropico	PROPN
ejpam-5918	286	3	,	,	PUNCT
ejpam-5918	286	4	i.	i.	PROPN
ejpam-5918	286	5	cabahug	cabahug	PROPN
ejpam-5918	286	6	,	,	PUNCT
ejpam-5918	286	7	jr	jr	PROPN
ejpam-5918	286	8	.	.	PROPN
ejpam-5918	286	9	/	/	SYM
ejpam-5918	286	10	eur	eur	PROPN
ejpam-5918	286	11	.	.	PUNCT
ejpam-5918	287	1	j.	j.	PROPN
ejpam-5918	287	2	pure	pure	PROPN
ejpam-5918	287	3	appl	appl	PROPN
ejpam-5918	287	4	.	.	PROPN
ejpam-5918	287	5	math	math	PROPN
ejpam-5918	287	6	,	,	PUNCT
ejpam-5918	287	7	18	18	NUM
ejpam-5918	287	8	(	(	PUNCT
ejpam-5918	287	9	2	2	NUM
ejpam-5918	287	10	)	)	PUNCT
ejpam-5918	287	11	(	(	PUNCT
ejpam-5918	287	12	2025	2025	NUM
ejpam-5918	287	13	)	)	PUNCT
ejpam-5918	287	14	,	,	PUNCT
ejpam-5918	287	15	5918	5918	NUM
ejpam-5918	287	16	11	11	NUM
ejpam-5918	287	17	of	of	ADP
ejpam-5918	287	18	21	21	NUM
ejpam-5918	287	19	conversely	conversely	ADV
ejpam-5918	287	20	,	,	PUNCT
ejpam-5918	287	21	assume	assume	VERB
ejpam-5918	287	22	conditions	condition	NOUN
ejpam-5918	287	23	(	(	PUNCT
ejpam-5918	287	24	i)−	i)−	PROPN
ejpam-5918	287	25	(	(	PUNCT
ejpam-5918	287	26	iv	iv	NOUN
ejpam-5918	287	27	)	)	PUNCT
ejpam-5918	287	28	hold	hold	NOUN
ejpam-5918	287	29	.	.	PUNCT
ejpam-5918	288	1	then	then	ADV
ejpam-5918	288	2	,	,	PUNCT
ejpam-5918	288	3	by	by	ADP
ejpam-5918	288	4	theorem	theorem	NOUN
ejpam-5918	288	5	4	4	NUM
ejpam-5918	288	6	,	,	PUNCT
ejpam-5918	288	7	i	i	PRON
ejpam-5918	288	8	is	be	AUX
ejpam-5918	288	9	a	a	DET
ejpam-5918	288	10	γli	γli	ADJ
ejpam-5918	288	11	−	−	NOUN
ejpam-5918	288	12	set	set	VERB
ejpam-5918	288	13	in	in	ADP
ejpam-5918	288	14	g.	g.	PROPN
ejpam-5918	288	15	corollary	corollary	PROPN
ejpam-5918	288	16	6	6	NUM
ejpam-5918	288	17	.	.	PUNCT
ejpam-5918	289	1	let	let	VERB
ejpam-5918	289	2	g	g	PRON
ejpam-5918	289	3	be	be	AUX
ejpam-5918	289	4	a	a	DET
ejpam-5918	289	5	lollipop	lollipop	NOUN
ejpam-5918	289	6	graph	graph	NOUN
ejpam-5918	289	7	lm	lm	PROPN
ejpam-5918	289	8	,	,	PUNCT
ejpam-5918	289	9	n	n	PROPN
ejpam-5918	289	10	with	with	ADP
ejpam-5918	289	11	m	m	PROPN
ejpam-5918	289	12	≥	≥	NUM
ejpam-5918	289	13	3	3	NUM
ejpam-5918	289	14	and	and	CCONJ
ejpam-5918	289	15	n	n	PRON
ejpam-5918	289	16	≥	≥	NOUN
ejpam-5918	289	17	4	4	NUM
ejpam-5918	289	18	.	.	PUNCT
ejpam-5918	290	1	then	then	ADV
ejpam-5918	290	2	,	,	PUNCT
ejpam-5918	290	3	γli(g	γli(g	PROPN
ejpam-5918	290	4	)	)	PUNCT
ejpam-5918	290	5	=	=	PUNCT
ejpam-5918	291	1			VERB
ejpam-5918	291	2	n+2	n+2	PRON
ejpam-5918	291	3	2	2	NUM
ejpam-5918	291	4	if	if	SCONJ
ejpam-5918	291	5	n	n	PRON
ejpam-5918	291	6	≡	≡	PROPN
ejpam-5918	291	7	0	0	NUM
ejpam-5918	291	8	,	,	PUNCT
ejpam-5918	291	9	2(mod	2(mod	NUM
ejpam-5918	291	10	4	4	X
ejpam-5918	291	11	)	)	PUNCT
ejpam-5918	291	12	n+1	n+1	NUM
ejpam-5918	291	13	2	2	NUM
ejpam-5918	291	14	if	if	SCONJ
ejpam-5918	291	15	n	n	PRON
ejpam-5918	291	16	≡	≡	PROPN
ejpam-5918	291	17	1(mod	1(mod	NUM
ejpam-5918	291	18	4	4	X
ejpam-5918	291	19	)	)	PUNCT
ejpam-5918	291	20	n+3	n+3	PROPN
ejpam-5918	291	21	2	2	NUM
ejpam-5918	291	22	if	if	SCONJ
ejpam-5918	291	23	n	n	PRON
ejpam-5918	291	24	≡	≡	PROPN
ejpam-5918	291	25	3(mod	3(mod	NUM
ejpam-5918	291	26	4	4	X
ejpam-5918	291	27	)	)	PUNCT
ejpam-5918	291	28	proof	proof	NOUN
ejpam-5918	291	29	.	.	PUNCT
ejpam-5918	292	1	let	let	VERB
ejpam-5918	292	2	g	g	PRON
ejpam-5918	292	3	be	be	AUX
ejpam-5918	292	4	a	a	DET
ejpam-5918	292	5	lollipop	lollipop	NOUN
ejpam-5918	292	6	graph	graph	NOUN
ejpam-5918	292	7	lm	lm	PROPN
ejpam-5918	292	8	,	,	PUNCT
ejpam-5918	292	9	n	n	PROPN
ejpam-5918	292	10	with	with	ADP
ejpam-5918	292	11	m	m	PROPN
ejpam-5918	292	12	≥	≥	NUM
ejpam-5918	292	13	3	3	NUM
ejpam-5918	292	14	and	and	CCONJ
ejpam-5918	292	15	n	n	PRON
ejpam-5918	292	16	≥	≥	NOUN
ejpam-5918	292	17	4	4	NUM
ejpam-5918	292	18	.	.	X
ejpam-5918	293	1	for	for	ADP
ejpam-5918	293	2	convenience	convenience	NOUN
ejpam-5918	293	3	,	,	PUNCT
ejpam-5918	293	4	v	v	X
ejpam-5918	293	5	(	(	PUNCT
ejpam-5918	293	6	lm	lm	INTJ
ejpam-5918	293	7	,	,	PUNCT
ejpam-5918	293	8	n	n	CCONJ
ejpam-5918	293	9	)	)	PUNCT
ejpam-5918	293	10	=	=	SYM
ejpam-5918	293	11	v	v	X
ejpam-5918	293	12	(	(	PUNCT
ejpam-5918	293	13	km)∪v	km)∪v	PROPN
ejpam-5918	293	14	(	(	PUNCT
ejpam-5918	293	15	pn	pn	NOUN
ejpam-5918	293	16	)	)	PUNCT
ejpam-5918	293	17	,	,	PUNCT
ejpam-5918	293	18	where	where	SCONJ
ejpam-5918	293	19	v	v	NOUN
ejpam-5918	293	20	(	(	PUNCT
ejpam-5918	293	21	km	km	NOUN
ejpam-5918	293	22	)	)	PUNCT
ejpam-5918	293	23	=	=	PRON
ejpam-5918	293	24	{	{	PUNCT
ejpam-5918	293	25	u1	u1	NOUN
ejpam-5918	293	26	,	,	PUNCT
ejpam-5918	293	27	u2	u2	NOUN
ejpam-5918	293	28	,	,	PUNCT
ejpam-5918	293	29	.	.	PUNCT
ejpam-5918	293	30	.	.	PUNCT
ejpam-5918	293	31	.	.	PUNCT
ejpam-5918	294	1	,	,	PUNCT
ejpam-5918	294	2	um	um	INTJ
ejpam-5918	294	3	}	}	PUNCT
ejpam-5918	294	4	and	and	CCONJ
ejpam-5918	294	5	v	v	NOUN
ejpam-5918	294	6	(	(	PUNCT
ejpam-5918	294	7	pn	pn	NOUN
ejpam-5918	294	8	)	)	PUNCT
ejpam-5918	294	9	=	=	SYM
ejpam-5918	294	10	{	{	PUNCT
ejpam-5918	294	11	v1	v1	PROPN
ejpam-5918	294	12	,	,	PUNCT
ejpam-5918	294	13	v2	v2	PROPN
ejpam-5918	294	14	,	,	PUNCT
ejpam-5918	294	15	.	.	PUNCT
ejpam-5918	294	16	.	.	PUNCT
ejpam-5918	295	1	.	.	PUNCT
ejpam-5918	296	1	,	,	PUNCT
ejpam-5918	296	2	vn	vn	VERB
ejpam-5918	296	3	}	}	PUNCT
ejpam-5918	296	4	such	such	ADJ
ejpam-5918	296	5	that	that	SCONJ
ejpam-5918	296	6	u1v1	u1v1	PROPN
ejpam-5918	296	7	∈	∈	PROPN
ejpam-5918	296	8	e(lm	e(lm	PROPN
ejpam-5918	296	9	,	,	PUNCT
ejpam-5918	296	10	n	n	CCONJ
ejpam-5918	296	11	)	)	PUNCT
ejpam-5918	296	12	.	.	PUNCT
ejpam-5918	297	1	now	now	ADV
ejpam-5918	297	2	,	,	PUNCT
ejpam-5918	297	3	consider	consider	VERB
ejpam-5918	297	4	the	the	DET
ejpam-5918	297	5	following	follow	VERB
ejpam-5918	297	6	cases	case	NOUN
ejpam-5918	297	7	:	:	PUNCT
ejpam-5918	297	8	case	case	NOUN
ejpam-5918	297	9	1	1	NUM
ejpam-5918	297	10	:	:	PUNCT
ejpam-5918	297	11	n	n	NUM
ejpam-5918	297	12	≡	≡	PROPN
ejpam-5918	297	13	0	0	PUNCT
ejpam-5918	298	1	(	(	PUNCT
ejpam-5918	298	2	mod	mod	PROPN
ejpam-5918	298	3	4	4	X
ejpam-5918	298	4	)	)	PUNCT
ejpam-5918	298	5	let	let	VERB
ejpam-5918	298	6	i	i	PRON
ejpam-5918	298	7	⊆	⊆	NUM
ejpam-5918	298	8	v	v	ADP
ejpam-5918	298	9	(	(	PUNCT
ejpam-5918	298	10	lm	lm	INTJ
ejpam-5918	298	11	,	,	PUNCT
ejpam-5918	298	12	n	n	CCONJ
ejpam-5918	298	13	)	)	PUNCT
ejpam-5918	298	14	with	with	ADP
ejpam-5918	298	15	i	i	PRON
ejpam-5918	298	16	=	=	SYM
ejpam-5918	298	17	{	{	PUNCT
ejpam-5918	298	18	u1	u1	NOUN
ejpam-5918	298	19	,	,	PUNCT
ejpam-5918	298	20	v2	v2	PROPN
ejpam-5918	298	21	,	,	PUNCT
ejpam-5918	298	22	v3	v3	PROPN
ejpam-5918	298	23	,	,	PUNCT
ejpam-5918	298	24	v6	v6	NOUN
ejpam-5918	298	25	,	,	PUNCT
ejpam-5918	298	26	v7	v7	NOUN
ejpam-5918	298	27	,	,	PUNCT
ejpam-5918	298	28	.	.	PUNCT
ejpam-5918	298	29	.	.	PUNCT
ejpam-5918	299	1	.	.	PUNCT
ejpam-5918	300	1	,	,	PUNCT
ejpam-5918	300	2	vn−2	vn−2	PROPN
ejpam-5918	300	3	,	,	PUNCT
ejpam-5918	300	4	vn−1	vn−1	ADJ
ejpam-5918	300	5	}	}	PUNCT
ejpam-5918	300	6	.	.	PUNCT
ejpam-5918	301	1	observe	observe	VERB
ejpam-5918	301	2	that	that	SCONJ
ejpam-5918	301	3	|i|	|i|	VERB
ejpam-5918	301	4	=	=	SYM
ejpam-5918	301	5	n+2	n+2	NUM
ejpam-5918	301	6	2	2	NUM
ejpam-5918	301	7	.	.	PUNCT
ejpam-5918	302	1	by	by	ADP
ejpam-5918	302	2	theorem	theorem	NOUN
ejpam-5918	302	3	7	7	NUM
ejpam-5918	302	4	,	,	PUNCT
ejpam-5918	302	5	i	i	PRON
ejpam-5918	302	6	is	be	AUX
ejpam-5918	302	7	a	a	DET
ejpam-5918	302	8	γli	γli	ADJ
ejpam-5918	302	9	−	−	PROPN
ejpam-5918	302	10	set	set	NOUN
ejpam-5918	302	11	.	.	PUNCT
ejpam-5918	303	1	therefore	therefore	ADV
ejpam-5918	303	2	,	,	PUNCT
ejpam-5918	303	3	γli(lm	γli(lm	NOUN
ejpam-5918	303	4	,	,	PUNCT
ejpam-5918	303	5	n	n	CCONJ
ejpam-5918	303	6	)	)	PUNCT
ejpam-5918	303	7	=	=	SYM
ejpam-5918	304	1	|i|	|i|	NOUN
ejpam-5918	304	2	=	=	SYM
ejpam-5918	304	3	n+2	n+2	NUM
ejpam-5918	304	4	2	2	NUM
ejpam-5918	304	5	.	.	PUNCT
ejpam-5918	305	1	case	case	NOUN
ejpam-5918	305	2	2	2	NUM
ejpam-5918	305	3	:	:	PUNCT
ejpam-5918	305	4	n	n	NUM
ejpam-5918	305	5	≡	≡	PROPN
ejpam-5918	305	6	1	1	NUM
ejpam-5918	305	7	(	(	PUNCT
ejpam-5918	305	8	mod	mod	NOUN
ejpam-5918	305	9	4	4	X
ejpam-5918	305	10	)	)	PUNCT
ejpam-5918	305	11	let	let	VERB
ejpam-5918	305	12	i	i	PRON
ejpam-5918	305	13	⊆	⊆	NUM
ejpam-5918	305	14	v	v	ADP
ejpam-5918	305	15	(	(	PUNCT
ejpam-5918	305	16	lm	lm	INTJ
ejpam-5918	305	17	,	,	PUNCT
ejpam-5918	305	18	n	n	CCONJ
ejpam-5918	305	19	)	)	PUNCT
ejpam-5918	305	20	with	with	ADP
ejpam-5918	305	21	i	i	PRON
ejpam-5918	305	22	=	=	SYM
ejpam-5918	305	23	{	{	PUNCT
ejpam-5918	305	24	u1	u1	PROPN
ejpam-5918	305	25	,	,	PUNCT
ejpam-5918	305	26	v3	v3	PROPN
ejpam-5918	305	27	,	,	PUNCT
ejpam-5918	305	28	v4	v4	NOUN
ejpam-5918	305	29	,	,	PUNCT
ejpam-5918	305	30	v7	v7	NUM
ejpam-5918	305	31	,	,	PUNCT
ejpam-5918	305	32	v8	v8	PROPN
ejpam-5918	305	33	,	,	PUNCT
ejpam-5918	305	34	.	.	PUNCT
ejpam-5918	305	35	.	.	PUNCT
ejpam-5918	306	1	.	.	PUNCT
ejpam-5918	307	1	,	,	PUNCT
ejpam-5918	307	2	vn−2	vn−2	PROPN
ejpam-5918	307	3	,	,	PUNCT
ejpam-5918	307	4	vn−1	vn−1	ADJ
ejpam-5918	307	5	}	}	PUNCT
ejpam-5918	307	6	.	.	PUNCT
ejpam-5918	308	1	observe	observe	VERB
ejpam-5918	308	2	that	that	SCONJ
ejpam-5918	308	3	|i|	|i|	VERB
ejpam-5918	308	4	=	=	SYM
ejpam-5918	308	5	n+1	n+1	PROPN
ejpam-5918	308	6	2	2	NUM
ejpam-5918	308	7	.	.	PUNCT
ejpam-5918	309	1	by	by	ADP
ejpam-5918	309	2	theorem	theorem	NOUN
ejpam-5918	309	3	7	7	NUM
ejpam-5918	309	4	,	,	PUNCT
ejpam-5918	309	5	i	i	PRON
ejpam-5918	309	6	is	be	AUX
ejpam-5918	309	7	a	a	DET
ejpam-5918	309	8	γli	γli	ADJ
ejpam-5918	309	9	−	−	PROPN
ejpam-5918	309	10	set	set	NOUN
ejpam-5918	309	11	.	.	PUNCT
ejpam-5918	310	1	therefore	therefore	ADV
ejpam-5918	310	2	,	,	PUNCT
ejpam-5918	310	3	γli(lm	γli(lm	NOUN
ejpam-5918	310	4	,	,	PUNCT
ejpam-5918	310	5	n	n	CCONJ
ejpam-5918	310	6	)	)	PUNCT
ejpam-5918	310	7	=	=	SYM
ejpam-5918	310	8	|i|	|i|	PROPN
ejpam-5918	310	9	=	=	SYM
ejpam-5918	310	10	n+1	n+1	PROPN
ejpam-5918	310	11	2	2	NUM
ejpam-5918	310	12	.	.	PUNCT
ejpam-5918	310	13	case	case	NOUN
ejpam-5918	310	14	3	3	NUM
ejpam-5918	310	15	:	:	PUNCT
ejpam-5918	310	16	n	n	NUM
ejpam-5918	310	17	≡	≡	PROPN
ejpam-5918	310	18	2	2	NUM
ejpam-5918	310	19	(	(	PUNCT
ejpam-5918	310	20	mod	mod	NOUN
ejpam-5918	310	21	4	4	X
ejpam-5918	310	22	)	)	PUNCT
ejpam-5918	310	23	let	let	VERB
ejpam-5918	310	24	i	i	PRON
ejpam-5918	310	25	⊆	⊆	NUM
ejpam-5918	310	26	v	v	ADP
ejpam-5918	310	27	(	(	PUNCT
ejpam-5918	310	28	lm	lm	INTJ
ejpam-5918	310	29	,	,	PUNCT
ejpam-5918	310	30	n	n	CCONJ
ejpam-5918	310	31	)	)	PUNCT
ejpam-5918	310	32	with	with	ADP
ejpam-5918	310	33	i	i	PRON
ejpam-5918	310	34	=	=	SYM
ejpam-5918	310	35	{	{	PUNCT
ejpam-5918	310	36	u1	u1	NOUN
ejpam-5918	310	37	,	,	PUNCT
ejpam-5918	310	38	v1	v1	NOUN
ejpam-5918	310	39	,	,	PUNCT
ejpam-5918	310	40	v4	v4	NOUN
ejpam-5918	310	41	,	,	PUNCT
ejpam-5918	310	42	v5	v5	PROPN
ejpam-5918	310	43	,	,	PUNCT
ejpam-5918	310	44	.	.	PUNCT
ejpam-5918	310	45	.	.	PUNCT
ejpam-5918	311	1	.	.	PUNCT
ejpam-5918	312	1	,	,	PUNCT
ejpam-5918	312	2	vn−2	vn−2	PROPN
ejpam-5918	312	3	,	,	PUNCT
ejpam-5918	312	4	vn−1	vn−1	ADJ
ejpam-5918	312	5	}	}	PUNCT
ejpam-5918	312	6	.	.	PUNCT
ejpam-5918	313	1	observe	observe	VERB
ejpam-5918	313	2	that	that	SCONJ
ejpam-5918	313	3	|i|	|i|	VERB
ejpam-5918	313	4	=	=	SYM
ejpam-5918	313	5	n+2	n+2	NUM
ejpam-5918	313	6	2	2	NUM
ejpam-5918	313	7	.	.	PUNCT
ejpam-5918	314	1	by	by	ADP
ejpam-5918	314	2	theorem	theorem	NOUN
ejpam-5918	314	3	7	7	NUM
ejpam-5918	314	4	,	,	PUNCT
ejpam-5918	314	5	i	i	PRON
ejpam-5918	314	6	is	be	AUX
ejpam-5918	314	7	a	a	DET
ejpam-5918	314	8	γli	γli	ADJ
ejpam-5918	314	9	−	−	PROPN
ejpam-5918	314	10	set	set	NOUN
ejpam-5918	314	11	.	.	PUNCT
ejpam-5918	315	1	therefore	therefore	ADV
ejpam-5918	315	2	,	,	PUNCT
ejpam-5918	315	3	γli(lm	γli(lm	NOUN
ejpam-5918	315	4	,	,	PUNCT
ejpam-5918	315	5	n	n	CCONJ
ejpam-5918	315	6	)	)	PUNCT
ejpam-5918	315	7	=	=	SYM
ejpam-5918	316	1	|i|	|i|	NOUN
ejpam-5918	316	2	=	=	SYM
ejpam-5918	316	3	n+2	n+2	NUM
ejpam-5918	316	4	2	2	NUM
ejpam-5918	316	5	.	.	PUNCT
ejpam-5918	316	6	case	case	NOUN
ejpam-5918	316	7	4	4	NUM
ejpam-5918	316	8	:	:	PUNCT
ejpam-5918	316	9	n	n	NUM
ejpam-5918	316	10	≡	≡	PROPN
ejpam-5918	316	11	3	3	NUM
ejpam-5918	316	12	(	(	PUNCT
ejpam-5918	316	13	mod	mod	NOUN
ejpam-5918	316	14	4	4	X
ejpam-5918	316	15	)	)	PUNCT
ejpam-5918	316	16	let	let	VERB
ejpam-5918	316	17	i	i	PRON
ejpam-5918	316	18	⊆	⊆	NUM
ejpam-5918	316	19	v	v	ADP
ejpam-5918	316	20	(	(	PUNCT
ejpam-5918	316	21	lm	lm	INTJ
ejpam-5918	316	22	,	,	PUNCT
ejpam-5918	316	23	n	n	CCONJ
ejpam-5918	316	24	)	)	PUNCT
ejpam-5918	316	25	with	with	ADP
ejpam-5918	316	26	i	i	PRON
ejpam-5918	316	27	=	=	SYM
ejpam-5918	316	28	{	{	PUNCT
ejpam-5918	316	29	u1	u1	NOUN
ejpam-5918	316	30	,	,	PUNCT
ejpam-5918	316	31	v1	v1	NOUN
ejpam-5918	316	32	,	,	PUNCT
ejpam-5918	316	33	v4	v4	NOUN
ejpam-5918	316	34	,	,	PUNCT
ejpam-5918	316	35	v5	v5	PROPN
ejpam-5918	316	36	,	,	PUNCT
ejpam-5918	316	37	.	.	PUNCT
ejpam-5918	316	38	.	.	PUNCT
ejpam-5918	317	1	.	.	PUNCT
ejpam-5918	318	1	,	,	PUNCT
ejpam-5918	318	2	vn−3	vn−3	PROPN
ejpam-5918	318	3	,	,	PUNCT
ejpam-5918	318	4	vn−2	vn−2	PROPN
ejpam-5918	318	5	,	,	PUNCT
ejpam-5918	318	6	vn	vn	PROPN
ejpam-5918	318	7	}	}	PUNCT
ejpam-5918	318	8	.	.	PUNCT
ejpam-5918	319	1	observe	observe	VERB
ejpam-5918	319	2	that	that	SCONJ
ejpam-5918	319	3	|i|	|i|	VERB
ejpam-5918	319	4	=	=	SYM
ejpam-5918	319	5	n+3	n+3	PROPN
ejpam-5918	319	6	3	3	NUM
ejpam-5918	319	7	.	.	PUNCT
ejpam-5918	320	1	by	by	ADP
ejpam-5918	320	2	theorem	theorem	NOUN
ejpam-5918	320	3	7	7	NUM
ejpam-5918	320	4	,	,	PUNCT
ejpam-5918	320	5	i	i	PRON
ejpam-5918	320	6	is	be	AUX
ejpam-5918	320	7	a	a	DET
ejpam-5918	320	8	γli	γli	ADJ
ejpam-5918	320	9	−	−	PROPN
ejpam-5918	320	10	set	set	NOUN
ejpam-5918	320	11	.	.	PUNCT
ejpam-5918	321	1	therefore	therefore	ADV
ejpam-5918	321	2	,	,	PUNCT
ejpam-5918	321	3	γli(lm	γli(lm	NOUN
ejpam-5918	321	4	,	,	PUNCT
ejpam-5918	321	5	n	n	CCONJ
ejpam-5918	321	6	)	)	PUNCT
ejpam-5918	321	7	=	=	SYM
ejpam-5918	321	8	|i|	|i|	PROPN
ejpam-5918	321	9	=	=	SYM
ejpam-5918	321	10	n+3	n+3	PROPN
ejpam-5918	321	11	2	2	NUM
ejpam-5918	321	12	.	.	PUNCT
ejpam-5918	322	1	theorem	theorem	VERB
ejpam-5918	322	2	8	8	NUM
ejpam-5918	322	3	.	.	PUNCT
ejpam-5918	323	1	let	let	VERB
ejpam-5918	323	2	g	g	PRON
ejpam-5918	323	3	be	be	AUX
ejpam-5918	323	4	a	a	DET
ejpam-5918	323	5	graph	graph	NOUN
ejpam-5918	323	6	with	with	ADP
ejpam-5918	323	7	∆(g	∆(g	NOUN
ejpam-5918	323	8	)	)	PUNCT
ejpam-5918	323	9	=	=	SYM
ejpam-5918	323	10	2	2	NUM
ejpam-5918	323	11	,	,	PUNCT
ejpam-5918	323	12	and	and	CCONJ
ejpam-5918	323	13	i	i	PRON
ejpam-5918	323	14	⊆	⊆	NUM
ejpam-5918	323	15	v	v	X
ejpam-5918	323	16	(	(	PUNCT
ejpam-5918	323	17	t	t	PROPN
ejpam-5918	323	18	(	(	PUNCT
ejpam-5918	323	19	g	g	NOUN
ejpam-5918	323	20	)	)	PUNCT
ejpam-5918	323	21	)	)	PUNCT
ejpam-5918	323	22	such	such	ADJ
ejpam-5918	323	23	that	that	PRON
ejpam-5918	323	24	|i|	|i|	VERB
ejpam-5918	323	25	≥	≥	NOUN
ejpam-5918	323	26	2	2	NUM
ejpam-5918	323	27	.	.	PUNCT
ejpam-5918	323	28	suppose	suppose	VERB
ejpam-5918	323	29	that	that	SCONJ
ejpam-5918	323	30	i	i	PRON
ejpam-5918	323	31	⊆	⊆	NUM
ejpam-5918	323	32	v	v	X
ejpam-5918	323	33	(	(	PUNCT
ejpam-5918	323	34	g	g	NOUN
ejpam-5918	323	35	)	)	PUNCT
ejpam-5918	323	36	.	.	PUNCT
ejpam-5918	324	1	then	then	ADV
ejpam-5918	324	2	i	i	PRON
ejpam-5918	324	3	is	be	AUX
ejpam-5918	324	4	an	an	DET
ejpam-5918	324	5	internally	internally	ADV
ejpam-5918	324	6	-	-	PUNCT
ejpam-5918	324	7	locating	locate	VERB
ejpam-5918	324	8	dominating	dominating	NOUN
ejpam-5918	324	9	set	set	VERB
ejpam-5918	324	10	in	in	ADP
ejpam-5918	324	11	t	t	PROPN
ejpam-5918	324	12	(	(	PUNCT
ejpam-5918	324	13	g	g	NOUN
ejpam-5918	324	14	)	)	PUNCT
ejpam-5918	324	15	if	if	SCONJ
ejpam-5918	325	1	and	and	CCONJ
ejpam-5918	325	2	only	only	ADV
ejpam-5918	325	3	if	if	SCONJ
ejpam-5918	325	4	i	i	PRON
ejpam-5918	325	5	is	be	AUX
ejpam-5918	325	6	an	an	DET
ejpam-5918	325	7	internally	internally	ADV
ejpam-5918	325	8	-	-	PUNCT
ejpam-5918	325	9	locating	locate	VERB
ejpam-5918	325	10	dominating	dominating	NOUN
ejpam-5918	325	11	set	set	VERB
ejpam-5918	325	12	in	in	ADP
ejpam-5918	325	13	v	v	NOUN
ejpam-5918	325	14	(	(	PUNCT
ejpam-5918	325	15	g	g	NOUN
ejpam-5918	325	16	)	)	PUNCT
ejpam-5918	325	17	such	such	ADJ
ejpam-5918	325	18	that	that	SCONJ
ejpam-5918	325	19	the	the	DET
ejpam-5918	325	20	component	component	NOUN
ejpam-5918	325	21	of	of	ADP
ejpam-5918	325	22	g[v	g[v	NOUN
ejpam-5918	325	23	(	(	PUNCT
ejpam-5918	325	24	g	g	NOUN
ejpam-5918	325	25	)	)	PUNCT
ejpam-5918	325	26	\	\	PUNCT
ejpam-5918	326	1	i	i	PRON
ejpam-5918	326	2	]	]	PUNCT
ejpam-5918	326	3	̸=	̸=	PROPN
ejpam-5918	326	4	p2	p2	NOUN
ejpam-5918	326	5	.	.	PUNCT
ejpam-5918	327	1	proof	proof	NOUN
ejpam-5918	327	2	.	.	PUNCT
ejpam-5918	328	1	let	let	VERB
ejpam-5918	328	2	g	g	PRON
ejpam-5918	328	3	be	be	AUX
ejpam-5918	328	4	a	a	DET
ejpam-5918	328	5	graph	graph	NOUN
ejpam-5918	328	6	with	with	ADP
ejpam-5918	328	7	∆(g	∆(g	NOUN
ejpam-5918	328	8	)	)	PUNCT
ejpam-5918	328	9	=	=	SYM
ejpam-5918	328	10	2	2	NUM
ejpam-5918	328	11	,	,	PUNCT
ejpam-5918	328	12	and	and	CCONJ
ejpam-5918	328	13	i	i	PRON
ejpam-5918	328	14	⊆	⊆	NUM
ejpam-5918	328	15	v	v	X
ejpam-5918	328	16	(	(	PUNCT
ejpam-5918	328	17	t	t	PROPN
ejpam-5918	328	18	(	(	PUNCT
ejpam-5918	328	19	g	g	NOUN
ejpam-5918	328	20	)	)	PUNCT
ejpam-5918	328	21	)	)	PUNCT
ejpam-5918	328	22	such	such	ADJ
ejpam-5918	328	23	that	that	PRON
ejpam-5918	328	24	|i|	|i|	VERB
ejpam-5918	328	25	≥	≥	NOUN
ejpam-5918	328	26	2	2	NUM
ejpam-5918	328	27	.	.	PUNCT
ejpam-5918	328	28	suppose	suppose	VERB
ejpam-5918	328	29	i	i	PRON
ejpam-5918	328	30	⊆	⊆	NUM
ejpam-5918	328	31	v	v	X
ejpam-5918	328	32	(	(	PUNCT
ejpam-5918	328	33	g	g	NOUN
ejpam-5918	328	34	)	)	PUNCT
ejpam-5918	328	35	.	.	PUNCT
ejpam-5918	329	1	assume	assume	VERB
ejpam-5918	329	2	i	i	PRON
ejpam-5918	329	3	is	be	AUX
ejpam-5918	329	4	an	an	DET
ejpam-5918	329	5	ilds	ild	NOUN
ejpam-5918	329	6	in	in	ADP
ejpam-5918	329	7	t	t	PROPN
ejpam-5918	329	8	(	(	PUNCT
ejpam-5918	329	9	g	g	NOUN
ejpam-5918	329	10	)	)	PUNCT
ejpam-5918	329	11	.	.	PUNCT
ejpam-5918	330	1	then	then	ADV
ejpam-5918	330	2	,	,	PUNCT
ejpam-5918	330	3	for	for	ADP
ejpam-5918	330	4	all	all	DET
ejpam-5918	330	5	u	u	NOUN
ejpam-5918	330	6	,	,	PUNCT
ejpam-5918	330	7	v	v	NOUN
ejpam-5918	330	8	∈	∈	X
ejpam-5918	331	1	i	i	PRON
ejpam-5918	331	2	,	,	PUNCT
ejpam-5918	331	3	nt	not	PART
ejpam-5918	331	4	(	(	PUNCT
ejpam-5918	331	5	g)(u	g)(u	ADJ
ejpam-5918	331	6	)	)	PUNCT
ejpam-5918	331	7	∩	∩	NOUN
ejpam-5918	331	8	i	i	PRON
ejpam-5918	331	9	̸=	̸=	PROPN
ejpam-5918	331	10	nt	not	PART
ejpam-5918	331	11	(	(	PUNCT
ejpam-5918	331	12	g)(u	g)(u	ADJ
ejpam-5918	331	13	)	)	PUNCT
ejpam-5918	331	14	∩	∩	PROPN
ejpam-5918	331	15	i.	i.	NOUN
ejpam-5918	331	16	thus	thus	ADV
ejpam-5918	331	17	,	,	PUNCT
ejpam-5918	331	18	nv	nv	PROPN
ejpam-5918	331	19	(	(	PUNCT
ejpam-5918	331	20	g)(u	g)(u	PROPN
ejpam-5918	331	21	)	)	PUNCT
ejpam-5918	331	22	∩	∩	NOUN
ejpam-5918	331	23	i	i	PRON
ejpam-5918	331	24	̸=	̸=	PROPN
ejpam-5918	331	25	nv	nv	PROPN
ejpam-5918	331	26	(	(	PUNCT
ejpam-5918	331	27	g)(v	g)(v	PROPN
ejpam-5918	331	28	)	)	PUNCT
ejpam-5918	331	29	∩	∩	PROPN
ejpam-5918	331	30	i	i	PRON
ejpam-5918	331	31	,	,	PUNCT
ejpam-5918	331	32	making	make	VERB
ejpam-5918	331	33	i	i	PRON
ejpam-5918	331	34	an	an	DET
ejpam-5918	331	35	ils	ils	NOUN
ejpam-5918	331	36	in	in	ADP
ejpam-5918	331	37	v	v	NOUN
ejpam-5918	331	38	(	(	PUNCT
ejpam-5918	331	39	g	g	NOUN
ejpam-5918	331	40	)	)	PUNCT
ejpam-5918	331	41	.	.	PUNCT
ejpam-5918	331	42	suppose	suppose	VERB
ejpam-5918	331	43	that	that	SCONJ
ejpam-5918	331	44	g[v	g[v	NOUN
ejpam-5918	331	45	(	(	PUNCT
ejpam-5918	331	46	g	g	NOUN
ejpam-5918	331	47	)	)	PUNCT
ejpam-5918	331	48	\	\	PUNCT
ejpam-5918	332	1	i	i	PRON
ejpam-5918	332	2	]	]	X
ejpam-5918	332	3	=	=	PUNCT
ejpam-5918	332	4	p2	p2	NOUN
ejpam-5918	332	5	,	,	PUNCT
ejpam-5918	332	6	the	the	DET
ejpam-5918	332	7	edge	edge	NOUN
ejpam-5918	332	8	corresponding	correspond	VERB
ejpam-5918	332	9	to	to	ADP
ejpam-5918	332	10	this	this	DET
ejpam-5918	332	11	path	path	NOUN
ejpam-5918	332	12	would	would	AUX
ejpam-5918	332	13	not	not	PART
ejpam-5918	332	14	be	be	AUX
ejpam-5918	332	15	dominated	dominate	VERB
ejpam-5918	332	16	by	by	ADP
ejpam-5918	332	17	i	i	PRON
ejpam-5918	332	18	in	in	ADP
ejpam-5918	332	19	t	t	PROPN
ejpam-5918	332	20	(	(	PUNCT
ejpam-5918	332	21	g	g	NOUN
ejpam-5918	332	22	)	)	PUNCT
ejpam-5918	332	23	.	.	PUNCT
ejpam-5918	333	1	this	this	PRON
ejpam-5918	333	2	violates	violate	VERB
ejpam-5918	333	3	the	the	DET
ejpam-5918	333	4	domination	domination	NOUN
ejpam-5918	333	5	condition	condition	NOUN
ejpam-5918	333	6	in	in	ADP
ejpam-5918	333	7	t	t	PROPN
ejpam-5918	333	8	(	(	PUNCT
ejpam-5918	333	9	g	g	NOUN
ejpam-5918	333	10	)	)	PUNCT
ejpam-5918	333	11	,	,	PUNCT
ejpam-5918	334	1	so	so	ADV
ejpam-5918	334	2	g[v	g[v	NOUN
ejpam-5918	334	3	(	(	PUNCT
ejpam-5918	334	4	g)\i	g)\i	PROPN
ejpam-5918	334	5	]	]	PUNCT
ejpam-5918	334	6	̸=	̸=	PROPN
ejpam-5918	334	7	p2	p2	NOUN
ejpam-5918	334	8	.	.	PUNCT
ejpam-5918	335	1	consequently	consequently	ADV
ejpam-5918	335	2	,	,	PUNCT
ejpam-5918	335	3	since	since	SCONJ
ejpam-5918	335	4	i	i	PRON
ejpam-5918	335	5	⊆	⊆	NUM
ejpam-5918	335	6	v	v	NOUN
ejpam-5918	335	7	(	(	PUNCT
ejpam-5918	335	8	g	g	NOUN
ejpam-5918	335	9	)	)	PUNCT
ejpam-5918	335	10	,	,	PUNCT
ejpam-5918	335	11	this	this	PRON
ejpam-5918	335	12	implies	imply	VERB
ejpam-5918	335	13	i	i	PRON
ejpam-5918	335	14	is	be	AUX
ejpam-5918	335	15	a	a	DET
ejpam-5918	335	16	dominating	dominating	NOUN
ejpam-5918	335	17	set	set	NOUN
ejpam-5918	335	18	in	in	ADP
ejpam-5918	335	19	v	v	NOUN
ejpam-5918	335	20	(	(	PUNCT
ejpam-5918	335	21	g	g	NOUN
ejpam-5918	335	22	)	)	PUNCT
ejpam-5918	335	23	.	.	PUNCT
ejpam-5918	336	1	hence	hence	ADV
ejpam-5918	336	2	,	,	PUNCT
ejpam-5918	336	3	i	i	PRON
ejpam-5918	336	4	is	be	AUX
ejpam-5918	336	5	an	an	DET
ejpam-5918	336	6	ilds	ild	NOUN
ejpam-5918	336	7	in	in	ADP
ejpam-5918	336	8	v	v	NOUN
ejpam-5918	336	9	(	(	PUNCT
ejpam-5918	336	10	g	g	NOUN
ejpam-5918	336	11	)	)	PUNCT
ejpam-5918	336	12	.	.	PUNCT
ejpam-5918	337	1	i.	i.	PROPN
ejpam-5918	337	2	tropico	tropico	PROPN
ejpam-5918	337	3	,	,	PUNCT
ejpam-5918	337	4	i.	i.	PROPN
ejpam-5918	337	5	cabahug	cabahug	PROPN
ejpam-5918	337	6	,	,	PUNCT
ejpam-5918	337	7	jr	jr	PROPN
ejpam-5918	337	8	.	.	PROPN
ejpam-5918	337	9	/	/	SYM
ejpam-5918	337	10	eur	eur	PROPN
ejpam-5918	337	11	.	.	PUNCT
ejpam-5918	338	1	j.	j.	PROPN
ejpam-5918	338	2	pure	pure	PROPN
ejpam-5918	338	3	appl	appl	PROPN
ejpam-5918	338	4	.	.	PROPN
ejpam-5918	338	5	math	math	PROPN
ejpam-5918	338	6	,	,	PUNCT
ejpam-5918	338	7	18	18	NUM
ejpam-5918	338	8	(	(	PUNCT
ejpam-5918	338	9	2	2	NUM
ejpam-5918	338	10	)	)	PUNCT
ejpam-5918	338	11	(	(	PUNCT
ejpam-5918	338	12	2025	2025	NUM
ejpam-5918	338	13	)	)	PUNCT
ejpam-5918	338	14	,	,	PUNCT
ejpam-5918	338	15	5918	5918	NUM
ejpam-5918	338	16	12	12	NUM
ejpam-5918	338	17	of	of	ADP
ejpam-5918	338	18	21	21	NUM
ejpam-5918	338	19	conversely	conversely	ADV
ejpam-5918	338	20	,	,	PUNCT
ejpam-5918	338	21	assume	assume	VERB
ejpam-5918	338	22	that	that	SCONJ
ejpam-5918	338	23	i	i	PRON
ejpam-5918	338	24	is	be	AUX
ejpam-5918	338	25	an	an	DET
ejpam-5918	338	26	ilds	ild	NOUN
ejpam-5918	338	27	in	in	ADP
ejpam-5918	338	28	v	v	NOUN
ejpam-5918	338	29	(	(	PUNCT
ejpam-5918	338	30	g	g	NOUN
ejpam-5918	338	31	)	)	PUNCT
ejpam-5918	338	32	and	and	CCONJ
ejpam-5918	338	33	g[v	g[v	NOUN
ejpam-5918	338	34	(	(	PUNCT
ejpam-5918	338	35	g	g	NOUN
ejpam-5918	338	36	)	)	PUNCT
ejpam-5918	338	37	\	\	PUNCT
ejpam-5918	339	1	i	i	PRON
ejpam-5918	339	2	]	]	PUNCT
ejpam-5918	339	3	̸=	̸=	PROPN
ejpam-5918	339	4	p2	p2	NOUN
ejpam-5918	339	5	.	.	PUNCT
ejpam-5918	340	1	now	now	ADV
ejpam-5918	340	2	,	,	PUNCT
ejpam-5918	340	3	for	for	ADP
ejpam-5918	340	4	all	all	DET
ejpam-5918	340	5	u	u	NOUN
ejpam-5918	340	6	,	,	PUNCT
ejpam-5918	340	7	v	v	NOUN
ejpam-5918	340	8	∈	∈	PROPN
ejpam-5918	340	9	i	i	PRON
ejpam-5918	340	10	,	,	PUNCT
ejpam-5918	340	11	nv	nv	PROPN
ejpam-5918	340	12	(	(	PUNCT
ejpam-5918	340	13	g)(u	g)(u	PROPN
ejpam-5918	340	14	)	)	PUNCT
ejpam-5918	340	15	∩	∩	NOUN
ejpam-5918	340	16	i	i	PRON
ejpam-5918	340	17	̸=	̸=	PROPN
ejpam-5918	340	18	nv	nv	PROPN
ejpam-5918	340	19	(	(	PUNCT
ejpam-5918	340	20	g)(v	g)(v	PROPN
ejpam-5918	340	21	)	)	PUNCT
ejpam-5918	340	22	∩	∩	PROPN
ejpam-5918	340	23	i.	i.	NOUN
ejpam-5918	340	24	this	this	PRON
ejpam-5918	340	25	implies	imply	VERB
ejpam-5918	340	26	nt	not	PART
ejpam-5918	340	27	(	(	PUNCT
ejpam-5918	340	28	g)(u	g)(u	ADJ
ejpam-5918	340	29	)	)	PUNCT
ejpam-5918	340	30	∩	∩	NOUN
ejpam-5918	340	31	i	i	PRON
ejpam-5918	340	32	̸=	̸=	PROPN
ejpam-5918	340	33	nt	not	PART
ejpam-5918	340	34	(	(	PUNCT
ejpam-5918	340	35	g)(v	g)(v	NOUN
ejpam-5918	340	36	)	)	PUNCT
ejpam-5918	340	37	∩	∩	PROPN
ejpam-5918	340	38	i	i	PRON
ejpam-5918	340	39	,	,	PUNCT
ejpam-5918	340	40	making	make	VERB
ejpam-5918	340	41	i	i	PRON
ejpam-5918	340	42	an	an	DET
ejpam-5918	340	43	ils	ils	NOUN
ejpam-5918	340	44	in	in	ADP
ejpam-5918	340	45	t	t	PROPN
ejpam-5918	340	46	(	(	PUNCT
ejpam-5918	340	47	g	g	NOUN
ejpam-5918	340	48	)	)	PUNCT
ejpam-5918	340	49	.	.	PUNCT
ejpam-5918	341	1	note	note	VERB
ejpam-5918	341	2	that	that	SCONJ
ejpam-5918	341	3	by	by	ADP
ejpam-5918	341	4	the	the	DET
ejpam-5918	341	5	definition	definition	NOUN
ejpam-5918	341	6	of	of	ADP
ejpam-5918	341	7	t	t	PROPN
ejpam-5918	341	8	(	(	PUNCT
ejpam-5918	341	9	g	g	NOUN
ejpam-5918	341	10	)	)	PUNCT
ejpam-5918	341	11	,	,	PUNCT
ejpam-5918	341	12	v	v	X
ejpam-5918	341	13	(	(	PUNCT
ejpam-5918	341	14	t	t	PROPN
ejpam-5918	341	15	(	(	PUNCT
ejpam-5918	341	16	g	g	NOUN
ejpam-5918	341	17	)	)	PUNCT
ejpam-5918	341	18	)	)	PUNCT
ejpam-5918	342	1	=	=	SYM
ejpam-5918	342	2	v	v	X
ejpam-5918	342	3	(	(	PUNCT
ejpam-5918	342	4	g	g	NOUN
ejpam-5918	342	5	)	)	PUNCT
ejpam-5918	342	6	∪	∪	ADP
ejpam-5918	342	7	e(g	e(g	PROPN
ejpam-5918	342	8	)	)	PUNCT
ejpam-5918	342	9	.	.	PUNCT
ejpam-5918	343	1	by	by	ADP
ejpam-5918	343	2	assumption	assumption	NOUN
ejpam-5918	343	3	that	that	SCONJ
ejpam-5918	343	4	i	i	PRON
ejpam-5918	343	5	is	be	AUX
ejpam-5918	343	6	an	an	DET
ejpam-5918	343	7	ilds	ild	NOUN
ejpam-5918	343	8	in	in	ADP
ejpam-5918	343	9	v	v	NOUN
ejpam-5918	343	10	(	(	PUNCT
ejpam-5918	343	11	g	g	NOUN
ejpam-5918	343	12	)	)	PUNCT
ejpam-5918	343	13	,	,	PUNCT
ejpam-5918	343	14	and	and	CCONJ
ejpam-5918	343	15	since	since	SCONJ
ejpam-5918	343	16	g[v	g[v	PROPN
ejpam-5918	343	17	(	(	PUNCT
ejpam-5918	343	18	g	g	NOUN
ejpam-5918	343	19	)	)	PUNCT
ejpam-5918	343	20	\	\	PUNCT
ejpam-5918	344	1	i	i	PRON
ejpam-5918	344	2	]	]	PUNCT
ejpam-5918	344	3	̸=	̸=	PROPN
ejpam-5918	344	4	p2	p2	NOUN
ejpam-5918	344	5	,	,	PUNCT
ejpam-5918	344	6	this	this	PRON
ejpam-5918	344	7	implies	imply	VERB
ejpam-5918	344	8	that	that	SCONJ
ejpam-5918	344	9	for	for	ADP
ejpam-5918	344	10	all	all	DET
ejpam-5918	344	11	ei	ei	ADP
ejpam-5918	344	12	∈	∈	PROPN
ejpam-5918	344	13	e(g	e(g	PROPN
ejpam-5918	344	14	)	)	PUNCT
ejpam-5918	344	15	,	,	PUNCT
ejpam-5918	344	16	ei	ei	PROPN
ejpam-5918	344	17	∈	∈	PROPN
ejpam-5918	344	18	n(u	n(u	PROPN
ejpam-5918	344	19	)	)	PUNCT
ejpam-5918	344	20	,	,	PUNCT
ejpam-5918	344	21	for	for	ADP
ejpam-5918	344	22	some	some	DET
ejpam-5918	344	23	u	u	PROPN
ejpam-5918	344	24	∈	∈	PROPN
ejpam-5918	344	25	i.	i.	NOUN
ejpam-5918	344	26	hence	hence	ADV
ejpam-5918	344	27	,	,	PUNCT
ejpam-5918	344	28	i	i	PRON
ejpam-5918	344	29	is	be	AUX
ejpam-5918	344	30	an	an	DET
ejpam-5918	344	31	ils	ils	NOUN
ejpam-5918	344	32	in	in	ADP
ejpam-5918	344	33	t	t	PROPN
ejpam-5918	344	34	(	(	PUNCT
ejpam-5918	344	35	g	g	NOUN
ejpam-5918	344	36	)	)	PUNCT
ejpam-5918	344	37	.	.	PUNCT
ejpam-5918	345	1	remark	remark	PROPN
ejpam-5918	345	2	1	1	NUM
ejpam-5918	345	3	.	.	PUNCT
ejpam-5918	346	1	let	let	VERB
ejpam-5918	346	2	g	g	PRON
ejpam-5918	346	3	be	be	AUX
ejpam-5918	346	4	a	a	DET
ejpam-5918	346	5	path	path	NOUN
ejpam-5918	346	6	graph	graph	NOUN
ejpam-5918	346	7	pn	pn	NOUN
ejpam-5918	346	8	or	or	CCONJ
ejpam-5918	346	9	cycle	cycle	NOUN
ejpam-5918	346	10	graph	graph	NOUN
ejpam-5918	346	11	cn	cn	VERB
ejpam-5918	346	12	with	with	ADP
ejpam-5918	346	13	n	n	NOUN
ejpam-5918	346	14	=	=	SYM
ejpam-5918	346	15	2	2	NUM
ejpam-5918	346	16	or	or	CCONJ
ejpam-5918	346	17	3	3	NUM
ejpam-5918	346	18	.	.	PUNCT
ejpam-5918	347	1	then	then	ADV
ejpam-5918	347	2	,	,	PUNCT
ejpam-5918	347	3	γli(t	γli(t	PROPN
ejpam-5918	347	4	(	(	PUNCT
ejpam-5918	347	5	g	g	NOUN
ejpam-5918	347	6	)	)	PUNCT
ejpam-5918	347	7	)	)	PUNCT
ejpam-5918	348	1	=	=	SYM
ejpam-5918	348	2	γli(t	γli(t	PROPN
ejpam-5918	348	3	(	(	PUNCT
ejpam-5918	348	4	pn	pn	NOUN
ejpam-5918	348	5	)	)	PUNCT
ejpam-5918	348	6	)	)	PUNCT
ejpam-5918	349	1	=	=	SYM
ejpam-5918	349	2	γli(t	γli(t	PROPN
ejpam-5918	349	3	(	(	PUNCT
ejpam-5918	349	4	cn	cn	NOUN
ejpam-5918	349	5	)	)	PUNCT
ejpam-5918	349	6	)	)	PUNCT
ejpam-5918	349	7	=	=	PUNCT
ejpam-5918	349	8	2	2	X
ejpam-5918	349	9	.	.	PUNCT
ejpam-5918	349	10	the	the	DET
ejpam-5918	349	11	result	result	NOUN
ejpam-5918	349	12	is	be	AUX
ejpam-5918	349	13	straighforward	straighforward	ADJ
ejpam-5918	349	14	and	and	CCONJ
ejpam-5918	349	15	can	can	AUX
ejpam-5918	349	16	be	be	AUX
ejpam-5918	349	17	directly	directly	ADV
ejpam-5918	349	18	verified	verify	VERB
ejpam-5918	349	19	from	from	ADP
ejpam-5918	349	20	the	the	DET
ejpam-5918	349	21	total	total	ADJ
ejpam-5918	349	22	graph	graph	NOUN
ejpam-5918	349	23	of	of	ADP
ejpam-5918	349	24	a	a	DET
ejpam-5918	349	25	path	path	NOUN
ejpam-5918	349	26	graph	graph	NOUN
ejpam-5918	349	27	or	or	CCONJ
ejpam-5918	349	28	cycle	cycle	NOUN
ejpam-5918	349	29	graph	graph	NOUN
ejpam-5918	349	30	of	of	ADP
ejpam-5918	349	31	order	order	NOUN
ejpam-5918	349	32	2	2	NUM
ejpam-5918	349	33	or	or	CCONJ
ejpam-5918	349	34	3	3	NUM
ejpam-5918	349	35	.	.	PUNCT
ejpam-5918	349	36	theorem	theorem	NOUN
ejpam-5918	349	37	9	9	NUM
ejpam-5918	349	38	.	.	PUNCT
ejpam-5918	350	1	let	let	VERB
ejpam-5918	350	2	g	g	PRON
ejpam-5918	350	3	be	be	AUX
ejpam-5918	350	4	a	a	DET
ejpam-5918	350	5	path	path	NOUN
ejpam-5918	350	6	graph	graph	NOUN
ejpam-5918	350	7	pn	pn	NOUN
ejpam-5918	350	8	with	with	ADP
ejpam-5918	350	9	n	n	PRON
ejpam-5918	350	10	≥	≥	NOUN
ejpam-5918	350	11	4	4	NUM
ejpam-5918	350	12	then	then	ADV
ejpam-5918	350	13	,	,	PUNCT
ejpam-5918	350	14	γli(t	γli(t	PROPN
ejpam-5918	350	15	(	(	PUNCT
ejpam-5918	350	16	g	g	NOUN
ejpam-5918	350	17	)	)	PUNCT
ejpam-5918	350	18	)	)	PUNCT
ejpam-5918	351	1	=	=	PUNCT
ejpam-5918	351	2			PROPN
ejpam-5918	351	3	4n	4n	VERB
ejpam-5918	351	4	7	7	NUM
ejpam-5918	351	5	if	if	SCONJ
ejpam-5918	351	6	n	n	PRON
ejpam-5918	351	7	≡	≡	PROPN
ejpam-5918	351	8	0	0	PUNCT
ejpam-5918	351	9	(	(	PUNCT
ejpam-5918	351	10	mod	mod	PROPN
ejpam-5918	351	11	7	7	NUM
ejpam-5918	351	12	)	)	PUNCT
ejpam-5918	351	13	⌈	⌈	NOUN
ejpam-5918	351	14	4n	4n	X
ejpam-5918	351	15	7	7	NUM
ejpam-5918	351	16	⌉	⌉	PROPN
ejpam-5918	351	17	if	if	SCONJ
ejpam-5918	351	18	n	n	PRON
ejpam-5918	351	19	≡	≡	PROPN
ejpam-5918	351	20	1	1	NUM
ejpam-5918	351	21	,	,	PUNCT
ejpam-5918	351	22	5	5	NUM
ejpam-5918	351	23	(	(	PUNCT
ejpam-5918	351	24	mod	mod	NOUN
ejpam-5918	351	25	7	7	NUM
ejpam-5918	351	26	)	)	PUNCT
ejpam-5918	351	27	⌊	⌊	ADP
ejpam-5918	351	28	4n	4n	VERB
ejpam-5918	351	29	7	7	NUM
ejpam-5918	351	30	⌋	⌋	NOUN
ejpam-5918	351	31	if	if	SCONJ
ejpam-5918	351	32	n	n	PRON
ejpam-5918	351	33	≡	≡	PROPN
ejpam-5918	351	34	2	2	NUM
ejpam-5918	351	35	,	,	PUNCT
ejpam-5918	351	36	3	3	NUM
ejpam-5918	351	37	,	,	PUNCT
ejpam-5918	351	38	4	4	NUM
ejpam-5918	351	39	,	,	PUNCT
ejpam-5918	351	40	6	6	NUM
ejpam-5918	351	41	(	(	PUNCT
ejpam-5918	351	42	mod	mod	ADJ
ejpam-5918	351	43	7	7	NUM
ejpam-5918	351	44	)	)	PUNCT
ejpam-5918	351	45	proof	proof	NOUN
ejpam-5918	351	46	.	.	PUNCT
ejpam-5918	352	1	let	let	VERB
ejpam-5918	352	2	g	g	PRON
ejpam-5918	352	3	be	be	AUX
ejpam-5918	352	4	a	a	DET
ejpam-5918	352	5	path	path	NOUN
ejpam-5918	352	6	graph	graph	NOUN
ejpam-5918	352	7	of	of	ADP
ejpam-5918	352	8	order	order	NOUN
ejpam-5918	352	9	n	n	PRON
ejpam-5918	352	10	≥	≥	NOUN
ejpam-5918	352	11	4	4	NUM
ejpam-5918	352	12	and	and	CCONJ
ejpam-5918	352	13	t	t	PROPN
ejpam-5918	352	14	(	(	PUNCT
ejpam-5918	352	15	g	g	NOUN
ejpam-5918	352	16	)	)	PUNCT
ejpam-5918	352	17	be	be	AUX
ejpam-5918	352	18	a	a	DET
ejpam-5918	352	19	total	total	ADJ
ejpam-5918	352	20	graph	graph	NOUN
ejpam-5918	352	21	of	of	ADP
ejpam-5918	352	22	g.	g.	PROPN
ejpam-5918	352	23	for	for	ADP
ejpam-5918	352	24	convenience	convenience	NOUN
ejpam-5918	352	25	,	,	PUNCT
ejpam-5918	352	26	let	let	VERB
ejpam-5918	352	27	v	v	NOUN
ejpam-5918	352	28	(	(	PUNCT
ejpam-5918	352	29	g	g	NOUN
ejpam-5918	352	30	)	)	PUNCT
ejpam-5918	352	31	=	=	NOUN
ejpam-5918	352	32	v	v	X
ejpam-5918	352	33	(	(	PUNCT
ejpam-5918	352	34	pn	pn	NOUN
ejpam-5918	352	35	)	)	PUNCT
ejpam-5918	352	36	=	=	SYM
ejpam-5918	352	37	{	{	PUNCT
ejpam-5918	352	38	v1	v1	PROPN
ejpam-5918	352	39	,	,	PUNCT
ejpam-5918	352	40	v2	v2	PROPN
ejpam-5918	352	41	,	,	PUNCT
ejpam-5918	352	42	.	.	PUNCT
ejpam-5918	352	43	.	.	PUNCT
ejpam-5918	353	1	.	.	PUNCT
ejpam-5918	354	1	,	,	PUNCT
ejpam-5918	354	2	vn−1	vn−1	PROPN
ejpam-5918	354	3	,	,	PUNCT
ejpam-5918	354	4	vn	vn	NOUN
ejpam-5918	354	5	}	}	PUNCT
ejpam-5918	354	6	,	,	PUNCT
ejpam-5918	354	7	e(g	e(g	PROPN
ejpam-5918	354	8	)	)	PUNCT
ejpam-5918	354	9	=	=	SYM
ejpam-5918	355	1	e(pn	e(pn	X
ejpam-5918	355	2	)	)	PUNCT
ejpam-5918	355	3	=	=	PRON
ejpam-5918	355	4	{	{	PUNCT
ejpam-5918	355	5	e1	e1	PROPN
ejpam-5918	355	6	,	,	PUNCT
ejpam-5918	355	7	e2	e2	PROPN
ejpam-5918	355	8	,	,	PUNCT
ejpam-5918	355	9	e3	e3	NOUN
ejpam-5918	355	10	.	.	PUNCT
ejpam-5918	355	11	.	.	PUNCT
ejpam-5918	356	1	.	.	PUNCT
ejpam-5918	357	1	,	,	PUNCT
ejpam-5918	357	2	en−2	en−2	PROPN
ejpam-5918	357	3	,	,	PUNCT
ejpam-5918	357	4	en−1	en−1	PROPN
ejpam-5918	357	5	}	}	PUNCT
ejpam-5918	357	6	where	where	SCONJ
ejpam-5918	357	7	e1	e1	NOUN
ejpam-5918	357	8	is	be	AUX
ejpam-5918	357	9	the	the	DET
ejpam-5918	357	10	edge	edge	NOUN
ejpam-5918	357	11	incident	incident	NOUN
ejpam-5918	357	12	with	with	ADP
ejpam-5918	357	13	v1	v1	NOUN
ejpam-5918	357	14	and	and	CCONJ
ejpam-5918	357	15	v2	v2	PROPN
ejpam-5918	357	16	,	,	PUNCT
ejpam-5918	357	17	e2	e2	PROPN
ejpam-5918	357	18	is	be	AUX
ejpam-5918	357	19	the	the	DET
ejpam-5918	357	20	edge	edge	NOUN
ejpam-5918	357	21	incident	incident	NOUN
ejpam-5918	357	22	to	to	PART
ejpam-5918	357	23	v2	v2	VERB
ejpam-5918	357	24	and	and	CCONJ
ejpam-5918	357	25	v3	v3	PROPN
ejpam-5918	357	26	,	,	PUNCT
ejpam-5918	357	27	and	and	CCONJ
ejpam-5918	357	28	so	so	ADV
ejpam-5918	357	29	on	on	ADV
ejpam-5918	357	30	and	and	CCONJ
ejpam-5918	357	31	so	so	ADV
ejpam-5918	357	32	forth	forth	ADV
ejpam-5918	357	33	.	.	PUNCT
ejpam-5918	358	1	by	by	ADP
ejpam-5918	358	2	definition	definition	NOUN
ejpam-5918	358	3	of	of	ADP
ejpam-5918	358	4	total	total	ADJ
ejpam-5918	358	5	graph	graph	NOUN
ejpam-5918	358	6	,	,	PUNCT
ejpam-5918	358	7	v	v	NOUN
ejpam-5918	358	8	(	(	PUNCT
ejpam-5918	358	9	t	t	PROPN
ejpam-5918	358	10	(	(	PUNCT
ejpam-5918	358	11	g	g	NOUN
ejpam-5918	358	12	)	)	PUNCT
ejpam-5918	358	13	)	)	PUNCT
ejpam-5918	359	1	=	=	SYM
ejpam-5918	359	2	v	v	X
ejpam-5918	359	3	(	(	PUNCT
ejpam-5918	359	4	g	g	NOUN
ejpam-5918	359	5	)	)	PUNCT
ejpam-5918	359	6	∪	∪	ADP
ejpam-5918	359	7	e(g	e(g	PROPN
ejpam-5918	359	8	)	)	PUNCT
ejpam-5918	359	9	.	.	PUNCT
ejpam-5918	360	1	suppose	suppose	VERB
ejpam-5918	360	2	i	i	PRON
ejpam-5918	360	3	is	be	AUX
ejpam-5918	360	4	an	an	DET
ejpam-5918	360	5	internally	internally	ADV
ejpam-5918	360	6	-	-	PUNCT
ejpam-5918	360	7	locating	locate	VERB
ejpam-5918	360	8	dominating	dominating	NOUN
ejpam-5918	360	9	set	set	NOUN
ejpam-5918	360	10	of	of	ADP
ejpam-5918	360	11	minimum	minimum	ADJ
ejpam-5918	360	12	cardinality	cardinality	NOUN
ejpam-5918	360	13	,	,	PUNCT
ejpam-5918	360	14	i.e.	i.e.	X
ejpam-5918	360	15	,	,	PUNCT
ejpam-5918	360	16	i	i	PRON
ejpam-5918	360	17	is	be	AUX
ejpam-5918	360	18	a	a	DET
ejpam-5918	360	19	γli	γli	ADJ
ejpam-5918	360	20	−	−	NOUN
ejpam-5918	360	21	set	set	NOUN
ejpam-5918	360	22	.	.	PUNCT
ejpam-5918	361	1	now	now	ADV
ejpam-5918	361	2	,	,	PUNCT
ejpam-5918	361	3	consider	consider	VERB
ejpam-5918	361	4	the	the	DET
ejpam-5918	361	5	following	follow	VERB
ejpam-5918	361	6	cases	case	NOUN
ejpam-5918	361	7	:	:	PUNCT
ejpam-5918	361	8	case	case	NOUN
ejpam-5918	361	9	1	1	NUM
ejpam-5918	361	10	:	:	PUNCT
ejpam-5918	361	11	n	n	NUM
ejpam-5918	361	12	≡	≡	PROPN
ejpam-5918	361	13	0	0	PUNCT
ejpam-5918	362	1	(	(	PUNCT
ejpam-5918	362	2	mod	mod	PROPN
ejpam-5918	362	3	7	7	NUM
ejpam-5918	362	4	)	)	PUNCT
ejpam-5918	362	5	.	.	PUNCT
ejpam-5918	363	1	let	let	VERB
ejpam-5918	363	2	s	s	PRON
ejpam-5918	363	3	⊆	⊆	NUM
ejpam-5918	363	4	v	v	NOUN
ejpam-5918	363	5	(	(	PUNCT
ejpam-5918	363	6	t	t	PROPN
ejpam-5918	363	7	(	(	PUNCT
ejpam-5918	363	8	g	g	NOUN
ejpam-5918	363	9	)	)	PUNCT
ejpam-5918	363	10	)	)	PUNCT
ejpam-5918	363	11	with	with	ADP
ejpam-5918	363	12	s	s	NOUN
ejpam-5918	363	13	=	=	PUNCT
ejpam-5918	363	14	{	{	PUNCT
ejpam-5918	363	15	v2	v2	PROPN
ejpam-5918	363	16	,	,	PUNCT
ejpam-5918	363	17	v3	v3	PROPN
ejpam-5918	363	18	,	,	PUNCT
ejpam-5918	363	19	v9	v9	PROPN
ejpam-5918	363	20	,	,	PUNCT
ejpam-5918	363	21	v10	v10	NOUN
ejpam-5918	363	22	,	,	PUNCT
ejpam-5918	363	23	.	.	PUNCT
ejpam-5918	363	24	.	.	PUNCT
ejpam-5918	364	1	.	.	PUNCT
ejpam-5918	365	1	,	,	PUNCT
ejpam-5918	365	2	vn−5	vn−5	NOUN
ejpam-5918	365	3	,	,	PUNCT
ejpam-5918	365	4	vn−4	vn−4	NOUN
ejpam-5918	365	5	}	}	PUNCT
ejpam-5918	365	6	∪	∪	NOUN
ejpam-5918	365	7	{	{	PUNCT
ejpam-5918	365	8	e5	e5	PROPN
ejpam-5918	365	9	,	,	PUNCT
ejpam-5918	365	10	e6	e6	PROPN
ejpam-5918	365	11	,	,	PUNCT
ejpam-5918	365	12	e12	e12	NOUN
ejpam-5918	365	13	,	,	PUNCT
ejpam-5918	365	14	e13	e13	PROPN
ejpam-5918	365	15	,	,	PUNCT
ejpam-5918	365	16	.	.	PUNCT
ejpam-5918	365	17	.	.	PUNCT
ejpam-5918	366	1	.	.	PUNCT
ejpam-5918	367	1	,	,	PUNCT
ejpam-5918	367	2	en−9	en−9	NOUN
ejpam-5918	367	3	,	,	PUNCT
ejpam-5918	367	4	en−8	en−8	PROPN
ejpam-5918	367	5	,	,	PUNCT
ejpam-5918	367	6	en−2	en−2	PROPN
ejpam-5918	367	7	,	,	PUNCT
ejpam-5918	367	8	en−1	en−1	PROPN
ejpam-5918	367	9	}	}	PUNCT
ejpam-5918	367	10	.	.	PUNCT
ejpam-5918	368	1	observe	observe	VERB
ejpam-5918	368	2	that	that	SCONJ
ejpam-5918	368	3	s	s	VERB
ejpam-5918	368	4	is	be	AUX
ejpam-5918	368	5	a	a	DET
ejpam-5918	368	6	dominating	dominating	NOUN
ejpam-5918	368	7	set	set	NOUN
ejpam-5918	368	8	and	and	CCONJ
ejpam-5918	368	9	for	for	ADP
ejpam-5918	368	10	all	all	DET
ejpam-5918	368	11	u	u	NOUN
ejpam-5918	368	12	,	,	PUNCT
ejpam-5918	368	13	v	v	ADP
ejpam-5918	368	14	∈	∈	PROPN
ejpam-5918	368	15	s	s	NOUN
ejpam-5918	368	16	,	,	PUNCT
ejpam-5918	368	17	n(u	n(u	PROPN
ejpam-5918	368	18	)	)	PUNCT
ejpam-5918	368	19	∩	∩	PROPN
ejpam-5918	368	20	s	s	PART
ejpam-5918	368	21	̸=	̸=	PROPN
ejpam-5918	368	22	n(v	n(v	PROPN
ejpam-5918	368	23	)	)	PUNCT
ejpam-5918	368	24	∩	∩	PROPN
ejpam-5918	368	25	s.	s.	PROPN
ejpam-5918	368	26	hence	hence	ADV
ejpam-5918	368	27	,	,	PUNCT
ejpam-5918	368	28	s	s	VERB
ejpam-5918	368	29	is	be	AUX
ejpam-5918	368	30	an	an	DET
ejpam-5918	368	31	ilds	ild	NOUN
ejpam-5918	368	32	.	.	PUNCT
ejpam-5918	369	1	to	to	PART
ejpam-5918	369	2	end	end	VERB
ejpam-5918	369	3	this	this	PRON
ejpam-5918	369	4	,	,	PUNCT
ejpam-5918	369	5	note	note	VERB
ejpam-5918	369	6	that	that	SCONJ
ejpam-5918	369	7	|s|	|s|	NOUN
ejpam-5918	369	8	=	=	NOUN
ejpam-5918	369	9	4n	4n	X
ejpam-5918	369	10	7	7	NUM
ejpam-5918	369	11	.	.	PUNCT
ejpam-5918	370	1	since	since	SCONJ
ejpam-5918	370	2	i	i	PRON
ejpam-5918	370	3	is	be	AUX
ejpam-5918	370	4	a	a	DET
ejpam-5918	370	5	γli	γli	ADJ
ejpam-5918	370	6	−	−	NOUN
ejpam-5918	370	7	set	set	NOUN
ejpam-5918	370	8	,	,	PUNCT
ejpam-5918	370	9	|s|	|s|	NOUN
ejpam-5918	370	10	≥	≥	NOUN
ejpam-5918	370	11	|i|	|i|	PROPN
ejpam-5918	370	12	.	.	PUNCT
ejpam-5918	371	1	so	so	ADV
ejpam-5918	371	2	,	,	PUNCT
ejpam-5918	371	3	|i|	|i|	VERB
ejpam-5918	371	4	≤	≤	NUM
ejpam-5918	371	5	|s|	|s|	NOUN
ejpam-5918	371	6	=	=	NOUN
ejpam-5918	371	7	4n	4n	X
ejpam-5918	371	8	7	7	NUM
ejpam-5918	371	9	.	.	PUNCT
ejpam-5918	372	1	on	on	ADP
ejpam-5918	372	2	the	the	DET
ejpam-5918	372	3	other	other	ADJ
ejpam-5918	372	4	hand	hand	NOUN
ejpam-5918	372	5	,	,	PUNCT
ejpam-5918	372	6	since	since	SCONJ
ejpam-5918	372	7	i	i	PRON
ejpam-5918	372	8	is	be	AUX
ejpam-5918	372	9	a	a	DET
ejpam-5918	372	10	γli	γli	ADJ
ejpam-5918	372	11	−	−	NOUN
ejpam-5918	372	12	set	set	NOUN
ejpam-5918	372	13	of	of	ADP
ejpam-5918	372	14	t	t	PROPN
ejpam-5918	372	15	(	(	PUNCT
ejpam-5918	372	16	g	g	NOUN
ejpam-5918	372	17	)	)	PUNCT
ejpam-5918	372	18	,	,	PUNCT
ejpam-5918	372	19	then	then	ADV
ejpam-5918	372	20	i	i	PRON
ejpam-5918	372	21	must	must	AUX
ejpam-5918	372	22	have	have	AUX
ejpam-5918	372	23	atleast	atleast	VERB
ejpam-5918	372	24	4n	4n	VERB
ejpam-5918	372	25	7	7	NUM
ejpam-5918	372	26	vertices	vertex	NOUN
ejpam-5918	372	27	in	in	ADP
ejpam-5918	372	28	t	t	PROPN
ejpam-5918	372	29	(	(	PUNCT
ejpam-5918	372	30	g	g	NOUN
ejpam-5918	372	31	)	)	PUNCT
ejpam-5918	372	32	.	.	PUNCT
ejpam-5918	373	1	hence	hence	ADV
ejpam-5918	373	2	,	,	PUNCT
ejpam-5918	373	3	|i|	|i|	VERB
ejpam-5918	373	4	≥	≥	NOUN
ejpam-5918	373	5	4n	4n	X
ejpam-5918	373	6	7	7	NUM
ejpam-5918	373	7	.	.	PUNCT
ejpam-5918	374	1	therefore	therefore	ADV
ejpam-5918	374	2	,	,	PUNCT
ejpam-5918	374	3	|i|	|i|	ADP
ejpam-5918	374	4	=	=	SYM
ejpam-5918	374	5	4n	4n	X
ejpam-5918	374	6	7	7	NUM
ejpam-5918	374	7	.	.	PUNCT
ejpam-5918	374	8	case	case	NOUN
ejpam-5918	374	9	2	2	NUM
ejpam-5918	374	10	:	:	PUNCT
ejpam-5918	374	11	n	n	NUM
ejpam-5918	374	12	≡	≡	PROPN
ejpam-5918	374	13	1	1	NUM
ejpam-5918	374	14	(	(	PUNCT
ejpam-5918	374	15	mod	mod	PROPN
ejpam-5918	374	16	7	7	NUM
ejpam-5918	374	17	)	)	PUNCT
ejpam-5918	374	18	.	.	PUNCT
ejpam-5918	375	1	let	let	VERB
ejpam-5918	375	2	s	s	PRON
ejpam-5918	375	3	⊆	⊆	NUM
ejpam-5918	375	4	v	v	NOUN
ejpam-5918	375	5	(	(	PUNCT
ejpam-5918	375	6	t	t	PROPN
ejpam-5918	375	7	(	(	PUNCT
ejpam-5918	375	8	g	g	NOUN
ejpam-5918	375	9	)	)	PUNCT
ejpam-5918	375	10	)	)	PUNCT
ejpam-5918	375	11	with	with	ADP
ejpam-5918	375	12	s	s	NOUN
ejpam-5918	375	13	=	=	PUNCT
ejpam-5918	375	14	{	{	PUNCT
ejpam-5918	375	15	v2	v2	PROPN
ejpam-5918	375	16	,	,	PUNCT
ejpam-5918	375	17	v3	v3	PROPN
ejpam-5918	375	18	,	,	PUNCT
ejpam-5918	375	19	v9	v9	PROPN
ejpam-5918	375	20	,	,	PUNCT
ejpam-5918	375	21	v10	v10	NOUN
ejpam-5918	375	22	,	,	PUNCT
ejpam-5918	375	23	.	.	PUNCT
ejpam-5918	375	24	.	.	PUNCT
ejpam-5918	376	1	.	.	PUNCT
ejpam-5918	377	1	,	,	PUNCT
ejpam-5918	377	2	vn	vn	VERB
ejpam-5918	377	3	}	}	PUNCT
ejpam-5918	377	4	∪	∪	NOUN
ejpam-5918	377	5	{	{	PUNCT
ejpam-5918	377	6	e5	e5	PROPN
ejpam-5918	377	7	,	,	PUNCT
ejpam-5918	377	8	e6	e6	PROPN
ejpam-5918	377	9	,	,	PUNCT
ejpam-5918	377	10	e11	e11	X
ejpam-5918	377	11	,	,	PUNCT
ejpam-5918	377	12	e12	e12	NOUN
ejpam-5918	377	13	,	,	PUNCT
ejpam-5918	377	14	.	.	PUNCT
ejpam-5918	377	15	.	.	PUNCT
ejpam-5918	378	1	.	.	PUNCT
ejpam-5918	379	1	,	,	PUNCT
ejpam-5918	380	1	en−10	en−10	PROPN
ejpam-5918	380	2	,	,	PUNCT
ejpam-5918	380	3	en−9	en−9	NOUN
ejpam-5918	380	4	,	,	PUNCT
ejpam-5918	380	5	en−3	en−3	PROPN
ejpam-5918	380	6	,	,	PUNCT
ejpam-5918	380	7	en−2	en−2	PROPN
ejpam-5918	380	8	}	}	PUNCT
ejpam-5918	380	9	.	.	PUNCT
ejpam-5918	381	1	i.	i.	PROPN
ejpam-5918	381	2	tropico	tropico	PROPN
ejpam-5918	381	3	,	,	PUNCT
ejpam-5918	381	4	i.	i.	PROPN
ejpam-5918	381	5	cabahug	cabahug	PROPN
ejpam-5918	381	6	,	,	PUNCT
ejpam-5918	381	7	jr	jr	PROPN
ejpam-5918	381	8	.	.	PROPN
ejpam-5918	381	9	/	/	SYM
ejpam-5918	381	10	eur	eur	PROPN
ejpam-5918	381	11	.	.	PUNCT
ejpam-5918	382	1	j.	j.	PROPN
ejpam-5918	382	2	pure	pure	PROPN
ejpam-5918	382	3	appl	appl	PROPN
ejpam-5918	382	4	.	.	PROPN
ejpam-5918	382	5	math	math	PROPN
ejpam-5918	382	6	,	,	PUNCT
ejpam-5918	382	7	18	18	NUM
ejpam-5918	382	8	(	(	PUNCT
ejpam-5918	382	9	2	2	NUM
ejpam-5918	382	10	)	)	PUNCT
ejpam-5918	382	11	(	(	PUNCT
ejpam-5918	382	12	2025	2025	NUM
ejpam-5918	382	13	)	)	PUNCT
ejpam-5918	382	14	,	,	PUNCT
ejpam-5918	382	15	5918	5918	NUM
ejpam-5918	382	16	13	13	NUM
ejpam-5918	382	17	of	of	ADP
ejpam-5918	382	18	21	21	NUM
ejpam-5918	382	19	observe	observe	VERB
ejpam-5918	382	20	that	that	SCONJ
ejpam-5918	382	21	s	s	VERB
ejpam-5918	382	22	is	be	AUX
ejpam-5918	382	23	a	a	DET
ejpam-5918	382	24	dominating	dominating	NOUN
ejpam-5918	382	25	set	set	NOUN
ejpam-5918	382	26	and	and	CCONJ
ejpam-5918	382	27	for	for	ADP
ejpam-5918	382	28	all	all	DET
ejpam-5918	382	29	u	u	NOUN
ejpam-5918	382	30	,	,	PUNCT
ejpam-5918	382	31	v	v	ADP
ejpam-5918	382	32	∈	∈	PROPN
ejpam-5918	382	33	s	s	NOUN
ejpam-5918	382	34	,	,	PUNCT
ejpam-5918	382	35	n(u	n(u	PROPN
ejpam-5918	382	36	)	)	PUNCT
ejpam-5918	382	37	∩	∩	PROPN
ejpam-5918	382	38	s	s	PART
ejpam-5918	382	39	̸=	̸=	PROPN
ejpam-5918	382	40	n(v	n(v	PROPN
ejpam-5918	382	41	)	)	PUNCT
ejpam-5918	382	42	∩	∩	PROPN
ejpam-5918	382	43	s.	s.	PROPN
ejpam-5918	382	44	hence	hence	ADV
ejpam-5918	382	45	,	,	PUNCT
ejpam-5918	382	46	s	s	VERB
ejpam-5918	382	47	is	be	AUX
ejpam-5918	382	48	an	an	DET
ejpam-5918	382	49	ilds	ild	NOUN
ejpam-5918	382	50	.	.	PUNCT
ejpam-5918	383	1	to	to	PART
ejpam-5918	383	2	end	end	VERB
ejpam-5918	383	3	this	this	PRON
ejpam-5918	383	4	,	,	PUNCT
ejpam-5918	383	5	note	note	VERB
ejpam-5918	383	6	that	that	SCONJ
ejpam-5918	383	7	|s|	|s|	NOUN
ejpam-5918	383	8	=	=	SYM
ejpam-5918	383	9	⌈4n7	⌈4n7	PRON
ejpam-5918	383	10	⌉.	⌉.	ADV
ejpam-5918	383	11	since	since	SCONJ
ejpam-5918	383	12	i	i	PRON
ejpam-5918	383	13	is	be	AUX
ejpam-5918	383	14	a	a	DET
ejpam-5918	383	15	γli	γli	ADJ
ejpam-5918	383	16	−	−	NOUN
ejpam-5918	383	17	set	set	NOUN
ejpam-5918	383	18	,	,	PUNCT
ejpam-5918	383	19	|s|	|s|	NOUN
ejpam-5918	383	20	≥	≥	NOUN
ejpam-5918	383	21	|i|	|i|	PROPN
ejpam-5918	383	22	.	.	PUNCT
ejpam-5918	384	1	so	so	ADV
ejpam-5918	384	2	,	,	PUNCT
ejpam-5918	384	3	|i|	|i|	VERB
ejpam-5918	384	4	≤	≤	NUM
ejpam-5918	384	5	|s|	|s|	PROPN
ejpam-5918	384	6	=	=	SYM
ejpam-5918	384	7	⌈4n7	⌈4n7	X
ejpam-5918	384	8	⌉.	⌉.	ADV
ejpam-5918	384	9	on	on	ADP
ejpam-5918	384	10	the	the	DET
ejpam-5918	384	11	other	other	ADJ
ejpam-5918	384	12	hand	hand	NOUN
ejpam-5918	384	13	,	,	PUNCT
ejpam-5918	384	14	since	since	SCONJ
ejpam-5918	384	15	i	i	PRON
ejpam-5918	384	16	is	be	AUX
ejpam-5918	384	17	a	a	DET
ejpam-5918	384	18	γli	γli	ADJ
ejpam-5918	384	19	−	−	NOUN
ejpam-5918	384	20	set	set	NOUN
ejpam-5918	384	21	of	of	ADP
ejpam-5918	384	22	t	t	PROPN
ejpam-5918	384	23	(	(	PUNCT
ejpam-5918	384	24	g	g	NOUN
ejpam-5918	384	25	)	)	PUNCT
ejpam-5918	384	26	,	,	PUNCT
ejpam-5918	384	27	then	then	ADV
ejpam-5918	384	28	i	i	PRON
ejpam-5918	384	29	must	must	AUX
ejpam-5918	384	30	have	have	AUX
ejpam-5918	384	31	atleast	atleast	VERB
ejpam-5918	384	32	⌈4n7	⌈4n7	NUM
ejpam-5918	384	33	⌉	⌉	X
ejpam-5918	384	34	vertices	vertice	VERB
ejpam-5918	384	35	in	in	ADP
ejpam-5918	384	36	t	t	PROPN
ejpam-5918	384	37	(	(	PUNCT
ejpam-5918	384	38	g	g	NOUN
ejpam-5918	384	39	)	)	PUNCT
ejpam-5918	384	40	.	.	PUNCT
ejpam-5918	385	1	hence	hence	ADV
ejpam-5918	385	2	,	,	PUNCT
ejpam-5918	385	3	|i|	|i|	VERB
ejpam-5918	385	4	≥	≥	NOUN
ejpam-5918	385	5	⌈4n7	⌈4n7	X
ejpam-5918	385	6	⌉.	⌉.	ADV
ejpam-5918	385	7	therefore	therefore	ADV
ejpam-5918	385	8	,	,	PUNCT
ejpam-5918	385	9	|i|	|i|	PROPN
ejpam-5918	385	10	=	=	SYM
ejpam-5918	385	11	⌈4n7	⌈4n7	ADP
ejpam-5918	385	12	⌉.	⌉.	ADJ
ejpam-5918	385	13	case	case	NOUN
ejpam-5918	385	14	3	3	NUM
ejpam-5918	385	15	:	:	PUNCT
ejpam-5918	385	16	n	n	NUM
ejpam-5918	385	17	≡	≡	PROPN
ejpam-5918	385	18	2	2	NUM
ejpam-5918	385	19	(	(	PUNCT
ejpam-5918	385	20	mod	mod	PROPN
ejpam-5918	385	21	7	7	NUM
ejpam-5918	385	22	)	)	PUNCT
ejpam-5918	385	23	.	.	PUNCT
ejpam-5918	386	1	let	let	VERB
ejpam-5918	386	2	s	s	PRON
ejpam-5918	386	3	⊆	⊆	NUM
ejpam-5918	386	4	v	v	NOUN
ejpam-5918	386	5	(	(	PUNCT
ejpam-5918	386	6	t	t	PROPN
ejpam-5918	386	7	(	(	PUNCT
ejpam-5918	386	8	g	g	NOUN
ejpam-5918	386	9	)	)	PUNCT
ejpam-5918	386	10	)	)	PUNCT
ejpam-5918	386	11	with	with	ADP
ejpam-5918	386	12	s	s	NOUN
ejpam-5918	386	13	=	=	PUNCT
ejpam-5918	386	14	{	{	PUNCT
ejpam-5918	386	15	v2	v2	PROPN
ejpam-5918	386	16	,	,	PUNCT
ejpam-5918	386	17	v3	v3	PROPN
ejpam-5918	386	18	,	,	PUNCT
ejpam-5918	386	19	v9	v9	PROPN
ejpam-5918	386	20	,	,	PUNCT
ejpam-5918	386	21	v10	v10	NOUN
ejpam-5918	386	22	,	,	PUNCT
ejpam-5918	386	23	.	.	PUNCT
ejpam-5918	386	24	.	.	PUNCT
ejpam-5918	387	1	.	.	PUNCT
ejpam-5918	388	1	,	,	PUNCT
ejpam-5918	388	2	vn	vn	VERB
ejpam-5918	388	3	}	}	PUNCT
ejpam-5918	388	4	∪	∪	NOUN
ejpam-5918	388	5	{	{	PUNCT
ejpam-5918	388	6	e5	e5	PROPN
ejpam-5918	388	7	,	,	PUNCT
ejpam-5918	388	8	e6	e6	PROPN
ejpam-5918	388	9	,	,	PUNCT
ejpam-5918	388	10	e12	e12	NOUN
ejpam-5918	388	11	,	,	PUNCT
ejpam-5918	388	12	e13	e13	PROPN
ejpam-5918	388	13	,	,	PUNCT
ejpam-5918	388	14	.	.	PUNCT
ejpam-5918	388	15	.	.	PUNCT
ejpam-5918	389	1	.	.	PUNCT
ejpam-5918	390	1	,	,	PUNCT
ejpam-5918	390	2	en−11	en−11	PROPN
ejpam-5918	390	3	,	,	PUNCT
ejpam-5918	390	4	en−10	en−10	PROPN
ejpam-5918	390	5	,	,	PUNCT
ejpam-5918	390	6	en−4	en−4	NOUN
ejpam-5918	390	7	,	,	PUNCT
ejpam-5918	390	8	en−3	en−3	PROPN
ejpam-5918	390	9	}	}	PUNCT
ejpam-5918	390	10	.	.	PUNCT
ejpam-5918	391	1	observe	observe	VERB
ejpam-5918	391	2	that	that	SCONJ
ejpam-5918	391	3	s	s	VERB
ejpam-5918	391	4	is	be	AUX
ejpam-5918	391	5	a	a	DET
ejpam-5918	391	6	dominating	dominating	NOUN
ejpam-5918	391	7	set	set	NOUN
ejpam-5918	391	8	and	and	CCONJ
ejpam-5918	391	9	for	for	ADP
ejpam-5918	391	10	all	all	DET
ejpam-5918	391	11	u	u	NOUN
ejpam-5918	391	12	,	,	PUNCT
ejpam-5918	391	13	v	v	ADP
ejpam-5918	391	14	∈	∈	PROPN
ejpam-5918	391	15	s	s	NOUN
ejpam-5918	391	16	,	,	PUNCT
ejpam-5918	391	17	n(u	n(u	PROPN
ejpam-5918	391	18	)	)	PUNCT
ejpam-5918	391	19	∩	∩	PROPN
ejpam-5918	391	20	s	s	PART
ejpam-5918	391	21	̸=	̸=	PROPN
ejpam-5918	391	22	n(v	n(v	PROPN
ejpam-5918	391	23	)	)	PUNCT
ejpam-5918	391	24	∩	∩	PROPN
ejpam-5918	391	25	s.	s.	PROPN
ejpam-5918	391	26	hence	hence	ADV
ejpam-5918	391	27	,	,	PUNCT
ejpam-5918	391	28	s	s	VERB
ejpam-5918	391	29	is	be	AUX
ejpam-5918	391	30	an	an	DET
ejpam-5918	391	31	ilds	ild	NOUN
ejpam-5918	391	32	.	.	PUNCT
ejpam-5918	392	1	to	to	PART
ejpam-5918	392	2	end	end	VERB
ejpam-5918	392	3	this	this	PRON
ejpam-5918	392	4	,	,	PUNCT
ejpam-5918	392	5	note	note	VERB
ejpam-5918	392	6	that	that	SCONJ
ejpam-5918	392	7	|s|	|s|	PROPN
ejpam-5918	392	8	=	=	SYM
ejpam-5918	392	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	392	10	⌋.	⌋.	NOUN
ejpam-5918	392	11	since	since	SCONJ
ejpam-5918	392	12	i	i	PRON
ejpam-5918	392	13	is	be	AUX
ejpam-5918	392	14	a	a	DET
ejpam-5918	392	15	γli	γli	ADJ
ejpam-5918	392	16	−	−	NOUN
ejpam-5918	392	17	set	set	NOUN
ejpam-5918	392	18	,	,	PUNCT
ejpam-5918	392	19	|s|	|s|	NOUN
ejpam-5918	392	20	≥	≥	NOUN
ejpam-5918	392	21	|i|	|i|	PROPN
ejpam-5918	392	22	.	.	PUNCT
ejpam-5918	393	1	so	so	ADV
ejpam-5918	393	2	,	,	PUNCT
ejpam-5918	393	3	|i|	|i|	VERB
ejpam-5918	393	4	≤	≤	NUM
ejpam-5918	393	5	|s|	|s|	PROPN
ejpam-5918	393	6	=	=	SYM
ejpam-5918	393	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	393	8	⌋.	⌋.	ADV
ejpam-5918	393	9	on	on	ADP
ejpam-5918	393	10	the	the	DET
ejpam-5918	393	11	other	other	ADJ
ejpam-5918	393	12	hand	hand	NOUN
ejpam-5918	393	13	,	,	PUNCT
ejpam-5918	393	14	since	since	SCONJ
ejpam-5918	393	15	i	i	PRON
ejpam-5918	393	16	is	be	AUX
ejpam-5918	393	17	a	a	DET
ejpam-5918	393	18	γli	γli	ADJ
ejpam-5918	393	19	−	−	NOUN
ejpam-5918	393	20	set	set	NOUN
ejpam-5918	393	21	of	of	ADP
ejpam-5918	393	22	t	t	PROPN
ejpam-5918	393	23	(	(	PUNCT
ejpam-5918	393	24	g	g	NOUN
ejpam-5918	393	25	)	)	PUNCT
ejpam-5918	393	26	,	,	PUNCT
ejpam-5918	393	27	then	then	ADV
ejpam-5918	393	28	i	i	PRON
ejpam-5918	393	29	must	must	AUX
ejpam-5918	393	30	have	have	VERB
ejpam-5918	393	31	atleast	atleast	VERB
ejpam-5918	393	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	393	33	⌋	⌋	NOUN
ejpam-5918	393	34	vertices	vertice	VERB
ejpam-5918	393	35	in	in	ADP
ejpam-5918	393	36	t	t	PROPN
ejpam-5918	393	37	(	(	PUNCT
ejpam-5918	393	38	g	g	NOUN
ejpam-5918	393	39	)	)	PUNCT
ejpam-5918	393	40	.	.	PUNCT
ejpam-5918	394	1	hence	hence	ADV
ejpam-5918	394	2	,	,	PUNCT
ejpam-5918	394	3	|i|	|i|	VERB
ejpam-5918	394	4	≥	≥	NOUN
ejpam-5918	394	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	394	6	⌋.	⌋.	PUNCT
ejpam-5918	395	1	therefore	therefore	ADV
ejpam-5918	395	2	,	,	PUNCT
ejpam-5918	395	3	|i|	|i|	PROPN
ejpam-5918	395	4	=	=	SYM
ejpam-5918	395	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	395	6	⌋.	⌋.	NOUN
ejpam-5918	395	7	case	case	NOUN
ejpam-5918	395	8	4	4	NUM
ejpam-5918	395	9	:	:	PUNCT
ejpam-5918	395	10	n	n	NUM
ejpam-5918	395	11	≡	≡	PROPN
ejpam-5918	395	12	3	3	NUM
ejpam-5918	395	13	(	(	PUNCT
ejpam-5918	395	14	mod	mod	PROPN
ejpam-5918	395	15	7	7	NUM
ejpam-5918	395	16	)	)	PUNCT
ejpam-5918	395	17	.	.	PUNCT
ejpam-5918	396	1	let	let	VERB
ejpam-5918	396	2	s	s	PRON
ejpam-5918	396	3	⊆	⊆	NUM
ejpam-5918	396	4	v	v	NOUN
ejpam-5918	396	5	(	(	PUNCT
ejpam-5918	396	6	t	t	PROPN
ejpam-5918	396	7	(	(	PUNCT
ejpam-5918	396	8	g	g	NOUN
ejpam-5918	396	9	)	)	PUNCT
ejpam-5918	396	10	)	)	PUNCT
ejpam-5918	396	11	with	with	ADP
ejpam-5918	396	12	s	s	NOUN
ejpam-5918	396	13	=	=	PUNCT
ejpam-5918	396	14	{	{	PUNCT
ejpam-5918	396	15	v2	v2	PROPN
ejpam-5918	396	16	,	,	PUNCT
ejpam-5918	396	17	v3	v3	PROPN
ejpam-5918	396	18	,	,	PUNCT
ejpam-5918	396	19	v9	v9	PROPN
ejpam-5918	396	20	,	,	PUNCT
ejpam-5918	396	21	v10	v10	NOUN
ejpam-5918	396	22	,	,	PUNCT
ejpam-5918	396	23	.	.	PUNCT
ejpam-5918	396	24	.	.	PUNCT
ejpam-5918	397	1	.	.	PUNCT
ejpam-5918	398	1	,	,	PUNCT
ejpam-5918	398	2	vn−1	vn−1	ADJ
ejpam-5918	398	3	}	}	PUNCT
ejpam-5918	398	4	∪	∪	NOUN
ejpam-5918	398	5	{	{	PUNCT
ejpam-5918	398	6	e5	e5	PROPN
ejpam-5918	398	7	,	,	PUNCT
ejpam-5918	398	8	e6	e6	PROPN
ejpam-5918	398	9	,	,	PUNCT
ejpam-5918	398	10	e12	e12	NOUN
ejpam-5918	398	11	,	,	PUNCT
ejpam-5918	398	12	e13	e13	PROPN
ejpam-5918	398	13	,	,	PUNCT
ejpam-5918	398	14	.	.	PUNCT
ejpam-5918	398	15	.	.	PUNCT
ejpam-5918	399	1	.	.	PUNCT
ejpam-5918	400	1	,	,	PUNCT
ejpam-5918	400	2	en−12	en−12	PROPN
ejpam-5918	400	3	,	,	PUNCT
ejpam-5918	400	4	en−11	en−11	PROPN
ejpam-5918	400	5	,	,	PUNCT
ejpam-5918	400	6	en−5	en−5	NOUN
ejpam-5918	400	7	,	,	PUNCT
ejpam-5918	400	8	en−4	en−4	PROPN
ejpam-5918	400	9	}	}	PUNCT
ejpam-5918	400	10	.	.	PUNCT
ejpam-5918	401	1	observe	observe	VERB
ejpam-5918	401	2	that	that	SCONJ
ejpam-5918	401	3	s	s	VERB
ejpam-5918	401	4	is	be	AUX
ejpam-5918	401	5	a	a	DET
ejpam-5918	401	6	dominating	dominating	NOUN
ejpam-5918	401	7	set	set	NOUN
ejpam-5918	401	8	and	and	CCONJ
ejpam-5918	401	9	for	for	ADP
ejpam-5918	401	10	all	all	DET
ejpam-5918	401	11	u	u	NOUN
ejpam-5918	401	12	,	,	PUNCT
ejpam-5918	401	13	v	v	ADP
ejpam-5918	401	14	∈	∈	PROPN
ejpam-5918	401	15	s	s	NOUN
ejpam-5918	401	16	,	,	PUNCT
ejpam-5918	401	17	n(u	n(u	PROPN
ejpam-5918	401	18	)	)	PUNCT
ejpam-5918	401	19	∩	∩	PROPN
ejpam-5918	401	20	s	s	PART
ejpam-5918	401	21	̸=	̸=	PROPN
ejpam-5918	401	22	n(v	n(v	PROPN
ejpam-5918	401	23	)	)	PUNCT
ejpam-5918	401	24	∩	∩	PROPN
ejpam-5918	401	25	s.	s.	PROPN
ejpam-5918	401	26	hence	hence	ADV
ejpam-5918	401	27	,	,	PUNCT
ejpam-5918	401	28	s	s	VERB
ejpam-5918	401	29	is	be	AUX
ejpam-5918	401	30	an	an	DET
ejpam-5918	401	31	ilds	ild	NOUN
ejpam-5918	401	32	.	.	PUNCT
ejpam-5918	402	1	to	to	PART
ejpam-5918	402	2	end	end	VERB
ejpam-5918	402	3	this	this	PRON
ejpam-5918	402	4	,	,	PUNCT
ejpam-5918	402	5	note	note	VERB
ejpam-5918	402	6	that	that	SCONJ
ejpam-5918	402	7	|s|	|s|	PROPN
ejpam-5918	402	8	=	=	SYM
ejpam-5918	402	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	402	10	⌋.	⌋.	NOUN
ejpam-5918	402	11	since	since	SCONJ
ejpam-5918	402	12	i	i	PRON
ejpam-5918	402	13	is	be	AUX
ejpam-5918	402	14	a	a	DET
ejpam-5918	402	15	γli	γli	ADJ
ejpam-5918	402	16	−	−	NOUN
ejpam-5918	402	17	set	set	NOUN
ejpam-5918	402	18	,	,	PUNCT
ejpam-5918	402	19	|s|	|s|	NOUN
ejpam-5918	402	20	≥	≥	NOUN
ejpam-5918	402	21	|i|	|i|	PROPN
ejpam-5918	402	22	.	.	PUNCT
ejpam-5918	403	1	so	so	ADV
ejpam-5918	403	2	,	,	PUNCT
ejpam-5918	403	3	|i|	|i|	VERB
ejpam-5918	403	4	≤	≤	NUM
ejpam-5918	403	5	|s|	|s|	PROPN
ejpam-5918	403	6	=	=	SYM
ejpam-5918	403	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	403	8	⌋.	⌋.	ADV
ejpam-5918	403	9	on	on	ADP
ejpam-5918	403	10	the	the	DET
ejpam-5918	403	11	other	other	ADJ
ejpam-5918	403	12	hand	hand	NOUN
ejpam-5918	403	13	,	,	PUNCT
ejpam-5918	403	14	since	since	SCONJ
ejpam-5918	403	15	i	i	PRON
ejpam-5918	403	16	is	be	AUX
ejpam-5918	403	17	a	a	DET
ejpam-5918	403	18	γli	γli	ADJ
ejpam-5918	403	19	−	−	NOUN
ejpam-5918	403	20	set	set	NOUN
ejpam-5918	403	21	of	of	ADP
ejpam-5918	403	22	t	t	PROPN
ejpam-5918	403	23	(	(	PUNCT
ejpam-5918	403	24	g	g	NOUN
ejpam-5918	403	25	)	)	PUNCT
ejpam-5918	403	26	,	,	PUNCT
ejpam-5918	403	27	then	then	ADV
ejpam-5918	403	28	i	i	PRON
ejpam-5918	403	29	must	must	AUX
ejpam-5918	403	30	have	have	VERB
ejpam-5918	403	31	atleast	atleast	VERB
ejpam-5918	403	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	403	33	⌋	⌋	NOUN
ejpam-5918	403	34	vertices	vertice	VERB
ejpam-5918	403	35	in	in	ADP
ejpam-5918	403	36	t	t	PROPN
ejpam-5918	403	37	(	(	PUNCT
ejpam-5918	403	38	g	g	NOUN
ejpam-5918	403	39	)	)	PUNCT
ejpam-5918	403	40	.	.	PUNCT
ejpam-5918	404	1	hence	hence	ADV
ejpam-5918	404	2	,	,	PUNCT
ejpam-5918	404	3	|i|	|i|	VERB
ejpam-5918	404	4	≥	≥	NOUN
ejpam-5918	404	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	404	6	⌋.	⌋.	PUNCT
ejpam-5918	405	1	therefore	therefore	ADV
ejpam-5918	405	2	,	,	PUNCT
ejpam-5918	405	3	|i|	|i|	PROPN
ejpam-5918	405	4	=	=	SYM
ejpam-5918	405	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	405	6	⌋.	⌋.	PRON
ejpam-5918	405	7	case	case	NOUN
ejpam-5918	405	8	5	5	NUM
ejpam-5918	405	9	:	:	PUNCT
ejpam-5918	405	10	n	n	NUM
ejpam-5918	405	11	≡	≡	PROPN
ejpam-5918	405	12	4	4	NUM
ejpam-5918	405	13	(	(	PUNCT
ejpam-5918	405	14	mod	mod	PROPN
ejpam-5918	405	15	7	7	NUM
ejpam-5918	405	16	)	)	PUNCT
ejpam-5918	405	17	.	.	PUNCT
ejpam-5918	406	1	let	let	VERB
ejpam-5918	406	2	s	s	PRON
ejpam-5918	406	3	⊆	⊆	NUM
ejpam-5918	406	4	v	v	NOUN
ejpam-5918	406	5	(	(	PUNCT
ejpam-5918	406	6	t	t	PROPN
ejpam-5918	406	7	(	(	PUNCT
ejpam-5918	406	8	g	g	NOUN
ejpam-5918	406	9	)	)	PUNCT
ejpam-5918	406	10	)	)	PUNCT
ejpam-5918	406	11	with	with	ADP
ejpam-5918	406	12	s	s	NOUN
ejpam-5918	406	13	=	=	PUNCT
ejpam-5918	406	14	{	{	PUNCT
ejpam-5918	406	15	v2	v2	PROPN
ejpam-5918	406	16	,	,	PUNCT
ejpam-5918	406	17	v3	v3	PROPN
ejpam-5918	406	18	,	,	PUNCT
ejpam-5918	406	19	v9	v9	PROPN
ejpam-5918	406	20	,	,	PUNCT
ejpam-5918	406	21	v10	v10	NOUN
ejpam-5918	406	22	,	,	PUNCT
ejpam-5918	406	23	.	.	PUNCT
ejpam-5918	406	24	.	.	PUNCT
ejpam-5918	407	1	.	.	PUNCT
ejpam-5918	408	1	,	,	PUNCT
ejpam-5918	408	2	vn−2	vn−2	PROPN
ejpam-5918	408	3	,	,	PUNCT
ejpam-5918	408	4	vn−1	vn−1	ADJ
ejpam-5918	408	5	}	}	PUNCT
ejpam-5918	408	6	∪	∪	NOUN
ejpam-5918	408	7	{	{	PUNCT
ejpam-5918	408	8	e5	e5	PROPN
ejpam-5918	408	9	,	,	PUNCT
ejpam-5918	408	10	e6	e6	PROPN
ejpam-5918	408	11	,	,	PUNCT
ejpam-5918	408	12	.	.	PUNCT
ejpam-5918	408	13	.	.	PUNCT
ejpam-5918	409	1	.	.	PUNCT
ejpam-5918	410	1	,	,	PUNCT
ejpam-5918	410	2	en−6	en−6	NOUN
ejpam-5918	410	3	,	,	PUNCT
ejpam-5918	410	4	en−5	en−5	NOUN
ejpam-5918	410	5	}	}	PUNCT
ejpam-5918	410	6	.	.	PUNCT
ejpam-5918	411	1	observe	observe	VERB
ejpam-5918	411	2	that	that	SCONJ
ejpam-5918	411	3	s	s	VERB
ejpam-5918	411	4	is	be	AUX
ejpam-5918	411	5	a	a	DET
ejpam-5918	411	6	dominating	dominating	NOUN
ejpam-5918	411	7	set	set	NOUN
ejpam-5918	411	8	and	and	CCONJ
ejpam-5918	411	9	for	for	ADP
ejpam-5918	411	10	all	all	DET
ejpam-5918	411	11	u	u	NOUN
ejpam-5918	411	12	,	,	PUNCT
ejpam-5918	411	13	v	v	ADP
ejpam-5918	411	14	∈	∈	PROPN
ejpam-5918	411	15	s	s	NOUN
ejpam-5918	411	16	,	,	PUNCT
ejpam-5918	411	17	n(u	n(u	PROPN
ejpam-5918	411	18	)	)	PUNCT
ejpam-5918	411	19	∩	∩	PROPN
ejpam-5918	411	20	s	s	PART
ejpam-5918	411	21	̸=	̸=	PROPN
ejpam-5918	411	22	n(v	n(v	PROPN
ejpam-5918	411	23	)	)	PUNCT
ejpam-5918	411	24	∩	∩	PROPN
ejpam-5918	411	25	s.	s.	PROPN
ejpam-5918	411	26	hence	hence	ADV
ejpam-5918	411	27	,	,	PUNCT
ejpam-5918	411	28	s	s	VERB
ejpam-5918	411	29	is	be	AUX
ejpam-5918	411	30	an	an	DET
ejpam-5918	411	31	ilds	ild	NOUN
ejpam-5918	411	32	.	.	PUNCT
ejpam-5918	412	1	to	to	PART
ejpam-5918	412	2	end	end	VERB
ejpam-5918	412	3	this	this	PRON
ejpam-5918	412	4	,	,	PUNCT
ejpam-5918	412	5	note	note	VERB
ejpam-5918	412	6	that	that	SCONJ
ejpam-5918	412	7	|s|	|s|	PROPN
ejpam-5918	412	8	=	=	SYM
ejpam-5918	412	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	412	10	⌋.	⌋.	NOUN
ejpam-5918	412	11	since	since	SCONJ
ejpam-5918	412	12	i	i	PRON
ejpam-5918	412	13	is	be	AUX
ejpam-5918	412	14	a	a	DET
ejpam-5918	412	15	γli	γli	ADJ
ejpam-5918	412	16	−	−	NOUN
ejpam-5918	412	17	set	set	NOUN
ejpam-5918	412	18	,	,	PUNCT
ejpam-5918	412	19	|s|	|s|	NOUN
ejpam-5918	412	20	≥	≥	NOUN
ejpam-5918	412	21	|i|	|i|	PROPN
ejpam-5918	412	22	.	.	PUNCT
ejpam-5918	413	1	so	so	ADV
ejpam-5918	413	2	,	,	PUNCT
ejpam-5918	413	3	|i|	|i|	VERB
ejpam-5918	413	4	≤	≤	NUM
ejpam-5918	413	5	|s|	|s|	PROPN
ejpam-5918	413	6	=	=	SYM
ejpam-5918	413	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	413	8	⌋.	⌋.	ADV
ejpam-5918	413	9	on	on	ADP
ejpam-5918	413	10	the	the	DET
ejpam-5918	413	11	other	other	ADJ
ejpam-5918	413	12	hand	hand	NOUN
ejpam-5918	413	13	,	,	PUNCT
ejpam-5918	413	14	since	since	SCONJ
ejpam-5918	413	15	i	i	PRON
ejpam-5918	413	16	is	be	AUX
ejpam-5918	413	17	a	a	DET
ejpam-5918	413	18	γli	γli	ADJ
ejpam-5918	413	19	−	−	NOUN
ejpam-5918	413	20	set	set	NOUN
ejpam-5918	413	21	of	of	ADP
ejpam-5918	413	22	t	t	PROPN
ejpam-5918	413	23	(	(	PUNCT
ejpam-5918	413	24	g	g	NOUN
ejpam-5918	413	25	)	)	PUNCT
ejpam-5918	413	26	,	,	PUNCT
ejpam-5918	413	27	then	then	ADV
ejpam-5918	413	28	i	i	PRON
ejpam-5918	413	29	must	must	AUX
ejpam-5918	413	30	have	have	VERB
ejpam-5918	413	31	atleast	atleast	VERB
ejpam-5918	413	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	413	33	⌋	⌋	NOUN
ejpam-5918	413	34	vertices	vertice	VERB
ejpam-5918	413	35	in	in	ADP
ejpam-5918	413	36	t	t	PROPN
ejpam-5918	413	37	(	(	PUNCT
ejpam-5918	413	38	g	g	NOUN
ejpam-5918	413	39	)	)	PUNCT
ejpam-5918	413	40	.	.	PUNCT
ejpam-5918	414	1	hence	hence	ADV
ejpam-5918	414	2	,	,	PUNCT
ejpam-5918	414	3	|i|	|i|	VERB
ejpam-5918	414	4	≥	≥	NOUN
ejpam-5918	414	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	414	6	⌋.	⌋.	PUNCT
ejpam-5918	415	1	therefore	therefore	ADV
ejpam-5918	415	2	,	,	PUNCT
ejpam-5918	415	3	|i|	|i|	PROPN
ejpam-5918	415	4	=	=	SYM
ejpam-5918	415	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	415	6	⌋.	⌋.	NOUN
ejpam-5918	415	7	case	case	NOUN
ejpam-5918	415	8	6	6	NUM
ejpam-5918	415	9	:	:	PUNCT
ejpam-5918	415	10	n	n	NUM
ejpam-5918	415	11	≡	≡	PROPN
ejpam-5918	415	12	5	5	NUM
ejpam-5918	415	13	(	(	PUNCT
ejpam-5918	415	14	mod	mod	PROPN
ejpam-5918	415	15	7	7	NUM
ejpam-5918	415	16	)	)	PUNCT
ejpam-5918	415	17	.	.	PUNCT
ejpam-5918	416	1	let	let	VERB
ejpam-5918	416	2	s	s	PRON
ejpam-5918	416	3	⊆	⊆	NUM
ejpam-5918	416	4	v	v	NOUN
ejpam-5918	416	5	(	(	PUNCT
ejpam-5918	416	6	t	t	PROPN
ejpam-5918	416	7	(	(	PUNCT
ejpam-5918	416	8	g	g	NOUN
ejpam-5918	416	9	)	)	PUNCT
ejpam-5918	416	10	)	)	PUNCT
ejpam-5918	416	11	with	with	ADP
ejpam-5918	416	12	s	s	NOUN
ejpam-5918	416	13	=	=	PUNCT
ejpam-5918	416	14	{	{	PUNCT
ejpam-5918	416	15	v2	v2	PROPN
ejpam-5918	416	16	,	,	PUNCT
ejpam-5918	416	17	v3	v3	PROPN
ejpam-5918	416	18	,	,	PUNCT
ejpam-5918	416	19	v8	v8	PROPN
ejpam-5918	416	20	,	,	PUNCT
ejpam-5918	416	21	v9	v9	PROPN
ejpam-5918	416	22	,	,	PUNCT
ejpam-5918	416	23	.	.	PUNCT
ejpam-5918	416	24	.	.	PUNCT
ejpam-5918	417	1	.	.	PUNCT
ejpam-5918	418	1	,	,	PUNCT
ejpam-5918	418	2	vn−4	vn−4	NOUN
ejpam-5918	418	3	,	,	PUNCT
ejpam-5918	418	4	vn−3	vn−3	PROPN
ejpam-5918	418	5	}	}	PUNCT
ejpam-5918	418	6	∪	∪	NOUN
ejpam-5918	418	7	{	{	PUNCT
ejpam-5918	418	8	e5	e5	PROPN
ejpam-5918	418	9	,	,	PUNCT
ejpam-5918	418	10	e6	e6	PROPN
ejpam-5918	418	11	,	,	PUNCT
ejpam-5918	418	12	.	.	PUNCT
ejpam-5918	418	13	.	.	PUNCT
ejpam-5918	419	1	.	.	PUNCT
ejpam-5918	420	1	,	,	PUNCT
ejpam-5918	420	2	en−7	en−7	PROPN
ejpam-5918	420	3	,	,	PUNCT
ejpam-5918	420	4	en−6	en−6	NOUN
ejpam-5918	420	5	,	,	PUNCT
ejpam-5918	420	6	en−1	en−1	PROPN
ejpam-5918	420	7	}	}	PUNCT
ejpam-5918	420	8	.	.	PUNCT
ejpam-5918	421	1	observe	observe	VERB
ejpam-5918	421	2	that	that	SCONJ
ejpam-5918	421	3	s	s	VERB
ejpam-5918	421	4	is	be	AUX
ejpam-5918	421	5	a	a	DET
ejpam-5918	421	6	dominating	dominating	NOUN
ejpam-5918	421	7	set	set	NOUN
ejpam-5918	421	8	and	and	CCONJ
ejpam-5918	421	9	for	for	ADP
ejpam-5918	421	10	all	all	DET
ejpam-5918	421	11	u	u	NOUN
ejpam-5918	421	12	,	,	PUNCT
ejpam-5918	421	13	v	v	ADP
ejpam-5918	421	14	∈	∈	PROPN
ejpam-5918	421	15	s	s	NOUN
ejpam-5918	421	16	,	,	PUNCT
ejpam-5918	421	17	n(u	n(u	PROPN
ejpam-5918	421	18	)	)	PUNCT
ejpam-5918	421	19	∩	∩	PROPN
ejpam-5918	421	20	s	s	PART
ejpam-5918	421	21	̸=	̸=	PROPN
ejpam-5918	421	22	n(v	n(v	PROPN
ejpam-5918	421	23	)	)	PUNCT
ejpam-5918	421	24	∩	∩	PROPN
ejpam-5918	421	25	s.	s.	PROPN
ejpam-5918	421	26	hence	hence	ADV
ejpam-5918	421	27	,	,	PUNCT
ejpam-5918	421	28	s	s	VERB
ejpam-5918	421	29	is	be	AUX
ejpam-5918	421	30	an	an	DET
ejpam-5918	421	31	ilds	ild	NOUN
ejpam-5918	421	32	.	.	PUNCT
ejpam-5918	422	1	to	to	PART
ejpam-5918	422	2	end	end	VERB
ejpam-5918	422	3	this	this	PRON
ejpam-5918	422	4	,	,	PUNCT
ejpam-5918	422	5	note	note	VERB
ejpam-5918	422	6	that	that	SCONJ
ejpam-5918	422	7	|s|	|s|	NOUN
ejpam-5918	422	8	=	=	SYM
ejpam-5918	422	9	⌈4n7	⌈4n7	PRON
ejpam-5918	422	10	⌉.	⌉.	ADV
ejpam-5918	422	11	since	since	SCONJ
ejpam-5918	422	12	i	i	PRON
ejpam-5918	422	13	is	be	AUX
ejpam-5918	422	14	a	a	DET
ejpam-5918	422	15	γli	γli	ADJ
ejpam-5918	422	16	−	−	NOUN
ejpam-5918	422	17	set	set	NOUN
ejpam-5918	422	18	,	,	PUNCT
ejpam-5918	422	19	|s|	|s|	NOUN
ejpam-5918	422	20	≥	≥	NOUN
ejpam-5918	422	21	|i|	|i|	PROPN
ejpam-5918	422	22	.	.	PUNCT
ejpam-5918	423	1	so	so	ADV
ejpam-5918	423	2	,	,	PUNCT
ejpam-5918	423	3	|i|	|i|	VERB
ejpam-5918	423	4	≤	≤	NUM
ejpam-5918	423	5	|s|	|s|	PROPN
ejpam-5918	423	6	=	=	SYM
ejpam-5918	423	7	⌈4n7	⌈4n7	X
ejpam-5918	423	8	⌉.	⌉.	ADV
ejpam-5918	423	9	on	on	ADP
ejpam-5918	423	10	the	the	DET
ejpam-5918	423	11	other	other	ADJ
ejpam-5918	423	12	hand	hand	NOUN
ejpam-5918	423	13	,	,	PUNCT
ejpam-5918	423	14	since	since	SCONJ
ejpam-5918	423	15	i	i	PRON
ejpam-5918	423	16	is	be	AUX
ejpam-5918	423	17	a	a	DET
ejpam-5918	423	18	γli	γli	ADJ
ejpam-5918	423	19	−	−	NOUN
ejpam-5918	423	20	set	set	NOUN
ejpam-5918	423	21	of	of	ADP
ejpam-5918	423	22	t	t	PROPN
ejpam-5918	423	23	(	(	PUNCT
ejpam-5918	423	24	g	g	NOUN
ejpam-5918	423	25	)	)	PUNCT
ejpam-5918	423	26	,	,	PUNCT
ejpam-5918	423	27	then	then	ADV
ejpam-5918	423	28	i	i	PRON
ejpam-5918	423	29	must	must	AUX
ejpam-5918	423	30	have	have	AUX
ejpam-5918	423	31	atleast	atleast	VERB
ejpam-5918	423	32	⌈4n7	⌈4n7	NUM
ejpam-5918	423	33	⌉	⌉	X
ejpam-5918	423	34	vertices	vertice	VERB
ejpam-5918	423	35	in	in	ADP
ejpam-5918	423	36	t	t	PROPN
ejpam-5918	423	37	(	(	PUNCT
ejpam-5918	423	38	g	g	NOUN
ejpam-5918	423	39	)	)	PUNCT
ejpam-5918	423	40	.	.	PUNCT
ejpam-5918	424	1	hence	hence	ADV
ejpam-5918	424	2	,	,	PUNCT
ejpam-5918	424	3	|i|	|i|	VERB
ejpam-5918	424	4	≥	≥	NOUN
ejpam-5918	424	5	⌈4n7	⌈4n7	X
ejpam-5918	424	6	⌉.	⌉.	ADV
ejpam-5918	424	7	therefore	therefore	ADV
ejpam-5918	424	8	,	,	PUNCT
ejpam-5918	424	9	|i|	|i|	PROPN
ejpam-5918	424	10	=	=	SYM
ejpam-5918	424	11	⌈4n7	⌈4n7	ADP
ejpam-5918	424	12	⌉.	⌉.	ADJ
ejpam-5918	424	13	case	case	NOUN
ejpam-5918	424	14	7	7	NUM
ejpam-5918	424	15	:	:	PUNCT
ejpam-5918	424	16	n	n	NUM
ejpam-5918	424	17	≡	≡	PROPN
ejpam-5918	424	18	6	6	NUM
ejpam-5918	424	19	(	(	PUNCT
ejpam-5918	424	20	mod	mod	PROPN
ejpam-5918	424	21	7	7	NUM
ejpam-5918	424	22	)	)	PUNCT
ejpam-5918	424	23	.	.	PUNCT
ejpam-5918	425	1	let	let	VERB
ejpam-5918	425	2	s	s	PRON
ejpam-5918	425	3	⊆	⊆	NUM
ejpam-5918	425	4	v	v	NOUN
ejpam-5918	425	5	(	(	PUNCT
ejpam-5918	425	6	t	t	PROPN
ejpam-5918	425	7	(	(	PUNCT
ejpam-5918	425	8	g	g	NOUN
ejpam-5918	425	9	)	)	PUNCT
ejpam-5918	425	10	)	)	PUNCT
ejpam-5918	425	11	with	with	ADP
ejpam-5918	425	12	s	s	NOUN
ejpam-5918	425	13	=	=	PUNCT
ejpam-5918	425	14	{	{	PUNCT
ejpam-5918	425	15	v2	v2	PROPN
ejpam-5918	425	16	,	,	PUNCT
ejpam-5918	425	17	v3	v3	PROPN
ejpam-5918	425	18	,	,	PUNCT
ejpam-5918	425	19	v9	v9	PROPN
ejpam-5918	425	20	,	,	PUNCT
ejpam-5918	425	21	v10	v10	NOUN
ejpam-5918	425	22	,	,	PUNCT
ejpam-5918	425	23	.	.	PUNCT
ejpam-5918	425	24	.	.	PUNCT
ejpam-5918	426	1	.	.	PUNCT
ejpam-5918	427	1	,	,	PUNCT
ejpam-5918	427	2	vn−4	vn−4	NOUN
ejpam-5918	427	3	,	,	PUNCT
ejpam-5918	427	4	vn−3	vn−3	PROPN
ejpam-5918	427	5	}	}	PUNCT
ejpam-5918	427	6	∪	∪	NOUN
ejpam-5918	427	7	{	{	PUNCT
ejpam-5918	427	8	e5	e5	PROPN
ejpam-5918	427	9	,	,	PUNCT
ejpam-5918	427	10	e6	e6	PROPN
ejpam-5918	427	11	,	,	PUNCT
ejpam-5918	427	12	.	.	PUNCT
ejpam-5918	427	13	.	.	PUNCT
ejpam-5918	428	1	.	.	PUNCT
ejpam-5918	429	1	,	,	PUNCT
ejpam-5918	429	2	en−8	en−8	PROPN
ejpam-5918	429	3	,	,	PUNCT
ejpam-5918	429	4	en−7	en−7	PROPN
ejpam-5918	429	5	,	,	PUNCT
ejpam-5918	429	6	en−2	en−2	PROPN
ejpam-5918	429	7	,	,	PUNCT
ejpam-5918	429	8	en−1	en−1	PROPN
ejpam-5918	429	9	}	}	PUNCT
ejpam-5918	429	10	.	.	PUNCT
ejpam-5918	430	1	observe	observe	VERB
ejpam-5918	430	2	that	that	SCONJ
ejpam-5918	430	3	s	s	VERB
ejpam-5918	430	4	is	be	AUX
ejpam-5918	430	5	a	a	DET
ejpam-5918	430	6	dominating	dominating	NOUN
ejpam-5918	430	7	set	set	NOUN
ejpam-5918	430	8	and	and	CCONJ
ejpam-5918	430	9	for	for	ADP
ejpam-5918	430	10	all	all	DET
ejpam-5918	430	11	u	u	NOUN
ejpam-5918	430	12	,	,	PUNCT
ejpam-5918	430	13	v	v	ADP
ejpam-5918	430	14	∈	∈	PROPN
ejpam-5918	430	15	s	s	NOUN
ejpam-5918	430	16	,	,	PUNCT
ejpam-5918	430	17	n(u	n(u	PROPN
ejpam-5918	430	18	)	)	PUNCT
ejpam-5918	430	19	∩	∩	PROPN
ejpam-5918	430	20	s	s	PART
ejpam-5918	430	21	̸=	̸=	PROPN
ejpam-5918	430	22	n(v	n(v	PROPN
ejpam-5918	430	23	)	)	PUNCT
ejpam-5918	430	24	∩	∩	PROPN
ejpam-5918	430	25	s.	s.	PROPN
ejpam-5918	430	26	hence	hence	ADV
ejpam-5918	430	27	,	,	PUNCT
ejpam-5918	430	28	s	s	VERB
ejpam-5918	430	29	is	be	AUX
ejpam-5918	430	30	an	an	DET
ejpam-5918	430	31	ilds	ild	NOUN
ejpam-5918	430	32	.	.	PUNCT
ejpam-5918	431	1	to	to	PART
ejpam-5918	431	2	end	end	VERB
ejpam-5918	431	3	this	this	PRON
ejpam-5918	431	4	,	,	PUNCT
ejpam-5918	431	5	note	note	VERB
ejpam-5918	431	6	that	that	SCONJ
ejpam-5918	431	7	|s|	|s|	PROPN
ejpam-5918	431	8	=	=	SYM
ejpam-5918	431	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	431	10	⌋.	⌋.	NOUN
ejpam-5918	431	11	since	since	SCONJ
ejpam-5918	431	12	i	i	PRON
ejpam-5918	431	13	is	be	AUX
ejpam-5918	431	14	a	a	DET
ejpam-5918	431	15	γli	γli	ADJ
ejpam-5918	431	16	−	−	NOUN
ejpam-5918	431	17	set	set	NOUN
ejpam-5918	431	18	,	,	PUNCT
ejpam-5918	431	19	|s|	|s|	NOUN
ejpam-5918	431	20	≥	≥	NOUN
ejpam-5918	431	21	|i|	|i|	PROPN
ejpam-5918	431	22	.	.	PUNCT
ejpam-5918	432	1	so	so	ADV
ejpam-5918	432	2	,	,	PUNCT
ejpam-5918	432	3	|i|	|i|	VERB
ejpam-5918	432	4	≤	≤	NUM
ejpam-5918	432	5	|s|	|s|	PROPN
ejpam-5918	432	6	=	=	SYM
ejpam-5918	432	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	432	8	⌋.	⌋.	ADV
ejpam-5918	432	9	on	on	ADP
ejpam-5918	432	10	the	the	DET
ejpam-5918	432	11	other	other	ADJ
ejpam-5918	432	12	hand	hand	NOUN
ejpam-5918	432	13	,	,	PUNCT
ejpam-5918	432	14	since	since	SCONJ
ejpam-5918	432	15	i	i	PRON
ejpam-5918	432	16	is	be	AUX
ejpam-5918	432	17	a	a	DET
ejpam-5918	432	18	γli	γli	ADJ
ejpam-5918	432	19	−	−	NOUN
ejpam-5918	432	20	set	set	NOUN
ejpam-5918	432	21	of	of	ADP
ejpam-5918	432	22	t	t	PROPN
ejpam-5918	432	23	(	(	PUNCT
ejpam-5918	432	24	g	g	NOUN
ejpam-5918	432	25	)	)	PUNCT
ejpam-5918	432	26	,	,	PUNCT
ejpam-5918	432	27	then	then	ADV
ejpam-5918	432	28	i	i	PRON
ejpam-5918	432	29	must	must	AUX
ejpam-5918	432	30	have	have	VERB
ejpam-5918	432	31	atleast	atleast	VERB
ejpam-5918	432	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	432	33	⌋	⌋	NOUN
ejpam-5918	432	34	vertices	vertice	VERB
ejpam-5918	432	35	in	in	ADP
ejpam-5918	432	36	t	t	PROPN
ejpam-5918	432	37	(	(	PUNCT
ejpam-5918	432	38	g	g	NOUN
ejpam-5918	432	39	)	)	PUNCT
ejpam-5918	432	40	.	.	PUNCT
ejpam-5918	433	1	hence	hence	ADV
ejpam-5918	433	2	,	,	PUNCT
ejpam-5918	433	3	|i|	|i|	VERB
ejpam-5918	433	4	≥	≥	NOUN
ejpam-5918	433	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	433	6	⌋.	⌋.	PUNCT
ejpam-5918	434	1	therefore	therefore	ADV
ejpam-5918	434	2	,	,	PUNCT
ejpam-5918	434	3	|i|	|i|	PROPN
ejpam-5918	434	4	=	=	SYM
ejpam-5918	434	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	434	6	⌋.	⌋.	PROPN
ejpam-5918	434	7	i.	i.	PROPN
ejpam-5918	434	8	tropico	tropico	PROPN
ejpam-5918	434	9	,	,	PUNCT
ejpam-5918	434	10	i.	i.	PROPN
ejpam-5918	434	11	cabahug	cabahug	PROPN
ejpam-5918	434	12	,	,	PUNCT
ejpam-5918	434	13	jr	jr	PROPN
ejpam-5918	434	14	.	.	PROPN
ejpam-5918	434	15	/	/	SYM
ejpam-5918	434	16	eur	eur	PROPN
ejpam-5918	434	17	.	.	PUNCT
ejpam-5918	435	1	j.	j.	PROPN
ejpam-5918	435	2	pure	pure	PROPN
ejpam-5918	435	3	appl	appl	PROPN
ejpam-5918	435	4	.	.	PROPN
ejpam-5918	435	5	math	math	PROPN
ejpam-5918	435	6	,	,	PUNCT
ejpam-5918	435	7	18	18	NUM
ejpam-5918	435	8	(	(	PUNCT
ejpam-5918	435	9	2	2	NUM
ejpam-5918	435	10	)	)	PUNCT
ejpam-5918	435	11	(	(	PUNCT
ejpam-5918	435	12	2025	2025	NUM
ejpam-5918	435	13	)	)	PUNCT
ejpam-5918	435	14	,	,	PUNCT
ejpam-5918	435	15	5918	5918	NUM
ejpam-5918	435	16	14	14	NUM
ejpam-5918	435	17	of	of	ADP
ejpam-5918	435	18	21	21	NUM
ejpam-5918	435	19	example	example	NOUN
ejpam-5918	435	20	8	8	NUM
ejpam-5918	435	21	.	.	PUNCT
ejpam-5918	435	22	consider	consider	VERB
ejpam-5918	435	23	figure	figure	NOUN
ejpam-5918	435	24	7	7	NUM
ejpam-5918	435	25	.	.	PUNCT
ejpam-5918	436	1	clearly	clearly	ADV
ejpam-5918	436	2	i	i	PRON
ejpam-5918	436	3	=	=	PUNCT
ejpam-5918	436	4	{	{	PUNCT
ejpam-5918	436	5	v2	v2	PROPN
ejpam-5918	436	6	,	,	PUNCT
ejpam-5918	436	7	v3	v3	PROPN
ejpam-5918	436	8	,	,	PUNCT
ejpam-5918	436	9	e5	e5	PROPN
ejpam-5918	436	10	}	}	PUNCT
ejpam-5918	436	11	is	be	AUX
ejpam-5918	436	12	a	a	DET
ejpam-5918	436	13	dominating	dominating	NOUN
ejpam-5918	436	14	set	set	NOUN
ejpam-5918	436	15	.	.	PUNCT
ejpam-5918	437	1	observe	observe	VERB
ejpam-5918	437	2	that	that	SCONJ
ejpam-5918	437	3	,	,	PUNCT
ejpam-5918	437	4	n(v2	n(v2	NOUN
ejpam-5918	437	5	)	)	PUNCT
ejpam-5918	437	6	∩	∩	NOUN
ejpam-5918	437	7	i	i	PRON
ejpam-5918	437	8	=	=	SYM
ejpam-5918	437	9	{	{	PUNCT
ejpam-5918	437	10	v3	v3	PROPN
ejpam-5918	437	11	}	}	PUNCT
ejpam-5918	437	12	,	,	PUNCT
ejpam-5918	437	13	n(v3	n(v3	NOUN
ejpam-5918	437	14	)	)	PUNCT
ejpam-5918	437	15	∩	∩	NOUN
ejpam-5918	437	16	i	i	PRON
ejpam-5918	437	17	=	=	SYM
ejpam-5918	437	18	{	{	PUNCT
ejpam-5918	437	19	v2	v2	NOUN
ejpam-5918	437	20	}	}	PUNCT
ejpam-5918	437	21	,	,	PUNCT
ejpam-5918	437	22	and	and	CCONJ
ejpam-5918	437	23	n(e5	n(e5	NOUN
ejpam-5918	437	24	)	)	PUNCT
ejpam-5918	437	25	∩	∩	NOUN
ejpam-5918	437	26	i	i	PRON
ejpam-5918	437	27	=	=	PUNCT
ejpam-5918	437	28	∅.	∅.	VERB
ejpam-5918	437	29	hence	hence	ADV
ejpam-5918	437	30	,	,	PUNCT
ejpam-5918	437	31	i	i	PRON
ejpam-5918	437	32	is	be	AUX
ejpam-5918	437	33	an	an	DET
ejpam-5918	437	34	internallylocating	internallylocate	VERB
ejpam-5918	437	35	dominating	dominating	NOUN
ejpam-5918	437	36	set	set	NOUN
ejpam-5918	437	37	of	of	ADP
ejpam-5918	437	38	minimum	minimum	ADJ
ejpam-5918	437	39	cardinality	cardinality	NOUN
ejpam-5918	437	40	,	,	PUNCT
ejpam-5918	437	41	so	so	SCONJ
ejpam-5918	437	42	γli(t	γli(t	PROPN
ejpam-5918	437	43	(	(	PUNCT
ejpam-5918	437	44	p6	p6	PROPN
ejpam-5918	437	45	)	)	PUNCT
ejpam-5918	437	46	)	)	PUNCT
ejpam-5918	438	1	=	=	SYM
ejpam-5918	438	2	3	3	X
ejpam-5918	438	3	.	.	PUNCT
ejpam-5918	438	4	by	by	ADP
ejpam-5918	438	5	theorem	theorem	NOUN
ejpam-5918	438	6	9	9	NUM
ejpam-5918	438	7	,	,	PUNCT
ejpam-5918	438	8	for	for	ADP
ejpam-5918	438	9	n	n	NOUN
ejpam-5918	438	10	=	=	SYM
ejpam-5918	438	11	6	6	NUM
ejpam-5918	438	12	≡	≡	PROPN
ejpam-5918	438	13	6	6	NUM
ejpam-5918	438	14	(	(	PUNCT
ejpam-5918	438	15	mod	mod	PROPN
ejpam-5918	438	16	7	7	NUM
ejpam-5918	438	17	)	)	PUNCT
ejpam-5918	438	18	,	,	PUNCT
ejpam-5918	438	19	γli(t	γli(t	PROPN
ejpam-5918	438	20	(	(	PUNCT
ejpam-5918	438	21	p6	p6	PROPN
ejpam-5918	438	22	)	)	PUNCT
ejpam-5918	438	23	)	)	PUNCT
ejpam-5918	439	1	=	=	SYM
ejpam-5918	439	2	⌊4(n)7	⌊4(n)7	NOUN
ejpam-5918	439	3	⌋	⌋	NOUN
ejpam-5918	439	4	=	=	PUNCT
ejpam-5918	439	5	⌊4(6)7	⌊4(6)7	NOUN
ejpam-5918	439	6	⌋	⌋	NOUN
ejpam-5918	440	1	=	=	PUNCT
ejpam-5918	441	1	⌊247	⌊247	PROPN
ejpam-5918	442	1	⌋	⌋	NOUN
ejpam-5918	443	1	=	=	SYM
ejpam-5918	444	1	3	3	X
ejpam-5918	444	2	.	.	X
ejpam-5918	444	3	v1	v1	PROPN
ejpam-5918	444	4	v2	v2	PROPN
ejpam-5918	444	5	v3	v3	PROPN
ejpam-5918	444	6	v4	v4	PROPN
ejpam-5918	444	7	v5	v5	PROPN
ejpam-5918	444	8	v6	v6	PROPN
ejpam-5918	444	9	e1	e1	PROPN
ejpam-5918	444	10	e2	e2	PROPN
ejpam-5918	444	11	e3	e3	NOUN
ejpam-5918	444	12	e4	e4	PROPN
ejpam-5918	444	13	e5	e5	PROPN
ejpam-5918	444	14	t	t	PROPN
ejpam-5918	444	15	(	(	PUNCT
ejpam-5918	444	16	p6	p6	PROPN
ejpam-5918	444	17	):	):	PUNCT
ejpam-5918	444	18	figure	figure	NOUN
ejpam-5918	444	19	7	7	NUM
ejpam-5918	444	20	:	:	PUNCT
ejpam-5918	444	21	the	the	DET
ejpam-5918	444	22	minimum	minimum	NOUN
ejpam-5918	444	23	internally	internally	ADV
ejpam-5918	444	24	-	-	PUNCT
ejpam-5918	444	25	locating	locate	VERB
ejpam-5918	444	26	dominating	dominating	NOUN
ejpam-5918	444	27	set	set	NOUN
ejpam-5918	444	28	of	of	ADP
ejpam-5918	444	29	t	t	PROPN
ejpam-5918	444	30	(	(	PUNCT
ejpam-5918	444	31	p6	p6	PROPN
ejpam-5918	444	32	)	)	PUNCT
ejpam-5918	444	33	theorem	theorem	VERB
ejpam-5918	444	34	10	10	NUM
ejpam-5918	444	35	.	.	PUNCT
ejpam-5918	445	1	let	let	VERB
ejpam-5918	445	2	g	g	PRON
ejpam-5918	445	3	be	be	AUX
ejpam-5918	445	4	a	a	DET
ejpam-5918	445	5	cycle	cycle	NOUN
ejpam-5918	445	6	graph	graph	NOUN
ejpam-5918	445	7	cn	cn	VERB
ejpam-5918	445	8	with	with	ADP
ejpam-5918	445	9	n	n	NUM
ejpam-5918	445	10	≥	≥	NOUN
ejpam-5918	445	11	4	4	NUM
ejpam-5918	445	12	then	then	ADV
ejpam-5918	445	13	,	,	PUNCT
ejpam-5918	445	14	γli(t	γli(t	PROPN
ejpam-5918	445	15	(	(	PUNCT
ejpam-5918	445	16	g	g	NOUN
ejpam-5918	445	17	)	)	PUNCT
ejpam-5918	445	18	)	)	PUNCT
ejpam-5918	446	1	=	=	PUNCT
ejpam-5918	446	2			PROPN
ejpam-5918	446	3	4n	4n	VERB
ejpam-5918	446	4	7	7	NUM
ejpam-5918	446	5	if	if	SCONJ
ejpam-5918	446	6	n	n	PRON
ejpam-5918	446	7	≡	≡	PROPN
ejpam-5918	446	8	0	0	PUNCT
ejpam-5918	446	9	(	(	PUNCT
ejpam-5918	446	10	mod	mod	PROPN
ejpam-5918	446	11	7	7	NUM
ejpam-5918	446	12	)	)	PUNCT
ejpam-5918	446	13	⌈	⌈	NOUN
ejpam-5918	446	14	4n	4n	X
ejpam-5918	446	15	7	7	NUM
ejpam-5918	446	16	⌉	⌉	PROPN
ejpam-5918	446	17	if	if	SCONJ
ejpam-5918	446	18	n	n	PRON
ejpam-5918	446	19	≡	≡	PROPN
ejpam-5918	446	20	1	1	NUM
ejpam-5918	446	21	,	,	PUNCT
ejpam-5918	446	22	3	3	NUM
ejpam-5918	446	23	,	,	PUNCT
ejpam-5918	446	24	4	4	NUM
ejpam-5918	446	25	,	,	PUNCT
ejpam-5918	446	26	5	5	NUM
ejpam-5918	446	27	(	(	PUNCT
ejpam-5918	446	28	mod	mod	NOUN
ejpam-5918	446	29	7	7	NUM
ejpam-5918	446	30	)	)	PUNCT
ejpam-5918	446	31	⌊	⌊	ADP
ejpam-5918	446	32	4n	4n	VERB
ejpam-5918	446	33	7	7	NUM
ejpam-5918	446	34	⌋	⌋	NOUN
ejpam-5918	446	35	if	if	SCONJ
ejpam-5918	446	36	n	n	PRON
ejpam-5918	446	37	≡	≡	PROPN
ejpam-5918	446	38	2	2	NUM
ejpam-5918	446	39	,	,	PUNCT
ejpam-5918	446	40	6	6	NUM
ejpam-5918	446	41	(	(	PUNCT
ejpam-5918	446	42	mod	mod	ADJ
ejpam-5918	446	43	7	7	NUM
ejpam-5918	446	44	)	)	PUNCT
ejpam-5918	446	45	proof	proof	NOUN
ejpam-5918	446	46	.	.	PUNCT
ejpam-5918	447	1	letg	letg	NOUN
ejpam-5918	447	2	be	be	AUX
ejpam-5918	447	3	a	a	DET
ejpam-5918	447	4	cycle	cycle	NOUN
ejpam-5918	447	5	graph	graph	NOUN
ejpam-5918	447	6	of	of	ADP
ejpam-5918	447	7	order	order	NOUN
ejpam-5918	447	8	n	n	PRON
ejpam-5918	447	9	≥	≥	NOUN
ejpam-5918	447	10	4	4	NUM
ejpam-5918	447	11	and	and	CCONJ
ejpam-5918	447	12	t	t	PROPN
ejpam-5918	447	13	(	(	PUNCT
ejpam-5918	447	14	g	g	NOUN
ejpam-5918	447	15	)	)	PUNCT
ejpam-5918	447	16	be	be	AUX
ejpam-5918	447	17	a	a	DET
ejpam-5918	447	18	total	total	ADJ
ejpam-5918	447	19	graph	graph	NOUN
ejpam-5918	447	20	ofg	ofg	PROPN
ejpam-5918	447	21	.	.	PUNCT
ejpam-5918	448	1	for	for	ADP
ejpam-5918	448	2	convenience	convenience	NOUN
ejpam-5918	448	3	,	,	PUNCT
ejpam-5918	448	4	let	let	VERB
ejpam-5918	448	5	v	v	NOUN
ejpam-5918	448	6	(	(	PUNCT
ejpam-5918	448	7	g	g	NOUN
ejpam-5918	448	8	)	)	PUNCT
ejpam-5918	448	9	=	=	NOUN
ejpam-5918	448	10	v	v	X
ejpam-5918	448	11	(	(	PUNCT
ejpam-5918	448	12	cn	cn	PROPN
ejpam-5918	448	13	)	)	PUNCT
ejpam-5918	448	14	=	=	SYM
ejpam-5918	448	15	{	{	PUNCT
ejpam-5918	448	16	v1	v1	PROPN
ejpam-5918	448	17	,	,	PUNCT
ejpam-5918	448	18	v2	v2	PROPN
ejpam-5918	448	19	,	,	PUNCT
ejpam-5918	448	20	.	.	PUNCT
ejpam-5918	448	21	.	.	PUNCT
ejpam-5918	449	1	.	.	PUNCT
ejpam-5918	450	1	,	,	PUNCT
ejpam-5918	450	2	vn−1	vn−1	PROPN
ejpam-5918	450	3	,	,	PUNCT
ejpam-5918	450	4	vn	vn	NOUN
ejpam-5918	450	5	}	}	PUNCT
ejpam-5918	450	6	,	,	PUNCT
ejpam-5918	450	7	e(g	e(g	PROPN
ejpam-5918	450	8	)	)	PUNCT
ejpam-5918	450	9	=	=	SYM
ejpam-5918	450	10	e(cn	e(cn	NOUN
ejpam-5918	450	11	)	)	PUNCT
ejpam-5918	450	12	=	=	SYM
ejpam-5918	450	13	{	{	PUNCT
ejpam-5918	450	14	e1	e1	PROPN
ejpam-5918	450	15	,	,	PUNCT
ejpam-5918	450	16	e2	e2	PROPN
ejpam-5918	450	17	,	,	PUNCT
ejpam-5918	450	18	e3	e3	NOUN
ejpam-5918	450	19	.	.	PUNCT
ejpam-5918	450	20	.	.	PUNCT
ejpam-5918	450	21	.	.	PUNCT
ejpam-5918	451	1	,	,	PUNCT
ejpam-5918	451	2	en−1	en−1	PROPN
ejpam-5918	451	3	,	,	PUNCT
ejpam-5918	451	4	en	en	ADP
ejpam-5918	451	5	}	}	PUNCT
ejpam-5918	451	6	where	where	SCONJ
ejpam-5918	451	7	e1	e1	NOUN
ejpam-5918	451	8	is	be	AUX
ejpam-5918	451	9	the	the	DET
ejpam-5918	451	10	edge	edge	NOUN
ejpam-5918	451	11	incident	incident	NOUN
ejpam-5918	451	12	with	with	ADP
ejpam-5918	451	13	v1	v1	NOUN
ejpam-5918	451	14	and	and	CCONJ
ejpam-5918	451	15	v2	v2	PROPN
ejpam-5918	451	16	,	,	PUNCT
ejpam-5918	451	17	e2	e2	PROPN
ejpam-5918	451	18	is	be	AUX
ejpam-5918	451	19	the	the	DET
ejpam-5918	451	20	edge	edge	NOUN
ejpam-5918	451	21	incident	incident	NOUN
ejpam-5918	451	22	to	to	PART
ejpam-5918	451	23	v2	v2	VERB
ejpam-5918	451	24	and	and	CCONJ
ejpam-5918	451	25	v3	v3	PROPN
ejpam-5918	451	26	,	,	PUNCT
ejpam-5918	451	27	and	and	CCONJ
ejpam-5918	451	28	so	so	ADV
ejpam-5918	451	29	on	on	ADV
ejpam-5918	451	30	,	,	PUNCT
ejpam-5918	451	31	up	up	ADP
ejpam-5918	451	32	to	to	ADP
ejpam-5918	451	33	en	en	ADP
ejpam-5918	451	34	which	which	PRON
ejpam-5918	451	35	is	be	AUX
ejpam-5918	451	36	incident	incident	NOUN
ejpam-5918	451	37	with	with	ADP
ejpam-5918	451	38	v1	v1	NOUN
ejpam-5918	451	39	and	and	CCONJ
ejpam-5918	451	40	vn	vn	NOUN
ejpam-5918	451	41	.	.	PUNCT
ejpam-5918	452	1	by	by	ADP
ejpam-5918	452	2	definition	definition	NOUN
ejpam-5918	452	3	of	of	ADP
ejpam-5918	452	4	total	total	ADJ
ejpam-5918	452	5	graph	graph	NOUN
ejpam-5918	452	6	,	,	PUNCT
ejpam-5918	452	7	v	v	NOUN
ejpam-5918	452	8	(	(	PUNCT
ejpam-5918	452	9	t	t	PROPN
ejpam-5918	452	10	(	(	PUNCT
ejpam-5918	452	11	g	g	NOUN
ejpam-5918	452	12	)	)	PUNCT
ejpam-5918	452	13	)	)	PUNCT
ejpam-5918	453	1	=	=	SYM
ejpam-5918	453	2	v	v	X
ejpam-5918	453	3	(	(	PUNCT
ejpam-5918	453	4	g	g	NOUN
ejpam-5918	453	5	)	)	PUNCT
ejpam-5918	453	6	∪	∪	ADP
ejpam-5918	453	7	e(g	e(g	PROPN
ejpam-5918	453	8	)	)	PUNCT
ejpam-5918	453	9	.	.	PUNCT
ejpam-5918	454	1	suppose	suppose	VERB
ejpam-5918	454	2	i	i	PRON
ejpam-5918	454	3	is	be	AUX
ejpam-5918	454	4	an	an	DET
ejpam-5918	454	5	internally	internally	ADV
ejpam-5918	454	6	-	-	PUNCT
ejpam-5918	454	7	locating	locate	VERB
ejpam-5918	454	8	dominating	dominating	NOUN
ejpam-5918	454	9	set	set	NOUN
ejpam-5918	454	10	of	of	ADP
ejpam-5918	454	11	minimum	minimum	ADJ
ejpam-5918	454	12	cardinality	cardinality	NOUN
ejpam-5918	454	13	,	,	PUNCT
ejpam-5918	454	14	i.e.	i.e.	X
ejpam-5918	454	15	,	,	PUNCT
ejpam-5918	454	16	i	i	PRON
ejpam-5918	454	17	is	be	AUX
ejpam-5918	454	18	a	a	DET
ejpam-5918	454	19	γli	γli	ADJ
ejpam-5918	454	20	−	−	NOUN
ejpam-5918	454	21	set	set	NOUN
ejpam-5918	454	22	.	.	PUNCT
ejpam-5918	455	1	now	now	ADV
ejpam-5918	455	2	,	,	PUNCT
ejpam-5918	455	3	consider	consider	VERB
ejpam-5918	455	4	the	the	DET
ejpam-5918	455	5	following	follow	VERB
ejpam-5918	455	6	cases	case	NOUN
ejpam-5918	455	7	:	:	PUNCT
ejpam-5918	455	8	case	case	NOUN
ejpam-5918	455	9	1	1	NUM
ejpam-5918	455	10	:	:	PUNCT
ejpam-5918	455	11	n	n	NUM
ejpam-5918	455	12	≡	≡	PROPN
ejpam-5918	455	13	0	0	PUNCT
ejpam-5918	456	1	(	(	PUNCT
ejpam-5918	456	2	mod	mod	PROPN
ejpam-5918	456	3	7	7	NUM
ejpam-5918	456	4	)	)	PUNCT
ejpam-5918	456	5	.	.	PUNCT
ejpam-5918	457	1	let	let	VERB
ejpam-5918	457	2	s	s	PRON
ejpam-5918	457	3	⊆	⊆	NUM
ejpam-5918	457	4	v	v	NOUN
ejpam-5918	457	5	(	(	PUNCT
ejpam-5918	457	6	t	t	PROPN
ejpam-5918	457	7	(	(	PUNCT
ejpam-5918	457	8	g	g	NOUN
ejpam-5918	457	9	)	)	PUNCT
ejpam-5918	457	10	)	)	PUNCT
ejpam-5918	457	11	with	with	ADP
ejpam-5918	457	12	s	s	NOUN
ejpam-5918	457	13	=	=	PUNCT
ejpam-5918	457	14	{	{	PUNCT
ejpam-5918	457	15	v2	v2	PROPN
ejpam-5918	457	16	,	,	PUNCT
ejpam-5918	457	17	v3	v3	PROPN
ejpam-5918	457	18	,	,	PUNCT
ejpam-5918	457	19	v9	v9	PROPN
ejpam-5918	457	20	,	,	PUNCT
ejpam-5918	457	21	v10	v10	NOUN
ejpam-5918	457	22	,	,	PUNCT
ejpam-5918	457	23	.	.	PUNCT
ejpam-5918	457	24	.	.	PUNCT
ejpam-5918	458	1	.	.	PUNCT
ejpam-5918	459	1	,	,	PUNCT
ejpam-5918	459	2	vn−5	vn−5	NOUN
ejpam-5918	459	3	,	,	PUNCT
ejpam-5918	459	4	vn−4	vn−4	NOUN
ejpam-5918	459	5	}	}	PUNCT
ejpam-5918	459	6	∪	∪	NOUN
ejpam-5918	459	7	{	{	PUNCT
ejpam-5918	459	8	e5	e5	PROPN
ejpam-5918	459	9	,	,	PUNCT
ejpam-5918	459	10	e6	e6	PROPN
ejpam-5918	459	11	,	,	PUNCT
ejpam-5918	459	12	e12	e12	NOUN
ejpam-5918	459	13	,	,	PUNCT
ejpam-5918	459	14	e13	e13	PROPN
ejpam-5918	459	15	,	,	PUNCT
ejpam-5918	459	16	.	.	PUNCT
ejpam-5918	459	17	.	.	PUNCT
ejpam-5918	460	1	.	.	PUNCT
ejpam-5918	461	1	,	,	PUNCT
ejpam-5918	461	2	en−9	en−9	NOUN
ejpam-5918	461	3	,	,	PUNCT
ejpam-5918	461	4	en−8	en−8	PROPN
ejpam-5918	461	5	,	,	PUNCT
ejpam-5918	461	6	en−2	en−2	PROPN
ejpam-5918	461	7	,	,	PUNCT
ejpam-5918	461	8	en−1	en−1	PROPN
ejpam-5918	461	9	}	}	PUNCT
ejpam-5918	461	10	.	.	PUNCT
ejpam-5918	462	1	observe	observe	VERB
ejpam-5918	462	2	that	that	SCONJ
ejpam-5918	462	3	s	s	VERB
ejpam-5918	462	4	is	be	AUX
ejpam-5918	462	5	a	a	DET
ejpam-5918	462	6	dominating	dominating	NOUN
ejpam-5918	462	7	set	set	NOUN
ejpam-5918	462	8	and	and	CCONJ
ejpam-5918	462	9	for	for	ADP
ejpam-5918	462	10	all	all	DET
ejpam-5918	462	11	u	u	NOUN
ejpam-5918	462	12	,	,	PUNCT
ejpam-5918	462	13	v	v	ADP
ejpam-5918	462	14	∈	∈	PROPN
ejpam-5918	462	15	s	s	NOUN
ejpam-5918	462	16	,	,	PUNCT
ejpam-5918	462	17	n(u	n(u	PROPN
ejpam-5918	462	18	)	)	PUNCT
ejpam-5918	462	19	∩	∩	PROPN
ejpam-5918	462	20	s	s	PART
ejpam-5918	462	21	̸=	̸=	PROPN
ejpam-5918	462	22	n(v	n(v	PROPN
ejpam-5918	462	23	)	)	PUNCT
ejpam-5918	462	24	∩	∩	PROPN
ejpam-5918	462	25	s.	s.	PROPN
ejpam-5918	462	26	hence	hence	ADV
ejpam-5918	462	27	,	,	PUNCT
ejpam-5918	462	28	s	s	VERB
ejpam-5918	462	29	is	be	AUX
ejpam-5918	462	30	an	an	DET
ejpam-5918	462	31	ilds	ild	NOUN
ejpam-5918	462	32	.	.	PUNCT
ejpam-5918	463	1	to	to	PART
ejpam-5918	463	2	end	end	VERB
ejpam-5918	463	3	this	this	PRON
ejpam-5918	463	4	,	,	PUNCT
ejpam-5918	463	5	note	note	VERB
ejpam-5918	463	6	that	that	SCONJ
ejpam-5918	463	7	|s|	|s|	NOUN
ejpam-5918	463	8	=	=	NOUN
ejpam-5918	463	9	4n	4n	X
ejpam-5918	463	10	7	7	NUM
ejpam-5918	463	11	.	.	PUNCT
ejpam-5918	464	1	since	since	SCONJ
ejpam-5918	464	2	i	i	PRON
ejpam-5918	464	3	is	be	AUX
ejpam-5918	464	4	a	a	DET
ejpam-5918	464	5	γli	γli	ADJ
ejpam-5918	464	6	−	−	NOUN
ejpam-5918	464	7	set	set	NOUN
ejpam-5918	464	8	,	,	PUNCT
ejpam-5918	464	9	|s|	|s|	NOUN
ejpam-5918	464	10	≥	≥	NOUN
ejpam-5918	464	11	|i|	|i|	PROPN
ejpam-5918	464	12	.	.	PUNCT
ejpam-5918	465	1	so	so	ADV
ejpam-5918	465	2	,	,	PUNCT
ejpam-5918	465	3	|i|	|i|	VERB
ejpam-5918	465	4	≤	≤	NUM
ejpam-5918	465	5	|s|	|s|	NOUN
ejpam-5918	465	6	=	=	NOUN
ejpam-5918	465	7	4n	4n	X
ejpam-5918	465	8	7	7	NUM
ejpam-5918	465	9	.	.	PUNCT
ejpam-5918	466	1	on	on	ADP
ejpam-5918	466	2	the	the	DET
ejpam-5918	466	3	other	other	ADJ
ejpam-5918	466	4	hand	hand	NOUN
ejpam-5918	466	5	,	,	PUNCT
ejpam-5918	466	6	since	since	SCONJ
ejpam-5918	466	7	i	i	PRON
ejpam-5918	466	8	is	be	AUX
ejpam-5918	466	9	a	a	DET
ejpam-5918	466	10	γli	γli	ADJ
ejpam-5918	466	11	−	−	NOUN
ejpam-5918	466	12	set	set	NOUN
ejpam-5918	466	13	of	of	ADP
ejpam-5918	466	14	t	t	PROPN
ejpam-5918	466	15	(	(	PUNCT
ejpam-5918	466	16	g	g	NOUN
ejpam-5918	466	17	)	)	PUNCT
ejpam-5918	466	18	,	,	PUNCT
ejpam-5918	466	19	then	then	ADV
ejpam-5918	466	20	i	i	PRON
ejpam-5918	466	21	must	must	AUX
ejpam-5918	466	22	have	have	AUX
ejpam-5918	466	23	atleast	atleast	VERB
ejpam-5918	466	24	4n	4n	VERB
ejpam-5918	466	25	7	7	NUM
ejpam-5918	466	26	vertices	vertex	NOUN
ejpam-5918	466	27	in	in	ADP
ejpam-5918	466	28	t	t	PROPN
ejpam-5918	466	29	(	(	PUNCT
ejpam-5918	466	30	g	g	NOUN
ejpam-5918	466	31	)	)	PUNCT
ejpam-5918	466	32	.	.	PUNCT
ejpam-5918	467	1	hence	hence	ADV
ejpam-5918	467	2	,	,	PUNCT
ejpam-5918	467	3	|i|	|i|	VERB
ejpam-5918	467	4	≥	≥	NOUN
ejpam-5918	467	5	4n	4n	X
ejpam-5918	467	6	7	7	NUM
ejpam-5918	467	7	.	.	PUNCT
ejpam-5918	468	1	therefore	therefore	ADV
ejpam-5918	468	2	,	,	PUNCT
ejpam-5918	468	3	|i|	|i|	ADP
ejpam-5918	468	4	=	=	SYM
ejpam-5918	468	5	4n	4n	X
ejpam-5918	468	6	7	7	NUM
ejpam-5918	468	7	.	.	PUNCT
ejpam-5918	468	8	case	case	NOUN
ejpam-5918	468	9	2	2	NUM
ejpam-5918	468	10	:	:	PUNCT
ejpam-5918	468	11	n	n	NUM
ejpam-5918	468	12	≡	≡	PROPN
ejpam-5918	468	13	1	1	NUM
ejpam-5918	468	14	(	(	PUNCT
ejpam-5918	468	15	mod	mod	PROPN
ejpam-5918	468	16	7	7	NUM
ejpam-5918	468	17	)	)	PUNCT
ejpam-5918	468	18	.	.	PUNCT
ejpam-5918	469	1	let	let	VERB
ejpam-5918	469	2	s	s	PRON
ejpam-5918	469	3	⊆	⊆	NUM
ejpam-5918	469	4	v	v	NOUN
ejpam-5918	469	5	(	(	PUNCT
ejpam-5918	469	6	t	t	PROPN
ejpam-5918	469	7	(	(	PUNCT
ejpam-5918	469	8	g	g	NOUN
ejpam-5918	469	9	)	)	PUNCT
ejpam-5918	469	10	)	)	PUNCT
ejpam-5918	469	11	with	with	ADP
ejpam-5918	469	12	i.	i.	PROPN
ejpam-5918	469	13	tropico	tropico	PROPN
ejpam-5918	469	14	,	,	PUNCT
ejpam-5918	469	15	i.	i.	PROPN
ejpam-5918	469	16	cabahug	cabahug	PROPN
ejpam-5918	469	17	,	,	PUNCT
ejpam-5918	469	18	jr	jr	PROPN
ejpam-5918	469	19	.	.	PROPN
ejpam-5918	469	20	/	/	SYM
ejpam-5918	469	21	eur	eur	PROPN
ejpam-5918	469	22	.	.	PUNCT
ejpam-5918	470	1	j.	j.	PROPN
ejpam-5918	470	2	pure	pure	PROPN
ejpam-5918	470	3	appl	appl	PROPN
ejpam-5918	470	4	.	.	PROPN
ejpam-5918	470	5	math	math	PROPN
ejpam-5918	470	6	,	,	PUNCT
ejpam-5918	470	7	18	18	NUM
ejpam-5918	470	8	(	(	PUNCT
ejpam-5918	470	9	2	2	NUM
ejpam-5918	470	10	)	)	PUNCT
ejpam-5918	470	11	(	(	PUNCT
ejpam-5918	470	12	2025	2025	NUM
ejpam-5918	470	13	)	)	PUNCT
ejpam-5918	470	14	,	,	PUNCT
ejpam-5918	470	15	5918	5918	NUM
ejpam-5918	470	16	15	15	NUM
ejpam-5918	470	17	of	of	ADP
ejpam-5918	470	18	21	21	NUM
ejpam-5918	470	19	s	s	NOUN
ejpam-5918	470	20	=	=	PUNCT
ejpam-5918	470	21	{	{	PUNCT
ejpam-5918	470	22	v2	v2	PROPN
ejpam-5918	470	23	,	,	PUNCT
ejpam-5918	470	24	v3	v3	PROPN
ejpam-5918	470	25	,	,	PUNCT
ejpam-5918	470	26	v9	v9	PROPN
ejpam-5918	470	27	,	,	PUNCT
ejpam-5918	470	28	v10	v10	NOUN
ejpam-5918	470	29	,	,	PUNCT
ejpam-5918	470	30	.	.	PUNCT
ejpam-5918	470	31	.	.	PUNCT
ejpam-5918	470	32	.	.	PUNCT
ejpam-5918	471	1	,	,	PUNCT
ejpam-5918	471	2	vn	vn	VERB
ejpam-5918	471	3	}	}	PUNCT
ejpam-5918	471	4	∪	∪	NOUN
ejpam-5918	471	5	{	{	PUNCT
ejpam-5918	471	6	e5	e5	PROPN
ejpam-5918	471	7	,	,	PUNCT
ejpam-5918	471	8	e6	e6	PROPN
ejpam-5918	471	9	,	,	PUNCT
ejpam-5918	471	10	e11	e11	X
ejpam-5918	471	11	,	,	PUNCT
ejpam-5918	471	12	e12	e12	NOUN
ejpam-5918	471	13	,	,	PUNCT
ejpam-5918	471	14	.	.	PUNCT
ejpam-5918	471	15	.	.	PUNCT
ejpam-5918	472	1	.	.	PUNCT
ejpam-5918	473	1	,	,	PUNCT
ejpam-5918	473	2	en−10	en−10	PROPN
ejpam-5918	473	3	,	,	PUNCT
ejpam-5918	473	4	en−9	en−9	NOUN
ejpam-5918	473	5	,	,	PUNCT
ejpam-5918	473	6	en−3	en−3	PROPN
ejpam-5918	473	7	,	,	PUNCT
ejpam-5918	473	8	en−2	en−2	PROPN
ejpam-5918	473	9	}	}	PUNCT
ejpam-5918	473	10	.	.	PUNCT
ejpam-5918	474	1	observe	observe	VERB
ejpam-5918	474	2	that	that	SCONJ
ejpam-5918	474	3	s	s	VERB
ejpam-5918	474	4	is	be	AUX
ejpam-5918	474	5	a	a	DET
ejpam-5918	474	6	dominating	dominating	NOUN
ejpam-5918	474	7	set	set	NOUN
ejpam-5918	474	8	and	and	CCONJ
ejpam-5918	474	9	for	for	ADP
ejpam-5918	474	10	all	all	DET
ejpam-5918	474	11	u	u	NOUN
ejpam-5918	474	12	,	,	PUNCT
ejpam-5918	474	13	v	v	ADP
ejpam-5918	474	14	∈	∈	PROPN
ejpam-5918	474	15	s	s	NOUN
ejpam-5918	474	16	,	,	PUNCT
ejpam-5918	474	17	n(u	n(u	PROPN
ejpam-5918	474	18	)	)	PUNCT
ejpam-5918	474	19	∩	∩	PROPN
ejpam-5918	474	20	s	s	PART
ejpam-5918	474	21	̸=	̸=	PROPN
ejpam-5918	474	22	n(v	n(v	PROPN
ejpam-5918	474	23	)	)	PUNCT
ejpam-5918	474	24	∩	∩	PROPN
ejpam-5918	474	25	s.	s.	PROPN
ejpam-5918	474	26	hence	hence	ADV
ejpam-5918	474	27	,	,	PUNCT
ejpam-5918	474	28	s	s	VERB
ejpam-5918	474	29	is	be	AUX
ejpam-5918	474	30	an	an	DET
ejpam-5918	474	31	ilds	ild	NOUN
ejpam-5918	474	32	.	.	PUNCT
ejpam-5918	475	1	to	to	PART
ejpam-5918	475	2	end	end	VERB
ejpam-5918	475	3	this	this	PRON
ejpam-5918	475	4	,	,	PUNCT
ejpam-5918	475	5	note	note	VERB
ejpam-5918	475	6	that	that	SCONJ
ejpam-5918	475	7	|s|	|s|	NOUN
ejpam-5918	475	8	=	=	SYM
ejpam-5918	475	9	⌈4n7	⌈4n7	PRON
ejpam-5918	475	10	⌉.	⌉.	ADV
ejpam-5918	475	11	since	since	SCONJ
ejpam-5918	475	12	i	i	PRON
ejpam-5918	475	13	is	be	AUX
ejpam-5918	475	14	a	a	DET
ejpam-5918	475	15	γli	γli	ADJ
ejpam-5918	475	16	−	−	NOUN
ejpam-5918	475	17	set	set	NOUN
ejpam-5918	475	18	,	,	PUNCT
ejpam-5918	475	19	|s|	|s|	NOUN
ejpam-5918	475	20	≥	≥	NOUN
ejpam-5918	475	21	|i|	|i|	PROPN
ejpam-5918	475	22	.	.	PUNCT
ejpam-5918	476	1	so	so	ADV
ejpam-5918	476	2	,	,	PUNCT
ejpam-5918	476	3	|i|	|i|	VERB
ejpam-5918	476	4	≤	≤	NUM
ejpam-5918	476	5	|s|	|s|	PROPN
ejpam-5918	476	6	=	=	SYM
ejpam-5918	476	7	⌈4n7	⌈4n7	X
ejpam-5918	476	8	⌉.	⌉.	ADV
ejpam-5918	476	9	on	on	ADP
ejpam-5918	476	10	the	the	DET
ejpam-5918	476	11	other	other	ADJ
ejpam-5918	476	12	hand	hand	NOUN
ejpam-5918	476	13	,	,	PUNCT
ejpam-5918	476	14	since	since	SCONJ
ejpam-5918	476	15	i	i	PRON
ejpam-5918	476	16	is	be	AUX
ejpam-5918	476	17	a	a	DET
ejpam-5918	476	18	γli	γli	ADJ
ejpam-5918	476	19	−	−	NOUN
ejpam-5918	476	20	set	set	NOUN
ejpam-5918	476	21	of	of	ADP
ejpam-5918	476	22	t	t	PROPN
ejpam-5918	476	23	(	(	PUNCT
ejpam-5918	476	24	g	g	NOUN
ejpam-5918	476	25	)	)	PUNCT
ejpam-5918	476	26	,	,	PUNCT
ejpam-5918	476	27	then	then	ADV
ejpam-5918	476	28	i	i	PRON
ejpam-5918	476	29	must	must	AUX
ejpam-5918	476	30	have	have	AUX
ejpam-5918	476	31	atleast	atleast	VERB
ejpam-5918	476	32	⌈4n7	⌈4n7	NUM
ejpam-5918	476	33	⌉	⌉	X
ejpam-5918	476	34	vertices	vertice	VERB
ejpam-5918	476	35	in	in	ADP
ejpam-5918	476	36	t	t	PROPN
ejpam-5918	476	37	(	(	PUNCT
ejpam-5918	476	38	g	g	NOUN
ejpam-5918	476	39	)	)	PUNCT
ejpam-5918	476	40	.	.	PUNCT
ejpam-5918	477	1	hence	hence	ADV
ejpam-5918	477	2	,	,	PUNCT
ejpam-5918	477	3	|i|	|i|	VERB
ejpam-5918	477	4	≥	≥	NOUN
ejpam-5918	477	5	⌈4n7	⌈4n7	X
ejpam-5918	477	6	⌉.	⌉.	ADV
ejpam-5918	477	7	therefore	therefore	ADV
ejpam-5918	477	8	,	,	PUNCT
ejpam-5918	477	9	|i|	|i|	PROPN
ejpam-5918	477	10	=	=	SYM
ejpam-5918	477	11	⌈4n7	⌈4n7	ADP
ejpam-5918	477	12	⌉.	⌉.	ADJ
ejpam-5918	477	13	case	case	NOUN
ejpam-5918	477	14	3	3	NUM
ejpam-5918	477	15	:	:	PUNCT
ejpam-5918	477	16	n	n	NUM
ejpam-5918	477	17	≡	≡	PROPN
ejpam-5918	477	18	2	2	NUM
ejpam-5918	477	19	(	(	PUNCT
ejpam-5918	477	20	mod	mod	PROPN
ejpam-5918	477	21	7	7	NUM
ejpam-5918	477	22	)	)	PUNCT
ejpam-5918	477	23	.	.	PUNCT
ejpam-5918	478	1	let	let	VERB
ejpam-5918	478	2	s	s	PRON
ejpam-5918	478	3	⊆	⊆	NUM
ejpam-5918	478	4	v	v	NOUN
ejpam-5918	478	5	(	(	PUNCT
ejpam-5918	478	6	t	t	PROPN
ejpam-5918	478	7	(	(	PUNCT
ejpam-5918	478	8	g	g	NOUN
ejpam-5918	478	9	)	)	PUNCT
ejpam-5918	478	10	)	)	PUNCT
ejpam-5918	478	11	with	with	ADP
ejpam-5918	478	12	s	s	NOUN
ejpam-5918	478	13	=	=	PUNCT
ejpam-5918	478	14	{	{	PUNCT
ejpam-5918	478	15	v2	v2	PROPN
ejpam-5918	478	16	,	,	PUNCT
ejpam-5918	478	17	v3	v3	PROPN
ejpam-5918	478	18	,	,	PUNCT
ejpam-5918	478	19	v9	v9	PROPN
ejpam-5918	478	20	,	,	PUNCT
ejpam-5918	478	21	v10	v10	NOUN
ejpam-5918	478	22	,	,	PUNCT
ejpam-5918	478	23	.	.	PUNCT
ejpam-5918	478	24	.	.	PUNCT
ejpam-5918	479	1	.	.	PUNCT
ejpam-5918	480	1	,	,	PUNCT
ejpam-5918	480	2	vn	vn	VERB
ejpam-5918	480	3	}	}	PUNCT
ejpam-5918	480	4	∪	∪	NOUN
ejpam-5918	480	5	{	{	PUNCT
ejpam-5918	480	6	e5	e5	PROPN
ejpam-5918	480	7	,	,	PUNCT
ejpam-5918	480	8	e6	e6	PROPN
ejpam-5918	480	9	,	,	PUNCT
ejpam-5918	480	10	e12	e12	NOUN
ejpam-5918	480	11	,	,	PUNCT
ejpam-5918	480	12	e13	e13	PROPN
ejpam-5918	480	13	,	,	PUNCT
ejpam-5918	480	14	.	.	PUNCT
ejpam-5918	480	15	.	.	PUNCT
ejpam-5918	481	1	.	.	PUNCT
ejpam-5918	482	1	,	,	PUNCT
ejpam-5918	482	2	en−11	en−11	PROPN
ejpam-5918	482	3	,	,	PUNCT
ejpam-5918	482	4	en−10	en−10	PROPN
ejpam-5918	482	5	,	,	PUNCT
ejpam-5918	482	6	en−4	en−4	NOUN
ejpam-5918	482	7	,	,	PUNCT
ejpam-5918	482	8	en−3	en−3	PROPN
ejpam-5918	482	9	}	}	PUNCT
ejpam-5918	482	10	.	.	PUNCT
ejpam-5918	483	1	observe	observe	VERB
ejpam-5918	483	2	that	that	SCONJ
ejpam-5918	483	3	s	s	VERB
ejpam-5918	483	4	is	be	AUX
ejpam-5918	483	5	a	a	DET
ejpam-5918	483	6	dominating	dominating	NOUN
ejpam-5918	483	7	set	set	NOUN
ejpam-5918	483	8	and	and	CCONJ
ejpam-5918	483	9	for	for	ADP
ejpam-5918	483	10	all	all	DET
ejpam-5918	483	11	u	u	NOUN
ejpam-5918	483	12	,	,	PUNCT
ejpam-5918	483	13	v	v	ADP
ejpam-5918	483	14	∈	∈	PROPN
ejpam-5918	483	15	s	s	NOUN
ejpam-5918	483	16	,	,	PUNCT
ejpam-5918	483	17	n(u	n(u	PROPN
ejpam-5918	483	18	)	)	PUNCT
ejpam-5918	483	19	∩	∩	PROPN
ejpam-5918	483	20	s	s	PART
ejpam-5918	483	21	̸=	̸=	PROPN
ejpam-5918	483	22	n(v	n(v	PROPN
ejpam-5918	483	23	)	)	PUNCT
ejpam-5918	483	24	∩	∩	PROPN
ejpam-5918	483	25	s.	s.	PROPN
ejpam-5918	483	26	hence	hence	ADV
ejpam-5918	483	27	,	,	PUNCT
ejpam-5918	483	28	s	s	VERB
ejpam-5918	483	29	is	be	AUX
ejpam-5918	483	30	an	an	DET
ejpam-5918	483	31	ilds	ild	NOUN
ejpam-5918	483	32	.	.	PUNCT
ejpam-5918	484	1	to	to	PART
ejpam-5918	484	2	end	end	VERB
ejpam-5918	484	3	this	this	PRON
ejpam-5918	484	4	,	,	PUNCT
ejpam-5918	484	5	note	note	VERB
ejpam-5918	484	6	that	that	SCONJ
ejpam-5918	484	7	|s|	|s|	PROPN
ejpam-5918	484	8	=	=	SYM
ejpam-5918	484	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	484	10	⌋.	⌋.	NOUN
ejpam-5918	484	11	since	since	SCONJ
ejpam-5918	484	12	i	i	PRON
ejpam-5918	484	13	is	be	AUX
ejpam-5918	484	14	a	a	DET
ejpam-5918	484	15	γli	γli	ADJ
ejpam-5918	484	16	−	−	NOUN
ejpam-5918	484	17	set	set	NOUN
ejpam-5918	484	18	,	,	PUNCT
ejpam-5918	484	19	|s|	|s|	NOUN
ejpam-5918	484	20	≥	≥	NOUN
ejpam-5918	484	21	|i|	|i|	PROPN
ejpam-5918	484	22	.	.	PUNCT
ejpam-5918	485	1	so	so	ADV
ejpam-5918	485	2	,	,	PUNCT
ejpam-5918	485	3	|i|	|i|	VERB
ejpam-5918	485	4	≤	≤	NUM
ejpam-5918	485	5	|s|	|s|	PROPN
ejpam-5918	485	6	=	=	SYM
ejpam-5918	485	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	485	8	⌋.	⌋.	ADV
ejpam-5918	485	9	on	on	ADP
ejpam-5918	485	10	the	the	DET
ejpam-5918	485	11	other	other	ADJ
ejpam-5918	485	12	hand	hand	NOUN
ejpam-5918	485	13	,	,	PUNCT
ejpam-5918	485	14	since	since	SCONJ
ejpam-5918	485	15	i	i	PRON
ejpam-5918	485	16	is	be	AUX
ejpam-5918	485	17	a	a	DET
ejpam-5918	485	18	γli	γli	ADJ
ejpam-5918	485	19	−	−	NOUN
ejpam-5918	485	20	set	set	NOUN
ejpam-5918	485	21	of	of	ADP
ejpam-5918	485	22	t	t	PROPN
ejpam-5918	485	23	(	(	PUNCT
ejpam-5918	485	24	g	g	NOUN
ejpam-5918	485	25	)	)	PUNCT
ejpam-5918	485	26	,	,	PUNCT
ejpam-5918	485	27	then	then	ADV
ejpam-5918	485	28	i	i	PRON
ejpam-5918	485	29	must	must	AUX
ejpam-5918	485	30	have	have	VERB
ejpam-5918	485	31	atleast	atleast	VERB
ejpam-5918	485	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	485	33	⌋	⌋	NOUN
ejpam-5918	485	34	vertices	vertice	VERB
ejpam-5918	485	35	in	in	ADP
ejpam-5918	485	36	t	t	PROPN
ejpam-5918	485	37	(	(	PUNCT
ejpam-5918	485	38	g	g	NOUN
ejpam-5918	485	39	)	)	PUNCT
ejpam-5918	485	40	.	.	PUNCT
ejpam-5918	486	1	hence	hence	ADV
ejpam-5918	486	2	,	,	PUNCT
ejpam-5918	486	3	|i|	|i|	VERB
ejpam-5918	486	4	≥	≥	NOUN
ejpam-5918	486	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	486	6	⌋.	⌋.	PUNCT
ejpam-5918	487	1	therefore	therefore	ADV
ejpam-5918	487	2	,	,	PUNCT
ejpam-5918	487	3	|i|	|i|	PROPN
ejpam-5918	487	4	=	=	SYM
ejpam-5918	487	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	487	6	⌋.	⌋.	NOUN
ejpam-5918	487	7	case	case	NOUN
ejpam-5918	487	8	4	4	NUM
ejpam-5918	487	9	:	:	PUNCT
ejpam-5918	487	10	n	n	NUM
ejpam-5918	487	11	≡	≡	PROPN
ejpam-5918	487	12	3	3	NUM
ejpam-5918	487	13	(	(	PUNCT
ejpam-5918	487	14	mod	mod	PROPN
ejpam-5918	487	15	7	7	NUM
ejpam-5918	487	16	)	)	PUNCT
ejpam-5918	487	17	.	.	PUNCT
ejpam-5918	488	1	let	let	VERB
ejpam-5918	488	2	s	s	PRON
ejpam-5918	488	3	⊆	⊆	NUM
ejpam-5918	488	4	v	v	NOUN
ejpam-5918	488	5	(	(	PUNCT
ejpam-5918	488	6	t	t	PROPN
ejpam-5918	488	7	(	(	PUNCT
ejpam-5918	488	8	g	g	NOUN
ejpam-5918	488	9	)	)	PUNCT
ejpam-5918	488	10	)	)	PUNCT
ejpam-5918	488	11	with	with	ADP
ejpam-5918	488	12	s	s	NOUN
ejpam-5918	488	13	=	=	PUNCT
ejpam-5918	488	14	{	{	PUNCT
ejpam-5918	488	15	v2	v2	PROPN
ejpam-5918	488	16	,	,	PUNCT
ejpam-5918	488	17	v3	v3	PROPN
ejpam-5918	488	18	,	,	PUNCT
ejpam-5918	488	19	v9	v9	PROPN
ejpam-5918	488	20	,	,	PUNCT
ejpam-5918	488	21	v10	v10	NOUN
ejpam-5918	488	22	,	,	PUNCT
ejpam-5918	488	23	.	.	PUNCT
ejpam-5918	488	24	.	.	PUNCT
ejpam-5918	489	1	.	.	PUNCT
ejpam-5918	490	1	,	,	PUNCT
ejpam-5918	490	2	vn−1	vn−1	PROPN
ejpam-5918	490	3	,	,	PUNCT
ejpam-5918	490	4	vn	vn	INTJ
ejpam-5918	490	5	}	}	PUNCT
ejpam-5918	490	6	∪	∪	ADJ
ejpam-5918	490	7	{	{	PUNCT
ejpam-5918	490	8	e5	e5	PROPN
ejpam-5918	490	9	,	,	PUNCT
ejpam-5918	490	10	e6	e6	PROPN
ejpam-5918	490	11	,	,	PUNCT
ejpam-5918	490	12	.	.	PUNCT
ejpam-5918	490	13	.	.	PUNCT
ejpam-5918	491	1	.	.	PUNCT
ejpam-5918	492	1	,	,	PUNCT
ejpam-5918	492	2	en−12	en−12	PROPN
ejpam-5918	492	3	,	,	PUNCT
ejpam-5918	492	4	en−11	en−11	PROPN
ejpam-5918	492	5	,	,	PUNCT
ejpam-5918	492	6	en−5	en−5	NOUN
ejpam-5918	492	7	,	,	PUNCT
ejpam-5918	492	8	en−4	en−4	PROPN
ejpam-5918	492	9	}	}	PUNCT
ejpam-5918	492	10	.	.	PUNCT
ejpam-5918	493	1	observe	observe	VERB
ejpam-5918	493	2	that	that	SCONJ
ejpam-5918	493	3	s	s	VERB
ejpam-5918	493	4	is	be	AUX
ejpam-5918	493	5	a	a	DET
ejpam-5918	493	6	dominating	dominating	NOUN
ejpam-5918	493	7	set	set	NOUN
ejpam-5918	493	8	and	and	CCONJ
ejpam-5918	493	9	for	for	ADP
ejpam-5918	493	10	all	all	DET
ejpam-5918	493	11	u	u	NOUN
ejpam-5918	493	12	,	,	PUNCT
ejpam-5918	493	13	v	v	ADP
ejpam-5918	493	14	∈	∈	PROPN
ejpam-5918	493	15	s	s	NOUN
ejpam-5918	493	16	,	,	PUNCT
ejpam-5918	493	17	n(u	n(u	PROPN
ejpam-5918	493	18	)	)	PUNCT
ejpam-5918	493	19	∩	∩	PROPN
ejpam-5918	493	20	s	s	PART
ejpam-5918	493	21	̸=	̸=	PROPN
ejpam-5918	493	22	n(v	n(v	PROPN
ejpam-5918	493	23	)	)	PUNCT
ejpam-5918	493	24	∩	∩	PROPN
ejpam-5918	493	25	s.	s.	PROPN
ejpam-5918	493	26	hence	hence	ADV
ejpam-5918	493	27	,	,	PUNCT
ejpam-5918	493	28	s	s	VERB
ejpam-5918	493	29	is	be	AUX
ejpam-5918	493	30	an	an	DET
ejpam-5918	493	31	ilds	ild	NOUN
ejpam-5918	493	32	.	.	PUNCT
ejpam-5918	494	1	to	to	PART
ejpam-5918	494	2	end	end	VERB
ejpam-5918	494	3	this	this	PRON
ejpam-5918	494	4	,	,	PUNCT
ejpam-5918	494	5	note	note	VERB
ejpam-5918	494	6	that	that	SCONJ
ejpam-5918	494	7	|s|	|s|	NOUN
ejpam-5918	494	8	=	=	SYM
ejpam-5918	494	9	⌈4n7	⌈4n7	PRON
ejpam-5918	494	10	⌉.	⌉.	ADV
ejpam-5918	494	11	since	since	SCONJ
ejpam-5918	494	12	i	i	PRON
ejpam-5918	494	13	is	be	AUX
ejpam-5918	494	14	a	a	DET
ejpam-5918	494	15	γli	γli	ADJ
ejpam-5918	494	16	−	−	NOUN
ejpam-5918	494	17	set	set	NOUN
ejpam-5918	494	18	,	,	PUNCT
ejpam-5918	494	19	|s|	|s|	NOUN
ejpam-5918	494	20	≥	≥	NOUN
ejpam-5918	494	21	|i|	|i|	PROPN
ejpam-5918	494	22	.	.	PUNCT
ejpam-5918	495	1	so	so	ADV
ejpam-5918	495	2	,	,	PUNCT
ejpam-5918	495	3	|i|	|i|	VERB
ejpam-5918	495	4	≤	≤	NUM
ejpam-5918	495	5	|s|	|s|	PROPN
ejpam-5918	495	6	=	=	SYM
ejpam-5918	495	7	⌈4n7	⌈4n7	X
ejpam-5918	495	8	⌉.	⌉.	ADV
ejpam-5918	495	9	on	on	ADP
ejpam-5918	495	10	the	the	DET
ejpam-5918	495	11	other	other	ADJ
ejpam-5918	495	12	hand	hand	NOUN
ejpam-5918	495	13	,	,	PUNCT
ejpam-5918	495	14	since	since	SCONJ
ejpam-5918	495	15	i	i	PRON
ejpam-5918	495	16	is	be	AUX
ejpam-5918	495	17	a	a	DET
ejpam-5918	495	18	γli	γli	ADJ
ejpam-5918	495	19	−	−	NOUN
ejpam-5918	495	20	set	set	NOUN
ejpam-5918	495	21	of	of	ADP
ejpam-5918	495	22	t	t	PROPN
ejpam-5918	495	23	(	(	PUNCT
ejpam-5918	495	24	g	g	NOUN
ejpam-5918	495	25	)	)	PUNCT
ejpam-5918	495	26	,	,	PUNCT
ejpam-5918	495	27	then	then	ADV
ejpam-5918	495	28	i	i	PRON
ejpam-5918	495	29	must	must	AUX
ejpam-5918	495	30	have	have	AUX
ejpam-5918	495	31	atleast	atleast	VERB
ejpam-5918	495	32	⌈4n7	⌈4n7	NUM
ejpam-5918	495	33	⌉	⌉	X
ejpam-5918	495	34	vertices	vertice	VERB
ejpam-5918	495	35	in	in	ADP
ejpam-5918	495	36	t	t	PROPN
ejpam-5918	495	37	(	(	PUNCT
ejpam-5918	495	38	g	g	NOUN
ejpam-5918	495	39	)	)	PUNCT
ejpam-5918	495	40	.	.	PUNCT
ejpam-5918	496	1	hence	hence	ADV
ejpam-5918	496	2	,	,	PUNCT
ejpam-5918	496	3	|i|	|i|	VERB
ejpam-5918	496	4	≥	≥	NOUN
ejpam-5918	496	5	⌈4n7	⌈4n7	X
ejpam-5918	496	6	⌉.	⌉.	ADV
ejpam-5918	496	7	therefore	therefore	ADV
ejpam-5918	496	8	,	,	PUNCT
ejpam-5918	496	9	|i|	|i|	PROPN
ejpam-5918	496	10	=	=	SYM
ejpam-5918	496	11	⌈4n7	⌈4n7	ADP
ejpam-5918	496	12	⌉.	⌉.	ADJ
ejpam-5918	496	13	case	case	NOUN
ejpam-5918	496	14	5	5	NUM
ejpam-5918	496	15	:	:	PUNCT
ejpam-5918	496	16	n	n	NUM
ejpam-5918	496	17	≡	≡	PROPN
ejpam-5918	496	18	4	4	NUM
ejpam-5918	496	19	(	(	PUNCT
ejpam-5918	496	20	mod	mod	PROPN
ejpam-5918	496	21	7	7	NUM
ejpam-5918	496	22	)	)	PUNCT
ejpam-5918	496	23	.	.	PUNCT
ejpam-5918	497	1	let	let	VERB
ejpam-5918	497	2	s	s	PRON
ejpam-5918	497	3	⊆	⊆	NUM
ejpam-5918	497	4	v	v	NOUN
ejpam-5918	497	5	(	(	PUNCT
ejpam-5918	497	6	t	t	PROPN
ejpam-5918	497	7	(	(	PUNCT
ejpam-5918	497	8	g	g	NOUN
ejpam-5918	497	9	)	)	PUNCT
ejpam-5918	497	10	)	)	PUNCT
ejpam-5918	497	11	with	with	ADP
ejpam-5918	497	12	s	s	NOUN
ejpam-5918	497	13	=	=	SYM
ejpam-5918	497	14	{	{	PUNCT
ejpam-5918	497	15	v1	v1	PROPN
ejpam-5918	497	16	,	,	PUNCT
ejpam-5918	497	17	v2	v2	PROPN
ejpam-5918	497	18	,	,	PUNCT
ejpam-5918	497	19	v8	v8	PROPN
ejpam-5918	497	20	,	,	PUNCT
ejpam-5918	497	21	v9	v9	PROPN
ejpam-5918	497	22	,	,	PUNCT
ejpam-5918	497	23	.	.	PUNCT
ejpam-5918	497	24	.	.	PUNCT
ejpam-5918	498	1	.	.	PUNCT
ejpam-5918	499	1	,	,	PUNCT
ejpam-5918	499	2	vn−3	vn−3	PROPN
ejpam-5918	499	3	,	,	PUNCT
ejpam-5918	499	4	vn−2	vn−2	PROPN
ejpam-5918	499	5	}	}	PUNCT
ejpam-5918	499	6	∪	∪	NOUN
ejpam-5918	499	7	{	{	PUNCT
ejpam-5918	499	8	e4	e4	PROPN
ejpam-5918	499	9	,	,	PUNCT
ejpam-5918	499	10	e5	e5	PROPN
ejpam-5918	499	11	,	,	PUNCT
ejpam-5918	499	12	.	.	PUNCT
ejpam-5918	499	13	.	.	PUNCT
ejpam-5918	500	1	.	.	PUNCT
ejpam-5918	501	1	,	,	PUNCT
ejpam-5918	501	2	en−7	en−7	PROPN
ejpam-5918	501	3	,	,	PUNCT
ejpam-5918	501	4	en−6	en−6	NOUN
ejpam-5918	501	5	,	,	PUNCT
ejpam-5918	501	6	en−1	en−1	PROPN
ejpam-5918	501	7	}	}	PUNCT
ejpam-5918	501	8	.	.	PUNCT
ejpam-5918	502	1	observe	observe	VERB
ejpam-5918	502	2	that	that	SCONJ
ejpam-5918	502	3	s	s	VERB
ejpam-5918	502	4	is	be	AUX
ejpam-5918	502	5	a	a	DET
ejpam-5918	502	6	dominating	dominating	NOUN
ejpam-5918	502	7	set	set	NOUN
ejpam-5918	502	8	and	and	CCONJ
ejpam-5918	502	9	for	for	ADP
ejpam-5918	502	10	all	all	DET
ejpam-5918	502	11	u	u	NOUN
ejpam-5918	502	12	,	,	PUNCT
ejpam-5918	502	13	v	v	ADP
ejpam-5918	502	14	∈	∈	PROPN
ejpam-5918	502	15	s	s	NOUN
ejpam-5918	502	16	,	,	PUNCT
ejpam-5918	502	17	n(u	n(u	PROPN
ejpam-5918	502	18	)	)	PUNCT
ejpam-5918	502	19	∩	∩	PROPN
ejpam-5918	502	20	s	s	PART
ejpam-5918	502	21	̸=	̸=	PROPN
ejpam-5918	502	22	n(v	n(v	PROPN
ejpam-5918	502	23	)	)	PUNCT
ejpam-5918	502	24	∩	∩	PROPN
ejpam-5918	502	25	s.	s.	PROPN
ejpam-5918	502	26	hence	hence	ADV
ejpam-5918	502	27	,	,	PUNCT
ejpam-5918	502	28	s	s	VERB
ejpam-5918	502	29	is	be	AUX
ejpam-5918	502	30	an	an	DET
ejpam-5918	502	31	ilds	ild	NOUN
ejpam-5918	502	32	.	.	PUNCT
ejpam-5918	503	1	to	to	PART
ejpam-5918	503	2	end	end	VERB
ejpam-5918	503	3	this	this	PRON
ejpam-5918	503	4	,	,	PUNCT
ejpam-5918	503	5	note	note	VERB
ejpam-5918	503	6	that	that	SCONJ
ejpam-5918	503	7	|s|	|s|	NOUN
ejpam-5918	503	8	=	=	SYM
ejpam-5918	503	9	⌈4n7	⌈4n7	PRON
ejpam-5918	503	10	⌉.	⌉.	ADV
ejpam-5918	503	11	since	since	SCONJ
ejpam-5918	503	12	i	i	PRON
ejpam-5918	503	13	is	be	AUX
ejpam-5918	503	14	a	a	DET
ejpam-5918	503	15	γli	γli	ADJ
ejpam-5918	503	16	−	−	NOUN
ejpam-5918	503	17	set	set	NOUN
ejpam-5918	503	18	,	,	PUNCT
ejpam-5918	503	19	|s|	|s|	NOUN
ejpam-5918	503	20	≥	≥	NOUN
ejpam-5918	503	21	|i|	|i|	PROPN
ejpam-5918	503	22	.	.	PUNCT
ejpam-5918	504	1	so	so	ADV
ejpam-5918	504	2	,	,	PUNCT
ejpam-5918	504	3	|i|	|i|	VERB
ejpam-5918	504	4	≤	≤	NUM
ejpam-5918	504	5	|s|	|s|	PROPN
ejpam-5918	504	6	=	=	SYM
ejpam-5918	504	7	⌈4n7	⌈4n7	X
ejpam-5918	504	8	⌉.	⌉.	ADV
ejpam-5918	504	9	on	on	ADP
ejpam-5918	504	10	the	the	DET
ejpam-5918	504	11	other	other	ADJ
ejpam-5918	504	12	hand	hand	NOUN
ejpam-5918	504	13	,	,	PUNCT
ejpam-5918	504	14	since	since	SCONJ
ejpam-5918	504	15	i	i	PRON
ejpam-5918	504	16	is	be	AUX
ejpam-5918	504	17	a	a	DET
ejpam-5918	504	18	γli	γli	ADJ
ejpam-5918	504	19	−	−	NOUN
ejpam-5918	504	20	set	set	NOUN
ejpam-5918	504	21	of	of	ADP
ejpam-5918	504	22	t	t	PROPN
ejpam-5918	504	23	(	(	PUNCT
ejpam-5918	504	24	g	g	NOUN
ejpam-5918	504	25	)	)	PUNCT
ejpam-5918	504	26	,	,	PUNCT
ejpam-5918	504	27	then	then	ADV
ejpam-5918	504	28	i	i	PRON
ejpam-5918	504	29	must	must	AUX
ejpam-5918	504	30	have	have	AUX
ejpam-5918	504	31	atleast	atleast	VERB
ejpam-5918	504	32	⌈4n7	⌈4n7	NUM
ejpam-5918	504	33	⌉	⌉	X
ejpam-5918	504	34	vertices	vertice	VERB
ejpam-5918	504	35	in	in	ADP
ejpam-5918	504	36	t	t	PROPN
ejpam-5918	504	37	(	(	PUNCT
ejpam-5918	504	38	g	g	NOUN
ejpam-5918	504	39	)	)	PUNCT
ejpam-5918	504	40	.	.	PUNCT
ejpam-5918	505	1	hence	hence	ADV
ejpam-5918	505	2	,	,	PUNCT
ejpam-5918	505	3	|i|	|i|	VERB
ejpam-5918	505	4	≥	≥	NOUN
ejpam-5918	505	5	⌈4n7	⌈4n7	X
ejpam-5918	505	6	⌉.	⌉.	ADV
ejpam-5918	505	7	therefore	therefore	ADV
ejpam-5918	505	8	,	,	PUNCT
ejpam-5918	505	9	|i|	|i|	PROPN
ejpam-5918	505	10	=	=	SYM
ejpam-5918	505	11	⌈4n7	⌈4n7	ADP
ejpam-5918	505	12	⌉.	⌉.	ADJ
ejpam-5918	505	13	case	case	NOUN
ejpam-5918	505	14	6	6	NUM
ejpam-5918	505	15	:	:	PUNCT
ejpam-5918	505	16	n	n	NUM
ejpam-5918	505	17	≡	≡	PROPN
ejpam-5918	505	18	5	5	NUM
ejpam-5918	505	19	(	(	PUNCT
ejpam-5918	505	20	mod	mod	PROPN
ejpam-5918	505	21	7	7	NUM
ejpam-5918	505	22	)	)	PUNCT
ejpam-5918	505	23	.	.	PUNCT
ejpam-5918	506	1	let	let	VERB
ejpam-5918	506	2	s	s	PRON
ejpam-5918	506	3	⊆	⊆	NUM
ejpam-5918	506	4	v	v	NOUN
ejpam-5918	506	5	(	(	PUNCT
ejpam-5918	506	6	t	t	PROPN
ejpam-5918	506	7	(	(	PUNCT
ejpam-5918	506	8	g	g	NOUN
ejpam-5918	506	9	)	)	PUNCT
ejpam-5918	506	10	)	)	PUNCT
ejpam-5918	506	11	with	with	ADP
ejpam-5918	506	12	s	s	NOUN
ejpam-5918	506	13	=	=	PUNCT
ejpam-5918	506	14	{	{	PUNCT
ejpam-5918	506	15	v2	v2	PROPN
ejpam-5918	506	16	,	,	PUNCT
ejpam-5918	506	17	v3	v3	PROPN
ejpam-5918	506	18	,	,	PUNCT
ejpam-5918	506	19	v9	v9	PROPN
ejpam-5918	506	20	,	,	PUNCT
ejpam-5918	506	21	v10	v10	NOUN
ejpam-5918	506	22	,	,	PUNCT
ejpam-5918	506	23	.	.	PUNCT
ejpam-5918	506	24	.	.	PUNCT
ejpam-5918	507	1	.	.	PUNCT
ejpam-5918	508	1	,	,	PUNCT
ejpam-5918	508	2	vn−3	vn−3	PROPN
ejpam-5918	508	3	,	,	PUNCT
ejpam-5918	508	4	vn−2	vn−2	PROPN
ejpam-5918	508	5	}	}	PUNCT
ejpam-5918	508	6	∪	∪	NOUN
ejpam-5918	508	7	{	{	PUNCT
ejpam-5918	508	8	e5	e5	PROPN
ejpam-5918	508	9	,	,	PUNCT
ejpam-5918	508	10	e6	e6	PROPN
ejpam-5918	508	11	,	,	PUNCT
ejpam-5918	508	12	.	.	PUNCT
ejpam-5918	508	13	.	.	PUNCT
ejpam-5918	509	1	.	.	PUNCT
ejpam-5918	510	1	,	,	PUNCT
ejpam-5918	510	2	en−7	en−7	PROPN
ejpam-5918	510	3	,	,	PUNCT
ejpam-5918	510	4	en−6	en−6	NOUN
ejpam-5918	510	5	,	,	PUNCT
ejpam-5918	510	6	en−1	en−1	PROPN
ejpam-5918	510	7	}	}	PUNCT
ejpam-5918	510	8	.	.	PUNCT
ejpam-5918	511	1	observe	observe	VERB
ejpam-5918	511	2	that	that	SCONJ
ejpam-5918	511	3	s	s	VERB
ejpam-5918	511	4	is	be	AUX
ejpam-5918	511	5	a	a	DET
ejpam-5918	511	6	dominating	dominating	NOUN
ejpam-5918	511	7	set	set	NOUN
ejpam-5918	511	8	and	and	CCONJ
ejpam-5918	511	9	for	for	ADP
ejpam-5918	511	10	all	all	DET
ejpam-5918	511	11	u	u	NOUN
ejpam-5918	511	12	,	,	PUNCT
ejpam-5918	511	13	v	v	ADP
ejpam-5918	511	14	∈	∈	PROPN
ejpam-5918	511	15	s	s	NOUN
ejpam-5918	511	16	,	,	PUNCT
ejpam-5918	511	17	n(u	n(u	PROPN
ejpam-5918	511	18	)	)	PUNCT
ejpam-5918	511	19	∩	∩	PROPN
ejpam-5918	511	20	s	s	PART
ejpam-5918	511	21	̸=	̸=	PROPN
ejpam-5918	511	22	n(v	n(v	PROPN
ejpam-5918	511	23	)	)	PUNCT
ejpam-5918	511	24	∩	∩	PROPN
ejpam-5918	511	25	s.	s.	PROPN
ejpam-5918	511	26	hence	hence	ADV
ejpam-5918	511	27	,	,	PUNCT
ejpam-5918	511	28	s	s	VERB
ejpam-5918	511	29	is	be	AUX
ejpam-5918	511	30	an	an	DET
ejpam-5918	511	31	ilds	ild	NOUN
ejpam-5918	511	32	.	.	PUNCT
ejpam-5918	512	1	to	to	PART
ejpam-5918	512	2	end	end	VERB
ejpam-5918	512	3	this	this	PRON
ejpam-5918	512	4	,	,	PUNCT
ejpam-5918	512	5	note	note	VERB
ejpam-5918	512	6	that	that	SCONJ
ejpam-5918	512	7	|s|	|s|	NOUN
ejpam-5918	512	8	=	=	SYM
ejpam-5918	512	9	⌈4n7	⌈4n7	PRON
ejpam-5918	512	10	⌉.	⌉.	ADV
ejpam-5918	512	11	since	since	SCONJ
ejpam-5918	512	12	i	i	PRON
ejpam-5918	512	13	is	be	AUX
ejpam-5918	512	14	a	a	DET
ejpam-5918	512	15	γli	γli	ADJ
ejpam-5918	512	16	−	−	NOUN
ejpam-5918	512	17	set	set	NOUN
ejpam-5918	512	18	,	,	PUNCT
ejpam-5918	512	19	|s|	|s|	NOUN
ejpam-5918	512	20	≥	≥	NOUN
ejpam-5918	512	21	|i|	|i|	PROPN
ejpam-5918	512	22	.	.	PUNCT
ejpam-5918	513	1	so	so	ADV
ejpam-5918	513	2	,	,	PUNCT
ejpam-5918	513	3	|i|	|i|	VERB
ejpam-5918	513	4	≤	≤	NUM
ejpam-5918	513	5	|s|	|s|	PROPN
ejpam-5918	513	6	=	=	SYM
ejpam-5918	513	7	⌈4n7	⌈4n7	X
ejpam-5918	513	8	⌉.	⌉.	ADV
ejpam-5918	513	9	on	on	ADP
ejpam-5918	513	10	the	the	DET
ejpam-5918	513	11	other	other	ADJ
ejpam-5918	513	12	hand	hand	NOUN
ejpam-5918	513	13	,	,	PUNCT
ejpam-5918	513	14	since	since	SCONJ
ejpam-5918	513	15	i	i	PRON
ejpam-5918	513	16	is	be	AUX
ejpam-5918	513	17	a	a	DET
ejpam-5918	513	18	γli	γli	ADJ
ejpam-5918	513	19	−	−	NOUN
ejpam-5918	513	20	set	set	NOUN
ejpam-5918	513	21	of	of	ADP
ejpam-5918	513	22	t	t	PROPN
ejpam-5918	513	23	(	(	PUNCT
ejpam-5918	513	24	g	g	NOUN
ejpam-5918	513	25	)	)	PUNCT
ejpam-5918	513	26	,	,	PUNCT
ejpam-5918	513	27	then	then	ADV
ejpam-5918	513	28	i	i	PRON
ejpam-5918	513	29	must	must	AUX
ejpam-5918	513	30	have	have	AUX
ejpam-5918	513	31	atleast	atleast	VERB
ejpam-5918	513	32	⌈4n7	⌈4n7	NUM
ejpam-5918	513	33	⌉	⌉	X
ejpam-5918	513	34	vertices	vertice	VERB
ejpam-5918	513	35	in	in	ADP
ejpam-5918	513	36	t	t	PROPN
ejpam-5918	513	37	(	(	PUNCT
ejpam-5918	513	38	g	g	NOUN
ejpam-5918	513	39	)	)	PUNCT
ejpam-5918	513	40	.	.	PUNCT
ejpam-5918	514	1	hence	hence	ADV
ejpam-5918	514	2	,	,	PUNCT
ejpam-5918	514	3	|i|	|i|	VERB
ejpam-5918	514	4	≥	≥	NOUN
ejpam-5918	514	5	⌈4n7	⌈4n7	X
ejpam-5918	514	6	⌉.	⌉.	ADV
ejpam-5918	514	7	therefore	therefore	ADV
ejpam-5918	514	8	,	,	PUNCT
ejpam-5918	514	9	|i|	|i|	PROPN
ejpam-5918	514	10	=	=	SYM
ejpam-5918	514	11	⌈4n7	⌈4n7	ADP
ejpam-5918	514	12	⌉.	⌉.	ADJ
ejpam-5918	514	13	case	case	NOUN
ejpam-5918	514	14	7	7	NUM
ejpam-5918	514	15	:	:	PUNCT
ejpam-5918	514	16	n	n	NUM
ejpam-5918	514	17	≡	≡	PROPN
ejpam-5918	514	18	6	6	NUM
ejpam-5918	514	19	(	(	PUNCT
ejpam-5918	514	20	mod	mod	PROPN
ejpam-5918	514	21	7	7	NUM
ejpam-5918	514	22	)	)	PUNCT
ejpam-5918	514	23	.	.	PUNCT
ejpam-5918	515	1	let	let	VERB
ejpam-5918	515	2	s	s	PRON
ejpam-5918	515	3	⊆	⊆	NUM
ejpam-5918	515	4	v	v	NOUN
ejpam-5918	515	5	(	(	PUNCT
ejpam-5918	515	6	t	t	PROPN
ejpam-5918	515	7	(	(	PUNCT
ejpam-5918	515	8	g	g	NOUN
ejpam-5918	515	9	)	)	PUNCT
ejpam-5918	515	10	)	)	PUNCT
ejpam-5918	515	11	with	with	ADP
ejpam-5918	515	12	s	s	NOUN
ejpam-5918	515	13	=	=	PUNCT
ejpam-5918	515	14	{	{	PUNCT
ejpam-5918	515	15	v2	v2	PROPN
ejpam-5918	515	16	,	,	PUNCT
ejpam-5918	515	17	v3	v3	PROPN
ejpam-5918	515	18	,	,	PUNCT
ejpam-5918	515	19	v9	v9	PROPN
ejpam-5918	515	20	,	,	PUNCT
ejpam-5918	515	21	v10	v10	NOUN
ejpam-5918	515	22	,	,	PUNCT
ejpam-5918	515	23	.	.	PUNCT
ejpam-5918	515	24	.	.	PUNCT
ejpam-5918	516	1	.	.	PUNCT
ejpam-5918	517	1	,	,	PUNCT
ejpam-5918	517	2	vn−4	vn−4	NOUN
ejpam-5918	517	3	,	,	PUNCT
ejpam-5918	517	4	vn−3	vn−3	PROPN
ejpam-5918	517	5	}	}	PUNCT
ejpam-5918	517	6	∪	∪	NOUN
ejpam-5918	517	7	{	{	PUNCT
ejpam-5918	517	8	e5	e5	PROPN
ejpam-5918	517	9	,	,	PUNCT
ejpam-5918	517	10	e6	e6	PROPN
ejpam-5918	517	11	,	,	PUNCT
ejpam-5918	517	12	.	.	PUNCT
ejpam-5918	517	13	.	.	PUNCT
ejpam-5918	518	1	.	.	PUNCT
ejpam-5918	519	1	,	,	PUNCT
ejpam-5918	519	2	en−8	en−8	PROPN
ejpam-5918	519	3	,	,	PUNCT
ejpam-5918	519	4	en−7	en−7	PROPN
ejpam-5918	519	5	,	,	PUNCT
ejpam-5918	519	6	en−1	en−1	PROPN
ejpam-5918	519	7	}	}	PUNCT
ejpam-5918	519	8	.	.	PUNCT
ejpam-5918	520	1	i.	i.	PROPN
ejpam-5918	520	2	tropico	tropico	PROPN
ejpam-5918	520	3	,	,	PUNCT
ejpam-5918	520	4	i.	i.	PROPN
ejpam-5918	520	5	cabahug	cabahug	PROPN
ejpam-5918	520	6	,	,	PUNCT
ejpam-5918	520	7	jr	jr	PROPN
ejpam-5918	520	8	.	.	PROPN
ejpam-5918	520	9	/	/	SYM
ejpam-5918	520	10	eur	eur	PROPN
ejpam-5918	520	11	.	.	PUNCT
ejpam-5918	521	1	j.	j.	PROPN
ejpam-5918	521	2	pure	pure	PROPN
ejpam-5918	521	3	appl	appl	PROPN
ejpam-5918	521	4	.	.	PROPN
ejpam-5918	521	5	math	math	PROPN
ejpam-5918	521	6	,	,	PUNCT
ejpam-5918	521	7	18	18	NUM
ejpam-5918	521	8	(	(	PUNCT
ejpam-5918	521	9	2	2	NUM
ejpam-5918	521	10	)	)	PUNCT
ejpam-5918	521	11	(	(	PUNCT
ejpam-5918	521	12	2025	2025	NUM
ejpam-5918	521	13	)	)	PUNCT
ejpam-5918	521	14	,	,	PUNCT
ejpam-5918	521	15	5918	5918	NUM
ejpam-5918	521	16	16	16	NUM
ejpam-5918	521	17	of	of	ADP
ejpam-5918	521	18	21	21	NUM
ejpam-5918	521	19	observe	observe	VERB
ejpam-5918	521	20	that	that	SCONJ
ejpam-5918	521	21	s	s	VERB
ejpam-5918	521	22	is	be	AUX
ejpam-5918	521	23	a	a	DET
ejpam-5918	521	24	dominating	dominating	NOUN
ejpam-5918	521	25	set	set	NOUN
ejpam-5918	521	26	and	and	CCONJ
ejpam-5918	521	27	for	for	ADP
ejpam-5918	521	28	all	all	DET
ejpam-5918	521	29	u	u	NOUN
ejpam-5918	521	30	,	,	PUNCT
ejpam-5918	521	31	v	v	ADP
ejpam-5918	521	32	∈	∈	PROPN
ejpam-5918	521	33	s	s	NOUN
ejpam-5918	521	34	,	,	PUNCT
ejpam-5918	521	35	n(u	n(u	PROPN
ejpam-5918	521	36	)	)	PUNCT
ejpam-5918	521	37	∩	∩	PROPN
ejpam-5918	521	38	s	s	PART
ejpam-5918	521	39	̸=	̸=	PROPN
ejpam-5918	521	40	n(v	n(v	PROPN
ejpam-5918	521	41	)	)	PUNCT
ejpam-5918	521	42	∩	∩	PROPN
ejpam-5918	521	43	s.	s.	PROPN
ejpam-5918	521	44	hence	hence	ADV
ejpam-5918	521	45	,	,	PUNCT
ejpam-5918	521	46	s	s	VERB
ejpam-5918	521	47	is	be	AUX
ejpam-5918	521	48	an	an	DET
ejpam-5918	521	49	ilds	ild	NOUN
ejpam-5918	521	50	.	.	PUNCT
ejpam-5918	522	1	to	to	PART
ejpam-5918	522	2	end	end	VERB
ejpam-5918	522	3	this	this	PRON
ejpam-5918	522	4	,	,	PUNCT
ejpam-5918	522	5	note	note	VERB
ejpam-5918	522	6	that	that	SCONJ
ejpam-5918	522	7	|s|	|s|	PROPN
ejpam-5918	522	8	=	=	SYM
ejpam-5918	522	9	⌊4n7	⌊4n7	PROPN
ejpam-5918	522	10	⌋.	⌋.	NOUN
ejpam-5918	522	11	since	since	SCONJ
ejpam-5918	522	12	i	i	PRON
ejpam-5918	522	13	is	be	AUX
ejpam-5918	522	14	a	a	DET
ejpam-5918	522	15	γli	γli	ADJ
ejpam-5918	522	16	−	−	NOUN
ejpam-5918	522	17	set	set	NOUN
ejpam-5918	522	18	,	,	PUNCT
ejpam-5918	522	19	|s|	|s|	NOUN
ejpam-5918	522	20	≥	≥	NOUN
ejpam-5918	522	21	|i|	|i|	PROPN
ejpam-5918	522	22	.	.	PUNCT
ejpam-5918	523	1	so	so	ADV
ejpam-5918	523	2	,	,	PUNCT
ejpam-5918	523	3	|i|	|i|	VERB
ejpam-5918	523	4	≤	≤	NUM
ejpam-5918	523	5	|s|	|s|	PROPN
ejpam-5918	523	6	=	=	SYM
ejpam-5918	523	7	⌊4n7	⌊4n7	PROPN
ejpam-5918	523	8	⌋.	⌋.	ADV
ejpam-5918	523	9	on	on	ADP
ejpam-5918	523	10	the	the	DET
ejpam-5918	523	11	other	other	ADJ
ejpam-5918	523	12	hand	hand	NOUN
ejpam-5918	523	13	,	,	PUNCT
ejpam-5918	523	14	since	since	SCONJ
ejpam-5918	523	15	i	i	PRON
ejpam-5918	523	16	is	be	AUX
ejpam-5918	523	17	a	a	DET
ejpam-5918	523	18	γli	γli	ADJ
ejpam-5918	523	19	−	−	NOUN
ejpam-5918	523	20	set	set	NOUN
ejpam-5918	523	21	of	of	ADP
ejpam-5918	523	22	t	t	PROPN
ejpam-5918	523	23	(	(	PUNCT
ejpam-5918	523	24	g	g	NOUN
ejpam-5918	523	25	)	)	PUNCT
ejpam-5918	523	26	,	,	PUNCT
ejpam-5918	523	27	then	then	ADV
ejpam-5918	523	28	i	i	PRON
ejpam-5918	523	29	must	must	AUX
ejpam-5918	523	30	have	have	VERB
ejpam-5918	523	31	atleast	atleast	VERB
ejpam-5918	523	32	⌊4n7	⌊4n7	PROPN
ejpam-5918	523	33	⌋	⌋	NOUN
ejpam-5918	523	34	vertices	vertice	VERB
ejpam-5918	523	35	in	in	ADP
ejpam-5918	523	36	t	t	PROPN
ejpam-5918	523	37	(	(	PUNCT
ejpam-5918	523	38	g	g	NOUN
ejpam-5918	523	39	)	)	PUNCT
ejpam-5918	523	40	.	.	PUNCT
ejpam-5918	524	1	hence	hence	ADV
ejpam-5918	524	2	,	,	PUNCT
ejpam-5918	524	3	|i|	|i|	VERB
ejpam-5918	524	4	≥	≥	NOUN
ejpam-5918	524	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	524	6	⌋.	⌋.	PUNCT
ejpam-5918	525	1	therefore	therefore	ADV
ejpam-5918	525	2	,	,	PUNCT
ejpam-5918	525	3	|i|	|i|	PROPN
ejpam-5918	525	4	=	=	SYM
ejpam-5918	525	5	⌊4n7	⌊4n7	PROPN
ejpam-5918	525	6	⌋.	⌋.	ADJ
ejpam-5918	525	7	example	example	VERB
ejpam-5918	525	8	9	9	NUM
ejpam-5918	525	9	.	.	X
ejpam-5918	525	10	consider	consider	VERB
ejpam-5918	525	11	figure	figure	NOUN
ejpam-5918	525	12	8	8	NUM
ejpam-5918	525	13	.	.	PUNCT
ejpam-5918	526	1	clearly	clearly	ADV
ejpam-5918	526	2	i	i	PRON
ejpam-5918	526	3	=	=	SYM
ejpam-5918	526	4	{	{	PUNCT
ejpam-5918	526	5	v1	v1	PROPN
ejpam-5918	526	6	,	,	PUNCT
ejpam-5918	526	7	v2	v2	PROPN
ejpam-5918	526	8	,	,	PUNCT
ejpam-5918	526	9	e3	e3	PROPN
ejpam-5918	526	10	}	}	PUNCT
ejpam-5918	526	11	is	be	AUX
ejpam-5918	526	12	a	a	DET
ejpam-5918	526	13	dominating	dominating	NOUN
ejpam-5918	526	14	set	set	NOUN
ejpam-5918	526	15	.	.	PUNCT
ejpam-5918	527	1	observe	observe	VERB
ejpam-5918	527	2	that	that	SCONJ
ejpam-5918	527	3	,	,	PUNCT
ejpam-5918	527	4	n(v1	n(v1	NOUN
ejpam-5918	527	5	)	)	PUNCT
ejpam-5918	527	6	∩	∩	NOUN
ejpam-5918	527	7	i	i	PRON
ejpam-5918	527	8	=	=	SYM
ejpam-5918	527	9	{	{	PUNCT
ejpam-5918	527	10	v2	v2	NOUN
ejpam-5918	527	11	}	}	PUNCT
ejpam-5918	527	12	,	,	PUNCT
ejpam-5918	527	13	n(v2	n(v2	NOUN
ejpam-5918	527	14	)	)	PUNCT
ejpam-5918	527	15	∩	∩	NOUN
ejpam-5918	527	16	i	i	PRON
ejpam-5918	527	17	=	=	SYM
ejpam-5918	527	18	{	{	PUNCT
ejpam-5918	527	19	v1	v1	NOUN
ejpam-5918	527	20	}	}	PUNCT
ejpam-5918	527	21	,	,	PUNCT
ejpam-5918	527	22	and	and	CCONJ
ejpam-5918	527	23	n(e3	n(e3	ADJ
ejpam-5918	527	24	)	)	PUNCT
ejpam-5918	527	25	∩	∩	NOUN
ejpam-5918	527	26	i	i	PRON
ejpam-5918	527	27	=	=	PUNCT
ejpam-5918	527	28	∅.	∅.	VERB
ejpam-5918	527	29	hence	hence	ADV
ejpam-5918	527	30	,	,	PUNCT
ejpam-5918	527	31	i	i	PRON
ejpam-5918	527	32	is	be	AUX
ejpam-5918	527	33	an	an	DET
ejpam-5918	527	34	internallylocating	internallylocate	VERB
ejpam-5918	527	35	dominating	dominating	NOUN
ejpam-5918	527	36	set	set	NOUN
ejpam-5918	527	37	of	of	ADP
ejpam-5918	527	38	minimum	minimum	ADJ
ejpam-5918	527	39	cardinality	cardinality	NOUN
ejpam-5918	527	40	,	,	PUNCT
ejpam-5918	527	41	so	so	SCONJ
ejpam-5918	527	42	γli(t	γli(t	PROPN
ejpam-5918	527	43	(	(	PUNCT
ejpam-5918	527	44	c4	c4	NOUN
ejpam-5918	527	45	)	)	PUNCT
ejpam-5918	527	46	)	)	PUNCT
ejpam-5918	528	1	=	=	SYM
ejpam-5918	528	2	3	3	X
ejpam-5918	528	3	.	.	PUNCT
ejpam-5918	528	4	by	by	ADP
ejpam-5918	528	5	theorem	theorem	NOUN
ejpam-5918	528	6	10	10	NUM
ejpam-5918	528	7	,	,	PUNCT
ejpam-5918	528	8	for	for	ADP
ejpam-5918	528	9	n	n	NOUN
ejpam-5918	528	10	=	=	SYM
ejpam-5918	528	11	4	4	NUM
ejpam-5918	528	12	≡	≡	PROPN
ejpam-5918	528	13	4	4	NUM
ejpam-5918	528	14	(	(	PUNCT
ejpam-5918	528	15	mod	mod	PROPN
ejpam-5918	528	16	7	7	NUM
ejpam-5918	528	17	)	)	PUNCT
ejpam-5918	528	18	,	,	PUNCT
ejpam-5918	528	19	γli(t	γli(t	PROPN
ejpam-5918	528	20	(	(	PUNCT
ejpam-5918	528	21	c4	c4	NOUN
ejpam-5918	528	22	)	)	PUNCT
ejpam-5918	528	23	)	)	PUNCT
ejpam-5918	529	1	=	=	PUNCT
ejpam-5918	529	2	⌈4(n)7	⌈4(n)7	NOUN
ejpam-5918	529	3	⌉	⌉	PRON
ejpam-5918	529	4	=	=	SYM
ejpam-5918	529	5	⌈4(4)7	⌈4(4)7	ADJ
ejpam-5918	529	6	⌉	⌉	SCONJ
ejpam-5918	529	7	=	=	SYM
ejpam-5918	529	8	⌈167	⌈167	PUNCT
ejpam-5918	529	9	⌉	⌉	X
ejpam-5918	529	10	=	=	SYM
ejpam-5918	529	11	3	3	X
ejpam-5918	529	12	.	.	X
ejpam-5918	529	13	v1	v1	PROPN
ejpam-5918	529	14	v2	v2	PROPN
ejpam-5918	529	15	v3	v3	PROPN
ejpam-5918	529	16	v4	v4	PROPN
ejpam-5918	529	17	e1	e1	PROPN
ejpam-5918	529	18	e2	e2	PROPN
ejpam-5918	529	19	e3	e3	PROPN
ejpam-5918	529	20	e4	e4	PROPN
ejpam-5918	529	21	t	t	PROPN
ejpam-5918	529	22	(	(	PUNCT
ejpam-5918	529	23	c4	c4	NOUN
ejpam-5918	529	24	):	):	PUNCT
ejpam-5918	529	25	figure	figure	NOUN
ejpam-5918	529	26	8	8	NUM
ejpam-5918	529	27	:	:	PUNCT
ejpam-5918	529	28	the	the	DET
ejpam-5918	529	29	minimum	minimum	NOUN
ejpam-5918	529	30	internally	internally	ADV
ejpam-5918	529	31	-	-	PUNCT
ejpam-5918	529	32	locating	locate	VERB
ejpam-5918	529	33	dominating	dominating	NOUN
ejpam-5918	529	34	set	set	VERB
ejpam-5918	529	35	in	in	ADP
ejpam-5918	529	36	t	t	PROPN
ejpam-5918	529	37	(	(	PUNCT
ejpam-5918	529	38	c4	c4	NOUN
ejpam-5918	529	39	)	)	PUNCT
ejpam-5918	529	40	theorem	theorem	NOUN
ejpam-5918	529	41	11	11	NUM
ejpam-5918	529	42	.	.	PUNCT
ejpam-5918	530	1	let	let	VERB
ejpam-5918	530	2	g	g	PRON
ejpam-5918	530	3	be	be	AUX
ejpam-5918	530	4	a	a	DET
ejpam-5918	530	5	graph	graph	NOUN
ejpam-5918	530	6	with	with	ADP
ejpam-5918	530	7	∆(g	∆(g	NOUN
ejpam-5918	530	8	)	)	PUNCT
ejpam-5918	530	9	=	=	SYM
ejpam-5918	530	10	2	2	NUM
ejpam-5918	530	11	,	,	PUNCT
ejpam-5918	530	12	and	and	CCONJ
ejpam-5918	530	13	i	i	PRON
ejpam-5918	530	14	⊆	⊆	NUM
ejpam-5918	530	15	v	v	X
ejpam-5918	530	16	(	(	PUNCT
ejpam-5918	530	17	t	t	PROPN
ejpam-5918	530	18	(	(	PUNCT
ejpam-5918	530	19	g	g	NOUN
ejpam-5918	530	20	)	)	PUNCT
ejpam-5918	530	21	)	)	PUNCT
ejpam-5918	530	22	such	such	ADJ
ejpam-5918	530	23	that	that	PRON
ejpam-5918	530	24	|i|	|i|	VERB
ejpam-5918	530	25	≥	≥	NOUN
ejpam-5918	530	26	2	2	NUM
ejpam-5918	530	27	.	.	PUNCT
ejpam-5918	530	28	suppose	suppose	VERB
ejpam-5918	530	29	that	that	SCONJ
ejpam-5918	530	30	i	i	PRON
ejpam-5918	530	31	⊆	⊆	NUM
ejpam-5918	530	32	v	v	X
ejpam-5918	530	33	(	(	PUNCT
ejpam-5918	530	34	g	g	NOUN
ejpam-5918	530	35	)	)	PUNCT
ejpam-5918	530	36	.	.	PUNCT
ejpam-5918	531	1	then	then	ADV
ejpam-5918	531	2	i	i	PRON
ejpam-5918	531	3	is	be	AUX
ejpam-5918	531	4	an	an	DET
ejpam-5918	531	5	internally	internally	ADV
ejpam-5918	531	6	-	-	PUNCT
ejpam-5918	531	7	locating	locate	VERB
ejpam-5918	531	8	dominating	dominating	NOUN
ejpam-5918	531	9	set	set	VERB
ejpam-5918	531	10	in	in	ADP
ejpam-5918	531	11	s(g	s(g	PROPN
ejpam-5918	531	12	)	)	PUNCT
ejpam-5918	531	13	if	if	SCONJ
ejpam-5918	531	14	and	and	CCONJ
ejpam-5918	531	15	only	only	ADV
ejpam-5918	531	16	if	if	SCONJ
ejpam-5918	531	17	the	the	DET
ejpam-5918	531	18	following	follow	VERB
ejpam-5918	531	19	holds	hold	VERB
ejpam-5918	531	20	:	:	PUNCT
ejpam-5918	531	21	(	(	PUNCT
ejpam-5918	531	22	i	i	NOUN
ejpam-5918	531	23	)	)	PUNCT
ejpam-5918	532	1	i	i	PRON
ejpam-5918	532	2	is	be	AUX
ejpam-5918	532	3	an	an	DET
ejpam-5918	532	4	internally	internally	ADV
ejpam-5918	532	5	-	-	PUNCT
ejpam-5918	532	6	locating	locate	VERB
ejpam-5918	532	7	dominating	dominating	NOUN
ejpam-5918	532	8	set	set	VERB
ejpam-5918	532	9	in	in	ADP
ejpam-5918	532	10	v	v	NOUN
ejpam-5918	532	11	(	(	PUNCT
ejpam-5918	532	12	g	g	NOUN
ejpam-5918	532	13	)	)	PUNCT
ejpam-5918	532	14	;	;	PUNCT
ejpam-5918	532	15	and	and	CCONJ
ejpam-5918	532	16	(	(	PUNCT
ejpam-5918	532	17	ii	ii	NOUN
ejpam-5918	532	18	)	)	PUNCT
ejpam-5918	532	19	for	for	ADP
ejpam-5918	532	20	all	all	PRON
ejpam-5918	532	21	u	u	PROPN
ejpam-5918	532	22	∈	∈	PROPN
ejpam-5918	532	23	i	i	PRON
ejpam-5918	532	24	,	,	PUNCT
ejpam-5918	532	25	degi(u	degi(u	PROPN
ejpam-5918	532	26	)	)	PUNCT
ejpam-5918	532	27	̸=	̸=	PROPN
ejpam-5918	532	28	0	0	NUM
ejpam-5918	532	29	.	.	PUNCT
ejpam-5918	533	1	proof	proof	NOUN
ejpam-5918	533	2	.	.	PUNCT
ejpam-5918	534	1	let	let	VERB
ejpam-5918	534	2	g	g	PRON
ejpam-5918	534	3	be	be	AUX
ejpam-5918	534	4	a	a	DET
ejpam-5918	534	5	graph	graph	NOUN
ejpam-5918	534	6	with	with	ADP
ejpam-5918	534	7	∆(g	∆(g	NOUN
ejpam-5918	534	8	)	)	PUNCT
ejpam-5918	534	9	=	=	SYM
ejpam-5918	534	10	2	2	NUM
ejpam-5918	534	11	,	,	PUNCT
ejpam-5918	534	12	and	and	CCONJ
ejpam-5918	534	13	i	i	PRON
ejpam-5918	534	14	⊆	⊆	NUM
ejpam-5918	534	15	v	v	X
ejpam-5918	534	16	(	(	PUNCT
ejpam-5918	534	17	s(g	s(g	PROPN
ejpam-5918	534	18	)	)	PUNCT
ejpam-5918	534	19	)	)	PUNCT
ejpam-5918	534	20	such	such	ADJ
ejpam-5918	534	21	that	that	PRON
ejpam-5918	534	22	|i|	|i|	VERB
ejpam-5918	534	23	≥	≥	NOUN
ejpam-5918	534	24	2	2	NUM
ejpam-5918	534	25	.	.	PUNCT
ejpam-5918	534	26	suppose	suppose	VERB
ejpam-5918	534	27	that	that	SCONJ
ejpam-5918	534	28	i	i	PRON
ejpam-5918	534	29	⊆	⊆	NUM
ejpam-5918	534	30	v	v	X
ejpam-5918	534	31	(	(	PUNCT
ejpam-5918	534	32	g	g	NOUN
ejpam-5918	534	33	)	)	PUNCT
ejpam-5918	534	34	.	.	PUNCT
ejpam-5918	535	1	assume	assume	VERB
ejpam-5918	535	2	i	i	PRON
ejpam-5918	535	3	⊆	⊆	NUM
ejpam-5918	535	4	v	v	ADP
ejpam-5918	535	5	(	(	PUNCT
ejpam-5918	535	6	g	g	NOUN
ejpam-5918	535	7	)	)	PUNCT
ejpam-5918	535	8	is	be	AUX
ejpam-5918	535	9	an	an	DET
ejpam-5918	535	10	ilds	ild	NOUN
ejpam-5918	535	11	in	in	ADP
ejpam-5918	535	12	s(g	s(g	PROPN
ejpam-5918	535	13	)	)	PUNCT
ejpam-5918	535	14	.	.	PUNCT
ejpam-5918	536	1	then	then	ADV
ejpam-5918	536	2	,	,	PUNCT
ejpam-5918	536	3	by	by	ADP
ejpam-5918	536	4	definition	definition	NOUN
ejpam-5918	536	5	of	of	ADP
ejpam-5918	536	6	s(g	s(g	PROPN
ejpam-5918	536	7	)	)	PUNCT
ejpam-5918	536	8	,	,	PUNCT
ejpam-5918	536	9	i	i	PRON
ejpam-5918	536	10	must	must	AUX
ejpam-5918	536	11	dominate	dominate	VERB
ejpam-5918	536	12	all	all	DET
ejpam-5918	536	13	vertices	vertex	NOUN
ejpam-5918	536	14	in	in	ADP
ejpam-5918	536	15	v	v	NOUN
ejpam-5918	536	16	(	(	PUNCT
ejpam-5918	536	17	s(g	s(g	PROPN
ejpam-5918	536	18	)	)	PUNCT
ejpam-5918	536	19	)	)	PUNCT
ejpam-5918	537	1	=	=	SYM
ejpam-5918	537	2	v	v	X
ejpam-5918	537	3	(	(	PUNCT
ejpam-5918	537	4	g	g	NOUN
ejpam-5918	537	5	)	)	PUNCT
ejpam-5918	537	6	∪	∪	ADP
ejpam-5918	537	7	v	v	ADP
ejpam-5918	537	8	′(g	′(g	NOUN
ejpam-5918	537	9	)	)	PUNCT
ejpam-5918	537	10	.	.	PUNCT
ejpam-5918	538	1	in	in	ADP
ejpam-5918	538	2	particular	particular	ADJ
ejpam-5918	538	3	,	,	PUNCT
ejpam-5918	538	4	i	i	PRON
ejpam-5918	538	5	dominates	dominate	VERB
ejpam-5918	538	6	v	v	ADP
ejpam-5918	538	7	(	(	PUNCT
ejpam-5918	538	8	g	g	NOUN
ejpam-5918	538	9	)	)	PUNCT
ejpam-5918	538	10	,	,	PUNCT
ejpam-5918	538	11	as	as	ADP
ejpam-5918	538	12	i	i	PRON
ejpam-5918	538	13	⊆	⊆	NUM
ejpam-5918	538	14	v	v	X
ejpam-5918	538	15	(	(	PUNCT
ejpam-5918	538	16	g	g	NOUN
ejpam-5918	538	17	)	)	PUNCT
ejpam-5918	538	18	.	.	PUNCT
ejpam-5918	539	1	also	also	ADV
ejpam-5918	539	2	,	,	PUNCT
ejpam-5918	539	3	the	the	DET
ejpam-5918	539	4	property	property	NOUN
ejpam-5918	539	5	of	of	ADP
ejpam-5918	539	6	i	i	PRON
ejpam-5918	539	7	as	as	ADP
ejpam-5918	539	8	ilds	ild	NOUN
ejpam-5918	539	9	for	for	ADP
ejpam-5918	539	10	s(g	s(g	PROPN
ejpam-5918	539	11	)	)	PUNCT
ejpam-5918	539	12	holds	hold	VERB
ejpam-5918	539	13	for	for	ADP
ejpam-5918	539	14	v	v	NOUN
ejpam-5918	539	15	(	(	PUNCT
ejpam-5918	539	16	g	g	NOUN
ejpam-5918	539	17	)	)	PUNCT
ejpam-5918	539	18	since	since	SCONJ
ejpam-5918	539	19	i	i	PRON
ejpam-5918	539	20	⊆	⊆	NUM
ejpam-5918	539	21	v	v	NOUN
ejpam-5918	539	22	(	(	PUNCT
ejpam-5918	539	23	g	g	NOUN
ejpam-5918	539	24	)	)	PUNCT
ejpam-5918	539	25	.	.	PUNCT
ejpam-5918	540	1	thus	thus	ADV
ejpam-5918	540	2	,	,	PUNCT
ejpam-5918	540	3	(	(	PUNCT
ejpam-5918	540	4	i	i	NOUN
ejpam-5918	540	5	)	)	PUNCT
ejpam-5918	540	6	holds	hold	VERB
ejpam-5918	540	7	.	.	PUNCT
ejpam-5918	541	1	i.	i.	PROPN
ejpam-5918	541	2	tropico	tropico	PROPN
ejpam-5918	541	3	,	,	PUNCT
ejpam-5918	541	4	i.	i.	PROPN
ejpam-5918	541	5	cabahug	cabahug	PROPN
ejpam-5918	541	6	,	,	PUNCT
ejpam-5918	541	7	jr	jr	PROPN
ejpam-5918	541	8	.	.	PROPN
ejpam-5918	541	9	/	/	SYM
ejpam-5918	541	10	eur	eur	PROPN
ejpam-5918	541	11	.	.	PUNCT
ejpam-5918	542	1	j.	j.	PROPN
ejpam-5918	542	2	pure	pure	PROPN
ejpam-5918	542	3	appl	appl	PROPN
ejpam-5918	542	4	.	.	PROPN
ejpam-5918	542	5	math	math	PROPN
ejpam-5918	542	6	,	,	PUNCT
ejpam-5918	542	7	18	18	NUM
ejpam-5918	542	8	(	(	PUNCT
ejpam-5918	542	9	2	2	NUM
ejpam-5918	542	10	)	)	PUNCT
ejpam-5918	542	11	(	(	PUNCT
ejpam-5918	542	12	2025	2025	NUM
ejpam-5918	542	13	)	)	PUNCT
ejpam-5918	542	14	,	,	PUNCT
ejpam-5918	542	15	5918	5918	NUM
ejpam-5918	542	16	17	17	NUM
ejpam-5918	542	17	of	of	ADP
ejpam-5918	542	18	21	21	NUM
ejpam-5918	542	19	now	now	ADV
ejpam-5918	542	20	,	,	PUNCT
ejpam-5918	542	21	if	if	SCONJ
ejpam-5918	542	22	degi(u	degi(u	NOUN
ejpam-5918	542	23	)	)	PUNCT
ejpam-5918	542	24	=	=	SYM
ejpam-5918	542	25	0	0	NUM
ejpam-5918	543	1	for	for	ADP
ejpam-5918	543	2	some	some	DET
ejpam-5918	543	3	u	u	NOUN
ejpam-5918	543	4	∈	∈	PROPN
ejpam-5918	543	5	i	i	PRON
ejpam-5918	543	6	,	,	PUNCT
ejpam-5918	543	7	then	then	ADV
ejpam-5918	543	8	u	u	PRON
ejpam-5918	543	9	would	would	AUX
ejpam-5918	543	10	not	not	PART
ejpam-5918	543	11	contribute	contribute	VERB
ejpam-5918	543	12	to	to	ADP
ejpam-5918	543	13	the	the	DET
ejpam-5918	543	14	domination	domination	NOUN
ejpam-5918	543	15	of	of	ADP
ejpam-5918	543	16	s(g	s(g	PROPN
ejpam-5918	543	17	)	)	PUNCT
ejpam-5918	543	18	.	.	PUNCT
ejpam-5918	544	1	specifically	specifically	ADV
ejpam-5918	544	2	,	,	PUNCT
ejpam-5918	544	3	u	u	PRON
ejpam-5918	544	4	would	would	AUX
ejpam-5918	544	5	fail	fail	VERB
ejpam-5918	544	6	to	to	PART
ejpam-5918	544	7	dominate	dominate	VERB
ejpam-5918	544	8	u′	u′	PRON
ejpam-5918	544	9	∈	∈	PROPN
ejpam-5918	544	10	v	v	ADP
ejpam-5918	544	11	′(g	′(g	NOUN
ejpam-5918	544	12	)	)	PUNCT
ejpam-5918	544	13	,	,	PUNCT
ejpam-5918	544	14	the	the	DET
ejpam-5918	544	15	shadow	shadow	NOUN
ejpam-5918	544	16	vertex	vertex	NOUN
ejpam-5918	544	17	corresponding	corresponding	NOUN
ejpam-5918	544	18	to	to	ADP
ejpam-5918	544	19	u	u	PRON
ejpam-5918	544	20	,	,	PUNCT
ejpam-5918	544	21	violating	violate	VERB
ejpam-5918	544	22	the	the	DET
ejpam-5918	544	23	domination	domination	NOUN
ejpam-5918	544	24	property	property	NOUN
ejpam-5918	544	25	of	of	ADP
ejpam-5918	544	26	i	i	PRON
ejpam-5918	544	27	in	in	ADP
ejpam-5918	544	28	s(g	s(g	PROPN
ejpam-5918	544	29	)	)	PUNCT
ejpam-5918	544	30	.	.	PUNCT
ejpam-5918	545	1	hence	hence	ADV
ejpam-5918	545	2	,	,	PUNCT
ejpam-5918	545	3	degi(u	degi(u	NOUN
ejpam-5918	545	4	)	)	PUNCT
ejpam-5918	545	5	̸=	̸=	PROPN
ejpam-5918	545	6	0	0	NUM
ejpam-5918	545	7	for	for	ADP
ejpam-5918	545	8	all	all	DET
ejpam-5918	545	9	u	u	PROPN
ejpam-5918	545	10	∈	∈	PROPN
ejpam-5918	545	11	i.	i.	NOUN
ejpam-5918	545	12	conversely	conversely	ADV
ejpam-5918	545	13	,	,	PUNCT
ejpam-5918	545	14	assume	assume	VERB
ejpam-5918	545	15	i	i	PRON
ejpam-5918	545	16	⊆	⊆	NUM
ejpam-5918	545	17	v	v	ADP
ejpam-5918	545	18	(	(	PUNCT
ejpam-5918	545	19	g	g	NOUN
ejpam-5918	545	20	)	)	PUNCT
ejpam-5918	545	21	satisfies	satisfie	NOUN
ejpam-5918	545	22	(	(	PUNCT
ejpam-5918	545	23	i	i	NOUN
ejpam-5918	545	24	)	)	PUNCT
ejpam-5918	545	25	and	and	CCONJ
ejpam-5918	545	26	(	(	PUNCT
ejpam-5918	545	27	ii	ii	NOUN
ejpam-5918	545	28	)	)	PUNCT
ejpam-5918	545	29	.	.	PUNCT
ejpam-5918	546	1	by	by	ADP
ejpam-5918	546	2	condition	condition	NOUN
ejpam-5918	546	3	(	(	PUNCT
ejpam-5918	546	4	i	i	NOUN
ejpam-5918	546	5	)	)	PUNCT
ejpam-5918	546	6	,	,	PUNCT
ejpam-5918	546	7	i	i	PRON
ejpam-5918	546	8	dominates	dominate	VERB
ejpam-5918	546	9	v	v	ADP
ejpam-5918	546	10	(	(	PUNCT
ejpam-5918	546	11	g	g	NOUN
ejpam-5918	546	12	)	)	PUNCT
ejpam-5918	546	13	.	.	PUNCT
ejpam-5918	547	1	this	this	PRON
ejpam-5918	547	2	follows	follow	VERB
ejpam-5918	547	3	,	,	PUNCT
ejpam-5918	547	4	each	each	DET
ejpam-5918	547	5	shadow	shadow	NOUN
ejpam-5918	547	6	vertex	vertex	NOUN
ejpam-5918	547	7	v′	v′	PROPN
ejpam-5918	547	8	∈	∈	PROPN
ejpam-5918	547	9	v	v	ADP
ejpam-5918	547	10	′(g	′(g	NOUN
ejpam-5918	547	11	)	)	PUNCT
ejpam-5918	547	12	is	be	AUX
ejpam-5918	547	13	adjacent	adjacent	ADJ
ejpam-5918	547	14	to	to	ADP
ejpam-5918	547	15	the	the	DET
ejpam-5918	547	16	neighbors	neighbor	NOUN
ejpam-5918	547	17	of	of	ADP
ejpam-5918	547	18	its	its	PRON
ejpam-5918	547	19	corresponding	correspond	VERB
ejpam-5918	547	20	vertex	vertex	NOUN
ejpam-5918	547	21	v	v	ADP
ejpam-5918	547	22	∈	∈	PROPN
ejpam-5918	547	23	v	v	NOUN
ejpam-5918	547	24	(	(	PUNCT
ejpam-5918	547	25	g	g	NOUN
ejpam-5918	547	26	)	)	PUNCT
ejpam-5918	547	27	.	.	PUNCT
ejpam-5918	548	1	since	since	SCONJ
ejpam-5918	548	2	i	i	PRON
ejpam-5918	548	3	dominates	dominate	VERB
ejpam-5918	548	4	v	v	ADP
ejpam-5918	548	5	(	(	PUNCT
ejpam-5918	548	6	g	g	NOUN
ejpam-5918	548	7	)	)	PUNCT
ejpam-5918	548	8	,	,	PUNCT
ejpam-5918	548	9	it	it	PRON
ejpam-5918	548	10	also	also	ADV
ejpam-5918	548	11	dominates	dominate	VERB
ejpam-5918	548	12	v	v	ADP
ejpam-5918	548	13	′(g	′(g	NOUN
ejpam-5918	548	14	)	)	PUNCT
ejpam-5918	548	15	.	.	PUNCT
ejpam-5918	549	1	hence	hence	ADV
ejpam-5918	549	2	,	,	PUNCT
ejpam-5918	549	3	i	i	PRON
ejpam-5918	549	4	dominates	dominate	VERB
ejpam-5918	549	5	all	all	PRON
ejpam-5918	549	6	of	of	ADP
ejpam-5918	549	7	v	v	NOUN
ejpam-5918	549	8	(	(	PUNCT
ejpam-5918	549	9	s(g	s(g	PROPN
ejpam-5918	549	10	)	)	PUNCT
ejpam-5918	549	11	)	)	PUNCT
ejpam-5918	550	1	=	=	SYM
ejpam-5918	550	2	v	v	X
ejpam-5918	550	3	(	(	PUNCT
ejpam-5918	550	4	g	g	NOUN
ejpam-5918	550	5	)	)	PUNCT
ejpam-5918	550	6	∪	∪	ADP
ejpam-5918	550	7	v	v	ADP
ejpam-5918	550	8	′(g	′(g	NOUN
ejpam-5918	550	9	)	)	PUNCT
ejpam-5918	550	10	.	.	PUNCT
ejpam-5918	551	1	now	now	ADV
ejpam-5918	551	2	,	,	PUNCT
ejpam-5918	551	3	by	by	ADP
ejpam-5918	551	4	(	(	PUNCT
ejpam-5918	551	5	i	i	NOUN
ejpam-5918	551	6	)	)	PUNCT
ejpam-5918	551	7	,	,	PUNCT
ejpam-5918	551	8	for	for	ADP
ejpam-5918	551	9	any	any	DET
ejpam-5918	551	10	distinct	distinct	ADJ
ejpam-5918	551	11	u	u	NOUN
ejpam-5918	551	12	,	,	PUNCT
ejpam-5918	551	13	v	v	NOUN
ejpam-5918	551	14	∈	∈	X
ejpam-5918	551	15	i	i	PRON
ejpam-5918	551	16	,	,	PUNCT
ejpam-5918	551	17	their	their	PRON
ejpam-5918	551	18	neighborhoods	neighborhood	NOUN
ejpam-5918	551	19	in	in	ADP
ejpam-5918	551	20	v	v	NOUN
ejpam-5918	551	21	(	(	PUNCT
ejpam-5918	551	22	g	g	NOUN
ejpam-5918	551	23	)	)	PUNCT
ejpam-5918	551	24	satisfy	satisfy	NOUN
ejpam-5918	551	25	n(u)∩	n(u)∩	ADV
ejpam-5918	551	26	i	i	PROPN
ejpam-5918	551	27	̸=	̸=	PROPN
ejpam-5918	551	28	n(v)∩i	n(v)∩i	NOUN
ejpam-5918	551	29	.	.	PUNCT
ejpam-5918	552	1	this	this	DET
ejpam-5918	552	2	uniqueness	uniqueness	NOUN
ejpam-5918	552	3	extends	extend	VERB
ejpam-5918	552	4	to	to	ADP
ejpam-5918	552	5	s(g	s(g	PROPN
ejpam-5918	552	6	)	)	PUNCT
ejpam-5918	552	7	because	because	SCONJ
ejpam-5918	552	8	the	the	DET
ejpam-5918	552	9	neighborhoods	neighborhood	NOUN
ejpam-5918	552	10	of	of	ADP
ejpam-5918	552	11	vertices	vertex	NOUN
ejpam-5918	552	12	in	in	ADP
ejpam-5918	552	13	v	v	NOUN
ejpam-5918	552	14	′(g	′(g	NOUN
ejpam-5918	552	15	)	)	PUNCT
ejpam-5918	552	16	are	be	AUX
ejpam-5918	552	17	determined	determine	VERB
ejpam-5918	552	18	by	by	ADP
ejpam-5918	552	19	their	their	PRON
ejpam-5918	552	20	neighbors	neighbor	NOUN
ejpam-5918	552	21	in	in	ADP
ejpam-5918	552	22	v	v	NOUN
ejpam-5918	552	23	(	(	PUNCT
ejpam-5918	552	24	g	g	NOUN
ejpam-5918	552	25	)	)	PUNCT
ejpam-5918	552	26	.	.	PUNCT
ejpam-5918	553	1	thus	thus	ADV
ejpam-5918	553	2	,	,	PUNCT
ejpam-5918	553	3	n(u	n(u	PROPN
ejpam-5918	553	4	)	)	PUNCT
ejpam-5918	553	5	∩	∩	NOUN
ejpam-5918	553	6	i	i	PRON
ejpam-5918	553	7	̸=	̸=	PROPN
ejpam-5918	553	8	n(v	n(v	PROPN
ejpam-5918	553	9	)	)	PUNCT
ejpam-5918	553	10	∩	∩	NOUN
ejpam-5918	553	11	i	i	PRON
ejpam-5918	553	12	for	for	ADP
ejpam-5918	553	13	any	any	DET
ejpam-5918	553	14	u	u	NOUN
ejpam-5918	553	15	,	,	PUNCT
ejpam-5918	553	16	v	v	NOUN
ejpam-5918	553	17	∈	∈	NOUN
ejpam-5918	553	18	i	i	PRON
ejpam-5918	553	19	in	in	ADP
ejpam-5918	553	20	s(g	s(g	PROPN
ejpam-5918	553	21	)	)	PUNCT
ejpam-5918	553	22	.	.	PUNCT
ejpam-5918	554	1	finally	finally	ADV
ejpam-5918	554	2	,	,	PUNCT
ejpam-5918	554	3	by	by	ADP
ejpam-5918	554	4	(	(	PUNCT
ejpam-5918	554	5	ii	ii	NOUN
ejpam-5918	554	6	)	)	PUNCT
ejpam-5918	554	7	,	,	PUNCT
ejpam-5918	554	8	degi(u	degi(u	NOUN
ejpam-5918	554	9	)	)	PUNCT
ejpam-5918	554	10	̸=	̸=	PROPN
ejpam-5918	554	11	0	0	NUM
ejpam-5918	554	12	for	for	ADP
ejpam-5918	554	13	all	all	PRON
ejpam-5918	554	14	u	u	NOUN
ejpam-5918	554	15	∈	∈	PROPN
ejpam-5918	554	16	i	i	PRON
ejpam-5918	554	17	,	,	PUNCT
ejpam-5918	554	18	ensuring	ensure	VERB
ejpam-5918	554	19	that	that	SCONJ
ejpam-5918	554	20	every	every	DET
ejpam-5918	554	21	vertex	vertex	NOUN
ejpam-5918	554	22	in	in	ADP
ejpam-5918	554	23	i	i	PRON
ejpam-5918	554	24	actively	actively	ADV
ejpam-5918	554	25	contributes	contribute	VERB
ejpam-5918	554	26	to	to	ADP
ejpam-5918	554	27	the	the	DET
ejpam-5918	554	28	domination	domination	NOUN
ejpam-5918	554	29	of	of	ADP
ejpam-5918	554	30	s(g	s(g	PROPN
ejpam-5918	554	31	)	)	PUNCT
ejpam-5918	554	32	.	.	PUNCT
ejpam-5918	555	1	therefore	therefore	ADV
ejpam-5918	555	2	,	,	PUNCT
ejpam-5918	555	3	i	i	PRON
ejpam-5918	555	4	satisfies	satisfy	VERB
ejpam-5918	555	5	the	the	DET
ejpam-5918	555	6	conditions	condition	NOUN
ejpam-5918	555	7	to	to	PART
ejpam-5918	555	8	be	be	AUX
ejpam-5918	555	9	an	an	DET
ejpam-5918	555	10	ilds	ild	NOUN
ejpam-5918	555	11	in	in	ADP
ejpam-5918	555	12	s(g	s(g	PROPN
ejpam-5918	555	13	)	)	PUNCT
ejpam-5918	555	14	.	.	PUNCT
ejpam-5918	556	1	lemma	lemma	PROPN
ejpam-5918	556	2	1	1	X
ejpam-5918	556	3	.	.	PUNCT
ejpam-5918	557	1	let	let	VERB
ejpam-5918	557	2	g	g	PRON
ejpam-5918	557	3	be	be	AUX
ejpam-5918	557	4	a	a	DET
ejpam-5918	557	5	path	path	NOUN
ejpam-5918	557	6	graph	graph	NOUN
ejpam-5918	557	7	pn	pn	NOUN
ejpam-5918	557	8	or	or	CCONJ
ejpam-5918	557	9	cycle	cycle	NOUN
ejpam-5918	557	10	graph	graph	NOUN
ejpam-5918	557	11	cn	cn	NOUN
ejpam-5918	557	12	of	of	ADP
ejpam-5918	557	13	order	order	NOUN
ejpam-5918	557	14	n	n	PRON
ejpam-5918	557	15	≥	≥	NUM
ejpam-5918	557	16	2	2	NUM
ejpam-5918	557	17	such	such	ADJ
ejpam-5918	557	18	that	that	SCONJ
ejpam-5918	557	19	n	n	NUM
ejpam-5918	557	20	≡	≡	PROPN
ejpam-5918	557	21	0	0	PUNCT
ejpam-5918	557	22	(	(	PUNCT
ejpam-5918	557	23	mod	mod	PROPN
ejpam-5918	557	24	4	4	NUM
ejpam-5918	557	25	)	)	PUNCT
ejpam-5918	557	26	.	.	PUNCT
ejpam-5918	558	1	then	then	ADV
ejpam-5918	558	2	i	i	PRON
ejpam-5918	558	3	⊆	⊆	NUM
ejpam-5918	558	4	v	v	X
ejpam-5918	558	5	(	(	PUNCT
ejpam-5918	558	6	s(g	s(g	PROPN
ejpam-5918	558	7	)	)	PUNCT
ejpam-5918	558	8	)	)	PUNCT
ejpam-5918	558	9	with	with	ADP
ejpam-5918	558	10	i	i	PRON
ejpam-5918	558	11	=	=	PUNCT
ejpam-5918	558	12	{	{	PUNCT
ejpam-5918	558	13	v2	v2	PROPN
ejpam-5918	558	14	,	,	PUNCT
ejpam-5918	558	15	v3	v3	PROPN
ejpam-5918	558	16	,	,	PUNCT
ejpam-5918	558	17	v6	v6	NOUN
ejpam-5918	558	18	,	,	PUNCT
ejpam-5918	558	19	v7	v7	NOUN
ejpam-5918	558	20	,	,	PUNCT
ejpam-5918	558	21	.	.	PUNCT
ejpam-5918	558	22	.	.	PUNCT
ejpam-5918	558	23	.	.	PUNCT
ejpam-5918	559	1	,	,	PUNCT
ejpam-5918	559	2	vn−2	vn−2	PROPN
ejpam-5918	559	3	,	,	PUNCT
ejpam-5918	559	4	vn−1	vn−1	ADJ
ejpam-5918	559	5	}	}	PUNCT
ejpam-5918	559	6	is	be	AUX
ejpam-5918	559	7	a	a	DET
ejpam-5918	559	8	minimum	minimum	ADJ
ejpam-5918	559	9	internallylocating	internallylocate	VERB
ejpam-5918	559	10	dominating	dominating	NOUN
ejpam-5918	559	11	set	set	VERB
ejpam-5918	559	12	in	in	ADP
ejpam-5918	559	13	g.	g.	PROPN
ejpam-5918	559	14	proof	proof	PROPN
ejpam-5918	559	15	.	.	PUNCT
ejpam-5918	560	1	let	let	VERB
ejpam-5918	560	2	i	i	PRON
ejpam-5918	560	3	⊆	⊆	NUM
ejpam-5918	560	4	v	v	X
ejpam-5918	560	5	(	(	PUNCT
ejpam-5918	560	6	s(g	s(g	PROPN
ejpam-5918	560	7	)	)	PUNCT
ejpam-5918	560	8	)	)	PUNCT
ejpam-5918	560	9	with	with	ADP
ejpam-5918	560	10	i	i	PRON
ejpam-5918	560	11	=	=	PUNCT
ejpam-5918	560	12	{	{	PUNCT
ejpam-5918	560	13	v2	v2	PROPN
ejpam-5918	560	14	,	,	PUNCT
ejpam-5918	560	15	v3	v3	PROPN
ejpam-5918	560	16	,	,	PUNCT
ejpam-5918	560	17	v6	v6	NOUN
ejpam-5918	560	18	,	,	PUNCT
ejpam-5918	560	19	v7	v7	NOUN
ejpam-5918	560	20	,	,	PUNCT
ejpam-5918	560	21	.	.	PUNCT
ejpam-5918	560	22	.	.	PUNCT
ejpam-5918	561	1	.	.	PUNCT
ejpam-5918	562	1	,	,	PUNCT
ejpam-5918	562	2	vn−2	vn−2	PROPN
ejpam-5918	562	3	,	,	PUNCT
ejpam-5918	562	4	vn−1	vn−1	ADJ
ejpam-5918	562	5	}	}	PUNCT
ejpam-5918	562	6	.	.	PUNCT
ejpam-5918	563	1	note	note	VERB
ejpam-5918	563	2	that	that	SCONJ
ejpam-5918	563	3	i	i	PRON
ejpam-5918	563	4	is	be	AUX
ejpam-5918	563	5	an	an	DET
ejpam-5918	563	6	internally	internally	ADV
ejpam-5918	563	7	-	-	PUNCT
ejpam-5918	563	8	locating	locate	VERB
ejpam-5918	563	9	dominating	dominating	NOUN
ejpam-5918	563	10	set	set	VERB
ejpam-5918	563	11	in	in	ADP
ejpam-5918	563	12	v	v	NOUN
ejpam-5918	563	13	(	(	PUNCT
ejpam-5918	563	14	g	g	NOUN
ejpam-5918	563	15	)	)	PUNCT
ejpam-5918	563	16	by	by	ADP
ejpam-5918	563	17	theorem	theorem	NOUN
ejpam-5918	563	18	4	4	NUM
ejpam-5918	563	19	.	.	PUNCT
ejpam-5918	564	1	so	so	ADV
ejpam-5918	564	2	,	,	PUNCT
ejpam-5918	564	3	theorem	theorem	VERB
ejpam-5918	564	4	11	11	NUM
ejpam-5918	564	5	(	(	PUNCT
ejpam-5918	564	6	i	i	NOUN
ejpam-5918	564	7	)	)	PUNCT
ejpam-5918	564	8	is	be	AUX
ejpam-5918	564	9	satisfied	satisfied	ADJ
ejpam-5918	564	10	.	.	PUNCT
ejpam-5918	565	1	additionally	additionally	ADV
ejpam-5918	565	2	,	,	PUNCT
ejpam-5918	565	3	for	for	ADP
ejpam-5918	565	4	all	all	DET
ejpam-5918	565	5	u	u	PRON
ejpam-5918	565	6	∈	∈	PROPN
ejpam-5918	565	7	i	i	PRON
ejpam-5918	565	8	,	,	PUNCT
ejpam-5918	565	9	degi(u	degi(u	PROPN
ejpam-5918	565	10	)	)	PUNCT
ejpam-5918	565	11	̸=	̸=	PROPN
ejpam-5918	565	12	0	0	NUM
ejpam-5918	565	13	.	.	PUNCT
ejpam-5918	566	1	this	this	PRON
ejpam-5918	566	2	implies	imply	VERB
ejpam-5918	566	3	,	,	PUNCT
ejpam-5918	566	4	theorem	theorem	VERB
ejpam-5918	566	5	11	11	NUM
ejpam-5918	566	6	(	(	PUNCT
ejpam-5918	566	7	i	i	NOUN
ejpam-5918	566	8	)	)	PUNCT
ejpam-5918	566	9	is	be	AUX
ejpam-5918	566	10	satisfied	satisfied	ADJ
ejpam-5918	566	11	.	.	PUNCT
ejpam-5918	567	1	now	now	ADV
ejpam-5918	567	2	,	,	PUNCT
ejpam-5918	567	3	removing	remove	VERB
ejpam-5918	567	4	a	a	DET
ejpam-5918	567	5	vertex	vertex	NOUN
ejpam-5918	567	6	v	v	NOUN
ejpam-5918	567	7	in	in	ADP
ejpam-5918	567	8	i	i	PROPN
ejpam-5918	567	9	,	,	PUNCT
ejpam-5918	567	10	contradicts	contradict	VERB
ejpam-5918	567	11	theorem	theorem	ADJ
ejpam-5918	567	12	11	11	NUM
ejpam-5918	567	13	(	(	PUNCT
ejpam-5918	567	14	ii	ii	NOUN
ejpam-5918	567	15	)	)	PUNCT
ejpam-5918	567	16	.	.	PUNCT
ejpam-5918	568	1	hence	hence	ADV
ejpam-5918	568	2	,	,	PUNCT
ejpam-5918	568	3	i	i	PRON
ejpam-5918	568	4	is	be	AUX
ejpam-5918	568	5	a	a	DET
ejpam-5918	568	6	γli	γli	ADJ
ejpam-5918	568	7	−	−	PROPN
ejpam-5918	568	8	set	set	NOUN
ejpam-5918	568	9	.	.	PUNCT
ejpam-5918	569	1	lemma	lemma	PROPN
ejpam-5918	569	2	2	2	X
ejpam-5918	569	3	.	.	PUNCT
ejpam-5918	570	1	let	let	VERB
ejpam-5918	570	2	g	g	PRON
ejpam-5918	570	3	be	be	AUX
ejpam-5918	570	4	a	a	DET
ejpam-5918	570	5	path	path	NOUN
ejpam-5918	570	6	graph	graph	NOUN
ejpam-5918	570	7	pn	pn	NOUN
ejpam-5918	570	8	or	or	CCONJ
ejpam-5918	570	9	cycle	cycle	NOUN
ejpam-5918	570	10	graph	graph	NOUN
ejpam-5918	570	11	cn	cn	NOUN
ejpam-5918	570	12	of	of	ADP
ejpam-5918	570	13	order	order	NOUN
ejpam-5918	570	14	n	n	PRON
ejpam-5918	570	15	≥	≥	NUM
ejpam-5918	570	16	2	2	NUM
ejpam-5918	570	17	such	such	ADJ
ejpam-5918	570	18	that	that	SCONJ
ejpam-5918	570	19	n	n	NUM
ejpam-5918	570	20	≡	≡	PROPN
ejpam-5918	570	21	1	1	NUM
ejpam-5918	570	22	(	(	PUNCT
ejpam-5918	570	23	mod	mod	NOUN
ejpam-5918	570	24	4	4	NUM
ejpam-5918	570	25	)	)	PUNCT
ejpam-5918	570	26	.	.	PUNCT
ejpam-5918	571	1	then	then	ADV
ejpam-5918	571	2	i	i	PRON
ejpam-5918	571	3	⊆	⊆	NUM
ejpam-5918	571	4	v	v	X
ejpam-5918	571	5	(	(	PUNCT
ejpam-5918	571	6	s(g	s(g	PROPN
ejpam-5918	571	7	)	)	PUNCT
ejpam-5918	571	8	)	)	PUNCT
ejpam-5918	571	9	with	with	ADP
ejpam-5918	571	10	i	i	PRON
ejpam-5918	571	11	=	=	SYM
ejpam-5918	571	12	{	{	PUNCT
ejpam-5918	571	13	v1	v1	PROPN
ejpam-5918	571	14	,	,	PUNCT
ejpam-5918	571	15	v2	v2	PROPN
ejpam-5918	571	16	,	,	PUNCT
ejpam-5918	571	17	v5	v5	PROPN
ejpam-5918	571	18	,	,	PUNCT
ejpam-5918	571	19	v6	v6	NOUN
ejpam-5918	571	20	,	,	PUNCT
ejpam-5918	571	21	.	.	PUNCT
ejpam-5918	571	22	.	.	PUNCT
ejpam-5918	571	23	.	.	PUNCT
ejpam-5918	572	1	,	,	PUNCT
ejpam-5918	572	2	vn−4	vn−4	NOUN
ejpam-5918	572	3	,	,	PUNCT
ejpam-5918	572	4	vn−3	vn−3	PROPN
ejpam-5918	572	5	,	,	PUNCT
ejpam-5918	572	6	vn−1	vn−1	ADJ
ejpam-5918	572	7	,	,	PUNCT
ejpam-5918	572	8	vn	vn	VERB
ejpam-5918	572	9	}	}	PUNCT
ejpam-5918	572	10	is	be	AUX
ejpam-5918	572	11	a	a	DET
ejpam-5918	572	12	minimum	minimum	NOUN
ejpam-5918	572	13	internally	internally	ADV
ejpam-5918	572	14	-	-	PUNCT
ejpam-5918	572	15	locating	locate	VERB
ejpam-5918	572	16	dominating	dominating	NOUN
ejpam-5918	572	17	set	set	VERB
ejpam-5918	572	18	in	in	ADP
ejpam-5918	572	19	g.	g.	PROPN
ejpam-5918	572	20	proof	proof	PROPN
ejpam-5918	572	21	.	.	PUNCT
ejpam-5918	573	1	let	let	VERB
ejpam-5918	573	2	i	i	PRON
ejpam-5918	573	3	⊆	⊆	NUM
ejpam-5918	573	4	v	v	X
ejpam-5918	573	5	(	(	PUNCT
ejpam-5918	573	6	s(g	s(g	PROPN
ejpam-5918	573	7	)	)	PUNCT
ejpam-5918	573	8	)	)	PUNCT
ejpam-5918	573	9	with	with	ADP
ejpam-5918	573	10	i	i	PRON
ejpam-5918	573	11	=	=	SYM
ejpam-5918	573	12	{	{	PUNCT
ejpam-5918	573	13	v1	v1	PROPN
ejpam-5918	573	14	,	,	PUNCT
ejpam-5918	573	15	v2	v2	PROPN
ejpam-5918	573	16	,	,	PUNCT
ejpam-5918	573	17	v5	v5	PROPN
ejpam-5918	573	18	,	,	PUNCT
ejpam-5918	573	19	v6	v6	NOUN
ejpam-5918	573	20	,	,	PUNCT
ejpam-5918	573	21	.	.	PUNCT
ejpam-5918	573	22	.	.	PUNCT
ejpam-5918	574	1	.	.	PUNCT
ejpam-5918	575	1	,	,	PUNCT
ejpam-5918	575	2	vn−4	vn−4	NOUN
ejpam-5918	575	3	,	,	PUNCT
ejpam-5918	575	4	vn−3	vn−3	PROPN
ejpam-5918	575	5	,	,	PUNCT
ejpam-5918	575	6	vn−1	vn−1	ADJ
ejpam-5918	575	7	,	,	PUNCT
ejpam-5918	575	8	vn	vn	NOUN
ejpam-5918	575	9	}	}	PUNCT
ejpam-5918	575	10	.	.	PUNCT
ejpam-5918	576	1	note	note	VERB
ejpam-5918	576	2	that	that	SCONJ
ejpam-5918	576	3	i	i	PRON
ejpam-5918	576	4	is	be	AUX
ejpam-5918	576	5	an	an	DET
ejpam-5918	576	6	internally	internally	ADV
ejpam-5918	576	7	-	-	PUNCT
ejpam-5918	576	8	locating	locate	VERB
ejpam-5918	576	9	dominating	dominating	NOUN
ejpam-5918	576	10	set	set	VERB
ejpam-5918	576	11	in	in	ADP
ejpam-5918	576	12	v	v	NOUN
ejpam-5918	576	13	(	(	PUNCT
ejpam-5918	576	14	g	g	NOUN
ejpam-5918	576	15	)	)	PUNCT
ejpam-5918	576	16	by	by	ADP
ejpam-5918	576	17	theorem	theorem	NOUN
ejpam-5918	576	18	4	4	NUM
ejpam-5918	576	19	.	.	PUNCT
ejpam-5918	577	1	so	so	ADV
ejpam-5918	577	2	,	,	PUNCT
ejpam-5918	577	3	theorem	theorem	VERB
ejpam-5918	577	4	11	11	NUM
ejpam-5918	577	5	(	(	PUNCT
ejpam-5918	577	6	i	i	NOUN
ejpam-5918	577	7	)	)	PUNCT
ejpam-5918	577	8	is	be	AUX
ejpam-5918	577	9	satisfied	satisfied	ADJ
ejpam-5918	577	10	.	.	PUNCT
ejpam-5918	578	1	additionally	additionally	ADV
ejpam-5918	578	2	,	,	PUNCT
ejpam-5918	578	3	for	for	ADP
ejpam-5918	578	4	all	all	DET
ejpam-5918	578	5	u	u	PRON
ejpam-5918	578	6	∈	∈	PROPN
ejpam-5918	578	7	i	i	PRON
ejpam-5918	578	8	,	,	PUNCT
ejpam-5918	578	9	degi(u	degi(u	PROPN
ejpam-5918	578	10	)	)	PUNCT
ejpam-5918	578	11	̸=	̸=	PROPN
ejpam-5918	578	12	0	0	NUM
ejpam-5918	578	13	.	.	PUNCT
ejpam-5918	579	1	this	this	PRON
ejpam-5918	579	2	implies	imply	VERB
ejpam-5918	579	3	,	,	PUNCT
ejpam-5918	579	4	theorem	theorem	VERB
ejpam-5918	579	5	11	11	NUM
ejpam-5918	579	6	(	(	PUNCT
ejpam-5918	579	7	i	i	NOUN
ejpam-5918	579	8	)	)	PUNCT
ejpam-5918	579	9	is	be	AUX
ejpam-5918	579	10	satisfied	satisfied	ADJ
ejpam-5918	579	11	.	.	PUNCT
ejpam-5918	580	1	now	now	ADV
ejpam-5918	580	2	,	,	PUNCT
ejpam-5918	580	3	removing	remove	VERB
ejpam-5918	580	4	a	a	DET
ejpam-5918	580	5	vertex	vertex	NOUN
ejpam-5918	580	6	v	v	NOUN
ejpam-5918	580	7	in	in	ADP
ejpam-5918	580	8	i	i	PROPN
ejpam-5918	580	9	,	,	PUNCT
ejpam-5918	580	10	contradicts	contradict	VERB
ejpam-5918	580	11	theorem	theorem	ADJ
ejpam-5918	580	12	11	11	NUM
ejpam-5918	580	13	(	(	PUNCT
ejpam-5918	580	14	ii	ii	NOUN
ejpam-5918	580	15	)	)	PUNCT
ejpam-5918	580	16	.	.	PUNCT
ejpam-5918	581	1	hence	hence	ADV
ejpam-5918	581	2	,	,	PUNCT
ejpam-5918	581	3	i	i	PRON
ejpam-5918	581	4	is	be	AUX
ejpam-5918	581	5	a	a	DET
ejpam-5918	581	6	γli	γli	ADJ
ejpam-5918	581	7	−	−	PROPN
ejpam-5918	581	8	set	set	NOUN
ejpam-5918	581	9	.	.	PUNCT
ejpam-5918	582	1	lemma	lemma	PROPN
ejpam-5918	582	2	3	3	X
ejpam-5918	582	3	.	.	PUNCT
ejpam-5918	583	1	let	let	VERB
ejpam-5918	583	2	g	g	PRON
ejpam-5918	583	3	be	be	AUX
ejpam-5918	583	4	a	a	DET
ejpam-5918	583	5	path	path	NOUN
ejpam-5918	583	6	graph	graph	NOUN
ejpam-5918	583	7	pn	pn	NOUN
ejpam-5918	583	8	or	or	CCONJ
ejpam-5918	583	9	cycle	cycle	NOUN
ejpam-5918	583	10	graph	graph	NOUN
ejpam-5918	583	11	cn	cn	NOUN
ejpam-5918	583	12	of	of	ADP
ejpam-5918	583	13	order	order	NOUN
ejpam-5918	583	14	n	n	PRON
ejpam-5918	583	15	≥	≥	NUM
ejpam-5918	583	16	2	2	NUM
ejpam-5918	583	17	such	such	ADJ
ejpam-5918	583	18	that	that	SCONJ
ejpam-5918	583	19	n	n	NUM
ejpam-5918	583	20	≡	≡	PROPN
ejpam-5918	583	21	2	2	NUM
ejpam-5918	583	22	(	(	PUNCT
ejpam-5918	583	23	mod	mod	NOUN
ejpam-5918	583	24	4	4	NUM
ejpam-5918	583	25	)	)	PUNCT
ejpam-5918	583	26	.	.	PUNCT
ejpam-5918	584	1	then	then	ADV
ejpam-5918	584	2	i	i	PRON
ejpam-5918	584	3	⊆	⊆	NUM
ejpam-5918	584	4	v	v	X
ejpam-5918	584	5	(	(	PUNCT
ejpam-5918	584	6	s(g	s(g	PROPN
ejpam-5918	584	7	)	)	PUNCT
ejpam-5918	584	8	)	)	PUNCT
ejpam-5918	584	9	with	with	ADP
ejpam-5918	584	10	i	i	PRON
ejpam-5918	584	11	=	=	SYM
ejpam-5918	584	12	{	{	PUNCT
ejpam-5918	584	13	v1	v1	PROPN
ejpam-5918	584	14	,	,	PUNCT
ejpam-5918	584	15	v2	v2	PROPN
ejpam-5918	584	16	,	,	PUNCT
ejpam-5918	584	17	v5	v5	PROPN
ejpam-5918	584	18	,	,	PUNCT
ejpam-5918	584	19	v6	v6	NOUN
ejpam-5918	584	20	,	,	PUNCT
ejpam-5918	584	21	.	.	PUNCT
ejpam-5918	584	22	.	.	PUNCT
ejpam-5918	584	23	.	.	PUNCT
ejpam-5918	585	1	,	,	PUNCT
ejpam-5918	585	2	vn−5	vn−5	PROPN
ejpam-5918	585	3	,	,	PUNCT
ejpam-5918	585	4	vn−4	vn−4	NOUN
ejpam-5918	585	5	,	,	PUNCT
ejpam-5918	585	6	vn−1	vn−1	PROPN
ejpam-5918	585	7	,	,	PUNCT
ejpam-5918	585	8	vn	vn	VERB
ejpam-5918	585	9	}	}	PUNCT
ejpam-5918	585	10	is	be	AUX
ejpam-5918	585	11	a	a	DET
ejpam-5918	585	12	minimum	minimum	NOUN
ejpam-5918	585	13	internally	internally	ADV
ejpam-5918	585	14	-	-	PUNCT
ejpam-5918	585	15	locating	locate	VERB
ejpam-5918	585	16	dominating	dominating	NOUN
ejpam-5918	585	17	set	set	VERB
ejpam-5918	585	18	in	in	ADP
ejpam-5918	585	19	g.	g.	PROPN
ejpam-5918	585	20	proof	proof	PROPN
ejpam-5918	585	21	.	.	PUNCT
ejpam-5918	586	1	let	let	VERB
ejpam-5918	586	2	i	i	PRON
ejpam-5918	586	3	⊆	⊆	NUM
ejpam-5918	586	4	v	v	X
ejpam-5918	586	5	(	(	PUNCT
ejpam-5918	586	6	s(g	s(g	PROPN
ejpam-5918	586	7	)	)	PUNCT
ejpam-5918	586	8	)	)	PUNCT
ejpam-5918	586	9	with	with	ADP
ejpam-5918	586	10	i	i	PRON
ejpam-5918	586	11	=	=	SYM
ejpam-5918	586	12	{	{	PUNCT
ejpam-5918	586	13	v1	v1	PROPN
ejpam-5918	586	14	,	,	PUNCT
ejpam-5918	586	15	v2	v2	PROPN
ejpam-5918	586	16	,	,	PUNCT
ejpam-5918	586	17	v5	v5	PROPN
ejpam-5918	586	18	,	,	PUNCT
ejpam-5918	586	19	v6	v6	NOUN
ejpam-5918	586	20	,	,	PUNCT
ejpam-5918	586	21	.	.	PUNCT
ejpam-5918	586	22	.	.	PUNCT
ejpam-5918	587	1	.	.	PUNCT
ejpam-5918	588	1	,	,	PUNCT
ejpam-5918	588	2	vn−5	vn−5	PROPN
ejpam-5918	588	3	,	,	PUNCT
ejpam-5918	588	4	vn−4	vn−4	NOUN
ejpam-5918	588	5	,	,	PUNCT
ejpam-5918	588	6	vn−1	vn−1	PROPN
ejpam-5918	588	7	,	,	PUNCT
ejpam-5918	588	8	vn	vn	NOUN
ejpam-5918	588	9	}	}	PUNCT
ejpam-5918	588	10	.	.	PUNCT
ejpam-5918	589	1	note	note	VERB
ejpam-5918	589	2	that	that	SCONJ
ejpam-5918	589	3	i	i	PRON
ejpam-5918	589	4	is	be	AUX
ejpam-5918	589	5	an	an	DET
ejpam-5918	589	6	internally	internally	ADV
ejpam-5918	589	7	-	-	PUNCT
ejpam-5918	589	8	locating	locate	VERB
ejpam-5918	589	9	dominating	dominating	NOUN
ejpam-5918	589	10	set	set	VERB
ejpam-5918	589	11	in	in	ADP
ejpam-5918	589	12	v	v	NOUN
ejpam-5918	589	13	(	(	PUNCT
ejpam-5918	589	14	g	g	NOUN
ejpam-5918	589	15	)	)	PUNCT
ejpam-5918	589	16	by	by	ADP
ejpam-5918	589	17	theorem	theorem	NOUN
ejpam-5918	589	18	4	4	NUM
ejpam-5918	589	19	.	.	PUNCT
ejpam-5918	590	1	so	so	ADV
ejpam-5918	590	2	,	,	PUNCT
ejpam-5918	590	3	theorem	theorem	VERB
ejpam-5918	590	4	11	11	NUM
ejpam-5918	590	5	(	(	PUNCT
ejpam-5918	590	6	i	i	NOUN
ejpam-5918	590	7	)	)	PUNCT
ejpam-5918	590	8	is	be	AUX
ejpam-5918	590	9	satisfied	satisfied	ADJ
ejpam-5918	590	10	.	.	PUNCT
ejpam-5918	591	1	additionally	additionally	ADV
ejpam-5918	591	2	,	,	PUNCT
ejpam-5918	591	3	for	for	ADP
ejpam-5918	591	4	all	all	DET
ejpam-5918	591	5	u	u	PRON
ejpam-5918	591	6	∈	∈	PROPN
ejpam-5918	591	7	i	i	PRON
ejpam-5918	591	8	,	,	PUNCT
ejpam-5918	591	9	degi(u	degi(u	PROPN
ejpam-5918	591	10	)	)	PUNCT
ejpam-5918	591	11	̸=	̸=	PROPN
ejpam-5918	591	12	0	0	NUM
ejpam-5918	591	13	.	.	PUNCT
ejpam-5918	592	1	this	this	PRON
ejpam-5918	592	2	implies	imply	VERB
ejpam-5918	592	3	,	,	PUNCT
ejpam-5918	592	4	theorem	theorem	VERB
ejpam-5918	592	5	11	11	NUM
ejpam-5918	592	6	(	(	PUNCT
ejpam-5918	592	7	i	i	NOUN
ejpam-5918	592	8	)	)	PUNCT
ejpam-5918	592	9	is	be	AUX
ejpam-5918	592	10	satisfied	satisfied	ADJ
ejpam-5918	592	11	.	.	PUNCT
ejpam-5918	593	1	now	now	ADV
ejpam-5918	593	2	,	,	PUNCT
ejpam-5918	593	3	removing	remove	VERB
ejpam-5918	593	4	a	a	DET
ejpam-5918	593	5	vertex	vertex	NOUN
ejpam-5918	593	6	v	v	NOUN
ejpam-5918	593	7	in	in	ADP
ejpam-5918	593	8	i	i	PROPN
ejpam-5918	593	9	,	,	PUNCT
ejpam-5918	593	10	contradicts	contradict	VERB
ejpam-5918	593	11	theorem	theorem	ADJ
ejpam-5918	593	12	11	11	NUM
ejpam-5918	593	13	(	(	PUNCT
ejpam-5918	593	14	ii	ii	NOUN
ejpam-5918	593	15	)	)	PUNCT
ejpam-5918	593	16	.	.	PUNCT
ejpam-5918	594	1	hence	hence	ADV
ejpam-5918	594	2	,	,	PUNCT
ejpam-5918	594	3	i	i	PRON
ejpam-5918	594	4	is	be	AUX
ejpam-5918	594	5	a	a	DET
ejpam-5918	594	6	γli	γli	ADJ
ejpam-5918	594	7	−	−	PROPN
ejpam-5918	594	8	set	set	NOUN
ejpam-5918	594	9	.	.	PUNCT
ejpam-5918	595	1	i.	i.	PROPN
ejpam-5918	595	2	tropico	tropico	PROPN
ejpam-5918	595	3	,	,	PUNCT
ejpam-5918	595	4	i.	i.	PROPN
ejpam-5918	595	5	cabahug	cabahug	PROPN
ejpam-5918	595	6	,	,	PUNCT
ejpam-5918	595	7	jr	jr	PROPN
ejpam-5918	595	8	.	.	PROPN
ejpam-5918	595	9	/	/	SYM
ejpam-5918	595	10	eur	eur	PROPN
ejpam-5918	595	11	.	.	PUNCT
ejpam-5918	596	1	j.	j.	PROPN
ejpam-5918	596	2	pure	pure	PROPN
ejpam-5918	596	3	appl	appl	PROPN
ejpam-5918	596	4	.	.	PROPN
ejpam-5918	596	5	math	math	PROPN
ejpam-5918	596	6	,	,	PUNCT
ejpam-5918	596	7	18	18	NUM
ejpam-5918	596	8	(	(	PUNCT
ejpam-5918	596	9	2	2	NUM
ejpam-5918	596	10	)	)	PUNCT
ejpam-5918	596	11	(	(	PUNCT
ejpam-5918	596	12	2025	2025	NUM
ejpam-5918	596	13	)	)	PUNCT
ejpam-5918	596	14	,	,	PUNCT
ejpam-5918	596	15	5918	5918	NUM
ejpam-5918	596	16	18	18	NUM
ejpam-5918	596	17	of	of	ADP
ejpam-5918	596	18	21	21	NUM
ejpam-5918	596	19	lemma	lemma	PROPN
ejpam-5918	596	20	4	4	NUM
ejpam-5918	596	21	.	.	PUNCT
ejpam-5918	597	1	let	let	VERB
ejpam-5918	597	2	g	g	PRON
ejpam-5918	597	3	be	be	AUX
ejpam-5918	597	4	a	a	DET
ejpam-5918	597	5	path	path	NOUN
ejpam-5918	597	6	graph	graph	NOUN
ejpam-5918	597	7	pn	pn	NOUN
ejpam-5918	597	8	or	or	CCONJ
ejpam-5918	597	9	cycle	cycle	NOUN
ejpam-5918	597	10	graph	graph	NOUN
ejpam-5918	597	11	cn	cn	NOUN
ejpam-5918	597	12	of	of	ADP
ejpam-5918	597	13	order	order	NOUN
ejpam-5918	597	14	n	n	PRON
ejpam-5918	597	15	≥	≥	NUM
ejpam-5918	597	16	2	2	NUM
ejpam-5918	597	17	such	such	ADJ
ejpam-5918	597	18	that	that	SCONJ
ejpam-5918	597	19	n	n	NUM
ejpam-5918	597	20	≡	≡	PROPN
ejpam-5918	597	21	3	3	NUM
ejpam-5918	597	22	(	(	PUNCT
ejpam-5918	597	23	mod	mod	NOUN
ejpam-5918	597	24	4	4	NUM
ejpam-5918	597	25	)	)	PUNCT
ejpam-5918	597	26	.	.	PUNCT
ejpam-5918	598	1	then	then	ADV
ejpam-5918	598	2	i	i	PRON
ejpam-5918	598	3	⊆	⊆	NUM
ejpam-5918	598	4	v	v	X
ejpam-5918	598	5	(	(	PUNCT
ejpam-5918	598	6	s(g	s(g	PROPN
ejpam-5918	598	7	)	)	PUNCT
ejpam-5918	598	8	)	)	PUNCT
ejpam-5918	598	9	with	with	ADP
ejpam-5918	598	10	i	i	PRON
ejpam-5918	598	11	=	=	PUNCT
ejpam-5918	598	12	{	{	PUNCT
ejpam-5918	598	13	v2	v2	PROPN
ejpam-5918	598	14	,	,	PUNCT
ejpam-5918	598	15	v3	v3	PROPN
ejpam-5918	598	16	,	,	PUNCT
ejpam-5918	598	17	v6	v6	NOUN
ejpam-5918	598	18	,	,	PUNCT
ejpam-5918	598	19	v7	v7	NOUN
ejpam-5918	598	20	,	,	PUNCT
ejpam-5918	598	21	.	.	PUNCT
ejpam-5918	598	22	.	.	PUNCT
ejpam-5918	598	23	.	.	PUNCT
ejpam-5918	599	1	,	,	PUNCT
ejpam-5918	599	2	vn−2	vn−2	PROPN
ejpam-5918	599	3	,	,	PUNCT
ejpam-5918	599	4	vn−1	vn−1	ADJ
ejpam-5918	599	5	}	}	PUNCT
ejpam-5918	599	6	is	be	AUX
ejpam-5918	599	7	a	a	DET
ejpam-5918	599	8	minimum	minimum	ADJ
ejpam-5918	599	9	internallylocating	internallylocate	VERB
ejpam-5918	599	10	dominating	dominating	NOUN
ejpam-5918	599	11	set	set	VERB
ejpam-5918	599	12	in	in	ADP
ejpam-5918	599	13	g.	g.	PROPN
ejpam-5918	599	14	proof	proof	PROPN
ejpam-5918	599	15	.	.	PUNCT
ejpam-5918	600	1	let	let	VERB
ejpam-5918	600	2	i	i	PRON
ejpam-5918	600	3	⊆	⊆	NUM
ejpam-5918	600	4	v	v	X
ejpam-5918	600	5	(	(	PUNCT
ejpam-5918	600	6	s(g	s(g	PROPN
ejpam-5918	600	7	)	)	PUNCT
ejpam-5918	600	8	)	)	PUNCT
ejpam-5918	600	9	with	with	ADP
ejpam-5918	600	10	i	i	PRON
ejpam-5918	600	11	=	=	PUNCT
ejpam-5918	600	12	{	{	PUNCT
ejpam-5918	600	13	v2	v2	PROPN
ejpam-5918	600	14	,	,	PUNCT
ejpam-5918	600	15	v3	v3	PROPN
ejpam-5918	600	16	,	,	PUNCT
ejpam-5918	600	17	v6	v6	NOUN
ejpam-5918	600	18	,	,	PUNCT
ejpam-5918	600	19	v7	v7	NOUN
ejpam-5918	600	20	,	,	PUNCT
ejpam-5918	600	21	.	.	PUNCT
ejpam-5918	600	22	.	.	PUNCT
ejpam-5918	601	1	.	.	PUNCT
ejpam-5918	602	1	,	,	PUNCT
ejpam-5918	602	2	vn−2	vn−2	PROPN
ejpam-5918	602	3	,	,	PUNCT
ejpam-5918	602	4	vn−1	vn−1	ADJ
ejpam-5918	602	5	}	}	PUNCT
ejpam-5918	602	6	.	.	PUNCT
ejpam-5918	603	1	note	note	VERB
ejpam-5918	603	2	that	that	SCONJ
ejpam-5918	603	3	i	i	PRON
ejpam-5918	603	4	is	be	AUX
ejpam-5918	603	5	an	an	DET
ejpam-5918	603	6	internally	internally	ADV
ejpam-5918	603	7	-	-	PUNCT
ejpam-5918	603	8	locating	locate	VERB
ejpam-5918	603	9	dominating	dominating	NOUN
ejpam-5918	603	10	set	set	VERB
ejpam-5918	603	11	in	in	ADP
ejpam-5918	603	12	v	v	NOUN
ejpam-5918	603	13	(	(	PUNCT
ejpam-5918	603	14	g	g	NOUN
ejpam-5918	603	15	)	)	PUNCT
ejpam-5918	603	16	by	by	ADP
ejpam-5918	603	17	theorem	theorem	NOUN
ejpam-5918	603	18	4	4	NUM
ejpam-5918	603	19	.	.	PUNCT
ejpam-5918	604	1	so	so	ADV
ejpam-5918	604	2	,	,	PUNCT
ejpam-5918	604	3	theorem	theorem	VERB
ejpam-5918	604	4	11	11	NUM
ejpam-5918	604	5	(	(	PUNCT
ejpam-5918	604	6	i	i	NOUN
ejpam-5918	604	7	)	)	PUNCT
ejpam-5918	604	8	is	be	AUX
ejpam-5918	604	9	satisfied	satisfied	ADJ
ejpam-5918	604	10	.	.	PUNCT
ejpam-5918	605	1	additionally	additionally	ADV
ejpam-5918	605	2	,	,	PUNCT
ejpam-5918	605	3	for	for	ADP
ejpam-5918	605	4	all	all	DET
ejpam-5918	605	5	u	u	PRON
ejpam-5918	605	6	∈	∈	PROPN
ejpam-5918	605	7	i	i	PRON
ejpam-5918	605	8	,	,	PUNCT
ejpam-5918	605	9	degi(u	degi(u	PROPN
ejpam-5918	605	10	)	)	PUNCT
ejpam-5918	605	11	̸=	̸=	PROPN
ejpam-5918	605	12	0	0	NUM
ejpam-5918	605	13	.	.	PUNCT
ejpam-5918	606	1	this	this	PRON
ejpam-5918	606	2	implies	imply	VERB
ejpam-5918	606	3	,	,	PUNCT
ejpam-5918	606	4	theorem	theorem	VERB
ejpam-5918	606	5	11	11	NUM
ejpam-5918	606	6	(	(	PUNCT
ejpam-5918	606	7	i	i	NOUN
ejpam-5918	606	8	)	)	PUNCT
ejpam-5918	606	9	is	be	AUX
ejpam-5918	606	10	satisfied	satisfied	ADJ
ejpam-5918	606	11	.	.	PUNCT
ejpam-5918	607	1	now	now	ADV
ejpam-5918	607	2	,	,	PUNCT
ejpam-5918	607	3	removing	remove	VERB
ejpam-5918	607	4	a	a	DET
ejpam-5918	607	5	vertex	vertex	NOUN
ejpam-5918	607	6	v	v	NOUN
ejpam-5918	607	7	in	in	ADP
ejpam-5918	607	8	i	i	PROPN
ejpam-5918	607	9	,	,	PUNCT
ejpam-5918	607	10	contradicts	contradict	VERB
ejpam-5918	607	11	theorem	theorem	ADJ
ejpam-5918	607	12	11	11	NUM
ejpam-5918	607	13	(	(	PUNCT
ejpam-5918	607	14	ii	ii	NOUN
ejpam-5918	607	15	)	)	PUNCT
ejpam-5918	607	16	.	.	PUNCT
ejpam-5918	608	1	hence	hence	ADV
ejpam-5918	608	2	,	,	PUNCT
ejpam-5918	608	3	i	i	PRON
ejpam-5918	608	4	is	be	AUX
ejpam-5918	608	5	a	a	DET
ejpam-5918	608	6	γli	γli	ADJ
ejpam-5918	608	7	−	−	NOUN
ejpam-5918	608	8	set	set	NOUN
ejpam-5918	608	9	.	.	PUNCT
ejpam-5918	609	1	corollary	corollary	ADJ
ejpam-5918	609	2	7	7	NUM
ejpam-5918	609	3	.	.	PUNCT
ejpam-5918	610	1	let	let	VERB
ejpam-5918	610	2	g	g	PRON
ejpam-5918	610	3	be	be	AUX
ejpam-5918	610	4	a	a	DET
ejpam-5918	610	5	path	path	NOUN
ejpam-5918	610	6	graph	graph	NOUN
ejpam-5918	610	7	pn	pn	NOUN
ejpam-5918	610	8	or	or	CCONJ
ejpam-5918	610	9	cycle	cycle	NOUN
ejpam-5918	610	10	graph	graph	NOUN
ejpam-5918	610	11	cn	cn	VERB
ejpam-5918	610	12	with	with	ADP
ejpam-5918	610	13	n	n	NUM
ejpam-5918	610	14	≥	≥	NUM
ejpam-5918	610	15	2	2	NUM
ejpam-5918	610	16	then	then	ADV
ejpam-5918	610	17	,	,	PUNCT
ejpam-5918	610	18	γli(s(g	γli(s(g	NOUN
ejpam-5918	610	19	)	)	PUNCT
ejpam-5918	610	20	)	)	PUNCT
ejpam-5918	611	1	=	=	SYM
ejpam-5918	611	2	γli(s(pn	γli(s(pn	NOUN
ejpam-5918	611	3	)	)	PUNCT
ejpam-5918	611	4	)	)	PUNCT
ejpam-5918	612	1	=	=	SYM
ejpam-5918	612	2	γli(s(cn	γli(s(cn	ADJ
ejpam-5918	612	3	)	)	PUNCT
ejpam-5918	612	4	)	)	PUNCT
ejpam-5918	613	1	=	=	PUNCT
ejpam-5918	613	2			PUNCT
ejpam-5918	613	3	n	n	ADV
ejpam-5918	613	4	2	2	NUM
ejpam-5918	613	5	if	if	SCONJ
ejpam-5918	613	6	n	n	PRON
ejpam-5918	613	7	≡	≡	PROPN
ejpam-5918	613	8	0	0	PUNCT
ejpam-5918	613	9	(	(	PUNCT
ejpam-5918	613	10	mod	mod	PROPN
ejpam-5918	613	11	4	4	NUM
ejpam-5918	613	12	)	)	PUNCT
ejpam-5918	613	13	n+3	n+3	PROPN
ejpam-5918	613	14	2	2	NUM
ejpam-5918	613	15	if	if	SCONJ
ejpam-5918	613	16	n	n	PRON
ejpam-5918	613	17	≡	≡	PROPN
ejpam-5918	613	18	1	1	NUM
ejpam-5918	613	19	(	(	PUNCT
ejpam-5918	613	20	mod	mod	NOUN
ejpam-5918	613	21	4	4	NUM
ejpam-5918	613	22	)	)	PUNCT
ejpam-5918	613	23	n+2	n+2	ADV
ejpam-5918	613	24	2	2	NUM
ejpam-5918	613	25	if	if	SCONJ
ejpam-5918	613	26	n	n	PRON
ejpam-5918	613	27	≡	≡	PROPN
ejpam-5918	613	28	2	2	NUM
ejpam-5918	613	29	(	(	PUNCT
ejpam-5918	613	30	mod	mod	NOUN
ejpam-5918	613	31	4	4	NUM
ejpam-5918	613	32	)	)	PUNCT
ejpam-5918	613	33	n+1	n+1	NUM
ejpam-5918	613	34	2	2	NUM
ejpam-5918	613	35	if	if	SCONJ
ejpam-5918	613	36	n	n	PRON
ejpam-5918	613	37	≡	≡	PROPN
ejpam-5918	613	38	3	3	NUM
ejpam-5918	613	39	(	(	PUNCT
ejpam-5918	613	40	mod	mod	NOUN
ejpam-5918	613	41	4	4	NUM
ejpam-5918	613	42	)	)	PUNCT
ejpam-5918	613	43	proof	proof	NOUN
ejpam-5918	613	44	.	.	PUNCT
ejpam-5918	614	1	let	let	VERB
ejpam-5918	614	2	g	g	PRON
ejpam-5918	614	3	be	be	AUX
ejpam-5918	614	4	a	a	DET
ejpam-5918	614	5	path	path	NOUN
ejpam-5918	614	6	graph	graph	NOUN
ejpam-5918	614	7	pn	pn	NOUN
ejpam-5918	614	8	or	or	CCONJ
ejpam-5918	614	9	a	a	DET
ejpam-5918	614	10	cycle	cycle	NOUN
ejpam-5918	614	11	graph	graph	NOUN
ejpam-5918	614	12	cn	cn	VERB
ejpam-5918	614	13	with	with	ADP
ejpam-5918	614	14	n	n	NUM
ejpam-5918	614	15	≥	≥	NUM
ejpam-5918	614	16	2	2	NUM
ejpam-5918	614	17	.	.	X
ejpam-5918	615	1	for	for	ADP
ejpam-5918	615	2	convenience	convenience	NOUN
ejpam-5918	615	3	,	,	PUNCT
ejpam-5918	615	4	let	let	VERB
ejpam-5918	615	5	v	v	NOUN
ejpam-5918	615	6	(	(	PUNCT
ejpam-5918	615	7	g	g	NOUN
ejpam-5918	615	8	)	)	PUNCT
ejpam-5918	615	9	=	=	NOUN
ejpam-5918	615	10	v	v	X
ejpam-5918	615	11	(	(	PUNCT
ejpam-5918	615	12	pn	pn	NOUN
ejpam-5918	615	13	)	)	PUNCT
ejpam-5918	615	14	=	=	NOUN
ejpam-5918	615	15	v	v	X
ejpam-5918	615	16	(	(	PUNCT
ejpam-5918	615	17	cn	cn	PROPN
ejpam-5918	615	18	)	)	PUNCT
ejpam-5918	615	19	=	=	SYM
ejpam-5918	615	20	{	{	PUNCT
ejpam-5918	615	21	v1	v1	PROPN
ejpam-5918	615	22	,	,	PUNCT
ejpam-5918	615	23	v2	v2	PROPN
ejpam-5918	615	24	,	,	PUNCT
ejpam-5918	615	25	v3	v3	PROPN
ejpam-5918	615	26	,	,	PUNCT
ejpam-5918	615	27	.	.	PUNCT
ejpam-5918	615	28	.	.	PUNCT
ejpam-5918	616	1	.	.	PUNCT
ejpam-5918	617	1	,	,	PUNCT
ejpam-5918	617	2	vn−1	vn−1	PROPN
ejpam-5918	617	3	,	,	PUNCT
ejpam-5918	617	4	vn	vn	NOUN
ejpam-5918	617	5	}	}	PUNCT
ejpam-5918	617	6	and	and	CCONJ
ejpam-5918	617	7	v	v	ADP
ejpam-5918	617	8	′(g	′(g	NOUN
ejpam-5918	617	9	)	)	PUNCT
ejpam-5918	618	1	=	=	PUNCT
ejpam-5918	618	2	v	v	ADP
ejpam-5918	618	3	′(pn	′(pn	NOUN
ejpam-5918	618	4	)	)	PUNCT
ejpam-5918	618	5	=	=	SYM
ejpam-5918	618	6	v	v	NUM
ejpam-5918	618	7	′(cn	′(cn	NOUN
ejpam-5918	618	8	)	)	PUNCT
ejpam-5918	618	9	=	=	PUNCT
ejpam-5918	618	10	{	{	PUNCT
ejpam-5918	618	11	v′1	v′1	ADJ
ejpam-5918	618	12	,	,	PUNCT
ejpam-5918	618	13	v′2	v′2	ADJ
ejpam-5918	618	14	,	,	PUNCT
ejpam-5918	618	15	v′3	v′3	NOUN
ejpam-5918	618	16	,	,	PUNCT
ejpam-5918	618	17	.	.	PUNCT
ejpam-5918	618	18	.	.	PUNCT
ejpam-5918	618	19	.	.	PUNCT
ejpam-5918	619	1	,	,	PUNCT
ejpam-5918	619	2	v′n−1	v′n−1	PROPN
ejpam-5918	619	3	,	,	PUNCT
ejpam-5918	619	4	v	v	ADP
ejpam-5918	619	5	′	′	NUM
ejpam-5918	619	6	n	n	CCONJ
ejpam-5918	619	7	}	}	PUNCT
ejpam-5918	619	8	as	as	ADP
ejpam-5918	619	9	the	the	DET
ejpam-5918	619	10	set	set	NOUN
ejpam-5918	619	11	of	of	ADP
ejpam-5918	619	12	all	all	DET
ejpam-5918	619	13	shadow	shadow	NOUN
ejpam-5918	619	14	vertices	vertex	NOUN
ejpam-5918	619	15	of	of	ADP
ejpam-5918	619	16	v	v	NOUN
ejpam-5918	619	17	(	(	PUNCT
ejpam-5918	619	18	g	g	NOUN
ejpam-5918	619	19	)	)	PUNCT
ejpam-5918	619	20	where	where	SCONJ
ejpam-5918	619	21	joining	join	VERB
ejpam-5918	619	22	v′i	v′i	ADV
ejpam-5918	619	23	to	to	ADP
ejpam-5918	619	24	the	the	DET
ejpam-5918	619	25	neighbors	neighbor	NOUN
ejpam-5918	619	26	of	of	ADP
ejpam-5918	619	27	vi	vi	PROPN
ejpam-5918	619	28	∈	∈	PROPN
ejpam-5918	619	29	v	v	NOUN
ejpam-5918	619	30	(	(	PUNCT
ejpam-5918	619	31	g	g	NOUN
ejpam-5918	619	32	)	)	PUNCT
ejpam-5918	619	33	.	.	PUNCT
ejpam-5918	620	1	by	by	ADP
ejpam-5918	620	2	definition	definition	NOUN
ejpam-5918	620	3	of	of	ADP
ejpam-5918	620	4	shadow	shadow	NOUN
ejpam-5918	620	5	graph	graph	NOUN
ejpam-5918	620	6	,	,	PUNCT
ejpam-5918	620	7	v	v	NOUN
ejpam-5918	620	8	(	(	PUNCT
ejpam-5918	620	9	s(g	s(g	PROPN
ejpam-5918	620	10	)	)	PUNCT
ejpam-5918	620	11	)	)	PUNCT
ejpam-5918	621	1	=	=	SYM
ejpam-5918	621	2	v	v	X
ejpam-5918	621	3	(	(	PUNCT
ejpam-5918	621	4	g	g	NOUN
ejpam-5918	621	5	)	)	PUNCT
ejpam-5918	621	6	∪	∪	ADP
ejpam-5918	621	7	v	v	ADP
ejpam-5918	621	8	′(g	′(g	NOUN
ejpam-5918	621	9	)	)	PUNCT
ejpam-5918	621	10	.	.	PUNCT
ejpam-5918	622	1	now	now	ADV
ejpam-5918	622	2	,	,	PUNCT
ejpam-5918	622	3	observe	observe	VERB
ejpam-5918	622	4	the	the	DET
ejpam-5918	622	5	following	follow	VERB
ejpam-5918	622	6	cases	case	NOUN
ejpam-5918	622	7	:	:	PUNCT
ejpam-5918	622	8	case	case	NOUN
ejpam-5918	622	9	1	1	NUM
ejpam-5918	622	10	:	:	PUNCT
ejpam-5918	622	11	n	n	NUM
ejpam-5918	622	12	≡	≡	PROPN
ejpam-5918	622	13	0	0	PUNCT
ejpam-5918	623	1	(	(	PUNCT
ejpam-5918	623	2	mod	mod	PROPN
ejpam-5918	623	3	4	4	X
ejpam-5918	623	4	)	)	PUNCT
ejpam-5918	623	5	let	let	VERB
ejpam-5918	623	6	i	i	PRON
ejpam-5918	623	7	=	=	PUNCT
ejpam-5918	623	8	{	{	PUNCT
ejpam-5918	623	9	v2	v2	PROPN
ejpam-5918	623	10	,	,	PUNCT
ejpam-5918	623	11	v3	v3	PROPN
ejpam-5918	623	12	,	,	PUNCT
ejpam-5918	623	13	v6	v6	NOUN
ejpam-5918	623	14	,	,	PUNCT
ejpam-5918	623	15	v7	v7	NOUN
ejpam-5918	623	16	,	,	PUNCT
ejpam-5918	623	17	.	.	PUNCT
ejpam-5918	623	18	.	.	PUNCT
ejpam-5918	624	1	.	.	PUNCT
ejpam-5918	625	1	,	,	PUNCT
ejpam-5918	625	2	vn−2	vn−2	PROPN
ejpam-5918	625	3	,	,	PUNCT
ejpam-5918	625	4	vn−1	vn−1	ADJ
ejpam-5918	625	5	}	}	PUNCT
ejpam-5918	625	6	.	.	PUNCT
ejpam-5918	626	1	by	by	ADP
ejpam-5918	626	2	lemma	lemma	PROPN
ejpam-5918	626	3	1	1	NUM
ejpam-5918	626	4	,	,	PUNCT
ejpam-5918	626	5	i	i	PRON
ejpam-5918	626	6	is	be	AUX
ejpam-5918	626	7	a	a	DET
ejpam-5918	626	8	γli	γli	ADJ
ejpam-5918	626	9	−	−	NOUN
ejpam-5918	626	10	set	set	VERB
ejpam-5918	626	11	in	in	ADP
ejpam-5918	626	12	g.	g.	PROPN
ejpam-5918	626	13	therefore	therefore	ADV
ejpam-5918	626	14	,	,	PUNCT
ejpam-5918	626	15	γli(g	γli(g	PROPN
ejpam-5918	626	16	)	)	PUNCT
ejpam-5918	627	1	=	=	SYM
ejpam-5918	627	2	|i|	|i|	NOUN
ejpam-5918	627	3	=	=	SYM
ejpam-5918	627	4	|{v2	|{v2	PROPN
ejpam-5918	627	5	,	,	PUNCT
ejpam-5918	627	6	v3	v3	PROPN
ejpam-5918	627	7	,	,	PUNCT
ejpam-5918	627	8	v6	v6	NOUN
ejpam-5918	627	9	,	,	PUNCT
ejpam-5918	627	10	v7	v7	NOUN
ejpam-5918	627	11	,	,	PUNCT
ejpam-5918	627	12	.	.	PUNCT
ejpam-5918	627	13	.	.	PUNCT
ejpam-5918	627	14	.	.	PUNCT
ejpam-5918	627	15	,	,	PUNCT
ejpam-5918	627	16	vn−2	vn−2	PROPN
ejpam-5918	627	17	,	,	PUNCT
ejpam-5918	627	18	vn−1}|	vn−1}|	PROPN
ejpam-5918	627	19	=	=	SYM
ejpam-5918	627	20	n	n	PRON
ejpam-5918	627	21	2	2	NUM
ejpam-5918	627	22	.	.	PUNCT
ejpam-5918	627	23	case	case	NOUN
ejpam-5918	627	24	2	2	NUM
ejpam-5918	627	25	:	:	PUNCT
ejpam-5918	627	26	n	n	NUM
ejpam-5918	627	27	≡	≡	PROPN
ejpam-5918	627	28	1	1	NUM
ejpam-5918	627	29	(	(	PUNCT
ejpam-5918	627	30	mod	mod	NOUN
ejpam-5918	627	31	4	4	X
ejpam-5918	627	32	)	)	PUNCT
ejpam-5918	627	33	let	let	VERB
ejpam-5918	627	34	i	i	PRON
ejpam-5918	627	35	=	=	PRON
ejpam-5918	627	36	{	{	PUNCT
ejpam-5918	627	37	v2,v3,v6,v7	v2,v3,v6,v7	PROPN
ejpam-5918	627	38	,	,	PUNCT
ejpam-5918	627	39	.	.	PUNCT
ejpam-5918	627	40	.	.	PUNCT
ejpam-5918	627	41	.	.	PUNCT
ejpam-5918	628	1	,	,	PUNCT
ejpam-5918	628	2	vn−4,vn−3,vn−1,vn	vn−4,vn−3,vn−1,vn	ADP
ejpam-5918	628	3	}	}	PUNCT
ejpam-5918	628	4	.	.	PUNCT
ejpam-5918	629	1	by	by	ADP
ejpam-5918	629	2	lemma	lemma	PROPN
ejpam-5918	629	3	2	2	NUM
ejpam-5918	629	4	,	,	PUNCT
ejpam-5918	629	5	i	i	PRON
ejpam-5918	629	6	is	be	AUX
ejpam-5918	629	7	a	a	DET
ejpam-5918	629	8	γli−set	γli−set	NOUN
ejpam-5918	629	9	ing	ing	NOUN
ejpam-5918	629	10	.	.	PUNCT
ejpam-5918	630	1	therefore	therefore	ADV
ejpam-5918	630	2	,	,	PUNCT
ejpam-5918	630	3	γli(g	γli(g	PROPN
ejpam-5918	630	4	)	)	PUNCT
ejpam-5918	631	1	=	=	SYM
ejpam-5918	631	2	|i|	|i|	NOUN
ejpam-5918	631	3	=	=	SYM
ejpam-5918	631	4	|{v2	|{v2	PROPN
ejpam-5918	631	5	,	,	PUNCT
ejpam-5918	631	6	v3	v3	PROPN
ejpam-5918	631	7	,	,	PUNCT
ejpam-5918	631	8	v6	v6	NOUN
ejpam-5918	631	9	,	,	PUNCT
ejpam-5918	631	10	v7	v7	NOUN
ejpam-5918	631	11	,	,	PUNCT
ejpam-5918	631	12	.	.	PUNCT
ejpam-5918	631	13	.	.	PUNCT
ejpam-5918	631	14	.	.	PUNCT
ejpam-5918	632	1	,	,	PUNCT
ejpam-5918	632	2	vn−4	vn−4	NOUN
ejpam-5918	632	3	,	,	PUNCT
ejpam-5918	632	4	vn−3	vn−3	PROPN
ejpam-5918	632	5	,	,	PUNCT
ejpam-5918	632	6	vn−1	vn−1	ADJ
ejpam-5918	632	7	,	,	PUNCT
ejpam-5918	632	8	vn}|	vn}|	X
ejpam-5918	632	9	=	=	SYM
ejpam-5918	632	10	n+	n+	X
ejpam-5918	632	11	3	3	NUM
ejpam-5918	632	12	2	2	NUM
ejpam-5918	632	13	.	.	PUNCT
ejpam-5918	633	1	case	case	NOUN
ejpam-5918	633	2	3	3	NUM
ejpam-5918	633	3	:	:	PUNCT
ejpam-5918	633	4	n	n	NUM
ejpam-5918	633	5	≡	≡	PROPN
ejpam-5918	633	6	2	2	NUM
ejpam-5918	633	7	(	(	PUNCT
ejpam-5918	633	8	mod	mod	NOUN
ejpam-5918	633	9	4	4	NUM
ejpam-5918	633	10	)	)	PUNCT
ejpam-5918	633	11	i.	i.	NOUN
ejpam-5918	633	12	tropico	tropico	PROPN
ejpam-5918	633	13	,	,	PUNCT
ejpam-5918	633	14	i.	i.	PROPN
ejpam-5918	633	15	cabahug	cabahug	PROPN
ejpam-5918	633	16	,	,	PUNCT
ejpam-5918	633	17	jr	jr	PROPN
ejpam-5918	633	18	.	.	PROPN
ejpam-5918	633	19	/	/	SYM
ejpam-5918	633	20	eur	eur	PROPN
ejpam-5918	633	21	.	.	PUNCT
ejpam-5918	634	1	j.	j.	PROPN
ejpam-5918	634	2	pure	pure	PROPN
ejpam-5918	634	3	appl	appl	PROPN
ejpam-5918	634	4	.	.	PROPN
ejpam-5918	634	5	math	math	PROPN
ejpam-5918	634	6	,	,	PUNCT
ejpam-5918	634	7	18	18	NUM
ejpam-5918	634	8	(	(	PUNCT
ejpam-5918	634	9	2	2	NUM
ejpam-5918	634	10	)	)	PUNCT
ejpam-5918	634	11	(	(	PUNCT
ejpam-5918	634	12	2025	2025	NUM
ejpam-5918	634	13	)	)	PUNCT
ejpam-5918	634	14	,	,	PUNCT
ejpam-5918	634	15	5918	5918	NUM
ejpam-5918	634	16	19	19	NUM
ejpam-5918	634	17	of	of	ADP
ejpam-5918	634	18	21	21	NUM
ejpam-5918	634	19	let	let	VERB
ejpam-5918	634	20	i	i	PRON
ejpam-5918	634	21	=	=	PRON
ejpam-5918	634	22	{	{	PUNCT
ejpam-5918	634	23	v2,v3,v6,v7	v2,v3,v6,v7	PROPN
ejpam-5918	634	24	,	,	PUNCT
ejpam-5918	634	25	.	.	PUNCT
ejpam-5918	634	26	.	.	PUNCT
ejpam-5918	634	27	.	.	PUNCT
ejpam-5918	635	1	,	,	PUNCT
ejpam-5918	635	2	vn−5,vn−4,vn−1,vn	vn−5,vn−4,vn−1,vn	X
ejpam-5918	635	3	}	}	PUNCT
ejpam-5918	635	4	.	.	PUNCT
ejpam-5918	636	1	by	by	ADP
ejpam-5918	636	2	lemma	lemma	PROPN
ejpam-5918	636	3	3	3	NUM
ejpam-5918	636	4	,	,	PUNCT
ejpam-5918	636	5	i	i	PRON
ejpam-5918	636	6	is	be	AUX
ejpam-5918	636	7	a	a	DET
ejpam-5918	636	8	γli−set	γli−set	NOUN
ejpam-5918	636	9	ing	ing	NOUN
ejpam-5918	636	10	.	.	PUNCT
ejpam-5918	637	1	therefore	therefore	ADV
ejpam-5918	637	2	,	,	PUNCT
ejpam-5918	637	3	γli(g	γli(g	PROPN
ejpam-5918	637	4	)	)	PUNCT
ejpam-5918	638	1	=	=	SYM
ejpam-5918	638	2	|i|	|i|	NOUN
ejpam-5918	638	3	=	=	SYM
ejpam-5918	638	4	|{v2	|{v2	PROPN
ejpam-5918	638	5	,	,	PUNCT
ejpam-5918	638	6	v3	v3	PROPN
ejpam-5918	638	7	,	,	PUNCT
ejpam-5918	638	8	v6	v6	NOUN
ejpam-5918	638	9	,	,	PUNCT
ejpam-5918	638	10	v7	v7	NOUN
ejpam-5918	638	11	,	,	PUNCT
ejpam-5918	638	12	.	.	PUNCT
ejpam-5918	638	13	.	.	PUNCT
ejpam-5918	638	14	.	.	PUNCT
ejpam-5918	639	1	,	,	PUNCT
ejpam-5918	639	2	vn−5	vn−5	PROPN
ejpam-5918	639	3	,	,	PUNCT
ejpam-5918	639	4	vn−4	vn−4	NOUN
ejpam-5918	639	5	,	,	PUNCT
ejpam-5918	639	6	vn−1	vn−1	ADJ
ejpam-5918	639	7	,	,	PUNCT
ejpam-5918	639	8	vn}|	vn}|	X
ejpam-5918	639	9	=	=	SYM
ejpam-5918	639	10	n+	n+	PUNCT
ejpam-5918	639	11	2	2	NUM
ejpam-5918	639	12	2	2	NUM
ejpam-5918	639	13	.	.	PUNCT
ejpam-5918	640	1	case	case	NOUN
ejpam-5918	640	2	4	4	NUM
ejpam-5918	640	3	:	:	PUNCT
ejpam-5918	640	4	n	n	NUM
ejpam-5918	640	5	≡	≡	PROPN
ejpam-5918	640	6	3	3	NUM
ejpam-5918	640	7	(	(	PUNCT
ejpam-5918	640	8	mod	mod	NOUN
ejpam-5918	640	9	4	4	X
ejpam-5918	640	10	)	)	PUNCT
ejpam-5918	640	11	let	let	VERB
ejpam-5918	640	12	i	i	PRON
ejpam-5918	640	13	=	=	PUNCT
ejpam-5918	640	14	{	{	PUNCT
ejpam-5918	640	15	v2	v2	PROPN
ejpam-5918	640	16	,	,	PUNCT
ejpam-5918	640	17	v3	v3	PROPN
ejpam-5918	640	18	,	,	PUNCT
ejpam-5918	640	19	v6	v6	NOUN
ejpam-5918	640	20	,	,	PUNCT
ejpam-5918	640	21	v7	v7	NOUN
ejpam-5918	640	22	,	,	PUNCT
ejpam-5918	640	23	.	.	PUNCT
ejpam-5918	640	24	.	.	PUNCT
ejpam-5918	641	1	.	.	PUNCT
ejpam-5918	642	1	,	,	PUNCT
ejpam-5918	642	2	vn−2	vn−2	PROPN
ejpam-5918	642	3	,	,	PUNCT
ejpam-5918	642	4	vn−1	vn−1	ADJ
ejpam-5918	642	5	}	}	PUNCT
ejpam-5918	642	6	.	.	PUNCT
ejpam-5918	643	1	by	by	ADP
ejpam-5918	643	2	lemma	lemma	PROPN
ejpam-5918	643	3	4	4	NUM
ejpam-5918	643	4	,	,	PUNCT
ejpam-5918	643	5	i	i	PRON
ejpam-5918	643	6	is	be	AUX
ejpam-5918	643	7	a	a	DET
ejpam-5918	643	8	γli	γli	ADJ
ejpam-5918	643	9	−	−	NOUN
ejpam-5918	643	10	set	set	VERB
ejpam-5918	643	11	in	in	ADP
ejpam-5918	643	12	g.	g.	PROPN
ejpam-5918	643	13	therefore	therefore	ADV
ejpam-5918	643	14	,	,	PUNCT
ejpam-5918	643	15	γli(g	γli(g	PROPN
ejpam-5918	643	16	)	)	PUNCT
ejpam-5918	644	1	=	=	SYM
ejpam-5918	644	2	|i|	|i|	NOUN
ejpam-5918	644	3	=	=	SYM
ejpam-5918	644	4	|{v2	|{v2	PROPN
ejpam-5918	644	5	,	,	PUNCT
ejpam-5918	644	6	v3	v3	PROPN
ejpam-5918	644	7	,	,	PUNCT
ejpam-5918	644	8	v6	v6	NOUN
ejpam-5918	644	9	,	,	PUNCT
ejpam-5918	644	10	v7	v7	NOUN
ejpam-5918	644	11	,	,	PUNCT
ejpam-5918	644	12	.	.	PUNCT
ejpam-5918	644	13	.	.	PUNCT
ejpam-5918	644	14	.	.	PUNCT
ejpam-5918	644	15	,	,	PUNCT
ejpam-5918	644	16	vn−2	vn−2	PROPN
ejpam-5918	644	17	,	,	PUNCT
ejpam-5918	644	18	vn−1}|	vn−1}|	PROPN
ejpam-5918	644	19	=	=	PUNCT
ejpam-5918	644	20	n+	n+	NUM
ejpam-5918	644	21	1	1	NUM
ejpam-5918	644	22	2	2	NUM
ejpam-5918	644	23	.	.	PUNCT
ejpam-5918	644	24	example	example	NOUN
ejpam-5918	644	25	10	10	NUM
ejpam-5918	644	26	.	.	PUNCT
ejpam-5918	645	1	consider	consider	VERB
ejpam-5918	645	2	figure	figure	NOUN
ejpam-5918	645	3	9	9	NUM
ejpam-5918	645	4	.	.	PUNCT
ejpam-5918	646	1	clearly	clearly	ADV
ejpam-5918	646	2	i	i	PRON
ejpam-5918	646	3	=	=	X
ejpam-5918	646	4	{	{	PUNCT
ejpam-5918	646	5	a	a	PRON
ejpam-5918	646	6	,	,	PUNCT
ejpam-5918	646	7	b	b	NOUN
ejpam-5918	646	8	,	,	PUNCT
ejpam-5918	646	9	d	d	NOUN
ejpam-5918	646	10	,	,	PUNCT
ejpam-5918	646	11	e	e	NOUN
ejpam-5918	646	12	}	}	PUNCT
ejpam-5918	646	13	is	be	AUX
ejpam-5918	646	14	a	a	DET
ejpam-5918	646	15	dominating	dominating	NOUN
ejpam-5918	646	16	set	set	NOUN
ejpam-5918	646	17	.	.	PUNCT
ejpam-5918	647	1	observe	observe	VERB
ejpam-5918	647	2	that	that	SCONJ
ejpam-5918	647	3	,	,	PUNCT
ejpam-5918	647	4	n(a	n(a	PRON
ejpam-5918	647	5	)	)	PUNCT
ejpam-5918	647	6	∩	∩	NOUN
ejpam-5918	647	7	i	i	PRON
ejpam-5918	647	8	=	=	PUNCT
ejpam-5918	647	9	{	{	PUNCT
ejpam-5918	647	10	b	b	NOUN
ejpam-5918	647	11	}	}	PUNCT
ejpam-5918	647	12	,	,	PUNCT
ejpam-5918	647	13	n(b	n(b	PROPN
ejpam-5918	647	14	)	)	PUNCT
ejpam-5918	647	15	∩	∩	NOUN
ejpam-5918	648	1	i	i	PRON
ejpam-5918	648	2	=	=	X
ejpam-5918	648	3	{	{	PUNCT
ejpam-5918	648	4	a	a	NOUN
ejpam-5918	648	5	}	}	PUNCT
ejpam-5918	648	6	,	,	PUNCT
ejpam-5918	648	7	n(d	n(d	NOUN
ejpam-5918	648	8	)	)	PUNCT
ejpam-5918	648	9	∩	∩	NOUN
ejpam-5918	648	10	i	i	PRON
ejpam-5918	648	11	=	=	SYM
ejpam-5918	648	12	{	{	PUNCT
ejpam-5918	648	13	e	e	NOUN
ejpam-5918	648	14	}	}	PUNCT
ejpam-5918	648	15	,	,	PUNCT
ejpam-5918	648	16	and	and	CCONJ
ejpam-5918	648	17	n(d	n(d	NOUN
ejpam-5918	648	18	)	)	PUNCT
ejpam-5918	648	19	∩	∩	NOUN
ejpam-5918	648	20	i	i	PRON
ejpam-5918	648	21	=	=	SYM
ejpam-5918	648	22	{	{	PUNCT
ejpam-5918	648	23	e	e	NOUN
ejpam-5918	648	24	}	}	PUNCT
ejpam-5918	648	25	.	.	PUNCT
ejpam-5918	649	1	hence	hence	ADV
ejpam-5918	649	2	,	,	PUNCT
ejpam-5918	649	3	i	i	PRON
ejpam-5918	649	4	is	be	AUX
ejpam-5918	649	5	an	an	DET
ejpam-5918	649	6	internally	internally	ADV
ejpam-5918	649	7	-	-	PUNCT
ejpam-5918	649	8	locating	locate	VERB
ejpam-5918	649	9	dominating	dominating	NOUN
ejpam-5918	649	10	set	set	NOUN
ejpam-5918	649	11	of	of	ADP
ejpam-5918	649	12	minimum	minimum	ADJ
ejpam-5918	649	13	cardinality	cardinality	NOUN
ejpam-5918	649	14	,	,	PUNCT
ejpam-5918	649	15	so	so	ADV
ejpam-5918	649	16	γli(s(p5	γli(s(p5	ADJ
ejpam-5918	649	17	)	)	PUNCT
ejpam-5918	649	18	)	)	PUNCT
ejpam-5918	650	1	=	=	SYM
ejpam-5918	650	2	4	4	X
ejpam-5918	650	3	.	.	PUNCT
ejpam-5918	650	4	by	by	ADP
ejpam-5918	650	5	corollary	corollary	ADJ
ejpam-5918	650	6	7	7	NUM
ejpam-5918	650	7	,	,	PUNCT
ejpam-5918	650	8	for	for	ADP
ejpam-5918	650	9	n	n	NOUN
ejpam-5918	650	10	=	=	SYM
ejpam-5918	650	11	5	5	NUM
ejpam-5918	650	12	≡	≡	PROPN
ejpam-5918	650	13	1	1	NUM
ejpam-5918	650	14	(	(	PUNCT
ejpam-5918	650	15	mod	mod	NOUN
ejpam-5918	650	16	4	4	NUM
ejpam-5918	650	17	)	)	PUNCT
ejpam-5918	650	18	,	,	PUNCT
ejpam-5918	650	19	γli(s(p5	γli(s(p5	NOUN
ejpam-5918	650	20	)	)	PUNCT
ejpam-5918	650	21	)	)	PUNCT
ejpam-5918	650	22	=	=	SYM
ejpam-5918	651	1	n+3	n+3	NUM
ejpam-5918	651	2	2	2	NUM
ejpam-5918	651	3	=	=	SYM
ejpam-5918	651	4	5	5	NUM
ejpam-5918	651	5	+	+	NOUN
ejpam-5918	651	6	3	3	NUM
ejpam-5918	651	7	2	2	NUM
ejpam-5918	651	8	=	=	SYM
ejpam-5918	651	9	8	8	NUM
ejpam-5918	651	10	2	2	NUM
ejpam-5918	651	11	=	=	SYM
ejpam-5918	651	12	4	4	NUM
ejpam-5918	651	13	.	.	PUNCT
ejpam-5918	652	1	a	a	DET
ejpam-5918	652	2	b	b	NOUN
ejpam-5918	652	3	c	c	NOUN
ejpam-5918	652	4	d	d	X
ejpam-5918	652	5	e	e	X
ejpam-5918	652	6	a′	a′	PROPN
ejpam-5918	652	7	b′	b′	NUM
ejpam-5918	652	8	c′	c′	NUM
ejpam-5918	652	9	d′	d′	NUM
ejpam-5918	652	10	e′	e′	X
ejpam-5918	652	11	s(p5	s(p5	X
ejpam-5918	652	12	):	):	PUNCT
ejpam-5918	652	13	figure	figure	NOUN
ejpam-5918	652	14	9	9	NUM
ejpam-5918	652	15	:	:	PUNCT
ejpam-5918	652	16	the	the	DET
ejpam-5918	652	17	minimum	minimum	NOUN
ejpam-5918	652	18	internally	internally	ADV
ejpam-5918	652	19	-	-	PUNCT
ejpam-5918	652	20	locating	locate	VERB
ejpam-5918	652	21	dominating	dominating	NOUN
ejpam-5918	652	22	set	set	VERB
ejpam-5918	652	23	in	in	ADP
ejpam-5918	652	24	s(p5	s(p5	NOUN
ejpam-5918	652	25	)	)	PUNCT
ejpam-5918	652	26	5	5	NUM
ejpam-5918	652	27	.	.	X
ejpam-5918	653	1	conclusion	conclusion	NOUN
ejpam-5918	653	2	it	it	PRON
ejpam-5918	653	3	was	be	AUX
ejpam-5918	653	4	shown	show	VERB
ejpam-5918	653	5	in	in	ADP
ejpam-5918	653	6	this	this	DET
ejpam-5918	653	7	paper	paper	NOUN
ejpam-5918	653	8	that	that	SCONJ
ejpam-5918	653	9	certain	certain	ADJ
ejpam-5918	653	10	properties	property	NOUN
ejpam-5918	653	11	of	of	ADP
ejpam-5918	653	12	this	this	DET
ejpam-5918	653	13	concept	concept	NOUN
ejpam-5918	653	14	are	be	AUX
ejpam-5918	653	15	identified	identify	VERB
ejpam-5918	653	16	,	,	PUNCT
ejpam-5918	653	17	and	and	CCONJ
ejpam-5918	653	18	characterizations	characterization	NOUN
ejpam-5918	653	19	of	of	ADP
ejpam-5918	653	20	special	special	ADJ
ejpam-5918	653	21	classes	class	NOUN
ejpam-5918	653	22	of	of	ADP
ejpam-5918	653	23	graphs	graph	NOUN
ejpam-5918	653	24	are	be	AUX
ejpam-5918	653	25	provided	provide	VERB
ejpam-5918	653	26	,	,	PUNCT
ejpam-5918	653	27	including	include	VERB
ejpam-5918	653	28	total	total	ADJ
ejpam-5918	653	29	graphs	graph	NOUN
ejpam-5918	653	30	and	and	CCONJ
ejpam-5918	653	31	shadow	shadow	NOUN
ejpam-5918	653	32	graphs	graph	NOUN
ejpam-5918	653	33	with	with	ADP
ejpam-5918	653	34	∆(g	∆(g	NOUN
ejpam-5918	653	35	)	)	PUNCT
ejpam-5918	653	36	=	=	SYM
ejpam-5918	653	37	2	2	NUM
ejpam-5918	653	38	,	,	PUNCT
ejpam-5918	653	39	along	along	ADP
ejpam-5918	653	40	with	with	ADP
ejpam-5918	653	41	their	their	PRON
ejpam-5918	653	42	corresponding	corresponding	ADJ
ejpam-5918	653	43	internally	internally	ADV
ejpam-5918	653	44	-	-	PUNCT
ejpam-5918	653	45	locating	locate	VERB
ejpam-5918	653	46	domination	domination	NOUN
ejpam-5918	653	47	numbers	number	NOUN
ejpam-5918	653	48	.	.	PUNCT
ejpam-5918	654	1	the	the	DET
ejpam-5918	654	2	paper	paper	NOUN
ejpam-5918	654	3	also	also	ADV
ejpam-5918	654	4	examines	examine	VERB
ejpam-5918	654	5	cases	case	NOUN
ejpam-5918	654	6	where	where	SCONJ
ejpam-5918	654	7	γli(g	γli(g	X
ejpam-5918	654	8	)	)	PUNCT
ejpam-5918	654	9	=	=	SYM
ejpam-5918	654	10	2	2	NUM
ejpam-5918	654	11	and	and	CCONJ
ejpam-5918	654	12	γ(g	γ(g	PROPN
ejpam-5918	654	13	)	)	PUNCT
ejpam-5918	654	14	=	=	PUNCT
ejpam-5918	654	15	γli(g	γli(g	PROPN
ejpam-5918	654	16	)	)	PUNCT
ejpam-5918	654	17	.	.	PUNCT
ejpam-5918	655	1	additionally	additionally	ADV
ejpam-5918	655	2	,	,	PUNCT
ejpam-5918	655	3	the	the	DET
ejpam-5918	655	4	authors	author	NOUN
ejpam-5918	655	5	intend	intend	VERB
ejpam-5918	655	6	to	to	PART
ejpam-5918	655	7	explore	explore	VERB
ejpam-5918	655	8	other	other	ADJ
ejpam-5918	655	9	properties	property	NOUN
ejpam-5918	655	10	of	of	ADP
ejpam-5918	655	11	internally	internally	ADV
ejpam-5918	655	12	-	-	PUNCT
ejpam-5918	655	13	locating	locate	VERB
ejpam-5918	655	14	sets	set	NOUN
ejpam-5918	655	15	and	and	CCONJ
ejpam-5918	655	16	internally	internally	ADV
ejpam-5918	655	17	-	-	PUNCT
ejpam-5918	655	18	locating	locate	VERB
ejpam-5918	655	19	dominating	dominating	NOUN
ejpam-5918	655	20	sets	set	NOUN
ejpam-5918	655	21	,	,	PUNCT
ejpam-5918	655	22	as	as	ADV
ejpam-5918	655	23	well	well	ADV
ejpam-5918	655	24	as	as	ADP
ejpam-5918	655	25	extend	extend	VERB
ejpam-5918	655	26	the	the	DET
ejpam-5918	655	27	study	study	NOUN
ejpam-5918	655	28	to	to	ADP
ejpam-5918	655	29	other	other	ADJ
ejpam-5918	655	30	binary	binary	ADJ
ejpam-5918	655	31	operations	operation	NOUN
ejpam-5918	655	32	on	on	ADP
ejpam-5918	655	33	graphs	graph	NOUN
ejpam-5918	655	34	,	,	PUNCT
ejpam-5918	655	35	such	such	ADJ
ejpam-5918	655	36	as	as	ADP
ejpam-5918	655	37	the	the	DET
ejpam-5918	655	38	join	join	NOUN
ejpam-5918	655	39	of	of	ADP
ejpam-5918	655	40	graphs	graph	NOUN
ejpam-5918	655	41	,	,	PUNCT
ejpam-5918	655	42	along	along	ADP
ejpam-5918	655	43	with	with	ADP
ejpam-5918	655	44	their	their	PRON
ejpam-5918	655	45	corresponding	corresponding	ADJ
ejpam-5918	655	46	internally	internally	ADV
ejpam-5918	655	47	-	-	PUNCT
ejpam-5918	655	48	locating	locate	VERB
ejpam-5918	655	49	domination	domination	NOUN
ejpam-5918	655	50	numbers	number	NOUN
ejpam-5918	655	51	.	.	PUNCT
ejpam-5918	656	1	i.	i.	PROPN
ejpam-5918	656	2	tropico	tropico	PROPN
ejpam-5918	656	3	,	,	PUNCT
ejpam-5918	656	4	i.	i.	PROPN
ejpam-5918	656	5	cabahug	cabahug	PROPN
ejpam-5918	656	6	,	,	PUNCT
ejpam-5918	656	7	jr	jr	PROPN
ejpam-5918	656	8	.	.	PROPN
ejpam-5918	656	9	/	/	SYM
ejpam-5918	656	10	eur	eur	PROPN
ejpam-5918	656	11	.	.	PUNCT
ejpam-5918	657	1	j.	j.	PROPN
ejpam-5918	657	2	pure	pure	PROPN
ejpam-5918	657	3	appl	appl	PROPN
ejpam-5918	657	4	.	.	PROPN
ejpam-5918	657	5	math	math	PROPN
ejpam-5918	657	6	,	,	PUNCT
ejpam-5918	657	7	18	18	NUM
ejpam-5918	657	8	(	(	PUNCT
ejpam-5918	657	9	2	2	NUM
ejpam-5918	657	10	)	)	PUNCT
ejpam-5918	657	11	(	(	PUNCT
ejpam-5918	657	12	2025	2025	NUM
ejpam-5918	657	13	)	)	PUNCT
ejpam-5918	657	14	,	,	PUNCT
ejpam-5918	657	15	5918	5918	NUM
ejpam-5918	657	16	20	20	NUM
ejpam-5918	657	17	of	of	ADP
ejpam-5918	657	18	21	21	NUM
ejpam-5918	657	19	acknowledgements	acknowledgement	NOUN
ejpam-5918	657	20	the	the	DET
ejpam-5918	657	21	authors	author	NOUN
ejpam-5918	657	22	extend	extend	VERB
ejpam-5918	657	23	their	their	PRON
ejpam-5918	657	24	sincere	sincere	ADJ
ejpam-5918	657	25	thanks	thank	NOUN
ejpam-5918	657	26	to	to	ADP
ejpam-5918	657	27	everyone	everyone	PRON
ejpam-5918	657	28	who	who	PRON
ejpam-5918	657	29	has	have	AUX
ejpam-5918	657	30	played	play	VERB
ejpam-5918	657	31	a	a	DET
ejpam-5918	657	32	vital	vital	ADJ
ejpam-5918	657	33	role	role	NOUN
ejpam-5918	657	34	in	in	ADP
ejpam-5918	657	35	the	the	DET
ejpam-5918	657	36	completion	completion	NOUN
ejpam-5918	657	37	of	of	ADP
ejpam-5918	657	38	this	this	DET
ejpam-5918	657	39	study	study	NOUN
ejpam-5918	657	40	,	,	PUNCT
ejpam-5918	657	41	with	with	ADP
ejpam-5918	657	42	special	special	ADJ
ejpam-5918	657	43	appreciation	appreciation	NOUN
ejpam-5918	657	44	to	to	ADP
ejpam-5918	657	45	the	the	DET
ejpam-5918	657	46	department	department	PROPN
ejpam-5918	657	47	of	of	ADP
ejpam-5918	657	48	science	science	NOUN
ejpam-5918	657	49	and	and	CCONJ
ejpam-5918	657	50	technology	technology	NOUN
ejpam-5918	657	51	-	-	PUNCT
ejpam-5918	657	52	science	science	NOUN
ejpam-5918	657	53	education	education	PROPN
ejpam-5918	657	54	institute	institute	PROPN
ejpam-5918	657	55	science	science	PROPN
ejpam-5918	657	56	and	and	CCONJ
ejpam-5918	657	57	technology	technology	NOUN
ejpam-5918	657	58	regional	regional	ADJ
ejpam-5918	657	59	alliance	alliance	NOUN
ejpam-5918	657	60	of	of	ADP
ejpam-5918	657	61	universities	university	NOUN
ejpam-5918	657	62	for	for	ADP
ejpam-5918	657	63	inclusive	inclusive	ADJ
ejpam-5918	657	64	national	national	ADJ
ejpam-5918	657	65	development	development	NOUN
ejpam-5918	657	66	(	(	PUNCT
ejpam-5918	657	67	dost	dost	NOUN
ejpam-5918	657	68	-	-	PUNCT
ejpam-5918	657	69	sei	sei	ADJ
ejpam-5918	657	70	strand	strand	NOUN
ejpam-5918	657	71	)	)	PUNCT
ejpam-5918	657	72	for	for	ADP
ejpam-5918	657	73	their	their	PRON
ejpam-5918	657	74	invaluable	invaluable	ADJ
ejpam-5918	657	75	support	support	NOUN
ejpam-5918	657	76	throughout	throughout	ADP
ejpam-5918	657	77	the	the	DET
ejpam-5918	657	78	research	research	NOUN
ejpam-5918	657	79	process	process	NOUN
ejpam-5918	657	80	.	.	PUNCT
ejpam-5918	658	1	references	reference	NOUN
ejpam-5918	658	2	[	[	X
ejpam-5918	658	3	1	1	X
ejpam-5918	658	4	]	]	PUNCT
ejpam-5918	658	5	t.	t.	PROPN
ejpam-5918	658	6	haynes	haynes	PROPN
ejpam-5918	658	7	,	,	PUNCT
ejpam-5918	658	8	s	s	VERB
ejpam-5918	658	9	hedetniemi	hedetniemi	ADV
ejpam-5918	658	10	,	,	PUNCT
ejpam-5918	658	11	and	and	CCONJ
ejpam-5918	658	12	p	p	X
ejpam-5918	658	13	slater	slater	NOUN
ejpam-5918	658	14	.	.	PUNCT
ejpam-5918	659	1	fundamentals	fundamental	NOUN
ejpam-5918	659	2	of	of	ADP
ejpam-5918	659	3	domination	domination	NOUN
ejpam-5918	659	4	in	in	ADP
ejpam-5918	659	5	graphs	graph	NOUN
ejpam-5918	659	6	.	.	PUNCT
ejpam-5918	660	1	crc	crc	PROPN
ejpam-5918	660	2	press	press	PROPN
ejpam-5918	660	3	,	,	PUNCT
ejpam-5918	660	4	boca	boca	PROPN
ejpam-5918	660	5	raton	raton	PROPN
ejpam-5918	660	6	,	,	PUNCT
ejpam-5918	660	7	florida	florida	PROPN
ejpam-5918	660	8	,	,	PUNCT
ejpam-5918	660	9	1st	1st	PROPN
ejpam-5918	660	10	edition	edition	NOUN
ejpam-5918	660	11	,	,	PUNCT
ejpam-5918	660	12	1998	1998	NUM
ejpam-5918	660	13	.	.	PUNCT
ejpam-5918	661	1	[	[	X
ejpam-5918	661	2	2	2	X
ejpam-5918	661	3	]	]	X
ejpam-5918	661	4	p	p	X
ejpam-5918	661	5	gupta	gupta	PROPN
ejpam-5918	661	6	.	.	PUNCT
ejpam-5918	662	1	domination	domination	NOUN
ejpam-5918	662	2	in	in	ADP
ejpam-5918	662	3	graph	graph	NOUN
ejpam-5918	662	4	with	with	ADP
ejpam-5918	662	5	application	application	NOUN
ejpam-5918	662	6	.	.	PUNCT
ejpam-5918	663	1	indian	indian	ADJ
ejpam-5918	663	2	journal	journal	PROPN
ejpam-5918	663	3	of	of	ADP
ejpam-5918	663	4	research	research	NOUN
ejpam-5918	663	5	,	,	PUNCT
ejpam-5918	663	6	2(3):115–116	2(3):115–116	PROPN
ejpam-5918	663	7	,	,	PUNCT
ejpam-5918	663	8	2013	2013	NUM
ejpam-5918	663	9	.	.	PUNCT
ejpam-5918	664	1	[	[	X
ejpam-5918	664	2	3	3	X
ejpam-5918	664	3	]	]	X
ejpam-5918	664	4	p	p	X
ejpam-5918	664	5	slater	slater	NOUN
ejpam-5918	664	6	.	.	PUNCT
ejpam-5918	665	1	leaves	leave	NOUN
ejpam-5918	665	2	of	of	ADP
ejpam-5918	665	3	trees	tree	NOUN
ejpam-5918	665	4	.	.	PUNCT
ejpam-5918	666	1	congressus	congressus	PROPN
ejpam-5918	666	2	numerantium	numerantium	PROPN
ejpam-5918	666	3	,	,	PUNCT
ejpam-5918	666	4	14(37):549–559	14(37):549–559	NUM
ejpam-5918	666	5	,	,	PUNCT
ejpam-5918	666	6	1975	1975	NUM
ejpam-5918	666	7	.	.	PUNCT
ejpam-5918	667	1	[	[	X
ejpam-5918	667	2	4	4	X
ejpam-5918	667	3	]	]	SYM
ejpam-5918	667	4	g	g	NOUN
ejpam-5918	667	5	chartrand	chartrand	NOUN
ejpam-5918	667	6	and	and	CCONJ
ejpam-5918	667	7	p	p	PROPN
ejpam-5918	667	8	zhang	zhang	PROPN
ejpam-5918	667	9	.	.	PUNCT
ejpam-5918	668	1	a	a	DET
ejpam-5918	668	2	first	first	ADJ
ejpam-5918	668	3	course	course	NOUN
ejpam-5918	668	4	in	in	ADP
ejpam-5918	668	5	graph	graph	NOUN
ejpam-5918	668	6	theory	theory	NOUN
ejpam-5918	668	7	.	.	PUNCT
ejpam-5918	669	1	dover	dover	PROPN
ejpam-5918	669	2	publication	publication	PROPN
ejpam-5918	669	3	,	,	PUNCT
ejpam-5918	669	4	garden	garden	NOUN
ejpam-5918	669	5	city	city	NOUN
ejpam-5918	669	6	,	,	PUNCT
ejpam-5918	669	7	new	new	PROPN
ejpam-5918	669	8	york	york	PROPN
ejpam-5918	669	9	,	,	PUNCT
ejpam-5918	669	10	2012	2012	NUM
ejpam-5918	669	11	.	.	PUNCT
ejpam-5918	670	1	[	[	X
ejpam-5918	670	2	5	5	X
ejpam-5918	670	3	]	]	X
ejpam-5918	670	4	p	p	X
ejpam-5918	670	5	slater	slater	NOUN
ejpam-5918	670	6	.	.	PUNCT
ejpam-5918	671	1	dominating	dominating	NOUN
ejpam-5918	671	2	and	and	CCONJ
ejpam-5918	671	3	reference	reference	NOUN
ejpam-5918	671	4	sets	set	NOUN
ejpam-5918	671	5	in	in	ADP
ejpam-5918	671	6	graphs	graph	NOUN
ejpam-5918	671	7	.	.	PUNCT
ejpam-5918	672	1	journal	journal	PROPN
ejpam-5918	672	2	of	of	ADP
ejpam-5918	672	3	mathematical	mathematical	ADJ
ejpam-5918	672	4	physics	physics	NOUN
ejpam-5918	672	5	,	,	PUNCT
ejpam-5918	672	6	22:445–455	22:445–455	PROPN
ejpam-5918	672	7	,	,	PUNCT
ejpam-5918	672	8	1998	1998	NUM
ejpam-5918	672	9	.	.	PUNCT
ejpam-5918	673	1	[	[	X
ejpam-5918	673	2	6	6	NUM
ejpam-5918	673	3	]	]	X
ejpam-5918	673	4	r	r	NOUN
ejpam-5918	673	5	skaggs	skaggs	PROPN
ejpam-5918	673	6	.	.	PUNCT
ejpam-5918	674	1	identifying	identify	VERB
ejpam-5918	674	2	vertices	vertex	NOUN
ejpam-5918	674	3	in	in	ADP
ejpam-5918	674	4	graphs	graph	NOUN
ejpam-5918	674	5	and	and	CCONJ
ejpam-5918	674	6	digraphs	digraph	NOUN
ejpam-5918	674	7	.	.	PUNCT
ejpam-5918	675	1	phd	phd	NOUN
ejpam-5918	675	2	thesis	thesis	NOUN
ejpam-5918	675	3	,	,	PUNCT
ejpam-5918	675	4	university	university	NOUN
ejpam-5918	675	5	of	of	ADP
ejpam-5918	675	6	south	south	PROPN
ejpam-5918	675	7	africa	africa	PROPN
ejpam-5918	675	8	,	,	PUNCT
ejpam-5918	675	9	pretoria	pretoria	PROPN
ejpam-5918	675	10	,	,	PUNCT
ejpam-5918	675	11	2009	2009	NUM
ejpam-5918	675	12	.	.	PUNCT
ejpam-5918	676	1	[	[	X
ejpam-5918	676	2	7	7	NUM
ejpam-5918	676	3	]	]	X
ejpam-5918	676	4	s	s	PART
ejpam-5918	676	5	omega	omega	NOUN
ejpam-5918	676	6	and	and	CCONJ
ejpam-5918	676	7	s	s	X
ejpam-5918	676	8	canoy	canoy	PROPN
ejpam-5918	676	9	jr	jr	PROPN
ejpam-5918	676	10	.	.	PUNCT
ejpam-5918	677	1	locating	locate	VERB
ejpam-5918	677	2	sets	set	NOUN
ejpam-5918	677	3	in	in	ADP
ejpam-5918	677	4	a	a	DET
ejpam-5918	677	5	graph	graph	NOUN
ejpam-5918	677	6	.	.	PUNCT
ejpam-5918	678	1	applied	apply	VERB
ejpam-5918	678	2	mathematics	mathematics	NOUN
ejpam-5918	678	3	sciences	science	NOUN
ejpam-5918	678	4	,	,	PUNCT
ejpam-5918	678	5	9:2957–2964	9:2957–2964	NUM
ejpam-5918	678	6	,	,	PUNCT
ejpam-5918	678	7	2015	2015	NUM
ejpam-5918	678	8	.	.	PUNCT
ejpam-5918	679	1	[	[	X
ejpam-5918	679	2	8	8	NUM
ejpam-5918	679	3	]	]	SYM
ejpam-5918	679	4	s	s	PART
ejpam-5918	679	5	jr	jr	PROPN
ejpam-5918	679	6	canoy	canoy	NOUN
ejpam-5918	679	7	,	,	PUNCT
ejpam-5918	679	8	g	g	NOUN
ejpam-5918	679	9	malacas	malacas	NOUN
ejpam-5918	679	10	,	,	PUNCT
ejpam-5918	679	11	and	and	CCONJ
ejpam-5918	679	12	d	d	X
ejpam-5918	679	13	tarepe	tarepe	NOUN
ejpam-5918	679	14	.	.	PUNCT
ejpam-5918	680	1	locating	locate	VERB
ejpam-5918	680	2	-	-	PUNCT
ejpam-5918	680	3	dominating	dominating	NOUN
ejpam-5918	680	4	sets	set	NOUN
ejpam-5918	680	5	in	in	ADP
ejpam-5918	680	6	graphs	graph	NOUN
ejpam-5918	680	7	.	.	PUNCT
ejpam-5918	681	1	applied	apply	VERB
ejpam-5918	681	2	mathematical	mathematical	ADJ
ejpam-5918	681	3	sciences	sciences	PROPN
ejpam-5918	681	4	,	,	PUNCT
ejpam-5918	681	5	8:4381–4388	8:4381–4388	NUM
ejpam-5918	681	6	,	,	PUNCT
ejpam-5918	681	7	2014	2014	NUM
ejpam-5918	681	8	.	.	PUNCT
ejpam-5918	682	1	[	[	X
ejpam-5918	682	2	9	9	NUM
ejpam-5918	682	3	]	]	SYM
ejpam-5918	682	4	l	l	NOUN
ejpam-5918	682	5	consistente	consistente	NOUN
ejpam-5918	682	6	and	and	CCONJ
ejpam-5918	682	7	jr	jr	PROPN
ejpam-5918	682	8	.	.	PUNCT
ejpam-5918	683	1	i	i	PRON
ejpam-5918	683	2	cabahug	cabahug	VERB
ejpam-5918	683	3	.	.	PUNCT
ejpam-5918	684	1	restrained	restrained	ADJ
ejpam-5918	684	2	global	global	ADJ
ejpam-5918	684	3	defensive	defensive	ADJ
ejpam-5918	684	4	alliances	alliance	NOUN
ejpam-5918	684	5	in	in	ADP
ejpam-5918	684	6	graphs	graph	NOUN
ejpam-5918	684	7	.	.	PUNCT
ejpam-5918	685	1	european	european	ADJ
ejpam-5918	685	2	journal	journal	PROPN
ejpam-5918	685	3	of	of	ADP
ejpam-5918	685	4	pure	pure	ADJ
ejpam-5918	685	5	and	and	CCONJ
ejpam-5918	685	6	applied	applied	ADJ
ejpam-5918	685	7	mathematics	mathematic	NOUN
ejpam-5918	685	8	,	,	PUNCT
ejpam-5918	685	9	17(3):2196–2209	17(3):2196–2209	NUM
ejpam-5918	685	10	,	,	PUNCT
ejpam-5918	685	11	2024	2024	NUM
ejpam-5918	685	12	.	.	PUNCT
ejpam-5918	686	1	[	[	X
ejpam-5918	686	2	10	10	NUM
ejpam-5918	686	3	]	]	SYM
ejpam-5918	686	4	s	s	X
ejpam-5918	686	5	alikhani	alikhani	NOUN
ejpam-5918	686	6	and	and	CCONJ
ejpam-5918	686	7	y	y	PROPN
ejpam-5918	686	8	peng	peng	PROPN
ejpam-5918	686	9	.	.	PUNCT
ejpam-5918	687	1	dominating	dominating	NOUN
ejpam-5918	687	2	sets	set	NOUN
ejpam-5918	687	3	and	and	CCONJ
ejpam-5918	687	4	domination	domination	NOUN
ejpam-5918	687	5	polynomials	polynomial	NOUN
ejpam-5918	687	6	of	of	ADP
ejpam-5918	687	7	paths	path	NOUN
ejpam-5918	687	8	.	.	PUNCT
ejpam-5918	688	1	international	international	ADJ
ejpam-5918	688	2	journal	journal	PROPN
ejpam-5918	688	3	of	of	ADP
ejpam-5918	688	4	mathematics	mathematics	PROPN
ejpam-5918	688	5	and	and	CCONJ
ejpam-5918	688	6	mathematical	mathematical	ADJ
ejpam-5918	688	7	sciences	science	NOUN
ejpam-5918	688	8	,	,	PUNCT
ejpam-5918	688	9	542040:10	542040:10	NUM
ejpam-5918	688	10	pages	page	NOUN
ejpam-5918	688	11	,	,	PUNCT
ejpam-5918	688	12	2009	2009	NUM
ejpam-5918	688	13	.	.	PUNCT
ejpam-5918	689	1	[	[	X
ejpam-5918	689	2	11	11	NUM
ejpam-5918	689	3	]	]	X
ejpam-5918	689	4	g	g	PROPN
ejpam-5918	689	5	chartrand	chartrand	NOUN
ejpam-5918	689	6	,	,	PUNCT
ejpam-5918	689	7	h	h	PROPN
ejpam-5918	689	8	jordon	jordon	PROPN
ejpam-5918	689	9	,	,	PUNCT
ejpam-5918	689	10	v	v	NOUN
ejpam-5918	689	11	vatter	vatter	NOUN
ejpam-5918	689	12	,	,	PUNCT
ejpam-5918	689	13	and	and	CCONJ
ejpam-5918	689	14	p	p	PROPN
ejpam-5918	689	15	zhang	zhang	PROPN
ejpam-5918	689	16	.	.	PUNCT
ejpam-5918	689	17	graphs	graph	NOUN
ejpam-5918	689	18	and	and	CCONJ
ejpam-5918	689	19	digraphs	digraph	NOUN
ejpam-5918	689	20	.	.	PUNCT
ejpam-5918	690	1	chapman	chapman	NOUN
ejpam-5918	690	2	and	and	CCONJ
ejpam-5918	690	3	hall	hall	PROPN
ejpam-5918	690	4	/	/	SYM
ejpam-5918	690	5	crc	crc	PROPN
ejpam-5918	690	6	,	,	PUNCT
ejpam-5918	690	7	boca	boca	PROPN
ejpam-5918	690	8	raton	raton	PROPN
ejpam-5918	690	9	,	,	PUNCT
ejpam-5918	690	10	florida	florida	PROPN
ejpam-5918	690	11	,	,	PUNCT
ejpam-5918	690	12	7	7	NUM
ejpam-5918	690	13	edition	edition	NOUN
ejpam-5918	690	14	,	,	PUNCT
ejpam-5918	690	15	2024	2024	NUM
ejpam-5918	690	16	.	.	PUNCT
ejpam-5918	691	1	[	[	X
ejpam-5918	691	2	12	12	NUM
ejpam-5918	691	3	]	]	X
ejpam-5918	691	4	m	m	NOUN
ejpam-5918	691	5	chellali	chellali	ADJ
ejpam-5918	691	6	,	,	PUNCT
ejpam-5918	691	7	m	m	PROPN
ejpam-5918	691	8	mimouni	mimouni	ADJ
ejpam-5918	691	9	,	,	PUNCT
ejpam-5918	691	10	and	and	CCONJ
ejpam-5918	691	11	p	p	NOUN
ejpam-5918	691	12	slater	slater	NOUN
ejpam-5918	691	13	.	.	PUNCT
ejpam-5918	692	1	on	on	ADP
ejpam-5918	692	2	locating	locate	VERB
ejpam-5918	692	3	-	-	PUNCT
ejpam-5918	692	4	domination	domination	NOUN
ejpam-5918	692	5	in	in	ADP
ejpam-5918	692	6	graphs	graph	NOUN
ejpam-5918	692	7	.	.	PUNCT
ejpam-5918	693	1	discussiones	discussione	NOUN
ejpam-5918	693	2	mathematicae	mathematicae	PROPN
ejpam-5918	693	3	graph	graph	NOUN
ejpam-5918	693	4	theory	theory	NOUN
ejpam-5918	693	5	,	,	PUNCT
ejpam-5918	693	6	30(2):223–235	30(2):223–235	PROPN
ejpam-5918	693	7	,	,	PUNCT
ejpam-5918	693	8	2010	2010	NUM
ejpam-5918	693	9	.	.	PUNCT
ejpam-5918	694	1	[	[	X
ejpam-5918	694	2	13	13	NUM
ejpam-5918	694	3	]	]	X
ejpam-5918	694	4	p	p	X
ejpam-5918	694	5	dankelmann	dankelmann	PROPN
ejpam-5918	694	6	,	,	PUNCT
ejpam-5918	694	7	a	a	DET
ejpam-5918	694	8	hellwig	hellwig	PROPN
ejpam-5918	694	9	,	,	PUNCT
ejpam-5918	694	10	and	and	CCONJ
ejpam-5918	694	11	l	l	PROPN
ejpam-5918	694	12	volkmann	volkmann	PROPN
ejpam-5918	694	13	.	.	PUNCT
ejpam-5918	695	1	on	on	ADP
ejpam-5918	695	2	the	the	DET
ejpam-5918	695	3	connectivity	connectivity	NOUN
ejpam-5918	695	4	of	of	ADP
ejpam-5918	695	5	diamond	diamond	NOUN
ejpam-5918	695	6	-	-	PUNCT
ejpam-5918	695	7	free	free	ADJ
ejpam-5918	695	8	graphs	graph	NOUN
ejpam-5918	695	9	.	.	PUNCT
ejpam-5918	696	1	discrete	discrete	ADJ
ejpam-5918	696	2	applied	apply	VERB
ejpam-5918	696	3	mathematics	mathematic	NOUN
ejpam-5918	696	4	,	,	PUNCT
ejpam-5918	696	5	155(16):2111–2117	155(16):2111–2117	NUM
ejpam-5918	696	6	,	,	PUNCT
ejpam-5918	696	7	2007	2007	NUM
ejpam-5918	696	8	.	.	PUNCT
ejpam-5918	697	1	[	[	X
ejpam-5918	697	2	14	14	NUM
ejpam-5918	697	3	]	]	X
ejpam-5918	697	4	f	f	PROPN
ejpam-5918	697	5	harary	harary	NOUN
ejpam-5918	697	6	.	.	PUNCT
ejpam-5918	698	1	graph	graph	NOUN
ejpam-5918	698	2	theory	theory	NOUN
ejpam-5918	698	3	.	.	PUNCT
ejpam-5918	699	1	addison	addison	PROPN
ejpam-5918	699	2	-	-	PUNCT
ejpam-5918	699	3	wesley	wesley	PROPN
ejpam-5918	699	4	,	,	PUNCT
ejpam-5918	699	5	boston	boston	PROPN
ejpam-5918	699	6	,	,	PUNCT
ejpam-5918	699	7	massachussets	massachusset	NOUN
ejpam-5918	699	8	,	,	PUNCT
ejpam-5918	699	9	1969	1969	NUM
ejpam-5918	699	10	.	.	PUNCT
ejpam-5918	700	1	[	[	X
ejpam-5918	700	2	15	15	NUM
ejpam-5918	700	3	]	]	X
ejpam-5918	700	4	s	s	PART
ejpam-5918	700	5	shah	shah	NOUN
ejpam-5918	700	6	,	,	PUNCT
ejpam-5918	700	7	m	m	VERB
ejpam-5918	700	8	sahni	sahni	VERB
ejpam-5918	700	9	,	,	PUNCT
ejpam-5918	700	10	r	r	NOUN
ejpam-5918	700	11	sahni	sahni	NOUN
ejpam-5918	700	12	,	,	PUNCT
ejpam-5918	700	13	e	e	PROPN
ejpam-5918	700	14	leon	leon	PROPN
ejpam-5918	700	15	-	-	PUNCT
ejpam-5918	700	16	castro	castro	PROPN
ejpam-5918	700	17	,	,	PUNCT
ejpam-5918	700	18	and	and	CCONJ
ejpam-5918	700	19	m	m	PRON
ejpam-5918	700	20	olazabal	olazabal	ADJ
ejpam-5918	700	21	-	-	PUNCT
ejpam-5918	700	22	lugo	lugo	NOUN
ejpam-5918	700	23	.	.	PUNCT
ejpam-5918	701	1	series	series	PROPN
ejpam-5918	701	2	of	of	ADP
ejpam-5918	701	3	floor	floor	NOUN
ejpam-5918	701	4	and	and	CCONJ
ejpam-5918	701	5	ceiling	ceiling	NOUN
ejpam-5918	701	6	function	function	VERB
ejpam-5918	701	7	part	part	NOUN
ejpam-5918	702	1	i	i	NOUN
ejpam-5918	702	2	:	:	PUNCT
ejpam-5918	702	3	partial	partial	ADJ
ejpam-5918	702	4	summations	summation	NOUN
ejpam-5918	702	5	.	.	PUNCT
ejpam-5918	703	1	mathematics	mathematic	NOUN
ejpam-5918	703	2	,	,	PUNCT
ejpam-5918	703	3	10(7):1178	10(7):1178	NUM
ejpam-5918	703	4	,	,	PUNCT
ejpam-5918	703	5	2022	2022	NUM
ejpam-5918	703	6	.	.	PUNCT
ejpam-5918	704	1	[	[	X
ejpam-5918	704	2	16	16	NUM
ejpam-5918	704	3	]	]	X
ejpam-5918	704	4	k	k	PROPN
ejpam-5918	704	5	vaithilingan	vaithilingan	PROPN
ejpam-5918	704	6	.	.	PUNCT
ejpam-5918	705	1	difference	difference	NOUN
ejpam-5918	705	2	labeling	labeling	NOUN
ejpam-5918	705	3	of	of	ADP
ejpam-5918	705	4	some	some	DET
ejpam-5918	705	5	graph	graph	NOUN
ejpam-5918	705	6	families	family	NOUN
ejpam-5918	705	7	.	.	PUNCT
ejpam-5918	706	1	international	international	ADJ
ejpam-5918	706	2	journal	journal	PROPN
ejpam-5918	706	3	of	of	ADP
ejpam-5918	706	4	mathematics	mathematics	PROPN
ejpam-5918	706	5	and	and	CCONJ
ejpam-5918	706	6	statistics	statistic	NOUN
ejpam-5918	706	7	invention	invention	NOUN
ejpam-5918	706	8	(	(	PUNCT
ejpam-5918	706	9	ijmsi	ijmsi	NOUN
ejpam-5918	706	10	)	)	PUNCT
ejpam-5918	706	11	,	,	PUNCT
ejpam-5918	706	12	2(6):37–43	2(6):37–43	NUM
ejpam-5918	706	13	,	,	PUNCT
ejpam-5918	706	14	2014	2014	NUM
ejpam-5918	706	15	.	.	PUNCT
ejpam-5918	707	1	[	[	X
ejpam-5918	707	2	17	17	NUM
ejpam-5918	707	3	]	]	X
ejpam-5918	707	4	z	z	PROPN
ejpam-5918	707	5	zaman	zaman	PROPN
ejpam-5918	707	6	,	,	PUNCT
ejpam-5918	707	7	m	m	PROPN
ejpam-5918	707	8	kamal	kamal	PROPN
ejpam-5918	707	9	kumar	kumar	PROPN
ejpam-5918	707	10	,	,	PUNCT
ejpam-5918	707	11	and	and	CCONJ
ejpam-5918	707	12	s	s	AUX
ejpam-5918	707	13	ahmad	ahmad	PROPN
ejpam-5918	707	14	.	.	PUNCT
ejpam-5918	708	1	roman	roman	ADJ
ejpam-5918	708	2	and	and	CCONJ
ejpam-5918	708	3	inverse	inverse	ADJ
ejpam-5918	708	4	roman	roman	ADJ
ejpam-5918	708	5	domination	domination	NOUN
ejpam-5918	708	6	in	in	ADP
ejpam-5918	708	7	graphs	graph	NOUN
ejpam-5918	708	8	.	.	PUNCT
ejpam-5918	709	1	notes	note	NOUN
ejpam-5918	709	2	on	on	ADP
ejpam-5918	709	3	number	number	NOUN
ejpam-5918	709	4	theory	theory	NOUN
ejpam-5918	709	5	and	and	CCONJ
ejpam-5918	709	6	discrete	discrete	ADJ
ejpam-5918	709	7	mathematics	mathematic	NOUN
ejpam-5918	709	8	,	,	PUNCT
ejpam-5918	709	9	24(3):142–150	24(3):142–150	PROPN
ejpam-5918	709	10	,	,	PUNCT
ejpam-5918	709	11	2018	2018	NUM
ejpam-5918	709	12	.	.	PUNCT
ejpam-5918	710	1	i.	i.	PROPN
ejpam-5918	710	2	tropico	tropico	PROPN
ejpam-5918	710	3	,	,	PUNCT
ejpam-5918	710	4	i.	i.	PROPN
ejpam-5918	710	5	cabahug	cabahug	PROPN
ejpam-5918	710	6	,	,	PUNCT
ejpam-5918	710	7	jr	jr	PROPN
ejpam-5918	710	8	.	.	PROPN
ejpam-5918	710	9	/	/	SYM
ejpam-5918	710	10	eur	eur	PROPN
ejpam-5918	710	11	.	.	PUNCT
ejpam-5918	711	1	j.	j.	PROPN
ejpam-5918	711	2	pure	pure	PROPN
ejpam-5918	711	3	appl	appl	PROPN
ejpam-5918	711	4	.	.	PROPN
ejpam-5918	711	5	math	math	PROPN
ejpam-5918	711	6	,	,	PUNCT
ejpam-5918	711	7	18	18	NUM
ejpam-5918	711	8	(	(	PUNCT
ejpam-5918	711	9	2	2	NUM
ejpam-5918	711	10	)	)	PUNCT
ejpam-5918	711	11	(	(	PUNCT
ejpam-5918	711	12	2025	2025	NUM
ejpam-5918	711	13	)	)	PUNCT
ejpam-5918	711	14	,	,	PUNCT
ejpam-5918	711	15	5918	5918	NUM
ejpam-5918	711	16	21	21	NUM
ejpam-5918	711	17	of	of	ADP
ejpam-5918	711	18	21	21	NUM
ejpam-5918	711	19	[	[	SYM
ejpam-5918	711	20	18	18	NUM
ejpam-5918	711	21	]	]	PUNCT
ejpam-5918	711	22	m	m	VERB
ejpam-5918	711	23	bhanumathi	bhanumathi	NOUN
ejpam-5918	711	24	and	and	CCONJ
ejpam-5918	711	25	m	m	VERB
ejpam-5918	711	26	thusleem	thusleem	NOUN
ejpam-5918	711	27	furjana	furjana	ADJ
ejpam-5918	711	28	.	.	PUNCT
ejpam-5918	712	1	on	on	ADP
ejpam-5918	712	2	locating	locate	VERB
ejpam-5918	712	3	domination	domination	NOUN
ejpam-5918	712	4	number	number	NOUN
ejpam-5918	712	5	of	of	ADP
ejpam-5918	712	6	total	total	ADJ
ejpam-5918	712	7	graph	graph	NOUN
ejpam-5918	712	8	t(g	t(g	NOUN
ejpam-5918	712	9	)	)	PUNCT
ejpam-5918	712	10	.	.	PUNCT
ejpam-5918	713	1	international	international	ADJ
ejpam-5918	713	2	journal	journal	NOUN
ejpam-5918	713	3	of	of	ADP
ejpam-5918	713	4	pure	pure	ADJ
ejpam-5918	713	5	and	and	CCONJ
ejpam-5918	713	6	applied	applied	ADJ
ejpam-5918	713	7	mathematics	mathematic	NOUN
ejpam-5918	713	8	,	,	PUNCT
ejpam-5918	713	9	117(11):283–288	117(11):283–288	NUM
ejpam-5918	713	10	,	,	PUNCT
ejpam-5918	713	11	2017	2017	NUM
ejpam-5918	713	12	.	.	PUNCT
ejpam-5918	714	1	[	[	X
ejpam-5918	714	2	19	19	NUM
ejpam-5918	714	3	]	]	X
ejpam-5918	714	4	c	c	PUNCT
ejpam-5918	714	5	go	go	VERB
ejpam-5918	714	6	and	and	CCONJ
ejpam-5918	714	7	s	s	VERB
ejpam-5918	714	8	jr	jr	PROPN
ejpam-5918	714	9	canoy	canoy	PROPN
ejpam-5918	714	10	.	.	PUNCT
ejpam-5918	715	1	domination	domination	NOUN
ejpam-5918	715	2	in	in	ADP
ejpam-5918	715	3	the	the	DET
ejpam-5918	715	4	corona	corona	NOUN
ejpam-5918	715	5	and	and	CCONJ
ejpam-5918	715	6	join	join	VERB
ejpam-5918	715	7	of	of	ADP
ejpam-5918	715	8	graphs	graph	NOUN
ejpam-5918	715	9	.	.	PUNCT
ejpam-5918	716	1	international	international	ADJ
ejpam-5918	716	2	mathematical	mathematical	PROPN
ejpam-5918	716	3	forum	forum	PROPN
ejpam-5918	716	4	,	,	PUNCT
ejpam-5918	716	5	6(16):763–771	6(16):763–771	NUM
ejpam-5918	716	6	,	,	PUNCT
ejpam-5918	716	7	2011	2011	NUM
ejpam-5918	716	8	.	.	PUNCT