id	sid	tid	token	lemma	pos
ejpam-5917	1	1	european	european	PROPN
ejpam-5917	1	2	journal	journal	PROPN
ejpam-5917	1	3	of	of	ADP
ejpam-5917	1	4	pure	pure	ADJ
ejpam-5917	1	5	and	and	CCONJ
ejpam-5917	1	6	applied	applied	ADJ
ejpam-5917	1	7	mathematics	mathematic	NOUN
ejpam-5917	1	8	2025	2025	NUM
ejpam-5917	1	9	,	,	PUNCT
ejpam-5917	1	10	vol	vol	NOUN
ejpam-5917	1	11	.	.	PROPN
ejpam-5917	1	12	18	18	NUM
ejpam-5917	1	13	,	,	PUNCT
ejpam-5917	1	14	issue	issue	NOUN
ejpam-5917	1	15	2	2	NUM
ejpam-5917	1	16	,	,	PUNCT
ejpam-5917	1	17	article	article	NOUN
ejpam-5917	1	18	number	number	NOUN
ejpam-5917	1	19	5917	5917	NUM
ejpam-5917	1	20	issn	issn	PROPN
ejpam-5917	1	21	1307	1307	NUM
ejpam-5917	1	22	-	-	SYM
ejpam-5917	1	23	5543	5543	NUM
ejpam-5917	1	24	–	–	PUNCT
ejpam-5917	1	25	ejpam.com	ejpam.com	X
ejpam-5917	1	26	published	publish	VERB
ejpam-5917	1	27	by	by	ADP
ejpam-5917	1	28	new	new	PROPN
ejpam-5917	1	29	york	york	PROPN
ejpam-5917	1	30	business	business	PROPN
ejpam-5917	1	31	global	global	ADJ
ejpam-5917	1	32	total	total	ADJ
ejpam-5917	1	33	safe	safe	ADJ
ejpam-5917	1	34	domination	domination	NOUN
ejpam-5917	1	35	on	on	ADP
ejpam-5917	1	36	some	some	DET
ejpam-5917	1	37	known	know	VERB
ejpam-5917	1	38	families	family	NOUN
ejpam-5917	1	39	of	of	ADP
ejpam-5917	1	40	graphs	graph	NOUN
ejpam-5917	1	41	wendel	wendel	PROPN
ejpam-5917	1	42	glenn	glenn	PROPN
ejpam-5917	1	43	c.	c.	PROPN
ejpam-5917	1	44	jumalon1,∗	jumalon1,∗	PROPN
ejpam-5917	1	45	,	,	PUNCT
ejpam-5917	1	46	isagani	isagani	PROPN
ejpam-5917	1	47	s.	s.	PROPN
ejpam-5917	1	48	cabahug	cabahug	PROPN
ejpam-5917	1	49	,	,	PUNCT
ejpam-5917	1	50	jr.1	jr.1	PROPN
ejpam-5917	1	51	1	1	NUM
ejpam-5917	1	52	department	department	NOUN
ejpam-5917	1	53	of	of	ADP
ejpam-5917	1	54	mathematics	mathematic	NOUN
ejpam-5917	1	55	,	,	PUNCT
ejpam-5917	1	56	college	college	NOUN
ejpam-5917	1	57	of	of	ADP
ejpam-5917	1	58	arts	art	NOUN
ejpam-5917	1	59	and	and	CCONJ
ejpam-5917	1	60	sciences	science	NOUN
ejpam-5917	1	61	,	,	PUNCT
ejpam-5917	1	62	central	central	ADJ
ejpam-5917	1	63	mindanao	mindanao	PROPN
ejpam-5917	1	64	university	university	PROPN
ejpam-5917	1	65	,	,	PUNCT
ejpam-5917	1	66	musuan	musuan	PROPN
ejpam-5917	1	67	,	,	PUNCT
ejpam-5917	1	68	maramag	maramag	NOUN
ejpam-5917	1	69	,	,	PUNCT
ejpam-5917	1	70	bukidnon	bukidnon	NOUN
ejpam-5917	1	71	,	,	PUNCT
ejpam-5917	1	72	8714	8714	NUM
ejpam-5917	1	73	philippines	philippine	NOUN
ejpam-5917	1	74	abstract	abstract	ADJ
ejpam-5917	1	75	.	.	PUNCT
ejpam-5917	2	1	a	a	DET
ejpam-5917	2	2	total	total	ADJ
ejpam-5917	2	3	dominating	dominating	NOUN
ejpam-5917	2	4	set	set	VERB
ejpam-5917	2	5	in	in	ADP
ejpam-5917	2	6	a	a	DET
ejpam-5917	2	7	graph	graph	NOUN
ejpam-5917	2	8	g	g	NOUN
ejpam-5917	2	9	is	be	AUX
ejpam-5917	2	10	a	a	DET
ejpam-5917	2	11	nonempty	nonempty	ADJ
ejpam-5917	2	12	set	set	VERB
ejpam-5917	2	13	s	s	PROPN
ejpam-5917	2	14	⊆	⊆	NUM
ejpam-5917	2	15	v	v	NOUN
ejpam-5917	2	16	(	(	PUNCT
ejpam-5917	2	17	g	g	NOUN
ejpam-5917	2	18	)	)	PUNCT
ejpam-5917	2	19	such	such	ADJ
ejpam-5917	2	20	that	that	SCONJ
ejpam-5917	2	21	every	every	DET
ejpam-5917	2	22	vertex	vertex	NOUN
ejpam-5917	2	23	v	v	ADP
ejpam-5917	2	24	∈	∈	NOUN
ejpam-5917	2	25	v	v	NOUN
ejpam-5917	2	26	(	(	PUNCT
ejpam-5917	2	27	g	g	NOUN
ejpam-5917	2	28	)	)	PUNCT
ejpam-5917	2	29	,	,	PUNCT
ejpam-5917	2	30	including	include	VERB
ejpam-5917	2	31	those	those	PRON
ejpam-5917	2	32	in	in	ADP
ejpam-5917	2	33	s	s	NOUN
ejpam-5917	2	34	,	,	PUNCT
ejpam-5917	2	35	is	be	AUX
ejpam-5917	2	36	adjacent	adjacent	ADJ
ejpam-5917	2	37	to	to	ADP
ejpam-5917	2	38	at	at	ADV
ejpam-5917	2	39	least	least	ADV
ejpam-5917	2	40	one	one	NUM
ejpam-5917	2	41	vertex	vertex	NOUN
ejpam-5917	2	42	in	in	ADP
ejpam-5917	2	43	s.	s.	PROPN
ejpam-5917	2	44	a	a	DET
ejpam-5917	2	45	safe	safe	ADJ
ejpam-5917	2	46	dominating	dominating	NOUN
ejpam-5917	2	47	set	set	VERB
ejpam-5917	2	48	in	in	ADP
ejpam-5917	2	49	g	g	PROPN
ejpam-5917	2	50	is	be	AUX
ejpam-5917	2	51	a	a	DET
ejpam-5917	2	52	nonempty	nonempty	ADJ
ejpam-5917	2	53	set	set	VERB
ejpam-5917	2	54	s	s	PROPN
ejpam-5917	2	55	⊆	⊆	NUM
ejpam-5917	2	56	v	v	NOUN
ejpam-5917	2	57	(	(	PUNCT
ejpam-5917	2	58	g	g	NOUN
ejpam-5917	2	59	)	)	PUNCT
ejpam-5917	2	60	that	that	PRON
ejpam-5917	2	61	is	be	AUX
ejpam-5917	2	62	a	a	DET
ejpam-5917	2	63	dominating	dominating	NOUN
ejpam-5917	2	64	set	set	NOUN
ejpam-5917	2	65	,	,	PUNCT
ejpam-5917	2	66	and	and	CCONJ
ejpam-5917	2	67	for	for	ADP
ejpam-5917	2	68	every	every	DET
ejpam-5917	2	69	component	component	NOUN
ejpam-5917	2	70	a	a	PRON
ejpam-5917	2	71	of	of	ADP
ejpam-5917	2	72	the	the	DET
ejpam-5917	2	73	induced	induced	ADJ
ejpam-5917	2	74	subgraph	subgraph	NOUN
ejpam-5917	2	75	g[s	g[	NOUN
ejpam-5917	2	76	]	]	PUNCT
ejpam-5917	2	77	and	and	CCONJ
ejpam-5917	2	78	every	every	DET
ejpam-5917	2	79	component	component	NOUN
ejpam-5917	2	80	b	b	PROPN
ejpam-5917	2	81	of	of	ADP
ejpam-5917	2	82	the	the	DET
ejpam-5917	2	83	induced	induced	ADJ
ejpam-5917	2	84	subgraph	subgraph	NOUN
ejpam-5917	2	85	g[v	g[v	PROPN
ejpam-5917	2	86	(	(	PUNCT
ejpam-5917	2	87	g	g	NOUN
ejpam-5917	2	88	)	)	PUNCT
ejpam-5917	2	89	∖	∖	X
ejpam-5917	3	1	s	s	PART
ejpam-5917	3	2	]	]	X
ejpam-5917	3	3	,	,	PUNCT
ejpam-5917	3	4	with	with	ADP
ejpam-5917	3	5	a	a	DET
ejpam-5917	3	6	adjacent	adjacent	ADJ
ejpam-5917	3	7	to	to	ADP
ejpam-5917	3	8	b	b	X
ejpam-5917	3	9	,	,	PUNCT
ejpam-5917	3	10	it	it	PRON
ejpam-5917	3	11	holds	hold	VERB
ejpam-5917	3	12	that	that	SCONJ
ejpam-5917	3	13	|v	|v	PROPN
ejpam-5917	3	14	(	(	PUNCT
ejpam-5917	3	15	a)|	a)|	X
ejpam-5917	3	16	≥	≥	NOUN
ejpam-5917	3	17	|v	|v	PROPN
ejpam-5917	3	18	(	(	PUNCT
ejpam-5917	3	19	b)|	b)|	NOUN
ejpam-5917	3	20	.	.	PUNCT
ejpam-5917	4	1	this	this	DET
ejpam-5917	4	2	study	study	NOUN
ejpam-5917	4	3	introduces	introduce	VERB
ejpam-5917	4	4	the	the	DET
ejpam-5917	4	5	concept	concept	NOUN
ejpam-5917	4	6	of	of	ADP
ejpam-5917	4	7	total	total	ADJ
ejpam-5917	4	8	safe	safe	ADJ
ejpam-5917	4	9	domination	domination	NOUN
ejpam-5917	4	10	in	in	ADP
ejpam-5917	4	11	graphs	graph	NOUN
ejpam-5917	4	12	which	which	PRON
ejpam-5917	4	13	combines	combine	VERB
ejpam-5917	4	14	total	total	ADJ
ejpam-5917	4	15	domination	domination	NOUN
ejpam-5917	4	16	and	and	CCONJ
ejpam-5917	4	17	safe	safe	ADJ
ejpam-5917	4	18	domination	domination	NOUN
ejpam-5917	4	19	.	.	PUNCT
ejpam-5917	5	1	total	total	ADJ
ejpam-5917	5	2	safe	safe	ADJ
ejpam-5917	5	3	domination	domination	NOUN
ejpam-5917	5	4	ensures	ensure	VERB
ejpam-5917	5	5	total	total	ADJ
ejpam-5917	5	6	accessibility	accessibility	NOUN
ejpam-5917	5	7	and	and	CCONJ
ejpam-5917	5	8	structural	structural	ADJ
ejpam-5917	5	9	resilience	resilience	NOUN
ejpam-5917	5	10	.	.	PUNCT
ejpam-5917	6	1	this	this	DET
ejpam-5917	6	2	paper	paper	NOUN
ejpam-5917	6	3	provides	provide	VERB
ejpam-5917	6	4	characterization	characterization	NOUN
ejpam-5917	6	5	of	of	ADP
ejpam-5917	6	6	total	total	ADJ
ejpam-5917	6	7	safe	safe	ADJ
ejpam-5917	6	8	dominating	dominating	NOUN
ejpam-5917	6	9	sets	set	NOUN
ejpam-5917	6	10	for	for	ADP
ejpam-5917	6	11	some	some	DET
ejpam-5917	6	12	well	well	ADV
ejpam-5917	6	13	-	-	PUNCT
ejpam-5917	6	14	known	know	VERB
ejpam-5917	6	15	graph	graph	NOUN
ejpam-5917	6	16	families	family	NOUN
ejpam-5917	6	17	,	,	PUNCT
ejpam-5917	6	18	including	include	VERB
ejpam-5917	6	19	:	:	PUNCT
ejpam-5917	6	20	path	path	NOUN
ejpam-5917	6	21	,	,	PUNCT
ejpam-5917	6	22	cycle	cycle	NOUN
ejpam-5917	6	23	,	,	PUNCT
ejpam-5917	6	24	complete	complete	ADJ
ejpam-5917	6	25	,	,	PUNCT
ejpam-5917	6	26	complete	complete	ADJ
ejpam-5917	6	27	bipartite	bipartite	PROPN
ejpam-5917	6	28	,	,	PUNCT
ejpam-5917	6	29	friendship	friendship	NOUN
ejpam-5917	6	30	,	,	PUNCT
ejpam-5917	6	31	sunlet	sunlet	NOUN
ejpam-5917	6	32	and	and	CCONJ
ejpam-5917	6	33	helm	helm	NOUN
ejpam-5917	6	34	graphs	graph	NOUN
ejpam-5917	6	35	.	.	PUNCT
ejpam-5917	7	1	it	it	PRON
ejpam-5917	7	2	also	also	ADV
ejpam-5917	7	3	presents	present	VERB
ejpam-5917	7	4	the	the	DET
ejpam-5917	7	5	total	total	ADJ
ejpam-5917	7	6	safe	safe	ADJ
ejpam-5917	7	7	domination	domination	NOUN
ejpam-5917	7	8	number	number	NOUN
ejpam-5917	7	9	for	for	ADP
ejpam-5917	7	10	each	each	PRON
ejpam-5917	7	11	of	of	ADP
ejpam-5917	7	12	these	these	DET
ejpam-5917	7	13	graph	graph	NOUN
ejpam-5917	7	14	families	family	NOUN
ejpam-5917	7	15	.	.	PUNCT
ejpam-5917	8	1	2020	2020	NUM
ejpam-5917	8	2	mathematics	mathematic	NOUN
ejpam-5917	8	3	subject	subject	NOUN
ejpam-5917	8	4	classifications	classification	NOUN
ejpam-5917	8	5	:	:	PUNCT
ejpam-5917	8	6	05c69	05c69	X
ejpam-5917	8	7	key	key	ADJ
ejpam-5917	8	8	words	word	NOUN
ejpam-5917	8	9	and	and	CCONJ
ejpam-5917	8	10	phrases	phrase	NOUN
ejpam-5917	8	11	:	:	PUNCT
ejpam-5917	8	12	total	total	ADJ
ejpam-5917	8	13	domination	domination	NOUN
ejpam-5917	8	14	,	,	PUNCT
ejpam-5917	8	15	safe	safe	ADJ
ejpam-5917	8	16	domination	domination	NOUN
ejpam-5917	8	17	,	,	PUNCT
ejpam-5917	8	18	safe	safe	ADJ
ejpam-5917	8	19	set	set	NOUN
ejpam-5917	8	20	,	,	PUNCT
ejpam-5917	8	21	total	total	ADJ
ejpam-5917	8	22	safe	safe	ADJ
ejpam-5917	8	23	domination	domination	NOUN
ejpam-5917	8	24	1	1	NUM
ejpam-5917	8	25	.	.	PUNCT
ejpam-5917	9	1	introduction	introduction	NOUN
ejpam-5917	9	2	the	the	DET
ejpam-5917	9	3	study	study	NOUN
ejpam-5917	9	4	of	of	ADP
ejpam-5917	9	5	domination	domination	NOUN
ejpam-5917	9	6	has	have	AUX
ejpam-5917	9	7	grown	grow	VERB
ejpam-5917	9	8	to	to	PART
ejpam-5917	9	9	be	be	AUX
ejpam-5917	9	10	one	one	NUM
ejpam-5917	9	11	of	of	ADP
ejpam-5917	9	12	the	the	DET
ejpam-5917	9	13	most	most	ADV
ejpam-5917	9	14	rapidly	rapidly	ADV
ejpam-5917	9	15	expanding	expand	VERB
ejpam-5917	9	16	areas	area	NOUN
ejpam-5917	9	17	in	in	ADP
ejpam-5917	9	18	graph	graph	NOUN
ejpam-5917	9	19	theory	theory	NOUN
ejpam-5917	9	20	.	.	PUNCT
ejpam-5917	10	1	domination	domination	NOUN
ejpam-5917	10	2	in	in	ADP
ejpam-5917	10	3	graphs	graph	NOUN
ejpam-5917	10	4	has	have	VERB
ejpam-5917	10	5	wide	wide	ADV
ejpam-5917	10	6	-	-	PUNCT
ejpam-5917	10	7	ranging	range	VERB
ejpam-5917	10	8	applications	application	NOUN
ejpam-5917	10	9	in	in	ADP
ejpam-5917	10	10	network	network	NOUN
ejpam-5917	10	11	design	design	NOUN
ejpam-5917	10	12	,	,	PUNCT
ejpam-5917	10	13	resource	resource	NOUN
ejpam-5917	10	14	allocation	allocation	NOUN
ejpam-5917	10	15	,	,	PUNCT
ejpam-5917	10	16	and	and	CCONJ
ejpam-5917	10	17	security	security	NOUN
ejpam-5917	10	18	management	management	NOUN
ejpam-5917	10	19	.	.	PUNCT
ejpam-5917	11	1	traditional	traditional	ADJ
ejpam-5917	11	2	domination	domination	NOUN
ejpam-5917	11	3	focuses	focus	VERB
ejpam-5917	11	4	on	on	ADP
ejpam-5917	11	5	identifying	identify	VERB
ejpam-5917	11	6	subsets	subset	NOUN
ejpam-5917	11	7	of	of	ADP
ejpam-5917	11	8	vertices	vertex	NOUN
ejpam-5917	11	9	that	that	PRON
ejpam-5917	11	10	can	can	AUX
ejpam-5917	11	11	control	control	VERB
ejpam-5917	11	12	or	or	CCONJ
ejpam-5917	11	13	influence	influence	VERB
ejpam-5917	11	14	the	the	DET
ejpam-5917	11	15	entire	entire	ADJ
ejpam-5917	11	16	graph	graph	NOUN
ejpam-5917	11	17	.	.	PUNCT
ejpam-5917	12	1	however	however	ADV
ejpam-5917	12	2	,	,	PUNCT
ejpam-5917	12	3	as	as	SCONJ
ejpam-5917	12	4	systems	system	NOUN
ejpam-5917	12	5	grow	grow	VERB
ejpam-5917	12	6	more	more	ADV
ejpam-5917	12	7	complex	complex	ADJ
ejpam-5917	12	8	,	,	PUNCT
ejpam-5917	12	9	there	there	PRON
ejpam-5917	12	10	is	be	VERB
ejpam-5917	12	11	a	a	DET
ejpam-5917	12	12	growing	grow	VERB
ejpam-5917	12	13	need	need	NOUN
ejpam-5917	12	14	for	for	ADP
ejpam-5917	12	15	more	more	ADJ
ejpam-5917	12	16	refined	refined	ADJ
ejpam-5917	12	17	approaches	approach	NOUN
ejpam-5917	12	18	.	.	PUNCT
ejpam-5917	13	1	this	this	PRON
ejpam-5917	13	2	has	have	AUX
ejpam-5917	13	3	led	lead	VERB
ejpam-5917	13	4	to	to	ADP
ejpam-5917	13	5	the	the	DET
ejpam-5917	13	6	emergence	emergence	NOUN
ejpam-5917	13	7	of	of	ADP
ejpam-5917	13	8	more	more	ADJ
ejpam-5917	13	9	variations	variation	NOUN
ejpam-5917	13	10	of	of	ADP
ejpam-5917	13	11	domination	domination	NOUN
ejpam-5917	13	12	,	,	PUNCT
ejpam-5917	13	13	such	such	ADJ
ejpam-5917	13	14	as	as	ADP
ejpam-5917	13	15	total	total	ADJ
ejpam-5917	13	16	domination	domination	NOUN
ejpam-5917	13	17	and	and	CCONJ
ejpam-5917	13	18	safe	safe	ADJ
ejpam-5917	13	19	domination	domination	NOUN
ejpam-5917	13	20	,	,	PUNCT
ejpam-5917	13	21	which	which	PRON
ejpam-5917	13	22	offer	offer	VERB
ejpam-5917	13	23	enhanced	enhance	VERB
ejpam-5917	13	24	perspectives	perspective	NOUN
ejpam-5917	13	25	and	and	CCONJ
ejpam-5917	13	26	more	more	ADV
ejpam-5917	13	27	effective	effective	ADJ
ejpam-5917	13	28	solutions	solution	NOUN
ejpam-5917	13	29	to	to	ADP
ejpam-5917	13	30	real	real	ADJ
ejpam-5917	13	31	-	-	PUNCT
ejpam-5917	13	32	world	world	NOUN
ejpam-5917	13	33	problems	problem	NOUN
ejpam-5917	13	34	.	.	PUNCT
ejpam-5917	14	1	the	the	DET
ejpam-5917	14	2	formal	formal	ADJ
ejpam-5917	14	3	study	study	NOUN
ejpam-5917	14	4	of	of	ADP
ejpam-5917	14	5	dominating	dominating	NOUN
ejpam-5917	14	6	sets	set	NOUN
ejpam-5917	14	7	in	in	ADP
ejpam-5917	14	8	graph	graph	NOUN
ejpam-5917	14	9	theory	theory	NOUN
ejpam-5917	14	10	began	begin	VERB
ejpam-5917	14	11	in	in	ADP
ejpam-5917	14	12	the	the	DET
ejpam-5917	14	13	1960s	1960	NOUN
ejpam-5917	14	14	.	.	PUNCT
ejpam-5917	15	1	in	in	ADP
ejpam-5917	15	2	1977	1977	NUM
ejpam-5917	15	3	,	,	PUNCT
ejpam-5917	15	4	cockayne	cockayne	NOUN
ejpam-5917	15	5	published	publish	VERB
ejpam-5917	15	6	a	a	DET
ejpam-5917	15	7	comprehensive	comprehensive	ADJ
ejpam-5917	15	8	survey	survey	NOUN
ejpam-5917	15	9	of	of	ADP
ejpam-5917	15	10	the	the	DET
ejpam-5917	15	11	results	result	NOUN
ejpam-5917	15	12	on	on	ADP
ejpam-5917	15	13	dominating	dominating	NOUN
ejpam-5917	15	14	sets	set	NOUN
ejpam-5917	15	15	known	know	VERB
ejpam-5917	15	16	at	at	ADP
ejpam-5917	15	17	∗corresponding	∗corresponde	VERB
ejpam-5917	15	18	author	author	NOUN
ejpam-5917	15	19	.	.	PUNCT
ejpam-5917	16	1	doi	doi	NOUN
ejpam-5917	16	2	:	:	PUNCT
ejpam-5917	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5917	https://doi.org/10.29020/nybg.ejpam.v18i2.5917	VERB
ejpam-5917	16	4	email	email	NOUN
ejpam-5917	16	5	addresses	address	NOUN
ejpam-5917	16	6	:	:	PUNCT
ejpam-5917	16	7	wendeljumalon@gmail.com	wendeljumalon@gmail.com	X
ejpam-5917	16	8	(	(	PUNCT
ejpam-5917	16	9	w.	w.	PROPN
ejpam-5917	16	10	g.	g.	PROPN
ejpam-5917	16	11	jumalon	jumalon	PROPN
ejpam-5917	16	12	)	)	PUNCT
ejpam-5917	16	13	,	,	PUNCT
ejpam-5917	16	14	isaganicabahugjr@cmu.edu.ph	isaganicabahugjr@cmu.edu.ph	PROPN
ejpam-5917	16	15	(	(	PUNCT
ejpam-5917	16	16	i.	i.	PROPN
ejpam-5917	16	17	cabahug	cabahug	PROPN
ejpam-5917	16	18	,	,	PUNCT
ejpam-5917	16	19	jr	jr	PROPN
ejpam-5917	16	20	.	.	PUNCT
ejpam-5917	16	21	)	)	PUNCT
ejpam-5917	16	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5917	17	1	1	1	NUM
ejpam-5917	17	2	copyright	copyright	NOUN
ejpam-5917	17	3	:	:	PUNCT
ejpam-5917	17	4	©	©	PROPN
ejpam-5917	17	5	2025	2025	NUM
ejpam-5917	17	6	the	the	DET
ejpam-5917	17	7	author(s	author(s	NOUN
ejpam-5917	17	8	)	)	PUNCT
ejpam-5917	17	9	.	.	PUNCT
ejpam-5917	18	1	(	(	PUNCT
ejpam-5917	18	2	cc	cc	NOUN
ejpam-5917	18	3	by	by	ADP
ejpam-5917	18	4	-	-	PUNCT
ejpam-5917	18	5	nc	nc	PROPN
ejpam-5917	18	6	4.0	4.0	NUM
ejpam-5917	18	7	)	)	PUNCT
ejpam-5917	18	8	w.	w.	PROPN
ejpam-5917	18	9	g.	g.	PROPN
ejpam-5917	18	10	jumalon	jumalon	PROPN
ejpam-5917	18	11	,	,	PUNCT
ejpam-5917	18	12	i.	i.	PROPN
ejpam-5917	18	13	cabahug	cabahug	PROPN
ejpam-5917	18	14	/	/	SYM
ejpam-5917	18	15	eur	eur	PROPN
ejpam-5917	18	16	.	.	PUNCT
ejpam-5917	19	1	j.	j.	PROPN
ejpam-5917	19	2	pure	pure	PROPN
ejpam-5917	19	3	appl	appl	PROPN
ejpam-5917	19	4	.	.	PROPN
ejpam-5917	19	5	math	math	PROPN
ejpam-5917	19	6	,	,	PUNCT
ejpam-5917	19	7	18	18	NUM
ejpam-5917	19	8	(	(	PUNCT
ejpam-5917	19	9	2	2	NUM
ejpam-5917	19	10	)	)	PUNCT
ejpam-5917	19	11	(	(	PUNCT
ejpam-5917	19	12	2025	2025	NUM
ejpam-5917	19	13	)	)	PUNCT
ejpam-5917	19	14	,	,	PUNCT
ejpam-5917	19	15	5917	5917	NUM
ejpam-5917	19	16	2	2	NUM
ejpam-5917	19	17	of	of	ADP
ejpam-5917	19	18	12	12	NUM
ejpam-5917	19	19	that	that	DET
ejpam-5917	19	20	time	time	NOUN
ejpam-5917	19	21	.	.	PUNCT
ejpam-5917	20	1	this	this	DET
ejpam-5917	20	2	survey	survey	NOUN
ejpam-5917	20	3	introduced	introduce	VERB
ejpam-5917	20	4	the	the	DET
ejpam-5917	20	5	notation	notation	PROPN
ejpam-5917	20	6	γ(g	γ(g	PROPN
ejpam-5917	20	7	)	)	PUNCT
ejpam-5917	20	8	for	for	SCONJ
ejpam-5917	20	9	the	the	DET
ejpam-5917	20	10	domination	domination	NOUN
ejpam-5917	20	11	number	number	NOUN
ejpam-5917	20	12	of	of	ADP
ejpam-5917	20	13	a	a	DET
ejpam-5917	20	14	graph	graph	NOUN
ejpam-5917	20	15	g	g	NOUN
ejpam-5917	20	16	,	,	PUNCT
ejpam-5917	20	17	which	which	PRON
ejpam-5917	20	18	has	have	AUX
ejpam-5917	20	19	since	since	SCONJ
ejpam-5917	20	20	become	become	AUX
ejpam-5917	20	21	widely	widely	ADV
ejpam-5917	20	22	adopted	adopt	VERB
ejpam-5917	20	23	[	[	X
ejpam-5917	20	24	1	1	NUM
ejpam-5917	20	25	]	]	PUNCT
ejpam-5917	20	26	.	.	PUNCT
ejpam-5917	21	1	in	in	ADP
ejpam-5917	21	2	1980	1980	NUM
ejpam-5917	21	3	,	,	PUNCT
ejpam-5917	21	4	cockayne	cockayne	NOUN
ejpam-5917	21	5	,	,	PUNCT
ejpam-5917	21	6	dawes	dawe	NOUN
ejpam-5917	21	7	and	and	CCONJ
ejpam-5917	21	8	hedetniemi	hedetniemi	ADP
ejpam-5917	21	9	published	publish	VERB
ejpam-5917	21	10	the	the	DET
ejpam-5917	21	11	first	first	ADJ
ejpam-5917	21	12	paper	paper	NOUN
ejpam-5917	21	13	on	on	ADP
ejpam-5917	21	14	total	total	ADJ
ejpam-5917	21	15	domination	domination	NOUN
ejpam-5917	21	16	in	in	ADP
ejpam-5917	21	17	graphs	graph	NOUN
ejpam-5917	21	18	.	.	PUNCT
ejpam-5917	22	1	they	they	PRON
ejpam-5917	22	2	obtained	obtain	VERB
ejpam-5917	22	3	results	result	NOUN
ejpam-5917	22	4	concerning	concern	VERB
ejpam-5917	22	5	the	the	DET
ejpam-5917	22	6	total	total	ADJ
ejpam-5917	22	7	domination	domination	NOUN
ejpam-5917	22	8	number	number	NOUN
ejpam-5917	22	9	of	of	ADP
ejpam-5917	22	10	a	a	DET
ejpam-5917	22	11	graph	graph	NOUN
ejpam-5917	22	12	and	and	CCONJ
ejpam-5917	22	13	the	the	DET
ejpam-5917	22	14	total	total	ADJ
ejpam-5917	22	15	domatic	domatic	ADJ
ejpam-5917	22	16	number	number	NOUN
ejpam-5917	22	17	of	of	ADP
ejpam-5917	22	18	a	a	DET
ejpam-5917	22	19	graph	graph	NOUN
ejpam-5917	22	20	(	(	PUNCT
ejpam-5917	22	21	the	the	DET
ejpam-5917	22	22	largest	large	ADJ
ejpam-5917	22	23	order	order	NOUN
ejpam-5917	22	24	of	of	ADP
ejpam-5917	22	25	a	a	DET
ejpam-5917	22	26	partition	partition	NOUN
ejpam-5917	22	27	of	of	ADP
ejpam-5917	22	28	a	a	DET
ejpam-5917	22	29	graph	graph	NOUN
ejpam-5917	22	30	into	into	ADP
ejpam-5917	22	31	total	total	ADJ
ejpam-5917	22	32	dominating	dominating	NOUN
ejpam-5917	22	33	sets	set	NOUN
ejpam-5917	22	34	)	)	PUNCT
ejpam-5917	23	1	[	[	X
ejpam-5917	23	2	2	2	NUM
ejpam-5917	23	3	]	]	PUNCT
ejpam-5917	23	4	.	.	PUNCT
ejpam-5917	24	1	in	in	ADP
ejpam-5917	24	2	recent	recent	ADJ
ejpam-5917	24	3	decades	decade	NOUN
ejpam-5917	24	4	,	,	PUNCT
ejpam-5917	24	5	a	a	DET
ejpam-5917	24	6	lot	lot	NOUN
ejpam-5917	24	7	of	of	ADP
ejpam-5917	24	8	variations	variation	NOUN
ejpam-5917	24	9	in	in	ADP
ejpam-5917	24	10	total	total	ADJ
ejpam-5917	24	11	domination	domination	NOUN
ejpam-5917	24	12	have	have	AUX
ejpam-5917	24	13	been	be	AUX
ejpam-5917	24	14	studied	study	VERB
ejpam-5917	24	15	.	.	PUNCT
ejpam-5917	25	1	some	some	PRON
ejpam-5917	25	2	of	of	ADP
ejpam-5917	25	3	the	the	DET
ejpam-5917	25	4	researches	research	NOUN
ejpam-5917	25	5	related	relate	VERB
ejpam-5917	25	6	to	to	ADP
ejpam-5917	25	7	this	this	DET
ejpam-5917	25	8	study	study	NOUN
ejpam-5917	25	9	are	be	AUX
ejpam-5917	25	10	given	give	VERB
ejpam-5917	25	11	as	as	SCONJ
ejpam-5917	25	12	follows	follow	VERB
ejpam-5917	25	13	:	:	PUNCT
ejpam-5917	25	14	in	in	ADP
ejpam-5917	25	15	2007	2007	NUM
ejpam-5917	25	16	,	,	PUNCT
ejpam-5917	25	17	lam	lam	PROPN
ejpam-5917	25	18	and	and	CCONJ
ejpam-5917	25	19	wei	wei	PROPN
ejpam-5917	25	20	published	publish	VERB
ejpam-5917	25	21	their	their	PRON
ejpam-5917	25	22	paper	paper	NOUN
ejpam-5917	25	23	entitled	entitle	VERB
ejpam-5917	25	24	“	"	PUNCT
ejpam-5917	25	25	on	on	ADP
ejpam-5917	25	26	the	the	DET
ejpam-5917	25	27	total	total	ADJ
ejpam-5917	25	28	domination	domination	NOUN
ejpam-5917	25	29	number	number	NOUN
ejpam-5917	25	30	of	of	ADP
ejpam-5917	25	31	graphs	graph	NOUN
ejpam-5917	25	32	”	"	PUNCT
ejpam-5917	25	33	,	,	PUNCT
ejpam-5917	25	34	where	where	SCONJ
ejpam-5917	25	35	they	they	PRON
ejpam-5917	25	36	developed	develop	VERB
ejpam-5917	25	37	theorems	theorem	NOUN
ejpam-5917	25	38	for	for	ADP
ejpam-5917	25	39	the	the	DET
ejpam-5917	25	40	bounds	bound	NOUN
ejpam-5917	25	41	of	of	ADP
ejpam-5917	25	42	the	the	DET
ejpam-5917	25	43	total	total	ADJ
ejpam-5917	25	44	domination	domination	NOUN
ejpam-5917	25	45	number	number	NOUN
ejpam-5917	25	46	of	of	ADP
ejpam-5917	25	47	connected	connected	ADJ
ejpam-5917	25	48	graphs	graph	NOUN
ejpam-5917	25	49	of	of	ADP
ejpam-5917	25	50	order	order	NOUN
ejpam-5917	25	51	at	at	ADV
ejpam-5917	25	52	least	least	ADJ
ejpam-5917	25	53	3	3	NUM
ejpam-5917	25	54	,	,	PUNCT
ejpam-5917	25	55	and	and	CCONJ
ejpam-5917	25	56	for	for	ADP
ejpam-5917	25	57	connected	connected	ADJ
ejpam-5917	25	58	graphs	graph	NOUN
ejpam-5917	25	59	with	with	ADP
ejpam-5917	25	60	degree	degree	NOUN
ejpam-5917	25	61	at	at	ADV
ejpam-5917	25	62	least	least	ADJ
ejpam-5917	25	63	2	2	NUM
ejpam-5917	25	64	[	[	X
ejpam-5917	25	65	3	3	NUM
ejpam-5917	25	66	]	]	PUNCT
ejpam-5917	25	67	.	.	PUNCT
ejpam-5917	26	1	in	in	ADP
ejpam-5917	26	2	2011	2011	NUM
ejpam-5917	26	3	,	,	PUNCT
ejpam-5917	26	4	go	go	VERB
ejpam-5917	26	5	and	and	CCONJ
ejpam-5917	26	6	canoy	canoy	NOUN
ejpam-5917	26	7	determined	determine	VERB
ejpam-5917	26	8	the	the	DET
ejpam-5917	26	9	domination	domination	NOUN
ejpam-5917	26	10	,	,	PUNCT
ejpam-5917	26	11	total	total	ADJ
ejpam-5917	26	12	domination	domination	NOUN
ejpam-5917	26	13	,	,	PUNCT
ejpam-5917	26	14	and	and	CCONJ
ejpam-5917	26	15	secure	secure	VERB
ejpam-5917	26	16	total	total	ADJ
ejpam-5917	26	17	domination	domination	NOUN
ejpam-5917	26	18	numbers	number	NOUN
ejpam-5917	26	19	in	in	ADP
ejpam-5917	26	20	the	the	DET
ejpam-5917	26	21	corona	corona	NOUN
ejpam-5917	26	22	and	and	CCONJ
ejpam-5917	26	23	join	join	VERB
ejpam-5917	26	24	of	of	ADP
ejpam-5917	26	25	graphs	graph	NOUN
ejpam-5917	26	26	[	[	X
ejpam-5917	26	27	4	4	NUM
ejpam-5917	26	28	]	]	PUNCT
ejpam-5917	26	29	.	.	PUNCT
ejpam-5917	27	1	the	the	DET
ejpam-5917	27	2	study	study	NOUN
ejpam-5917	27	3	was	be	AUX
ejpam-5917	27	4	continued	continue	VERB
ejpam-5917	27	5	by	by	ADP
ejpam-5917	27	6	eballe	eballe	NOUN
ejpam-5917	27	7	and	and	CCONJ
ejpam-5917	27	8	miranda	miranda	NOUN
ejpam-5917	27	9	in	in	ADP
ejpam-5917	27	10	2021	2021	NUM
ejpam-5917	27	11	,	,	PUNCT
ejpam-5917	27	12	where	where	SCONJ
ejpam-5917	27	13	they	they	PRON
ejpam-5917	27	14	presented	present	VERB
ejpam-5917	27	15	the	the	DET
ejpam-5917	27	16	domination	domination	NOUN
ejpam-5917	27	17	defect	defect	NOUN
ejpam-5917	27	18	for	for	ADP
ejpam-5917	27	19	the	the	DET
ejpam-5917	27	20	join	join	NOUN
ejpam-5917	27	21	and	and	CCONJ
ejpam-5917	27	22	corona	corona	NOUN
ejpam-5917	27	23	of	of	ADP
ejpam-5917	27	24	graphs	graph	NOUN
ejpam-5917	27	25	[	[	X
ejpam-5917	27	26	5	5	NUM
ejpam-5917	27	27	]	]	PUNCT
ejpam-5917	27	28	.	.	PUNCT
ejpam-5917	28	1	in	in	ADP
ejpam-5917	28	2	2021	2021	NUM
ejpam-5917	28	3	,	,	PUNCT
ejpam-5917	28	4	jose	jose	PROPN
ejpam-5917	28	5	sigarreta	sigarreta	NOUN
ejpam-5917	28	6	published	publish	VERB
ejpam-5917	28	7	his	his	PRON
ejpam-5917	28	8	study	study	NOUN
ejpam-5917	28	9	entitled	entitle	VERB
ejpam-5917	28	10	“	"	PUNCT
ejpam-5917	28	11	total	total	ADJ
ejpam-5917	28	12	domination	domination	NOUN
ejpam-5917	28	13	on	on	ADP
ejpam-5917	28	14	some	some	DET
ejpam-5917	28	15	graph	graph	NOUN
ejpam-5917	28	16	operators	operator	NOUN
ejpam-5917	28	17	”	"	PUNCT
ejpam-5917	28	18	.	.	PUNCT
ejpam-5917	29	1	in	in	ADP
ejpam-5917	29	2	his	his	PRON
ejpam-5917	29	3	paper	paper	NOUN
ejpam-5917	29	4	,	,	PUNCT
ejpam-5917	29	5	he	he	PRON
ejpam-5917	29	6	introduced	introduce	VERB
ejpam-5917	29	7	bounds	bound	NOUN
ejpam-5917	29	8	for	for	ADP
ejpam-5917	29	9	the	the	DET
ejpam-5917	29	10	exact	exact	ADJ
ejpam-5917	29	11	value	value	NOUN
ejpam-5917	29	12	of	of	ADP
ejpam-5917	29	13	the	the	DET
ejpam-5917	29	14	total	total	ADJ
ejpam-5917	29	15	domination	domination	NOUN
ejpam-5917	29	16	number	number	NOUN
ejpam-5917	29	17	of	of	ADP
ejpam-5917	29	18	some	some	DET
ejpam-5917	29	19	graph	graph	NOUN
ejpam-5917	29	20	operators	operator	NOUN
ejpam-5917	29	21	using	use	VERB
ejpam-5917	29	22	some	some	DET
ejpam-5917	29	23	parameters	parameter	NOUN
ejpam-5917	29	24	in	in	ADP
ejpam-5917	29	25	the	the	DET
ejpam-5917	29	26	original	original	ADJ
ejpam-5917	29	27	graph	graph	NOUN
ejpam-5917	29	28	[	[	X
ejpam-5917	29	29	6	6	NUM
ejpam-5917	29	30	]	]	PUNCT
ejpam-5917	29	31	.	.	PUNCT
ejpam-5917	30	1	the	the	DET
ejpam-5917	30	2	study	study	NOUN
ejpam-5917	30	3	published	publish	VERB
ejpam-5917	30	4	by	by	ADP
ejpam-5917	30	5	klostermeyer	klostermeyer	NOUN
ejpam-5917	30	6	in	in	ADP
ejpam-5917	30	7	2008	2008	NUM
ejpam-5917	30	8	with	with	ADP
ejpam-5917	30	9	the	the	DET
ejpam-5917	30	10	title	title	NOUN
ejpam-5917	30	11	“	"	PUNCT
ejpam-5917	30	12	secure	secure	ADJ
ejpam-5917	30	13	domination	domination	NOUN
ejpam-5917	30	14	and	and	CCONJ
ejpam-5917	30	15	secure	secure	VERB
ejpam-5917	30	16	total	total	ADJ
ejpam-5917	30	17	domination	domination	NOUN
ejpam-5917	30	18	in	in	ADP
ejpam-5917	30	19	graphs	graph	NOUN
ejpam-5917	30	20	”	"	PUNCT
ejpam-5917	30	21	has	have	VERB
ejpam-5917	30	22	a	a	DET
ejpam-5917	30	23	related	related	ADJ
ejpam-5917	30	24	title	title	NOUN
ejpam-5917	30	25	but	but	CCONJ
ejpam-5917	30	26	has	have	VERB
ejpam-5917	30	27	a	a	DET
ejpam-5917	30	28	totally	totally	ADV
ejpam-5917	30	29	different	different	ADJ
ejpam-5917	30	30	concept	concept	NOUN
ejpam-5917	30	31	.	.	PUNCT
ejpam-5917	31	1	the	the	DET
ejpam-5917	31	2	paper	paper	NOUN
ejpam-5917	31	3	states	state	VERB
ejpam-5917	31	4	that	that	SCONJ
ejpam-5917	31	5	a	a	DET
ejpam-5917	31	6	secure	secure	ADJ
ejpam-5917	31	7	(	(	PUNCT
ejpam-5917	31	8	total	total	ADJ
ejpam-5917	31	9	)	)	PUNCT
ejpam-5917	31	10	dominating	dominating	NOUN
ejpam-5917	31	11	set	set	NOUN
ejpam-5917	31	12	of	of	ADP
ejpam-5917	31	13	a	a	DET
ejpam-5917	31	14	graph	graph	NOUN
ejpam-5917	31	15	g	g	NOUN
ejpam-5917	31	16	=	=	PUNCT
ejpam-5917	31	17	(	(	PUNCT
ejpam-5917	31	18	v	v	NOUN
ejpam-5917	31	19	,	,	PUNCT
ejpam-5917	31	20	e	e	NOUN
ejpam-5917	31	21	)	)	PUNCT
ejpam-5917	31	22	is	be	AUX
ejpam-5917	31	23	as	as	ADP
ejpam-5917	31	24	a	a	DET
ejpam-5917	31	25	(	(	PUNCT
ejpam-5917	31	26	total	total	ADJ
ejpam-5917	31	27	)	)	PUNCT
ejpam-5917	31	28	dominating	dominating	NOUN
ejpam-5917	31	29	set	set	NOUN
ejpam-5917	31	30	x	x	PUNCT
ejpam-5917	31	31	⊆	⊆	NUM
ejpam-5917	31	32	v	v	NOUN
ejpam-5917	31	33	with	with	ADP
ejpam-5917	31	34	the	the	DET
ejpam-5917	31	35	property	property	NOUN
ejpam-5917	31	36	that	that	PRON
ejpam-5917	31	37	for	for	ADP
ejpam-5917	31	38	each	each	DET
ejpam-5917	31	39	u	u	NOUN
ejpam-5917	31	40	∈	∈	PROPN
ejpam-5917	31	41	v	v	ADP
ejpam-5917	31	42	−	−	NOUN
ejpam-5917	31	43	x	x	SYM
ejpam-5917	31	44	,	,	PUNCT
ejpam-5917	31	45	there	there	PRON
ejpam-5917	31	46	exists	exist	VERB
ejpam-5917	31	47	x	x	X
ejpam-5917	31	48	∈	∈	PROPN
ejpam-5917	31	49	x	x	SYM
ejpam-5917	31	50	adjacent	adjacent	ADJ
ejpam-5917	31	51	to	to	ADP
ejpam-5917	31	52	u	u	PRON
ejpam-5917	31	53	such	such	ADJ
ejpam-5917	31	54	that	that	SCONJ
ejpam-5917	31	55	(	(	PUNCT
ejpam-5917	31	56	x	x	X
ejpam-5917	31	57	−	−	PROPN
ejpam-5917	31	58	{	{	PUNCT
ejpam-5917	31	59	x	x	NOUN
ejpam-5917	31	60	}	}	PUNCT
ejpam-5917	31	61	)	)	PUNCT
ejpam-5917	31	62	∪	∪	ADP
ejpam-5917	31	63	{	{	PUNCT
ejpam-5917	31	64	u	u	NOUN
ejpam-5917	31	65	}	}	PUNCT
ejpam-5917	31	66	is	be	AUX
ejpam-5917	31	67	a	a	DET
ejpam-5917	31	68	(	(	PUNCT
ejpam-5917	31	69	total	total	ADJ
ejpam-5917	31	70	)	)	PUNCT
ejpam-5917	31	71	dominating	dominating	NOUN
ejpam-5917	31	72	set	set	NOUN
ejpam-5917	31	73	[	[	X
ejpam-5917	31	74	7	7	NUM
ejpam-5917	31	75	]	]	PUNCT
ejpam-5917	31	76	.	.	PUNCT
ejpam-5917	32	1	the	the	DET
ejpam-5917	32	2	study	study	NOUN
ejpam-5917	32	3	entitled	entitle	VERB
ejpam-5917	32	4	“	"	PUNCT
ejpam-5917	32	5	defensive	defensive	ADJ
ejpam-5917	32	6	alliances	alliance	NOUN
ejpam-5917	32	7	in	in	ADP
ejpam-5917	32	8	graphs	graph	NOUN
ejpam-5917	32	9	”	"	PUNCT
ejpam-5917	32	10	by	by	ADP
ejpam-5917	32	11	gaikwad	gaikwad	NOUN
ejpam-5917	32	12	and	and	CCONJ
ejpam-5917	32	13	maity	maity	NOUN
ejpam-5917	32	14	which	which	PRON
ejpam-5917	32	15	was	be	AUX
ejpam-5917	32	16	published	publish	VERB
ejpam-5917	32	17	in	in	ADP
ejpam-5917	32	18	2022	2022	NUM
ejpam-5917	32	19	also	also	ADV
ejpam-5917	32	20	seems	seem	VERB
ejpam-5917	32	21	similar	similar	ADJ
ejpam-5917	32	22	to	to	ADP
ejpam-5917	32	23	this	this	DET
ejpam-5917	32	24	study	study	NOUN
ejpam-5917	32	25	but	but	CCONJ
ejpam-5917	32	26	the	the	DET
ejpam-5917	32	27	concept	concept	NOUN
ejpam-5917	32	28	is	be	AUX
ejpam-5917	32	29	also	also	ADV
ejpam-5917	32	30	different	different	ADJ
ejpam-5917	32	31	.	.	PUNCT
ejpam-5917	33	1	as	as	SCONJ
ejpam-5917	33	2	defined	define	VERB
ejpam-5917	33	3	,	,	PUNCT
ejpam-5917	33	4	a	a	DET
ejpam-5917	33	5	set	set	NOUN
ejpam-5917	33	6	s	s	NOUN
ejpam-5917	33	7	of	of	ADP
ejpam-5917	33	8	vertices	vertex	NOUN
ejpam-5917	33	9	of	of	ADP
ejpam-5917	33	10	a	a	DET
ejpam-5917	33	11	graph	graph	NOUN
ejpam-5917	33	12	is	be	AUX
ejpam-5917	33	13	a	a	DET
ejpam-5917	33	14	defensive	defensive	ADJ
ejpam-5917	33	15	alliance	alliance	NOUN
ejpam-5917	33	16	if	if	SCONJ
ejpam-5917	33	17	,	,	PUNCT
ejpam-5917	33	18	for	for	ADP
ejpam-5917	33	19	each	each	DET
ejpam-5917	33	20	element	element	NOUN
ejpam-5917	33	21	of	of	ADP
ejpam-5917	33	22	s	s	PROPN
ejpam-5917	33	23	,	,	PUNCT
ejpam-5917	33	24	the	the	DET
ejpam-5917	33	25	majority	majority	NOUN
ejpam-5917	33	26	of	of	ADP
ejpam-5917	33	27	its	its	PRON
ejpam-5917	33	28	neighbours	neighbour	NOUN
ejpam-5917	33	29	are	be	AUX
ejpam-5917	33	30	in	in	ADP
ejpam-5917	33	31	s	s	PRON
ejpam-5917	33	32	[	[	X
ejpam-5917	33	33	8	8	NUM
ejpam-5917	33	34	]	]	PUNCT
ejpam-5917	33	35	.	.	PUNCT
ejpam-5917	34	1	in	in	ADP
ejpam-5917	34	2	2024	2024	NUM
ejpam-5917	34	3	,	,	PUNCT
ejpam-5917	34	4	chatterjee	chatterjee	NOUN
ejpam-5917	34	5	,	,	PUNCT
ejpam-5917	34	6	jent	jent	NOUN
ejpam-5917	34	7	,	,	PUNCT
ejpam-5917	34	8	osborn	osborn	PROPN
ejpam-5917	34	9	and	and	CCONJ
ejpam-5917	34	10	zhang	zhang	PROPN
ejpam-5917	34	11	published	publish	VERB
ejpam-5917	34	12	their	their	PRON
ejpam-5917	34	13	paper	paper	NOUN
ejpam-5917	34	14	“	"	PUNCT
ejpam-5917	34	15	proper	proper	ADJ
ejpam-5917	34	16	total	total	ADJ
ejpam-5917	34	17	domination	domination	NOUN
ejpam-5917	34	18	in	in	ADP
ejpam-5917	34	19	graphs	graph	NOUN
ejpam-5917	34	20	”	"	PUNCT
ejpam-5917	34	21	.	.	PUNCT
ejpam-5917	35	1	the	the	DET
ejpam-5917	35	2	paper	paper	NOUN
ejpam-5917	35	3	states	state	VERB
ejpam-5917	35	4	that	that	SCONJ
ejpam-5917	35	5	a	a	DET
ejpam-5917	35	6	total	total	ADJ
ejpam-5917	35	7	dominating	dominating	NOUN
ejpam-5917	35	8	set	set	NOUN
ejpam-5917	35	9	s	s	VERB
ejpam-5917	35	10	in	in	ADP
ejpam-5917	35	11	a	a	DET
ejpam-5917	35	12	graph	graph	NOUN
ejpam-5917	35	13	g	g	NOUN
ejpam-5917	35	14	is	be	AUX
ejpam-5917	35	15	called	call	VERB
ejpam-5917	35	16	a	a	DET
ejpam-5917	35	17	proper	proper	ADJ
ejpam-5917	35	18	total	total	ADJ
ejpam-5917	35	19	dominating	dominating	NOUN
ejpam-5917	35	20	set	set	NOUN
ejpam-5917	35	21	if	if	SCONJ
ejpam-5917	35	22	σs(u	σs(u	VERB
ejpam-5917	35	23	)	)	PUNCT
ejpam-5917	35	24	̸=	̸=	PROPN
ejpam-5917	35	25	σs(v	σs(v	NOUN
ejpam-5917	35	26	)	)	PUNCT
ejpam-5917	35	27	for	for	ADP
ejpam-5917	35	28	every	every	DET
ejpam-5917	35	29	two	two	NUM
ejpam-5917	35	30	adjacent	adjacent	ADJ
ejpam-5917	35	31	vertices	vertex	NOUN
ejpam-5917	35	32	u	u	NOUN
ejpam-5917	35	33	and	and	CCONJ
ejpam-5917	35	34	v	v	NOUN
ejpam-5917	35	35	of	of	ADP
ejpam-5917	35	36	g	g	NOUN
ejpam-5917	35	37	[	[	X
ejpam-5917	35	38	9	9	NUM
ejpam-5917	35	39	]	]	PUNCT
ejpam-5917	35	40	.	.	PUNCT
ejpam-5917	36	1	from	from	ADP
ejpam-5917	36	2	available	available	ADJ
ejpam-5917	36	3	resources	resource	NOUN
ejpam-5917	36	4	and	and	CCONJ
ejpam-5917	36	5	online	online	ADJ
ejpam-5917	36	6	publications	publication	NOUN
ejpam-5917	36	7	,	,	PUNCT
ejpam-5917	36	8	the	the	DET
ejpam-5917	36	9	authors	author	NOUN
ejpam-5917	36	10	found	find	VERB
ejpam-5917	36	11	none	none	NOUN
ejpam-5917	36	12	that	that	PRON
ejpam-5917	36	13	is	be	AUX
ejpam-5917	36	14	of	of	ADP
ejpam-5917	36	15	exact	exact	ADJ
ejpam-5917	36	16	same	same	ADJ
ejpam-5917	36	17	concept	concept	NOUN
ejpam-5917	36	18	as	as	ADP
ejpam-5917	36	19	this	this	DET
ejpam-5917	36	20	study	study	NOUN
ejpam-5917	36	21	.	.	PUNCT
ejpam-5917	37	1	in	in	ADP
ejpam-5917	37	2	particular	particular	ADJ
ejpam-5917	37	3	,	,	PUNCT
ejpam-5917	37	4	there	there	PRON
ejpam-5917	37	5	is	be	VERB
ejpam-5917	37	6	no	no	DET
ejpam-5917	37	7	published	publish	VERB
ejpam-5917	37	8	study	study	NOUN
ejpam-5917	37	9	about	about	ADP
ejpam-5917	37	10	total	total	ADJ
ejpam-5917	37	11	domination	domination	NOUN
ejpam-5917	37	12	which	which	PRON
ejpam-5917	37	13	incorporates	incorporate	VERB
ejpam-5917	37	14	the	the	DET
ejpam-5917	37	15	concept	concept	NOUN
ejpam-5917	37	16	of	of	ADP
ejpam-5917	37	17	safe	safe	ADJ
ejpam-5917	37	18	set	set	NOUN
ejpam-5917	37	19	or	or	CCONJ
ejpam-5917	37	20	safe	safe	ADJ
ejpam-5917	37	21	domination	domination	NOUN
ejpam-5917	37	22	.	.	PUNCT
ejpam-5917	38	1	the	the	DET
ejpam-5917	38	2	idea	idea	NOUN
ejpam-5917	38	3	of	of	ADP
ejpam-5917	38	4	a	a	DET
ejpam-5917	38	5	safe	safe	ADJ
ejpam-5917	38	6	set	set	NOUN
ejpam-5917	38	7	in	in	ADP
ejpam-5917	38	8	graphs	graph	NOUN
ejpam-5917	38	9	was	be	AUX
ejpam-5917	38	10	introduced	introduce	VERB
ejpam-5917	38	11	by	by	ADP
ejpam-5917	38	12	fujita	fujita	PROPN
ejpam-5917	38	13	,	,	PUNCT
ejpam-5917	38	14	macgillivray	macgillivray	NOUN
ejpam-5917	38	15	and	and	CCONJ
ejpam-5917	38	16	sakuma	sakuma	NOUN
ejpam-5917	38	17	in	in	ADP
ejpam-5917	38	18	2016	2016	NUM
ejpam-5917	39	1	[	[	X
ejpam-5917	39	2	10	10	NUM
ejpam-5917	39	3	]	]	PUNCT
ejpam-5917	39	4	.	.	PUNCT
ejpam-5917	40	1	their	their	PRON
ejpam-5917	40	2	work	work	NOUN
ejpam-5917	40	3	was	be	AUX
ejpam-5917	40	4	motivated	motivate	VERB
ejpam-5917	40	5	by	by	ADP
ejpam-5917	40	6	applications	application	NOUN
ejpam-5917	40	7	related	relate	VERB
ejpam-5917	40	8	to	to	ADP
ejpam-5917	40	9	facility	facility	NOUN
ejpam-5917	40	10	location	location	NOUN
ejpam-5917	40	11	problems	problem	NOUN
ejpam-5917	40	12	,	,	PUNCT
ejpam-5917	40	13	where	where	SCONJ
ejpam-5917	40	14	the	the	DET
ejpam-5917	40	15	goal	goal	NOUN
ejpam-5917	40	16	is	be	AUX
ejpam-5917	40	17	to	to	PART
ejpam-5917	40	18	find	find	VERB
ejpam-5917	40	19	a	a	DET
ejpam-5917	40	20	“	"	PUNCT
ejpam-5917	40	21	safe	safe	ADJ
ejpam-5917	40	22	”	"	PUNCT
ejpam-5917	40	23	subset	subset	NOUN
ejpam-5917	40	24	of	of	ADP
ejpam-5917	40	25	nodes	node	NOUN
ejpam-5917	40	26	for	for	ADP
ejpam-5917	40	27	placing	place	VERB
ejpam-5917	40	28	facilities	facility	NOUN
ejpam-5917	40	29	in	in	ADP
ejpam-5917	40	30	a	a	DET
ejpam-5917	40	31	network	network	NOUN
ejpam-5917	40	32	.	.	PUNCT
ejpam-5917	41	1	the	the	DET
ejpam-5917	41	2	paper	paper	NOUN
ejpam-5917	41	3	states	state	VERB
ejpam-5917	41	4	that	that	SCONJ
ejpam-5917	41	5	a	a	DET
ejpam-5917	41	6	safe	safe	ADJ
ejpam-5917	41	7	set	set	NOUN
ejpam-5917	41	8	is	be	AUX
ejpam-5917	41	9	a	a	DET
ejpam-5917	41	10	set	set	NOUN
ejpam-5917	41	11	in	in	ADP
ejpam-5917	41	12	which	which	PRON
ejpam-5917	41	13	every	every	DET
ejpam-5917	41	14	component	component	NOUN
ejpam-5917	41	15	of	of	ADP
ejpam-5917	41	16	the	the	DET
ejpam-5917	41	17	set	set	NOUN
ejpam-5917	41	18	has	have	VERB
ejpam-5917	41	19	order	order	NOUN
ejpam-5917	41	20	at	at	ADV
ejpam-5917	41	21	least	least	ADJ
ejpam-5917	41	22	as	as	ADV
ejpam-5917	41	23	large	large	ADJ
ejpam-5917	41	24	as	as	ADP
ejpam-5917	41	25	the	the	DET
ejpam-5917	41	26	order	order	NOUN
ejpam-5917	41	27	of	of	ADP
ejpam-5917	41	28	any	any	DET
ejpam-5917	41	29	adjacent	adjacent	ADJ
ejpam-5917	41	30	component	component	NOUN
ejpam-5917	41	31	of	of	ADP
ejpam-5917	41	32	the	the	DET
ejpam-5917	41	33	complement	complement	NOUN
ejpam-5917	41	34	set	set	NOUN
ejpam-5917	41	35	.	.	PUNCT
ejpam-5917	42	1	the	the	DET
ejpam-5917	42	2	concept	concept	NOUN
ejpam-5917	42	3	of	of	ADP
ejpam-5917	42	4	safe	safe	ADJ
ejpam-5917	42	5	domination	domination	NOUN
ejpam-5917	42	6	in	in	ADP
ejpam-5917	42	7	graphs	graph	NOUN
ejpam-5917	42	8	was	be	AUX
ejpam-5917	42	9	introduced	introduce	VERB
ejpam-5917	42	10	by	by	ADP
ejpam-5917	42	11	griño	griño	PROPN
ejpam-5917	42	12	,	,	PUNCT
ejpam-5917	42	13	maceren	maceren	NOUN
ejpam-5917	42	14	,	,	PUNCT
ejpam-5917	42	15	and	and	CCONJ
ejpam-5917	42	16	cabahug	cabahug	ADJ
ejpam-5917	42	17	in	in	ADP
ejpam-5917	42	18	2023	2023	NUM
ejpam-5917	42	19	[	[	X
ejpam-5917	42	20	11	11	NUM
ejpam-5917	42	21	]	]	PUNCT
ejpam-5917	42	22	.	.	PUNCT
ejpam-5917	43	1	in	in	ADP
ejpam-5917	43	2	their	their	PRON
ejpam-5917	43	3	paper	paper	NOUN
ejpam-5917	43	4	,	,	PUNCT
ejpam-5917	43	5	they	they	PRON
ejpam-5917	43	6	defined	define	VERB
ejpam-5917	43	7	a	a	DET
ejpam-5917	43	8	safe	safe	ADJ
ejpam-5917	43	9	dominating	dominating	NOUN
ejpam-5917	43	10	set	set	NOUN
ejpam-5917	43	11	as	as	ADP
ejpam-5917	43	12	a	a	DET
ejpam-5917	43	13	set	set	NOUN
ejpam-5917	43	14	that	that	PRON
ejpam-5917	43	15	is	be	AUX
ejpam-5917	43	16	both	both	PRON
ejpam-5917	43	17	dominating	dominate	VERB
ejpam-5917	43	18	and	and	CCONJ
ejpam-5917	43	19	safe	safe	ADJ
ejpam-5917	43	20	.	.	PUNCT
ejpam-5917	44	1	w.	w.	PROPN
ejpam-5917	44	2	g.	g.	PROPN
ejpam-5917	44	3	jumalon	jumalon	PROPN
ejpam-5917	44	4	,	,	PUNCT
ejpam-5917	44	5	i.	i.	PROPN
ejpam-5917	44	6	cabahug	cabahug	PROPN
ejpam-5917	44	7	/	/	SYM
ejpam-5917	44	8	eur	eur	PROPN
ejpam-5917	44	9	.	.	PUNCT
ejpam-5917	45	1	j.	j.	PROPN
ejpam-5917	45	2	pure	pure	PROPN
ejpam-5917	45	3	appl	appl	PROPN
ejpam-5917	45	4	.	.	PROPN
ejpam-5917	45	5	math	math	PROPN
ejpam-5917	45	6	,	,	PUNCT
ejpam-5917	45	7	18	18	NUM
ejpam-5917	45	8	(	(	PUNCT
ejpam-5917	45	9	2	2	NUM
ejpam-5917	45	10	)	)	PUNCT
ejpam-5917	45	11	(	(	PUNCT
ejpam-5917	45	12	2025	2025	NUM
ejpam-5917	45	13	)	)	PUNCT
ejpam-5917	45	14	,	,	PUNCT
ejpam-5917	45	15	5917	5917	NUM
ejpam-5917	45	16	3	3	NUM
ejpam-5917	45	17	of	of	ADP
ejpam-5917	45	18	12	12	NUM
ejpam-5917	45	19	this	this	DET
ejpam-5917	45	20	study	study	NOUN
ejpam-5917	45	21	introduces	introduce	VERB
ejpam-5917	45	22	the	the	DET
ejpam-5917	45	23	concept	concept	NOUN
ejpam-5917	45	24	of	of	ADP
ejpam-5917	45	25	total	total	ADJ
ejpam-5917	45	26	safe	safe	ADJ
ejpam-5917	45	27	dominating	dominating	NOUN
ejpam-5917	45	28	set	set	VERB
ejpam-5917	45	29	in	in	ADP
ejpam-5917	45	30	a	a	DET
ejpam-5917	45	31	graph	graph	NOUN
ejpam-5917	45	32	.	.	PUNCT
ejpam-5917	46	1	this	this	PRON
ejpam-5917	46	2	guarantees	guarantee	VERB
ejpam-5917	46	3	total	total	ADJ
ejpam-5917	46	4	coverage	coverage	NOUN
ejpam-5917	46	5	and	and	CCONJ
ejpam-5917	46	6	structural	structural	ADJ
ejpam-5917	46	7	resilience	resilience	NOUN
ejpam-5917	46	8	.	.	PUNCT
ejpam-5917	47	1	the	the	DET
ejpam-5917	47	2	concept	concept	NOUN
ejpam-5917	47	3	may	may	AUX
ejpam-5917	47	4	have	have	VERB
ejpam-5917	47	5	unique	unique	ADJ
ejpam-5917	47	6	potential	potential	ADJ
ejpam-5917	47	7	applications	application	NOUN
ejpam-5917	47	8	in	in	ADP
ejpam-5917	47	9	areas	area	NOUN
ejpam-5917	47	10	such	such	ADJ
ejpam-5917	47	11	as	as	ADP
ejpam-5917	47	12	network	network	NOUN
ejpam-5917	47	13	coverage	coverage	NOUN
ejpam-5917	47	14	,	,	PUNCT
ejpam-5917	47	15	facility	facility	NOUN
ejpam-5917	47	16	location	location	NOUN
ejpam-5917	47	17	and	and	CCONJ
ejpam-5917	47	18	defense	defense	NOUN
ejpam-5917	47	19	infrastructure	infrastructure	NOUN
ejpam-5917	47	20	.	.	PUNCT
ejpam-5917	48	1	this	this	DET
ejpam-5917	48	2	study	study	NOUN
ejpam-5917	48	3	is	be	AUX
ejpam-5917	48	4	limited	limit	VERB
ejpam-5917	48	5	to	to	ADP
ejpam-5917	48	6	undirected	undirected	ADJ
ejpam-5917	48	7	graphs	graph	NOUN
ejpam-5917	48	8	that	that	PRON
ejpam-5917	48	9	are	be	AUX
ejpam-5917	48	10	nontrivial	nontrivial	ADJ
ejpam-5917	48	11	,	,	PUNCT
ejpam-5917	48	12	connected	connected	ADJ
ejpam-5917	48	13	and	and	CCONJ
ejpam-5917	48	14	simple	simple	ADJ
ejpam-5917	48	15	.	.	PUNCT
ejpam-5917	49	1	2	2	X
ejpam-5917	49	2	.	.	X
ejpam-5917	49	3	terminology	terminology	NOUN
ejpam-5917	49	4	and	and	CCONJ
ejpam-5917	49	5	notation	notation	NOUN
ejpam-5917	49	6	a	a	DET
ejpam-5917	49	7	graph	graph	NOUN
ejpam-5917	49	8	g	g	NOUN
ejpam-5917	49	9	=	=	PUNCT
ejpam-5917	49	10	(	(	PUNCT
ejpam-5917	49	11	v	v	NOUN
ejpam-5917	49	12	(	(	PUNCT
ejpam-5917	49	13	g	g	NOUN
ejpam-5917	49	14	)	)	PUNCT
ejpam-5917	49	15	,	,	PUNCT
ejpam-5917	49	16	e(g	e(g	PROPN
ejpam-5917	49	17	)	)	PUNCT
ejpam-5917	49	18	)	)	PUNCT
ejpam-5917	49	19	is	be	AUX
ejpam-5917	49	20	a	a	DET
ejpam-5917	49	21	finite	finite	NOUN
ejpam-5917	49	22	nonempty	nonempty	ADV
ejpam-5917	49	23	set	set	VERB
ejpam-5917	49	24	v	v	NOUN
ejpam-5917	49	25	(	(	PUNCT
ejpam-5917	49	26	g	g	NOUN
ejpam-5917	49	27	)	)	PUNCT
ejpam-5917	49	28	of	of	ADP
ejpam-5917	49	29	objects	object	NOUN
ejpam-5917	49	30	called	call	VERB
ejpam-5917	49	31	vertices	vertex	NOUN
ejpam-5917	49	32	together	together	ADV
ejpam-5917	49	33	with	with	ADP
ejpam-5917	49	34	a	a	DET
ejpam-5917	49	35	possibly	possibly	ADV
ejpam-5917	49	36	empty	empty	ADJ
ejpam-5917	49	37	set	set	VERB
ejpam-5917	49	38	e(g	e(g	NOUN
ejpam-5917	49	39	)	)	PUNCT
ejpam-5917	49	40	of	of	ADP
ejpam-5917	49	41	2	2	NUM
ejpam-5917	49	42	-	-	PUNCT
ejpam-5917	49	43	element	element	NOUN
ejpam-5917	49	44	subsets	subset	NOUN
ejpam-5917	49	45	of	of	ADP
ejpam-5917	49	46	v	v	NOUN
ejpam-5917	49	47	(	(	PUNCT
ejpam-5917	49	48	g	g	NOUN
ejpam-5917	49	49	)	)	PUNCT
ejpam-5917	49	50	called	call	VERB
ejpam-5917	49	51	edges	edge	NOUN
ejpam-5917	49	52	.	.	PUNCT
ejpam-5917	50	1	a	a	DET
ejpam-5917	50	2	graphh	graphh	NOUN
ejpam-5917	50	3	is	be	AUX
ejpam-5917	50	4	a	a	DET
ejpam-5917	50	5	subgraph	subgraph	NOUN
ejpam-5917	50	6	of	of	ADP
ejpam-5917	50	7	a	a	DET
ejpam-5917	50	8	graph	graph	NOUN
ejpam-5917	50	9	g	g	NOUN
ejpam-5917	50	10	if	if	SCONJ
ejpam-5917	50	11	v	v	X
ejpam-5917	50	12	(	(	PUNCT
ejpam-5917	50	13	h	h	NOUN
ejpam-5917	50	14	)	)	PUNCT
ejpam-5917	50	15	⊆	⊆	NUM
ejpam-5917	50	16	v	v	NOUN
ejpam-5917	50	17	(	(	PUNCT
ejpam-5917	50	18	g	g	NOUN
ejpam-5917	50	19	)	)	PUNCT
ejpam-5917	50	20	and	and	CCONJ
ejpam-5917	50	21	e(h	e(h	NOUN
ejpam-5917	50	22	)	)	PUNCT
ejpam-5917	50	23	⊆	⊆	NUM
ejpam-5917	50	24	e(g	e(g	PROPN
ejpam-5917	50	25	)	)	PUNCT
ejpam-5917	50	26	.	.	PUNCT
ejpam-5917	51	1	ifh	ifh	ADJ
ejpam-5917	51	2	is	be	AUX
ejpam-5917	51	3	a	a	DET
ejpam-5917	51	4	subgraph	subgraph	NOUN
ejpam-5917	51	5	of	of	ADP
ejpam-5917	51	6	a	a	DET
ejpam-5917	51	7	graph	graph	NOUN
ejpam-5917	51	8	g	g	NOUN
ejpam-5917	51	9	where	where	SCONJ
ejpam-5917	51	10	h	h	NOUN
ejpam-5917	51	11	≇	≇	PROPN
ejpam-5917	51	12	g	g	PROPN
ejpam-5917	51	13	,	,	PUNCT
ejpam-5917	51	14	then	then	ADV
ejpam-5917	51	15	h	h	NOUN
ejpam-5917	51	16	is	be	AUX
ejpam-5917	51	17	a	a	DET
ejpam-5917	51	18	proper	proper	ADJ
ejpam-5917	51	19	subgraph	subgraph	NOUN
ejpam-5917	51	20	of	of	ADP
ejpam-5917	51	21	g.	g.	PROPN
ejpam-5917	51	22	if	if	SCONJ
ejpam-5917	51	23	s	s	X
ejpam-5917	51	24	is	be	AUX
ejpam-5917	51	25	a	a	DET
ejpam-5917	51	26	nonempty	nonempty	ADJ
ejpam-5917	51	27	subset	subset	NOUN
ejpam-5917	51	28	of	of	ADP
ejpam-5917	51	29	v	v	NOUN
ejpam-5917	51	30	(	(	PUNCT
ejpam-5917	51	31	g	g	NOUN
ejpam-5917	51	32	)	)	PUNCT
ejpam-5917	51	33	,	,	PUNCT
ejpam-5917	51	34	then	then	ADV
ejpam-5917	51	35	the	the	DET
ejpam-5917	51	36	induced	induced	ADJ
ejpam-5917	51	37	subgraph	subgraph	NOUN
ejpam-5917	51	38	g[s	g[s	PROPN
ejpam-5917	51	39	]	]	PUNCT
ejpam-5917	51	40	of	of	ADP
ejpam-5917	51	41	s	s	PRON
ejpam-5917	51	42	in	in	ADP
ejpam-5917	51	43	g	g	NOUN
ejpam-5917	51	44	,	,	PUNCT
ejpam-5917	51	45	is	be	AUX
ejpam-5917	51	46	the	the	DET
ejpam-5917	51	47	graph	graph	NOUN
ejpam-5917	51	48	whose	whose	DET
ejpam-5917	51	49	vertex	vertex	NOUN
ejpam-5917	51	50	set	set	NOUN
ejpam-5917	51	51	is	be	AUX
ejpam-5917	51	52	s	s	PRON
ejpam-5917	51	53	and	and	CCONJ
ejpam-5917	51	54	whose	whose	DET
ejpam-5917	51	55	edge	edge	NOUN
ejpam-5917	51	56	set	set	VERB
ejpam-5917	51	57	consists	consist	VERB
ejpam-5917	51	58	of	of	ADP
ejpam-5917	51	59	all	all	PRON
ejpam-5917	51	60	of	of	ADP
ejpam-5917	51	61	the	the	DET
ejpam-5917	51	62	edges	edge	NOUN
ejpam-5917	51	63	in	in	ADP
ejpam-5917	51	64	v	v	NOUN
ejpam-5917	51	65	(	(	PUNCT
ejpam-5917	51	66	e	e	NOUN
ejpam-5917	51	67	)	)	PUNCT
ejpam-5917	51	68	that	that	PRON
ejpam-5917	51	69	have	have	VERB
ejpam-5917	51	70	both	both	DET
ejpam-5917	51	71	endpoints	endpoint	NOUN
ejpam-5917	51	72	in	in	ADP
ejpam-5917	51	73	s	s	PRON
ejpam-5917	51	74	[	[	X
ejpam-5917	51	75	12	12	NUM
ejpam-5917	51	76	]	]	PUNCT
ejpam-5917	51	77	.	.	PUNCT
ejpam-5917	52	1	a	a	DET
ejpam-5917	52	2	component	component	NOUN
ejpam-5917	52	3	of	of	ADP
ejpam-5917	52	4	a	a	DET
ejpam-5917	52	5	graph	graph	NOUN
ejpam-5917	52	6	g	g	NOUN
ejpam-5917	52	7	is	be	AUX
ejpam-5917	52	8	defined	define	VERB
ejpam-5917	52	9	as	as	ADP
ejpam-5917	52	10	a	a	DET
ejpam-5917	52	11	maximal	maximal	ADJ
ejpam-5917	52	12	subgraph	subgraph	NOUN
ejpam-5917	52	13	in	in	ADP
ejpam-5917	52	14	which	which	PRON
ejpam-5917	52	15	every	every	DET
ejpam-5917	52	16	pair	pair	NOUN
ejpam-5917	52	17	of	of	ADP
ejpam-5917	52	18	vertices	vertex	NOUN
ejpam-5917	52	19	is	be	AUX
ejpam-5917	52	20	connected	connect	VERB
ejpam-5917	52	21	by	by	ADP
ejpam-5917	52	22	a	a	DET
ejpam-5917	52	23	path	path	NOUN
ejpam-5917	52	24	.	.	PUNCT
ejpam-5917	53	1	the	the	DET
ejpam-5917	53	2	connected	connected	ADJ
ejpam-5917	53	3	graph	graph	NOUN
ejpam-5917	53	4	and	and	CCONJ
ejpam-5917	53	5	the	the	DET
ejpam-5917	53	6	trivial	trivial	ADJ
ejpam-5917	53	7	graph	graph	NOUN
ejpam-5917	53	8	both	both	PRON
ejpam-5917	53	9	have	have	VERB
ejpam-5917	53	10	one	one	NUM
ejpam-5917	53	11	component	component	NOUN
ejpam-5917	53	12	.	.	PUNCT
ejpam-5917	54	1	a	a	DET
ejpam-5917	54	2	subgraph	subgraph	NOUN
ejpam-5917	54	3	induced	induce	VERB
ejpam-5917	54	4	by	by	ADP
ejpam-5917	54	5	a	a	DET
ejpam-5917	54	6	subset	subset	NOUN
ejpam-5917	54	7	of	of	ADP
ejpam-5917	54	8	v	v	NOUN
ejpam-5917	54	9	(	(	PUNCT
ejpam-5917	54	10	g	g	NOUN
ejpam-5917	54	11	)	)	PUNCT
ejpam-5917	54	12	may	may	AUX
ejpam-5917	54	13	have	have	VERB
ejpam-5917	54	14	more	more	ADJ
ejpam-5917	54	15	than	than	ADP
ejpam-5917	54	16	one	one	NUM
ejpam-5917	54	17	component	component	NOUN
ejpam-5917	54	18	.	.	PUNCT
ejpam-5917	55	1	a	a	DET
ejpam-5917	55	2	component	component	NOUN
ejpam-5917	55	3	a	a	PRON
ejpam-5917	55	4	of	of	ADP
ejpam-5917	55	5	the	the	DET
ejpam-5917	55	6	induced	induced	ADJ
ejpam-5917	55	7	subgraph	subgraph	NOUN
ejpam-5917	55	8	g[s	g[s	PROPN
ejpam-5917	55	9	]	]	PUNCT
ejpam-5917	55	10	is	be	AUX
ejpam-5917	55	11	said	say	VERB
ejpam-5917	55	12	to	to	PART
ejpam-5917	55	13	be	be	AUX
ejpam-5917	55	14	adjacent	adjacent	ADJ
ejpam-5917	55	15	to	to	ADP
ejpam-5917	55	16	a	a	DET
ejpam-5917	55	17	component	component	NOUN
ejpam-5917	55	18	b	b	NOUN
ejpam-5917	55	19	of	of	ADP
ejpam-5917	55	20	the	the	DET
ejpam-5917	55	21	induced	induced	ADJ
ejpam-5917	55	22	subgraph	subgraph	NOUN
ejpam-5917	55	23	g[v	g[v	PROPN
ejpam-5917	55	24	(	(	PUNCT
ejpam-5917	55	25	g)∖s	g)∖	NOUN
ejpam-5917	55	26	]	]	PUNCT
ejpam-5917	55	27	,	,	PUNCT
ejpam-5917	55	28	if	if	SCONJ
ejpam-5917	55	29	there	there	PRON
ejpam-5917	55	30	is	be	VERB
ejpam-5917	55	31	at	at	ADV
ejpam-5917	55	32	least	least	ADJ
ejpam-5917	55	33	one	one	NUM
ejpam-5917	55	34	edge	edge	NOUN
ejpam-5917	55	35	joining	join	VERB
ejpam-5917	55	36	a	a	DET
ejpam-5917	55	37	vertex	vertex	NOUN
ejpam-5917	55	38	u	u	NOUN
ejpam-5917	55	39	∈	∈	PROPN
ejpam-5917	55	40	v	v	ADP
ejpam-5917	55	41	(	(	PUNCT
ejpam-5917	55	42	a	a	NOUN
ejpam-5917	55	43	)	)	PUNCT
ejpam-5917	55	44	to	to	ADP
ejpam-5917	55	45	a	a	DET
ejpam-5917	55	46	vertex	vertex	NOUN
ejpam-5917	55	47	v	v	ADP
ejpam-5917	55	48	∈	∈	PROPN
ejpam-5917	55	49	v	v	ADP
ejpam-5917	55	50	(	(	PUNCT
ejpam-5917	55	51	b	b	NOUN
ejpam-5917	55	52	)	)	PUNCT
ejpam-5917	56	1	[	[	X
ejpam-5917	56	2	12	12	NUM
ejpam-5917	56	3	]	]	PUNCT
ejpam-5917	56	4	.	.	PUNCT
ejpam-5917	57	1	for	for	ADP
ejpam-5917	57	2	an	an	DET
ejpam-5917	57	3	integer	integer	NOUN
ejpam-5917	57	4	n	n	PRON
ejpam-5917	57	5	≥	≥	NOUN
ejpam-5917	57	6	1	1	NUM
ejpam-5917	57	7	,	,	PUNCT
ejpam-5917	57	8	the	the	DET
ejpam-5917	57	9	path	path	NOUN
ejpam-5917	57	10	pn	pn	PROPN
ejpam-5917	57	11	is	be	AUX
ejpam-5917	57	12	a	a	DET
ejpam-5917	57	13	graph	graph	NOUN
ejpam-5917	57	14	of	of	ADP
ejpam-5917	57	15	order	order	NOUN
ejpam-5917	57	16	n	n	NOUN
ejpam-5917	57	17	and	and	CCONJ
ejpam-5917	57	18	size	size	NOUN
ejpam-5917	57	19	n−	n−	PROPN
ejpam-5917	57	20	1	1	NUM
ejpam-5917	57	21	whose	whose	DET
ejpam-5917	57	22	vertices	vertex	NOUN
ejpam-5917	57	23	can	can	AUX
ejpam-5917	57	24	be	be	AUX
ejpam-5917	57	25	labeled	label	VERB
ejpam-5917	57	26	by	by	ADP
ejpam-5917	57	27	v1	v1	NOUN
ejpam-5917	57	28	,	,	PUNCT
ejpam-5917	57	29	v2	v2	PROPN
ejpam-5917	57	30	,	,	PUNCT
ejpam-5917	57	31	.	.	PUNCT
ejpam-5917	57	32	.	.	PUNCT
ejpam-5917	58	1	.	.	PUNCT
ejpam-5917	59	1	,	,	PUNCT
ejpam-5917	59	2	vn	vn	PROPN
ejpam-5917	59	3	and	and	CCONJ
ejpam-5917	59	4	whose	whose	DET
ejpam-5917	59	5	edges	edge	NOUN
ejpam-5917	59	6	are	be	AUX
ejpam-5917	59	7	vivi+1	vivi+1	ADJ
ejpam-5917	59	8	for	for	ADP
ejpam-5917	59	9	i	i	PRON
ejpam-5917	59	10	=	=	NOUN
ejpam-5917	59	11	1	1	NUM
ejpam-5917	59	12	,	,	PUNCT
ejpam-5917	59	13	2	2	NUM
ejpam-5917	59	14	,	,	PUNCT
ejpam-5917	59	15	.	.	PUNCT
ejpam-5917	59	16	.	.	PUNCT
ejpam-5917	60	1	.	.	PUNCT
ejpam-5917	61	1	,	,	PUNCT
ejpam-5917	61	2	n−	n−	NOUN
ejpam-5917	61	3	1	1	NUM
ejpam-5917	62	1	[	[	X
ejpam-5917	62	2	13	13	NUM
ejpam-5917	62	3	]	]	PUNCT
ejpam-5917	62	4	.	.	PUNCT
ejpam-5917	63	1	for	for	ADP
ejpam-5917	63	2	n	n	PRON
ejpam-5917	63	3	≥	≥	NUM
ejpam-5917	63	4	3	3	NUM
ejpam-5917	63	5	,	,	PUNCT
ejpam-5917	63	6	the	the	DET
ejpam-5917	63	7	cycle	cycle	NOUN
ejpam-5917	63	8	cn	cn	PROPN
ejpam-5917	63	9	is	be	AUX
ejpam-5917	63	10	a	a	DET
ejpam-5917	63	11	graph	graph	NOUN
ejpam-5917	63	12	of	of	ADP
ejpam-5917	63	13	order	order	NOUN
ejpam-5917	63	14	n	n	NOUN
ejpam-5917	63	15	and	and	CCONJ
ejpam-5917	63	16	size	size	NOUN
ejpam-5917	63	17	n	n	CCONJ
ejpam-5917	63	18	whose	whose	DET
ejpam-5917	63	19	vertices	vertex	NOUN
ejpam-5917	63	20	can	can	AUX
ejpam-5917	63	21	be	be	AUX
ejpam-5917	63	22	labeled	label	VERB
ejpam-5917	63	23	by	by	ADP
ejpam-5917	63	24	v1	v1	NOUN
ejpam-5917	63	25	,	,	PUNCT
ejpam-5917	63	26	v2	v2	PROPN
ejpam-5917	63	27	,	,	PUNCT
ejpam-5917	63	28	.	.	PUNCT
ejpam-5917	63	29	.	.	PUNCT
ejpam-5917	64	1	.	.	PUNCT
ejpam-5917	65	1	,	,	PUNCT
ejpam-5917	65	2	vn	vn	PROPN
ejpam-5917	65	3	and	and	CCONJ
ejpam-5917	65	4	whose	whose	DET
ejpam-5917	65	5	edges	edge	NOUN
ejpam-5917	65	6	are	be	AUX
ejpam-5917	65	7	v1v2	v1v2	X
ejpam-5917	65	8	,	,	PUNCT
ejpam-5917	65	9	v2v3	v2v3	NUM
ejpam-5917	65	10	,	,	PUNCT
ejpam-5917	65	11	...	...	PUNCT
ejpam-5917	65	12	,	,	PUNCT
ejpam-5917	65	13	vn−1vn	vn−1vn	NUM
ejpam-5917	65	14	,	,	PUNCT
ejpam-5917	65	15	vnv1	vnv1	NOUN
ejpam-5917	65	16	[	[	X
ejpam-5917	65	17	13	13	NUM
ejpam-5917	65	18	]	]	PUNCT
ejpam-5917	65	19	.	.	PUNCT
ejpam-5917	66	1	for	for	ADP
ejpam-5917	66	2	n	n	PRON
ejpam-5917	66	3	≥	≥	NUM
ejpam-5917	66	4	2	2	NUM
ejpam-5917	66	5	,	,	PUNCT
ejpam-5917	66	6	the	the	DET
ejpam-5917	66	7	complete	complete	ADJ
ejpam-5917	66	8	graph	graph	NOUN
ejpam-5917	66	9	kn	kn	PROPN
ejpam-5917	66	10	is	be	AUX
ejpam-5917	66	11	a	a	DET
ejpam-5917	66	12	graph	graph	NOUN
ejpam-5917	66	13	of	of	ADP
ejpam-5917	66	14	order	order	NOUN
ejpam-5917	66	15	n	n	NOUN
ejpam-5917	66	16	and	and	CCONJ
ejpam-5917	66	17	size	size	VERB
ejpam-5917	66	18	n(n−1	n(n−1	NUM
ejpam-5917	66	19	)	)	PUNCT
ejpam-5917	66	20	2	2	NUM
ejpam-5917	66	21	whose	whose	DET
ejpam-5917	66	22	vertices	vertex	NOUN
ejpam-5917	66	23	can	can	AUX
ejpam-5917	66	24	be	be	AUX
ejpam-5917	66	25	labeled	label	VERB
ejpam-5917	66	26	by	by	ADP
ejpam-5917	66	27	v1	v1	NOUN
ejpam-5917	66	28	,	,	PUNCT
ejpam-5917	66	29	v2	v2	PROPN
ejpam-5917	66	30	,	,	PUNCT
ejpam-5917	66	31	.	.	PUNCT
ejpam-5917	66	32	.	.	PUNCT
ejpam-5917	67	1	.	.	PUNCT
ejpam-5917	68	1	,	,	PUNCT
ejpam-5917	68	2	vn	vn	PROPN
ejpam-5917	68	3	and	and	CCONJ
ejpam-5917	68	4	whose	whose	DET
ejpam-5917	68	5	edges	edge	NOUN
ejpam-5917	68	6	are	be	AUX
ejpam-5917	68	7	represented	represent	VERB
ejpam-5917	68	8	as	as	ADP
ejpam-5917	68	9	vivj	vivj	NOUN
ejpam-5917	68	10	for	for	ADP
ejpam-5917	68	11	all	all	DET
ejpam-5917	68	12	pairs	pair	NOUN
ejpam-5917	68	13	of	of	ADP
ejpam-5917	68	14	vertices	vertex	NOUN
ejpam-5917	68	15	where	where	SCONJ
ejpam-5917	68	16	1	1	NUM
ejpam-5917	68	17	≤	≤	PUNCT
ejpam-5917	69	1	i	i	PRON
ejpam-5917	69	2	<	<	X
ejpam-5917	69	3	j	j	PROPN
ejpam-5917	69	4	≤	≤	PUNCT
ejpam-5917	69	5	n	n	CCONJ
ejpam-5917	70	1	[	[	X
ejpam-5917	70	2	12	12	NUM
ejpam-5917	70	3	]	]	PUNCT
ejpam-5917	70	4	.	.	PUNCT
ejpam-5917	71	1	a	a	DET
ejpam-5917	71	2	graph	graph	NOUN
ejpam-5917	71	3	g	g	NOUN
ejpam-5917	71	4	is	be	AUX
ejpam-5917	71	5	a	a	DET
ejpam-5917	71	6	complete	complete	ADJ
ejpam-5917	71	7	bipartite	bipartite	NOUN
ejpam-5917	71	8	graph	graph	NOUN
ejpam-5917	71	9	if	if	SCONJ
ejpam-5917	71	10	v	v	X
ejpam-5917	71	11	(	(	PUNCT
ejpam-5917	71	12	g	g	NOUN
ejpam-5917	71	13	)	)	PUNCT
ejpam-5917	71	14	can	can	AUX
ejpam-5917	71	15	be	be	AUX
ejpam-5917	71	16	partitioned	partition	VERB
ejpam-5917	71	17	into	into	ADP
ejpam-5917	71	18	two	two	NUM
ejpam-5917	71	19	sets	set	NOUN
ejpam-5917	71	20	u	u	NOUN
ejpam-5917	71	21	and	and	CCONJ
ejpam-5917	71	22	w	w	PROPN
ejpam-5917	71	23	(	(	PUNCT
ejpam-5917	71	24	called	call	VERB
ejpam-5917	71	25	partite	partite	ADJ
ejpam-5917	71	26	sets	set	NOUN
ejpam-5917	71	27	)	)	PUNCT
ejpam-5917	71	28	such	such	ADJ
ejpam-5917	71	29	that	that	SCONJ
ejpam-5917	71	30	uw	uw	PROPN
ejpam-5917	71	31	is	be	AUX
ejpam-5917	71	32	an	an	DET
ejpam-5917	71	33	edge	edge	NOUN
ejpam-5917	71	34	of	of	ADP
ejpam-5917	71	35	g	g	NOUN
ejpam-5917	71	36	if	if	SCONJ
ejpam-5917	71	37	and	and	CCONJ
ejpam-5917	71	38	only	only	ADV
ejpam-5917	71	39	if	if	SCONJ
ejpam-5917	71	40	u	u	PROPN
ejpam-5917	71	41	∈	∈	PROPN
ejpam-5917	71	42	u	u	NOUN
ejpam-5917	71	43	and	and	CCONJ
ejpam-5917	71	44	w	w	PROPN
ejpam-5917	71	45	∈	∈	PROPN
ejpam-5917	71	46	w	w	NOUN
ejpam-5917	71	47	.	.	PUNCT
ejpam-5917	72	1	if	if	SCONJ
ejpam-5917	72	2	|u	|u	ADJ
ejpam-5917	72	3	|	|	NOUN
ejpam-5917	72	4	=	=	SYM
ejpam-5917	72	5	m	m	PROPN
ejpam-5917	72	6	and	and	CCONJ
ejpam-5917	72	7	|w	|w	ADJ
ejpam-5917	72	8	|	|	NOUN
ejpam-5917	72	9	=	=	SYM
ejpam-5917	72	10	n	n	CCONJ
ejpam-5917	72	11	,	,	PUNCT
ejpam-5917	72	12	then	then	ADV
ejpam-5917	72	13	the	the	DET
ejpam-5917	72	14	complete	complete	ADJ
ejpam-5917	72	15	bipartite	bipartite	NOUN
ejpam-5917	72	16	graph	graph	NOUN
ejpam-5917	72	17	is	be	AUX
ejpam-5917	72	18	denoted	denote	VERB
ejpam-5917	72	19	by	by	ADP
ejpam-5917	72	20	km	km	PROPN
ejpam-5917	72	21	,	,	PUNCT
ejpam-5917	72	22	n	n	X
ejpam-5917	72	23	[	[	X
ejpam-5917	72	24	12	12	NUM
ejpam-5917	72	25	]	]	PUNCT
ejpam-5917	72	26	.	.	PUNCT
ejpam-5917	73	1	the	the	DET
ejpam-5917	73	2	friendship	friendship	NOUN
ejpam-5917	73	3	graph	graph	NOUN
ejpam-5917	73	4	fn	fn	NOUN
ejpam-5917	73	5	,	,	PUNCT
ejpam-5917	73	6	also	also	ADV
ejpam-5917	73	7	called	call	VERB
ejpam-5917	73	8	the	the	DET
ejpam-5917	73	9	dutch	dutch	ADJ
ejpam-5917	73	10	windmill	windmill	NOUN
ejpam-5917	73	11	graph	graph	NOUN
ejpam-5917	73	12	d3	d3	PROPN
ejpam-5917	73	13	(	(	PUNCT
ejpam-5917	73	14	n	n	CCONJ
ejpam-5917	73	15	)	)	PUNCT
ejpam-5917	73	16	,	,	PUNCT
ejpam-5917	73	17	is	be	AUX
ejpam-5917	73	18	the	the	DET
ejpam-5917	73	19	graph	graph	NOUN
ejpam-5917	73	20	with	with	ADP
ejpam-5917	73	21	2n	2n	NUM
ejpam-5917	73	22	+	+	CCONJ
ejpam-5917	73	23	1	1	NUM
ejpam-5917	73	24	vertices	vertex	NOUN
ejpam-5917	73	25	obtained	obtain	VERB
ejpam-5917	73	26	by	by	ADP
ejpam-5917	73	27	taking	take	VERB
ejpam-5917	73	28	n	n	PRON
ejpam-5917	73	29	copies	copy	NOUN
ejpam-5917	73	30	of	of	ADP
ejpam-5917	73	31	the	the	DET
ejpam-5917	73	32	cycle	cycle	NOUN
ejpam-5917	73	33	graph	graph	NOUN
ejpam-5917	73	34	c3	c3	PROPN
ejpam-5917	73	35	with	with	ADP
ejpam-5917	73	36	a	a	DET
ejpam-5917	73	37	common	common	ADJ
ejpam-5917	73	38	vertex	vertex	NOUN
ejpam-5917	73	39	,	,	PUNCT
ejpam-5917	73	40	called	call	VERB
ejpam-5917	73	41	the	the	DET
ejpam-5917	73	42	central	central	ADJ
ejpam-5917	73	43	vertex	vertex	NOUN
ejpam-5917	73	44	[	[	X
ejpam-5917	73	45	14	14	NUM
ejpam-5917	73	46	]	]	PUNCT
ejpam-5917	73	47	.	.	PUNCT
ejpam-5917	74	1	the	the	DET
ejpam-5917	74	2	sunlet	sunlet	NOUN
ejpam-5917	74	3	graph	graph	PROPN
ejpam-5917	74	4	sn	sn	PROPN
ejpam-5917	74	5	,	,	PUNCT
ejpam-5917	74	6	also	also	ADV
ejpam-5917	74	7	called	call	VERB
ejpam-5917	74	8	as	as	ADP
ejpam-5917	74	9	n	n	NUM
ejpam-5917	74	10	-	-	PUNCT
ejpam-5917	74	11	sunlet	sunlet	NOUN
ejpam-5917	74	12	graph	graph	NOUN
ejpam-5917	74	13	,	,	PUNCT
ejpam-5917	74	14	is	be	AUX
ejpam-5917	74	15	the	the	DET
ejpam-5917	74	16	graph	graph	NOUN
ejpam-5917	74	17	with	with	ADP
ejpam-5917	74	18	2n	2n	ADJ
ejpam-5917	74	19	vertices	vertex	NOUN
ejpam-5917	74	20	obtained	obtain	VERB
ejpam-5917	74	21	by	by	ADP
ejpam-5917	74	22	attaching	attach	VERB
ejpam-5917	74	23	a	a	DET
ejpam-5917	74	24	pendant	pendant	ADJ
ejpam-5917	74	25	edge	edge	NOUN
ejpam-5917	74	26	at	at	ADP
ejpam-5917	74	27	each	each	DET
ejpam-5917	74	28	vertex	vertex	NOUN
ejpam-5917	74	29	of	of	ADP
ejpam-5917	74	30	a	a	DET
ejpam-5917	74	31	cycle	cycle	NOUN
ejpam-5917	74	32	cn	cn	PROPN
ejpam-5917	75	1	[	[	X
ejpam-5917	75	2	15	15	NUM
ejpam-5917	75	3	]	]	PUNCT
ejpam-5917	75	4	.	.	PUNCT
ejpam-5917	76	1	the	the	DET
ejpam-5917	76	2	helm	helm	NOUN
ejpam-5917	76	3	graph	graph	NOUN
ejpam-5917	76	4	hn	hn	PROPN
ejpam-5917	76	5	is	be	AUX
ejpam-5917	76	6	the	the	DET
ejpam-5917	76	7	graph	graph	NOUN
ejpam-5917	76	8	with	with	ADP
ejpam-5917	76	9	2n+1	2n+1	PROPN
ejpam-5917	76	10	vertices	vertex	NOUN
ejpam-5917	76	11	obtained	obtain	VERB
ejpam-5917	76	12	by	by	ADP
ejpam-5917	76	13	adjoining	adjoin	VERB
ejpam-5917	76	14	a	a	DET
ejpam-5917	76	15	pendant	pendant	ADJ
ejpam-5917	76	16	edge	edge	NOUN
ejpam-5917	76	17	at	at	ADP
ejpam-5917	76	18	each	each	DET
ejpam-5917	76	19	node	node	NOUN
ejpam-5917	76	20	of	of	ADP
ejpam-5917	76	21	the	the	DET
ejpam-5917	76	22	cycle	cycle	NOUN
ejpam-5917	76	23	,	,	PUNCT
ejpam-5917	76	24	whose	whose	DET
ejpam-5917	76	25	vertices	vertex	NOUN
ejpam-5917	76	26	are	be	AUX
ejpam-5917	76	27	adjacent	adjacent	ADJ
ejpam-5917	76	28	to	to	ADP
ejpam-5917	76	29	a	a	DET
ejpam-5917	76	30	common	common	ADJ
ejpam-5917	76	31	vertex	vertex	NOUN
ejpam-5917	76	32	,	,	PUNCT
ejpam-5917	76	33	called	call	VERB
ejpam-5917	76	34	the	the	DET
ejpam-5917	76	35	hub	hub	NOUN
ejpam-5917	76	36	[	[	X
ejpam-5917	76	37	15	15	NUM
ejpam-5917	76	38	]	]	PUNCT
ejpam-5917	76	39	.	.	PUNCT
ejpam-5917	77	1	for	for	ADP
ejpam-5917	77	2	the	the	DET
ejpam-5917	77	3	main	main	ADJ
ejpam-5917	77	4	concepts	concept	NOUN
ejpam-5917	77	5	included	include	VERB
ejpam-5917	77	6	in	in	ADP
ejpam-5917	77	7	this	this	DET
ejpam-5917	77	8	study	study	NOUN
ejpam-5917	77	9	,	,	PUNCT
ejpam-5917	77	10	consider	consider	VERB
ejpam-5917	77	11	the	the	DET
ejpam-5917	77	12	following	follow	VERB
ejpam-5917	77	13	definitions	definition	NOUN
ejpam-5917	77	14	:	:	PUNCT
ejpam-5917	77	15	let	let	VERB
ejpam-5917	77	16	g	g	PRON
ejpam-5917	77	17	be	be	AUX
ejpam-5917	77	18	a	a	DET
ejpam-5917	77	19	simple	simple	ADJ
ejpam-5917	77	20	connected	connect	VERB
ejpam-5917	77	21	nontrivial	nontrivial	ADJ
ejpam-5917	77	22	graph	graph	NOUN
ejpam-5917	77	23	.	.	PUNCT
ejpam-5917	78	1	a	a	DET
ejpam-5917	78	2	nonempty	nonempty	ADV
ejpam-5917	78	3	set	set	VERB
ejpam-5917	78	4	s	s	PROPN
ejpam-5917	78	5	⊆	⊆	NUM
ejpam-5917	78	6	v	v	NOUN
ejpam-5917	78	7	(	(	PUNCT
ejpam-5917	78	8	g	g	NOUN
ejpam-5917	78	9	)	)	PUNCT
ejpam-5917	78	10	is	be	AUX
ejpam-5917	78	11	a	a	DET
ejpam-5917	78	12	dominating	dominating	NOUN
ejpam-5917	78	13	set	set	NOUN
ejpam-5917	78	14	if	if	SCONJ
ejpam-5917	78	15	every	every	DET
ejpam-5917	78	16	vertex	vertex	NOUN
ejpam-5917	78	17	in	in	ADP
ejpam-5917	78	18	v	v	NOUN
ejpam-5917	78	19	(	(	PUNCT
ejpam-5917	78	20	g)∖s	g)∖	NOUN
ejpam-5917	78	21	is	be	AUX
ejpam-5917	78	22	adjacent	adjacent	ADJ
ejpam-5917	78	23	to	to	ADP
ejpam-5917	78	24	at	at	ADV
ejpam-5917	78	25	least	least	ADV
ejpam-5917	78	26	one	one	NUM
ejpam-5917	78	27	vertex	vertex	NOUN
ejpam-5917	78	28	in	in	ADP
ejpam-5917	78	29	s.	s.	PROPN
ejpam-5917	78	30	the	the	DET
ejpam-5917	78	31	minimum	minimum	ADJ
ejpam-5917	78	32	cardinality	cardinality	NOUN
ejpam-5917	78	33	of	of	ADP
ejpam-5917	78	34	a	a	DET
ejpam-5917	78	35	dominating	dominating	NOUN
ejpam-5917	78	36	set	set	NOUN
ejpam-5917	78	37	in	in	ADP
ejpam-5917	78	38	g	g	PROPN
ejpam-5917	78	39	is	be	AUX
ejpam-5917	78	40	called	call	VERB
ejpam-5917	78	41	domination	domination	NOUN
ejpam-5917	78	42	number	number	NOUN
ejpam-5917	78	43	of	of	ADP
ejpam-5917	78	44	g	g	NOUN
ejpam-5917	78	45	,	,	PUNCT
ejpam-5917	78	46	denoted	denote	VERB
ejpam-5917	78	47	by	by	ADP
ejpam-5917	78	48	γ(g	γ(g	NOUN
ejpam-5917	78	49	)	)	PUNCT
ejpam-5917	79	1	[	[	X
ejpam-5917	79	2	16	16	NUM
ejpam-5917	79	3	]	]	PUNCT
ejpam-5917	79	4	.	.	PUNCT
ejpam-5917	80	1	w.	w.	PROPN
ejpam-5917	80	2	g.	g.	PROPN
ejpam-5917	80	3	jumalon	jumalon	PROPN
ejpam-5917	80	4	,	,	PUNCT
ejpam-5917	80	5	i.	i.	PROPN
ejpam-5917	80	6	cabahug	cabahug	PROPN
ejpam-5917	80	7	/	/	SYM
ejpam-5917	80	8	eur	eur	PROPN
ejpam-5917	80	9	.	.	PUNCT
ejpam-5917	81	1	j.	j.	PROPN
ejpam-5917	81	2	pure	pure	PROPN
ejpam-5917	81	3	appl	appl	PROPN
ejpam-5917	81	4	.	.	PROPN
ejpam-5917	81	5	math	math	PROPN
ejpam-5917	81	6	,	,	PUNCT
ejpam-5917	81	7	18	18	NUM
ejpam-5917	81	8	(	(	PUNCT
ejpam-5917	81	9	2	2	NUM
ejpam-5917	81	10	)	)	PUNCT
ejpam-5917	81	11	(	(	PUNCT
ejpam-5917	81	12	2025	2025	NUM
ejpam-5917	81	13	)	)	PUNCT
ejpam-5917	81	14	,	,	PUNCT
ejpam-5917	81	15	5917	5917	NUM
ejpam-5917	81	16	4	4	NUM
ejpam-5917	81	17	of	of	ADP
ejpam-5917	81	18	12	12	NUM
ejpam-5917	81	19	a	a	DET
ejpam-5917	81	20	nonempty	nonempty	ADJ
ejpam-5917	81	21	set	set	VERB
ejpam-5917	81	22	s	s	PROPN
ejpam-5917	81	23	⊆	⊆	NUM
ejpam-5917	81	24	v	v	NOUN
ejpam-5917	81	25	(	(	PUNCT
ejpam-5917	81	26	g	g	NOUN
ejpam-5917	81	27	)	)	PUNCT
ejpam-5917	81	28	of	of	ADP
ejpam-5917	81	29	vertices	vertex	NOUN
ejpam-5917	81	30	is	be	AUX
ejpam-5917	81	31	a	a	DET
ejpam-5917	81	32	safe	safe	ADJ
ejpam-5917	81	33	set	set	NOUN
ejpam-5917	81	34	if	if	SCONJ
ejpam-5917	81	35	for	for	ADP
ejpam-5917	81	36	every	every	DET
ejpam-5917	81	37	component	component	NOUN
ejpam-5917	81	38	a	a	PRON
ejpam-5917	81	39	of	of	ADP
ejpam-5917	81	40	g[s	g[	NOUN
ejpam-5917	81	41	]	]	PUNCT
ejpam-5917	81	42	and	and	CCONJ
ejpam-5917	81	43	every	every	DET
ejpam-5917	81	44	component	component	NOUN
ejpam-5917	81	45	b	b	PROPN
ejpam-5917	81	46	of	of	ADP
ejpam-5917	81	47	g[v	g[v	NOUN
ejpam-5917	81	48	(	(	PUNCT
ejpam-5917	81	49	g	g	NOUN
ejpam-5917	81	50	)	)	PUNCT
ejpam-5917	81	51	∖	∖	X
ejpam-5917	82	1	s	s	PART
ejpam-5917	82	2	]	]	X
ejpam-5917	82	3	adjacent	adjacent	ADJ
ejpam-5917	82	4	to	to	ADP
ejpam-5917	82	5	a	a	PRON
ejpam-5917	82	6	,	,	PUNCT
ejpam-5917	82	7	it	it	PRON
ejpam-5917	82	8	holds	hold	VERB
ejpam-5917	82	9	that	that	SCONJ
ejpam-5917	82	10	|v	|v	PROPN
ejpam-5917	82	11	(	(	PUNCT
ejpam-5917	82	12	a)|	a)|	X
ejpam-5917	82	13	≥	≥	NOUN
ejpam-5917	82	14	|v	|v	PROPN
ejpam-5917	82	15	(	(	PUNCT
ejpam-5917	82	16	b)|	b)|	NOUN
ejpam-5917	82	17	.	.	PUNCT
ejpam-5917	83	1	the	the	DET
ejpam-5917	83	2	minimum	minimum	ADJ
ejpam-5917	83	3	cardinality	cardinality	NOUN
ejpam-5917	83	4	of	of	ADP
ejpam-5917	83	5	a	a	DET
ejpam-5917	83	6	safe	safe	ADJ
ejpam-5917	83	7	set	set	NOUN
ejpam-5917	83	8	in	in	ADP
ejpam-5917	83	9	g	g	PROPN
ejpam-5917	83	10	is	be	AUX
ejpam-5917	83	11	called	call	VERB
ejpam-5917	83	12	safe	safe	ADJ
ejpam-5917	83	13	number	number	NOUN
ejpam-5917	83	14	of	of	ADP
ejpam-5917	83	15	g	g	NOUN
ejpam-5917	83	16	,	,	PUNCT
ejpam-5917	83	17	denoted	denote	VERB
ejpam-5917	83	18	by	by	ADP
ejpam-5917	83	19	s(g	s(g	PROPN
ejpam-5917	83	20	)	)	PUNCT
ejpam-5917	84	1	[	[	X
ejpam-5917	84	2	17	17	NUM
ejpam-5917	84	3	]	]	PUNCT
ejpam-5917	84	4	.	.	PUNCT
ejpam-5917	85	1	a	a	DET
ejpam-5917	85	2	nonempty	nonempty	NOUN
ejpam-5917	85	3	subset	subset	VERB
ejpam-5917	85	4	s	s	NOUN
ejpam-5917	85	5	of	of	ADP
ejpam-5917	85	6	v	v	NOUN
ejpam-5917	85	7	(	(	PUNCT
ejpam-5917	85	8	g	g	NOUN
ejpam-5917	85	9	)	)	PUNCT
ejpam-5917	85	10	is	be	AUX
ejpam-5917	85	11	a	a	DET
ejpam-5917	85	12	safe	safe	ADJ
ejpam-5917	85	13	dominating	dominating	NOUN
ejpam-5917	85	14	set	set	VERB
ejpam-5917	85	15	if	if	SCONJ
ejpam-5917	85	16	and	and	CCONJ
ejpam-5917	85	17	only	only	ADV
ejpam-5917	85	18	if	if	SCONJ
ejpam-5917	85	19	it	it	PRON
ejpam-5917	85	20	is	be	AUX
ejpam-5917	85	21	both	both	CCONJ
ejpam-5917	85	22	a	a	DET
ejpam-5917	85	23	dominating	dominating	NOUN
ejpam-5917	85	24	set	set	NOUN
ejpam-5917	85	25	and	and	CCONJ
ejpam-5917	85	26	a	a	DET
ejpam-5917	85	27	safe	safe	ADJ
ejpam-5917	85	28	set	set	NOUN
ejpam-5917	85	29	.	.	PUNCT
ejpam-5917	86	1	the	the	DET
ejpam-5917	86	2	minimum	minimum	ADJ
ejpam-5917	86	3	cardinality	cardinality	NOUN
ejpam-5917	86	4	of	of	ADP
ejpam-5917	86	5	a	a	DET
ejpam-5917	86	6	safe	safe	ADJ
ejpam-5917	86	7	dominating	dominating	NOUN
ejpam-5917	86	8	set	set	VERB
ejpam-5917	86	9	in	in	ADP
ejpam-5917	86	10	g	g	PROPN
ejpam-5917	86	11	is	be	AUX
ejpam-5917	86	12	called	call	VERB
ejpam-5917	86	13	safe	safe	ADJ
ejpam-5917	86	14	domination	domination	NOUN
ejpam-5917	86	15	number	number	NOUN
ejpam-5917	86	16	of	of	ADP
ejpam-5917	86	17	g	g	NOUN
ejpam-5917	86	18	,	,	PUNCT
ejpam-5917	86	19	denoted	denote	VERB
ejpam-5917	86	20	by	by	ADP
ejpam-5917	86	21	γs(g	γs(g	NOUN
ejpam-5917	86	22	)	)	PUNCT
ejpam-5917	87	1	[	[	X
ejpam-5917	87	2	11	11	NUM
ejpam-5917	87	3	]	]	PUNCT
ejpam-5917	87	4	.	.	PUNCT
ejpam-5917	88	1	a	a	DET
ejpam-5917	88	2	total	total	ADJ
ejpam-5917	88	3	dominating	dominating	NOUN
ejpam-5917	88	4	set	set	NOUN
ejpam-5917	88	5	s	s	VERB
ejpam-5917	88	6	in	in	ADP
ejpam-5917	88	7	a	a	DET
ejpam-5917	88	8	graph	graph	NOUN
ejpam-5917	88	9	g	g	NOUN
ejpam-5917	88	10	is	be	AUX
ejpam-5917	88	11	a	a	DET
ejpam-5917	88	12	nonempty	nonempty	ADJ
ejpam-5917	88	13	subset	subset	NOUN
ejpam-5917	88	14	of	of	ADP
ejpam-5917	88	15	v	v	NOUN
ejpam-5917	88	16	(	(	PUNCT
ejpam-5917	88	17	g	g	NOUN
ejpam-5917	88	18	)	)	PUNCT
ejpam-5917	88	19	such	such	ADJ
ejpam-5917	88	20	that	that	SCONJ
ejpam-5917	88	21	every	every	DET
ejpam-5917	88	22	vertex	vertex	NOUN
ejpam-5917	88	23	in	in	ADP
ejpam-5917	88	24	v	v	NOUN
ejpam-5917	88	25	(	(	PUNCT
ejpam-5917	88	26	g	g	NOUN
ejpam-5917	88	27	)	)	PUNCT
ejpam-5917	88	28	,	,	PUNCT
ejpam-5917	88	29	including	include	VERB
ejpam-5917	88	30	those	those	PRON
ejpam-5917	88	31	in	in	ADP
ejpam-5917	88	32	s	s	NOUN
ejpam-5917	88	33	,	,	PUNCT
ejpam-5917	88	34	is	be	AUX
ejpam-5917	88	35	adjacent	adjacent	ADJ
ejpam-5917	88	36	to	to	ADP
ejpam-5917	88	37	at	at	ADV
ejpam-5917	88	38	least	least	ADV
ejpam-5917	88	39	one	one	NUM
ejpam-5917	88	40	vertex	vertex	NOUN
ejpam-5917	88	41	in	in	ADP
ejpam-5917	88	42	s.	s.	PROPN
ejpam-5917	88	43	the	the	DET
ejpam-5917	88	44	minimum	minimum	ADJ
ejpam-5917	88	45	cardinality	cardinality	NOUN
ejpam-5917	88	46	of	of	ADP
ejpam-5917	88	47	a	a	DET
ejpam-5917	88	48	total	total	ADJ
ejpam-5917	88	49	dominating	dominating	NOUN
ejpam-5917	88	50	set	set	NOUN
ejpam-5917	88	51	in	in	ADP
ejpam-5917	88	52	g	g	PROPN
ejpam-5917	88	53	is	be	AUX
ejpam-5917	88	54	called	call	VERB
ejpam-5917	88	55	total	total	ADJ
ejpam-5917	88	56	domination	domination	NOUN
ejpam-5917	88	57	number	number	NOUN
ejpam-5917	88	58	of	of	ADP
ejpam-5917	88	59	g	g	NOUN
ejpam-5917	88	60	,	,	PUNCT
ejpam-5917	88	61	denoted	denote	VERB
ejpam-5917	88	62	by	by	ADP
ejpam-5917	88	63	γt(g	γt(g	NOUN
ejpam-5917	88	64	)	)	PUNCT
ejpam-5917	89	1	[	[	X
ejpam-5917	89	2	2	2	NUM
ejpam-5917	89	3	]	]	PUNCT
ejpam-5917	89	4	.	.	PUNCT
ejpam-5917	90	1	3	3	X
ejpam-5917	90	2	.	.	X
ejpam-5917	90	3	results	result	VERB
ejpam-5917	90	4	definition	definition	NOUN
ejpam-5917	90	5	1	1	NUM
ejpam-5917	90	6	.	.	PUNCT
ejpam-5917	91	1	a	a	DET
ejpam-5917	91	2	nonempty	nonempty	NOUN
ejpam-5917	91	3	subset	subset	VERB
ejpam-5917	91	4	s	s	NOUN
ejpam-5917	91	5	of	of	ADP
ejpam-5917	91	6	v	v	NOUN
ejpam-5917	91	7	(	(	PUNCT
ejpam-5917	91	8	g	g	NOUN
ejpam-5917	91	9	)	)	PUNCT
ejpam-5917	91	10	is	be	AUX
ejpam-5917	91	11	a	a	DET
ejpam-5917	91	12	total	total	ADJ
ejpam-5917	91	13	safe	safe	ADJ
ejpam-5917	91	14	dominating	dominating	NOUN
ejpam-5917	91	15	set	set	VERB
ejpam-5917	91	16	in	in	ADP
ejpam-5917	91	17	g	g	PROPN
ejpam-5917	91	18	if	if	SCONJ
ejpam-5917	91	19	it	it	PRON
ejpam-5917	91	20	is	be	AUX
ejpam-5917	91	21	both	both	CCONJ
ejpam-5917	91	22	a	a	DET
ejpam-5917	91	23	total	total	ADJ
ejpam-5917	91	24	dominating	dominating	NOUN
ejpam-5917	91	25	set	set	NOUN
ejpam-5917	91	26	and	and	CCONJ
ejpam-5917	91	27	a	a	DET
ejpam-5917	91	28	safe	safe	ADJ
ejpam-5917	91	29	dominating	dominating	NOUN
ejpam-5917	91	30	set	set	VERB
ejpam-5917	91	31	in	in	ADP
ejpam-5917	91	32	g.	g.	PROPN
ejpam-5917	91	33	the	the	DET
ejpam-5917	91	34	minimum	minimum	ADJ
ejpam-5917	91	35	cardinality	cardinality	NOUN
ejpam-5917	91	36	of	of	ADP
ejpam-5917	91	37	a	a	DET
ejpam-5917	91	38	total	total	ADJ
ejpam-5917	91	39	safe	safe	ADJ
ejpam-5917	91	40	dominating	dominating	NOUN
ejpam-5917	91	41	set	set	VERB
ejpam-5917	91	42	in	in	ADP
ejpam-5917	91	43	g	g	PROPN
ejpam-5917	91	44	is	be	AUX
ejpam-5917	91	45	called	call	VERB
ejpam-5917	91	46	total	total	ADJ
ejpam-5917	91	47	safe	safe	ADJ
ejpam-5917	91	48	domination	domination	NOUN
ejpam-5917	91	49	number	number	NOUN
ejpam-5917	91	50	of	of	ADP
ejpam-5917	91	51	g	g	NOUN
ejpam-5917	91	52	,	,	PUNCT
ejpam-5917	91	53	denoted	denote	VERB
ejpam-5917	91	54	by	by	ADP
ejpam-5917	91	55	γts(g	γts(g	PROPN
ejpam-5917	91	56	)	)	PUNCT
ejpam-5917	91	57	.	.	PUNCT
ejpam-5917	92	1	example	example	NOUN
ejpam-5917	93	1	1	1	NUM
ejpam-5917	93	2	.	.	X
ejpam-5917	93	3	consider	consider	VERB
ejpam-5917	93	4	figure	figure	NOUN
ejpam-5917	93	5	1	1	NUM
ejpam-5917	93	6	that	that	PRON
ejpam-5917	93	7	shows	show	VERB
ejpam-5917	93	8	a	a	DET
ejpam-5917	93	9	graph	graph	NOUN
ejpam-5917	93	10	g	g	NOUN
ejpam-5917	93	11	together	together	ADV
ejpam-5917	93	12	with	with	ADP
ejpam-5917	93	13	different	different	ADJ
ejpam-5917	93	14	dominating	dominating	NOUN
ejpam-5917	93	15	sets	set	NOUN
ejpam-5917	93	16	as	as	ADP
ejpam-5917	93	17	in	in	ADP
ejpam-5917	93	18	g1	g1	PROPN
ejpam-5917	93	19	,	,	PUNCT
ejpam-5917	93	20	g2	g2	PROPN
ejpam-5917	93	21	,	,	PUNCT
ejpam-5917	93	22	and	and	CCONJ
ejpam-5917	93	23	g3	g3	PROPN
ejpam-5917	93	24	.	.	PUNCT
ejpam-5917	94	1	in	in	ADP
ejpam-5917	94	2	g1	g1	PROPN
ejpam-5917	94	3	,	,	PUNCT
ejpam-5917	94	4	s1	s1	PROPN
ejpam-5917	94	5	=	=	SYM
ejpam-5917	94	6	{	{	PUNCT
ejpam-5917	94	7	v3	v3	PROPN
ejpam-5917	94	8	,	,	PUNCT
ejpam-5917	94	9	v4	v4	PROPN
ejpam-5917	94	10	}	}	PUNCT
ejpam-5917	94	11	shows	show	VERB
ejpam-5917	94	12	a	a	DET
ejpam-5917	94	13	total	total	ADJ
ejpam-5917	94	14	safe	safe	ADJ
ejpam-5917	94	15	dominating	dominating	NOUN
ejpam-5917	94	16	set	set	VERB
ejpam-5917	94	17	in	in	ADP
ejpam-5917	94	18	g	g	PROPN
ejpam-5917	94	19	since	since	SCONJ
ejpam-5917	94	20	it	it	PRON
ejpam-5917	94	21	is	be	AUX
ejpam-5917	94	22	a	a	DET
ejpam-5917	94	23	total	total	ADJ
ejpam-5917	94	24	dominating	dominating	NOUN
ejpam-5917	94	25	set	set	NOUN
ejpam-5917	94	26	and	and	CCONJ
ejpam-5917	94	27	the	the	DET
ejpam-5917	94	28	order	order	NOUN
ejpam-5917	94	29	of	of	ADP
ejpam-5917	94	30	the	the	DET
ejpam-5917	94	31	component	component	NOUN
ejpam-5917	94	32	of	of	ADP
ejpam-5917	94	33	g[s1	g[s1	NOUN
ejpam-5917	94	34	]	]	PUNCT
ejpam-5917	94	35	is	be	AUX
ejpam-5917	94	36	at	at	ADV
ejpam-5917	94	37	least	least	ADJ
ejpam-5917	94	38	as	as	ADV
ejpam-5917	94	39	large	large	ADJ
ejpam-5917	94	40	as	as	ADP
ejpam-5917	94	41	the	the	DET
ejpam-5917	94	42	order	order	NOUN
ejpam-5917	94	43	of	of	ADP
ejpam-5917	94	44	any	any	DET
ejpam-5917	94	45	adjacent	adjacent	ADJ
ejpam-5917	94	46	component	component	NOUN
ejpam-5917	94	47	of	of	ADP
ejpam-5917	94	48	g[v	g[v	NOUN
ejpam-5917	94	49	(	(	PUNCT
ejpam-5917	94	50	g	g	NOUN
ejpam-5917	94	51	)	)	PUNCT
ejpam-5917	94	52	∖	∖	NOUN
ejpam-5917	94	53	s1	s1	NOUN
ejpam-5917	94	54	]	]	PUNCT
ejpam-5917	94	55	.	.	PUNCT
ejpam-5917	95	1	in	in	ADP
ejpam-5917	95	2	g2	g2	PROPN
ejpam-5917	95	3	,	,	PUNCT
ejpam-5917	95	4	s2	s2	PROPN
ejpam-5917	95	5	=	=	SYM
ejpam-5917	95	6	{	{	PUNCT
ejpam-5917	95	7	v3	v3	PROPN
ejpam-5917	95	8	,	,	PUNCT
ejpam-5917	95	9	v5	v5	PROPN
ejpam-5917	95	10	}	}	PUNCT
ejpam-5917	95	11	is	be	AUX
ejpam-5917	95	12	not	not	PART
ejpam-5917	95	13	a	a	DET
ejpam-5917	95	14	total	total	ADJ
ejpam-5917	95	15	safe	safe	ADJ
ejpam-5917	95	16	dominating	dominating	NOUN
ejpam-5917	95	17	set	set	NOUN
ejpam-5917	95	18	.	.	PUNCT
ejpam-5917	96	1	it	it	PRON
ejpam-5917	96	2	is	be	AUX
ejpam-5917	96	3	a	a	DET
ejpam-5917	96	4	total	total	ADJ
ejpam-5917	96	5	dominating	dominating	NOUN
ejpam-5917	96	6	set	set	NOUN
ejpam-5917	96	7	but	but	CCONJ
ejpam-5917	96	8	not	not	PART
ejpam-5917	96	9	a	a	DET
ejpam-5917	96	10	safe	safe	ADJ
ejpam-5917	96	11	dominating	dominating	NOUN
ejpam-5917	96	12	set	set	NOUN
ejpam-5917	96	13	since	since	SCONJ
ejpam-5917	96	14	g[v	g[v	NOUN
ejpam-5917	96	15	(	(	PUNCT
ejpam-5917	96	16	g	g	NOUN
ejpam-5917	96	17	)	)	PUNCT
ejpam-5917	96	18	∖	∖	PROPN
ejpam-5917	96	19	s2	s2	PROPN
ejpam-5917	96	20	]	]	PUNCT
ejpam-5917	96	21	has	have	VERB
ejpam-5917	96	22	a	a	DET
ejpam-5917	96	23	component	component	NOUN
ejpam-5917	96	24	with	with	ADP
ejpam-5917	96	25	order	order	NOUN
ejpam-5917	96	26	3	3	NUM
ejpam-5917	96	27	which	which	PRON
ejpam-5917	96	28	is	be	AUX
ejpam-5917	96	29	greater	great	ADJ
ejpam-5917	96	30	than	than	ADP
ejpam-5917	96	31	the	the	DET
ejpam-5917	96	32	order	order	NOUN
ejpam-5917	96	33	of	of	ADP
ejpam-5917	96	34	the	the	DET
ejpam-5917	96	35	component	component	NOUN
ejpam-5917	96	36	of	of	ADP
ejpam-5917	96	37	g[s2	g[s2	NOUN
ejpam-5917	96	38	]	]	PUNCT
ejpam-5917	96	39	.	.	PUNCT
ejpam-5917	97	1	finally	finally	ADV
ejpam-5917	97	2	,	,	PUNCT
ejpam-5917	97	3	in	in	ADP
ejpam-5917	97	4	g3	g3	PROPN
ejpam-5917	97	5	,	,	PUNCT
ejpam-5917	97	6	s3	s3	NOUN
ejpam-5917	97	7	=	=	SYM
ejpam-5917	97	8	{	{	PUNCT
ejpam-5917	97	9	v1	v1	PROPN
ejpam-5917	97	10	,	,	PUNCT
ejpam-5917	97	11	v2	v2	PROPN
ejpam-5917	97	12	,	,	PUNCT
ejpam-5917	97	13	v4	v4	NOUN
ejpam-5917	97	14	,	,	PUNCT
ejpam-5917	97	15	v5	v5	PROPN
ejpam-5917	97	16	}	}	PUNCT
ejpam-5917	97	17	is	be	AUX
ejpam-5917	97	18	not	not	PART
ejpam-5917	97	19	a	a	DET
ejpam-5917	97	20	total	total	ADJ
ejpam-5917	97	21	safe	safe	ADJ
ejpam-5917	97	22	dominating	dominating	NOUN
ejpam-5917	97	23	set	set	NOUN
ejpam-5917	97	24	.	.	PUNCT
ejpam-5917	98	1	it	it	PRON
ejpam-5917	98	2	is	be	AUX
ejpam-5917	98	3	a	a	DET
ejpam-5917	98	4	safe	safe	ADJ
ejpam-5917	98	5	dominating	dominating	NOUN
ejpam-5917	98	6	set	set	NOUN
ejpam-5917	98	7	but	but	CCONJ
ejpam-5917	98	8	not	not	PART
ejpam-5917	98	9	a	a	DET
ejpam-5917	98	10	total	total	ADJ
ejpam-5917	98	11	dominating	dominating	NOUN
ejpam-5917	98	12	set	set	NOUN
ejpam-5917	98	13	since	since	SCONJ
ejpam-5917	98	14	v2	v2	PROPN
ejpam-5917	98	15	is	be	AUX
ejpam-5917	98	16	isolated	isolate	VERB
ejpam-5917	98	17	.	.	PUNCT
ejpam-5917	99	1	w.	w.	PROPN
ejpam-5917	99	2	g.	g.	PROPN
ejpam-5917	99	3	jumalon	jumalon	PROPN
ejpam-5917	99	4	,	,	PUNCT
ejpam-5917	99	5	i.	i.	PROPN
ejpam-5917	99	6	cabahug	cabahug	PROPN
ejpam-5917	99	7	/	/	SYM
ejpam-5917	99	8	eur	eur	PROPN
ejpam-5917	99	9	.	.	PUNCT
ejpam-5917	100	1	j.	j.	PROPN
ejpam-5917	100	2	pure	pure	PROPN
ejpam-5917	100	3	appl	appl	PROPN
ejpam-5917	100	4	.	.	PROPN
ejpam-5917	100	5	math	math	PROPN
ejpam-5917	100	6	,	,	PUNCT
ejpam-5917	100	7	18	18	NUM
ejpam-5917	100	8	(	(	PUNCT
ejpam-5917	100	9	2	2	NUM
ejpam-5917	100	10	)	)	PUNCT
ejpam-5917	100	11	(	(	PUNCT
ejpam-5917	100	12	2025	2025	NUM
ejpam-5917	100	13	)	)	PUNCT
ejpam-5917	100	14	,	,	PUNCT
ejpam-5917	100	15	5917	5917	NUM
ejpam-5917	100	16	5	5	NUM
ejpam-5917	100	17	of	of	ADP
ejpam-5917	100	18	12	12	NUM
ejpam-5917	100	19	v1	v1	NOUN
ejpam-5917	100	20	v2	v2	PROPN
ejpam-5917	100	21	v3	v3	PROPN
ejpam-5917	100	22	v4	v4	PROPN
ejpam-5917	100	23	v5	v5	PROPN
ejpam-5917	100	24	v6	v6	PROPN
ejpam-5917	100	25	v1	v1	PROPN
ejpam-5917	100	26	v2	v2	PROPN
ejpam-5917	100	27	v3	v3	PROPN
ejpam-5917	100	28	v4	v4	PROPN
ejpam-5917	100	29	v5	v5	PROPN
ejpam-5917	100	30	v6	v6	PROPN
ejpam-5917	100	31	v1	v1	PROPN
ejpam-5917	100	32	v2	v2	PROPN
ejpam-5917	100	33	v3	v3	PROPN
ejpam-5917	100	34	v4	v4	PROPN
ejpam-5917	100	35	v5	v5	PROPN
ejpam-5917	100	36	v6	v6	PROPN
ejpam-5917	100	37	v1	v1	PROPN
ejpam-5917	100	38	v2	v2	PROPN
ejpam-5917	100	39	v3	v3	PROPN
ejpam-5917	100	40	v4	v4	PROPN
ejpam-5917	100	41	v5	v5	PROPN
ejpam-5917	100	42	v6	v6	PROPN
ejpam-5917	100	43	g	g	NOUN
ejpam-5917	100	44	:	:	PUNCT
ejpam-5917	100	45	g1	g1	PROPN
ejpam-5917	100	46	:	:	PUNCT
ejpam-5917	100	47	g2	g2	PROPN
ejpam-5917	100	48	:	:	PUNCT
ejpam-5917	100	49	g3	g3	NOUN
ejpam-5917	100	50	:	:	PUNCT
ejpam-5917	100	51	figure	figure	NOUN
ejpam-5917	100	52	1	1	NUM
ejpam-5917	100	53	:	:	PUNCT
ejpam-5917	100	54	a	a	DET
ejpam-5917	100	55	graph	graph	NOUN
ejpam-5917	100	56	g	g	NOUN
ejpam-5917	100	57	with	with	ADP
ejpam-5917	100	58	examples	example	NOUN
ejpam-5917	100	59	of	of	ADP
ejpam-5917	100	60	dominating	dominating	NOUN
ejpam-5917	100	61	sets	set	NOUN
ejpam-5917	100	62	,	,	PUNCT
ejpam-5917	100	63	where	where	SCONJ
ejpam-5917	100	64	g1	g1	PROPN
ejpam-5917	100	65	shows	show	VERB
ejpam-5917	100	66	a	a	DET
ejpam-5917	100	67	total	total	ADJ
ejpam-5917	100	68	safe	safe	ADJ
ejpam-5917	100	69	dominating	dominating	NOUN
ejpam-5917	100	70	set	set	NOUN
ejpam-5917	100	71	.	.	PUNCT
ejpam-5917	101	1	3.1	3.1	NUM
ejpam-5917	101	2	.	.	PUNCT
ejpam-5917	102	1	some	some	DET
ejpam-5917	102	2	realization	realization	NOUN
ejpam-5917	102	3	results	result	NOUN
ejpam-5917	102	4	on	on	ADP
ejpam-5917	102	5	total	total	ADJ
ejpam-5917	102	6	safe	safe	ADJ
ejpam-5917	102	7	domination	domination	NOUN
ejpam-5917	102	8	by	by	ADP
ejpam-5917	102	9	assumption	assumption	NOUN
ejpam-5917	102	10	,	,	PUNCT
ejpam-5917	102	11	g	g	PROPN
ejpam-5917	102	12	is	be	AUX
ejpam-5917	102	13	a	a	DET
ejpam-5917	102	14	nontrivial	nontrivial	ADJ
ejpam-5917	102	15	connected	connect	VERB
ejpam-5917	102	16	graph	graph	NOUN
ejpam-5917	102	17	.	.	PUNCT
ejpam-5917	103	1	hence	hence	ADV
ejpam-5917	103	2	,	,	PUNCT
ejpam-5917	103	3	the	the	DET
ejpam-5917	103	4	following	follow	VERB
ejpam-5917	103	5	remark	remark	NOUN
ejpam-5917	103	6	follows	follow	VERB
ejpam-5917	103	7	.	.	PUNCT
ejpam-5917	104	1	remark	remark	PROPN
ejpam-5917	104	2	1	1	NUM
ejpam-5917	104	3	.	.	PUNCT
ejpam-5917	105	1	let	let	VERB
ejpam-5917	105	2	g	g	PRON
ejpam-5917	105	3	be	be	AUX
ejpam-5917	105	4	a	a	DET
ejpam-5917	105	5	nontrivial	nontrivial	ADJ
ejpam-5917	105	6	connected	connect	VERB
ejpam-5917	105	7	graph	graph	NOUN
ejpam-5917	105	8	.	.	PUNCT
ejpam-5917	106	1	then	then	ADV
ejpam-5917	106	2	v	v	X
ejpam-5917	106	3	(	(	PUNCT
ejpam-5917	106	4	g	g	NOUN
ejpam-5917	106	5	)	)	PUNCT
ejpam-5917	106	6	is	be	AUX
ejpam-5917	106	7	a	a	DET
ejpam-5917	106	8	total	total	ADJ
ejpam-5917	106	9	safe	safe	ADJ
ejpam-5917	106	10	dominating	dominating	NOUN
ejpam-5917	106	11	set	set	NOUN
ejpam-5917	106	12	.	.	PUNCT
ejpam-5917	107	1	by	by	ADP
ejpam-5917	107	2	definition	definition	NOUN
ejpam-5917	107	3	,	,	PUNCT
ejpam-5917	107	4	the	the	DET
ejpam-5917	107	5	following	follow	VERB
ejpam-5917	107	6	remarks	remark	NOUN
ejpam-5917	107	7	also	also	ADV
ejpam-5917	107	8	follow	follow	VERB
ejpam-5917	107	9	.	.	PUNCT
ejpam-5917	108	1	remark	remark	NOUN
ejpam-5917	108	2	2	2	NUM
ejpam-5917	108	3	.	.	PUNCT
ejpam-5917	109	1	every	every	DET
ejpam-5917	109	2	total	total	ADJ
ejpam-5917	109	3	safe	safe	ADJ
ejpam-5917	109	4	dominating	dominating	NOUN
ejpam-5917	109	5	set	set	NOUN
ejpam-5917	109	6	of	of	ADP
ejpam-5917	109	7	a	a	DET
ejpam-5917	109	8	graph	graph	NOUN
ejpam-5917	109	9	g	g	NOUN
ejpam-5917	109	10	is	be	AUX
ejpam-5917	109	11	a	a	DET
ejpam-5917	109	12	safe	safe	ADJ
ejpam-5917	109	13	dominating	dominating	NOUN
ejpam-5917	109	14	set	set	NOUN
ejpam-5917	109	15	.	.	PUNCT
ejpam-5917	110	1	thus	thus	ADV
ejpam-5917	110	2	,	,	PUNCT
ejpam-5917	110	3	γs(g	γs(g	PUNCT
ejpam-5917	110	4	)	)	PUNCT
ejpam-5917	110	5	≤	≤	NUM
ejpam-5917	110	6	γts(g	γts(g	PROPN
ejpam-5917	110	7	)	)	PUNCT
ejpam-5917	110	8	.	.	PUNCT
ejpam-5917	111	1	remark	remark	PROPN
ejpam-5917	111	2	3	3	NUM
ejpam-5917	111	3	.	.	PUNCT
ejpam-5917	112	1	every	every	DET
ejpam-5917	112	2	total	total	ADJ
ejpam-5917	112	3	safe	safe	ADJ
ejpam-5917	112	4	dominating	dominating	NOUN
ejpam-5917	112	5	set	set	NOUN
ejpam-5917	112	6	of	of	ADP
ejpam-5917	112	7	a	a	DET
ejpam-5917	112	8	graph	graph	NOUN
ejpam-5917	112	9	g	g	NOUN
ejpam-5917	112	10	is	be	AUX
ejpam-5917	112	11	a	a	DET
ejpam-5917	112	12	total	total	ADJ
ejpam-5917	112	13	dominating	dominating	NOUN
ejpam-5917	112	14	set	set	NOUN
ejpam-5917	112	15	.	.	PUNCT
ejpam-5917	113	1	hence	hence	ADV
ejpam-5917	113	2	,	,	PUNCT
ejpam-5917	113	3	γt(g	γt(g	PUNCT
ejpam-5917	113	4	)	)	PUNCT
ejpam-5917	113	5	≤	≤	NUM
ejpam-5917	113	6	γts(g	γts(g	PROPN
ejpam-5917	113	7	)	)	PUNCT
ejpam-5917	113	8	.	.	PUNCT
ejpam-5917	114	1	theorem	theorem	NOUN
ejpam-5917	114	2	1	1	X
ejpam-5917	114	3	.	.	PUNCT
ejpam-5917	115	1	let	let	VERB
ejpam-5917	115	2	g	g	PRON
ejpam-5917	115	3	be	be	AUX
ejpam-5917	115	4	a	a	DET
ejpam-5917	115	5	nontrivial	nontrivial	ADJ
ejpam-5917	115	6	connected	connect	VERB
ejpam-5917	115	7	graph	graph	NOUN
ejpam-5917	115	8	and	and	CCONJ
ejpam-5917	115	9	s	s	AUX
ejpam-5917	115	10	⊊	⊊	VERB
ejpam-5917	115	11	v	v	NOUN
ejpam-5917	115	12	(	(	PUNCT
ejpam-5917	115	13	g	g	NOUN
ejpam-5917	115	14	)	)	PUNCT
ejpam-5917	115	15	be	be	AUX
ejpam-5917	115	16	a	a	DET
ejpam-5917	115	17	total	total	ADJ
ejpam-5917	115	18	dominating	dominating	NOUN
ejpam-5917	115	19	set	set	VERB
ejpam-5917	115	20	in	in	ADP
ejpam-5917	115	21	g.	g.	PROPN
ejpam-5917	115	22	then	then	ADV
ejpam-5917	115	23	γts(g	γts(g	PROPN
ejpam-5917	115	24	)	)	PUNCT
ejpam-5917	115	25	=	=	SYM
ejpam-5917	115	26	2	2	NUM
ejpam-5917	116	1	if	if	SCONJ
ejpam-5917	116	2	and	and	CCONJ
ejpam-5917	116	3	only	only	ADV
ejpam-5917	116	4	if	if	SCONJ
ejpam-5917	116	5	γt(g	γt(g	NOUN
ejpam-5917	116	6	)	)	PUNCT
ejpam-5917	116	7	=	=	SYM
ejpam-5917	116	8	2	2	NUM
ejpam-5917	116	9	and	and	CCONJ
ejpam-5917	116	10	for	for	ADP
ejpam-5917	116	11	every	every	DET
ejpam-5917	116	12	component	component	NOUN
ejpam-5917	116	13	b	b	PROPN
ejpam-5917	116	14	of	of	ADP
ejpam-5917	116	15	g[v	g[v	NOUN
ejpam-5917	116	16	(	(	PUNCT
ejpam-5917	116	17	g)∖	g)∖	PROPN
ejpam-5917	116	18	s	s	PROPN
ejpam-5917	116	19	]	]	X
ejpam-5917	116	20	,	,	PUNCT
ejpam-5917	116	21	|v	|v	PROPN
ejpam-5917	116	22	(	(	PUNCT
ejpam-5917	116	23	b)|	b)|	ADJ
ejpam-5917	116	24	≤	≤	NOUN
ejpam-5917	116	25	2	2	NUM
ejpam-5917	116	26	.	.	PUNCT
ejpam-5917	116	27	proof	proof	NOUN
ejpam-5917	116	28	.	.	PUNCT
ejpam-5917	117	1	assume	assume	VERB
ejpam-5917	117	2	that	that	SCONJ
ejpam-5917	117	3	g	g	PROPN
ejpam-5917	117	4	is	be	AUX
ejpam-5917	117	5	a	a	DET
ejpam-5917	117	6	nontrivial	nontrivial	ADJ
ejpam-5917	117	7	connected	connect	VERB
ejpam-5917	117	8	graph	graph	NOUN
ejpam-5917	117	9	and	and	CCONJ
ejpam-5917	117	10	s	s	AUX
ejpam-5917	117	11	⊊	⊊	VERB
ejpam-5917	117	12	v	v	NOUN
ejpam-5917	117	13	(	(	PUNCT
ejpam-5917	117	14	g	g	NOUN
ejpam-5917	117	15	)	)	PUNCT
ejpam-5917	117	16	is	be	AUX
ejpam-5917	117	17	a	a	DET
ejpam-5917	117	18	total	total	ADJ
ejpam-5917	117	19	dominating	dominating	NOUN
ejpam-5917	117	20	set	set	VERB
ejpam-5917	117	21	in	in	ADP
ejpam-5917	117	22	g.	g.	PROPN
ejpam-5917	117	23	suppose	suppose	VERB
ejpam-5917	117	24	that	that	SCONJ
ejpam-5917	117	25	γts(g	γts(g	PROPN
ejpam-5917	117	26	)	)	PUNCT
ejpam-5917	117	27	=	=	SYM
ejpam-5917	117	28	2	2	X
ejpam-5917	117	29	.	.	PUNCT
ejpam-5917	117	30	clearly	clearly	ADV
ejpam-5917	117	31	,	,	PUNCT
ejpam-5917	117	32	γt(g	γt(g	PUNCT
ejpam-5917	117	33	)	)	PUNCT
ejpam-5917	118	1	=	=	SYM
ejpam-5917	118	2	2	2	X
ejpam-5917	118	3	.	.	PUNCT
ejpam-5917	118	4	also	also	ADV
ejpam-5917	118	5	,	,	PUNCT
ejpam-5917	118	6	for	for	ADP
ejpam-5917	118	7	every	every	DET
ejpam-5917	118	8	component	component	NOUN
ejpam-5917	118	9	b	b	PROPN
ejpam-5917	118	10	of	of	ADP
ejpam-5917	118	11	g[v	g[v	NOUN
ejpam-5917	118	12	(	(	PUNCT
ejpam-5917	118	13	g)∖	g)∖	PROPN
ejpam-5917	118	14	s	s	PROPN
ejpam-5917	118	15	]	]	X
ejpam-5917	118	16	,	,	PUNCT
ejpam-5917	118	17	|v	|v	PROPN
ejpam-5917	118	18	(	(	PUNCT
ejpam-5917	118	19	g[s])|	g[s])|	X
ejpam-5917	118	20	≥	≥	PROPN
ejpam-5917	118	21	|v	|v	PROPN
ejpam-5917	118	22	(	(	PUNCT
ejpam-5917	118	23	b)|	b)|	NOUN
ejpam-5917	118	24	.	.	PUNCT
ejpam-5917	119	1	thus	thus	ADV
ejpam-5917	119	2	,	,	PUNCT
ejpam-5917	119	3	|v	|v	PROPN
ejpam-5917	119	4	(	(	PUNCT
ejpam-5917	119	5	b)|	b)|	ADJ
ejpam-5917	119	6	≤	≤	NOUN
ejpam-5917	119	7	2	2	NUM
ejpam-5917	119	8	.	.	PUNCT
ejpam-5917	119	9	w.	w.	PROPN
ejpam-5917	119	10	g.	g.	PROPN
ejpam-5917	119	11	jumalon	jumalon	PROPN
ejpam-5917	119	12	,	,	PUNCT
ejpam-5917	119	13	i.	i.	PROPN
ejpam-5917	119	14	cabahug	cabahug	PROPN
ejpam-5917	119	15	/	/	SYM
ejpam-5917	119	16	eur	eur	PROPN
ejpam-5917	119	17	.	.	PUNCT
ejpam-5917	120	1	j.	j.	PROPN
ejpam-5917	120	2	pure	pure	PROPN
ejpam-5917	120	3	appl	appl	PROPN
ejpam-5917	120	4	.	.	PROPN
ejpam-5917	120	5	math	math	PROPN
ejpam-5917	120	6	,	,	PUNCT
ejpam-5917	120	7	18	18	NUM
ejpam-5917	120	8	(	(	PUNCT
ejpam-5917	120	9	2	2	NUM
ejpam-5917	120	10	)	)	PUNCT
ejpam-5917	120	11	(	(	PUNCT
ejpam-5917	120	12	2025	2025	NUM
ejpam-5917	120	13	)	)	PUNCT
ejpam-5917	120	14	,	,	PUNCT
ejpam-5917	120	15	5917	5917	NUM
ejpam-5917	120	16	6	6	NUM
ejpam-5917	120	17	of	of	ADP
ejpam-5917	120	18	12	12	NUM
ejpam-5917	120	19	for	for	ADP
ejpam-5917	120	20	the	the	DET
ejpam-5917	120	21	converse	converse	NOUN
ejpam-5917	120	22	,	,	PUNCT
ejpam-5917	120	23	suppose	suppose	VERB
ejpam-5917	120	24	that	that	SCONJ
ejpam-5917	120	25	γt(g	γt(g	PUNCT
ejpam-5917	120	26	)	)	PUNCT
ejpam-5917	120	27	=	=	SYM
ejpam-5917	120	28	2	2	NUM
ejpam-5917	120	29	and	and	CCONJ
ejpam-5917	120	30	for	for	ADP
ejpam-5917	120	31	every	every	DET
ejpam-5917	120	32	component	component	NOUN
ejpam-5917	120	33	b	b	PROPN
ejpam-5917	120	34	of	of	ADP
ejpam-5917	120	35	g[v	g[v	NOUN
ejpam-5917	120	36	(	(	PUNCT
ejpam-5917	120	37	g)∖	g)∖	PROPN
ejpam-5917	120	38	s	s	PROPN
ejpam-5917	120	39	]	]	X
ejpam-5917	120	40	,	,	PUNCT
ejpam-5917	120	41	|v	|v	PROPN
ejpam-5917	120	42	(	(	PUNCT
ejpam-5917	120	43	b)|	b)|	ADJ
ejpam-5917	120	44	≤	≤	NOUN
ejpam-5917	120	45	2	2	NUM
ejpam-5917	120	46	.	.	PUNCT
ejpam-5917	121	1	then	then	ADV
ejpam-5917	121	2	,	,	PUNCT
ejpam-5917	121	3	γts(g	γts(g	PROPN
ejpam-5917	121	4	)	)	PUNCT
ejpam-5917	121	5	≥	≥	NOUN
ejpam-5917	121	6	2	2	NUM
ejpam-5917	121	7	.	.	PUNCT
ejpam-5917	121	8	since	since	SCONJ
ejpam-5917	121	9	γt(g	γt(g	NOUN
ejpam-5917	121	10	)	)	PUNCT
ejpam-5917	121	11	=	=	SYM
ejpam-5917	122	1	2	2	NUM
ejpam-5917	122	2	,	,	PUNCT
ejpam-5917	122	3	there	there	PRON
ejpam-5917	122	4	exists	exist	VERB
ejpam-5917	122	5	a	a	DET
ejpam-5917	122	6	total	total	ADJ
ejpam-5917	122	7	dominating	dominating	NOUN
ejpam-5917	122	8	set	set	NOUN
ejpam-5917	122	9	s	s	NOUN
ejpam-5917	122	10	with	with	ADP
ejpam-5917	122	11	|s|	|s|	NOUN
ejpam-5917	122	12	=	=	SYM
ejpam-5917	122	13	2	2	NUM
ejpam-5917	122	14	.	.	PUNCT
ejpam-5917	123	1	since	since	SCONJ
ejpam-5917	123	2	|v	|v	PROPN
ejpam-5917	123	3	(	(	PUNCT
ejpam-5917	123	4	b)|	b)|	ADJ
ejpam-5917	123	5	≤	≤	NOUN
ejpam-5917	123	6	2	2	NUM
ejpam-5917	123	7	for	for	ADP
ejpam-5917	123	8	every	every	DET
ejpam-5917	123	9	component	component	NOUN
ejpam-5917	123	10	b	b	PROPN
ejpam-5917	123	11	of	of	ADP
ejpam-5917	123	12	g[v	g[v	NOUN
ejpam-5917	123	13	(	(	PUNCT
ejpam-5917	123	14	g	g	NOUN
ejpam-5917	123	15	)	)	PUNCT
ejpam-5917	123	16	∖	∖	X
ejpam-5917	123	17	s	s	PART
ejpam-5917	123	18	]	]	X
ejpam-5917	123	19	,	,	PUNCT
ejpam-5917	123	20	and	and	CCONJ
ejpam-5917	123	21	since	since	SCONJ
ejpam-5917	123	22	|s|	|s|	PROPN
ejpam-5917	123	23	=	=	SYM
ejpam-5917	123	24	2	2	NUM
ejpam-5917	123	25	,	,	PUNCT
ejpam-5917	123	26	it	it	PRON
ejpam-5917	123	27	follows	follow	VERB
ejpam-5917	123	28	that	that	SCONJ
ejpam-5917	123	29	s	s	VERB
ejpam-5917	123	30	is	be	AUX
ejpam-5917	123	31	a	a	DET
ejpam-5917	123	32	safe	safe	ADJ
ejpam-5917	123	33	dominating	dominating	NOUN
ejpam-5917	123	34	set	set	VERB
ejpam-5917	123	35	in	in	ADP
ejpam-5917	123	36	g.	g.	PROPN
ejpam-5917	124	1	so	so	ADV
ejpam-5917	124	2	,	,	PUNCT
ejpam-5917	124	3	s	s	VERB
ejpam-5917	124	4	is	be	AUX
ejpam-5917	124	5	a	a	DET
ejpam-5917	124	6	total	total	ADJ
ejpam-5917	124	7	safe	safe	ADJ
ejpam-5917	124	8	dominating	dominating	NOUN
ejpam-5917	124	9	set	set	VERB
ejpam-5917	124	10	in	in	ADP
ejpam-5917	124	11	g.	g.	PROPN
ejpam-5917	124	12	this	this	PRON
ejpam-5917	124	13	implies	imply	VERB
ejpam-5917	124	14	that	that	SCONJ
ejpam-5917	124	15	γts(g	γts(g	PROPN
ejpam-5917	124	16	)	)	PUNCT
ejpam-5917	124	17	≤	≤	NUM
ejpam-5917	124	18	|s|	|s|	PROPN
ejpam-5917	124	19	=	=	SYM
ejpam-5917	124	20	2	2	NUM
ejpam-5917	124	21	.	.	PUNCT
ejpam-5917	124	22	hence	hence	ADV
ejpam-5917	124	23	,	,	PUNCT
ejpam-5917	124	24	γts(g	γts(g	PROPN
ejpam-5917	124	25	)	)	PUNCT
ejpam-5917	124	26	=	=	SYM
ejpam-5917	124	27	2	2	X
ejpam-5917	124	28	.	.	X
ejpam-5917	125	1	in	in	ADP
ejpam-5917	125	2	the	the	DET
ejpam-5917	125	3	following	follow	VERB
ejpam-5917	125	4	results	result	NOUN
ejpam-5917	125	5	,	,	PUNCT
ejpam-5917	125	6	we	we	PRON
ejpam-5917	125	7	show	show	VERB
ejpam-5917	125	8	by	by	ADP
ejpam-5917	125	9	construction	construction	NOUN
ejpam-5917	125	10	the	the	DET
ejpam-5917	125	11	existence	existence	NOUN
ejpam-5917	125	12	of	of	ADP
ejpam-5917	125	13	a	a	DET
ejpam-5917	125	14	graph	graph	NOUN
ejpam-5917	125	15	where	where	SCONJ
ejpam-5917	125	16	the	the	DET
ejpam-5917	125	17	parameters	parameter	NOUN
ejpam-5917	125	18	γts(g	γts(g	PRON
ejpam-5917	125	19	)	)	PUNCT
ejpam-5917	125	20	and	and	CCONJ
ejpam-5917	125	21	γt(g	γt(g	PUNCT
ejpam-5917	125	22	)	)	PUNCT
ejpam-5917	125	23	are	be	AUX
ejpam-5917	125	24	equal	equal	ADJ
ejpam-5917	125	25	,	,	PUNCT
ejpam-5917	125	26	strictly	strictly	ADV
ejpam-5917	125	27	unequal	unequal	ADJ
ejpam-5917	125	28	and	and	CCONJ
ejpam-5917	125	29	whose	whose	DET
ejpam-5917	125	30	difference	difference	NOUN
ejpam-5917	125	31	can	can	AUX
ejpam-5917	125	32	be	be	AUX
ejpam-5917	125	33	made	make	VERB
ejpam-5917	125	34	arbitrarily	arbitrarily	ADV
ejpam-5917	125	35	large	large	ADJ
ejpam-5917	125	36	.	.	PUNCT
ejpam-5917	126	1	theorem	theorem	NOUN
ejpam-5917	126	2	2	2	NUM
ejpam-5917	126	3	.	.	PUNCT
ejpam-5917	126	4	let	let	VERB
ejpam-5917	126	5	a	a	PRON
ejpam-5917	126	6	and	and	CCONJ
ejpam-5917	126	7	b	b	NOUN
ejpam-5917	126	8	be	be	AUX
ejpam-5917	126	9	positive	positive	ADJ
ejpam-5917	126	10	integers	integer	NOUN
ejpam-5917	126	11	such	such	ADJ
ejpam-5917	126	12	that	that	SCONJ
ejpam-5917	126	13	2	2	NUM
ejpam-5917	126	14	≤	≤	NUM
ejpam-5917	126	15	a	a	DET
ejpam-5917	126	16	≤	≤	PROPN
ejpam-5917	126	17	b.	b.	NOUN
ejpam-5917	127	1	then	then	ADV
ejpam-5917	127	2	there	there	PRON
ejpam-5917	127	3	exists	exist	VERB
ejpam-5917	127	4	a	a	DET
ejpam-5917	127	5	connected	connected	ADJ
ejpam-5917	127	6	graph	graph	NOUN
ejpam-5917	127	7	g	g	ADP
ejpam-5917	127	8	such	such	ADJ
ejpam-5917	127	9	that	that	PRON
ejpam-5917	127	10	γt(g	γt(g	PUNCT
ejpam-5917	127	11	)	)	PUNCT
ejpam-5917	127	12	=	=	SYM
ejpam-5917	127	13	a	a	PRON
ejpam-5917	127	14	and	and	CCONJ
ejpam-5917	127	15	γts(g	γts(g	NOUN
ejpam-5917	127	16	)	)	PUNCT
ejpam-5917	127	17	=	=	SYM
ejpam-5917	127	18	b.	b.	PROPN
ejpam-5917	127	19	proof	proof	NOUN
ejpam-5917	127	20	.	.	PUNCT
ejpam-5917	128	1	let	let	VERB
ejpam-5917	128	2	a	a	DET
ejpam-5917	128	3	,	,	PUNCT
ejpam-5917	128	4	b	b	PROPN
ejpam-5917	128	5	∈	∈	PROPN
ejpam-5917	128	6	z+	z+	NUM
ejpam-5917	128	7	and	and	CCONJ
ejpam-5917	128	8	consider	consider	VERB
ejpam-5917	128	9	the	the	DET
ejpam-5917	128	10	following	follow	VERB
ejpam-5917	128	11	cases	case	NOUN
ejpam-5917	128	12	:	:	PUNCT
ejpam-5917	128	13	case	case	NOUN
ejpam-5917	128	14	1	1	NUM
ejpam-5917	128	15	:	:	PUNCT
ejpam-5917	128	16	a	a	DET
ejpam-5917	128	17	=	=	X
ejpam-5917	128	18	b	b	NOUN
ejpam-5917	128	19	consider	consider	VERB
ejpam-5917	128	20	graph	graph	NOUN
ejpam-5917	128	21	g	g	NOUN
ejpam-5917	128	22	in	in	ADP
ejpam-5917	128	23	figure	figure	NOUN
ejpam-5917	128	24	2	2	NUM
ejpam-5917	128	25	.	.	PUNCT
ejpam-5917	128	26	take	take	VERB
ejpam-5917	128	27	a	a	DET
ejpam-5917	128	28	≥	≥	NOUN
ejpam-5917	128	29	m.	m.	NOUN
ejpam-5917	128	30	clearly	clearly	ADV
ejpam-5917	128	31	,	,	PUNCT
ejpam-5917	128	32	p	p	X
ejpam-5917	128	33	=	=	X
ejpam-5917	128	34	{	{	PUNCT
ejpam-5917	128	35	xi	xi	X
ejpam-5917	128	36	:	:	PUNCT
ejpam-5917	128	37	i	i	NOUN
ejpam-5917	128	38	=	=	NOUN
ejpam-5917	128	39	1	1	NUM
ejpam-5917	128	40	,	,	PUNCT
ejpam-5917	128	41	2	2	NUM
ejpam-5917	128	42	,	,	PUNCT
ejpam-5917	128	43	...	...	PUNCT
ejpam-5917	128	44	,	,	PUNCT
ejpam-5917	128	45	a	a	PRON
ejpam-5917	128	46	}	}	PUNCT
ejpam-5917	128	47	is	be	AUX
ejpam-5917	128	48	both	both	CCONJ
ejpam-5917	128	49	a	a	DET
ejpam-5917	128	50	minimum	minimum	ADJ
ejpam-5917	128	51	total	total	ADJ
ejpam-5917	128	52	dominating	dominating	NOUN
ejpam-5917	128	53	set	set	NOUN
ejpam-5917	128	54	and	and	CCONJ
ejpam-5917	128	55	a	a	DET
ejpam-5917	128	56	minimum	minimum	ADJ
ejpam-5917	128	57	total	total	ADJ
ejpam-5917	128	58	safe	safe	ADJ
ejpam-5917	128	59	dominating	dominating	NOUN
ejpam-5917	128	60	set	set	NOUN
ejpam-5917	128	61	.	.	PUNCT
ejpam-5917	129	1	thus	thus	ADV
ejpam-5917	129	2	,	,	PUNCT
ejpam-5917	129	3	2	2	NUM
ejpam-5917	129	4	≤	≤	NOUN
ejpam-5917	129	5	γt(g	γt(g	PUNCT
ejpam-5917	129	6	)	)	PUNCT
ejpam-5917	130	1	=	=	PRON
ejpam-5917	130	2	|p	|p	X
ejpam-5917	131	1	|	|	ADV
ejpam-5917	131	2	=	=	SYM
ejpam-5917	131	3	a	a	PROPN
ejpam-5917	131	4	=	=	SYM
ejpam-5917	131	5	b	b	PROPN
ejpam-5917	131	6	=	=	SYM
ejpam-5917	131	7	γts(g	γts(g	PROPN
ejpam-5917	131	8	)	)	PUNCT
ejpam-5917	131	9	.	.	PUNCT
ejpam-5917	132	1	x1	x1	NUM
ejpam-5917	133	1	x2	x2	PROPN
ejpam-5917	134	1	x3	x3	PROPN
ejpam-5917	134	2	xa−1	xa−1	PROPN
ejpam-5917	134	3	xa	xa	PROPN
ejpam-5917	134	4	y1	y1	NOUN
ejpam-5917	134	5	y2	y2	PROPN
ejpam-5917	134	6	y3	y3	NOUN
ejpam-5917	134	7	ym−1	ym−1	PROPN
ejpam-5917	134	8	ym	ym	PROPN
ejpam-5917	134	9	figure	figure	NOUN
ejpam-5917	134	10	2	2	NUM
ejpam-5917	134	11	:	:	PUNCT
ejpam-5917	134	12	a	a	DET
ejpam-5917	134	13	graph	graph	NOUN
ejpam-5917	134	14	g	g	NOUN
ejpam-5917	134	15	with	with	ADP
ejpam-5917	134	16	γt(g	γt(g	NOUN
ejpam-5917	134	17	)	)	PUNCT
ejpam-5917	134	18	=	=	SYM
ejpam-5917	135	1	a	a	DET
ejpam-5917	135	2	=	=	SYM
ejpam-5917	135	3	b	b	PROPN
ejpam-5917	135	4	=	=	SYM
ejpam-5917	135	5	γts(g	γts(g	PROPN
ejpam-5917	135	6	)	)	PUNCT
ejpam-5917	135	7	,	,	PUNCT
ejpam-5917	135	8	where	where	SCONJ
ejpam-5917	135	9	a	a	DET
ejpam-5917	135	10	≥	≥	NOUN
ejpam-5917	135	11	m.	m.	NOUN
ejpam-5917	135	12	w.	w.	PROPN
ejpam-5917	135	13	g.	g.	PROPN
ejpam-5917	135	14	jumalon	jumalon	PROPN
ejpam-5917	135	15	,	,	PUNCT
ejpam-5917	135	16	i.	i.	PROPN
ejpam-5917	135	17	cabahug	cabahug	PROPN
ejpam-5917	135	18	/	/	SYM
ejpam-5917	135	19	eur	eur	PROPN
ejpam-5917	135	20	.	.	PUNCT
ejpam-5917	136	1	j.	j.	PROPN
ejpam-5917	136	2	pure	pure	PROPN
ejpam-5917	136	3	appl	appl	PROPN
ejpam-5917	136	4	.	.	PROPN
ejpam-5917	136	5	math	math	PROPN
ejpam-5917	136	6	,	,	PUNCT
ejpam-5917	136	7	18	18	NUM
ejpam-5917	136	8	(	(	PUNCT
ejpam-5917	136	9	2	2	NUM
ejpam-5917	136	10	)	)	PUNCT
ejpam-5917	136	11	(	(	PUNCT
ejpam-5917	136	12	2025	2025	NUM
ejpam-5917	136	13	)	)	PUNCT
ejpam-5917	136	14	,	,	PUNCT
ejpam-5917	136	15	5917	5917	NUM
ejpam-5917	136	16	7	7	NUM
ejpam-5917	136	17	of	of	ADP
ejpam-5917	136	18	12	12	NUM
ejpam-5917	136	19	case	case	NOUN
ejpam-5917	136	20	2	2	NUM
ejpam-5917	136	21	:	:	PUNCT
ejpam-5917	136	22	a	a	DET
ejpam-5917	136	23	<	<	X
ejpam-5917	136	24	b	b	NOUN
ejpam-5917	136	25	consider	consider	VERB
ejpam-5917	136	26	graph	graph	NOUN
ejpam-5917	136	27	g	g	NOUN
ejpam-5917	136	28	in	in	ADP
ejpam-5917	136	29	figure	figure	NOUN
ejpam-5917	136	30	3	3	NUM
ejpam-5917	136	31	.	.	PUNCT
ejpam-5917	136	32	take	take	VERB
ejpam-5917	136	33	a	a	DET
ejpam-5917	136	34	<	<	X
ejpam-5917	136	35	m.	m.	NOUN
ejpam-5917	136	36	let	let	VERB
ejpam-5917	136	37	b	b	NOUN
ejpam-5917	136	38	=	=	PUNCT
ejpam-5917	136	39	|p	|p	PRON
ejpam-5917	136	40	∪	∪	PROPN
ejpam-5917	136	41	q|	q|	NOUN
ejpam-5917	136	42	,	,	PUNCT
ejpam-5917	136	43	where	where	SCONJ
ejpam-5917	136	44	p	p	NOUN
ejpam-5917	136	45	=	=	X
ejpam-5917	136	46	{	{	PUNCT
ejpam-5917	136	47	xi	xi	X
ejpam-5917	136	48	:	:	PUNCT
ejpam-5917	136	49	i	i	NOUN
ejpam-5917	136	50	=	=	NOUN
ejpam-5917	136	51	1	1	NUM
ejpam-5917	136	52	,	,	PUNCT
ejpam-5917	136	53	2	2	NUM
ejpam-5917	136	54	,	,	PUNCT
ejpam-5917	136	55	...	...	PUNCT
ejpam-5917	136	56	,	,	PUNCT
ejpam-5917	136	57	a	a	PRON
ejpam-5917	136	58	}	}	PUNCT
ejpam-5917	136	59	and	and	CCONJ
ejpam-5917	136	60	q	q	NOUN
ejpam-5917	136	61	=	=	PUNCT
ejpam-5917	136	62	{	{	PUNCT
ejpam-5917	136	63	yj	yj	PROPN
ejpam-5917	136	64	:	:	PUNCT
ejpam-5917	136	65	j	j	PROPN
ejpam-5917	136	66	=	=	SYM
ejpam-5917	136	67	1	1	NUM
ejpam-5917	136	68	,	,	PUNCT
ejpam-5917	136	69	2	2	NUM
ejpam-5917	136	70	,	,	PUNCT
ejpam-5917	136	71	...	...	PUNCT
ejpam-5917	136	72	,	,	PUNCT
ejpam-5917	136	73	y⌈m−a	y⌈m−a	NOUN
ejpam-5917	136	74	2	2	NUM
ejpam-5917	136	75	⌉	⌉	NOUN
ejpam-5917	136	76	}	}	PUNCT
ejpam-5917	136	77	.	.	PUNCT
ejpam-5917	137	1	then	then	ADV
ejpam-5917	137	2	,	,	PUNCT
ejpam-5917	137	3	γt(g	γt(g	PUNCT
ejpam-5917	137	4	)	)	PUNCT
ejpam-5917	137	5	=	=	PRON
ejpam-5917	137	6	|p	|p	X
ejpam-5917	138	1	|	|	ADV
ejpam-5917	138	2	=	=	SYM
ejpam-5917	138	3	a	a	PRON
ejpam-5917	138	4	and	and	CCONJ
ejpam-5917	138	5	γts(g	γts(g	NOUN
ejpam-5917	138	6	)	)	PUNCT
ejpam-5917	138	7	=	=	SYM
ejpam-5917	138	8	b	b	X
ejpam-5917	138	9	=	=	PUNCT
ejpam-5917	138	10	|p	|p	NOUN
ejpam-5917	138	11	∪q|	∪q|	NOUN
ejpam-5917	138	12	=	=	SYM
ejpam-5917	138	13	a+	a+	PUNCT
ejpam-5917	138	14	⌈	⌈	X
ejpam-5917	138	15	m−a	m−a	PROPN
ejpam-5917	138	16	2	2	NUM
ejpam-5917	138	17	⌉	⌉	NOUN
ejpam-5917	138	18	=	=	SYM
ejpam-5917	138	19	⌈	⌈	NOUN
ejpam-5917	138	20	a+m	a+m	NUM
ejpam-5917	138	21	2	2	NUM
ejpam-5917	138	22	⌉	⌉	X
ejpam-5917	138	23	.	.	PUNCT
ejpam-5917	139	1	hence	hence	ADV
ejpam-5917	139	2	,	,	PUNCT
ejpam-5917	139	3	γt(g	γt(g	PUNCT
ejpam-5917	139	4	)	)	PUNCT
ejpam-5917	139	5	=	=	PUNCT
ejpam-5917	139	6	a	a	DET
ejpam-5917	139	7	<	<	X
ejpam-5917	139	8	b	b	X
ejpam-5917	139	9	=	=	SYM
ejpam-5917	139	10	γts(g	γts(g	PROPN
ejpam-5917	139	11	)	)	PUNCT
ejpam-5917	139	12	.	.	PUNCT
ejpam-5917	140	1	x1	x1	NUM
ejpam-5917	141	1	x2	x2	PROPN
ejpam-5917	142	1	x3	x3	PROPN
ejpam-5917	142	2	xa−1	xa−1	PROPN
ejpam-5917	142	3	xa	xa	PROPN
ejpam-5917	142	4	y1	y1	NOUN
ejpam-5917	142	5	y2	y2	NOUN
ejpam-5917	142	6	y3	y3	NOUN
ejpam-5917	142	7	y⌈m−a	y⌈m−a	NOUN
ejpam-5917	142	8	2	2	NUM
ejpam-5917	142	9	⌉	⌉	PRON
ejpam-5917	142	10	y⌈m−a	y⌈m−a	NOUN
ejpam-5917	142	11	2	2	NUM
ejpam-5917	142	12	⌉+1	⌉+1	NUM
ejpam-5917	142	13	ym−1	ym−1	NOUN
ejpam-5917	142	14	ym	ym	PRON
ejpam-5917	142	15	figure	figure	NOUN
ejpam-5917	142	16	3	3	NUM
ejpam-5917	142	17	:	:	PUNCT
ejpam-5917	142	18	a	a	DET
ejpam-5917	142	19	graph	graph	NOUN
ejpam-5917	142	20	g	g	NOUN
ejpam-5917	142	21	with	with	ADP
ejpam-5917	142	22	γt(g	γt(g	NOUN
ejpam-5917	142	23	)	)	PUNCT
ejpam-5917	142	24	=	=	PUNCT
ejpam-5917	143	1	a	a	DET
ejpam-5917	143	2	<	<	X
ejpam-5917	143	3	b	b	X
ejpam-5917	143	4	=	=	SYM
ejpam-5917	143	5	γts(g	γts(g	PROPN
ejpam-5917	143	6	)	)	PUNCT
ejpam-5917	143	7	,	,	PUNCT
ejpam-5917	143	8	where	where	SCONJ
ejpam-5917	143	9	b	b	X
ejpam-5917	143	10	=	=	SYM
ejpam-5917	143	11	⌈	⌈	NOUN
ejpam-5917	143	12	a+m	a+m	NUM
ejpam-5917	143	13	2	2	NUM
ejpam-5917	143	14	⌉	⌉	X
ejpam-5917	143	15	.	.	PUNCT
ejpam-5917	144	1	this	this	PRON
ejpam-5917	144	2	completes	complete	VERB
ejpam-5917	144	3	the	the	DET
ejpam-5917	144	4	proof	proof	NOUN
ejpam-5917	144	5	.	.	PUNCT
ejpam-5917	145	1	from	from	ADP
ejpam-5917	145	2	theorem	theorem	NOUN
ejpam-5917	145	3	2	2	NUM
ejpam-5917	145	4	,	,	PUNCT
ejpam-5917	145	5	the	the	DET
ejpam-5917	145	6	following	follow	VERB
ejpam-5917	145	7	corollary	corollary	NOUN
ejpam-5917	145	8	immediately	immediately	ADV
ejpam-5917	145	9	follows	follow	VERB
ejpam-5917	145	10	.	.	PUNCT
ejpam-5917	146	1	corollary	corollary	ADJ
ejpam-5917	146	2	1	1	NUM
ejpam-5917	146	3	.	.	PUNCT
ejpam-5917	147	1	for	for	ADP
ejpam-5917	147	2	each	each	DET
ejpam-5917	147	3	positive	positive	ADJ
ejpam-5917	147	4	integer	integer	NOUN
ejpam-5917	147	5	n	n	CCONJ
ejpam-5917	147	6	,	,	PUNCT
ejpam-5917	147	7	there	there	PRON
ejpam-5917	147	8	exists	exist	VERB
ejpam-5917	147	9	a	a	DET
ejpam-5917	147	10	connected	connected	ADJ
ejpam-5917	147	11	graph	graph	NOUN
ejpam-5917	147	12	g	g	ADP
ejpam-5917	147	13	such	such	ADJ
ejpam-5917	147	14	that	that	DET
ejpam-5917	147	15	γts(g)−γt(g	γts(g)−γt(g	NOUN
ejpam-5917	147	16	)	)	PUNCT
ejpam-5917	147	17	=	=	SYM
ejpam-5917	148	1	n	n	CCONJ
ejpam-5917	148	2	,	,	PUNCT
ejpam-5917	148	3	that	that	ADV
ejpam-5917	148	4	is	is	ADV
ejpam-5917	148	5	,	,	PUNCT
ejpam-5917	148	6	the	the	DET
ejpam-5917	148	7	difference	difference	NOUN
ejpam-5917	148	8	between	between	ADP
ejpam-5917	148	9	γts(g	γts(g	PROPN
ejpam-5917	148	10	)	)	PUNCT
ejpam-5917	148	11	and	and	CCONJ
ejpam-5917	148	12	γt(g	γt(g	PUNCT
ejpam-5917	148	13	)	)	PUNCT
ejpam-5917	148	14	can	can	AUX
ejpam-5917	148	15	be	be	AUX
ejpam-5917	148	16	made	make	VERB
ejpam-5917	148	17	arbitrarily	arbitrarily	ADV
ejpam-5917	148	18	large	large	ADJ
ejpam-5917	148	19	.	.	PUNCT
ejpam-5917	149	1	3.2	3.2	NUM
ejpam-5917	149	2	.	.	PUNCT
ejpam-5917	149	3	results	result	NOUN
ejpam-5917	149	4	on	on	ADP
ejpam-5917	149	5	total	total	ADJ
ejpam-5917	149	6	safe	safe	ADJ
ejpam-5917	149	7	domination	domination	NOUN
ejpam-5917	149	8	on	on	ADP
ejpam-5917	149	9	some	some	DET
ejpam-5917	149	10	known	know	VERB
ejpam-5917	149	11	graph	graph	NOUN
ejpam-5917	149	12	families	family	NOUN
ejpam-5917	149	13	the	the	DET
ejpam-5917	149	14	following	follow	VERB
ejpam-5917	149	15	results	result	NOUN
ejpam-5917	149	16	give	give	VERB
ejpam-5917	149	17	the	the	DET
ejpam-5917	149	18	characterization	characterization	NOUN
ejpam-5917	149	19	of	of	ADP
ejpam-5917	149	20	total	total	ADJ
ejpam-5917	149	21	safe	safe	ADJ
ejpam-5917	149	22	dominating	dominating	NOUN
ejpam-5917	149	23	sets	set	NOUN
ejpam-5917	149	24	on	on	ADP
ejpam-5917	149	25	some	some	DET
ejpam-5917	149	26	well	well	ADV
ejpam-5917	149	27	-	-	PUNCT
ejpam-5917	149	28	known	know	VERB
ejpam-5917	149	29	graph	graph	NOUN
ejpam-5917	149	30	families	family	NOUN
ejpam-5917	149	31	.	.	PUNCT
ejpam-5917	150	1	theorem	theorem	NOUN
ejpam-5917	150	2	3	3	X
ejpam-5917	150	3	.	.	PUNCT
ejpam-5917	151	1	let	let	VERB
ejpam-5917	151	2	g	g	PRON
ejpam-5917	151	3	be	be	AUX
ejpam-5917	151	4	a	a	DET
ejpam-5917	151	5	nontrivial	nontrivial	ADJ
ejpam-5917	151	6	connected	connect	VERB
ejpam-5917	151	7	graph	graph	NOUN
ejpam-5917	151	8	of	of	ADP
ejpam-5917	151	9	order	order	NOUN
ejpam-5917	151	10	n	n	PRON
ejpam-5917	151	11	such	such	ADJ
ejpam-5917	151	12	that	that	DET
ejpam-5917	151	13	∆(g	∆(g	NOUN
ejpam-5917	151	14	)	)	PUNCT
ejpam-5917	151	15	=	=	SYM
ejpam-5917	152	1	2	2	X
ejpam-5917	152	2	.	.	PUNCT
ejpam-5917	152	3	then	then	ADV
ejpam-5917	152	4	a	a	DET
ejpam-5917	152	5	nonempty	nonempty	ADJ
ejpam-5917	152	6	set	set	VERB
ejpam-5917	152	7	s	s	PRON
ejpam-5917	152	8	⊊	⊊	NOUN
ejpam-5917	152	9	v	v	NOUN
ejpam-5917	152	10	(	(	PUNCT
ejpam-5917	152	11	g	g	NOUN
ejpam-5917	152	12	)	)	PUNCT
ejpam-5917	152	13	is	be	AUX
ejpam-5917	152	14	a	a	DET
ejpam-5917	152	15	total	total	ADJ
ejpam-5917	152	16	safe	safe	ADJ
ejpam-5917	152	17	dominating	dominating	NOUN
ejpam-5917	152	18	set	set	VERB
ejpam-5917	152	19	in	in	ADP
ejpam-5917	152	20	g	g	PROPN
ejpam-5917	152	21	if	if	SCONJ
ejpam-5917	153	1	and	and	CCONJ
ejpam-5917	153	2	only	only	ADV
ejpam-5917	153	3	if	if	SCONJ
ejpam-5917	153	4	every	every	DET
ejpam-5917	153	5	component	component	NOUN
ejpam-5917	153	6	of	of	ADP
ejpam-5917	153	7	g[s	g[s	PROPN
ejpam-5917	153	8	]	]	PUNCT
ejpam-5917	153	9	is	be	AUX
ejpam-5917	153	10	a	a	DET
ejpam-5917	153	11	pk	pk	NOUN
ejpam-5917	153	12	,	,	PUNCT
ejpam-5917	153	13	2	2	NUM
ejpam-5917	153	14	≤	≤	NUM
ejpam-5917	153	15	k	k	X
ejpam-5917	153	16	≤	≤	PROPN
ejpam-5917	153	17	n−	n−	PROPN
ejpam-5917	153	18	1	1	NUM
ejpam-5917	153	19	,	,	PUNCT
ejpam-5917	153	20	and	and	CCONJ
ejpam-5917	153	21	every	every	DET
ejpam-5917	153	22	component	component	NOUN
ejpam-5917	153	23	of	of	ADP
ejpam-5917	153	24	g[v	g[v	NOUN
ejpam-5917	153	25	(	(	PUNCT
ejpam-5917	153	26	g)∖	g)∖	PROPN
ejpam-5917	153	27	s	s	PROPN
ejpam-5917	153	28	]	]	X
ejpam-5917	153	29	is	be	AUX
ejpam-5917	153	30	a	a	DET
ejpam-5917	153	31	trivial	trivial	ADJ
ejpam-5917	153	32	graph	graph	NOUN
ejpam-5917	153	33	or	or	CCONJ
ejpam-5917	153	34	a	a	DET
ejpam-5917	153	35	p2	p2	NOUN
ejpam-5917	153	36	with	with	ADP
ejpam-5917	153	37	no	no	DET
ejpam-5917	153	38	end	end	NOUN
ejpam-5917	153	39	vertex	vertex	NOUN
ejpam-5917	153	40	in	in	ADP
ejpam-5917	153	41	g.	g.	PROPN
ejpam-5917	153	42	proof	proof	PROPN
ejpam-5917	153	43	.	.	PUNCT
ejpam-5917	154	1	assume	assume	VERB
ejpam-5917	154	2	that	that	SCONJ
ejpam-5917	154	3	s	s	VERB
ejpam-5917	154	4	is	be	AUX
ejpam-5917	154	5	a	a	DET
ejpam-5917	154	6	total	total	ADJ
ejpam-5917	154	7	safe	safe	ADJ
ejpam-5917	154	8	dominating	dominating	NOUN
ejpam-5917	154	9	set	set	VERB
ejpam-5917	154	10	in	in	ADP
ejpam-5917	154	11	g.	g.	PROPN
ejpam-5917	154	12	suppose	suppose	VERB
ejpam-5917	154	13	that	that	SCONJ
ejpam-5917	154	14	there	there	PRON
ejpam-5917	154	15	exists	exist	VERB
ejpam-5917	154	16	a	a	DET
ejpam-5917	154	17	component	component	NOUN
ejpam-5917	154	18	of	of	ADP
ejpam-5917	154	19	g[s	g[	NOUN
ejpam-5917	154	20	]	]	PUNCT
ejpam-5917	154	21	that	that	PRON
ejpam-5917	154	22	is	be	AUX
ejpam-5917	154	23	a	a	DET
ejpam-5917	154	24	p1	p1	NOUN
ejpam-5917	154	25	,	,	PUNCT
ejpam-5917	154	26	or	or	CCONJ
ejpam-5917	154	27	there	there	PRON
ejpam-5917	154	28	exists	exist	VERB
ejpam-5917	154	29	a	a	DET
ejpam-5917	154	30	component	component	NOUN
ejpam-5917	154	31	of	of	ADP
ejpam-5917	154	32	g[v	g[v	NOUN
ejpam-5917	154	33	(	(	PUNCT
ejpam-5917	154	34	g)∖	g)∖	PROPN
ejpam-5917	154	35	s	s	PROPN
ejpam-5917	154	36	]	]	X
ejpam-5917	154	37	that	that	PRON
ejpam-5917	154	38	is	be	AUX
ejpam-5917	154	39	not	not	PART
ejpam-5917	154	40	a	a	DET
ejpam-5917	154	41	trivial	trivial	ADJ
ejpam-5917	154	42	graph	graph	NOUN
ejpam-5917	154	43	and	and	CCONJ
ejpam-5917	154	44	a	a	DET
ejpam-5917	154	45	p2	p2	NOUN
ejpam-5917	154	46	with	with	ADP
ejpam-5917	154	47	an	an	DET
ejpam-5917	154	48	end	end	NOUN
ejpam-5917	154	49	vertex	vertex	NOUN
ejpam-5917	154	50	in	in	ADP
ejpam-5917	154	51	g.	g.	PROPN
ejpam-5917	154	52	the	the	DET
ejpam-5917	154	53	first	first	ADJ
ejpam-5917	154	54	part	part	NOUN
ejpam-5917	154	55	implies	imply	VERB
ejpam-5917	154	56	that	that	SCONJ
ejpam-5917	154	57	g[s	g[s	PROPN
ejpam-5917	154	58	]	]	PUNCT
ejpam-5917	154	59	contains	contain	VERB
ejpam-5917	154	60	an	an	DET
ejpam-5917	154	61	isolated	isolated	ADJ
ejpam-5917	154	62	vertex	vertex	NOUN
ejpam-5917	154	63	and	and	CCONJ
ejpam-5917	154	64	the	the	DET
ejpam-5917	154	65	latter	latter	ADJ
ejpam-5917	154	66	implies	imply	VERB
ejpam-5917	154	67	that	that	SCONJ
ejpam-5917	154	68	s	s	VERB
ejpam-5917	154	69	is	be	AUX
ejpam-5917	154	70	not	not	PART
ejpam-5917	154	71	a	a	DET
ejpam-5917	154	72	dominating	dominating	NOUN
ejpam-5917	154	73	set	set	NOUN
ejpam-5917	154	74	.	.	PUNCT
ejpam-5917	155	1	both	both	DET
ejpam-5917	155	2	implications	implication	NOUN
ejpam-5917	155	3	contradict	contradict	VERB
ejpam-5917	155	4	the	the	DET
ejpam-5917	155	5	assumption	assumption	NOUN
ejpam-5917	155	6	of	of	ADP
ejpam-5917	155	7	s.	s.	PROPN
ejpam-5917	155	8	thus	thus	ADV
ejpam-5917	155	9	,	,	PUNCT
ejpam-5917	155	10	every	every	DET
ejpam-5917	155	11	component	component	NOUN
ejpam-5917	155	12	of	of	ADP
ejpam-5917	155	13	g[s	g[s	PROPN
ejpam-5917	155	14	]	]	PUNCT
ejpam-5917	155	15	is	be	AUX
ejpam-5917	155	16	a	a	DET
ejpam-5917	155	17	pk	pk	NOUN
ejpam-5917	155	18	,	,	PUNCT
ejpam-5917	155	19	2	2	NUM
ejpam-5917	155	20	≤	≤	NUM
ejpam-5917	155	21	k	k	NOUN
ejpam-5917	155	22	≤	≤	PROPN
ejpam-5917	155	23	n	n	CCONJ
ejpam-5917	155	24	−	−	PROPN
ejpam-5917	155	25	1	1	NUM
ejpam-5917	155	26	,	,	PUNCT
ejpam-5917	155	27	and	and	CCONJ
ejpam-5917	155	28	every	every	DET
ejpam-5917	155	29	component	component	NOUN
ejpam-5917	155	30	of	of	ADP
ejpam-5917	155	31	g[v	g[v	NOUN
ejpam-5917	155	32	(	(	PUNCT
ejpam-5917	155	33	g)∖	g)∖	PROPN
ejpam-5917	155	34	s	s	PROPN
ejpam-5917	155	35	]	]	X
ejpam-5917	155	36	is	be	AUX
ejpam-5917	155	37	a	a	DET
ejpam-5917	155	38	trivial	trivial	ADJ
ejpam-5917	155	39	graph	graph	NOUN
ejpam-5917	155	40	or	or	CCONJ
ejpam-5917	155	41	a	a	DET
ejpam-5917	155	42	p2	p2	NOUN
ejpam-5917	155	43	with	with	ADP
ejpam-5917	155	44	no	no	DET
ejpam-5917	155	45	end	end	NOUN
ejpam-5917	155	46	vertex	vertex	NOUN
ejpam-5917	155	47	in	in	ADP
ejpam-5917	155	48	g.	g.	PROPN
ejpam-5917	155	49	for	for	ADP
ejpam-5917	155	50	the	the	DET
ejpam-5917	155	51	converse	converse	NOUN
ejpam-5917	155	52	,	,	PUNCT
ejpam-5917	155	53	suppose	suppose	VERB
ejpam-5917	155	54	that	that	SCONJ
ejpam-5917	155	55	s	s	VERB
ejpam-5917	155	56	⊊	⊊	VERB
ejpam-5917	155	57	v	v	NOUN
ejpam-5917	155	58	(	(	PUNCT
ejpam-5917	155	59	g	g	NOUN
ejpam-5917	155	60	)	)	PUNCT
ejpam-5917	155	61	such	such	ADJ
ejpam-5917	155	62	that	that	SCONJ
ejpam-5917	155	63	every	every	DET
ejpam-5917	155	64	component	component	NOUN
ejpam-5917	155	65	of	of	ADP
ejpam-5917	155	66	g[s	g[s	PROPN
ejpam-5917	155	67	]	]	PUNCT
ejpam-5917	155	68	is	be	AUX
ejpam-5917	155	69	a	a	DET
ejpam-5917	155	70	pk	pk	NOUN
ejpam-5917	155	71	,	,	PUNCT
ejpam-5917	155	72	2	2	NUM
ejpam-5917	155	73	≤	≤	NUM
ejpam-5917	155	74	k	k	X
ejpam-5917	155	75	≤	≤	PROPN
ejpam-5917	155	76	n−	n−	PROPN
ejpam-5917	155	77	1	1	NUM
ejpam-5917	155	78	,	,	PUNCT
ejpam-5917	155	79	and	and	CCONJ
ejpam-5917	155	80	every	every	DET
ejpam-5917	155	81	component	component	NOUN
ejpam-5917	155	82	of	of	ADP
ejpam-5917	155	83	g[v	g[v	NOUN
ejpam-5917	155	84	(	(	PUNCT
ejpam-5917	155	85	g)∖s	g)∖	NOUN
ejpam-5917	155	86	]	]	PUNCT
ejpam-5917	155	87	is	be	AUX
ejpam-5917	155	88	a	a	DET
ejpam-5917	155	89	trivial	trivial	ADJ
ejpam-5917	155	90	graph	graph	NOUN
ejpam-5917	155	91	or	or	CCONJ
ejpam-5917	155	92	a	a	DET
ejpam-5917	155	93	p2	p2	NOUN
ejpam-5917	155	94	with	with	SCONJ
ejpam-5917	155	95	no	no	DET
ejpam-5917	155	96	end	end	NOUN
ejpam-5917	155	97	vertex	vertex	NOUN
ejpam-5917	155	98	in	in	ADP
ejpam-5917	155	99	g.	g.	PROPN
ejpam-5917	155	100	clearyly	clearyly	PROPN
ejpam-5917	155	101	,	,	PUNCT
ejpam-5917	155	102	g[s	g[s	PROPN
ejpam-5917	155	103	]	]	PUNCT
ejpam-5917	155	104	has	have	VERB
ejpam-5917	155	105	no	no	DET
ejpam-5917	155	106	isolated	isolated	ADJ
ejpam-5917	155	107	vertex	vertex	NOUN
ejpam-5917	155	108	and	and	CCONJ
ejpam-5917	155	109	s	s	NOUN
ejpam-5917	155	110	is	be	AUX
ejpam-5917	155	111	a	a	DET
ejpam-5917	155	112	dominating	dominating	NOUN
ejpam-5917	155	113	set	set	NOUN
ejpam-5917	155	114	.	.	PUNCT
ejpam-5917	156	1	if	if	SCONJ
ejpam-5917	156	2	a	a	PRON
ejpam-5917	156	3	and	and	CCONJ
ejpam-5917	156	4	b	b	NOUN
ejpam-5917	156	5	are	be	AUX
ejpam-5917	156	6	components	component	NOUN
ejpam-5917	156	7	of	of	ADP
ejpam-5917	156	8	g[s	g[	NOUN
ejpam-5917	156	9	]	]	PUNCT
ejpam-5917	156	10	and	and	CCONJ
ejpam-5917	156	11	g[v	g[v	NOUN
ejpam-5917	156	12	(	(	PUNCT
ejpam-5917	156	13	g)∖	g)∖	PROPN
ejpam-5917	156	14	s	s	PROPN
ejpam-5917	156	15	]	]	X
ejpam-5917	156	16	,	,	PUNCT
ejpam-5917	156	17	respectively	respectively	ADV
ejpam-5917	156	18	,	,	PUNCT
ejpam-5917	156	19	then	then	ADV
ejpam-5917	156	20	|v	|v	PROPN
ejpam-5917	156	21	(	(	PUNCT
ejpam-5917	156	22	a)|	a)|	X
ejpam-5917	156	23	≥	≥	NOUN
ejpam-5917	156	24	|v	|v	PROPN
ejpam-5917	156	25	(	(	PUNCT
ejpam-5917	156	26	b)|	b)|	PROPN
ejpam-5917	156	27	.	.	PUNCT
ejpam-5917	157	1	therefore	therefore	ADV
ejpam-5917	157	2	,	,	PUNCT
ejpam-5917	157	3	s	s	VERB
ejpam-5917	157	4	is	be	AUX
ejpam-5917	157	5	a	a	DET
ejpam-5917	157	6	total	total	ADJ
ejpam-5917	157	7	safe	safe	ADJ
ejpam-5917	157	8	dominating	dominating	NOUN
ejpam-5917	157	9	set	set	VERB
ejpam-5917	157	10	in	in	ADP
ejpam-5917	157	11	g.	g.	PROPN
ejpam-5917	157	12	w.	w.	PROPN
ejpam-5917	157	13	g.	g.	PROPN
ejpam-5917	157	14	jumalon	jumalon	PROPN
ejpam-5917	157	15	,	,	PUNCT
ejpam-5917	157	16	i.	i.	PROPN
ejpam-5917	157	17	cabahug	cabahug	PROPN
ejpam-5917	157	18	/	/	SYM
ejpam-5917	157	19	eur	eur	PROPN
ejpam-5917	157	20	.	.	PUNCT
ejpam-5917	158	1	j.	j.	PROPN
ejpam-5917	158	2	pure	pure	PROPN
ejpam-5917	158	3	appl	appl	PROPN
ejpam-5917	158	4	.	.	PROPN
ejpam-5917	158	5	math	math	PROPN
ejpam-5917	158	6	,	,	PUNCT
ejpam-5917	158	7	18	18	NUM
ejpam-5917	158	8	(	(	PUNCT
ejpam-5917	158	9	2	2	NUM
ejpam-5917	158	10	)	)	PUNCT
ejpam-5917	158	11	(	(	PUNCT
ejpam-5917	158	12	2025	2025	NUM
ejpam-5917	158	13	)	)	PUNCT
ejpam-5917	158	14	,	,	PUNCT
ejpam-5917	158	15	5917	5917	NUM
ejpam-5917	158	16	8	8	NUM
ejpam-5917	158	17	of	of	ADP
ejpam-5917	158	18	12	12	NUM
ejpam-5917	158	19	corollary	corollary	ADJ
ejpam-5917	158	20	2	2	NUM
ejpam-5917	158	21	.	.	PUNCT
ejpam-5917	158	22	for	for	ADP
ejpam-5917	158	23	n	n	PRON
ejpam-5917	158	24	≥	≥	NUM
ejpam-5917	158	25	3	3	NUM
ejpam-5917	158	26	,	,	PUNCT
ejpam-5917	158	27	γts(pn	γts(pn	NOUN
ejpam-5917	158	28	)	)	PUNCT
ejpam-5917	158	29	=	=	SYM
ejpam-5917	158	30	γts(cn	γts(cn	NOUN
ejpam-5917	158	31	)	)	PUNCT
ejpam-5917	158	32	=	=	PUNCT
ejpam-5917	159	1			PROPN
ejpam-5917	159	2	n	n	PRON
ejpam-5917	159	3	2	2	NUM
ejpam-5917	159	4	,	,	PUNCT
ejpam-5917	159	5	if	if	SCONJ
ejpam-5917	159	6	n	n	PRON
ejpam-5917	159	7	≡	≡	PROPN
ejpam-5917	159	8	0(mod	0(mod	NOUN
ejpam-5917	159	9	4	4	X
ejpam-5917	159	10	)	)	PUNCT
ejpam-5917	159	11	n+1	n+1	NUM
ejpam-5917	159	12	2	2	NUM
ejpam-5917	159	13	,	,	PUNCT
ejpam-5917	159	14	if	if	SCONJ
ejpam-5917	159	15	n	n	PRON
ejpam-5917	159	16	≡	≡	PROPN
ejpam-5917	159	17	1	1	NUM
ejpam-5917	159	18	or	or	CCONJ
ejpam-5917	159	19	3(mod	3(mod	NUM
ejpam-5917	159	20	4	4	NUM
ejpam-5917	159	21	)	)	PUNCT
ejpam-5917	159	22	n+2	n+2	NUM
ejpam-5917	159	23	2	2	NUM
ejpam-5917	159	24	,	,	PUNCT
ejpam-5917	159	25	if	if	SCONJ
ejpam-5917	159	26	n	n	PRON
ejpam-5917	159	27	≡	≡	PROPN
ejpam-5917	159	28	2(mod	2(mod	NUM
ejpam-5917	159	29	4	4	NUM
ejpam-5917	159	30	)	)	PUNCT
ejpam-5917	159	31	.	.	PUNCT
ejpam-5917	160	1	proof	proof	NOUN
ejpam-5917	160	2	.	.	PUNCT
ejpam-5917	161	1	let	let	VERB
ejpam-5917	161	2	pn	pn	VERB
ejpam-5917	161	3	=	=	PUNCT
ejpam-5917	162	1	[	[	X
ejpam-5917	162	2	v1	v1	NOUN
ejpam-5917	162	3	,	,	PUNCT
ejpam-5917	162	4	v2	v2	PROPN
ejpam-5917	162	5	,	,	PUNCT
ejpam-5917	162	6	...	...	PUNCT
ejpam-5917	162	7	,	,	PUNCT
ejpam-5917	162	8	vn	vn	X
ejpam-5917	162	9	]	]	PUNCT
ejpam-5917	162	10	and	and	CCONJ
ejpam-5917	162	11	s	s	VERB
ejpam-5917	162	12	⊊	⊊	VERB
ejpam-5917	162	13	v	v	NOUN
ejpam-5917	162	14	(	(	PUNCT
ejpam-5917	162	15	pn	pn	NOUN
ejpam-5917	162	16	)	)	PUNCT
ejpam-5917	162	17	.	.	PUNCT
ejpam-5917	163	1	consider	consider	VERB
ejpam-5917	163	2	the	the	DET
ejpam-5917	163	3	following	follow	VERB
ejpam-5917	163	4	cases	case	NOUN
ejpam-5917	163	5	:	:	PUNCT
ejpam-5917	163	6	case	case	NOUN
ejpam-5917	163	7	1	1	NUM
ejpam-5917	163	8	:	:	PUNCT
ejpam-5917	163	9	n	n	NUM
ejpam-5917	163	10	≡	≡	PROPN
ejpam-5917	163	11	0(mod	0(mod	NOUN
ejpam-5917	163	12	4	4	X
ejpam-5917	163	13	)	)	PUNCT
ejpam-5917	163	14	choose	choose	VERB
ejpam-5917	163	15	s	s	NOUN
ejpam-5917	163	16	=	=	PUNCT
ejpam-5917	163	17	{	{	PUNCT
ejpam-5917	163	18	v2	v2	PROPN
ejpam-5917	163	19	,	,	PUNCT
ejpam-5917	163	20	v3	v3	PROPN
ejpam-5917	163	21	,	,	PUNCT
ejpam-5917	163	22	v6	v6	NOUN
ejpam-5917	163	23	,	,	PUNCT
ejpam-5917	163	24	v7	v7	VERB
ejpam-5917	163	25	,	,	PUNCT
ejpam-5917	163	26	...	...	PUNCT
ejpam-5917	163	27	,	,	PUNCT
ejpam-5917	163	28	vn−2	vn−2	PROPN
ejpam-5917	163	29	,	,	PUNCT
ejpam-5917	163	30	vn−1	vn−1	ADJ
ejpam-5917	163	31	}	}	PUNCT
ejpam-5917	163	32	.	.	PUNCT
ejpam-5917	164	1	then	then	ADV
ejpam-5917	164	2	,	,	PUNCT
ejpam-5917	164	3	|s|	|s|	PROPN
ejpam-5917	164	4	=	=	SYM
ejpam-5917	164	5	n	n	PRON
ejpam-5917	164	6	2	2	NUM
ejpam-5917	164	7	.	.	PUNCT
ejpam-5917	165	1	by	by	ADP
ejpam-5917	165	2	theorem	theorem	NOUN
ejpam-5917	165	3	3	3	NUM
ejpam-5917	165	4	,	,	PUNCT
ejpam-5917	165	5	s	s	VERB
ejpam-5917	165	6	is	be	AUX
ejpam-5917	165	7	a	a	DET
ejpam-5917	165	8	total	total	ADJ
ejpam-5917	165	9	safe	safe	ADJ
ejpam-5917	165	10	dominating	dominating	NOUN
ejpam-5917	165	11	set	set	VERB
ejpam-5917	165	12	in	in	ADP
ejpam-5917	165	13	pn	pn	PROPN
ejpam-5917	165	14	.	.	PUNCT
ejpam-5917	166	1	thus	thus	ADV
ejpam-5917	166	2	,	,	PUNCT
ejpam-5917	166	3	γts(pn	γts(pn	NOUN
ejpam-5917	166	4	)	)	PUNCT
ejpam-5917	166	5	≤	≤	NUM
ejpam-5917	166	6	|s|	|s|	PROPN
ejpam-5917	166	7	=	=	PROPN
ejpam-5917	166	8	n	n	PRON
ejpam-5917	166	9	2	2	NUM
ejpam-5917	166	10	.	.	PUNCT
ejpam-5917	167	1	by	by	ADP
ejpam-5917	167	2	vertex	vertex	NOUN
ejpam-5917	167	3	selection	selection	NOUN
ejpam-5917	167	4	and	and	CCONJ
ejpam-5917	167	5	labeling	labeling	NOUN
ejpam-5917	167	6	,	,	PUNCT
ejpam-5917	167	7	we	we	PRON
ejpam-5917	167	8	can	can	AUX
ejpam-5917	167	9	not	not	PART
ejpam-5917	167	10	find	find	VERB
ejpam-5917	167	11	a	a	DET
ejpam-5917	167	12	total	total	ADJ
ejpam-5917	167	13	safe	safe	ADJ
ejpam-5917	167	14	dominating	dominating	NOUN
ejpam-5917	167	15	set	set	VERB
ejpam-5917	167	16	in	in	ADP
ejpam-5917	167	17	pn	pn	PROPN
ejpam-5917	167	18	with	with	ADP
ejpam-5917	167	19	cardinality	cardinality	NOUN
ejpam-5917	167	20	less	less	ADJ
ejpam-5917	167	21	than	than	ADP
ejpam-5917	167	22	the	the	DET
ejpam-5917	167	23	cardinality	cardinality	NOUN
ejpam-5917	167	24	of	of	ADP
ejpam-5917	167	25	s.	s.	PROPN
ejpam-5917	167	26	therefore	therefore	ADV
ejpam-5917	167	27	,	,	PUNCT
ejpam-5917	167	28	γts(pn	γts(pn	NOUN
ejpam-5917	167	29	)	)	PUNCT
ejpam-5917	167	30	=	=	PUNCT
ejpam-5917	167	31	|s|	|s|	NOUN
ejpam-5917	167	32	=	=	PROPN
ejpam-5917	167	33	n	n	PRON
ejpam-5917	167	34	2	2	NUM
ejpam-5917	167	35	.	.	PUNCT
ejpam-5917	168	1	case	case	NOUN
ejpam-5917	168	2	2	2	NUM
ejpam-5917	168	3	:	:	PUNCT
ejpam-5917	168	4	n	n	NUM
ejpam-5917	168	5	≡	≡	PROPN
ejpam-5917	168	6	1(mod	1(mod	NUM
ejpam-5917	168	7	4	4	X
ejpam-5917	168	8	)	)	PUNCT
ejpam-5917	168	9	choose	choose	VERB
ejpam-5917	168	10	s	s	NOUN
ejpam-5917	168	11	=	=	PUNCT
ejpam-5917	168	12	{	{	PUNCT
ejpam-5917	168	13	v2	v2	PROPN
ejpam-5917	168	14	,	,	PUNCT
ejpam-5917	168	15	v3	v3	PROPN
ejpam-5917	168	16	,	,	PUNCT
ejpam-5917	168	17	v4	v4	NOUN
ejpam-5917	168	18	,	,	PUNCT
ejpam-5917	168	19	v7	v7	NUM
ejpam-5917	168	20	,	,	PUNCT
ejpam-5917	168	21	v8	v8	PROPN
ejpam-5917	168	22	,	,	PUNCT
ejpam-5917	168	23	...	...	PUNCT
ejpam-5917	168	24	,	,	PUNCT
ejpam-5917	168	25	vn−2	vn−2	PROPN
ejpam-5917	168	26	,	,	PUNCT
ejpam-5917	168	27	vn−1	vn−1	ADJ
ejpam-5917	168	28	}	}	PUNCT
ejpam-5917	168	29	.	.	PUNCT
ejpam-5917	169	1	then	then	ADV
ejpam-5917	169	2	,	,	PUNCT
ejpam-5917	169	3	|s|	|s|	PROPN
ejpam-5917	169	4	=	=	SYM
ejpam-5917	169	5	n+1	n+1	PROPN
ejpam-5917	169	6	2	2	NUM
ejpam-5917	169	7	.	.	PUNCT
ejpam-5917	170	1	by	by	ADP
ejpam-5917	170	2	theorem	theorem	NOUN
ejpam-5917	170	3	3	3	NUM
ejpam-5917	170	4	,	,	PUNCT
ejpam-5917	170	5	s	s	VERB
ejpam-5917	170	6	is	be	AUX
ejpam-5917	170	7	a	a	DET
ejpam-5917	170	8	total	total	ADJ
ejpam-5917	170	9	safe	safe	ADJ
ejpam-5917	170	10	dominating	dominating	NOUN
ejpam-5917	170	11	set	set	VERB
ejpam-5917	170	12	in	in	ADP
ejpam-5917	170	13	pn	pn	PROPN
ejpam-5917	170	14	.	.	PUNCT
ejpam-5917	171	1	by	by	ADP
ejpam-5917	171	2	the	the	DET
ejpam-5917	171	3	same	same	ADJ
ejpam-5917	171	4	argument	argument	NOUN
ejpam-5917	171	5	as	as	ADP
ejpam-5917	171	6	in	in	ADP
ejpam-5917	171	7	case	case	NOUN
ejpam-5917	171	8	1	1	NUM
ejpam-5917	171	9	,	,	PUNCT
ejpam-5917	171	10	we	we	PRON
ejpam-5917	171	11	have	have	VERB
ejpam-5917	171	12	γts(pn	γts(pn	NOUN
ejpam-5917	171	13	)	)	PUNCT
ejpam-5917	171	14	=	=	SYM
ejpam-5917	171	15	n+1	n+1	PROPN
ejpam-5917	171	16	2	2	NUM
ejpam-5917	171	17	.	.	PUNCT
ejpam-5917	172	1	case	case	NOUN
ejpam-5917	172	2	3	3	NUM
ejpam-5917	172	3	:	:	PUNCT
ejpam-5917	172	4	n	n	NUM
ejpam-5917	172	5	≡	≡	PROPN
ejpam-5917	172	6	2(mod	2(mod	NUM
ejpam-5917	172	7	4	4	X
ejpam-5917	172	8	)	)	PUNCT
ejpam-5917	172	9	choose	choose	VERB
ejpam-5917	172	10	s	s	NOUN
ejpam-5917	172	11	=	=	PUNCT
ejpam-5917	172	12	{	{	PUNCT
ejpam-5917	172	13	v2	v2	PROPN
ejpam-5917	172	14	,	,	PUNCT
ejpam-5917	172	15	v3	v3	PROPN
ejpam-5917	172	16	,	,	PUNCT
ejpam-5917	172	17	v5	v5	PROPN
ejpam-5917	172	18	,	,	PUNCT
ejpam-5917	172	19	v6	v6	NOUN
ejpam-5917	172	20	,	,	PUNCT
ejpam-5917	172	21	...	...	PUNCT
ejpam-5917	172	22	,	,	PUNCT
ejpam-5917	172	23	vn−1	vn−1	PROPN
ejpam-5917	172	24	,	,	PUNCT
ejpam-5917	172	25	vn	vn	NOUN
ejpam-5917	172	26	}	}	PUNCT
ejpam-5917	172	27	.	.	PUNCT
ejpam-5917	173	1	by	by	ADP
ejpam-5917	173	2	similar	similar	ADJ
ejpam-5917	173	3	argument	argument	NOUN
ejpam-5917	173	4	as	as	ADP
ejpam-5917	173	5	in	in	ADP
ejpam-5917	173	6	the	the	DET
ejpam-5917	173	7	previous	previous	ADJ
ejpam-5917	173	8	cases	case	NOUN
ejpam-5917	173	9	,	,	PUNCT
ejpam-5917	173	10	we	we	PRON
ejpam-5917	173	11	have	have	VERB
ejpam-5917	173	12	γts(pn	γts(pn	NOUN
ejpam-5917	173	13	)	)	PUNCT
ejpam-5917	173	14	=	=	SYM
ejpam-5917	173	15	n+2	n+2	NUM
ejpam-5917	173	16	2	2	NUM
ejpam-5917	173	17	.	.	PUNCT
ejpam-5917	174	1	case	case	NOUN
ejpam-5917	174	2	4	4	NUM
ejpam-5917	174	3	:	:	PUNCT
ejpam-5917	174	4	n	n	X
ejpam-5917	174	5	≡	≡	PROPN
ejpam-5917	174	6	3(mod	3(mod	NUM
ejpam-5917	174	7	4	4	X
ejpam-5917	174	8	)	)	PUNCT
ejpam-5917	174	9	choose	choose	VERB
ejpam-5917	174	10	s	s	NOUN
ejpam-5917	174	11	=	=	PUNCT
ejpam-5917	174	12	{	{	PUNCT
ejpam-5917	174	13	v2	v2	PROPN
ejpam-5917	174	14	,	,	PUNCT
ejpam-5917	174	15	v3	v3	PROPN
ejpam-5917	174	16	,	,	PUNCT
ejpam-5917	174	17	v6	v6	NOUN
ejpam-5917	174	18	,	,	PUNCT
ejpam-5917	174	19	v7	v7	VERB
ejpam-5917	174	20	,	,	PUNCT
ejpam-5917	174	21	...	...	PUNCT
ejpam-5917	174	22	,	,	PUNCT
ejpam-5917	174	23	vn−1	vn−1	PROPN
ejpam-5917	174	24	,	,	PUNCT
ejpam-5917	174	25	vn	vn	NOUN
ejpam-5917	174	26	}	}	PUNCT
ejpam-5917	174	27	.	.	PUNCT
ejpam-5917	175	1	so	so	ADV
ejpam-5917	175	2	,	,	PUNCT
ejpam-5917	175	3	|s|	|s|	PROPN
ejpam-5917	175	4	=	=	SYM
ejpam-5917	175	5	n+1	n+1	PROPN
ejpam-5917	175	6	2	2	NUM
ejpam-5917	175	7	.	.	PUNCT
ejpam-5917	176	1	again	again	ADV
ejpam-5917	176	2	,	,	PUNCT
ejpam-5917	176	3	by	by	ADP
ejpam-5917	176	4	theorem	theorem	NOUN
ejpam-5917	176	5	3	3	NUM
ejpam-5917	176	6	,	,	PUNCT
ejpam-5917	176	7	s	s	VERB
ejpam-5917	176	8	is	be	AUX
ejpam-5917	176	9	a	a	DET
ejpam-5917	176	10	total	total	ADJ
ejpam-5917	176	11	safe	safe	ADJ
ejpam-5917	176	12	dominating	dominating	NOUN
ejpam-5917	176	13	set	set	VERB
ejpam-5917	176	14	in	in	ADP
ejpam-5917	176	15	pn	pn	PROPN
ejpam-5917	176	16	.	.	PROPN
ejpam-5917	177	1	hence	hence	ADV
ejpam-5917	177	2	,	,	PUNCT
ejpam-5917	177	3	γts(pn	γts(pn	NOUN
ejpam-5917	177	4	)	)	PUNCT
ejpam-5917	177	5	≤	≤	NUM
ejpam-5917	177	6	|s|	|s|	PROPN
ejpam-5917	177	7	=	=	SYM
ejpam-5917	177	8	n+1	n+1	PROPN
ejpam-5917	177	9	2	2	NUM
ejpam-5917	177	10	.	.	PUNCT
ejpam-5917	178	1	by	by	ADP
ejpam-5917	178	2	vertex	vertex	NOUN
ejpam-5917	178	3	selection	selection	NOUN
ejpam-5917	178	4	and	and	CCONJ
ejpam-5917	178	5	labeling	labeling	NOUN
ejpam-5917	178	6	,	,	PUNCT
ejpam-5917	178	7	we	we	PRON
ejpam-5917	178	8	can	can	AUX
ejpam-5917	178	9	not	not	PART
ejpam-5917	178	10	find	find	VERB
ejpam-5917	178	11	a	a	DET
ejpam-5917	178	12	total	total	ADJ
ejpam-5917	178	13	safe	safe	ADJ
ejpam-5917	178	14	dominating	dominating	NOUN
ejpam-5917	178	15	set	set	VERB
ejpam-5917	178	16	in	in	ADP
ejpam-5917	178	17	pn	pn	PROPN
ejpam-5917	178	18	with	with	ADP
ejpam-5917	178	19	cardinality	cardinality	NOUN
ejpam-5917	178	20	less	less	ADJ
ejpam-5917	178	21	than	than	ADP
ejpam-5917	178	22	the	the	DET
ejpam-5917	178	23	cardinality	cardinality	NOUN
ejpam-5917	178	24	of	of	ADP
ejpam-5917	178	25	s.	s.	PROPN
ejpam-5917	178	26	thus	thus	ADV
ejpam-5917	178	27	,	,	PUNCT
ejpam-5917	178	28	γts(pn	γts(pn	NOUN
ejpam-5917	178	29	)	)	PUNCT
ejpam-5917	178	30	=	=	PUNCT
ejpam-5917	178	31	|s|	|s|	NOUN
ejpam-5917	178	32	=	=	SYM
ejpam-5917	178	33	n+1	n+1	PROPN
ejpam-5917	178	34	2	2	NUM
ejpam-5917	178	35	.	.	PUNCT
ejpam-5917	179	1	similarly	similarly	ADV
ejpam-5917	179	2	,	,	PUNCT
ejpam-5917	179	3	for	for	ADP
ejpam-5917	179	4	cn	cn	PROPN
ejpam-5917	179	5	=	=	PUNCT
ejpam-5917	180	1	[	[	X
ejpam-5917	180	2	v1	v1	NOUN
ejpam-5917	180	3	,	,	PUNCT
ejpam-5917	180	4	v2	v2	PROPN
ejpam-5917	180	5	,	,	PUNCT
ejpam-5917	180	6	...	...	PUNCT
ejpam-5917	180	7	,	,	PUNCT
ejpam-5917	180	8	vn	vn	INTJ
ejpam-5917	180	9	,	,	PUNCT
ejpam-5917	180	10	v1	v1	PROPN
ejpam-5917	180	11	]	]	PUNCT
ejpam-5917	180	12	and	and	CCONJ
ejpam-5917	180	13	s	s	VERB
ejpam-5917	180	14	⊊	⊊	VERB
ejpam-5917	180	15	v	v	NOUN
ejpam-5917	180	16	(	(	PUNCT
ejpam-5917	180	17	cn	cn	PROPN
ejpam-5917	180	18	)	)	PUNCT
ejpam-5917	180	19	,	,	PUNCT
ejpam-5917	180	20	choose	choose	VERB
ejpam-5917	180	21	the	the	DET
ejpam-5917	180	22	same	same	ADJ
ejpam-5917	180	23	vertex	vertex	NOUN
ejpam-5917	180	24	labeling	labeling	NOUN
ejpam-5917	180	25	for	for	ADP
ejpam-5917	180	26	s	s	PRON
ejpam-5917	180	27	in	in	ADP
ejpam-5917	180	28	each	each	DET
ejpam-5917	180	29	case	case	NOUN
ejpam-5917	180	30	above	above	ADV
ejpam-5917	180	31	.	.	PUNCT
ejpam-5917	181	1	by	by	ADP
ejpam-5917	181	2	the	the	DET
ejpam-5917	181	3	same	same	ADJ
ejpam-5917	181	4	arguments	argument	NOUN
ejpam-5917	181	5	as	as	ADP
ejpam-5917	181	6	above	above	ADV
ejpam-5917	181	7	,	,	PUNCT
ejpam-5917	181	8	we	we	PRON
ejpam-5917	181	9	have	have	VERB
ejpam-5917	181	10	γts(cn	γts(cn	NOUN
ejpam-5917	181	11	)	)	PUNCT
ejpam-5917	182	1	=	=	PUNCT
ejpam-5917	183	1			PROPN
ejpam-5917	183	2	n	n	PRON
ejpam-5917	183	3	2	2	NUM
ejpam-5917	183	4	,	,	PUNCT
ejpam-5917	183	5	if	if	SCONJ
ejpam-5917	183	6	n	n	PRON
ejpam-5917	183	7	≡	≡	PROPN
ejpam-5917	183	8	0(mod	0(mod	NOUN
ejpam-5917	183	9	4	4	X
ejpam-5917	183	10	)	)	PUNCT
ejpam-5917	183	11	n+1	n+1	NUM
ejpam-5917	183	12	2	2	NUM
ejpam-5917	183	13	,	,	PUNCT
ejpam-5917	183	14	if	if	SCONJ
ejpam-5917	183	15	n	n	PRON
ejpam-5917	183	16	≡	≡	PROPN
ejpam-5917	183	17	1	1	NUM
ejpam-5917	183	18	or	or	CCONJ
ejpam-5917	183	19	3(mod	3(mod	NUM
ejpam-5917	183	20	4	4	NUM
ejpam-5917	183	21	)	)	PUNCT
ejpam-5917	183	22	n+2	n+2	NUM
ejpam-5917	183	23	2	2	NUM
ejpam-5917	183	24	,	,	PUNCT
ejpam-5917	183	25	if	if	SCONJ
ejpam-5917	183	26	n	n	PRON
ejpam-5917	183	27	≡	≡	PROPN
ejpam-5917	183	28	2(mod	2(mod	NUM
ejpam-5917	183	29	4	4	NUM
ejpam-5917	183	30	)	)	PUNCT
ejpam-5917	183	31	.	.	PUNCT
ejpam-5917	184	1	theorem	theorem	ADJ
ejpam-5917	184	2	4	4	NUM
ejpam-5917	184	3	.	.	PUNCT
ejpam-5917	185	1	let	let	VERB
ejpam-5917	185	2	kn	kn	PROPN
ejpam-5917	185	3	be	be	AUX
ejpam-5917	185	4	a	a	DET
ejpam-5917	185	5	complete	complete	ADJ
ejpam-5917	185	6	graph	graph	NOUN
ejpam-5917	185	7	of	of	ADP
ejpam-5917	185	8	order	order	NOUN
ejpam-5917	185	9	n	n	PRON
ejpam-5917	185	10	≥	≥	NOUN
ejpam-5917	185	11	3	3	NUM
ejpam-5917	185	12	.	.	PUNCT
ejpam-5917	186	1	then	then	ADV
ejpam-5917	186	2	a	a	DET
ejpam-5917	186	3	nonempty	nonempty	ADJ
ejpam-5917	186	4	set	set	VERB
ejpam-5917	186	5	s	s	PRON
ejpam-5917	186	6	⊊	⊊	NOUN
ejpam-5917	186	7	v	v	NOUN
ejpam-5917	186	8	(	(	PUNCT
ejpam-5917	186	9	kn	kn	PROPN
ejpam-5917	186	10	)	)	PUNCT
ejpam-5917	186	11	is	be	AUX
ejpam-5917	186	12	a	a	DET
ejpam-5917	186	13	total	total	ADJ
ejpam-5917	186	14	safe	safe	ADJ
ejpam-5917	186	15	dominating	dominating	NOUN
ejpam-5917	186	16	set	set	VERB
ejpam-5917	186	17	in	in	ADP
ejpam-5917	186	18	kn	kn	PROPN
ejpam-5917	186	19	if	if	SCONJ
ejpam-5917	186	20	and	and	CCONJ
ejpam-5917	186	21	only	only	ADV
ejpam-5917	186	22	if	if	SCONJ
ejpam-5917	186	23	|s|	|s|	NOUN
ejpam-5917	186	24	≥	≥	NOUN
ejpam-5917	186	25	⌈	⌈	NOUN
ejpam-5917	186	26	n	n	CCONJ
ejpam-5917	186	27	2	2	NUM
ejpam-5917	186	28	⌉	⌉	X
ejpam-5917	186	29	.	.	PUNCT
ejpam-5917	187	1	proof	proof	NOUN
ejpam-5917	187	2	.	.	PUNCT
ejpam-5917	188	1	assume	assume	VERB
ejpam-5917	188	2	that	that	SCONJ
ejpam-5917	188	3	s	s	VERB
ejpam-5917	188	4	is	be	AUX
ejpam-5917	188	5	a	a	DET
ejpam-5917	188	6	total	total	ADJ
ejpam-5917	188	7	safe	safe	ADJ
ejpam-5917	188	8	dominating	dominating	NOUN
ejpam-5917	188	9	set	set	NOUN
ejpam-5917	188	10	in	in	ADP
ejpam-5917	188	11	kn	kn	PROPN
ejpam-5917	188	12	.	.	PUNCT
ejpam-5917	189	1	now	now	ADV
ejpam-5917	189	2	,	,	PUNCT
ejpam-5917	189	3	suppose	suppose	VERB
ejpam-5917	189	4	that	that	SCONJ
ejpam-5917	189	5	|s|	|s|	VERB
ejpam-5917	189	6	<	<	X
ejpam-5917	189	7	⌈	⌈	NOUN
ejpam-5917	189	8	n	n	PRON
ejpam-5917	189	9	2	2	NUM
ejpam-5917	189	10	⌉	⌉	X
ejpam-5917	189	11	.	.	PUNCT
ejpam-5917	190	1	then	then	ADV
ejpam-5917	190	2	we	we	PRON
ejpam-5917	190	3	have	have	VERB
ejpam-5917	190	4	|v	|v	PROPN
ejpam-5917	190	5	(	(	PUNCT
ejpam-5917	190	6	kn	kn	PROPN
ejpam-5917	190	7	)	)	PUNCT
ejpam-5917	190	8	∖	∖	X
ejpam-5917	190	9	s|	s|	VERB
ejpam-5917	190	10	≥	≥	NOUN
ejpam-5917	190	11	⌈	⌈	SYM
ejpam-5917	190	12	n	n	CCONJ
ejpam-5917	190	13	2	2	NUM
ejpam-5917	190	14	⌉	⌉	X
ejpam-5917	190	15	.	.	PUNCT
ejpam-5917	191	1	since	since	SCONJ
ejpam-5917	191	2	kn[s	kn[s	PROPN
ejpam-5917	191	3	]	]	PUNCT
ejpam-5917	191	4	and	and	CCONJ
ejpam-5917	191	5	kn[v	kn[v	PROPN
ejpam-5917	191	6	(	(	PUNCT
ejpam-5917	191	7	kn	kn	PROPN
ejpam-5917	191	8	)	)	PUNCT
ejpam-5917	191	9	∖	∖	X
ejpam-5917	191	10	s	s	PART
ejpam-5917	191	11	]	]	X
ejpam-5917	191	12	both	both	PRON
ejpam-5917	191	13	consist	consist	VERB
ejpam-5917	191	14	of	of	ADP
ejpam-5917	191	15	a	a	DET
ejpam-5917	191	16	single	single	ADJ
ejpam-5917	191	17	component	component	NOUN
ejpam-5917	191	18	,	,	PUNCT
ejpam-5917	191	19	this	this	PRON
ejpam-5917	191	20	implies	imply	VERB
ejpam-5917	191	21	that	that	SCONJ
ejpam-5917	191	22	s	s	VERB
ejpam-5917	191	23	is	be	AUX
ejpam-5917	191	24	not	not	PART
ejpam-5917	191	25	a	a	DET
ejpam-5917	191	26	safe	safe	ADJ
ejpam-5917	191	27	set	set	NOUN
ejpam-5917	191	28	in	in	ADP
ejpam-5917	191	29	kn	kn	PROPN
ejpam-5917	191	30	.	.	PUNCT
ejpam-5917	192	1	this	this	PRON
ejpam-5917	192	2	contradicts	contradict	VERB
ejpam-5917	192	3	our	our	PRON
ejpam-5917	192	4	assumption	assumption	NOUN
ejpam-5917	192	5	that	that	SCONJ
ejpam-5917	192	6	s	s	VERB
ejpam-5917	192	7	is	be	AUX
ejpam-5917	192	8	a	a	DET
ejpam-5917	192	9	total	total	ADJ
ejpam-5917	192	10	safe	safe	ADJ
ejpam-5917	192	11	dominating	dominating	NOUN
ejpam-5917	192	12	set	set	NOUN
ejpam-5917	192	13	.	.	PUNCT
ejpam-5917	193	1	thus	thus	ADV
ejpam-5917	193	2	,	,	PUNCT
ejpam-5917	193	3	|s|	|s|	VERB
ejpam-5917	193	4	≥	≥	NOUN
ejpam-5917	193	5	⌈	⌈	SYM
ejpam-5917	193	6	n	n	CCONJ
ejpam-5917	193	7	2	2	NUM
ejpam-5917	193	8	⌉	⌉	X
ejpam-5917	193	9	.	.	PUNCT
ejpam-5917	194	1	w.	w.	PROPN
ejpam-5917	194	2	g.	g.	PROPN
ejpam-5917	194	3	jumalon	jumalon	PROPN
ejpam-5917	194	4	,	,	PUNCT
ejpam-5917	194	5	i.	i.	PROPN
ejpam-5917	194	6	cabahug	cabahug	PROPN
ejpam-5917	194	7	/	/	SYM
ejpam-5917	194	8	eur	eur	PROPN
ejpam-5917	194	9	.	.	PUNCT
ejpam-5917	195	1	j.	j.	PROPN
ejpam-5917	195	2	pure	pure	PROPN
ejpam-5917	195	3	appl	appl	PROPN
ejpam-5917	195	4	.	.	PROPN
ejpam-5917	195	5	math	math	PROPN
ejpam-5917	195	6	,	,	PUNCT
ejpam-5917	195	7	18	18	NUM
ejpam-5917	195	8	(	(	PUNCT
ejpam-5917	195	9	2	2	NUM
ejpam-5917	195	10	)	)	PUNCT
ejpam-5917	195	11	(	(	PUNCT
ejpam-5917	195	12	2025	2025	NUM
ejpam-5917	195	13	)	)	PUNCT
ejpam-5917	195	14	,	,	PUNCT
ejpam-5917	195	15	5917	5917	NUM
ejpam-5917	195	16	9	9	NUM
ejpam-5917	195	17	of	of	ADP
ejpam-5917	195	18	12	12	NUM
ejpam-5917	195	19	conversely	conversely	ADV
ejpam-5917	195	20	,	,	PUNCT
ejpam-5917	195	21	suppose	suppose	VERB
ejpam-5917	195	22	that	that	SCONJ
ejpam-5917	195	23	|s|	|s|	VERB
ejpam-5917	195	24	≥	≥	NOUN
ejpam-5917	195	25	⌈	⌈	SYM
ejpam-5917	195	26	n	n	PRON
ejpam-5917	195	27	2	2	NUM
ejpam-5917	195	28	⌉	⌉	X
ejpam-5917	195	29	.	.	PUNCT
ejpam-5917	196	1	since	since	SCONJ
ejpam-5917	196	2	any	any	DET
ejpam-5917	196	3	vertex	vertex	NOUN
ejpam-5917	196	4	in	in	ADP
ejpam-5917	196	5	v	v	PROPN
ejpam-5917	196	6	(	(	PUNCT
ejpam-5917	196	7	kn	kn	PROPN
ejpam-5917	196	8	)	)	PUNCT
ejpam-5917	196	9	is	be	AUX
ejpam-5917	196	10	adjacent	adjacent	ADJ
ejpam-5917	196	11	to	to	ADP
ejpam-5917	196	12	a	a	DET
ejpam-5917	196	13	vertex	vertex	NOUN
ejpam-5917	196	14	in	in	ADP
ejpam-5917	196	15	s	s	PROPN
ejpam-5917	196	16	,	,	PUNCT
ejpam-5917	196	17	s	s	VERB
ejpam-5917	196	18	is	be	AUX
ejpam-5917	196	19	a	a	DET
ejpam-5917	196	20	total	total	ADJ
ejpam-5917	196	21	dominating	dominating	NOUN
ejpam-5917	196	22	set	set	NOUN
ejpam-5917	196	23	.	.	PUNCT
ejpam-5917	197	1	additionally	additionally	ADV
ejpam-5917	197	2	,	,	PUNCT
ejpam-5917	197	3	since	since	SCONJ
ejpam-5917	197	4	|s|	|s|	NOUN
ejpam-5917	197	5	≥	≥	PROPN
ejpam-5917	197	6	⌈	⌈	SYM
ejpam-5917	197	7	n	n	PRON
ejpam-5917	197	8	2	2	NUM
ejpam-5917	197	9	⌉	⌉	NOUN
ejpam-5917	197	10	,	,	PUNCT
ejpam-5917	197	11	we	we	PRON
ejpam-5917	197	12	have	have	VERB
ejpam-5917	197	13	enough	enough	ADJ
ejpam-5917	197	14	vertices	vertex	NOUN
ejpam-5917	197	15	in	in	ADP
ejpam-5917	197	16	s	s	NOUN
ejpam-5917	197	17	to	to	PART
ejpam-5917	197	18	satisfy	satisfy	VERB
ejpam-5917	197	19	the	the	DET
ejpam-5917	197	20	safe	safe	ADJ
ejpam-5917	197	21	set	set	NOUN
ejpam-5917	197	22	condition	condition	NOUN
ejpam-5917	197	23	.	.	PUNCT
ejpam-5917	198	1	hence	hence	ADV
ejpam-5917	198	2	,	,	PUNCT
ejpam-5917	198	3	s	s	VERB
ejpam-5917	198	4	is	be	AUX
ejpam-5917	198	5	a	a	DET
ejpam-5917	198	6	total	total	ADJ
ejpam-5917	198	7	safe	safe	ADJ
ejpam-5917	198	8	dominating	dominating	NOUN
ejpam-5917	198	9	set	set	NOUN
ejpam-5917	198	10	in	in	ADP
ejpam-5917	198	11	kn	kn	PROPN
ejpam-5917	198	12	.	.	PUNCT
ejpam-5917	198	13	corollary	corollary	PROPN
ejpam-5917	198	14	3	3	NUM
ejpam-5917	198	15	.	.	PUNCT
ejpam-5917	199	1	for	for	ADP
ejpam-5917	199	2	kn	kn	PROPN
ejpam-5917	199	3	,	,	PUNCT
ejpam-5917	199	4	n	n	PRON
ejpam-5917	199	5	≥	≥	NOUN
ejpam-5917	199	6	3	3	NUM
ejpam-5917	199	7	,	,	PUNCT
ejpam-5917	199	8	γts(kn	γts(kn	NOUN
ejpam-5917	199	9	)	)	PUNCT
ejpam-5917	199	10	=	=	PUNCT
ejpam-5917	199	11	⌈n	⌈n	NOUN
ejpam-5917	199	12	2	2	NUM
ejpam-5917	199	13	⌉	⌉	X
ejpam-5917	199	14	.	.	PUNCT
ejpam-5917	200	1	proof	proof	NOUN
ejpam-5917	200	2	.	.	PUNCT
ejpam-5917	201	1	by	by	ADP
ejpam-5917	201	2	theorem	theorem	NOUN
ejpam-5917	201	3	4	4	NUM
ejpam-5917	201	4	,	,	PUNCT
ejpam-5917	201	5	the	the	DET
ejpam-5917	201	6	lower	lower	ADV
ejpam-5917	201	7	bound	bind	VERB
ejpam-5917	201	8	for	for	ADP
ejpam-5917	201	9	a	a	DET
ejpam-5917	201	10	total	total	ADJ
ejpam-5917	201	11	safe	safe	ADJ
ejpam-5917	201	12	dominating	dominating	NOUN
ejpam-5917	201	13	set	set	NOUN
ejpam-5917	201	14	in	in	ADP
ejpam-5917	201	15	kn	kn	PROPN
ejpam-5917	201	16	is	be	AUX
ejpam-5917	201	17	⌈	⌈	NUM
ejpam-5917	201	18	n	n	PRON
ejpam-5917	201	19	2	2	NUM
ejpam-5917	201	20	⌉	⌉	X
ejpam-5917	201	21	.	.	PUNCT
ejpam-5917	202	1	hence	hence	ADV
ejpam-5917	202	2	,	,	PUNCT
ejpam-5917	202	3	γts(kn	γts(kn	NOUN
ejpam-5917	202	4	)	)	PUNCT
ejpam-5917	202	5	=	=	PUNCT
ejpam-5917	203	1	⌈	⌈	NOUN
ejpam-5917	203	2	n	n	CCONJ
ejpam-5917	203	3	2	2	NUM
ejpam-5917	203	4	⌉	⌉	X
ejpam-5917	203	5	.	.	PUNCT
ejpam-5917	204	1	theorem	theorem	NOUN
ejpam-5917	204	2	5	5	NUM
ejpam-5917	204	3	.	.	PUNCT
ejpam-5917	205	1	let	let	VERB
ejpam-5917	205	2	km	km	PROPN
ejpam-5917	205	3	,	,	PUNCT
ejpam-5917	205	4	n	n	PRON
ejpam-5917	205	5	be	be	VERB
ejpam-5917	205	6	a	a	DET
ejpam-5917	205	7	complete	complete	ADJ
ejpam-5917	205	8	bipartite	bipartite	NOUN
ejpam-5917	205	9	graph	graph	NOUN
ejpam-5917	205	10	with	with	ADP
ejpam-5917	205	11	partite	partite	ADJ
ejpam-5917	205	12	sets	set	NOUN
ejpam-5917	205	13	u	u	NOUN
ejpam-5917	205	14	and	and	CCONJ
ejpam-5917	205	15	w	w	ADP
ejpam-5917	205	16	such	such	ADJ
ejpam-5917	205	17	that	that	PRON
ejpam-5917	205	18	|u	|u	ADJ
ejpam-5917	205	19	|	|	NOUN
ejpam-5917	205	20	=	=	SYM
ejpam-5917	205	21	m	m	PROPN
ejpam-5917	205	22	,	,	PUNCT
ejpam-5917	205	23	|w	|w	NOUN
ejpam-5917	205	24	|	|	NOUN
ejpam-5917	205	25	=	=	SYM
ejpam-5917	205	26	n	n	CCONJ
ejpam-5917	205	27	,	,	PUNCT
ejpam-5917	205	28	and	and	CCONJ
ejpam-5917	205	29	m	m	PROPN
ejpam-5917	205	30	+	+	ADJ
ejpam-5917	205	31	n	n	CCONJ
ejpam-5917	205	32	≥	≥	NOUN
ejpam-5917	205	33	3	3	NUM
ejpam-5917	205	34	.	.	PUNCT
ejpam-5917	206	1	then	then	ADV
ejpam-5917	206	2	a	a	DET
ejpam-5917	206	3	nonempty	nonempty	ADJ
ejpam-5917	206	4	set	set	VERB
ejpam-5917	206	5	s	s	PRON
ejpam-5917	206	6	⊊	⊊	NOUN
ejpam-5917	206	7	v	v	NOUN
ejpam-5917	206	8	(	(	PUNCT
ejpam-5917	206	9	km	km	NOUN
ejpam-5917	206	10	,	,	PUNCT
ejpam-5917	206	11	n	n	CCONJ
ejpam-5917	206	12	)	)	PUNCT
ejpam-5917	206	13	is	be	AUX
ejpam-5917	206	14	a	a	DET
ejpam-5917	206	15	total	total	ADJ
ejpam-5917	206	16	safe	safe	ADJ
ejpam-5917	206	17	dominating	dominating	NOUN
ejpam-5917	206	18	set	set	NOUN
ejpam-5917	206	19	in	in	ADP
ejpam-5917	206	20	km	km	PROPN
ejpam-5917	206	21	,	,	PUNCT
ejpam-5917	206	22	n	n	CCONJ
ejpam-5917	206	23	if	if	SCONJ
ejpam-5917	206	24	and	and	CCONJ
ejpam-5917	206	25	only	only	ADV
ejpam-5917	206	26	if	if	SCONJ
ejpam-5917	206	27	the	the	DET
ejpam-5917	206	28	following	follow	VERB
ejpam-5917	206	29	hold	hold	NOUN
ejpam-5917	206	30	:	:	PUNCT
ejpam-5917	206	31	(	(	PUNCT
ejpam-5917	206	32	i	i	NOUN
ejpam-5917	206	33	)	)	PUNCT
ejpam-5917	206	34	s	s	PART
ejpam-5917	206	35	=	=	NOUN
ejpam-5917	206	36	s1	s1	PROPN
ejpam-5917	206	37	∪	∪	X
ejpam-5917	206	38	s2	s2	NOUN
ejpam-5917	206	39	such	such	ADJ
ejpam-5917	206	40	that	that	PRON
ejpam-5917	206	41	∅	∅	NOUN
ejpam-5917	206	42	=	=	NOUN
ejpam-5917	206	43	̸	̸	NUM
ejpam-5917	206	44	s1	s1	NOUN
ejpam-5917	206	45	⊆	⊆	NUM
ejpam-5917	206	46	u	u	NOUN
ejpam-5917	206	47	and	and	CCONJ
ejpam-5917	206	48	∅	∅	NOUN
ejpam-5917	206	49	=	=	NOUN
ejpam-5917	206	50	̸	̸	NUM
ejpam-5917	206	51	s2	s2	VERB
ejpam-5917	206	52	⊆	⊆	NUM
ejpam-5917	206	53	w	w	NOUN
ejpam-5917	206	54	;	;	PUNCT
ejpam-5917	206	55	(	(	PUNCT
ejpam-5917	206	56	ii	ii	NOUN
ejpam-5917	206	57	)	)	PUNCT
ejpam-5917	206	58	|s|	|s|	VERB
ejpam-5917	206	59	≥	≥	PROPN
ejpam-5917	206	60	⌈	⌈	SYM
ejpam-5917	206	61	m+n	m+n	NUM
ejpam-5917	206	62	2	2	NUM
ejpam-5917	206	63	⌉	⌉	X
ejpam-5917	206	64	.	.	PUNCT
ejpam-5917	207	1	proof	proof	NOUN
ejpam-5917	207	2	.	.	PUNCT
ejpam-5917	208	1	assume	assume	VERB
ejpam-5917	208	2	that	that	SCONJ
ejpam-5917	208	3	s	s	VERB
ejpam-5917	208	4	is	be	AUX
ejpam-5917	208	5	a	a	DET
ejpam-5917	208	6	total	total	ADJ
ejpam-5917	208	7	safe	safe	ADJ
ejpam-5917	208	8	dominating	dominating	NOUN
ejpam-5917	208	9	set	set	NOUN
ejpam-5917	208	10	in	in	ADP
ejpam-5917	208	11	km	km	PROPN
ejpam-5917	208	12	,	,	PUNCT
ejpam-5917	208	13	n.	n.	PROPN
ejpam-5917	208	14	suppose	suppose	VERB
ejpam-5917	208	15	that	that	SCONJ
ejpam-5917	208	16	s	s	VERB
ejpam-5917	208	17	⊆	⊆	NUM
ejpam-5917	208	18	u	u	NOUN
ejpam-5917	208	19	or	or	CCONJ
ejpam-5917	208	20	s	s	NOUN
ejpam-5917	208	21	⊆	⊆	NUM
ejpam-5917	208	22	w	w	NOUN
ejpam-5917	208	23	.	.	PUNCT
ejpam-5917	209	1	in	in	ADP
ejpam-5917	209	2	either	either	DET
ejpam-5917	209	3	case	case	NOUN
ejpam-5917	209	4	,	,	PUNCT
ejpam-5917	209	5	km	km	NOUN
ejpam-5917	209	6	,	,	PUNCT
ejpam-5917	209	7	n[s	n[s	PROPN
ejpam-5917	209	8	]	]	PUNCT
ejpam-5917	209	9	is	be	AUX
ejpam-5917	209	10	an	an	DET
ejpam-5917	209	11	empty	empty	ADJ
ejpam-5917	209	12	graph	graph	NOUN
ejpam-5917	209	13	and	and	CCONJ
ejpam-5917	209	14	so	so	ADV
ejpam-5917	209	15	s	s	VERB
ejpam-5917	209	16	is	be	AUX
ejpam-5917	209	17	not	not	PART
ejpam-5917	209	18	a	a	DET
ejpam-5917	209	19	total	total	ADJ
ejpam-5917	209	20	safe	safe	ADJ
ejpam-5917	209	21	dominating	dominating	NOUN
ejpam-5917	209	22	set	set	NOUN
ejpam-5917	209	23	in	in	ADP
ejpam-5917	209	24	km	km	PROPN
ejpam-5917	209	25	,	,	PUNCT
ejpam-5917	209	26	n.	n.	NOUN
ejpam-5917	209	27	this	this	PRON
ejpam-5917	209	28	is	be	AUX
ejpam-5917	209	29	a	a	DET
ejpam-5917	209	30	contradiction	contradiction	NOUN
ejpam-5917	209	31	to	to	ADP
ejpam-5917	209	32	the	the	DET
ejpam-5917	209	33	assumption	assumption	NOUN
ejpam-5917	209	34	of	of	ADP
ejpam-5917	209	35	s.	s.	PROPN
ejpam-5917	209	36	so	so	ADV
ejpam-5917	209	37	,	,	PUNCT
ejpam-5917	209	38	s	s	VERB
ejpam-5917	209	39	can	can	AUX
ejpam-5917	209	40	not	not	PART
ejpam-5917	209	41	be	be	AUX
ejpam-5917	209	42	contained	contain	VERB
ejpam-5917	209	43	entirely	entirely	ADV
ejpam-5917	209	44	in	in	ADP
ejpam-5917	209	45	either	either	CCONJ
ejpam-5917	209	46	u	u	NOUN
ejpam-5917	209	47	or	or	CCONJ
ejpam-5917	209	48	w	w	NOUN
ejpam-5917	209	49	.	.	PUNCT
ejpam-5917	210	1	thus	thus	ADV
ejpam-5917	210	2	,	,	PUNCT
ejpam-5917	210	3	s	s	PART
ejpam-5917	210	4	=	=	NOUN
ejpam-5917	210	5	s1	s1	PROPN
ejpam-5917	210	6	∪	∪	X
ejpam-5917	210	7	s2	s2	NOUN
ejpam-5917	210	8	such	such	ADJ
ejpam-5917	210	9	that	that	PRON
ejpam-5917	210	10	∅	∅	NOUN
ejpam-5917	210	11	=	=	NOUN
ejpam-5917	210	12	̸	̸	NUM
ejpam-5917	210	13	s1	s1	NOUN
ejpam-5917	210	14	⊆	⊆	NUM
ejpam-5917	210	15	u	u	NOUN
ejpam-5917	210	16	and	and	CCONJ
ejpam-5917	210	17	∅	∅	NOUN
ejpam-5917	210	18	=	=	NOUN
ejpam-5917	210	19	̸	̸	NUM
ejpam-5917	210	20	s2	s2	VERB
ejpam-5917	210	21	⊆	⊆	NUM
ejpam-5917	210	22	w	w	NOUN
ejpam-5917	210	23	.	.	PUNCT
ejpam-5917	211	1	now	now	ADV
ejpam-5917	211	2	,	,	PUNCT
ejpam-5917	211	3	suppose	suppose	VERB
ejpam-5917	211	4	that	that	SCONJ
ejpam-5917	211	5	|s|	|s|	VERB
ejpam-5917	211	6	<	<	X
ejpam-5917	211	7	⌈	⌈	PROPN
ejpam-5917	211	8	m+n	m+n	NUM
ejpam-5917	211	9	2	2	NUM
ejpam-5917	211	10	⌉	⌉	X
ejpam-5917	211	11	.	.	PUNCT
ejpam-5917	212	1	then	then	ADV
ejpam-5917	212	2	,	,	PUNCT
ejpam-5917	212	3	|v	|v	PROPN
ejpam-5917	212	4	(	(	PUNCT
ejpam-5917	212	5	km	km	PROPN
ejpam-5917	212	6	,	,	PUNCT
ejpam-5917	212	7	n	n	CCONJ
ejpam-5917	212	8	)	)	PUNCT
ejpam-5917	212	9	∖	∖	NOUN
ejpam-5917	212	10	s|	s|	VERB
ejpam-5917	212	11	≥	≥	NUM
ejpam-5917	212	12	⌈	⌈	NOUN
ejpam-5917	212	13	m+n	m+n	NUM
ejpam-5917	212	14	2	2	NUM
ejpam-5917	212	15	⌉	⌉	X
ejpam-5917	212	16	.	.	PUNCT
ejpam-5917	213	1	since	since	SCONJ
ejpam-5917	213	2	km	km	PROPN
ejpam-5917	213	3	,	,	PUNCT
ejpam-5917	213	4	n[s	n[	NOUN
ejpam-5917	213	5	]	]	PUNCT
ejpam-5917	213	6	and	and	CCONJ
ejpam-5917	213	7	km	km	PROPN
ejpam-5917	213	8	,	,	PUNCT
ejpam-5917	213	9	n[v	n[v	ADV
ejpam-5917	213	10	(	(	PUNCT
ejpam-5917	213	11	km	km	NOUN
ejpam-5917	213	12	,	,	PUNCT
ejpam-5917	213	13	n	n	CCONJ
ejpam-5917	213	14	)	)	PUNCT
ejpam-5917	213	15	∖	∖	X
ejpam-5917	214	1	s	s	PART
ejpam-5917	214	2	]	]	X
ejpam-5917	214	3	both	both	PRON
ejpam-5917	214	4	consist	consist	VERB
ejpam-5917	214	5	of	of	ADP
ejpam-5917	214	6	a	a	DET
ejpam-5917	214	7	single	single	ADJ
ejpam-5917	214	8	component	component	NOUN
ejpam-5917	214	9	,	,	PUNCT
ejpam-5917	214	10	this	this	PRON
ejpam-5917	214	11	means	mean	VERB
ejpam-5917	214	12	that	that	SCONJ
ejpam-5917	214	13	s	s	VERB
ejpam-5917	214	14	is	be	AUX
ejpam-5917	214	15	not	not	PART
ejpam-5917	214	16	a	a	DET
ejpam-5917	214	17	safe	safe	ADJ
ejpam-5917	214	18	set	set	NOUN
ejpam-5917	214	19	in	in	ADP
ejpam-5917	214	20	km	km	PROPN
ejpam-5917	214	21	,	,	PUNCT
ejpam-5917	214	22	n	n	CCONJ
ejpam-5917	214	23	,	,	PUNCT
ejpam-5917	214	24	a	a	DET
ejpam-5917	214	25	contradiction	contradiction	NOUN
ejpam-5917	214	26	to	to	ADP
ejpam-5917	214	27	the	the	DET
ejpam-5917	214	28	assumption	assumption	NOUN
ejpam-5917	214	29	of	of	ADP
ejpam-5917	214	30	s.	s.	PROPN
ejpam-5917	214	31	therefore	therefore	ADV
ejpam-5917	214	32	,	,	PUNCT
ejpam-5917	214	33	|s|	|s|	PRON
ejpam-5917	214	34	≥	≥	PROPN
ejpam-5917	214	35	⌈	⌈	NOUN
ejpam-5917	214	36	m+n	m+n	NUM
ejpam-5917	214	37	2	2	NUM
ejpam-5917	214	38	⌉	⌉	X
ejpam-5917	214	39	.	.	PUNCT
ejpam-5917	215	1	for	for	ADP
ejpam-5917	215	2	the	the	DET
ejpam-5917	215	3	converse	converse	NOUN
ejpam-5917	215	4	,	,	PUNCT
ejpam-5917	215	5	suppose	suppose	VERB
ejpam-5917	215	6	that	that	SCONJ
ejpam-5917	215	7	s	s	AUX
ejpam-5917	215	8	=	=	NOUN
ejpam-5917	215	9	s1	s1	PROPN
ejpam-5917	215	10	∪	∪	X
ejpam-5917	215	11	s2	s2	NOUN
ejpam-5917	215	12	such	such	ADJ
ejpam-5917	215	13	that	that	PRON
ejpam-5917	215	14	∅	∅	NOUN
ejpam-5917	215	15	=	=	NOUN
ejpam-5917	215	16	̸	̸	NUM
ejpam-5917	215	17	s1	s1	NOUN
ejpam-5917	215	18	⊆	⊆	NUM
ejpam-5917	215	19	u	u	NOUN
ejpam-5917	215	20	and	and	CCONJ
ejpam-5917	215	21	∅	∅	NOUN
ejpam-5917	215	22	=	=	NOUN
ejpam-5917	215	23	̸	̸	NUM
ejpam-5917	215	24	s2	s2	VERB
ejpam-5917	215	25	⊆	⊆	NUM
ejpam-5917	215	26	w	w	NOUN
ejpam-5917	215	27	,	,	PUNCT
ejpam-5917	215	28	and	and	CCONJ
ejpam-5917	215	29	|s|	|s|	PROPN
ejpam-5917	215	30	≥	≥	PROPN
ejpam-5917	215	31	⌈	⌈	NOUN
ejpam-5917	215	32	m+n	m+n	NUM
ejpam-5917	215	33	2	2	NUM
ejpam-5917	215	34	⌉	⌉	X
ejpam-5917	215	35	.	.	PUNCT
ejpam-5917	216	1	the	the	DET
ejpam-5917	216	2	first	first	ADJ
ejpam-5917	216	3	part	part	NOUN
ejpam-5917	216	4	guarantees	guarantee	VERB
ejpam-5917	216	5	total	total	ADJ
ejpam-5917	216	6	domination	domination	NOUN
ejpam-5917	216	7	of	of	ADP
ejpam-5917	216	8	s	s	PRON
ejpam-5917	216	9	in	in	ADP
ejpam-5917	216	10	km	km	PROPN
ejpam-5917	216	11	,	,	PUNCT
ejpam-5917	216	12	n	n	CCONJ
ejpam-5917	216	13	,	,	PUNCT
ejpam-5917	216	14	and	and	CCONJ
ejpam-5917	216	15	together	together	ADV
ejpam-5917	216	16	with	with	ADP
ejpam-5917	216	17	the	the	DET
ejpam-5917	216	18	latter	latter	ADJ
ejpam-5917	216	19	,	,	PUNCT
ejpam-5917	216	20	it	it	PRON
ejpam-5917	216	21	follows	follow	VERB
ejpam-5917	216	22	that	that	SCONJ
ejpam-5917	216	23	s	s	VERB
ejpam-5917	216	24	is	be	AUX
ejpam-5917	216	25	a	a	DET
ejpam-5917	216	26	safe	safe	ADJ
ejpam-5917	216	27	dominating	dominating	NOUN
ejpam-5917	216	28	set	set	NOUN
ejpam-5917	216	29	in	in	ADP
ejpam-5917	216	30	km	km	PROPN
ejpam-5917	216	31	,	,	PUNCT
ejpam-5917	216	32	n.	n.	PROPN
ejpam-5917	216	33	thus	thus	ADV
ejpam-5917	216	34	,	,	PUNCT
ejpam-5917	216	35	s	s	VERB
ejpam-5917	216	36	is	be	AUX
ejpam-5917	216	37	a	a	DET
ejpam-5917	216	38	total	total	ADJ
ejpam-5917	216	39	safe	safe	ADJ
ejpam-5917	216	40	dominating	dominating	NOUN
ejpam-5917	216	41	set	set	NOUN
ejpam-5917	216	42	in	in	ADP
ejpam-5917	216	43	km	km	PROPN
ejpam-5917	216	44	,	,	PUNCT
ejpam-5917	216	45	n.	n.	NOUN
ejpam-5917	216	46	corollary	corollary	NOUN
ejpam-5917	216	47	4	4	NUM
ejpam-5917	216	48	.	.	PUNCT
ejpam-5917	216	49	for	for	ADP
ejpam-5917	216	50	a	a	DET
ejpam-5917	216	51	complete	complete	ADJ
ejpam-5917	216	52	bipartite	bipartite	NOUN
ejpam-5917	216	53	graph	graph	NOUN
ejpam-5917	216	54	km	km	PROPN
ejpam-5917	216	55	,	,	PUNCT
ejpam-5917	216	56	n	n	PRON
ejpam-5917	216	57	such	such	ADJ
ejpam-5917	216	58	that	that	DET
ejpam-5917	216	59	m+	m+	NOUN
ejpam-5917	216	60	n	n	CCONJ
ejpam-5917	216	61	≥	≥	NOUN
ejpam-5917	216	62	3	3	NUM
ejpam-5917	216	63	,	,	PUNCT
ejpam-5917	216	64	γts(km	γts(km	NUM
ejpam-5917	216	65	,	,	PUNCT
ejpam-5917	216	66	n	n	CCONJ
ejpam-5917	216	67	)	)	PUNCT
ejpam-5917	216	68	=	=	PUNCT
ejpam-5917	217	1	⌈	⌈	SYM
ejpam-5917	217	2	m+n	m+n	NUM
ejpam-5917	217	3	2	2	NUM
ejpam-5917	217	4	⌉	⌉	X
ejpam-5917	217	5	.	.	PUNCT
ejpam-5917	218	1	proof	proof	NOUN
ejpam-5917	218	2	.	.	PUNCT
ejpam-5917	219	1	by	by	ADP
ejpam-5917	219	2	theorem	theorem	NOUN
ejpam-5917	219	3	5	5	NUM
ejpam-5917	219	4	(	(	PUNCT
ejpam-5917	219	5	ii	ii	NOUN
ejpam-5917	219	6	)	)	PUNCT
ejpam-5917	219	7	,	,	PUNCT
ejpam-5917	219	8	the	the	DET
ejpam-5917	219	9	lower	lower	ADV
ejpam-5917	219	10	bound	bind	VERB
ejpam-5917	219	11	for	for	ADP
ejpam-5917	219	12	a	a	DET
ejpam-5917	219	13	total	total	ADJ
ejpam-5917	219	14	safe	safe	ADJ
ejpam-5917	219	15	dominating	dominating	NOUN
ejpam-5917	219	16	set	set	NOUN
ejpam-5917	219	17	in	in	ADP
ejpam-5917	219	18	km	km	PROPN
ejpam-5917	219	19	,	,	PUNCT
ejpam-5917	219	20	n	n	PROPN
ejpam-5917	219	21	is⌈	is⌈	PROPN
ejpam-5917	219	22	m+n	m+n	NOUN
ejpam-5917	219	23	2	2	NUM
ejpam-5917	219	24	⌉	⌉	X
ejpam-5917	219	25	.	.	PUNCT
ejpam-5917	220	1	thus	thus	ADV
ejpam-5917	220	2	,	,	PUNCT
ejpam-5917	220	3	γts(km	γts(km	NUM
ejpam-5917	220	4	,	,	PUNCT
ejpam-5917	220	5	n	n	CCONJ
ejpam-5917	220	6	)	)	PUNCT
ejpam-5917	220	7	=	=	PUNCT
ejpam-5917	221	1	⌈	⌈	SYM
ejpam-5917	221	2	m+n	m+n	NUM
ejpam-5917	221	3	2	2	NUM
ejpam-5917	221	4	⌉	⌉	X
ejpam-5917	221	5	.	.	PUNCT
ejpam-5917	222	1	remark	remark	NOUN
ejpam-5917	222	2	4	4	NUM
ejpam-5917	222	3	.	.	PUNCT
ejpam-5917	223	1	let	let	VERB
ejpam-5917	223	2	km	km	PROPN
ejpam-5917	223	3	,	,	PUNCT
ejpam-5917	223	4	n	n	PRON
ejpam-5917	223	5	be	be	VERB
ejpam-5917	223	6	a	a	DET
ejpam-5917	223	7	complete	complete	ADJ
ejpam-5917	223	8	bipartite	bipartite	NOUN
ejpam-5917	223	9	graph	graph	NOUN
ejpam-5917	223	10	with	with	ADP
ejpam-5917	223	11	partite	partite	ADJ
ejpam-5917	223	12	sets	set	NOUN
ejpam-5917	223	13	u	u	NOUN
ejpam-5917	223	14	and	and	CCONJ
ejpam-5917	223	15	w	w	ADP
ejpam-5917	223	16	such	such	ADJ
ejpam-5917	223	17	that	that	PRON
ejpam-5917	223	18	|u	|u	ADJ
ejpam-5917	223	19	|	|	NOUN
ejpam-5917	223	20	=	=	SYM
ejpam-5917	223	21	m	m	PROPN
ejpam-5917	223	22	,	,	PUNCT
ejpam-5917	223	23	|w	|w	NOUN
ejpam-5917	223	24	|	|	NOUN
ejpam-5917	224	1	=	=	PUNCT
ejpam-5917	224	2	n.	n.	NOUN
ejpam-5917	224	3	if	if	SCONJ
ejpam-5917	224	4	s	s	VERB
ejpam-5917	224	5	⊆	⊆	NUM
ejpam-5917	224	6	u	u	NOUN
ejpam-5917	224	7	or	or	CCONJ
ejpam-5917	224	8	s	s	NOUN
ejpam-5917	224	9	⊆	⊆	NUM
ejpam-5917	224	10	w	w	NOUN
ejpam-5917	224	11	,	,	PUNCT
ejpam-5917	224	12	then	then	ADV
ejpam-5917	224	13	s	s	VERB
ejpam-5917	224	14	is	be	AUX
ejpam-5917	224	15	not	not	PART
ejpam-5917	224	16	a	a	DET
ejpam-5917	224	17	total	total	ADJ
ejpam-5917	224	18	safe	safe	ADJ
ejpam-5917	224	19	dominating	dominating	NOUN
ejpam-5917	224	20	set	set	NOUN
ejpam-5917	224	21	in	in	ADP
ejpam-5917	224	22	km	km	PROPN
ejpam-5917	224	23	,	,	PUNCT
ejpam-5917	224	24	n.	n.	PROPN
ejpam-5917	224	25	w.	w.	PROPN
ejpam-5917	224	26	g.	g.	PROPN
ejpam-5917	224	27	jumalon	jumalon	PROPN
ejpam-5917	224	28	,	,	PUNCT
ejpam-5917	224	29	i.	i.	PROPN
ejpam-5917	224	30	cabahug	cabahug	PROPN
ejpam-5917	224	31	/	/	SYM
ejpam-5917	224	32	eur	eur	PROPN
ejpam-5917	224	33	.	.	PUNCT
ejpam-5917	225	1	j.	j.	PROPN
ejpam-5917	225	2	pure	pure	PROPN
ejpam-5917	225	3	appl	appl	PROPN
ejpam-5917	225	4	.	.	PROPN
ejpam-5917	225	5	math	math	PROPN
ejpam-5917	225	6	,	,	PUNCT
ejpam-5917	225	7	18	18	NUM
ejpam-5917	225	8	(	(	PUNCT
ejpam-5917	225	9	2	2	NUM
ejpam-5917	225	10	)	)	PUNCT
ejpam-5917	225	11	(	(	PUNCT
ejpam-5917	225	12	2025	2025	NUM
ejpam-5917	225	13	)	)	PUNCT
ejpam-5917	225	14	,	,	PUNCT
ejpam-5917	225	15	5917	5917	NUM
ejpam-5917	225	16	10	10	NUM
ejpam-5917	225	17	of	of	ADP
ejpam-5917	225	18	12	12	NUM
ejpam-5917	225	19	theorem	theorem	NOUN
ejpam-5917	225	20	6	6	NUM
ejpam-5917	225	21	.	.	PUNCT
ejpam-5917	226	1	let	let	VERB
ejpam-5917	226	2	fn	fn	PRON
ejpam-5917	226	3	be	be	AUX
ejpam-5917	226	4	a	a	DET
ejpam-5917	226	5	friendship	friendship	NOUN
ejpam-5917	226	6	graph	graph	NOUN
ejpam-5917	226	7	of	of	ADP
ejpam-5917	226	8	order	order	NOUN
ejpam-5917	226	9	2n	2n	NUM
ejpam-5917	227	1	+	+	CCONJ
ejpam-5917	227	2	1	1	NUM
ejpam-5917	227	3	with	with	ADP
ejpam-5917	227	4	central	central	ADJ
ejpam-5917	227	5	vertex	vertex	NOUN
ejpam-5917	227	6	x.	x.	NOUN
ejpam-5917	227	7	then	then	ADV
ejpam-5917	227	8	a	a	DET
ejpam-5917	227	9	nonempty	nonempty	ADJ
ejpam-5917	227	10	set	set	VERB
ejpam-5917	227	11	s	s	PRON
ejpam-5917	227	12	⊊	⊊	NOUN
ejpam-5917	227	13	v	v	NOUN
ejpam-5917	227	14	(	(	PUNCT
ejpam-5917	227	15	fn	fn	NOUN
ejpam-5917	227	16	)	)	PUNCT
ejpam-5917	227	17	is	be	AUX
ejpam-5917	227	18	a	a	DET
ejpam-5917	227	19	total	total	ADJ
ejpam-5917	227	20	safe	safe	ADJ
ejpam-5917	227	21	dominating	dominating	NOUN
ejpam-5917	227	22	set	set	VERB
ejpam-5917	227	23	in	in	ADP
ejpam-5917	227	24	fn	fn	NOUN
ejpam-5917	227	25	if	if	SCONJ
ejpam-5917	227	26	and	and	CCONJ
ejpam-5917	227	27	only	only	ADV
ejpam-5917	227	28	if	if	SCONJ
ejpam-5917	227	29	one	one	NUM
ejpam-5917	227	30	of	of	ADP
ejpam-5917	227	31	the	the	DET
ejpam-5917	227	32	following	follow	VERB
ejpam-5917	227	33	holds	hold	VERB
ejpam-5917	227	34	:	:	PUNCT
ejpam-5917	227	35	(	(	PUNCT
ejpam-5917	227	36	i	i	NOUN
ejpam-5917	227	37	)	)	PUNCT
ejpam-5917	227	38	|s|	|s|	PROPN
ejpam-5917	227	39	≥	≥	NOUN
ejpam-5917	227	40	2	2	NUM
ejpam-5917	227	41	,	,	PUNCT
ejpam-5917	227	42	if	if	SCONJ
ejpam-5917	227	43	x	x	SYM
ejpam-5917	227	44	∈	∈	PROPN
ejpam-5917	227	45	s	s	X
ejpam-5917	227	46	(	(	PUNCT
ejpam-5917	227	47	ii	ii	NOUN
ejpam-5917	227	48	)	)	PUNCT
ejpam-5917	227	49	|s|	|s|	PROPN
ejpam-5917	227	50	=	=	SYM
ejpam-5917	227	51	2n	2n	NUM
ejpam-5917	227	52	,	,	PUNCT
ejpam-5917	227	53	otherwise	otherwise	ADV
ejpam-5917	227	54	proof	proof	NOUN
ejpam-5917	227	55	.	.	PUNCT
ejpam-5917	228	1	let	let	VERB
ejpam-5917	228	2	s	s	PRON
ejpam-5917	228	3	be	be	AUX
ejpam-5917	228	4	a	a	DET
ejpam-5917	228	5	total	total	ADJ
ejpam-5917	228	6	safe	safe	ADJ
ejpam-5917	228	7	dominating	dominating	NOUN
ejpam-5917	228	8	set	set	VERB
ejpam-5917	228	9	in	in	ADP
ejpam-5917	228	10	fn	fn	PROPN
ejpam-5917	228	11	.	.	PUNCT
ejpam-5917	228	12	suppose	suppose	VERB
ejpam-5917	228	13	that	that	SCONJ
ejpam-5917	228	14	x	x	PUNCT
ejpam-5917	228	15	∈	∈	NOUN
ejpam-5917	228	16	s	s	X
ejpam-5917	228	17	and	and	CCONJ
ejpam-5917	228	18	|s|	|s|	VERB
ejpam-5917	228	19	<	<	X
ejpam-5917	228	20	2	2	NUM
ejpam-5917	228	21	.	.	PUNCT
ejpam-5917	228	22	then	then	ADV
ejpam-5917	228	23	|s|	|s|	PROPN
ejpam-5917	228	24	=	=	SYM
ejpam-5917	228	25	1	1	NUM
ejpam-5917	228	26	,	,	PUNCT
ejpam-5917	228	27	that	that	ADV
ejpam-5917	228	28	is	be	AUX
ejpam-5917	228	29	,	,	PUNCT
ejpam-5917	228	30	s	s	PART
ejpam-5917	228	31	=	=	PUNCT
ejpam-5917	228	32	{	{	PUNCT
ejpam-5917	228	33	x	x	NOUN
ejpam-5917	228	34	}	}	PUNCT
ejpam-5917	228	35	.	.	PUNCT
ejpam-5917	229	1	so	so	ADV
ejpam-5917	229	2	,	,	PUNCT
ejpam-5917	229	3	s	s	VERB
ejpam-5917	229	4	is	be	AUX
ejpam-5917	229	5	not	not	PART
ejpam-5917	229	6	a	a	DET
ejpam-5917	229	7	total	total	ADJ
ejpam-5917	229	8	dominating	dominating	NOUN
ejpam-5917	229	9	set	set	NOUN
ejpam-5917	229	10	in	in	ADP
ejpam-5917	229	11	fn	fn	NOUN
ejpam-5917	229	12	,	,	PUNCT
ejpam-5917	229	13	a	a	DET
ejpam-5917	229	14	contradiction	contradiction	NOUN
ejpam-5917	229	15	to	to	ADP
ejpam-5917	229	16	the	the	DET
ejpam-5917	229	17	assumption	assumption	NOUN
ejpam-5917	229	18	of	of	ADP
ejpam-5917	229	19	s.	s.	PROPN
ejpam-5917	229	20	therefore	therefore	ADV
ejpam-5917	229	21	,	,	PUNCT
ejpam-5917	229	22	|s|	|s|	X
ejpam-5917	229	23	≥	≥	NOUN
ejpam-5917	229	24	2	2	NUM
ejpam-5917	229	25	if	if	SCONJ
ejpam-5917	229	26	x	x	PROPN
ejpam-5917	229	27	∈	∈	PROPN
ejpam-5917	229	28	s.	s.	PROPN
ejpam-5917	229	29	now	now	ADV
ejpam-5917	229	30	,	,	PUNCT
ejpam-5917	229	31	suppose	suppose	VERB
ejpam-5917	229	32	that	that	SCONJ
ejpam-5917	229	33	x	x	X
ejpam-5917	229	34	/∈	/∈	PRON
ejpam-5917	229	35	s	s	PART
ejpam-5917	229	36	and	and	CCONJ
ejpam-5917	229	37	|s|	|s|	PROPN
ejpam-5917	229	38	̸=	̸=	PROPN
ejpam-5917	229	39	2n	2n	NUM
ejpam-5917	229	40	.	.	PUNCT
ejpam-5917	230	1	then	then	ADV
ejpam-5917	230	2	|s|	|s|	VERB
ejpam-5917	230	3	<	<	X
ejpam-5917	230	4	2n	2n	NUM
ejpam-5917	230	5	.	.	PUNCT
ejpam-5917	231	1	without	without	ADP
ejpam-5917	231	2	loss	loss	NOUN
ejpam-5917	231	3	of	of	ADP
ejpam-5917	231	4	generality	generality	NOUN
ejpam-5917	231	5	,	,	PUNCT
ejpam-5917	231	6	suppose	suppose	VERB
ejpam-5917	231	7	|s|	|s|	PROPN
ejpam-5917	231	8	=	=	SYM
ejpam-5917	231	9	2n−	2n−	PROPN
ejpam-5917	231	10	1	1	NUM
ejpam-5917	231	11	.	.	PUNCT
ejpam-5917	232	1	let	let	VERB
ejpam-5917	232	2	v	v	ADP
ejpam-5917	232	3	̸∈	̸∈	PROPN
ejpam-5917	232	4	s	s	PROPN
ejpam-5917	232	5	with	with	ADP
ejpam-5917	232	6	v	v	NOUN
ejpam-5917	232	7	̸=	̸=	PROPN
ejpam-5917	232	8	x.	x.	NOUN
ejpam-5917	232	9	since	since	SCONJ
ejpam-5917	232	10	s	s	PROPN
ejpam-5917	232	11	is	be	AUX
ejpam-5917	232	12	a	a	DET
ejpam-5917	232	13	dominating	dominating	NOUN
ejpam-5917	232	14	set	set	NOUN
ejpam-5917	232	15	in	in	ADP
ejpam-5917	232	16	fn	fn	PROPN
ejpam-5917	232	17	,	,	PUNCT
ejpam-5917	232	18	then	then	ADV
ejpam-5917	232	19	there	there	PRON
ejpam-5917	232	20	exists	exist	VERB
ejpam-5917	232	21	a	a	DET
ejpam-5917	232	22	vertex	vertex	NOUN
ejpam-5917	232	23	u	u	NOUN
ejpam-5917	232	24	∈	∈	NOUN
ejpam-5917	232	25	s	s	VERB
ejpam-5917	232	26	such	such	ADJ
ejpam-5917	232	27	that	that	DET
ejpam-5917	232	28	v	v	NUM
ejpam-5917	232	29	∈	∈	PROPN
ejpam-5917	232	30	n(u	n(u	PROPN
ejpam-5917	232	31	)	)	PUNCT
ejpam-5917	232	32	.	.	PUNCT
ejpam-5917	233	1	this	this	PRON
ejpam-5917	233	2	implies	imply	VERB
ejpam-5917	233	3	that	that	SCONJ
ejpam-5917	233	4	fn[s	fn[	NOUN
ejpam-5917	233	5	]	]	PUNCT
ejpam-5917	233	6	has	have	VERB
ejpam-5917	233	7	an	an	DET
ejpam-5917	233	8	isolated	isolated	ADJ
ejpam-5917	233	9	vertex	vertex	NOUN
ejpam-5917	233	10	,	,	PUNCT
ejpam-5917	233	11	a	a	DET
ejpam-5917	233	12	contradiction	contradiction	NOUN
ejpam-5917	233	13	to	to	ADP
ejpam-5917	233	14	the	the	DET
ejpam-5917	233	15	assumption	assumption	NOUN
ejpam-5917	233	16	of	of	ADP
ejpam-5917	233	17	s.	s.	PROPN
ejpam-5917	233	18	thus	thus	ADV
ejpam-5917	233	19	,	,	PUNCT
ejpam-5917	233	20	|s|	|s|	PROPN
ejpam-5917	233	21	=	=	SYM
ejpam-5917	233	22	2n	2n	NUM
ejpam-5917	233	23	if	if	SCONJ
ejpam-5917	233	24	x	x	PROPN
ejpam-5917	233	25	/∈	/∈	PUNCT
ejpam-5917	233	26	s.	s.	PROPN
ejpam-5917	233	27	for	for	ADP
ejpam-5917	233	28	the	the	DET
ejpam-5917	233	29	converse	converse	NOUN
ejpam-5917	233	30	,	,	PUNCT
ejpam-5917	233	31	suppose	suppose	VERB
ejpam-5917	233	32	that	that	SCONJ
ejpam-5917	233	33	x	x	PUNCT
ejpam-5917	233	34	∈	∈	NOUN
ejpam-5917	233	35	s	s	X
ejpam-5917	233	36	and	and	CCONJ
ejpam-5917	233	37	|s|	|s|	PROPN
ejpam-5917	233	38	≥	≥	PROPN
ejpam-5917	233	39	2	2	NUM
ejpam-5917	233	40	.	.	PUNCT
ejpam-5917	233	41	clearly	clearly	ADV
ejpam-5917	233	42	,	,	PUNCT
ejpam-5917	233	43	s	s	VERB
ejpam-5917	233	44	is	be	AUX
ejpam-5917	233	45	a	a	DET
ejpam-5917	233	46	total	total	ADJ
ejpam-5917	233	47	safe	safe	ADJ
ejpam-5917	233	48	dominating	dominating	NOUN
ejpam-5917	233	49	set	set	VERB
ejpam-5917	233	50	in	in	ADP
ejpam-5917	233	51	fn	fn	NOUN
ejpam-5917	233	52	since	since	SCONJ
ejpam-5917	233	53	x	x	PRON
ejpam-5917	233	54	is	be	AUX
ejpam-5917	233	55	adjacent	adjacent	ADJ
ejpam-5917	233	56	to	to	ADP
ejpam-5917	233	57	all	all	DET
ejpam-5917	233	58	other	other	ADJ
ejpam-5917	233	59	vertices	vertex	NOUN
ejpam-5917	233	60	of	of	ADP
ejpam-5917	233	61	fn	fn	NOUN
ejpam-5917	233	62	.	.	PUNCT
ejpam-5917	234	1	now	now	ADV
ejpam-5917	234	2	,	,	PUNCT
ejpam-5917	234	3	suppose	suppose	VERB
ejpam-5917	234	4	x	x	X
ejpam-5917	234	5	/∈	/∈	PRON
ejpam-5917	234	6	s	s	PART
ejpam-5917	234	7	and	and	CCONJ
ejpam-5917	234	8	|s|	|s|	PROPN
ejpam-5917	234	9	=	=	SYM
ejpam-5917	234	10	2n	2n	NUM
ejpam-5917	234	11	.	.	PUNCT
ejpam-5917	235	1	again	again	ADV
ejpam-5917	235	2	,	,	PUNCT
ejpam-5917	235	3	clearly	clearly	ADV
ejpam-5917	235	4	,	,	PUNCT
ejpam-5917	235	5	s	s	VERB
ejpam-5917	235	6	is	be	AUX
ejpam-5917	235	7	a	a	DET
ejpam-5917	235	8	total	total	ADJ
ejpam-5917	235	9	safe	safe	ADJ
ejpam-5917	235	10	dominating	dominating	NOUN
ejpam-5917	235	11	set	set	VERB
ejpam-5917	235	12	in	in	ADP
ejpam-5917	235	13	fn	fn	PROPN
ejpam-5917	235	14	.	.	PUNCT
ejpam-5917	236	1	corollary	corollary	ADJ
ejpam-5917	236	2	5	5	NUM
ejpam-5917	236	3	.	.	PUNCT
ejpam-5917	237	1	for	for	ADP
ejpam-5917	237	2	any	any	DET
ejpam-5917	237	3	friendship	friendship	NOUN
ejpam-5917	237	4	graph	graph	NOUN
ejpam-5917	237	5	fn	fn	NOUN
ejpam-5917	237	6	of	of	ADP
ejpam-5917	237	7	order	order	NOUN
ejpam-5917	237	8	2n+	2n+	NUM
ejpam-5917	237	9	1	1	NUM
ejpam-5917	237	10	,	,	PUNCT
ejpam-5917	237	11	γts(fn	γts(fn	NUM
ejpam-5917	237	12	)	)	PUNCT
ejpam-5917	237	13	=	=	SYM
ejpam-5917	237	14	2	2	X
ejpam-5917	237	15	.	.	PUNCT
ejpam-5917	237	16	proof	proof	NOUN
ejpam-5917	237	17	.	.	PUNCT
ejpam-5917	238	1	by	by	ADP
ejpam-5917	238	2	theorem	theorem	NOUN
ejpam-5917	238	3	6	6	NUM
ejpam-5917	238	4	(	(	PUNCT
ejpam-5917	238	5	i	i	NOUN
ejpam-5917	238	6	)	)	PUNCT
ejpam-5917	238	7	,	,	PUNCT
ejpam-5917	238	8	clearly	clearly	ADV
ejpam-5917	238	9	,	,	PUNCT
ejpam-5917	238	10	γts(fn	γts(fn	NUM
ejpam-5917	238	11	)	)	PUNCT
ejpam-5917	238	12	=	=	SYM
ejpam-5917	238	13	|s|	|s|	NOUN
ejpam-5917	238	14	=	=	SYM
ejpam-5917	238	15	2	2	X
ejpam-5917	238	16	.	.	PUNCT
ejpam-5917	238	17	theorem	theorem	NOUN
ejpam-5917	238	18	7	7	NUM
ejpam-5917	238	19	.	.	PUNCT
ejpam-5917	239	1	let	let	VERB
ejpam-5917	239	2	sn	sn	PROPN
ejpam-5917	239	3	be	be	AUX
ejpam-5917	239	4	a	a	DET
ejpam-5917	239	5	sunlet	sunlet	NOUN
ejpam-5917	239	6	graph	graph	NOUN
ejpam-5917	239	7	of	of	ADP
ejpam-5917	239	8	order	order	NOUN
ejpam-5917	239	9	2n	2n	NUM
ejpam-5917	239	10	with	with	ADP
ejpam-5917	239	11	vertex	vertex	NOUN
ejpam-5917	239	12	set	set	VERB
ejpam-5917	239	13	v	v	NOUN
ejpam-5917	239	14	(	(	PUNCT
ejpam-5917	239	15	cn	cn	NOUN
ejpam-5917	239	16	)	)	PUNCT
ejpam-5917	239	17	∪	∪	ADP
ejpam-5917	239	18	p	p	NOUN
ejpam-5917	239	19	,	,	PUNCT
ejpam-5917	239	20	where	where	SCONJ
ejpam-5917	239	21	p	p	NOUN
ejpam-5917	239	22	is	be	AUX
ejpam-5917	239	23	the	the	DET
ejpam-5917	239	24	set	set	NOUN
ejpam-5917	239	25	of	of	ADP
ejpam-5917	239	26	pendant	pendant	ADJ
ejpam-5917	239	27	vertices	vertex	NOUN
ejpam-5917	239	28	in	in	ADP
ejpam-5917	239	29	sn	sn	PROPN
ejpam-5917	239	30	.	.	PUNCT
ejpam-5917	240	1	then	then	ADV
ejpam-5917	240	2	a	a	DET
ejpam-5917	240	3	nonempty	nonempty	ADJ
ejpam-5917	240	4	set	set	VERB
ejpam-5917	240	5	s	s	PRON
ejpam-5917	240	6	⊊	⊊	NOUN
ejpam-5917	240	7	v	v	NOUN
ejpam-5917	240	8	(	(	PUNCT
ejpam-5917	240	9	sn	sn	PROPN
ejpam-5917	240	10	)	)	PUNCT
ejpam-5917	240	11	is	be	AUX
ejpam-5917	240	12	a	a	DET
ejpam-5917	240	13	total	total	ADJ
ejpam-5917	240	14	safe	safe	ADJ
ejpam-5917	240	15	dominating	dominating	NOUN
ejpam-5917	240	16	set	set	VERB
ejpam-5917	240	17	in	in	ADP
ejpam-5917	240	18	sn	sn	PROPN
ejpam-5917	240	19	if	if	SCONJ
ejpam-5917	241	1	and	and	CCONJ
ejpam-5917	241	2	only	only	ADV
ejpam-5917	241	3	if	if	SCONJ
ejpam-5917	241	4	v	v	X
ejpam-5917	241	5	(	(	PUNCT
ejpam-5917	241	6	cn	cn	PROPN
ejpam-5917	241	7	)	)	PUNCT
ejpam-5917	241	8	⊆	⊆	NUM
ejpam-5917	241	9	s.	s.	PROPN
ejpam-5917	241	10	proof	proof	PROPN
ejpam-5917	241	11	.	.	PUNCT
ejpam-5917	242	1	assume	assume	VERB
ejpam-5917	242	2	that	that	SCONJ
ejpam-5917	242	3	s	s	VERB
ejpam-5917	242	4	is	be	AUX
ejpam-5917	242	5	a	a	DET
ejpam-5917	242	6	total	total	ADJ
ejpam-5917	242	7	safe	safe	ADJ
ejpam-5917	242	8	dominating	dominating	NOUN
ejpam-5917	242	9	set	set	VERB
ejpam-5917	242	10	in	in	ADP
ejpam-5917	242	11	sn	sn	PROPN
ejpam-5917	242	12	.	.	PUNCT
ejpam-5917	242	13	suppose	suppose	VERB
ejpam-5917	242	14	that	that	SCONJ
ejpam-5917	242	15	v	v	INTJ
ejpam-5917	242	16	(	(	PUNCT
ejpam-5917	242	17	cn	cn	PROPN
ejpam-5917	242	18	)	)	PUNCT
ejpam-5917	242	19	̸⊆	̸⊆	NOUN
ejpam-5917	242	20	s.	s.	PROPN
ejpam-5917	242	21	then	then	ADV
ejpam-5917	242	22	there	there	PRON
ejpam-5917	242	23	exists	exist	VERB
ejpam-5917	242	24	a	a	DET
ejpam-5917	242	25	vertex	vertex	NOUN
ejpam-5917	242	26	,	,	PUNCT
ejpam-5917	242	27	say	say	VERB
ejpam-5917	242	28	v	v	ADP
ejpam-5917	242	29	∈	∈	PROPN
ejpam-5917	242	30	v	v	NOUN
ejpam-5917	242	31	(	(	PUNCT
ejpam-5917	242	32	cn	cn	PROPN
ejpam-5917	242	33	)	)	PUNCT
ejpam-5917	242	34	,	,	PUNCT
ejpam-5917	242	35	that	that	PRON
ejpam-5917	242	36	is	be	AUX
ejpam-5917	242	37	not	not	PART
ejpam-5917	242	38	in	in	ADP
ejpam-5917	242	39	s.	s.	PROPN
ejpam-5917	242	40	let	let	VERB
ejpam-5917	242	41	u	u	PRON
ejpam-5917	242	42	∈	∈	PROPN
ejpam-5917	242	43	v	v	X
ejpam-5917	242	44	(	(	PUNCT
ejpam-5917	242	45	sn	sn	INTJ
ejpam-5917	242	46	)	)	PUNCT
ejpam-5917	242	47	be	be	AUX
ejpam-5917	242	48	a	a	DET
ejpam-5917	242	49	pendant	pendant	ADJ
ejpam-5917	242	50	vertex	vertex	NOUN
ejpam-5917	242	51	such	such	ADJ
ejpam-5917	242	52	that	that	SCONJ
ejpam-5917	242	53	u	u	PROPN
ejpam-5917	242	54	∈	∈	PROPN
ejpam-5917	242	55	n(v	n(v	PROPN
ejpam-5917	242	56	)	)	PUNCT
ejpam-5917	242	57	.	.	PUNCT
ejpam-5917	243	1	then	then	ADV
ejpam-5917	243	2	u	u	PRON
ejpam-5917	243	3	must	must	AUX
ejpam-5917	243	4	be	be	AUX
ejpam-5917	243	5	in	in	ADP
ejpam-5917	243	6	s	s	PRON
ejpam-5917	243	7	since	since	SCONJ
ejpam-5917	243	8	v	v	NUM
ejpam-5917	243	9	̸∈	̸∈	PROPN
ejpam-5917	243	10	s	s	PART
ejpam-5917	243	11	and	and	CCONJ
ejpam-5917	243	12	s	s	VERB
ejpam-5917	243	13	is	be	AUX
ejpam-5917	243	14	a	a	DET
ejpam-5917	243	15	dominating	dominating	NOUN
ejpam-5917	243	16	set	set	VERB
ejpam-5917	243	17	in	in	ADP
ejpam-5917	243	18	sn	sn	PROPN
ejpam-5917	243	19	.	.	PUNCT
ejpam-5917	244	1	thus	thus	ADV
ejpam-5917	244	2	,	,	PUNCT
ejpam-5917	244	3	u	u	NOUN
ejpam-5917	244	4	is	be	AUX
ejpam-5917	244	5	an	an	DET
ejpam-5917	244	6	isolated	isolated	ADJ
ejpam-5917	244	7	vertex	vertex	NOUN
ejpam-5917	244	8	in	in	ADP
ejpam-5917	244	9	sn[s	sn[	NOUN
ejpam-5917	244	10	]	]	PUNCT
ejpam-5917	244	11	,	,	PUNCT
ejpam-5917	244	12	and	and	CCONJ
ejpam-5917	244	13	so	so	ADV
ejpam-5917	244	14	s	s	VERB
ejpam-5917	244	15	is	be	AUX
ejpam-5917	244	16	not	not	PART
ejpam-5917	244	17	a	a	DET
ejpam-5917	244	18	total	total	ADJ
ejpam-5917	244	19	dominating	dominating	NOUN
ejpam-5917	244	20	set	set	NOUN
ejpam-5917	244	21	in	in	ADP
ejpam-5917	244	22	sn	sn	PROPN
ejpam-5917	244	23	,	,	PUNCT
ejpam-5917	244	24	a	a	DET
ejpam-5917	244	25	contradiction	contradiction	NOUN
ejpam-5917	244	26	to	to	ADP
ejpam-5917	244	27	the	the	DET
ejpam-5917	244	28	assumption	assumption	NOUN
ejpam-5917	244	29	of	of	ADP
ejpam-5917	244	30	s.	s.	PROPN
ejpam-5917	244	31	hence	hence	PROPN
ejpam-5917	244	32	,	,	PUNCT
ejpam-5917	244	33	v	v	PROPN
ejpam-5917	244	34	(	(	PUNCT
ejpam-5917	244	35	cn	cn	PROPN
ejpam-5917	244	36	)	)	PUNCT
ejpam-5917	244	37	⊆	⊆	NUM
ejpam-5917	244	38	s.	s.	PROPN
ejpam-5917	244	39	for	for	ADP
ejpam-5917	244	40	the	the	DET
ejpam-5917	244	41	converse	converse	NOUN
ejpam-5917	244	42	,	,	PUNCT
ejpam-5917	244	43	let	let	VERB
ejpam-5917	244	44	v	v	X
ejpam-5917	244	45	(	(	PUNCT
ejpam-5917	244	46	cn	cn	PROPN
ejpam-5917	244	47	)	)	PUNCT
ejpam-5917	244	48	⊆	⊆	NUM
ejpam-5917	244	49	s.	s.	PROPN
ejpam-5917	244	50	clearly	clearly	ADV
ejpam-5917	244	51	,	,	PUNCT
ejpam-5917	244	52	v	v	PROPN
ejpam-5917	244	53	(	(	PUNCT
ejpam-5917	244	54	cn	cn	PROPN
ejpam-5917	244	55	)	)	PUNCT
ejpam-5917	244	56	is	be	AUX
ejpam-5917	244	57	a	a	DET
ejpam-5917	244	58	total	total	ADJ
ejpam-5917	244	59	safe	safe	ADJ
ejpam-5917	244	60	dominating	dominating	NOUN
ejpam-5917	244	61	set	set	VERB
ejpam-5917	244	62	in	in	ADP
ejpam-5917	244	63	sn	sn	PROPN
ejpam-5917	244	64	.	.	PUNCT
ejpam-5917	245	1	therefore	therefore	ADV
ejpam-5917	245	2	,	,	PUNCT
ejpam-5917	245	3	s	s	VERB
ejpam-5917	245	4	is	be	AUX
ejpam-5917	245	5	a	a	DET
ejpam-5917	245	6	total	total	ADJ
ejpam-5917	245	7	safe	safe	ADJ
ejpam-5917	245	8	dominating	dominating	NOUN
ejpam-5917	245	9	set	set	VERB
ejpam-5917	245	10	in	in	ADP
ejpam-5917	245	11	sn	sn	PROPN
ejpam-5917	245	12	.	.	PUNCT
ejpam-5917	246	1	corollary	corollary	ADJ
ejpam-5917	246	2	6	6	NUM
ejpam-5917	246	3	.	.	PUNCT
ejpam-5917	247	1	for	for	ADP
ejpam-5917	247	2	any	any	DET
ejpam-5917	247	3	sunlet	sunlet	NOUN
ejpam-5917	247	4	graph	graph	NOUN
ejpam-5917	247	5	sn	sn	PROPN
ejpam-5917	247	6	of	of	ADP
ejpam-5917	247	7	order	order	NOUN
ejpam-5917	247	8	2n	2n	NUM
ejpam-5917	247	9	,	,	PUNCT
ejpam-5917	247	10	γts(sn	γts(sn	NOUN
ejpam-5917	247	11	)	)	PUNCT
ejpam-5917	247	12	=	=	SYM
ejpam-5917	247	13	n.	n.	NOUN
ejpam-5917	247	14	proof	proof	NOUN
ejpam-5917	247	15	.	.	PUNCT
ejpam-5917	248	1	by	by	ADP
ejpam-5917	248	2	theorem	theorem	NOUN
ejpam-5917	248	3	7	7	NUM
ejpam-5917	248	4	,	,	PUNCT
ejpam-5917	248	5	v	v	NOUN
ejpam-5917	248	6	(	(	PUNCT
ejpam-5917	248	7	cn	cn	PROPN
ejpam-5917	248	8	)	)	PUNCT
ejpam-5917	248	9	is	be	AUX
ejpam-5917	248	10	the	the	DET
ejpam-5917	248	11	minimum	minimum	ADJ
ejpam-5917	248	12	total	total	ADJ
ejpam-5917	248	13	safe	safe	ADJ
ejpam-5917	248	14	dominating	dominating	NOUN
ejpam-5917	248	15	set	set	VERB
ejpam-5917	248	16	in	in	ADP
ejpam-5917	248	17	sn	sn	PROPN
ejpam-5917	248	18	.	.	PUNCT
ejpam-5917	249	1	therefore	therefore	ADV
ejpam-5917	249	2	,	,	PUNCT
ejpam-5917	249	3	γts(sn	γts(sn	NOUN
ejpam-5917	249	4	)	)	PUNCT
ejpam-5917	249	5	=	=	SYM
ejpam-5917	249	6	|v	|v	X
ejpam-5917	249	7	(	(	PUNCT
ejpam-5917	249	8	cn)|	cn)|	X
ejpam-5917	249	9	=	=	SYM
ejpam-5917	249	10	n.	n.	PROPN
ejpam-5917	249	11	w.	w.	PROPN
ejpam-5917	249	12	g.	g.	PROPN
ejpam-5917	249	13	jumalon	jumalon	PROPN
ejpam-5917	249	14	,	,	PUNCT
ejpam-5917	249	15	i.	i.	PROPN
ejpam-5917	249	16	cabahug	cabahug	PROPN
ejpam-5917	249	17	/	/	SYM
ejpam-5917	249	18	eur	eur	PROPN
ejpam-5917	249	19	.	.	PUNCT
ejpam-5917	250	1	j.	j.	PROPN
ejpam-5917	250	2	pure	pure	PROPN
ejpam-5917	250	3	appl	appl	PROPN
ejpam-5917	250	4	.	.	PROPN
ejpam-5917	250	5	math	math	PROPN
ejpam-5917	250	6	,	,	PUNCT
ejpam-5917	250	7	18	18	NUM
ejpam-5917	250	8	(	(	PUNCT
ejpam-5917	250	9	2	2	NUM
ejpam-5917	250	10	)	)	PUNCT
ejpam-5917	250	11	(	(	PUNCT
ejpam-5917	250	12	2025	2025	NUM
ejpam-5917	250	13	)	)	PUNCT
ejpam-5917	250	14	,	,	PUNCT
ejpam-5917	250	15	5917	5917	NUM
ejpam-5917	250	16	11	11	NUM
ejpam-5917	250	17	of	of	ADP
ejpam-5917	250	18	12	12	NUM
ejpam-5917	250	19	theorem	theorem	NOUN
ejpam-5917	250	20	8	8	NUM
ejpam-5917	250	21	.	.	PUNCT
ejpam-5917	251	1	let	let	VERB
ejpam-5917	251	2	hn	hn	PRON
ejpam-5917	251	3	be	be	AUX
ejpam-5917	251	4	a	a	DET
ejpam-5917	251	5	helm	helm	NOUN
ejpam-5917	251	6	graph	graph	NOUN
ejpam-5917	251	7	of	of	ADP
ejpam-5917	251	8	order	order	NOUN
ejpam-5917	251	9	2n	2n	NUM
ejpam-5917	252	1	+	+	CCONJ
ejpam-5917	252	2	1	1	NUM
ejpam-5917	252	3	with	with	ADP
ejpam-5917	252	4	central	central	ADJ
ejpam-5917	252	5	vertex	vertex	NOUN
ejpam-5917	252	6	x	x	PUNCT
ejpam-5917	252	7	and	and	CCONJ
ejpam-5917	252	8	vertex	vertex	NOUN
ejpam-5917	252	9	set	set	VERB
ejpam-5917	252	10	v	v	NOUN
ejpam-5917	252	11	(	(	PUNCT
ejpam-5917	252	12	cn	cn	PROPN
ejpam-5917	252	13	)	)	PUNCT
ejpam-5917	252	14	∪	∪	NOUN
ejpam-5917	252	15	{	{	PUNCT
ejpam-5917	252	16	x	x	NOUN
ejpam-5917	252	17	}	}	PUNCT
ejpam-5917	252	18	∪	∪	ADP
ejpam-5917	252	19	p	p	NOUN
ejpam-5917	252	20	,	,	PUNCT
ejpam-5917	252	21	where	where	SCONJ
ejpam-5917	252	22	p	p	NOUN
ejpam-5917	252	23	is	be	AUX
ejpam-5917	252	24	the	the	DET
ejpam-5917	252	25	set	set	NOUN
ejpam-5917	252	26	of	of	ADP
ejpam-5917	252	27	pendant	pendant	ADJ
ejpam-5917	252	28	vertices	vertex	NOUN
ejpam-5917	252	29	in	in	ADP
ejpam-5917	252	30	hn	hn	PROPN
ejpam-5917	252	31	.	.	PUNCT
ejpam-5917	253	1	then	then	ADV
ejpam-5917	253	2	a	a	DET
ejpam-5917	253	3	nonempty	nonempty	ADJ
ejpam-5917	253	4	set	set	VERB
ejpam-5917	253	5	s	s	PRON
ejpam-5917	253	6	⊊	⊊	NOUN
ejpam-5917	253	7	v	v	NOUN
ejpam-5917	253	8	(	(	PUNCT
ejpam-5917	253	9	hn	hn	NOUN
ejpam-5917	253	10	)	)	PUNCT
ejpam-5917	253	11	is	be	AUX
ejpam-5917	253	12	a	a	DET
ejpam-5917	253	13	total	total	ADJ
ejpam-5917	253	14	safe	safe	ADJ
ejpam-5917	253	15	dominating	dominating	NOUN
ejpam-5917	253	16	set	set	NOUN
ejpam-5917	253	17	in	in	ADP
ejpam-5917	253	18	hn	hn	PROPN
ejpam-5917	254	1	if	if	SCONJ
ejpam-5917	255	1	and	and	CCONJ
ejpam-5917	255	2	only	only	ADV
ejpam-5917	255	3	if	if	SCONJ
ejpam-5917	255	4	v	v	X
ejpam-5917	255	5	(	(	PUNCT
ejpam-5917	255	6	cn	cn	PROPN
ejpam-5917	255	7	)	)	PUNCT
ejpam-5917	255	8	⊆	⊆	NUM
ejpam-5917	255	9	s.	s.	PROPN
ejpam-5917	255	10	proof	proof	NOUN
ejpam-5917	255	11	.	.	PUNCT
ejpam-5917	256	1	let	let	VERB
ejpam-5917	256	2	s	s	PRON
ejpam-5917	256	3	be	be	AUX
ejpam-5917	256	4	a	a	DET
ejpam-5917	256	5	total	total	ADJ
ejpam-5917	256	6	safe	safe	ADJ
ejpam-5917	256	7	dominating	dominating	NOUN
ejpam-5917	256	8	set	set	NOUN
ejpam-5917	256	9	in	in	ADP
ejpam-5917	256	10	hn	hn	PROPN
ejpam-5917	256	11	.	.	PUNCT
ejpam-5917	256	12	suppose	suppose	VERB
ejpam-5917	256	13	that	that	SCONJ
ejpam-5917	256	14	v	v	INTJ
ejpam-5917	256	15	(	(	PUNCT
ejpam-5917	256	16	cn	cn	PROPN
ejpam-5917	256	17	)	)	PUNCT
ejpam-5917	256	18	̸⊆	̸⊆	NOUN
ejpam-5917	256	19	s.	s.	PROPN
ejpam-5917	256	20	then	then	ADV
ejpam-5917	256	21	there	there	PRON
ejpam-5917	256	22	exists	exist	VERB
ejpam-5917	256	23	a	a	DET
ejpam-5917	256	24	vertex	vertex	NOUN
ejpam-5917	256	25	v	v	ADP
ejpam-5917	256	26	∈	∈	NOUN
ejpam-5917	256	27	v	v	NOUN
ejpam-5917	256	28	(	(	PUNCT
ejpam-5917	256	29	cn	cn	PROPN
ejpam-5917	256	30	)	)	PUNCT
ejpam-5917	256	31	with	with	ADP
ejpam-5917	256	32	v	v	X
ejpam-5917	256	33	̸∈	̸∈	PROPN
ejpam-5917	256	34	s.	s.	PROPN
ejpam-5917	256	35	let	let	VERB
ejpam-5917	256	36	u	u	PRON
ejpam-5917	256	37	∈	∈	PROPN
ejpam-5917	256	38	v	v	NOUN
ejpam-5917	256	39	(	(	PUNCT
ejpam-5917	256	40	hn	hn	NOUN
ejpam-5917	256	41	)	)	PUNCT
ejpam-5917	256	42	be	be	AUX
ejpam-5917	256	43	a	a	DET
ejpam-5917	256	44	pendant	pendant	ADJ
ejpam-5917	256	45	vertex	vertex	NOUN
ejpam-5917	256	46	such	such	ADJ
ejpam-5917	256	47	that	that	SCONJ
ejpam-5917	256	48	u	u	PROPN
ejpam-5917	256	49	∈	∈	PROPN
ejpam-5917	256	50	n(v	n(v	PROPN
ejpam-5917	256	51	)	)	PUNCT
ejpam-5917	256	52	.	.	PUNCT
ejpam-5917	257	1	then	then	ADV
ejpam-5917	257	2	u	u	PROPN
ejpam-5917	257	3	∈	∈	PROPN
ejpam-5917	257	4	s	s	X
ejpam-5917	257	5	since	since	SCONJ
ejpam-5917	257	6	s	s	NOUN
ejpam-5917	257	7	is	be	AUX
ejpam-5917	257	8	a	a	DET
ejpam-5917	257	9	dominating	dominating	NOUN
ejpam-5917	257	10	set	set	NOUN
ejpam-5917	257	11	in	in	ADP
ejpam-5917	257	12	hn	hn	PROPN
ejpam-5917	257	13	.	.	PUNCT
ejpam-5917	258	1	so	so	ADV
ejpam-5917	258	2	,	,	PUNCT
ejpam-5917	258	3	u	u	NOUN
ejpam-5917	258	4	is	be	AUX
ejpam-5917	258	5	an	an	DET
ejpam-5917	258	6	isolated	isolated	ADJ
ejpam-5917	258	7	vertex	vertex	NOUN
ejpam-5917	258	8	in	in	ADP
ejpam-5917	258	9	hn[s	hn[	NOUN
ejpam-5917	258	10	]	]	PUNCT
ejpam-5917	258	11	,	,	PUNCT
ejpam-5917	258	12	and	and	CCONJ
ejpam-5917	258	13	so	so	ADV
ejpam-5917	258	14	s	s	VERB
ejpam-5917	258	15	is	be	AUX
ejpam-5917	258	16	not	not	PART
ejpam-5917	258	17	a	a	DET
ejpam-5917	258	18	total	total	ADJ
ejpam-5917	258	19	dominating	dominating	NOUN
ejpam-5917	258	20	set	set	NOUN
ejpam-5917	258	21	in	in	ADP
ejpam-5917	258	22	sn	sn	PROPN
ejpam-5917	258	23	,	,	PUNCT
ejpam-5917	258	24	a	a	DET
ejpam-5917	258	25	clear	clear	ADJ
ejpam-5917	258	26	contradiction	contradiction	NOUN
ejpam-5917	258	27	to	to	ADP
ejpam-5917	258	28	the	the	DET
ejpam-5917	258	29	assumption	assumption	NOUN
ejpam-5917	258	30	of	of	ADP
ejpam-5917	258	31	s.	s.	PROPN
ejpam-5917	258	32	hence	hence	PROPN
ejpam-5917	258	33	,	,	PUNCT
ejpam-5917	258	34	v	v	PROPN
ejpam-5917	258	35	(	(	PUNCT
ejpam-5917	258	36	cn	cn	PROPN
ejpam-5917	258	37	)	)	PUNCT
ejpam-5917	258	38	⊆	⊆	NUM
ejpam-5917	258	39	s.	s.	PROPN
ejpam-5917	258	40	conversely	conversely	ADV
ejpam-5917	258	41	,	,	PUNCT
ejpam-5917	258	42	let	let	VERB
ejpam-5917	258	43	v	v	X
ejpam-5917	258	44	(	(	PUNCT
ejpam-5917	258	45	cn	cn	PROPN
ejpam-5917	258	46	)	)	PUNCT
ejpam-5917	258	47	⊆	⊆	NUM
ejpam-5917	258	48	s.	s.	PROPN
ejpam-5917	258	49	clearly	clearly	ADV
ejpam-5917	258	50	,	,	PUNCT
ejpam-5917	258	51	v	v	PROPN
ejpam-5917	258	52	(	(	PUNCT
ejpam-5917	258	53	cn	cn	PROPN
ejpam-5917	258	54	)	)	PUNCT
ejpam-5917	258	55	is	be	AUX
ejpam-5917	258	56	a	a	DET
ejpam-5917	258	57	total	total	ADJ
ejpam-5917	258	58	safe	safe	ADJ
ejpam-5917	258	59	dominating	dominating	NOUN
ejpam-5917	258	60	set	set	NOUN
ejpam-5917	258	61	in	in	ADP
ejpam-5917	258	62	hn	hn	PROPN
ejpam-5917	258	63	.	.	PUNCT
ejpam-5917	259	1	thus	thus	ADV
ejpam-5917	259	2	,	,	PUNCT
ejpam-5917	259	3	s	s	VERB
ejpam-5917	259	4	is	be	AUX
ejpam-5917	259	5	a	a	DET
ejpam-5917	259	6	total	total	ADJ
ejpam-5917	259	7	safe	safe	ADJ
ejpam-5917	259	8	dominating	dominating	NOUN
ejpam-5917	259	9	set	set	NOUN
ejpam-5917	259	10	in	in	ADP
ejpam-5917	259	11	hn	hn	PROPN
ejpam-5917	259	12	.	.	PUNCT
ejpam-5917	260	1	corollary	corollary	ADJ
ejpam-5917	260	2	7	7	NUM
ejpam-5917	260	3	.	.	PUNCT
ejpam-5917	261	1	for	for	ADP
ejpam-5917	261	2	any	any	DET
ejpam-5917	261	3	helm	helm	NOUN
ejpam-5917	261	4	graph	graph	NOUN
ejpam-5917	261	5	hn	hn	PROPN
ejpam-5917	261	6	of	of	ADP
ejpam-5917	261	7	order	order	NOUN
ejpam-5917	261	8	2n+	2n+	NUM
ejpam-5917	261	9	1	1	NUM
ejpam-5917	261	10	,	,	PUNCT
ejpam-5917	261	11	γts(hn	γts(hn	ADV
ejpam-5917	261	12	)	)	PUNCT
ejpam-5917	261	13	=	=	SYM
ejpam-5917	261	14	n.	n.	NOUN
ejpam-5917	261	15	proof	proof	NOUN
ejpam-5917	261	16	.	.	PUNCT
ejpam-5917	262	1	by	by	ADP
ejpam-5917	262	2	theorem	theorem	NOUN
ejpam-5917	262	3	8	8	NUM
ejpam-5917	262	4	,	,	PUNCT
ejpam-5917	262	5	v	v	NOUN
ejpam-5917	262	6	(	(	PUNCT
ejpam-5917	262	7	cn	cn	PROPN
ejpam-5917	262	8	)	)	PUNCT
ejpam-5917	262	9	is	be	AUX
ejpam-5917	262	10	the	the	DET
ejpam-5917	262	11	minimum	minimum	ADJ
ejpam-5917	262	12	total	total	ADJ
ejpam-5917	262	13	safe	safe	ADJ
ejpam-5917	262	14	dominating	dominating	NOUN
ejpam-5917	262	15	set	set	NOUN
ejpam-5917	262	16	in	in	ADP
ejpam-5917	262	17	hn	hn	PROPN
ejpam-5917	262	18	.	.	PUNCT
ejpam-5917	263	1	hence	hence	ADV
ejpam-5917	263	2	,	,	PUNCT
ejpam-5917	263	3	γts(hn	γts(hn	ADV
ejpam-5917	263	4	)	)	PUNCT
ejpam-5917	263	5	=	=	SYM
ejpam-5917	263	6	|v	|v	X
ejpam-5917	263	7	(	(	PUNCT
ejpam-5917	263	8	cn)|	cn)|	X
ejpam-5917	263	9	=	=	SYM
ejpam-5917	263	10	n.	n.	NOUN
ejpam-5917	263	11	conclusions	conclusion	VERB
ejpam-5917	263	12	the	the	DET
ejpam-5917	263	13	concept	concept	NOUN
ejpam-5917	263	14	of	of	ADP
ejpam-5917	263	15	total	total	ADJ
ejpam-5917	263	16	safe	safe	ADJ
ejpam-5917	263	17	domination	domination	NOUN
ejpam-5917	263	18	has	have	AUX
ejpam-5917	263	19	been	be	AUX
ejpam-5917	263	20	introduced	introduce	VERB
ejpam-5917	263	21	and	and	CCONJ
ejpam-5917	263	22	explored	explore	VERB
ejpam-5917	263	23	in	in	ADP
ejpam-5917	263	24	this	this	DET
ejpam-5917	263	25	study	study	NOUN
ejpam-5917	263	26	.	.	PUNCT
ejpam-5917	264	1	some	some	DET
ejpam-5917	264	2	realizations	realization	NOUN
ejpam-5917	264	3	on	on	ADP
ejpam-5917	264	4	how	how	SCONJ
ejpam-5917	264	5	the	the	DET
ejpam-5917	264	6	total	total	ADJ
ejpam-5917	264	7	safe	safe	ADJ
ejpam-5917	264	8	domination	domination	NOUN
ejpam-5917	264	9	number	number	NOUN
ejpam-5917	264	10	relate	relate	VERB
ejpam-5917	264	11	with	with	ADP
ejpam-5917	264	12	the	the	DET
ejpam-5917	264	13	total	total	ADJ
ejpam-5917	264	14	domination	domination	NOUN
ejpam-5917	264	15	number	number	NOUN
ejpam-5917	264	16	and	and	CCONJ
ejpam-5917	264	17	the	the	DET
ejpam-5917	264	18	safe	safe	ADJ
ejpam-5917	264	19	domination	domination	NOUN
ejpam-5917	264	20	number	number	NOUN
ejpam-5917	264	21	are	be	AUX
ejpam-5917	264	22	presented	present	VERB
ejpam-5917	264	23	.	.	PUNCT
ejpam-5917	265	1	characterizations	characterization	NOUN
ejpam-5917	265	2	of	of	ADP
ejpam-5917	265	3	total	total	ADJ
ejpam-5917	265	4	safe	safe	ADJ
ejpam-5917	265	5	dominating	dominating	NOUN
ejpam-5917	265	6	sets	set	NOUN
ejpam-5917	265	7	in	in	ADP
ejpam-5917	265	8	several	several	ADJ
ejpam-5917	265	9	well	well	ADV
ejpam-5917	265	10	-	-	PUNCT
ejpam-5917	265	11	known	know	VERB
ejpam-5917	265	12	families	family	NOUN
ejpam-5917	265	13	of	of	ADP
ejpam-5917	265	14	graphs	graph	NOUN
ejpam-5917	265	15	are	be	AUX
ejpam-5917	265	16	provided	provide	VERB
ejpam-5917	265	17	and	and	CCONJ
ejpam-5917	265	18	used	use	VERB
ejpam-5917	265	19	to	to	PART
ejpam-5917	265	20	determine	determine	VERB
ejpam-5917	265	21	the	the	DET
ejpam-5917	265	22	exact	exact	ADJ
ejpam-5917	265	23	values	value	NOUN
ejpam-5917	265	24	of	of	ADP
ejpam-5917	265	25	total	total	ADJ
ejpam-5917	265	26	safe	safe	ADJ
ejpam-5917	265	27	domination	domination	NOUN
ejpam-5917	265	28	number	number	NOUN
ejpam-5917	265	29	of	of	ADP
ejpam-5917	265	30	those	those	DET
ejpam-5917	265	31	graphs	graph	NOUN
ejpam-5917	265	32	.	.	PUNCT
ejpam-5917	266	1	for	for	ADP
ejpam-5917	266	2	those	those	PRON
ejpam-5917	266	3	interested	interested	ADJ
ejpam-5917	266	4	in	in	ADP
ejpam-5917	266	5	further	further	ADJ
ejpam-5917	266	6	study	study	NOUN
ejpam-5917	266	7	on	on	ADP
ejpam-5917	266	8	this	this	DET
ejpam-5917	266	9	topic	topic	NOUN
ejpam-5917	266	10	,	,	PUNCT
ejpam-5917	266	11	it	it	PRON
ejpam-5917	266	12	would	would	AUX
ejpam-5917	266	13	be	be	AUX
ejpam-5917	266	14	valuable	valuable	ADJ
ejpam-5917	266	15	to	to	PART
ejpam-5917	266	16	explore	explore	VERB
ejpam-5917	266	17	other	other	ADJ
ejpam-5917	266	18	variations	variation	NOUN
ejpam-5917	266	19	of	of	ADP
ejpam-5917	266	20	total	total	ADJ
ejpam-5917	266	21	safe	safe	ADJ
ejpam-5917	266	22	dominating	dominating	NOUN
ejpam-5917	266	23	sets	set	NOUN
ejpam-5917	266	24	,	,	PUNCT
ejpam-5917	266	25	such	such	ADJ
ejpam-5917	266	26	as	as	ADP
ejpam-5917	266	27	restrained	restrained	ADJ
ejpam-5917	266	28	,	,	PUNCT
ejpam-5917	266	29	forcing	force	VERB
ejpam-5917	266	30	,	,	PUNCT
ejpam-5917	266	31	and	and	CCONJ
ejpam-5917	266	32	locating	locating	NOUN
ejpam-5917	266	33	sets	set	NOUN
ejpam-5917	266	34	.	.	PUNCT
ejpam-5917	267	1	the	the	DET
ejpam-5917	267	2	study	study	NOUN
ejpam-5917	267	3	of	of	ADP
ejpam-5917	267	4	domination	domination	NOUN
ejpam-5917	267	5	in	in	ADP
ejpam-5917	267	6	graphs	graph	NOUN
ejpam-5917	267	7	resulting	result	VERB
ejpam-5917	267	8	from	from	ADP
ejpam-5917	267	9	unary	unary	ADJ
ejpam-5917	267	10	operations	operation	NOUN
ejpam-5917	267	11	is	be	AUX
ejpam-5917	267	12	relatively	relatively	ADV
ejpam-5917	267	13	underexplored	underexplored	ADJ
ejpam-5917	267	14	and	and	CCONJ
ejpam-5917	267	15	less	less	ADV
ejpam-5917	267	16	studied	studied	ADJ
ejpam-5917	267	17	.	.	PUNCT
ejpam-5917	268	1	exploring	explore	VERB
ejpam-5917	268	2	total	total	ADJ
ejpam-5917	268	3	safe	safe	ADJ
ejpam-5917	268	4	domination	domination	NOUN
ejpam-5917	268	5	in	in	ADP
ejpam-5917	268	6	such	such	ADJ
ejpam-5917	268	7	graphs	graph	NOUN
ejpam-5917	268	8	is	be	AUX
ejpam-5917	268	9	worthwhile	worthwhile	ADJ
ejpam-5917	268	10	.	.	PUNCT
ejpam-5917	269	1	with	with	ADP
ejpam-5917	269	2	existing	exist	VERB
ejpam-5917	269	3	results	result	NOUN
ejpam-5917	269	4	on	on	ADP
ejpam-5917	269	5	safe	safe	ADJ
ejpam-5917	269	6	domination	domination	NOUN
ejpam-5917	269	7	in	in	ADP
ejpam-5917	269	8	ladder	ladder	NOUN
ejpam-5917	269	9	graphs	graph	NOUN
ejpam-5917	269	10	,	,	PUNCT
ejpam-5917	269	11	a	a	DET
ejpam-5917	269	12	special	special	ADJ
ejpam-5917	269	13	type	type	NOUN
ejpam-5917	269	14	of	of	ADP
ejpam-5917	269	15	grid	grid	NOUN
ejpam-5917	269	16	graph	graph	NOUN
ejpam-5917	269	17	(	(	PUNCT
ejpam-5917	269	18	denoted	denote	VERB
ejpam-5917	269	19	as	as	ADP
ejpam-5917	269	20	(	(	PUNCT
ejpam-5917	269	21	pm	pm	NOUN
ejpam-5917	269	22	×	×	PROPN
ejpam-5917	269	23	pn	pn	NOUN
ejpam-5917	269	24	)	)	PUNCT
ejpam-5917	269	25	)	)	PUNCT
ejpam-5917	269	26	,	,	PUNCT
ejpam-5917	269	27	exploration	exploration	NOUN
ejpam-5917	269	28	of	of	ADP
ejpam-5917	269	29	total	total	ADJ
ejpam-5917	269	30	safe	safe	ADJ
ejpam-5917	269	31	domination	domination	NOUN
ejpam-5917	269	32	within	within	ADP
ejpam-5917	269	33	these	these	DET
ejpam-5917	269	34	graphs	graph	NOUN
ejpam-5917	269	35	is	be	AUX
ejpam-5917	269	36	also	also	ADV
ejpam-5917	269	37	interesting	interesting	ADJ
ejpam-5917	269	38	.	.	PUNCT
ejpam-5917	270	1	finally	finally	ADV
ejpam-5917	270	2	,	,	PUNCT
ejpam-5917	270	3	the	the	DET
ejpam-5917	270	4	authors	author	NOUN
ejpam-5917	270	5	encourage	encourage	VERB
ejpam-5917	270	6	other	other	ADJ
ejpam-5917	270	7	researchers	researcher	NOUN
ejpam-5917	270	8	to	to	PART
ejpam-5917	270	9	investigate	investigate	VERB
ejpam-5917	270	10	inequalities	inequality	NOUN
ejpam-5917	270	11	related	relate	VERB
ejpam-5917	270	12	to	to	ADP
ejpam-5917	270	13	vizing	vize	VERB
ejpam-5917	270	14	’s	’s	PART
ejpam-5917	270	15	conjecture	conjecture	NOUN
ejpam-5917	270	16	and	and	CCONJ
ejpam-5917	270	17	nordhaus	nordhaus	NOUN
ejpam-5917	270	18	-	-	PUNCT
ejpam-5917	270	19	gaddum	gaddum	NOUN
ejpam-5917	270	20	-	-	PUNCT
ejpam-5917	270	21	type	type	NOUN
ejpam-5917	270	22	inequalities	inequality	NOUN
ejpam-5917	270	23	.	.	PUNCT
ejpam-5917	271	1	acknowledgements	acknowledgement	NOUN
ejpam-5917	271	2	the	the	DET
ejpam-5917	271	3	authors	author	NOUN
ejpam-5917	271	4	would	would	AUX
ejpam-5917	271	5	like	like	VERB
ejpam-5917	271	6	to	to	PART
ejpam-5917	271	7	express	express	VERB
ejpam-5917	271	8	their	their	PRON
ejpam-5917	271	9	sincere	sincere	ADJ
ejpam-5917	271	10	thanks	thank	NOUN
ejpam-5917	271	11	to	to	ADP
ejpam-5917	271	12	the	the	DET
ejpam-5917	271	13	anonymous	anonymous	ADJ
ejpam-5917	271	14	referees	referee	NOUN
ejpam-5917	271	15	for	for	ADP
ejpam-5917	271	16	their	their	PRON
ejpam-5917	271	17	helpful	helpful	ADJ
ejpam-5917	271	18	and	and	CCONJ
ejpam-5917	271	19	valuable	valuable	ADJ
ejpam-5917	271	20	comments	comment	NOUN
ejpam-5917	271	21	.	.	PUNCT
ejpam-5917	272	1	heartfelt	heartfelt	ADJ
ejpam-5917	272	2	gratitude	gratitude	NOUN
ejpam-5917	272	3	is	be	AUX
ejpam-5917	272	4	also	also	ADV
ejpam-5917	272	5	extended	extend	VERB
ejpam-5917	272	6	to	to	ADP
ejpam-5917	272	7	the	the	DET
ejpam-5917	272	8	department	department	NOUN
ejpam-5917	272	9	of	of	ADP
ejpam-5917	272	10	science	science	NOUN
ejpam-5917	272	11	and	and	CCONJ
ejpam-5917	272	12	technology	technology	NOUN
ejpam-5917	272	13	,	,	PUNCT
ejpam-5917	272	14	philippines	philippine	NOUN
ejpam-5917	272	15	,	,	PUNCT
ejpam-5917	272	16	for	for	ADP
ejpam-5917	272	17	the	the	DET
ejpam-5917	272	18	financial	financial	ADJ
ejpam-5917	272	19	support	support	NOUN
ejpam-5917	272	20	given	give	VERB
ejpam-5917	272	21	to	to	ADP
ejpam-5917	272	22	the	the	DET
ejpam-5917	272	23	authors	author	NOUN
ejpam-5917	272	24	through	through	ADP
ejpam-5917	272	25	the	the	DET
ejpam-5917	272	26	dost	dost	NOUN
ejpam-5917	272	27	-	-	PUNCT
ejpam-5917	272	28	sei	sei	ADJ
ejpam-5917	272	29	strand	strand	NOUN
ejpam-5917	272	30	scholarship	scholarship	NOUN
ejpam-5917	272	31	program	program	NOUN
ejpam-5917	272	32	.	.	PUNCT
ejpam-5917	273	1	references	reference	NOUN
ejpam-5917	273	2	[	[	X
ejpam-5917	273	3	1	1	NUM
ejpam-5917	273	4	]	]	PUNCT
ejpam-5917	273	5	e	e	X
ejpam-5917	273	6	cockayne	cockayne	NOUN
ejpam-5917	273	7	and	and	CCONJ
ejpam-5917	273	8	s	s	VERB
ejpam-5917	273	9	hedetniemi	hedetniemi	ADV
ejpam-5917	273	10	.	.	PUNCT
ejpam-5917	274	1	towards	towards	ADP
ejpam-5917	274	2	a	a	DET
ejpam-5917	274	3	theory	theory	NOUN
ejpam-5917	274	4	of	of	ADP
ejpam-5917	274	5	domination	domination	NOUN
ejpam-5917	274	6	in	in	ADP
ejpam-5917	274	7	graphs	graph	NOUN
ejpam-5917	274	8	.	.	PUNCT
ejpam-5917	275	1	networks	network	NOUN
ejpam-5917	275	2	,	,	PUNCT
ejpam-5917	275	3	7(4):247–261	7(4):247–261	NUM
ejpam-5917	275	4	,	,	PUNCT
ejpam-5917	275	5	1977	1977	NUM
ejpam-5917	275	6	.	.	PUNCT
ejpam-5917	276	1	w.	w.	PROPN
ejpam-5917	276	2	g.	g.	PROPN
ejpam-5917	276	3	jumalon	jumalon	PROPN
ejpam-5917	276	4	,	,	PUNCT
ejpam-5917	276	5	i.	i.	PROPN
ejpam-5917	276	6	cabahug	cabahug	PROPN
ejpam-5917	276	7	/	/	SYM
ejpam-5917	276	8	eur	eur	PROPN
ejpam-5917	276	9	.	.	PUNCT
ejpam-5917	277	1	j.	j.	PROPN
ejpam-5917	277	2	pure	pure	PROPN
ejpam-5917	277	3	appl	appl	PROPN
ejpam-5917	277	4	.	.	PROPN
ejpam-5917	277	5	math	math	PROPN
ejpam-5917	277	6	,	,	PUNCT
ejpam-5917	277	7	18	18	NUM
ejpam-5917	277	8	(	(	PUNCT
ejpam-5917	277	9	2	2	NUM
ejpam-5917	277	10	)	)	PUNCT
ejpam-5917	277	11	(	(	PUNCT
ejpam-5917	277	12	2025	2025	NUM
ejpam-5917	277	13	)	)	PUNCT
ejpam-5917	277	14	,	,	PUNCT
ejpam-5917	277	15	5917	5917	NUM
ejpam-5917	277	16	12	12	NUM
ejpam-5917	277	17	of	of	ADP
ejpam-5917	277	18	12	12	NUM
ejpam-5917	277	19	[	[	X
ejpam-5917	277	20	2	2	NUM
ejpam-5917	277	21	]	]	PUNCT
ejpam-5917	277	22	e	e	NOUN
ejpam-5917	277	23	cockayne	cockayne	NOUN
ejpam-5917	277	24	,	,	PUNCT
ejpam-5917	277	25	r	r	NOUN
ejpam-5917	277	26	dawes	dawe	NOUN
ejpam-5917	277	27	,	,	PUNCT
ejpam-5917	277	28	and	and	CCONJ
ejpam-5917	277	29	s	s	VERB
ejpam-5917	277	30	hedetniemi	hedetniemi	NOUN
ejpam-5917	277	31	.	.	PUNCT
ejpam-5917	278	1	total	total	ADJ
ejpam-5917	278	2	domination	domination	NOUN
ejpam-5917	278	3	in	in	ADP
ejpam-5917	278	4	graphs	graph	NOUN
ejpam-5917	278	5	.	.	PUNCT
ejpam-5917	279	1	networks	network	NOUN
ejpam-5917	279	2	,	,	PUNCT
ejpam-5917	279	3	10(1):85–95	10(1):85–95	NUM
ejpam-5917	279	4	,	,	PUNCT
ejpam-5917	279	5	1980	1980	NUM
ejpam-5917	279	6	.	.	PUNCT
ejpam-5917	280	1	[	[	X
ejpam-5917	280	2	3	3	X
ejpam-5917	280	3	]	]	X
ejpam-5917	280	4	p	p	X
ejpam-5917	280	5	lam	lam	PROPN
ejpam-5917	280	6	and	and	CCONJ
ejpam-5917	280	7	b	b	PROPN
ejpam-5917	280	8	wei	wei	PROPN
ejpam-5917	280	9	.	.	PUNCT
ejpam-5917	281	1	on	on	ADP
ejpam-5917	281	2	the	the	DET
ejpam-5917	281	3	total	total	ADJ
ejpam-5917	281	4	domination	domination	NOUN
ejpam-5917	281	5	number	number	NOUN
ejpam-5917	281	6	of	of	ADP
ejpam-5917	281	7	graphs	graph	NOUN
ejpam-5917	281	8	.	.	PUNCT
ejpam-5917	282	1	utilitas	utilitas	PROPN
ejpam-5917	282	2	mathematica	mathematica	PROPN
ejpam-5917	282	3	,	,	PUNCT
ejpam-5917	282	4	72	72	NUM
ejpam-5917	282	5	,	,	PUNCT
ejpam-5917	282	6	2007	2007	NUM
ejpam-5917	282	7	.	.	PUNCT
ejpam-5917	283	1	[	[	X
ejpam-5917	283	2	4	4	X
ejpam-5917	283	3	]	]	X
ejpam-5917	283	4	c	c	PUNCT
ejpam-5917	283	5	go	go	VERB
ejpam-5917	283	6	and	and	CCONJ
ejpam-5917	283	7	s	s	VERB
ejpam-5917	283	8	canoy	canoy	PROPN
ejpam-5917	283	9	jr	jr	PROPN
ejpam-5917	283	10	.	.	PROPN
ejpam-5917	283	11	domination	domination	NOUN
ejpam-5917	283	12	in	in	ADP
ejpam-5917	283	13	the	the	DET
ejpam-5917	283	14	corona	corona	NOUN
ejpam-5917	283	15	and	and	CCONJ
ejpam-5917	283	16	join	join	VERB
ejpam-5917	283	17	of	of	ADP
ejpam-5917	283	18	graphs	graph	NOUN
ejpam-5917	283	19	.	.	PUNCT
ejpam-5917	284	1	international	international	ADJ
ejpam-5917	284	2	mathematical	mathematical	PROPN
ejpam-5917	284	3	forum	forum	PROPN
ejpam-5917	284	4	,	,	PUNCT
ejpam-5917	284	5	6(16):767–776	6(16):767–776	PROPN
ejpam-5917	284	6	,	,	PUNCT
ejpam-5917	284	7	2011	2011	NUM
ejpam-5917	284	8	.	.	PUNCT
ejpam-5917	285	1	[	[	X
ejpam-5917	285	2	5	5	NUM
ejpam-5917	285	3	]	]	SYM
ejpam-5917	285	4	r	r	NOUN
ejpam-5917	285	5	eballe	eballe	NOUN
ejpam-5917	285	6	and	and	CCONJ
ejpam-5917	285	7	a	a	DET
ejpam-5917	285	8	miranda	miranda	NOUN
ejpam-5917	285	9	.	.	PUNCT
ejpam-5917	286	1	domination	domination	NOUN
ejpam-5917	286	2	defect	defect	NOUN
ejpam-5917	286	3	for	for	ADP
ejpam-5917	286	4	the	the	DET
ejpam-5917	286	5	join	join	NOUN
ejpam-5917	286	6	and	and	CCONJ
ejpam-5917	286	7	corona	corona	NOUN
ejpam-5917	286	8	of	of	ADP
ejpam-5917	286	9	graphs	graph	NOUN
ejpam-5917	286	10	.	.	PUNCT
ejpam-5917	287	1	applied	apply	VERB
ejpam-5917	287	2	mathematical	mathematical	ADJ
ejpam-5917	287	3	sciences	science	NOUN
ejpam-5917	287	4	,	,	PUNCT
ejpam-5917	287	5	15(12):597–609	15(12):597–609	NOUN
ejpam-5917	287	6	,	,	PUNCT
ejpam-5917	287	7	2021	2021	NUM
ejpam-5917	287	8	.	.	PUNCT
ejpam-5917	288	1	[	[	X
ejpam-5917	288	2	6	6	NUM
ejpam-5917	288	3	]	]	PUNCT
ejpam-5917	288	4	j	j	PROPN
ejpam-5917	288	5	sigarreta	sigarreta	PROPN
ejpam-5917	288	6	.	.	PUNCT
ejpam-5917	289	1	total	total	ADJ
ejpam-5917	289	2	domination	domination	NOUN
ejpam-5917	289	3	on	on	ADP
ejpam-5917	289	4	some	some	DET
ejpam-5917	289	5	graph	graph	NOUN
ejpam-5917	289	6	operators	operator	NOUN
ejpam-5917	289	7	.	.	PUNCT
ejpam-5917	290	1	mathematics	mathematic	NOUN
ejpam-5917	290	2	,	,	PUNCT
ejpam-5917	290	3	9(3):241	9(3):241	NUM
ejpam-5917	290	4	,	,	PUNCT
ejpam-5917	290	5	2021	2021	NUM
ejpam-5917	290	6	.	.	PUNCT
ejpam-5917	291	1	[	[	X
ejpam-5917	291	2	7	7	NUM
ejpam-5917	291	3	]	]	X
ejpam-5917	291	4	w	w	PROPN
ejpam-5917	291	5	klostermeyer	klostermeyer	NOUN
ejpam-5917	291	6	.	.	PUNCT
ejpam-5917	292	1	secure	secure	ADJ
ejpam-5917	292	2	domination	domination	NOUN
ejpam-5917	292	3	and	and	CCONJ
ejpam-5917	292	4	secure	secure	VERB
ejpam-5917	292	5	total	total	ADJ
ejpam-5917	292	6	domination	domination	NOUN
ejpam-5917	292	7	in	in	ADP
ejpam-5917	292	8	graphs	graph	NOUN
ejpam-5917	292	9	.	.	PUNCT
ejpam-5917	293	1	discussiones	discussione	NOUN
ejpam-5917	293	2	mathematicae	mathematicae	PROPN
ejpam-5917	293	3	graph	graph	NOUN
ejpam-5917	293	4	theory	theory	NOUN
ejpam-5917	293	5	,	,	PUNCT
ejpam-5917	293	6	28(2):267–284	28(2):267–284	NUM
ejpam-5917	293	7	,	,	PUNCT
ejpam-5917	293	8	2008	2008	NUM
ejpam-5917	293	9	.	.	PUNCT
ejpam-5917	294	1	[	[	X
ejpam-5917	294	2	8	8	NUM
ejpam-5917	294	3	]	]	X
ejpam-5917	294	4	a	a	DET
ejpam-5917	294	5	gaikwad	gaikwad	NOUN
ejpam-5917	294	6	and	and	CCONJ
ejpam-5917	294	7	s	s	VERB
ejpam-5917	294	8	maity	maity	NOUN
ejpam-5917	294	9	.	.	PUNCT
ejpam-5917	295	1	defensive	defensive	ADJ
ejpam-5917	295	2	alliances	alliance	NOUN
ejpam-5917	295	3	in	in	ADP
ejpam-5917	295	4	graphs	graph	NOUN
ejpam-5917	295	5	.	.	PUNCT
ejpam-5917	296	1	theoretical	theoretical	ADJ
ejpam-5917	296	2	computer	computer	NOUN
ejpam-5917	296	3	science	science	NOUN
ejpam-5917	296	4	,	,	PUNCT
ejpam-5917	296	5	928:136–150	928:136–150	NUM
ejpam-5917	296	6	,	,	PUNCT
ejpam-5917	296	7	2022	2022	NUM
ejpam-5917	296	8	.	.	PUNCT
ejpam-5917	297	1	[	[	X
ejpam-5917	297	2	9	9	NUM
ejpam-5917	297	3	]	]	X
ejpam-5917	297	4	r	r	NOUN
ejpam-5917	297	5	chatterjee	chatterjee	NOUN
ejpam-5917	297	6	,	,	PUNCT
ejpam-5917	297	7	e	e	NOUN
ejpam-5917	297	8	jent	jent	NOUN
ejpam-5917	297	9	,	,	PUNCT
ejpam-5917	297	10	s	s	PROPN
ejpam-5917	297	11	osborn	osborn	PROPN
ejpam-5917	297	12	,	,	PUNCT
ejpam-5917	297	13	and	and	CCONJ
ejpam-5917	297	14	p	p	PROPN
ejpam-5917	297	15	zhang	zhang	PROPN
ejpam-5917	297	16	.	.	PUNCT
ejpam-5917	298	1	proper	proper	ADJ
ejpam-5917	298	2	total	total	ADJ
ejpam-5917	298	3	domination	domination	NOUN
ejpam-5917	298	4	in	in	ADP
ejpam-5917	298	5	graphs	graph	NOUN
ejpam-5917	298	6	.	.	PUNCT
ejpam-5917	299	1	electronic	electronic	ADJ
ejpam-5917	299	2	journal	journal	NOUN
ejpam-5917	299	3	of	of	ADP
ejpam-5917	299	4	mathematics	mathematic	NOUN
ejpam-5917	299	5	,	,	PUNCT
ejpam-5917	299	6	7:58–68	7:58–68	NUM
ejpam-5917	299	7	,	,	PUNCT
ejpam-5917	299	8	2024	2024	NUM
ejpam-5917	299	9	.	.	PUNCT
ejpam-5917	300	1	[	[	X
ejpam-5917	300	2	10	10	NUM
ejpam-5917	300	3	]	]	SYM
ejpam-5917	300	4	s	s	X
ejpam-5917	300	5	fujita	fujita	PROPN
ejpam-5917	300	6	,	,	PUNCT
ejpam-5917	300	7	g	g	PROPN
ejpam-5917	300	8	macgillivray	macgillivray	NOUN
ejpam-5917	300	9	,	,	PUNCT
ejpam-5917	300	10	and	and	CCONJ
ejpam-5917	300	11	t	t	PROPN
ejpam-5917	300	12	sakuma	sakuma	PROPN
ejpam-5917	300	13	.	.	PUNCT
ejpam-5917	301	1	safe	safe	ADJ
ejpam-5917	301	2	set	set	VERB
ejpam-5917	301	3	problem	problem	NOUN
ejpam-5917	301	4	on	on	ADP
ejpam-5917	301	5	graphs	graph	NOUN
ejpam-5917	301	6	.	.	PUNCT
ejpam-5917	302	1	discrete	discrete	ADJ
ejpam-5917	302	2	applied	apply	VERB
ejpam-5917	302	3	mathematics	mathematic	NOUN
ejpam-5917	302	4	,	,	PUNCT
ejpam-5917	302	5	215:106–111	215:106–111	NUM
ejpam-5917	302	6	,	,	PUNCT
ejpam-5917	302	7	2016	2016	NUM
ejpam-5917	302	8	.	.	PUNCT
ejpam-5917	303	1	[	[	X
ejpam-5917	303	2	11	11	NUM
ejpam-5917	303	3	]	]	X
ejpam-5917	303	4	d	d	X
ejpam-5917	303	5	f	f	PROPN
ejpam-5917	303	6	griño	griño	PROPN
ejpam-5917	303	7	,	,	PUNCT
ejpam-5917	303	8	m	m	VERB
ejpam-5917	303	9	maceren	maceren	NOUN
ejpam-5917	303	10	,	,	PUNCT
ejpam-5917	303	11	and	and	CCONJ
ejpam-5917	303	12	i	i	PRON
ejpam-5917	303	13	cabahug	cabahug	VERB
ejpam-5917	303	14	jr	jr	PROPN
ejpam-5917	303	15	.	.	PUNCT
ejpam-5917	303	16	introducing	introduce	VERB
ejpam-5917	303	17	safe	safe	ADJ
ejpam-5917	303	18	domination	domination	NOUN
ejpam-5917	303	19	in	in	ADP
ejpam-5917	303	20	graphs	graph	NOUN
ejpam-5917	303	21	.	.	PUNCT
ejpam-5917	304	1	international	international	ADJ
ejpam-5917	304	2	journal	journal	PROPN
ejpam-5917	304	3	of	of	ADP
ejpam-5917	304	4	mathematics	mathematics	NOUN
ejpam-5917	304	5	trends	trend	NOUN
ejpam-5917	304	6	and	and	CCONJ
ejpam-5917	304	7	technology	technology	NOUN
ejpam-5917	304	8	,	,	PUNCT
ejpam-5917	304	9	69(10):17–24	69(10):17–24	NOUN
ejpam-5917	304	10	,	,	PUNCT
ejpam-5917	304	11	2023	2023	NUM
ejpam-5917	304	12	.	.	PUNCT
ejpam-5917	305	1	[	[	X
ejpam-5917	305	2	12	12	NUM
ejpam-5917	305	3	]	]	X
ejpam-5917	305	4	g	g	PROPN
ejpam-5917	305	5	chartrand	chartrand	NOUN
ejpam-5917	305	6	,	,	PUNCT
ejpam-5917	305	7	l	l	PROPN
ejpam-5917	305	8	lesniak	lesniak	PROPN
ejpam-5917	305	9	,	,	PUNCT
ejpam-5917	305	10	and	and	CCONJ
ejpam-5917	305	11	p	p	PROPN
ejpam-5917	305	12	zhang	zhang	PROPN
ejpam-5917	305	13	.	.	PUNCT
ejpam-5917	306	1	graphs	graphs	PROPN
ejpam-5917	306	2	digraphs	digraphs	VERB
ejpam-5917	306	3	.	.	PUNCT
ejpam-5917	307	1	crc	crc	PROPN
ejpam-5917	307	2	press	press	PROPN
ejpam-5917	307	3	,	,	PUNCT
ejpam-5917	307	4	united	united	ADJ
ejpam-5917	307	5	kingdom	kingdom	PROPN
ejpam-5917	307	6	,	,	PUNCT
ejpam-5917	307	7	2015	2015	NUM
ejpam-5917	307	8	.	.	PUNCT
ejpam-5917	308	1	[	[	X
ejpam-5917	308	2	13	13	NUM
ejpam-5917	308	3	]	]	X
ejpam-5917	308	4	j	j	PROPN
ejpam-5917	308	5	bondy	bondy	PROPN
ejpam-5917	308	6	and	and	CCONJ
ejpam-5917	308	7	u	u	NOUN
ejpam-5917	308	8	s	s	NOUN
ejpam-5917	308	9	murty	murty	NOUN
ejpam-5917	308	10	.	.	PUNCT
ejpam-5917	309	1	graph	graph	NOUN
ejpam-5917	309	2	theory	theory	NOUN
ejpam-5917	309	3	with	with	ADP
ejpam-5917	309	4	applications	application	NOUN
ejpam-5917	309	5	.	.	PUNCT
ejpam-5917	310	1	springer	springer	PROPN
ejpam-5917	310	2	,	,	PUNCT
ejpam-5917	310	3	london	london	PROPN
ejpam-5917	310	4	,	,	PUNCT
ejpam-5917	310	5	2008	2008	NUM
ejpam-5917	310	6	.	.	PUNCT
ejpam-5917	311	1	[	[	X
ejpam-5917	311	2	14	14	NUM
ejpam-5917	311	3	]	]	X
ejpam-5917	311	4	j	j	PROPN
ejpam-5917	311	5	gallian	gallian	PROPN
ejpam-5917	311	6	.	.	PUNCT
ejpam-5917	312	1	dynamic	dynamic	ADJ
ejpam-5917	312	2	survey	survey	NOUN
ejpam-5917	312	3	of	of	ADP
ejpam-5917	312	4	graph	graph	NOUN
ejpam-5917	312	5	labeling	labeling	NOUN
ejpam-5917	312	6	.	.	PUNCT
ejpam-5917	313	1	the	the	DET
ejpam-5917	313	2	electronic	electronic	ADJ
ejpam-5917	313	3	journal	journal	NOUN
ejpam-5917	313	4	of	of	ADP
ejpam-5917	313	5	combinatorics	combinatorics	PROPN
ejpam-5917	313	6	,	,	PUNCT
ejpam-5917	313	7	ds6	ds6	NOUN
ejpam-5917	313	8	,	,	PUNCT
ejpam-5917	313	9	2000	2000	NUM
ejpam-5917	313	10	.	.	PUNCT
ejpam-5917	314	1	[	[	X
ejpam-5917	314	2	15	15	NUM
ejpam-5917	314	3	]	]	X
ejpam-5917	314	4	r	r	NOUN
ejpam-5917	314	5	frucht	frucht	NOUN
ejpam-5917	314	6	.	.	PUNCT
ejpam-5917	315	1	graceful	graceful	ADJ
ejpam-5917	315	2	numbering	numbering	NOUN
ejpam-5917	315	3	of	of	ADP
ejpam-5917	315	4	wheels	wheel	NOUN
ejpam-5917	315	5	and	and	CCONJ
ejpam-5917	315	6	related	related	ADJ
ejpam-5917	315	7	graphs	graph	NOUN
ejpam-5917	315	8	.	.	PUNCT
ejpam-5917	316	1	annals	annal	NOUN
ejpam-5917	316	2	of	of	ADP
ejpam-5917	316	3	the	the	DET
ejpam-5917	316	4	new	new	PROPN
ejpam-5917	316	5	york	york	PROPN
ejpam-5917	316	6	academy	academy	PROPN
ejpam-5917	316	7	of	of	ADP
ejpam-5917	316	8	sciences	sciences	PROPN
ejpam-5917	316	9	,	,	PUNCT
ejpam-5917	316	10	319:219–229	319:219–229	NUM
ejpam-5917	316	11	,	,	PUNCT
ejpam-5917	316	12	1979	1979	NUM
ejpam-5917	316	13	.	.	PUNCT
ejpam-5917	317	1	[	[	X
ejpam-5917	317	2	16	16	NUM
ejpam-5917	317	3	]	]	PUNCT
ejpam-5917	317	4	t	t	PROPN
ejpam-5917	317	5	haynes	haynes	PROPN
ejpam-5917	317	6	,	,	PUNCT
ejpam-5917	317	7	s	s	VERB
ejpam-5917	317	8	hedetniemi	hedetniemi	ADV
ejpam-5917	317	9	,	,	PUNCT
ejpam-5917	317	10	and	and	CCONJ
ejpam-5917	317	11	m	m	PROPN
ejpam-5917	317	12	henning	henning	NOUN
ejpam-5917	317	13	.	.	PUNCT
ejpam-5917	318	1	fundamentals	fundamental	NOUN
ejpam-5917	318	2	of	of	ADP
ejpam-5917	318	3	domination	domination	NOUN
ejpam-5917	318	4	in	in	ADP
ejpam-5917	318	5	graphs	graph	NOUN
ejpam-5917	318	6	.	.	PUNCT
ejpam-5917	319	1	crc	crc	PROPN
ejpam-5917	319	2	press	press	PROPN
ejpam-5917	319	3	,	,	PUNCT
ejpam-5917	319	4	united	united	ADJ
ejpam-5917	319	5	kingdom	kingdom	PROPN
ejpam-5917	319	6	,	,	PUNCT
ejpam-5917	319	7	1998	1998	NUM
ejpam-5917	319	8	.	.	PUNCT
ejpam-5917	320	1	[	[	X
ejpam-5917	320	2	17	17	NUM
ejpam-5917	320	3	]	]	X
ejpam-5917	320	4	k	k	PROPN
ejpam-5917	320	5	tan	tan	PROPN
ejpam-5917	320	6	and	and	CCONJ
ejpam-5917	320	7	i	i	PRON
ejpam-5917	320	8	cabahug	cabahug	VERB
ejpam-5917	320	9	jr	jr	PROPN
ejpam-5917	320	10	.	.	PUNCT
ejpam-5917	321	1	safe	safe	ADJ
ejpam-5917	321	2	sets	set	NOUN
ejpam-5917	321	3	in	in	ADP
ejpam-5917	321	4	some	some	DET
ejpam-5917	321	5	graph	graph	NOUN
ejpam-5917	321	6	families	family	NOUN
ejpam-5917	321	7	.	.	PUNCT
ejpam-5917	322	1	asian	asian	ADJ
ejpam-5917	322	2	research	research	PROPN
ejpam-5917	322	3	journal	journal	NOUN
ejpam-5917	322	4	of	of	ADP
ejpam-5917	322	5	mathematics	mathematic	NOUN
ejpam-5917	322	6	,	,	PUNCT
ejpam-5917	322	7	18(9):1–7	18(9):1–7	NUM
ejpam-5917	322	8	,	,	PUNCT
ejpam-5917	322	9	2022	2022	NUM
ejpam-5917	322	10	.	.	PUNCT