id	sid	tid	token	lemma	pos
ejpam-4461	1	1	european	european	PROPN
ejpam-4461	1	2	journal	journal	PROPN
ejpam-4461	1	3	of	of	ADP
ejpam-4461	1	4	pure	pure	ADJ
ejpam-4461	1	5	and	and	CCONJ
ejpam-4461	1	6	applied	apply	VERB
ejpam-4461	1	7	mathematics	mathematic	NOUN
ejpam-4461	1	8	vol	vol	NOUN
ejpam-4461	1	9	.	.	PROPN
ejpam-4461	2	1	15	15	NUM
ejpam-4461	2	2	,	,	PUNCT
ejpam-4461	2	3	no	no	INTJ
ejpam-4461	2	4	.	.	NOUN
ejpam-4461	2	5	3	3	NUM
ejpam-4461	2	6	,	,	PUNCT
ejpam-4461	2	7	2022	2022	NUM
ejpam-4461	2	8	,	,	PUNCT
ejpam-4461	2	9	1265	1265	NUM
ejpam-4461	2	10	-	-	SYM
ejpam-4461	2	11	1279	1279	NUM
ejpam-4461	2	12	issn	issn	PROPN
ejpam-4461	2	13	1307	1307	NUM
ejpam-4461	2	14	-	-	SYM
ejpam-4461	2	15	5543	5543	NUM
ejpam-4461	2	16	–	–	PUNCT
ejpam-4461	2	17	ejpam.com	ejpam.com	X
ejpam-4461	2	18	published	publish	VERB
ejpam-4461	2	19	by	by	ADP
ejpam-4461	2	20	new	new	PROPN
ejpam-4461	2	21	york	york	PROPN
ejpam-4461	2	22	business	business	PROPN
ejpam-4461	2	23	global	global	ADJ
ejpam-4461	2	24	outer	outer	ADV
ejpam-4461	2	25	-	-	PUNCT
ejpam-4461	2	26	connected	connect	VERB
ejpam-4461	2	27	semitotal	semitotal	ADJ
ejpam-4461	2	28	domination	domination	NOUN
ejpam-4461	2	29	in	in	ADP
ejpam-4461	2	30	graphs	graph	NOUN
ejpam-4461	2	31	alkajim	alkajim	PROPN
ejpam-4461	2	32	ahadi	ahadi	PROPN
ejpam-4461	2	33	aradais1,∗	aradais1,∗	PROPN
ejpam-4461	2	34	,	,	PUNCT
ejpam-4461	3	1	ferdinand	ferdinand	PROPN
ejpam-4461	3	2	p.	p.	PROPN
ejpam-4461	3	3	jamil2,3	jamil2,3	PROPN
ejpam-4461	3	4	1	1	NUM
ejpam-4461	3	5	intergrated	intergrate	VERB
ejpam-4461	3	6	laboratory	laboratory	NOUN
ejpam-4461	3	7	school	school	NOUN
ejpam-4461	3	8	,	,	PUNCT
ejpam-4461	3	9	college	college	NOUN
ejpam-4461	3	10	of	of	ADP
ejpam-4461	3	11	education	education	NOUN
ejpam-4461	3	12	,	,	PUNCT
ejpam-4461	3	13	msu	msu	PROPN
ejpam-4461	3	14	tawi	tawi	PROPN
ejpam-4461	3	15	-	-	PUNCT
ejpam-4461	3	16	tawi	tawi	PROPN
ejpam-4461	3	17	college	college	PROPN
ejpam-4461	3	18	of	of	ADP
ejpam-4461	3	19	technology	technology	NOUN
ejpam-4461	3	20	and	and	CCONJ
ejpam-4461	3	21	oceanography	oceanography	NOUN
ejpam-4461	3	22	,	,	PUNCT
ejpam-4461	3	23	bongao	bongao	NOUN
ejpam-4461	3	24	,	,	PUNCT
ejpam-4461	3	25	tawi	tawi	NOUN
ejpam-4461	3	26	-	-	PUNCT
ejpam-4461	3	27	tawi	tawi	NOUN
ejpam-4461	3	28	,	,	PUNCT
ejpam-4461	3	29	philippines	philippines	PROPN
ejpam-4461	3	30	2	2	NUM
ejpam-4461	3	31	department	department	NOUN
ejpam-4461	3	32	of	of	ADP
ejpam-4461	3	33	mathematics	mathematic	NOUN
ejpam-4461	3	34	and	and	CCONJ
ejpam-4461	3	35	statistics	statistic	NOUN
ejpam-4461	3	36	,	,	PUNCT
ejpam-4461	3	37	college	college	NOUN
ejpam-4461	3	38	of	of	ADP
ejpam-4461	3	39	science	science	NOUN
ejpam-4461	3	40	and	and	CCONJ
ejpam-4461	3	41	mathematics	mathematic	NOUN
ejpam-4461	3	42	,	,	PUNCT
ejpam-4461	3	43	3	3	NUM
ejpam-4461	3	44	center	center	NOUN
ejpam-4461	3	45	for	for	ADP
ejpam-4461	3	46	graph	graph	NOUN
ejpam-4461	3	47	theory	theory	NOUN
ejpam-4461	3	48	,	,	PUNCT
ejpam-4461	3	49	premier	premier	PROPN
ejpam-4461	3	50	research	research	PROPN
ejpam-4461	3	51	institute	institute	PROPN
ejpam-4461	3	52	of	of	ADP
ejpam-4461	3	53	science	science	NOUN
ejpam-4461	3	54	and	and	CCONJ
ejpam-4461	3	55	mathematics	mathematic	NOUN
ejpam-4461	3	56	,	,	PUNCT
ejpam-4461	3	57	msu	msu	PROPN
ejpam-4461	3	58	-	-	PUNCT
ejpam-4461	3	59	iligan	iligan	PROPN
ejpam-4461	3	60	institute	institute	PROPN
ejpam-4461	3	61	of	of	ADP
ejpam-4461	3	62	technology	technology	PROPN
ejpam-4461	3	63	,	,	PUNCT
ejpam-4461	3	64	9200	9200	NUM
ejpam-4461	3	65	iligan	iligan	ADJ
ejpam-4461	3	66	city	city	NOUN
ejpam-4461	3	67	,	,	PUNCT
ejpam-4461	3	68	philippines	philippine	NOUN
ejpam-4461	3	69	abstract	abstract	ADJ
ejpam-4461	3	70	.	.	PUNCT
ejpam-4461	4	1	in	in	ADP
ejpam-4461	4	2	this	this	DET
ejpam-4461	4	3	paper	paper	NOUN
ejpam-4461	4	4	,	,	PUNCT
ejpam-4461	4	5	we	we	PRON
ejpam-4461	4	6	introduce	introduce	VERB
ejpam-4461	4	7	and	and	CCONJ
ejpam-4461	4	8	initiate	initiate	VERB
ejpam-4461	4	9	the	the	DET
ejpam-4461	4	10	study	study	NOUN
ejpam-4461	4	11	of	of	ADP
ejpam-4461	4	12	outer	outer	ADV
ejpam-4461	4	13	-	-	PUNCT
ejpam-4461	4	14	connected	connect	VERB
ejpam-4461	4	15	semitotal	semitotal	ADJ
ejpam-4461	4	16	domination	domination	NOUN
ejpam-4461	4	17	in	in	ADP
ejpam-4461	4	18	graphs	graph	NOUN
ejpam-4461	4	19	.	.	PUNCT
ejpam-4461	5	1	given	give	VERB
ejpam-4461	5	2	a	a	DET
ejpam-4461	5	3	graph	graph	NOUN
ejpam-4461	5	4	g	g	NOUN
ejpam-4461	5	5	without	without	ADP
ejpam-4461	5	6	isolated	isolated	ADJ
ejpam-4461	5	7	vertices	vertex	NOUN
ejpam-4461	5	8	,	,	PUNCT
ejpam-4461	5	9	a	a	DET
ejpam-4461	5	10	set	set	NOUN
ejpam-4461	5	11	s	s	NOUN
ejpam-4461	5	12	of	of	ADP
ejpam-4461	5	13	vertices	vertex	NOUN
ejpam-4461	5	14	of	of	ADP
ejpam-4461	5	15	g	g	PROPN
ejpam-4461	5	16	is	be	AUX
ejpam-4461	5	17	a	a	DET
ejpam-4461	5	18	semitotal	semitotal	ADJ
ejpam-4461	5	19	dominating	dominating	NOUN
ejpam-4461	5	20	set	set	NOUN
ejpam-4461	5	21	if	if	SCONJ
ejpam-4461	5	22	every	every	DET
ejpam-4461	5	23	vertex	vertex	NOUN
ejpam-4461	5	24	outside	outside	ADP
ejpam-4461	5	25	of	of	ADP
ejpam-4461	5	26	s	s	NOUN
ejpam-4461	5	27	is	be	AUX
ejpam-4461	5	28	adjacent	adjacent	ADJ
ejpam-4461	5	29	to	to	ADP
ejpam-4461	5	30	a	a	DET
ejpam-4461	5	31	vertex	vertex	NOUN
ejpam-4461	5	32	in	in	ADP
ejpam-4461	5	33	s	s	PRON
ejpam-4461	5	34	and	and	CCONJ
ejpam-4461	5	35	every	every	DET
ejpam-4461	5	36	vertex	vertex	NOUN
ejpam-4461	5	37	in	in	ADP
ejpam-4461	5	38	s	s	PROPN
ejpam-4461	5	39	is	be	AUX
ejpam-4461	5	40	of	of	ADP
ejpam-4461	5	41	distance	distance	NOUN
ejpam-4461	5	42	at	at	ADP
ejpam-4461	5	43	most	most	ADJ
ejpam-4461	5	44	2	2	NUM
ejpam-4461	5	45	units	unit	NOUN
ejpam-4461	5	46	from	from	ADP
ejpam-4461	5	47	another	another	DET
ejpam-4461	5	48	vertex	vertex	NOUN
ejpam-4461	5	49	in	in	ADP
ejpam-4461	5	50	s.	s.	PROPN
ejpam-4461	5	51	a	a	DET
ejpam-4461	5	52	semitotal	semitotal	ADJ
ejpam-4461	5	53	dominating	dominating	NOUN
ejpam-4461	5	54	set	set	NOUN
ejpam-4461	5	55	s	s	NOUN
ejpam-4461	5	56	of	of	ADP
ejpam-4461	5	57	g	g	PROPN
ejpam-4461	5	58	is	be	AUX
ejpam-4461	5	59	an	an	DET
ejpam-4461	5	60	outer	outer	ADV
ejpam-4461	5	61	-	-	PUNCT
ejpam-4461	5	62	connected	connect	VERB
ejpam-4461	5	63	semitotal	semitotal	ADJ
ejpam-4461	5	64	dominating	dominating	NOUN
ejpam-4461	5	65	set	set	NOUN
ejpam-4461	5	66	if	if	SCONJ
ejpam-4461	5	67	either	either	PRON
ejpam-4461	5	68	s	s	VERB
ejpam-4461	5	69	=	=	SYM
ejpam-4461	5	70	v	v	PROPN
ejpam-4461	5	71	(	(	PUNCT
ejpam-4461	5	72	g	g	NOUN
ejpam-4461	5	73	)	)	PUNCT
ejpam-4461	5	74	or	or	CCONJ
ejpam-4461	5	75	s	s	AUX
ejpam-4461	5	76	̸=	̸=	PROPN
ejpam-4461	5	77	v	v	NOUN
ejpam-4461	5	78	(	(	PUNCT
ejpam-4461	5	79	g	g	NOUN
ejpam-4461	5	80	)	)	PUNCT
ejpam-4461	5	81	satisfying	satisfy	VERB
ejpam-4461	5	82	the	the	DET
ejpam-4461	5	83	property	property	NOUN
ejpam-4461	5	84	that	that	PRON
ejpam-4461	5	85	the	the	DET
ejpam-4461	5	86	subgraph	subgraph	NOUN
ejpam-4461	5	87	induced	induce	VERB
ejpam-4461	5	88	by	by	ADP
ejpam-4461	5	89	v	v	NOUN
ejpam-4461	5	90	(	(	PUNCT
ejpam-4461	5	91	g	g	NOUN
ejpam-4461	5	92	)	)	PUNCT
ejpam-4461	5	93	\	\	PROPN
ejpam-4461	6	1	s	s	PART
ejpam-4461	6	2	is	be	AUX
ejpam-4461	6	3	connected	connect	VERB
ejpam-4461	6	4	.	.	PUNCT
ejpam-4461	7	1	the	the	DET
ejpam-4461	7	2	smallest	small	ADJ
ejpam-4461	7	3	cardinality	cardinality	NOUN
ejpam-4461	7	4	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	7	5	)	)	PUNCT
ejpam-4461	7	6	of	of	ADP
ejpam-4461	7	7	an	an	DET
ejpam-4461	7	8	outer	outer	ADV
ejpam-4461	7	9	-	-	PUNCT
ejpam-4461	7	10	connected	connect	VERB
ejpam-4461	7	11	semitotal	semitotal	ADJ
ejpam-4461	7	12	dominating	dominating	NOUN
ejpam-4461	7	13	set	set	NOUN
ejpam-4461	7	14	is	be	AUX
ejpam-4461	7	15	the	the	DET
ejpam-4461	7	16	outer	outer	ADV
ejpam-4461	7	17	-	-	PUNCT
ejpam-4461	7	18	connected	connect	VERB
ejpam-4461	7	19	semitotal	semitotal	ADJ
ejpam-4461	7	20	domination	domination	NOUN
ejpam-4461	7	21	number	number	NOUN
ejpam-4461	7	22	of	of	ADP
ejpam-4461	7	23	g.	g.	PROPN
ejpam-4461	7	24	first	first	ADV
ejpam-4461	7	25	,	,	PUNCT
ejpam-4461	7	26	we	we	PRON
ejpam-4461	7	27	determine	determine	VERB
ejpam-4461	7	28	the	the	DET
ejpam-4461	7	29	specific	specific	ADJ
ejpam-4461	7	30	values	value	NOUN
ejpam-4461	7	31	of	of	ADP
ejpam-4461	7	32	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	7	33	)	)	PUNCT
ejpam-4461	7	34	for	for	ADP
ejpam-4461	7	35	some	some	DET
ejpam-4461	7	36	special	special	ADJ
ejpam-4461	7	37	graphs	graph	NOUN
ejpam-4461	7	38	and	and	CCONJ
ejpam-4461	7	39	characterize	characterize	VERB
ejpam-4461	7	40	graphs	graph	NOUN
ejpam-4461	7	41	g	g	NOUN
ejpam-4461	7	42	for	for	ADP
ejpam-4461	7	43	specific	specific	ADJ
ejpam-4461	7	44	(	(	PUNCT
ejpam-4461	7	45	small	small	ADJ
ejpam-4461	7	46	)	)	PUNCT
ejpam-4461	7	47	values	value	NOUN
ejpam-4461	7	48	of	of	ADP
ejpam-4461	7	49	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	7	50	)	)	PUNCT
ejpam-4461	7	51	.	.	PUNCT
ejpam-4461	8	1	finally	finally	ADV
ejpam-4461	8	2	,	,	PUNCT
ejpam-4461	8	3	we	we	PRON
ejpam-4461	8	4	investigate	investigate	VERB
ejpam-4461	8	5	the	the	DET
ejpam-4461	8	6	outer	outer	ADV
ejpam-4461	8	7	-	-	PUNCT
ejpam-4461	8	8	connected	connect	VERB
ejpam-4461	8	9	semitotal	semitotal	ADJ
ejpam-4461	8	10	dominating	dominating	NOUN
ejpam-4461	8	11	sets	set	NOUN
ejpam-4461	8	12	in	in	ADP
ejpam-4461	8	13	the	the	DET
ejpam-4461	8	14	join	join	NOUN
ejpam-4461	8	15	,	,	PUNCT
ejpam-4461	8	16	corona	corona	PROPN
ejpam-4461	8	17	,	,	PUNCT
ejpam-4461	8	18	and	and	CCONJ
ejpam-4461	8	19	composition	composition	NOUN
ejpam-4461	8	20	of	of	ADP
ejpam-4461	8	21	graphs	graph	NOUN
ejpam-4461	8	22	and	and	CCONJ
ejpam-4461	8	23	,	,	PUNCT
ejpam-4461	8	24	as	as	ADP
ejpam-4461	8	25	a	a	DET
ejpam-4461	8	26	consequence	consequence	NOUN
ejpam-4461	8	27	,	,	PUNCT
ejpam-4461	8	28	we	we	PRON
ejpam-4461	8	29	determine	determine	VERB
ejpam-4461	8	30	their	their	PRON
ejpam-4461	8	31	corresponding	correspond	VERB
ejpam-4461	8	32	outer	outer	ADV
ejpam-4461	8	33	-	-	PUNCT
ejpam-4461	8	34	connected	connect	VERB
ejpam-4461	8	35	semitotal	semitotal	ADJ
ejpam-4461	8	36	domination	domination	NOUN
ejpam-4461	8	37	numbers	number	NOUN
ejpam-4461	8	38	.	.	PUNCT
ejpam-4461	9	1	2020	2020	NUM
ejpam-4461	9	2	mathematics	mathematic	NOUN
ejpam-4461	9	3	subject	subject	NOUN
ejpam-4461	9	4	classifications	classification	NOUN
ejpam-4461	9	5	:	:	PUNCT
ejpam-4461	9	6	05c69	05c69	X
ejpam-4461	9	7	key	key	ADJ
ejpam-4461	9	8	words	word	NOUN
ejpam-4461	9	9	and	and	CCONJ
ejpam-4461	9	10	phrases	phrase	NOUN
ejpam-4461	9	11	:	:	PUNCT
ejpam-4461	9	12	semitotal	semitotal	ADJ
ejpam-4461	9	13	dominating	dominating	NOUN
ejpam-4461	9	14	set	set	NOUN
ejpam-4461	9	15	,	,	PUNCT
ejpam-4461	9	16	semitotal	semitotal	ADJ
ejpam-4461	9	17	domination	domination	NOUN
ejpam-4461	9	18	number	number	NOUN
ejpam-4461	9	19	,	,	PUNCT
ejpam-4461	9	20	outerconnected	outerconnecte	VERB
ejpam-4461	9	21	dominating	dominating	NOUN
ejpam-4461	9	22	set	set	NOUN
ejpam-4461	9	23	,	,	PUNCT
ejpam-4461	9	24	outer	outer	ADV
ejpam-4461	9	25	-	-	PUNCT
ejpam-4461	9	26	connected	connect	VERB
ejpam-4461	9	27	domination	domination	NOUN
ejpam-4461	9	28	number	number	NOUN
ejpam-4461	9	29	1	1	NUM
ejpam-4461	9	30	.	.	PUNCT
ejpam-4461	9	31	introduction	introduction	NOUN
ejpam-4461	9	32	in	in	ADP
ejpam-4461	9	33	2014	2014	NUM
ejpam-4461	9	34	,	,	PUNCT
ejpam-4461	9	35	the	the	DET
ejpam-4461	9	36	concept	concept	NOUN
ejpam-4461	9	37	of	of	ADP
ejpam-4461	9	38	semitotal	semitotal	ADJ
ejpam-4461	9	39	domintion	domintion	NOUN
ejpam-4461	9	40	was	be	AUX
ejpam-4461	9	41	introduced	introduce	VERB
ejpam-4461	9	42	and	and	CCONJ
ejpam-4461	9	43	investigated	investigate	VERB
ejpam-4461	9	44	by	by	ADP
ejpam-4461	9	45	w.	w.	PROPN
ejpam-4461	9	46	goddard	goddard	PROPN
ejpam-4461	9	47	,	,	PUNCT
ejpam-4461	9	48	m.	m.	NOUN
ejpam-4461	9	49	henning	henning	PROPN
ejpam-4461	9	50	,	,	PUNCT
ejpam-4461	9	51	and	and	CCONJ
ejpam-4461	9	52	c.	c.	PROPN
ejpam-4461	9	53	mcpillan	mcpillan	NOUN
ejpam-4461	9	54	(	(	PUNCT
ejpam-4461	9	55	see	see	VERB
ejpam-4461	9	56	[	[	X
ejpam-4461	9	57	6	6	NUM
ejpam-4461	9	58	]	]	NUM
ejpam-4461	9	59	)	)	PUNCT
ejpam-4461	9	60	.	.	PUNCT
ejpam-4461	10	1	accordingly	accordingly	ADV
ejpam-4461	10	2	,	,	PUNCT
ejpam-4461	10	3	it	it	PRON
ejpam-4461	10	4	strengthens	strengthen	VERB
ejpam-4461	10	5	the	the	DET
ejpam-4461	10	6	concept	concept	NOUN
ejpam-4461	10	7	of	of	ADP
ejpam-4461	10	8	domination	domination	NOUN
ejpam-4461	10	9	but	but	CCONJ
ejpam-4461	10	10	relaxes	relax	VERB
ejpam-4461	10	11	the	the	DET
ejpam-4461	10	12	concept	concept	NOUN
ejpam-4461	10	13	of	of	ADP
ejpam-4461	10	14	total	total	ADJ
ejpam-4461	10	15	domination	domination	NOUN
ejpam-4461	10	16	.	.	PUNCT
ejpam-4461	11	1	semitotal	semitotal	ADJ
ejpam-4461	11	2	domination	domination	NOUN
ejpam-4461	11	3	was	be	AUX
ejpam-4461	11	4	further	far	ADV
ejpam-4461	11	5	studied	study	VERB
ejpam-4461	11	6	by	by	ADP
ejpam-4461	11	7	m.	m.	NOUN
ejpam-4461	11	8	henning	henning	PROPN
ejpam-4461	11	9	and	and	CCONJ
ejpam-4461	11	10	a.	a.	NOUN
ejpam-4461	11	11	marcon	marcon	PROPN
ejpam-4461	11	12	(	(	PUNCT
ejpam-4461	11	13	see	see	VERB
ejpam-4461	11	14	[	[	X
ejpam-4461	11	15	8	8	NUM
ejpam-4461	11	16	]	]	SYM
ejpam-4461	11	17	)	)	PUNCT
ejpam-4461	11	18	in	in	ADP
ejpam-4461	11	19	2014	2014	NUM
ejpam-4461	11	20	and	and	CCONJ
ejpam-4461	11	21	2016	2016	NUM
ejpam-4461	11	22	,	,	PUNCT
ejpam-4461	11	23	by	by	ADP
ejpam-4461	11	24	g.	g.	PROPN
ejpam-4461	11	25	hao	hao	PROPN
ejpam-4461	11	26	and	and	CCONJ
ejpam-4461	11	27	w.	w.	PROPN
ejpam-4461	11	28	zhuang	zhuang	PROPN
ejpam-4461	11	29	(	(	PUNCT
ejpam-4461	11	30	see	see	VERB
ejpam-4461	11	31	[	[	X
ejpam-4461	11	32	7	7	NUM
ejpam-4461	11	33	]	]	PUNCT
ejpam-4461	11	34	)	)	PUNCT
ejpam-4461	11	35	in	in	ADP
ejpam-4461	11	36	2018	2018	NUM
ejpam-4461	11	37	,	,	PUNCT
ejpam-4461	11	38	and	and	CCONJ
ejpam-4461	11	39	by	by	ADP
ejpam-4461	11	40	i.	i.	PROPN
ejpam-4461	11	41	aniversario	aniversario	PROPN
ejpam-4461	11	42	et	et	PROPN
ejpam-4461	11	43	al	al	PROPN
ejpam-4461	11	44	.	.	PUNCT
ejpam-4461	12	1	[	[	X
ejpam-4461	12	2	1	1	X
ejpam-4461	12	3	]	]	PUNCT
ejpam-4461	12	4	in	in	ADP
ejpam-4461	12	5	2019	2019	NUM
ejpam-4461	12	6	.	.	PUNCT
ejpam-4461	13	1	in	in	ADP
ejpam-4461	13	2	this	this	DET
ejpam-4461	13	3	present	present	ADJ
ejpam-4461	13	4	paper	paper	NOUN
ejpam-4461	13	5	,	,	PUNCT
ejpam-4461	13	6	inspired	inspire	VERB
ejpam-4461	13	7	by	by	ADP
ejpam-4461	13	8	the	the	DET
ejpam-4461	13	9	work	work	NOUN
ejpam-4461	13	10	of	of	ADP
ejpam-4461	13	11	j.	j.	PROPN
ejpam-4461	13	12	cyman	cyman	PROPN
ejpam-4461	13	13	[	[	X
ejpam-4461	13	14	4	4	NUM
ejpam-4461	13	15	]	]	PUNCT
ejpam-4461	13	16	,	,	PUNCT
ejpam-4461	13	17	on	on	ADP
ejpam-4461	13	18	outer	outer	ADV
ejpam-4461	13	19	-	-	PUNCT
ejpam-4461	13	20	connected	connect	VERB
ejpam-4461	13	21	domination	domination	NOUN
ejpam-4461	13	22	,	,	PUNCT
ejpam-4461	13	23	we	we	PRON
ejpam-4461	13	24	introduce	introduce	VERB
ejpam-4461	13	25	and	and	CCONJ
ejpam-4461	13	26	initiate	initiate	VERB
ejpam-4461	13	27	the	the	DET
ejpam-4461	13	28	study	study	NOUN
ejpam-4461	13	29	of	of	ADP
ejpam-4461	13	30	the	the	DET
ejpam-4461	13	31	outer	outer	ADV
ejpam-4461	13	32	-	-	PUNCT
ejpam-4461	13	33	connected	connect	VERB
ejpam-4461	13	34	semitotal	semitotal	ADJ
ejpam-4461	13	35	domination	domination	NOUN
ejpam-4461	13	36	in	in	ADP
ejpam-4461	13	37	graphs	graph	NOUN
ejpam-4461	13	38	.	.	PUNCT
ejpam-4461	14	1	we	we	PRON
ejpam-4461	14	2	investigate	investigate	VERB
ejpam-4461	14	3	the	the	DET
ejpam-4461	14	4	concept	concept	NOUN
ejpam-4461	14	5	in	in	ADP
ejpam-4461	14	6	some	some	DET
ejpam-4461	14	7	special	special	ADJ
ejpam-4461	14	8	graphs	graph	NOUN
ejpam-4461	14	9	and	and	CCONJ
ejpam-4461	14	10	in	in	ADP
ejpam-4461	14	11	graphs	graph	NOUN
ejpam-4461	14	12	under	under	ADP
ejpam-4461	14	13	some	some	DET
ejpam-4461	14	14	binary	binary	ADJ
ejpam-4461	14	15	operations	operation	NOUN
ejpam-4461	14	16	,	,	PUNCT
ejpam-4461	14	17	such	such	ADJ
ejpam-4461	14	18	as	as	ADP
ejpam-4461	14	19	the	the	DET
ejpam-4461	14	20	join	join	NOUN
ejpam-4461	14	21	,	,	PUNCT
ejpam-4461	14	22	corona	corona	PROPN
ejpam-4461	14	23	,	,	PUNCT
ejpam-4461	14	24	and	and	CCONJ
ejpam-4461	14	25	lexicographic	lexicographic	ADJ
ejpam-4461	14	26	products	product	NOUN
ejpam-4461	14	27	of	of	ADP
ejpam-4461	14	28	graphs	graph	NOUN
ejpam-4461	14	29	.	.	PUNCT
ejpam-4461	15	1	∗corresponding	∗corresponde	VERB
ejpam-4461	15	2	author	author	NOUN
ejpam-4461	15	3	.	.	PUNCT
ejpam-4461	16	1	doi	doi	NOUN
ejpam-4461	16	2	:	:	PUNCT
ejpam-4461	16	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4461	https://doi.org/10.29020/nybg.ejpam.v15i3.4461	ADJ
ejpam-4461	16	4	email	email	NOUN
ejpam-4461	16	5	addresses	address	NOUN
ejpam-4461	16	6	:	:	PUNCT
ejpam-4461	16	7	alkajimaradais@msutawi-tawi.edu.ph	alkajimaradais@msutawi-tawi.edu.ph	PROPN
ejpam-4461	16	8	(	(	PUNCT
ejpam-4461	16	9	a.	a.	PROPN
ejpam-4461	16	10	aradais	aradais	PROPN
ejpam-4461	16	11	)	)	PUNCT
ejpam-4461	16	12	,	,	PUNCT
ejpam-4461	16	13	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-4461	16	14	(	(	PUNCT
ejpam-4461	16	15	f.	f.	PROPN
ejpam-4461	16	16	jamil	jamil	PROPN
ejpam-4461	16	17	)	)	PUNCT
ejpam-4461	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4461	16	19	1265	1265	NUM
ejpam-4461	17	1	©	©	ADP
ejpam-4461	17	2	2022	2022	NUM
ejpam-4461	17	3	ejpam	ejpam	VERB
ejpam-4461	17	4	all	all	DET
ejpam-4461	17	5	rights	right	NOUN
ejpam-4461	17	6	reserved	reserve	VERB
ejpam-4461	17	7	.	.	PUNCT
ejpam-4461	18	1	a.	a.	PROPN
ejpam-4461	18	2	aradais	aradais	PROPN
ejpam-4461	18	3	,	,	PUNCT
ejpam-4461	18	4	f.	f.	PROPN
ejpam-4461	18	5	jamil	jamil	PROPN
ejpam-4461	18	6	/	/	SYM
ejpam-4461	18	7	eur	eur	PROPN
ejpam-4461	18	8	.	.	PUNCT
ejpam-4461	19	1	j.	j.	PROPN
ejpam-4461	19	2	pure	pure	PROPN
ejpam-4461	19	3	appl	appl	PROPN
ejpam-4461	19	4	.	.	PROPN
ejpam-4461	19	5	math	math	PROPN
ejpam-4461	19	6	,	,	PUNCT
ejpam-4461	19	7	15	15	NUM
ejpam-4461	19	8	(	(	PUNCT
ejpam-4461	19	9	3	3	NUM
ejpam-4461	19	10	)	)	PUNCT
ejpam-4461	19	11	(	(	PUNCT
ejpam-4461	19	12	2022	2022	NUM
ejpam-4461	19	13	)	)	PUNCT
ejpam-4461	19	14	,	,	PUNCT
ejpam-4461	19	15	1265	1265	NUM
ejpam-4461	19	16	-	-	SYM
ejpam-4461	19	17	1279	1279	NUM
ejpam-4461	19	18	1266	1266	NUM
ejpam-4461	19	19	2	2	NUM
ejpam-4461	19	20	.	.	PUNCT
ejpam-4461	19	21	terminology	terminology	NOUN
ejpam-4461	19	22	and	and	CCONJ
ejpam-4461	19	23	notation	notation	NOUN
ejpam-4461	19	24	the	the	DET
ejpam-4461	19	25	symbols	symbol	NOUN
ejpam-4461	19	26	v	v	ADP
ejpam-4461	19	27	(	(	PUNCT
ejpam-4461	19	28	g	g	NOUN
ejpam-4461	19	29	)	)	PUNCT
ejpam-4461	19	30	and	and	CCONJ
ejpam-4461	19	31	e(g	e(g	PROPN
ejpam-4461	19	32	)	)	PUNCT
ejpam-4461	19	33	denote	denote	VERB
ejpam-4461	19	34	the	the	DET
ejpam-4461	19	35	vertex	vertex	NOUN
ejpam-4461	19	36	set	set	NOUN
ejpam-4461	19	37	and	and	CCONJ
ejpam-4461	19	38	edge	edge	NOUN
ejpam-4461	19	39	set	set	NOUN
ejpam-4461	19	40	,	,	PUNCT
ejpam-4461	19	41	respectively	respectively	ADV
ejpam-4461	19	42	,	,	PUNCT
ejpam-4461	19	43	of	of	ADP
ejpam-4461	19	44	a	a	DET
ejpam-4461	19	45	graph	graph	NOUN
ejpam-4461	19	46	g.	g.	NOUN
ejpam-4461	19	47	for	for	ADP
ejpam-4461	19	48	s	s	PROPN
ejpam-4461	19	49	⊆	⊆	NUM
ejpam-4461	19	50	v	v	NOUN
ejpam-4461	19	51	(	(	PUNCT
ejpam-4461	19	52	g	g	NOUN
ejpam-4461	19	53	)	)	PUNCT
ejpam-4461	19	54	,	,	PUNCT
ejpam-4461	19	55	|s|	|s|	PROPN
ejpam-4461	19	56	is	be	AUX
ejpam-4461	19	57	the	the	DET
ejpam-4461	19	58	cardinality	cardinality	NOUN
ejpam-4461	19	59	of	of	ADP
ejpam-4461	19	60	s.	s.	PROPN
ejpam-4461	19	61	in	in	ADP
ejpam-4461	19	62	particular	particular	ADJ
ejpam-4461	19	63	,	,	PUNCT
ejpam-4461	19	64	|v	|v	PROPN
ejpam-4461	19	65	(	(	PUNCT
ejpam-4461	19	66	g)|	g)|	NOUN
ejpam-4461	19	67	and	and	CCONJ
ejpam-4461	19	68	|e(g)|	|e(g)|	PROPN
ejpam-4461	19	69	are	be	AUX
ejpam-4461	19	70	the	the	DET
ejpam-4461	19	71	order	order	NOUN
ejpam-4461	19	72	and	and	CCONJ
ejpam-4461	19	73	size	size	NOUN
ejpam-4461	19	74	,	,	PUNCT
ejpam-4461	19	75	respectively	respectively	ADV
ejpam-4461	19	76	,	,	PUNCT
ejpam-4461	19	77	of	of	ADP
ejpam-4461	19	78	g.	g.	PROPN
ejpam-4461	19	79	the	the	DET
ejpam-4461	19	80	induced	induce	VERB
ejpam-4461	19	81	subgraph	subgraph	NOUN
ejpam-4461	19	82	⟨s⟩	⟨s⟩	PROPN
ejpam-4461	19	83	is	be	AUX
ejpam-4461	19	84	the	the	DET
ejpam-4461	19	85	graph	graph	NOUN
ejpam-4461	19	86	with	with	ADP
ejpam-4461	19	87	vertex	vertex	NOUN
ejpam-4461	19	88	set	set	NOUN
ejpam-4461	19	89	s	s	X
ejpam-4461	19	90	and	and	CCONJ
ejpam-4461	19	91	such	such	ADJ
ejpam-4461	19	92	that	that	SCONJ
ejpam-4461	19	93	uv	uv	PROPN
ejpam-4461	19	94	∈	∈	PROPN
ejpam-4461	19	95	e(⟨s⟩	e(⟨s⟩	ADV
ejpam-4461	19	96	)	)	PUNCT
ejpam-4461	20	1	if	if	SCONJ
ejpam-4461	20	2	and	and	CCONJ
ejpam-4461	20	3	only	only	ADV
ejpam-4461	20	4	if	if	SCONJ
ejpam-4461	20	5	u	u	NOUN
ejpam-4461	20	6	,	,	PUNCT
ejpam-4461	20	7	v	v	ADP
ejpam-4461	20	8	∈	∈	NOUN
ejpam-4461	20	9	s	s	NOUN
ejpam-4461	20	10	and	and	CCONJ
ejpam-4461	20	11	uv	uv	PROPN
ejpam-4461	20	12	∈	∈	PROPN
ejpam-4461	20	13	e(g	e(g	PROPN
ejpam-4461	20	14	)	)	PUNCT
ejpam-4461	20	15	.	.	PUNCT
ejpam-4461	21	1	all	all	DET
ejpam-4461	21	2	graph	graph	NOUN
ejpam-4461	21	3	terminologies	terminology	NOUN
ejpam-4461	21	4	that	that	PRON
ejpam-4461	21	5	are	be	AUX
ejpam-4461	21	6	not	not	PART
ejpam-4461	21	7	introduced	introduce	VERB
ejpam-4461	21	8	but	but	CCONJ
ejpam-4461	21	9	are	be	AUX
ejpam-4461	21	10	being	be	AUX
ejpam-4461	21	11	used	use	VERB
ejpam-4461	21	12	here	here	ADV
ejpam-4461	21	13	are	be	AUX
ejpam-4461	21	14	adopted	adopt	VERB
ejpam-4461	21	15	from	from	ADP
ejpam-4461	21	16	[	[	X
ejpam-4461	21	17	2	2	NUM
ejpam-4461	21	18	]	]	PUNCT
ejpam-4461	21	19	.	.	PUNCT
ejpam-4461	22	1	given	give	VERB
ejpam-4461	22	2	two	two	NUM
ejpam-4461	22	3	graphs	graph	NOUN
ejpam-4461	22	4	g	g	NOUN
ejpam-4461	22	5	and	and	CCONJ
ejpam-4461	22	6	h	h	NOUN
ejpam-4461	22	7	with	with	ADP
ejpam-4461	22	8	disjoint	disjoint	ADJ
ejpam-4461	22	9	vertex	vertex	NOUN
ejpam-4461	22	10	sets	set	NOUN
ejpam-4461	22	11	,	,	PUNCT
ejpam-4461	22	12	the	the	DET
ejpam-4461	22	13	join	join	NOUN
ejpam-4461	22	14	g+h	g+h	PROPN
ejpam-4461	22	15	of	of	ADP
ejpam-4461	22	16	graphs	graph	NOUN
ejpam-4461	22	17	g	g	PROPN
ejpam-4461	22	18	and	and	CCONJ
ejpam-4461	22	19	h	h	NOUN
ejpam-4461	22	20	,	,	PUNCT
ejpam-4461	22	21	is	be	AUX
ejpam-4461	22	22	the	the	DET
ejpam-4461	22	23	graph	graph	NOUN
ejpam-4461	22	24	with	with	ADP
ejpam-4461	22	25	vertex	vertex	NOUN
ejpam-4461	22	26	-	-	PUNCT
ejpam-4461	22	27	set	set	VERB
ejpam-4461	22	28	v	v	NOUN
ejpam-4461	22	29	(	(	PUNCT
ejpam-4461	22	30	g+h	g+h	NOUN
ejpam-4461	22	31	)	)	PUNCT
ejpam-4461	22	32	=	=	SYM
ejpam-4461	22	33	v	v	X
ejpam-4461	22	34	(	(	PUNCT
ejpam-4461	22	35	g)∪v	g)∪v	NOUN
ejpam-4461	22	36	(	(	PUNCT
ejpam-4461	22	37	h	h	NOUN
ejpam-4461	22	38	)	)	PUNCT
ejpam-4461	22	39	and	and	CCONJ
ejpam-4461	22	40	edge	edge	NOUN
ejpam-4461	22	41	-	-	PUNCT
ejpam-4461	22	42	set	set	VERB
ejpam-4461	22	43	e(g	e(g	NOUN
ejpam-4461	22	44	+	+	CCONJ
ejpam-4461	22	45	h	h	NOUN
ejpam-4461	22	46	)	)	PUNCT
ejpam-4461	22	47	=	=	SYM
ejpam-4461	22	48	e(g	e(g	PROPN
ejpam-4461	22	49	)	)	PUNCT
ejpam-4461	22	50	∪	∪	ADP
ejpam-4461	22	51	e(h	e(h	PROPN
ejpam-4461	22	52	)	)	PUNCT
ejpam-4461	22	53	∪	∪	NOUN
ejpam-4461	22	54	{	{	PUNCT
ejpam-4461	22	55	uv	uv	NOUN
ejpam-4461	22	56	:	:	PUNCT
ejpam-4461	22	57	u	u	PROPN
ejpam-4461	22	58	∈	∈	PROPN
ejpam-4461	22	59	v	v	ADP
ejpam-4461	22	60	(	(	PUNCT
ejpam-4461	22	61	g	g	NOUN
ejpam-4461	22	62	)	)	PUNCT
ejpam-4461	22	63	and	and	CCONJ
ejpam-4461	22	64	v	v	ADP
ejpam-4461	22	65	∈	∈	PROPN
ejpam-4461	22	66	v	v	NOUN
ejpam-4461	22	67	(	(	PUNCT
ejpam-4461	22	68	h	h	NOUN
ejpam-4461	22	69	)	)	PUNCT
ejpam-4461	22	70	}	}	PUNCT
ejpam-4461	22	71	.	.	PUNCT
ejpam-4461	23	1	the	the	DET
ejpam-4461	23	2	corona	corona	NOUN
ejpam-4461	23	3	of	of	ADP
ejpam-4461	23	4	g	g	PROPN
ejpam-4461	23	5	and	and	CCONJ
ejpam-4461	23	6	h	h	NOUN
ejpam-4461	23	7	is	be	AUX
ejpam-4461	23	8	the	the	DET
ejpam-4461	23	9	graph	graph	NOUN
ejpam-4461	23	10	g	g	PROPN
ejpam-4461	23	11	◦	◦	NOUN
ejpam-4461	23	12	h	h	NOUN
ejpam-4461	23	13	obtained	obtain	VERB
ejpam-4461	23	14	by	by	ADP
ejpam-4461	23	15	taking	take	VERB
ejpam-4461	23	16	one	one	NUM
ejpam-4461	23	17	copy	copy	NOUN
ejpam-4461	23	18	of	of	ADP
ejpam-4461	23	19	g	g	PROPN
ejpam-4461	23	20	and	and	CCONJ
ejpam-4461	23	21	|v	|v	PROPN
ejpam-4461	23	22	(	(	PUNCT
ejpam-4461	23	23	g)|	g)|	NOUN
ejpam-4461	23	24	copies	copy	NOUN
ejpam-4461	23	25	of	of	ADP
ejpam-4461	23	26	h	h	NOUN
ejpam-4461	23	27	,	,	PUNCT
ejpam-4461	23	28	and	and	CCONJ
ejpam-4461	23	29	then	then	ADV
ejpam-4461	23	30	joining	join	VERB
ejpam-4461	23	31	the	the	DET
ejpam-4461	23	32	ith	ith	PROPN
ejpam-4461	23	33	vertex	vertex	NOUN
ejpam-4461	23	34	of	of	ADP
ejpam-4461	23	35	g	g	NOUN
ejpam-4461	23	36	to	to	ADP
ejpam-4461	23	37	every	every	DET
ejpam-4461	23	38	vertex	vertex	NOUN
ejpam-4461	23	39	of	of	ADP
ejpam-4461	23	40	the	the	DET
ejpam-4461	23	41	ith	ith	PROPN
ejpam-4461	23	42	copy	copy	NOUN
ejpam-4461	23	43	of	of	ADP
ejpam-4461	23	44	h.	h.	PROPN
ejpam-4461	23	45	the	the	DET
ejpam-4461	23	46	lexicographic	lexicographic	ADJ
ejpam-4461	23	47	product	product	NOUN
ejpam-4461	23	48	or	or	CCONJ
ejpam-4461	23	49	composition	composition	NOUN
ejpam-4461	23	50	of	of	ADP
ejpam-4461	23	51	g	g	PROPN
ejpam-4461	23	52	and	and	CCONJ
ejpam-4461	23	53	h	h	NOUN
ejpam-4461	23	54	,	,	PUNCT
ejpam-4461	23	55	denoted	denote	VERB
ejpam-4461	23	56	by	by	ADP
ejpam-4461	23	57	g[h	g[h	NOUN
ejpam-4461	23	58	]	]	PUNCT
ejpam-4461	23	59	,	,	PUNCT
ejpam-4461	23	60	is	be	AUX
ejpam-4461	23	61	the	the	DET
ejpam-4461	23	62	graph	graph	NOUN
ejpam-4461	23	63	with	with	ADP
ejpam-4461	23	64	vertex	vertex	NOUN
ejpam-4461	23	65	set	set	VERB
ejpam-4461	23	66	v	v	NOUN
ejpam-4461	23	67	(	(	PUNCT
ejpam-4461	23	68	g[h	g[h	PROPN
ejpam-4461	23	69	]	]	PUNCT
ejpam-4461	23	70	)	)	PUNCT
ejpam-4461	24	1	=	=	SYM
ejpam-4461	24	2	v	v	X
ejpam-4461	24	3	(	(	PUNCT
ejpam-4461	24	4	g)×v	g)×v	PROPN
ejpam-4461	24	5	(	(	PUNCT
ejpam-4461	24	6	h	h	NOUN
ejpam-4461	24	7	)	)	PUNCT
ejpam-4461	24	8	and	and	CCONJ
ejpam-4461	24	9	edge	edge	VERB
ejpam-4461	24	10	set	set	VERB
ejpam-4461	24	11	e(g[h	e(g[h	NOUN
ejpam-4461	24	12	]	]	PUNCT
ejpam-4461	24	13	)	)	PUNCT
ejpam-4461	24	14	satisfying	satisfy	VERB
ejpam-4461	24	15	the	the	DET
ejpam-4461	24	16	following	follow	VERB
ejpam-4461	24	17	conditions	condition	NOUN
ejpam-4461	24	18	:	:	PUNCT
ejpam-4461	24	19	(	(	PUNCT
ejpam-4461	24	20	u1	u1	PROPN
ejpam-4461	24	21	,	,	PUNCT
ejpam-4461	24	22	v1)(u2	v1)(u2	PROPN
ejpam-4461	24	23	,	,	PUNCT
ejpam-4461	24	24	v2	v2	PROPN
ejpam-4461	24	25	)	)	PUNCT
ejpam-4461	24	26	∈	∈	NOUN
ejpam-4461	24	27	e(g[h	e(g[h	NOUN
ejpam-4461	24	28	]	]	PUNCT
ejpam-4461	24	29	)	)	PUNCT
ejpam-4461	25	1	if	if	SCONJ
ejpam-4461	25	2	and	and	CCONJ
ejpam-4461	25	3	only	only	ADV
ejpam-4461	25	4	if	if	SCONJ
ejpam-4461	25	5	either	either	PRON
ejpam-4461	25	6	u1u2	u1u2	PROPN
ejpam-4461	25	7	∈	∈	PROPN
ejpam-4461	25	8	e(g	e(g	PROPN
ejpam-4461	25	9	)	)	PUNCT
ejpam-4461	25	10	or	or	CCONJ
ejpam-4461	25	11	u1	u1	NOUN
ejpam-4461	25	12	=	=	SYM
ejpam-4461	25	13	u2	u2	PROPN
ejpam-4461	25	14	and	and	CCONJ
ejpam-4461	25	15	v1v2	v1v2	PUNCT
ejpam-4461	25	16	∈	∈	PROPN
ejpam-4461	25	17	e(h	e(h	PROPN
ejpam-4461	25	18	)	)	PUNCT
ejpam-4461	25	19	.	.	PUNCT
ejpam-4461	26	1	for	for	ADP
ejpam-4461	26	2	vertex	vertex	NOUN
ejpam-4461	26	3	u	u	NOUN
ejpam-4461	26	4	of	of	ADP
ejpam-4461	26	5	g	g	NOUN
ejpam-4461	26	6	,	,	PUNCT
ejpam-4461	26	7	all	all	PRON
ejpam-4461	26	8	vertices	vertice	VERB
ejpam-4461	26	9	adjacent	adjacent	ADJ
ejpam-4461	26	10	to	to	ADP
ejpam-4461	26	11	u	u	NOUN
ejpam-4461	26	12	constitute	constitute	VERB
ejpam-4461	26	13	the	the	DET
ejpam-4461	26	14	set	set	NOUN
ejpam-4461	26	15	ng(u	ng(u	NOUN
ejpam-4461	26	16	)	)	PUNCT
ejpam-4461	26	17	called	call	VERB
ejpam-4461	26	18	the	the	DET
ejpam-4461	26	19	open	open	ADJ
ejpam-4461	26	20	neighborhood	neighborhood	NOUN
ejpam-4461	26	21	of	of	ADP
ejpam-4461	26	22	u.	u.	VERB
ejpam-4461	26	23	the	the	DET
ejpam-4461	26	24	closed	closed	ADJ
ejpam-4461	26	25	neighborhood	neighborhood	NOUN
ejpam-4461	26	26	of	of	ADP
ejpam-4461	26	27	u	u	NOUN
ejpam-4461	26	28	in	in	ADP
ejpam-4461	26	29	g	g	PROPN
ejpam-4461	26	30	is	be	AUX
ejpam-4461	26	31	the	the	DET
ejpam-4461	26	32	set	set	NOUN
ejpam-4461	26	33	ng[u	ng[u	PROPN
ejpam-4461	26	34	]	]	X
ejpam-4461	26	35	=	=	SYM
ejpam-4461	26	36	ng(u	ng(u	PROPN
ejpam-4461	26	37	)	)	PUNCT
ejpam-4461	26	38	∪	∪	NOUN
ejpam-4461	26	39	{	{	PUNCT
ejpam-4461	26	40	u	u	NOUN
ejpam-4461	26	41	}	}	PUNCT
ejpam-4461	26	42	.	.	PUNCT
ejpam-4461	27	1	if	if	SCONJ
ejpam-4461	27	2	s	s	VERB
ejpam-4461	27	3	⊆	⊆	NUM
ejpam-4461	27	4	v	v	NOUN
ejpam-4461	27	5	(	(	PUNCT
ejpam-4461	27	6	g	g	NOUN
ejpam-4461	27	7	)	)	PUNCT
ejpam-4461	27	8	,	,	PUNCT
ejpam-4461	27	9	the	the	DET
ejpam-4461	27	10	open	open	ADJ
ejpam-4461	27	11	neighborhood	neighborhood	NOUN
ejpam-4461	27	12	of	of	ADP
ejpam-4461	27	13	s	s	NOUN
ejpam-4461	27	14	in	in	ADP
ejpam-4461	27	15	g	g	PROPN
ejpam-4461	27	16	is	be	AUX
ejpam-4461	27	17	the	the	DET
ejpam-4461	27	18	set	set	NOUN
ejpam-4461	27	19	ng(s	ng(s	NOUN
ejpam-4461	27	20	)	)	PUNCT
ejpam-4461	27	21	=	=	SYM
ejpam-4461	27	22	∪u∈sng(u	∪u∈sng(u	PROPN
ejpam-4461	27	23	)	)	PUNCT
ejpam-4461	27	24	.	.	PUNCT
ejpam-4461	28	1	the	the	DET
ejpam-4461	28	2	closed	closed	ADJ
ejpam-4461	28	3	neighborhood	neighborhood	NOUN
ejpam-4461	28	4	of	of	ADP
ejpam-4461	28	5	s	s	NOUN
ejpam-4461	28	6	in	in	ADP
ejpam-4461	28	7	g	g	PROPN
ejpam-4461	28	8	is	be	AUX
ejpam-4461	28	9	the	the	DET
ejpam-4461	28	10	set	set	VERB
ejpam-4461	28	11	ng[s	ng[	NOUN
ejpam-4461	28	12	]	]	PUNCT
ejpam-4461	28	13	=	=	PUNCT
ejpam-4461	28	14	ng(s)∪s	ng(s)∪s	PROPN
ejpam-4461	28	15	.	.	PUNCT
ejpam-4461	29	1	we	we	PRON
ejpam-4461	29	2	define	define	VERB
ejpam-4461	29	3	ng(s	ng(s	PUNCT
ejpam-4461	29	4	)	)	PUNCT
ejpam-4461	29	5	=	=	SYM
ejpam-4461	29	6	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4461	29	7	)	)	PUNCT
ejpam-4461	29	8	and	and	CCONJ
ejpam-4461	29	9	ng[s	ng[s	PROPN
ejpam-4461	29	10	]	]	PUNCT
ejpam-4461	30	1	=	=	SYM
ejpam-4461	30	2	s	s	NOUN
ejpam-4461	30	3	∪ng(s	∪ng(s	NOUN
ejpam-4461	30	4	)	)	PUNCT
ejpam-4461	30	5	.	.	PUNCT
ejpam-4461	31	1	a	a	DET
ejpam-4461	31	2	set	set	NOUN
ejpam-4461	31	3	s	s	NOUN
ejpam-4461	31	4	⊆	⊆	NUM
ejpam-4461	31	5	v	v	NOUN
ejpam-4461	31	6	(	(	PUNCT
ejpam-4461	31	7	g	g	NOUN
ejpam-4461	31	8	)	)	PUNCT
ejpam-4461	31	9	is	be	AUX
ejpam-4461	31	10	a	a	DET
ejpam-4461	31	11	dominating	dominating	NOUN
ejpam-4461	31	12	set	set	NOUN
ejpam-4461	31	13	of	of	ADP
ejpam-4461	31	14	g	g	PROPN
ejpam-4461	31	15	if	if	SCONJ
ejpam-4461	31	16	ng[s	ng[	NOUN
ejpam-4461	31	17	]	]	PUNCT
ejpam-4461	31	18	=	=	SYM
ejpam-4461	31	19	v	v	NOUN
ejpam-4461	31	20	(	(	PUNCT
ejpam-4461	31	21	g	g	NOUN
ejpam-4461	31	22	)	)	PUNCT
ejpam-4461	31	23	.	.	PUNCT
ejpam-4461	32	1	thus	thus	ADV
ejpam-4461	32	2	,	,	PUNCT
ejpam-4461	32	3	s	s	VERB
ejpam-4461	32	4	is	be	AUX
ejpam-4461	32	5	a	a	DET
ejpam-4461	32	6	dominating	dominating	NOUN
ejpam-4461	32	7	set	set	NOUN
ejpam-4461	32	8	of	of	ADP
ejpam-4461	32	9	g	g	PROPN
ejpam-4461	32	10	if	if	SCONJ
ejpam-4461	32	11	and	and	CCONJ
ejpam-4461	32	12	only	only	ADV
ejpam-4461	32	13	if	if	SCONJ
ejpam-4461	32	14	for	for	ADP
ejpam-4461	32	15	each	each	PRON
ejpam-4461	32	16	v	v	NUM
ejpam-4461	32	17	∈	∈	PROPN
ejpam-4461	32	18	v	v	NOUN
ejpam-4461	32	19	(	(	PUNCT
ejpam-4461	32	20	g	g	NOUN
ejpam-4461	32	21	)	)	PUNCT
ejpam-4461	32	22	\	\	PROPN
ejpam-4461	33	1	s	s	X
ejpam-4461	33	2	,	,	PUNCT
ejpam-4461	33	3	there	there	PRON
ejpam-4461	33	4	exists	exist	VERB
ejpam-4461	33	5	u	u	PROPN
ejpam-4461	33	6	∈	∈	PROPN
ejpam-4461	33	7	s	s	VERB
ejpam-4461	33	8	such	such	ADJ
ejpam-4461	33	9	that	that	DET
ejpam-4461	33	10	uv	uv	PROPN
ejpam-4461	33	11	∈	∈	PROPN
ejpam-4461	33	12	e(g	e(g	PROPN
ejpam-4461	33	13	)	)	PUNCT
ejpam-4461	33	14	.	.	PUNCT
ejpam-4461	34	1	a	a	DET
ejpam-4461	34	2	set	set	NOUN
ejpam-4461	34	3	s	s	NOUN
ejpam-4461	34	4	⊆	⊆	NUM
ejpam-4461	34	5	v	v	NOUN
ejpam-4461	34	6	(	(	PUNCT
ejpam-4461	34	7	g	g	NOUN
ejpam-4461	34	8	)	)	PUNCT
ejpam-4461	34	9	is	be	AUX
ejpam-4461	34	10	a	a	DET
ejpam-4461	34	11	total	total	ADJ
ejpam-4461	34	12	dominating	dominating	NOUN
ejpam-4461	34	13	set	set	NOUN
ejpam-4461	34	14	of	of	ADP
ejpam-4461	34	15	g	g	PROPN
ejpam-4461	34	16	if	if	SCONJ
ejpam-4461	34	17	for	for	ADP
ejpam-4461	34	18	every	every	DET
ejpam-4461	34	19	v	v	NUM
ejpam-4461	34	20	∈	∈	NOUN
ejpam-4461	34	21	v	v	NOUN
ejpam-4461	34	22	(	(	PUNCT
ejpam-4461	34	23	g	g	NOUN
ejpam-4461	34	24	)	)	PUNCT
ejpam-4461	34	25	,	,	PUNCT
ejpam-4461	34	26	there	there	PRON
ejpam-4461	34	27	exists	exist	VERB
ejpam-4461	34	28	u	u	PROPN
ejpam-4461	34	29	∈	∈	PROPN
ejpam-4461	34	30	s	s	VERB
ejpam-4461	34	31	such	such	ADJ
ejpam-4461	34	32	that	that	DET
ejpam-4461	34	33	uv	uv	PROPN
ejpam-4461	34	34	∈	∈	PROPN
ejpam-4461	34	35	e(g	e(g	PROPN
ejpam-4461	34	36	)	)	PUNCT
ejpam-4461	34	37	.	.	PUNCT
ejpam-4461	35	1	the	the	DET
ejpam-4461	35	2	minimum	minimum	ADJ
ejpam-4461	35	3	cardinality	cardinality	NOUN
ejpam-4461	35	4	of	of	ADP
ejpam-4461	35	5	a	a	DET
ejpam-4461	35	6	dominating	dominating	NOUN
ejpam-4461	35	7	set	set	NOUN
ejpam-4461	35	8	(	(	PUNCT
ejpam-4461	35	9	resp	resp	NOUN
ejpam-4461	35	10	.	.	PUNCT
ejpam-4461	36	1	total	total	ADJ
ejpam-4461	36	2	dominating	dominating	NOUN
ejpam-4461	36	3	set	set	NOUN
ejpam-4461	36	4	)	)	PUNCT
ejpam-4461	36	5	of	of	ADP
ejpam-4461	36	6	g	g	NOUN
ejpam-4461	36	7	,	,	PUNCT
ejpam-4461	36	8	denoted	denote	VERB
ejpam-4461	36	9	by	by	ADP
ejpam-4461	36	10	γ(g	γ(g	PROPN
ejpam-4461	36	11	)	)	PUNCT
ejpam-4461	36	12	(	(	PUNCT
ejpam-4461	36	13	resp	resp	NOUN
ejpam-4461	36	14	.	.	PUNCT
ejpam-4461	36	15	γt(g	γt(g	PUNCT
ejpam-4461	36	16	)	)	PUNCT
ejpam-4461	36	17	)	)	PUNCT
ejpam-4461	36	18	,	,	PUNCT
ejpam-4461	36	19	is	be	AUX
ejpam-4461	36	20	the	the	DET
ejpam-4461	36	21	domination	domination	NOUN
ejpam-4461	36	22	number	number	NOUN
ejpam-4461	36	23	(	(	PUNCT
ejpam-4461	36	24	resp	resp	NOUN
ejpam-4461	36	25	.	.	PUNCT
ejpam-4461	37	1	total	total	ADJ
ejpam-4461	37	2	domination	domination	NOUN
ejpam-4461	37	3	number	number	NOUN
ejpam-4461	37	4	)	)	PUNCT
ejpam-4461	37	5	of	of	ADP
ejpam-4461	37	6	g.	g.	PROPN
ejpam-4461	37	7	a	a	DET
ejpam-4461	37	8	dominating	dominating	NOUN
ejpam-4461	37	9	set	set	NOUN
ejpam-4461	37	10	(	(	PUNCT
ejpam-4461	37	11	resp	resp	NOUN
ejpam-4461	37	12	.	.	PUNCT
ejpam-4461	38	1	total	total	ADJ
ejpam-4461	38	2	dominating	dominating	NOUN
ejpam-4461	38	3	set	set	NOUN
ejpam-4461	38	4	)	)	PUNCT
ejpam-4461	38	5	s	s	PROPN
ejpam-4461	38	6	of	of	ADP
ejpam-4461	38	7	g	g	NOUN
ejpam-4461	38	8	with	with	ADP
ejpam-4461	38	9	|s|	|s|	PROPN
ejpam-4461	38	10	=	=	SYM
ejpam-4461	38	11	γ(g	γ(g	PROPN
ejpam-4461	38	12	)	)	PUNCT
ejpam-4461	38	13	(	(	PUNCT
ejpam-4461	38	14	resp	resp	NOUN
ejpam-4461	38	15	.	.	PUNCT
ejpam-4461	39	1	|s|	|s|	PROPN
ejpam-4461	39	2	=	=	SYM
ejpam-4461	39	3	γt(g	γt(g	NUM
ejpam-4461	39	4	)	)	PUNCT
ejpam-4461	39	5	)	)	PUNCT
ejpam-4461	39	6	is	be	AUX
ejpam-4461	39	7	called	call	VERB
ejpam-4461	39	8	a	a	DET
ejpam-4461	39	9	γ	γ	NOUN
ejpam-4461	39	10	-	-	PUNCT
ejpam-4461	39	11	set	set	ADJ
ejpam-4461	39	12	(	(	PUNCT
ejpam-4461	39	13	resp	resp	NOUN
ejpam-4461	39	14	.	.	PUNCT
ejpam-4461	40	1	γt	γt	NOUN
ejpam-4461	40	2	-	-	PUNCT
ejpam-4461	40	3	set	set	NOUN
ejpam-4461	40	4	)	)	PUNCT
ejpam-4461	40	5	of	of	ADP
ejpam-4461	40	6	g.	g.	PROPN
ejpam-4461	40	7	the	the	DET
ejpam-4461	40	8	authors	author	NOUN
ejpam-4461	40	9	always	always	ADV
ejpam-4461	40	10	refer	refer	VERB
ejpam-4461	40	11	to	to	ADP
ejpam-4461	40	12	[	[	X
ejpam-4461	40	13	3	3	X
ejpam-4461	40	14	]	]	PUNCT
ejpam-4461	40	15	for	for	ADP
ejpam-4461	40	16	the	the	DET
ejpam-4461	40	17	introduction	introduction	NOUN
ejpam-4461	40	18	and	and	CCONJ
ejpam-4461	40	19	more	more	ADV
ejpam-4461	40	20	comprehensive	comprehensive	ADJ
ejpam-4461	40	21	discussion	discussion	NOUN
ejpam-4461	40	22	of	of	ADP
ejpam-4461	40	23	the	the	DET
ejpam-4461	40	24	development	development	NOUN
ejpam-4461	40	25	of	of	ADP
ejpam-4461	40	26	the	the	DET
ejpam-4461	40	27	concept	concept	NOUN
ejpam-4461	40	28	of	of	ADP
ejpam-4461	40	29	domination	domination	NOUN
ejpam-4461	40	30	in	in	ADP
ejpam-4461	40	31	graphs	graph	NOUN
ejpam-4461	40	32	.	.	PUNCT
ejpam-4461	41	1	a	a	DET
ejpam-4461	41	2	set	set	NOUN
ejpam-4461	41	3	s	s	NOUN
ejpam-4461	41	4	⊆	⊆	NUM
ejpam-4461	41	5	v	v	NOUN
ejpam-4461	41	6	(	(	PUNCT
ejpam-4461	41	7	g	g	NOUN
ejpam-4461	41	8	)	)	PUNCT
ejpam-4461	41	9	of	of	ADP
ejpam-4461	41	10	a	a	DET
ejpam-4461	41	11	graph	graph	NOUN
ejpam-4461	41	12	g	g	NOUN
ejpam-4461	41	13	=	=	PUNCT
ejpam-4461	41	14	(	(	PUNCT
ejpam-4461	41	15	v	v	NOUN
ejpam-4461	41	16	,	,	PUNCT
ejpam-4461	41	17	e	e	NOUN
ejpam-4461	41	18	)	)	PUNCT
ejpam-4461	41	19	is	be	AUX
ejpam-4461	41	20	called	call	VERB
ejpam-4461	41	21	an	an	DET
ejpam-4461	41	22	outer	outer	ADV
ejpam-4461	41	23	-	-	PUNCT
ejpam-4461	41	24	connected	connect	VERB
ejpam-4461	41	25	dominating	dominating	NOUN
ejpam-4461	41	26	set	set	NOUN
ejpam-4461	41	27	of	of	ADP
ejpam-4461	41	28	g	g	PROPN
ejpam-4461	41	29	if	if	SCONJ
ejpam-4461	41	30	the	the	DET
ejpam-4461	41	31	following	follow	VERB
ejpam-4461	41	32	hold	hold	NOUN
ejpam-4461	41	33	:	:	PUNCT
ejpam-4461	41	34	(	(	PUNCT
ejpam-4461	41	35	i	i	NOUN
ejpam-4461	41	36	)	)	PUNCT
ejpam-4461	41	37	s	s	AUX
ejpam-4461	41	38	is	be	AUX
ejpam-4461	41	39	a	a	DET
ejpam-4461	41	40	dominating	dominating	NOUN
ejpam-4461	41	41	set	set	NOUN
ejpam-4461	41	42	of	of	ADP
ejpam-4461	41	43	g	g	NOUN
ejpam-4461	41	44	,	,	PUNCT
ejpam-4461	41	45	and	and	CCONJ
ejpam-4461	41	46	(	(	PUNCT
ejpam-4461	41	47	ii	ii	NOUN
ejpam-4461	41	48	)	)	PUNCT
ejpam-4461	41	49	either	either	CCONJ
ejpam-4461	41	50	s	s	VERB
ejpam-4461	41	51	=	=	SYM
ejpam-4461	41	52	v	v	X
ejpam-4461	41	53	(	(	PUNCT
ejpam-4461	41	54	g	g	NOUN
ejpam-4461	41	55	)	)	PUNCT
ejpam-4461	41	56	or	or	CCONJ
ejpam-4461	41	57	the	the	DET
ejpam-4461	41	58	induced	induced	ADJ
ejpam-4461	41	59	subgraph	subgraph	NOUN
ejpam-4461	41	60	⟨v	⟨v	NOUN
ejpam-4461	41	61	(	(	PUNCT
ejpam-4461	41	62	g	g	NOUN
ejpam-4461	41	63	)	)	PUNCT
ejpam-4461	41	64	\	\	PROPN
ejpam-4461	42	1	s⟩	s⟩	NOUN
ejpam-4461	42	2	of	of	ADP
ejpam-4461	42	3	v	v	NOUN
ejpam-4461	42	4	(	(	PUNCT
ejpam-4461	42	5	g	g	NOUN
ejpam-4461	42	6	)	)	PUNCT
ejpam-4461	42	7	\	\	PROPN
ejpam-4461	43	1	s	s	PART
ejpam-4461	43	2	is	be	AUX
ejpam-4461	43	3	connected	connect	VERB
ejpam-4461	43	4	.	.	PUNCT
ejpam-4461	44	1	the	the	DET
ejpam-4461	44	2	cardinality	cardinality	NOUN
ejpam-4461	44	3	of	of	ADP
ejpam-4461	44	4	a	a	DET
ejpam-4461	44	5	minimum	minimum	ADJ
ejpam-4461	44	6	outer	outer	ADV
ejpam-4461	44	7	-	-	PUNCT
ejpam-4461	44	8	connected	connect	VERB
ejpam-4461	44	9	dominating	dominating	NOUN
ejpam-4461	44	10	set	set	NOUN
ejpam-4461	44	11	of	of	ADP
ejpam-4461	44	12	g	g	PROPN
ejpam-4461	44	13	is	be	AUX
ejpam-4461	44	14	called	call	VERB
ejpam-4461	44	15	the	the	DET
ejpam-4461	44	16	outer	outer	ADV
ejpam-4461	44	17	-	-	PUNCT
ejpam-4461	44	18	connected	connect	VERB
ejpam-4461	44	19	domination	domination	NOUN
ejpam-4461	44	20	number	number	NOUN
ejpam-4461	44	21	of	of	ADP
ejpam-4461	44	22	g	g	NOUN
ejpam-4461	44	23	,	,	PUNCT
ejpam-4461	44	24	and	and	CCONJ
ejpam-4461	44	25	is	be	AUX
ejpam-4461	44	26	denoted	denote	VERB
ejpam-4461	44	27	by	by	ADP
ejpam-4461	44	28	γ̃(g	γ̃(g	PROPN
ejpam-4461	44	29	)	)	PUNCT
ejpam-4461	44	30	.	.	PUNCT
ejpam-4461	45	1	for	for	ADP
ejpam-4461	45	2	a	a	DET
ejpam-4461	45	3	graph	graph	NOUN
ejpam-4461	45	4	g	g	NOUN
ejpam-4461	45	5	without	without	ADP
ejpam-4461	45	6	isolated	isolated	ADJ
ejpam-4461	45	7	vertices	vertex	NOUN
ejpam-4461	45	8	,	,	PUNCT
ejpam-4461	45	9	a	a	DET
ejpam-4461	45	10	set	set	NOUN
ejpam-4461	45	11	s	s	NOUN
ejpam-4461	45	12	⊆	⊆	NUM
ejpam-4461	45	13	v	v	NOUN
ejpam-4461	45	14	(	(	PUNCT
ejpam-4461	45	15	g	g	NOUN
ejpam-4461	45	16	)	)	PUNCT
ejpam-4461	45	17	is	be	AUX
ejpam-4461	45	18	a	a	DET
ejpam-4461	45	19	total	total	ADJ
ejpam-4461	45	20	outer	outer	ADV
ejpam-4461	45	21	-	-	PUNCT
ejpam-4461	45	22	connected	connect	VERB
ejpam-4461	45	23	dominating	dominating	NOUN
ejpam-4461	45	24	set	set	NOUN
ejpam-4461	45	25	if	if	SCONJ
ejpam-4461	45	26	s	s	VERB
ejpam-4461	45	27	is	be	AUX
ejpam-4461	45	28	a	a	DET
ejpam-4461	45	29	total	total	ADJ
ejpam-4461	45	30	dominating	dominating	NOUN
ejpam-4461	45	31	set	set	NOUN
ejpam-4461	45	32	of	of	ADP
ejpam-4461	45	33	g	g	PROPN
ejpam-4461	45	34	and	and	CCONJ
ejpam-4461	45	35	the	the	DET
ejpam-4461	45	36	subgraph	subgraph	NOUN
ejpam-4461	45	37	induced	induce	VERB
ejpam-4461	45	38	by	by	ADP
ejpam-4461	45	39	v	v	NOUN
ejpam-4461	45	40	(	(	PUNCT
ejpam-4461	45	41	g	g	NOUN
ejpam-4461	45	42	)	)	PUNCT
ejpam-4461	45	43	\	\	PROPN
ejpam-4461	46	1	s	s	PART
ejpam-4461	46	2	is	be	AUX
ejpam-4461	46	3	connected	connect	VERB
ejpam-4461	46	4	.	.	PUNCT
ejpam-4461	47	1	the	the	DET
ejpam-4461	47	2	minimum	minimum	ADJ
ejpam-4461	47	3	cardinality	cardinality	NOUN
ejpam-4461	47	4	of	of	ADP
ejpam-4461	47	5	a	a	DET
ejpam-4461	47	6	total	total	ADJ
ejpam-4461	47	7	outer	outer	ADV
ejpam-4461	47	8	-	-	PUNCT
ejpam-4461	47	9	connected	connect	VERB
ejpam-4461	47	10	dominating	dominating	NOUN
ejpam-4461	47	11	set	set	VERB
ejpam-4461	47	12	in	in	ADP
ejpam-4461	47	13	g	g	PROPN
ejpam-4461	47	14	is	be	AUX
ejpam-4461	47	15	the	the	DET
ejpam-4461	47	16	total	total	ADJ
ejpam-4461	47	17	outer	outer	ADV
ejpam-4461	47	18	-	-	PUNCT
ejpam-4461	47	19	connected	connect	VERB
ejpam-4461	47	20	domination	domination	NOUN
ejpam-4461	47	21	number	number	NOUN
ejpam-4461	47	22	denoted	denote	VERB
ejpam-4461	47	23	by	by	ADP
ejpam-4461	47	24	γ̃t(g	γ̃t(g	NOUN
ejpam-4461	47	25	)	)	PUNCT
ejpam-4461	47	26	.	.	PUNCT
ejpam-4461	48	1	we	we	PRON
ejpam-4461	48	2	refer	refer	VERB
ejpam-4461	48	3	to	to	ADP
ejpam-4461	48	4	[	[	X
ejpam-4461	48	5	4	4	NUM
ejpam-4461	48	6	]	]	PUNCT
ejpam-4461	48	7	and	and	CCONJ
ejpam-4461	48	8	[	[	X
ejpam-4461	48	9	5	5	NUM
ejpam-4461	48	10	]	]	PUNCT
ejpam-4461	48	11	for	for	ADP
ejpam-4461	48	12	the	the	DET
ejpam-4461	48	13	introduction	introduction	NOUN
ejpam-4461	48	14	and	and	CCONJ
ejpam-4461	48	15	results	result	NOUN
ejpam-4461	48	16	concerning	concern	VERB
ejpam-4461	48	17	outer	outer	ADV
ejpam-4461	48	18	-	-	PUNCT
ejpam-4461	48	19	connected	connect	VERB
ejpam-4461	48	20	domination	domination	NOUN
ejpam-4461	48	21	and	and	CCONJ
ejpam-4461	48	22	total	total	ADJ
ejpam-4461	48	23	outer	outer	ADV
ejpam-4461	48	24	-	-	PUNCT
ejpam-4461	48	25	connected	connect	VERB
ejpam-4461	48	26	domination	domination	NOUN
ejpam-4461	48	27	,	,	PUNCT
ejpam-4461	48	28	respectively	respectively	ADV
ejpam-4461	48	29	,	,	PUNCT
ejpam-4461	48	30	that	that	PRON
ejpam-4461	48	31	are	be	AUX
ejpam-4461	48	32	of	of	ADP
ejpam-4461	48	33	interest	interest	NOUN
ejpam-4461	48	34	in	in	ADP
ejpam-4461	48	35	this	this	DET
ejpam-4461	48	36	study	study	NOUN
ejpam-4461	48	37	.	.	PUNCT
ejpam-4461	49	1	suppose	suppose	VERB
ejpam-4461	49	2	that	that	SCONJ
ejpam-4461	49	3	g	g	PROPN
ejpam-4461	49	4	has	have	VERB
ejpam-4461	49	5	no	no	DET
ejpam-4461	49	6	isolated	isolated	ADJ
ejpam-4461	49	7	vertices	vertex	NOUN
ejpam-4461	49	8	.	.	PUNCT
ejpam-4461	50	1	a	a	DET
ejpam-4461	50	2	set	set	NOUN
ejpam-4461	50	3	s	s	NOUN
ejpam-4461	50	4	⊆	⊆	NUM
ejpam-4461	50	5	v	v	NOUN
ejpam-4461	50	6	(	(	PUNCT
ejpam-4461	50	7	g	g	NOUN
ejpam-4461	50	8	)	)	PUNCT
ejpam-4461	50	9	is	be	AUX
ejpam-4461	50	10	a	a	DET
ejpam-4461	50	11	semitotal	semitotal	ADJ
ejpam-4461	50	12	dominating	dominating	NOUN
ejpam-4461	50	13	set	set	NOUN
ejpam-4461	50	14	of	of	ADP
ejpam-4461	50	15	g	g	PROPN
ejpam-4461	50	16	if	if	SCONJ
ejpam-4461	50	17	s	s	VERB
ejpam-4461	50	18	is	be	AUX
ejpam-4461	50	19	a	a	DET
ejpam-4461	50	20	dominating	dominating	NOUN
ejpam-4461	50	21	set	set	VERB
ejpam-4461	50	22	in	in	ADP
ejpam-4461	50	23	g	g	PROPN
ejpam-4461	50	24	such	such	ADJ
ejpam-4461	50	25	that	that	PRON
ejpam-4461	50	26	for	for	ADP
ejpam-4461	50	27	every	every	DET
ejpam-4461	50	28	x	x	SYM
ejpam-4461	50	29	∈	∈	PROPN
ejpam-4461	50	30	s	s	VERB
ejpam-4461	50	31	there	there	PRON
ejpam-4461	50	32	exists	exist	VERB
ejpam-4461	50	33	y	y	PROPN
ejpam-4461	50	34	∈	∈	PROPN
ejpam-4461	50	35	s	s	PART
ejpam-4461	50	36	\	\	X
ejpam-4461	50	37	{	{	PUNCT
ejpam-4461	50	38	x	x	NOUN
ejpam-4461	50	39	}	}	PUNCT
ejpam-4461	50	40	for	for	ADP
ejpam-4461	50	41	which	which	PRON
ejpam-4461	50	42	dg(x	dg(x	NUM
ejpam-4461	50	43	,	,	PUNCT
ejpam-4461	50	44	y	y	NOUN
ejpam-4461	50	45	)	)	PUNCT
ejpam-4461	50	46	≤	≤	NOUN
ejpam-4461	50	47	2	2	NUM
ejpam-4461	50	48	.	.	PUNCT
ejpam-4461	50	49	the	the	DET
ejpam-4461	50	50	smallest	small	ADJ
ejpam-4461	50	51	cardinality	cardinality	NOUN
ejpam-4461	50	52	of	of	ADP
ejpam-4461	50	53	a	a	DET
ejpam-4461	50	54	semitotal	semitotal	ADJ
ejpam-4461	50	55	dominating	dominating	NOUN
ejpam-4461	50	56	set	set	NOUN
ejpam-4461	50	57	in	in	ADP
ejpam-4461	50	58	g	g	NOUN
ejpam-4461	50	59	,	,	PUNCT
ejpam-4461	50	60	denoted	denote	VERB
ejpam-4461	50	61	by	by	ADP
ejpam-4461	50	62	γt2(g	γt2(g	PROPN
ejpam-4461	50	63	)	)	PUNCT
ejpam-4461	50	64	,	,	PUNCT
ejpam-4461	50	65	is	be	AUX
ejpam-4461	50	66	called	call	VERB
ejpam-4461	50	67	a	a	DET
ejpam-4461	50	68	semitotal	semitotal	ADJ
ejpam-4461	50	69	domination	domination	NOUN
ejpam-4461	50	70	number	number	NOUN
ejpam-4461	50	71	of	of	ADP
ejpam-4461	50	72	g.	g.	PROPN
ejpam-4461	50	73	a	a	DET
ejpam-4461	50	74	semitotal	semitotal	ADJ
ejpam-4461	50	75	dominating	dominating	NOUN
ejpam-4461	50	76	set	set	NOUN
ejpam-4461	50	77	of	of	ADP
ejpam-4461	50	78	g	g	PROPN
ejpam-4461	50	79	with	with	ADP
ejpam-4461	50	80	cardinality	cardinality	NOUN
ejpam-4461	50	81	γt2(g	γt2(g	PROPN
ejpam-4461	50	82	)	)	PUNCT
ejpam-4461	50	83	is	be	AUX
ejpam-4461	50	84	called	call	VERB
ejpam-4461	50	85	a	a	DET
ejpam-4461	50	86	γt2	γt2	NOUN
ejpam-4461	50	87	-	-	PUNCT
ejpam-4461	50	88	set	set	NOUN
ejpam-4461	50	89	.	.	PUNCT
ejpam-4461	51	1	some	some	DET
ejpam-4461	51	2	results	result	NOUN
ejpam-4461	51	3	on	on	ADP
ejpam-4461	51	4	semitotal	semitotal	ADJ
ejpam-4461	51	5	domination	domination	NOUN
ejpam-4461	51	6	in	in	ADP
ejpam-4461	51	7	graphs	graph	NOUN
ejpam-4461	51	8	a.	a.	PROPN
ejpam-4461	51	9	aradais	aradais	PROPN
ejpam-4461	51	10	,	,	PUNCT
ejpam-4461	51	11	f.	f.	PROPN
ejpam-4461	51	12	jamil	jamil	PROPN
ejpam-4461	51	13	/	/	SYM
ejpam-4461	51	14	eur	eur	PROPN
ejpam-4461	51	15	.	.	PUNCT
ejpam-4461	52	1	j.	j.	PROPN
ejpam-4461	52	2	pure	pure	PROPN
ejpam-4461	52	3	appl	appl	PROPN
ejpam-4461	52	4	.	.	PROPN
ejpam-4461	52	5	math	math	PROPN
ejpam-4461	52	6	,	,	PUNCT
ejpam-4461	52	7	15	15	NUM
ejpam-4461	52	8	(	(	PUNCT
ejpam-4461	52	9	3	3	NUM
ejpam-4461	52	10	)	)	PUNCT
ejpam-4461	52	11	(	(	PUNCT
ejpam-4461	52	12	2022	2022	NUM
ejpam-4461	52	13	)	)	PUNCT
ejpam-4461	52	14	,	,	PUNCT
ejpam-4461	52	15	1265	1265	NUM
ejpam-4461	52	16	-	-	SYM
ejpam-4461	52	17	1279	1279	NUM
ejpam-4461	52	18	1267	1267	NUM
ejpam-4461	52	19	are	be	AUX
ejpam-4461	52	20	found	find	VERB
ejpam-4461	52	21	in	in	ADP
ejpam-4461	52	22	[	[	X
ejpam-4461	52	23	1	1	NUM
ejpam-4461	52	24	,	,	PUNCT
ejpam-4461	52	25	6–8	6–8	NOUN
ejpam-4461	52	26	]	]	X
ejpam-4461	52	27	.	.	PUNCT
ejpam-4461	53	1	a	a	DET
ejpam-4461	53	2	semitotal	semitotal	ADJ
ejpam-4461	53	3	dominating	dominating	NOUN
ejpam-4461	53	4	set	set	NOUN
ejpam-4461	53	5	s	s	VERB
ejpam-4461	53	6	is	be	AUX
ejpam-4461	53	7	an	an	DET
ejpam-4461	53	8	outer	outer	ADV
ejpam-4461	53	9	-	-	PUNCT
ejpam-4461	53	10	connected	connect	VERB
ejpam-4461	53	11	semitotal	semitotal	ADJ
ejpam-4461	53	12	dominating	dominating	NOUN
ejpam-4461	53	13	set	set	NOUN
ejpam-4461	53	14	of	of	ADP
ejpam-4461	53	15	g	g	PROPN
ejpam-4461	53	16	if	if	SCONJ
ejpam-4461	53	17	either	either	CCONJ
ejpam-4461	53	18	s	s	VERB
ejpam-4461	53	19	=	=	SYM
ejpam-4461	53	20	v	v	PROPN
ejpam-4461	53	21	(	(	PUNCT
ejpam-4461	53	22	g	g	NOUN
ejpam-4461	53	23	)	)	PUNCT
ejpam-4461	53	24	or	or	CCONJ
ejpam-4461	53	25	s	s	VERB
ejpam-4461	53	26	̸=	̸=	PROPN
ejpam-4461	53	27	v	v	NOUN
ejpam-4461	53	28	(	(	PUNCT
ejpam-4461	53	29	g	g	NOUN
ejpam-4461	53	30	)	)	PUNCT
ejpam-4461	53	31	and	and	CCONJ
ejpam-4461	53	32	the	the	DET
ejpam-4461	53	33	induced	induced	ADJ
ejpam-4461	53	34	subgraph	subgraph	NOUN
ejpam-4461	53	35	⟨v	⟨v	NOUN
ejpam-4461	53	36	(	(	PUNCT
ejpam-4461	53	37	g	g	NOUN
ejpam-4461	53	38	)	)	PUNCT
ejpam-4461	54	1	\	\	PROPN
ejpam-4461	55	1	s⟩	s⟩	PROPN
ejpam-4461	55	2	is	be	AUX
ejpam-4461	55	3	connected	connect	VERB
ejpam-4461	55	4	.	.	PUNCT
ejpam-4461	56	1	the	the	DET
ejpam-4461	56	2	smallest	small	ADJ
ejpam-4461	56	3	cardinality	cardinality	NOUN
ejpam-4461	56	4	of	of	ADP
ejpam-4461	56	5	an	an	DET
ejpam-4461	56	6	outer	outer	ADV
ejpam-4461	56	7	-	-	PUNCT
ejpam-4461	56	8	connected	connect	VERB
ejpam-4461	56	9	semitotal	semitotal	ADJ
ejpam-4461	56	10	dominating	dominating	NOUN
ejpam-4461	56	11	set	set	NOUN
ejpam-4461	56	12	in	in	ADP
ejpam-4461	56	13	g	g	NOUN
ejpam-4461	56	14	,	,	PUNCT
ejpam-4461	56	15	denoted	denote	VERB
ejpam-4461	56	16	by	by	ADP
ejpam-4461	56	17	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	56	18	)	)	PUNCT
ejpam-4461	56	19	,	,	PUNCT
ejpam-4461	56	20	is	be	AUX
ejpam-4461	56	21	called	call	VERB
ejpam-4461	56	22	the	the	DET
ejpam-4461	56	23	outer	outer	ADV
ejpam-4461	56	24	-	-	PUNCT
ejpam-4461	56	25	connected	connect	VERB
ejpam-4461	56	26	semitotal	semitotal	ADJ
ejpam-4461	56	27	domination	domination	NOUN
ejpam-4461	56	28	number	number	NOUN
ejpam-4461	56	29	of	of	ADP
ejpam-4461	56	30	g.	g.	PROPN
ejpam-4461	56	31	an	an	DET
ejpam-4461	56	32	outerconnected	outerconnecte	VERB
ejpam-4461	56	33	semitotal	semitotal	ADJ
ejpam-4461	56	34	dominating	dominating	NOUN
ejpam-4461	56	35	set	set	VERB
ejpam-4461	56	36	in	in	ADP
ejpam-4461	56	37	g	g	PROPN
ejpam-4461	56	38	with	with	ADP
ejpam-4461	56	39	cardinality	cardinality	NOUN
ejpam-4461	56	40	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	56	41	)	)	PUNCT
ejpam-4461	56	42	,	,	PUNCT
ejpam-4461	56	43	is	be	AUX
ejpam-4461	56	44	called	call	VERB
ejpam-4461	56	45	a	a	DET
ejpam-4461	56	46	γ̃t2	γ̃t2	PROPN
ejpam-4461	56	47	-	-	PUNCT
ejpam-4461	56	48	set	set	NOUN
ejpam-4461	56	49	.	.	PUNCT
ejpam-4461	57	1	for	for	ADP
ejpam-4461	57	2	the	the	DET
ejpam-4461	57	3	purposes	purpose	NOUN
ejpam-4461	57	4	of	of	ADP
ejpam-4461	57	5	this	this	DET
ejpam-4461	57	6	study	study	NOUN
ejpam-4461	57	7	,	,	PUNCT
ejpam-4461	57	8	we	we	PRON
ejpam-4461	57	9	write	write	VERB
ejpam-4461	57	10	for	for	ADP
ejpam-4461	57	11	v	v	NOUN
ejpam-4461	57	12	∈	∈	PROPN
ejpam-4461	57	13	v	v	NOUN
ejpam-4461	57	14	(	(	PUNCT
ejpam-4461	57	15	g	g	NOUN
ejpam-4461	57	16	)	)	PUNCT
ejpam-4461	57	17	,	,	PUNCT
ejpam-4461	57	18	n2	n2	ADJ
ejpam-4461	57	19	g(v	g(v	X
ejpam-4461	57	20	)	)	PUNCT
ejpam-4461	57	21	=	=	PRON
ejpam-4461	57	22	{	{	PUNCT
ejpam-4461	57	23	u	u	NOUN
ejpam-4461	57	24	∈	∈	PROPN
ejpam-4461	57	25	v	v	NOUN
ejpam-4461	57	26	(	(	PUNCT
ejpam-4461	57	27	g	g	NOUN
ejpam-4461	57	28	)	)	PUNCT
ejpam-4461	57	29	\	\	NOUN
ejpam-4461	58	1	{	{	PUNCT
ejpam-4461	58	2	v	v	NOUN
ejpam-4461	58	3	}	}	PUNCT
ejpam-4461	58	4	:	:	PUNCT
ejpam-4461	58	5	dg(u	dg(u	X
ejpam-4461	58	6	,	,	PUNCT
ejpam-4461	58	7	v	v	NOUN
ejpam-4461	58	8	)	)	PUNCT
ejpam-4461	58	9	≤	≤	NOUN
ejpam-4461	58	10	2	2	NUM
ejpam-4461	58	11	}	}	PUNCT
ejpam-4461	58	12	,	,	PUNCT
ejpam-4461	58	13	and	and	CCONJ
ejpam-4461	58	14	write	write	VERB
ejpam-4461	58	15	for	for	ADP
ejpam-4461	58	16	s	s	PROPN
ejpam-4461	58	17	⊆	⊆	NUM
ejpam-4461	58	18	v	v	NOUN
ejpam-4461	58	19	(	(	PUNCT
ejpam-4461	58	20	g	g	NOUN
ejpam-4461	58	21	)	)	PUNCT
ejpam-4461	58	22	,	,	PUNCT
ejpam-4461	58	23	n2	n2	ADJ
ejpam-4461	58	24	g(s	g(s	NOUN
ejpam-4461	58	25	)	)	PUNCT
ejpam-4461	58	26	=	=	PUNCT
ejpam-4461	58	27	∪v∈sn	∪v∈sn	VERB
ejpam-4461	58	28	2	2	NUM
ejpam-4461	58	29	g(v	g(v	NOUN
ejpam-4461	58	30	)	)	PUNCT
ejpam-4461	58	31	.	.	PUNCT
ejpam-4461	59	1	3	3	X
ejpam-4461	59	2	.	.	X
ejpam-4461	59	3	results	result	NOUN
ejpam-4461	59	4	observe	observe	VERB
ejpam-4461	59	5	that	that	SCONJ
ejpam-4461	59	6	an	an	DET
ejpam-4461	59	7	outer	outer	ADV
ejpam-4461	59	8	-	-	PUNCT
ejpam-4461	59	9	connected	connect	VERB
ejpam-4461	59	10	semitotal	semitotal	ADJ
ejpam-4461	59	11	dominating	dominating	NOUN
ejpam-4461	59	12	set	set	NOUN
ejpam-4461	59	13	is	be	AUX
ejpam-4461	59	14	both	both	CCONJ
ejpam-4461	59	15	a	a	DET
ejpam-4461	59	16	semitotal	semitotal	ADJ
ejpam-4461	59	17	dominating	dominating	NOUN
ejpam-4461	59	18	set	set	NOUN
ejpam-4461	59	19	and	and	CCONJ
ejpam-4461	59	20	an	an	DET
ejpam-4461	59	21	outer	outer	ADV
ejpam-4461	59	22	-	-	PUNCT
ejpam-4461	59	23	connected	connect	VERB
ejpam-4461	59	24	dominating	dominating	NOUN
ejpam-4461	59	25	set	set	NOUN
ejpam-4461	59	26	.	.	PUNCT
ejpam-4461	60	1	on	on	ADP
ejpam-4461	60	2	the	the	DET
ejpam-4461	60	3	other	other	ADJ
ejpam-4461	60	4	hand	hand	NOUN
ejpam-4461	60	5	,	,	PUNCT
ejpam-4461	60	6	a	a	DET
ejpam-4461	60	7	total	total	ADJ
ejpam-4461	60	8	outer	outer	ADV
ejpam-4461	60	9	-	-	PUNCT
ejpam-4461	60	10	connected	connect	VERB
ejpam-4461	60	11	dominating	dominating	NOUN
ejpam-4461	60	12	set	set	NOUN
ejpam-4461	60	13	is	be	AUX
ejpam-4461	60	14	an	an	DET
ejpam-4461	60	15	outer	outer	ADV
ejpam-4461	60	16	-	-	PUNCT
ejpam-4461	60	17	connected	connect	VERB
ejpam-4461	60	18	semitotal	semitotal	ADJ
ejpam-4461	60	19	dominating	dominating	NOUN
ejpam-4461	60	20	set	set	NOUN
ejpam-4461	60	21	.	.	PUNCT
ejpam-4461	61	1	thus	thus	ADV
ejpam-4461	61	2	,	,	PUNCT
ejpam-4461	61	3	max{2	max{2	PROPN
ejpam-4461	61	4	,	,	PUNCT
ejpam-4461	61	5	γt2(g	γt2(g	NOUN
ejpam-4461	61	6	)	)	PUNCT
ejpam-4461	61	7	,	,	PUNCT
ejpam-4461	61	8	γ̃(g	γ̃(g	NOUN
ejpam-4461	61	9	)	)	PUNCT
ejpam-4461	61	10	}	}	PUNCT
ejpam-4461	61	11	≤	≤	NUM
ejpam-4461	61	12	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	61	13	)	)	PUNCT
ejpam-4461	61	14	≤	≤	NOUN
ejpam-4461	61	15	γ̃t(g	γ̃t(g	NUM
ejpam-4461	61	16	)	)	PUNCT
ejpam-4461	61	17	.	.	PUNCT
ejpam-4461	62	1	(	(	PUNCT
ejpam-4461	62	2	1	1	X
ejpam-4461	62	3	)	)	PUNCT
ejpam-4461	62	4	strict	strict	ADJ
ejpam-4461	62	5	inequalities	inequality	NOUN
ejpam-4461	62	6	in	in	ADP
ejpam-4461	62	7	equation	equation	NOUN
ejpam-4461	62	8	1	1	NUM
ejpam-4461	62	9	can	can	AUX
ejpam-4461	62	10	be	be	AUX
ejpam-4461	62	11	attained	attain	VERB
ejpam-4461	62	12	for	for	ADP
ejpam-4461	62	13	a	a	DET
ejpam-4461	62	14	graph	graph	NOUN
ejpam-4461	62	15	.	.	PUNCT
ejpam-4461	63	1	to	to	PART
ejpam-4461	63	2	see	see	VERB
ejpam-4461	63	3	this	this	PRON
ejpam-4461	63	4	,	,	PUNCT
ejpam-4461	63	5	consider	consider	VERB
ejpam-4461	63	6	the	the	DET
ejpam-4461	63	7	graph	graph	NOUN
ejpam-4461	63	8	g	g	NOUN
ejpam-4461	63	9	in	in	ADP
ejpam-4461	63	10	figure	figure	NOUN
ejpam-4461	63	11	1	1	NUM
ejpam-4461	63	12	.	.	PUNCT
ejpam-4461	64	1	it	it	PRON
ejpam-4461	64	2	can	can	AUX
ejpam-4461	64	3	be	be	AUX
ejpam-4461	64	4	verified	verify	VERB
ejpam-4461	64	5	that	that	SCONJ
ejpam-4461	64	6	{	{	PUNCT
ejpam-4461	64	7	a	a	DET
ejpam-4461	64	8	,	,	PUNCT
ejpam-4461	64	9	b	b	NOUN
ejpam-4461	64	10	,	,	PUNCT
ejpam-4461	64	11	c	c	NOUN
ejpam-4461	64	12	,	,	PUNCT
ejpam-4461	64	13	d	d	NOUN
ejpam-4461	64	14	}	}	PUNCT
ejpam-4461	64	15	,	,	PUNCT
ejpam-4461	64	16	{	{	PUNCT
ejpam-4461	64	17	x	x	NOUN
ejpam-4461	64	18	,	,	PUNCT
ejpam-4461	64	19	y	y	PROPN
ejpam-4461	64	20	,	,	PUNCT
ejpam-4461	64	21	z	z	PROPN
ejpam-4461	64	22	,	,	PUNCT
ejpam-4461	64	23	w	w	PROPN
ejpam-4461	64	24	}	}	PUNCT
ejpam-4461	64	25	,	,	PUNCT
ejpam-4461	64	26	{	{	PUNCT
ejpam-4461	64	27	x	x	NOUN
ejpam-4461	64	28	,	,	PUNCT
ejpam-4461	64	29	y	y	PROPN
ejpam-4461	64	30	,	,	PUNCT
ejpam-4461	64	31	z	z	PROPN
ejpam-4461	64	32	,	,	PUNCT
ejpam-4461	64	33	w	w	PROPN
ejpam-4461	64	34	,	,	PUNCT
ejpam-4461	64	35	a	a	DET
ejpam-4461	64	36	,	,	PUNCT
ejpam-4461	64	37	b	b	NOUN
ejpam-4461	64	38	}	}	PUNCT
ejpam-4461	64	39	and	and	CCONJ
ejpam-4461	64	40	{	{	PUNCT
ejpam-4461	64	41	a	a	PRON
ejpam-4461	64	42	,	,	PUNCT
ejpam-4461	64	43	b	b	NOUN
ejpam-4461	64	44	,	,	PUNCT
ejpam-4461	64	45	c	c	NOUN
ejpam-4461	64	46	,	,	PUNCT
ejpam-4461	64	47	d	d	NOUN
ejpam-4461	64	48	,	,	PUNCT
ejpam-4461	64	49	x	x	NOUN
ejpam-4461	64	50	,	,	PUNCT
ejpam-4461	64	51	y	y	PROPN
ejpam-4461	64	52	,	,	PUNCT
ejpam-4461	64	53	z	z	NOUN
ejpam-4461	64	54	}	}	PUNCT
ejpam-4461	64	55	are	be	AUX
ejpam-4461	64	56	γt2	γt2	NOUN
ejpam-4461	64	57	-	-	PUNCT
ejpam-4461	64	58	set	set	ADJ
ejpam-4461	64	59	,	,	PUNCT
ejpam-4461	64	60	γ̃-set	γ̃-set	NOUN
ejpam-4461	64	61	,	,	PUNCT
ejpam-4461	64	62	γ̃t2	γ̃t2	PROPN
ejpam-4461	64	63	-	-	PUNCT
ejpam-4461	64	64	set	set	VERB
ejpam-4461	64	65	and	and	CCONJ
ejpam-4461	64	66	γ̃t	γ̃t	NOUN
ejpam-4461	64	67	-	-	PUNCT
ejpam-4461	64	68	set	set	ADJ
ejpam-4461	64	69	,	,	PUNCT
ejpam-4461	64	70	respectively	respectively	ADV
ejpam-4461	64	71	.	.	PUNCT
ejpam-4461	65	1	thus	thus	ADV
ejpam-4461	65	2	,	,	PUNCT
ejpam-4461	65	3	γ̃(g	γ̃(g	NOUN
ejpam-4461	65	4	)	)	PUNCT
ejpam-4461	65	5	=	=	SYM
ejpam-4461	65	6	4	4	NUM
ejpam-4461	65	7	=	=	SYM
ejpam-4461	65	8	γt2(g	γt2(g	NOUN
ejpam-4461	65	9	)	)	PUNCT
ejpam-4461	65	10	,	,	PUNCT
ejpam-4461	65	11	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	65	12	)	)	PUNCT
ejpam-4461	65	13	=	=	NOUN
ejpam-4461	65	14	6	6	NUM
ejpam-4461	65	15	and	and	CCONJ
ejpam-4461	65	16	γ̃t(g	γ̃t(g	NUM
ejpam-4461	65	17	)	)	PUNCT
ejpam-4461	66	1	=	=	SYM
ejpam-4461	66	2	7	7	X
ejpam-4461	66	3	.	.	PUNCT
ejpam-4461	66	4	....................................	....................................	PUNCT
ejpam-4461	66	5	....................................	....................................	PUNCT
ejpam-4461	67	1	....................................	....................................	PUNCT
ejpam-4461	67	2	....................................	....................................	PUNCT
ejpam-4461	68	1	....................................	....................................	PUNCT
ejpam-4461	68	2	....................................	....................................	PUNCT
ejpam-4461	69	1	....................................	....................................	PUNCT
ejpam-4461	69	2	....................................	....................................	PUNCT
ejpam-4461	70	1	...................................................................	...................................................................	PUNCT
ejpam-4461	70	2	............	............	PUNCT
ejpam-4461	70	3	...........	...........	PUNCT
ejpam-4461	70	4	...........	...........	PUNCT
ejpam-4461	70	5	...........	...........	PUNCT
ejpam-4461	70	6	...........	...........	PUNCT
ejpam-4461	70	7	...........	...........	PUNCT
ejpam-4461	70	8	...................................................................	...................................................................	PUNCT
ejpam-4461	70	9	............	............	PUNCT
ejpam-4461	70	10	...........	...........	PUNCT
ejpam-4461	70	11	...........	...........	PUNCT
ejpam-4461	70	12	...........	...........	PUNCT
ejpam-4461	70	13	...........	...........	PUNCT
ejpam-4461	70	14	...........	...........	PUNCT
ejpam-4461	70	15	.........	.........	PUNCT
ejpam-4461	70	16	........	........	PUNCT
ejpam-4461	70	17	........	........	PUNCT
ejpam-4461	70	18	........	........	PUNCT
ejpam-4461	70	19	........	........	PUNCT
ejpam-4461	70	20	...	...	PUNCT
ejpam-4461	71	1	............................................	............................................	PUNCT
ejpam-4461	71	2	.........	.........	PUNCT
ejpam-4461	71	3	........	........	PUNCT
ejpam-4461	71	4	........	........	PUNCT
ejpam-4461	71	5	........	........	PUNCT
ejpam-4461	71	6	........	........	PUNCT
ejpam-4461	71	7	...	...	PUNCT
ejpam-4461	72	1	............................................	............................................	PUNCT
ejpam-4461	73	1	a	a	DET
ejpam-4461	73	2	b	b	X
ejpam-4461	73	3	c	c	NOUN
ejpam-4461	73	4	d	d	X
ejpam-4461	73	5	x	x	X
ejpam-4461	73	6	y	y	PROPN
ejpam-4461	73	7	z	z	PROPN
ejpam-4461	73	8	w	w	PROPN
ejpam-4461	73	9	figure	figure	NOUN
ejpam-4461	73	10	1	1	NUM
ejpam-4461	73	11	:	:	PUNCT
ejpam-4461	73	12	graph	graph	VERB
ejpam-4461	73	13	g	g	NOUN
ejpam-4461	73	14	with	with	ADP
ejpam-4461	73	15	max{2	max{2	PROPN
ejpam-4461	73	16	,	,	PUNCT
ejpam-4461	73	17	γt2(g	γt2(g	NOUN
ejpam-4461	73	18	)	)	PUNCT
ejpam-4461	73	19	,	,	PUNCT
ejpam-4461	73	20	γ̃(g	γ̃(g	NOUN
ejpam-4461	73	21	)	)	PUNCT
ejpam-4461	73	22	}	}	PUNCT
ejpam-4461	73	23	<	<	X
ejpam-4461	73	24	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	73	25	)	)	PUNCT
ejpam-4461	73	26	<	<	X
ejpam-4461	73	27	γ̃t(g	γ̃t(g	NOUN
ejpam-4461	73	28	)	)	PUNCT
ejpam-4461	73	29	proposition	proposition	NOUN
ejpam-4461	73	30	1	1	NUM
ejpam-4461	73	31	.	.	X
ejpam-4461	74	1	for	for	ADP
ejpam-4461	74	2	path	path	NOUN
ejpam-4461	74	3	pn	pn	PROPN
ejpam-4461	74	4	on	on	ADP
ejpam-4461	74	5	n	n	PRON
ejpam-4461	74	6	≥	≥	NUM
ejpam-4461	74	7	2	2	NUM
ejpam-4461	74	8	vertices	vertex	NOUN
ejpam-4461	74	9	γ̃t2(pn	γ̃t2(pn	NOUN
ejpam-4461	74	10	)	)	PUNCT
ejpam-4461	75	1	=	=	PUNCT
ejpam-4461	76	1			NOUN
ejpam-4461	76	2	2	2	NUM
ejpam-4461	76	3	,	,	PUNCT
ejpam-4461	76	4	if	if	SCONJ
ejpam-4461	76	5	n	n	NOUN
ejpam-4461	76	6	=	=	SYM
ejpam-4461	76	7	2	2	NUM
ejpam-4461	76	8	n−	n−	NOUN
ejpam-4461	76	9	1	1	NUM
ejpam-4461	76	10	,	,	PUNCT
ejpam-4461	76	11	if	if	SCONJ
ejpam-4461	76	12	3	3	NUM
ejpam-4461	76	13	≤	≤	NUM
ejpam-4461	76	14	n	n	PRON
ejpam-4461	76	15	≤	≤	NUM
ejpam-4461	76	16	5	5	NUM
ejpam-4461	76	17	n−	n−	NOUN
ejpam-4461	76	18	2	2	NUM
ejpam-4461	76	19	,	,	PUNCT
ejpam-4461	76	20	if	if	SCONJ
ejpam-4461	76	21	n	n	PRON
ejpam-4461	76	22	≥	≥	NOUN
ejpam-4461	76	23	6	6	NUM
ejpam-4461	76	24	.	.	PUNCT
ejpam-4461	77	1	proof	proof	NOUN
ejpam-4461	77	2	.	.	PUNCT
ejpam-4461	78	1	the	the	DET
ejpam-4461	78	2	case	case	NOUN
ejpam-4461	78	3	where	where	SCONJ
ejpam-4461	78	4	n	n	NOUN
ejpam-4461	78	5	=	=	SYM
ejpam-4461	78	6	2	2	NUM
ejpam-4461	78	7	is	be	AUX
ejpam-4461	78	8	obvious	obvious	ADJ
ejpam-4461	78	9	.	.	PUNCT
ejpam-4461	79	1	assume	assume	VERB
ejpam-4461	79	2	n	n	PRON
ejpam-4461	79	3	≥	≥	NUM
ejpam-4461	79	4	3	3	X
ejpam-4461	79	5	.	.	PUNCT
ejpam-4461	80	1	let	let	VERB
ejpam-4461	80	2	s	s	PRON
ejpam-4461	80	3	⊆	⊆	NUM
ejpam-4461	80	4	v	v	NOUN
ejpam-4461	80	5	(	(	PUNCT
ejpam-4461	80	6	pn	pn	NOUN
ejpam-4461	80	7	)	)	PUNCT
ejpam-4461	80	8	,	,	PUNCT
ejpam-4461	80	9	be	be	AUX
ejpam-4461	80	10	γ̃t2	γ̃t2	PROPN
ejpam-4461	80	11	set	set	NOUN
ejpam-4461	80	12	of	of	ADP
ejpam-4461	80	13	pn	pn	PROPN
ejpam-4461	80	14	with	with	ADP
ejpam-4461	80	15	s	s	PROPN
ejpam-4461	80	16	̸=	̸=	PROPN
ejpam-4461	80	17	v	v	NOUN
ejpam-4461	80	18	(	(	PUNCT
ejpam-4461	80	19	pn	pn	NOUN
ejpam-4461	80	20	)	)	PUNCT
ejpam-4461	80	21	.	.	PUNCT
ejpam-4461	81	1	then	then	ADV
ejpam-4461	81	2	p	p	X
ejpam-4461	81	3	=	=	X
ejpam-4461	81	4	⟨v	⟨v	PROPN
ejpam-4461	81	5	(	(	PUNCT
ejpam-4461	81	6	pn	pn	NOUN
ejpam-4461	81	7	)	)	PUNCT
ejpam-4461	81	8	\	\	PROPN
ejpam-4461	81	9	s⟩	s⟩	PROPN
ejpam-4461	81	10	is	be	AUX
ejpam-4461	81	11	a	a	DET
ejpam-4461	81	12	path	path	NOUN
ejpam-4461	81	13	.	.	PUNCT
ejpam-4461	82	1	suppose	suppose	VERB
ejpam-4461	82	2	that	that	SCONJ
ejpam-4461	82	3	[	[	X
ejpam-4461	82	4	x	x	X
ejpam-4461	82	5	,	,	PUNCT
ejpam-4461	82	6	y	y	PROPN
ejpam-4461	82	7	,	,	PUNCT
ejpam-4461	82	8	z	z	X
ejpam-4461	82	9	]	]	X
ejpam-4461	82	10	is	be	AUX
ejpam-4461	82	11	a	a	DET
ejpam-4461	82	12	a.	a.	NOUN
ejpam-4461	82	13	aradais	aradais	PROPN
ejpam-4461	82	14	,	,	PUNCT
ejpam-4461	82	15	f.	f.	PROPN
ejpam-4461	82	16	jamil	jamil	PROPN
ejpam-4461	82	17	/	/	SYM
ejpam-4461	82	18	eur	eur	PROPN
ejpam-4461	82	19	.	.	PUNCT
ejpam-4461	83	1	j.	j.	PROPN
ejpam-4461	83	2	pure	pure	PROPN
ejpam-4461	83	3	appl	appl	PROPN
ejpam-4461	83	4	.	.	PROPN
ejpam-4461	83	5	math	math	PROPN
ejpam-4461	83	6	,	,	PUNCT
ejpam-4461	83	7	15	15	NUM
ejpam-4461	83	8	(	(	PUNCT
ejpam-4461	83	9	3	3	NUM
ejpam-4461	83	10	)	)	PUNCT
ejpam-4461	83	11	(	(	PUNCT
ejpam-4461	83	12	2022	2022	NUM
ejpam-4461	83	13	)	)	PUNCT
ejpam-4461	83	14	,	,	PUNCT
ejpam-4461	83	15	1265	1265	NUM
ejpam-4461	83	16	-	-	SYM
ejpam-4461	83	17	1279	1279	NUM
ejpam-4461	83	18	1268	1268	NUM
ejpam-4461	83	19	geodesic	geodesic	NOUN
ejpam-4461	83	20	in	in	ADP
ejpam-4461	83	21	p	p	PROPN
ejpam-4461	83	22	.	.	PUNCT
ejpam-4461	84	1	then	then	ADV
ejpam-4461	84	2	y	y	PROPN
ejpam-4461	84	3	/∈	/∈	PUNCT
ejpam-4461	84	4	npn	npn	PROPN
ejpam-4461	84	5	[	[	X
ejpam-4461	84	6	s	s	X
ejpam-4461	84	7	]	]	X
ejpam-4461	84	8	,	,	PUNCT
ejpam-4461	84	9	a	a	DET
ejpam-4461	84	10	contradiction	contradiction	NOUN
ejpam-4461	84	11	.	.	PUNCT
ejpam-4461	85	1	thus	thus	ADV
ejpam-4461	85	2	,	,	PUNCT
ejpam-4461	85	3	|v	|v	PROPN
ejpam-4461	85	4	(	(	PUNCT
ejpam-4461	85	5	p	p	NOUN
ejpam-4461	85	6	)	)	PUNCT
ejpam-4461	85	7	|	|	ADV
ejpam-4461	85	8	=	=	SYM
ejpam-4461	85	9	1	1	NUM
ejpam-4461	85	10	or	or	CCONJ
ejpam-4461	85	11	2	2	NUM
ejpam-4461	85	12	.	.	PUNCT
ejpam-4461	85	13	consequently	consequently	ADV
ejpam-4461	85	14	,	,	PUNCT
ejpam-4461	85	15	γ̃t2(pn	γ̃t2(pn	PROPN
ejpam-4461	85	16	)	)	PUNCT
ejpam-4461	86	1	=	=	SYM
ejpam-4461	86	2	|s|	|s|	PROPN
ejpam-4461	86	3	≥	≥	NOUN
ejpam-4461	86	4	n	n	CCONJ
ejpam-4461	86	5	−	−	PROPN
ejpam-4461	86	6	2	2	NUM
ejpam-4461	86	7	.	.	PUNCT
ejpam-4461	87	1	it	it	PRON
ejpam-4461	87	2	is	be	AUX
ejpam-4461	87	3	can	can	AUX
ejpam-4461	87	4	readily	readily	ADV
ejpam-4461	87	5	be	be	AUX
ejpam-4461	87	6	verified	verify	VERB
ejpam-4461	87	7	that	that	SCONJ
ejpam-4461	87	8	if	if	SCONJ
ejpam-4461	87	9	3	3	NUM
ejpam-4461	87	10	≤	≤	NOUN
ejpam-4461	87	11	n	n	PRON
ejpam-4461	87	12	≤	≤	NUM
ejpam-4461	87	13	5	5	NUM
ejpam-4461	87	14	,	,	PUNCT
ejpam-4461	87	15	|s|	|s|	NOUN
ejpam-4461	87	16	=	=	SYM
ejpam-4461	87	17	n	n	CCONJ
ejpam-4461	87	18	−	−	PROPN
ejpam-4461	87	19	1	1	NUM
ejpam-4461	87	20	.	.	PUNCT
ejpam-4461	88	1	that	that	PRON
ejpam-4461	88	2	is	be	AUX
ejpam-4461	88	3	,	,	PUNCT
ejpam-4461	88	4	γ̃t2(pn	γ̃t2(pn	X
ejpam-4461	88	5	)	)	PUNCT
ejpam-4461	89	1	=	=	PUNCT
ejpam-4461	89	2	n−	n−	NOUN
ejpam-4461	89	3	1	1	NUM
ejpam-4461	89	4	.	.	PUNCT
ejpam-4461	89	5	suppose	suppose	VERB
ejpam-4461	89	6	that	that	SCONJ
ejpam-4461	89	7	n	n	PROPN
ejpam-4461	89	8	≥	≥	NUM
ejpam-4461	89	9	6	6	NUM
ejpam-4461	89	10	.	.	PUNCT
ejpam-4461	90	1	put	put	VERB
ejpam-4461	90	2	pn	pn	NOUN
ejpam-4461	90	3	=	=	PUNCT
ejpam-4461	91	1	[	[	X
ejpam-4461	91	2	x1	x1	PROPN
ejpam-4461	91	3	,	,	PUNCT
ejpam-4461	91	4	x2	x2	PROPN
ejpam-4461	91	5	,	,	PUNCT
ejpam-4461	91	6	.	.	PUNCT
ejpam-4461	91	7	.	.	PUNCT
ejpam-4461	92	1	.	.	PUNCT
ejpam-4461	93	1	,	,	PUNCT
ejpam-4461	93	2	xn	xn	PROPN
ejpam-4461	93	3	]	]	X
ejpam-4461	93	4	.	.	PUNCT
ejpam-4461	94	1	since	since	SCONJ
ejpam-4461	94	2	s	s	PART
ejpam-4461	94	3	=	=	PUNCT
ejpam-4461	94	4	{	{	PUNCT
ejpam-4461	94	5	x1	x1	PROPN
ejpam-4461	94	6	,	,	PUNCT
ejpam-4461	94	7	x2	x2	PROPN
ejpam-4461	94	8	,	,	PUNCT
ejpam-4461	94	9	x5	x5	PROPN
ejpam-4461	94	10	,	,	PUNCT
ejpam-4461	94	11	x6	x6	PROPN
ejpam-4461	94	12	,	,	PUNCT
ejpam-4461	94	13	.	.	PUNCT
ejpam-4461	94	14	.	.	PUNCT
ejpam-4461	94	15	.	.	PUNCT
ejpam-4461	95	1	,	,	PUNCT
ejpam-4461	95	2	xn	xn	X
ejpam-4461	95	3	}	}	PUNCT
ejpam-4461	95	4	is	be	AUX
ejpam-4461	95	5	an	an	DET
ejpam-4461	95	6	outer	outer	ADV
ejpam-4461	95	7	-	-	PUNCT
ejpam-4461	95	8	connected	connect	VERB
ejpam-4461	95	9	semitotal	semitotal	ADJ
ejpam-4461	95	10	dominating	dominating	NOUN
ejpam-4461	95	11	set	set	NOUN
ejpam-4461	95	12	of	of	ADP
ejpam-4461	95	13	pn	pn	PROPN
ejpam-4461	95	14	,	,	PUNCT
ejpam-4461	95	15	γ̃t2(pn	γ̃t2(pn	PROPN
ejpam-4461	95	16	)	)	PUNCT
ejpam-4461	95	17	≤	≤	NUM
ejpam-4461	95	18	|s|	|s|	PROPN
ejpam-4461	95	19	=	=	PUNCT
ejpam-4461	95	20	n	n	CCONJ
ejpam-4461	95	21	−	−	PROPN
ejpam-4461	95	22	2	2	NUM
ejpam-4461	95	23	.	.	PUNCT
ejpam-4461	95	24	therefore	therefore	ADV
ejpam-4461	95	25	,	,	PUNCT
ejpam-4461	95	26	γ̃t2(pn	γ̃t2(pn	X
ejpam-4461	95	27	)	)	PUNCT
ejpam-4461	96	1	=	=	PUNCT
ejpam-4461	96	2	n−	n−	NOUN
ejpam-4461	96	3	2	2	NUM
ejpam-4461	96	4	.	.	PUNCT
ejpam-4461	96	5	proposition	proposition	NOUN
ejpam-4461	96	6	2	2	NUM
ejpam-4461	96	7	.	.	X
ejpam-4461	97	1	for	for	ADP
ejpam-4461	97	2	cycle	cycle	NOUN
ejpam-4461	97	3	cn	cn	PROPN
ejpam-4461	97	4	on	on	ADP
ejpam-4461	97	5	n	n	PRON
ejpam-4461	97	6	≥	≥	NUM
ejpam-4461	97	7	3	3	NUM
ejpam-4461	97	8	vertices	vertice	VERB
ejpam-4461	97	9	γ̃t2(cn	γ̃t2(cn	PROPN
ejpam-4461	97	10	)	)	PUNCT
ejpam-4461	98	1	=	=	PRON
ejpam-4461	98	2	{	{	PUNCT
ejpam-4461	98	3	2	2	NUM
ejpam-4461	98	4	,	,	PUNCT
ejpam-4461	98	5	if	if	SCONJ
ejpam-4461	98	6	n	n	NOUN
ejpam-4461	98	7	=	=	SYM
ejpam-4461	98	8	3	3	NUM
ejpam-4461	98	9	n−	n−	NOUN
ejpam-4461	98	10	2	2	NUM
ejpam-4461	98	11	,	,	PUNCT
ejpam-4461	98	12	if	if	SCONJ
ejpam-4461	98	13	n	n	PRON
ejpam-4461	98	14	≥	≥	NOUN
ejpam-4461	98	15	4	4	NUM
ejpam-4461	98	16	.	.	PUNCT
ejpam-4461	99	1	proof	proof	NOUN
ejpam-4461	99	2	.	.	PUNCT
ejpam-4461	100	1	the	the	DET
ejpam-4461	100	2	case	case	NOUN
ejpam-4461	100	3	for	for	ADP
ejpam-4461	100	4	n	n	NOUN
ejpam-4461	100	5	=	=	SYM
ejpam-4461	100	6	3	3	NUM
ejpam-4461	100	7	is	be	AUX
ejpam-4461	100	8	trivial	trivial	ADJ
ejpam-4461	100	9	.	.	PUNCT
ejpam-4461	101	1	assume	assume	VERB
ejpam-4461	101	2	that	that	SCONJ
ejpam-4461	101	3	n	n	NUM
ejpam-4461	101	4	≥	≥	NOUN
ejpam-4461	101	5	4	4	NUM
ejpam-4461	101	6	,	,	PUNCT
ejpam-4461	101	7	and	and	CCONJ
ejpam-4461	101	8	say	say	VERB
ejpam-4461	101	9	c	c	NOUN
ejpam-4461	101	10	=	=	PUNCT
ejpam-4461	102	1	[	[	X
ejpam-4461	102	2	x1	x1	PROPN
ejpam-4461	102	3	,	,	PUNCT
ejpam-4461	102	4	x2	x2	PROPN
ejpam-4461	102	5	,	,	PUNCT
ejpam-4461	102	6	.	.	PUNCT
ejpam-4461	102	7	.	.	PUNCT
ejpam-4461	103	1	.	.	PUNCT
ejpam-4461	104	1	,	,	PUNCT
ejpam-4461	104	2	xn	xn	PROPN
ejpam-4461	104	3	,	,	PUNCT
ejpam-4461	104	4	x1	x1	PROPN
ejpam-4461	104	5	]	]	PUNCT
ejpam-4461	104	6	.	.	PUNCT
ejpam-4461	105	1	since	since	SCONJ
ejpam-4461	105	2	{	{	PUNCT
ejpam-4461	105	3	x3	x3	ADJ
ejpam-4461	105	4	,	,	PUNCT
ejpam-4461	105	5	x4	x4	PROPN
ejpam-4461	105	6	,	,	PUNCT
ejpam-4461	105	7	.	.	PUNCT
ejpam-4461	105	8	.	.	PUNCT
ejpam-4461	105	9	.	.	PUNCT
ejpam-4461	106	1	,	,	PUNCT
ejpam-4461	106	2	xn	xn	X
ejpam-4461	106	3	}	}	PUNCT
ejpam-4461	106	4	is	be	AUX
ejpam-4461	106	5	an	an	DET
ejpam-4461	106	6	outer	outer	ADV
ejpam-4461	106	7	-	-	PUNCT
ejpam-4461	106	8	connected	connect	VERB
ejpam-4461	106	9	semitotal	semitotal	ADJ
ejpam-4461	106	10	dominating	dominating	NOUN
ejpam-4461	106	11	set	set	NOUN
ejpam-4461	106	12	of	of	ADP
ejpam-4461	106	13	cn	cn	PROPN
ejpam-4461	106	14	,	,	PUNCT
ejpam-4461	106	15	γ̃t2(cn	γ̃t2(cn	PROPN
ejpam-4461	106	16	)	)	PUNCT
ejpam-4461	106	17	≤	≤	NOUN
ejpam-4461	107	1	n	n	CCONJ
ejpam-4461	107	2	−	−	PROPN
ejpam-4461	107	3	2	2	NUM
ejpam-4461	107	4	.	.	PUNCT
ejpam-4461	108	1	following	follow	VERB
ejpam-4461	108	2	similar	similar	ADJ
ejpam-4461	108	3	arguments	argument	NOUN
ejpam-4461	108	4	used	use	VERB
ejpam-4461	108	5	above	above	ADV
ejpam-4461	108	6	,	,	PUNCT
ejpam-4461	108	7	if	if	SCONJ
ejpam-4461	108	8	s	s	VERB
ejpam-4461	108	9	⊆	⊆	NUM
ejpam-4461	108	10	v	v	NOUN
ejpam-4461	108	11	(	(	PUNCT
ejpam-4461	108	12	cn	cn	PROPN
ejpam-4461	108	13	)	)	PUNCT
ejpam-4461	108	14	is	be	AUX
ejpam-4461	108	15	a	a	DET
ejpam-4461	108	16	γ̃t2set	γ̃t2set	NOUN
ejpam-4461	108	17	of	of	ADP
ejpam-4461	108	18	cn	cn	PROPN
ejpam-4461	108	19	and	and	CCONJ
ejpam-4461	108	20	p	p	NOUN
ejpam-4461	108	21	=	=	X
ejpam-4461	108	22	⟨v	⟨v	PROPN
ejpam-4461	108	23	(	(	PUNCT
ejpam-4461	108	24	cn	cn	PROPN
ejpam-4461	108	25	)	)	PUNCT
ejpam-4461	108	26	\	\	PROPN
ejpam-4461	108	27	s⟩	s⟩	PROPN
ejpam-4461	108	28	,	,	PUNCT
ejpam-4461	108	29	then	then	ADV
ejpam-4461	108	30	p	p	NOUN
ejpam-4461	108	31	is	be	AUX
ejpam-4461	108	32	a	a	DET
ejpam-4461	108	33	path	path	NOUN
ejpam-4461	108	34	with	with	ADP
ejpam-4461	108	35	1	1	NUM
ejpam-4461	108	36	≤	≤	NOUN
ejpam-4461	108	37	|v	|v	NOUN
ejpam-4461	108	38	(	(	PUNCT
ejpam-4461	108	39	p	p	NOUN
ejpam-4461	108	40	)	)	PUNCT
ejpam-4461	108	41	|	|	ADV
ejpam-4461	108	42	≤	≤	NUM
ejpam-4461	108	43	2	2	NUM
ejpam-4461	108	44	.	.	PUNCT
ejpam-4461	109	1	consequently	consequently	ADV
ejpam-4461	109	2	,	,	PUNCT
ejpam-4461	109	3	γ̃t2(cn	γ̃t2(cn	PROPN
ejpam-4461	109	4	)	)	PUNCT
ejpam-4461	110	1	=	=	SYM
ejpam-4461	110	2	|s|	|s|	PROPN
ejpam-4461	110	3	≥	≥	PROPN
ejpam-4461	110	4	n−	n−	NOUN
ejpam-4461	110	5	2	2	NUM
ejpam-4461	110	6	.	.	PUNCT
ejpam-4461	110	7	proposition	proposition	NOUN
ejpam-4461	110	8	3	3	NUM
ejpam-4461	110	9	.	.	PUNCT
ejpam-4461	111	1	for	for	ADP
ejpam-4461	111	2	complete	complete	ADJ
ejpam-4461	111	3	multipartite	multipartite	ADJ
ejpam-4461	111	4	graph	graph	NOUN
ejpam-4461	111	5	kn1,n2,	kn1,n2,	NOUN
ejpam-4461	111	6	...	...	PUNCT
ejpam-4461	111	7	,nt	,nt	PUNCT
ejpam-4461	111	8	of	of	ADP
ejpam-4461	111	9	order	order	NOUN
ejpam-4461	111	10	n	n	PROPN
ejpam-4461	111	11	=	=	SYM
ejpam-4461	111	12	n1+n2	n1+n2	PROPN
ejpam-4461	111	13	+	+	NUM
ejpam-4461	111	14	...	...	PUNCT
ejpam-4461	111	15	+	+	ADJ
ejpam-4461	111	16	nt	not	PART
ejpam-4461	111	17	,	,	PUNCT
ejpam-4461	111	18	where	where	SCONJ
ejpam-4461	111	19	1	1	NUM
ejpam-4461	111	20	≤	≤	NUM
ejpam-4461	111	21	n1	n1	ADJ
ejpam-4461	111	22	≤	≤	NOUN
ejpam-4461	111	23	n2	n2	NOUN
ejpam-4461	111	24	≤	≤	NOUN
ejpam-4461	111	25	·	·	PUNCT
ejpam-4461	111	26	·	·	PUNCT
ejpam-4461	111	27	·	·	PUNCT
ejpam-4461	111	28	≤	≤	PROPN
ejpam-4461	111	29	nt	not	PART
ejpam-4461	111	30	and	and	CCONJ
ejpam-4461	111	31	t	t	X
ejpam-4461	111	32	≥	≥	NUM
ejpam-4461	111	33	2	2	NUM
ejpam-4461	111	34	,	,	PUNCT
ejpam-4461	111	35	γ̃t2(kn1,n2,	γ̃t2(kn1,n2,	PROPN
ejpam-4461	111	36	...	...	PUNCT
ejpam-4461	111	37	,nt	,nt	PUNCT
ejpam-4461	111	38	)	)	PUNCT
ejpam-4461	111	39	=	=	PRON
ejpam-4461	111	40	{	{	PUNCT
ejpam-4461	111	41	n2	n2	NOUN
ejpam-4461	111	42	,	,	PUNCT
ejpam-4461	111	43	if	if	SCONJ
ejpam-4461	111	44	t	t	NOUN
ejpam-4461	111	45	=	=	SYM
ejpam-4461	111	46	2	2	NUM
ejpam-4461	111	47	and	and	CCONJ
ejpam-4461	111	48	n1	n1	NOUN
ejpam-4461	111	49	=	=	SYM
ejpam-4461	111	50	1	1	NUM
ejpam-4461	111	51	,	,	PUNCT
ejpam-4461	111	52	n2	n2	ADJ
ejpam-4461	111	53	≥	≥	NUM
ejpam-4461	111	54	2	2	NUM
ejpam-4461	111	55	2	2	NUM
ejpam-4461	111	56	,	,	PUNCT
ejpam-4461	111	57	else	else	ADV
ejpam-4461	111	58	.	.	PUNCT
ejpam-4461	112	1	proof	proof	NOUN
ejpam-4461	112	2	.	.	PUNCT
ejpam-4461	113	1	put	put	VERB
ejpam-4461	113	2	g	g	PROPN
ejpam-4461	113	3	=	=	PUNCT
ejpam-4461	113	4	kn1,n2,	kn1,n2,	NOUN
ejpam-4461	113	5	...	...	PUNCT
ejpam-4461	113	6	,nt	,nt	PUNCT
ejpam-4461	113	7	,	,	PUNCT
ejpam-4461	113	8	and	and	CCONJ
ejpam-4461	113	9	let	let	VERB
ejpam-4461	113	10	u1	u1	NOUN
ejpam-4461	113	11	,	,	PUNCT
ejpam-4461	113	12	u2	u2	NOUN
ejpam-4461	113	13	,	,	PUNCT
ejpam-4461	113	14	.	.	PUNCT
ejpam-4461	113	15	.	.	PUNCT
ejpam-4461	114	1	.	.	PUNCT
ejpam-4461	115	1	,	,	PUNCT
ejpam-4461	115	2	ut	ut	PROPN
ejpam-4461	115	3	be	be	AUX
ejpam-4461	115	4	the	the	DET
ejpam-4461	115	5	partite	partite	ADJ
ejpam-4461	115	6	sets	set	NOUN
ejpam-4461	115	7	of	of	ADP
ejpam-4461	115	8	g.	g.	PROPN
ejpam-4461	115	9	first	first	ADV
ejpam-4461	115	10	,	,	PUNCT
ejpam-4461	115	11	observe	observe	VERB
ejpam-4461	115	12	that	that	SCONJ
ejpam-4461	115	13	if	if	SCONJ
ejpam-4461	115	14	nt	not	PART
ejpam-4461	115	15	=	=	NOUN
ejpam-4461	115	16	1	1	NUM
ejpam-4461	115	17	,	,	PUNCT
ejpam-4461	115	18	then	then	ADV
ejpam-4461	115	19	g	g	PROPN
ejpam-4461	115	20	=	=	SYM
ejpam-4461	115	21	kt	kt	PROPN
ejpam-4461	115	22	and	and	CCONJ
ejpam-4461	115	23	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	115	24	)	)	PUNCT
ejpam-4461	115	25	=	=	SYM
ejpam-4461	115	26	2	2	X
ejpam-4461	115	27	.	.	X
ejpam-4461	115	28	assume	assume	VERB
ejpam-4461	115	29	that	that	SCONJ
ejpam-4461	115	30	nt	not	PART
ejpam-4461	115	31	≥	≥	NOUN
ejpam-4461	115	32	2	2	X
ejpam-4461	115	33	.	.	PUNCT
ejpam-4461	116	1	we	we	PRON
ejpam-4461	116	2	consider	consider	VERB
ejpam-4461	116	3	the	the	DET
ejpam-4461	116	4	following	follow	VERB
ejpam-4461	116	5	cases	case	NOUN
ejpam-4461	116	6	:	:	PUNCT
ejpam-4461	116	7	case	case	NOUN
ejpam-4461	116	8	1	1	NUM
ejpam-4461	116	9	:	:	PUNCT
ejpam-4461	116	10	suppose	suppose	VERB
ejpam-4461	116	11	that	that	SCONJ
ejpam-4461	116	12	n1	n1	PROPN
ejpam-4461	116	13	=	=	SYM
ejpam-4461	116	14	1	1	X
ejpam-4461	116	15	.	.	X
ejpam-4461	117	1	we	we	PRON
ejpam-4461	117	2	consider	consider	VERB
ejpam-4461	117	3	the	the	DET
ejpam-4461	117	4	following	follow	VERB
ejpam-4461	117	5	subcases	subcase	NOUN
ejpam-4461	117	6	:	:	PUNCT
ejpam-4461	117	7	subcase	subcase	VERB
ejpam-4461	117	8	1.1	1.1	NUM
ejpam-4461	117	9	:	:	PUNCT
ejpam-4461	117	10	if	if	SCONJ
ejpam-4461	117	11	t	t	PROPN
ejpam-4461	117	12	=	=	SYM
ejpam-4461	117	13	2	2	NUM
ejpam-4461	117	14	and	and	CCONJ
ejpam-4461	117	15	n2	n2	ADJ
ejpam-4461	117	16	≥	≥	NOUN
ejpam-4461	117	17	2	2	NUM
ejpam-4461	117	18	,	,	PUNCT
ejpam-4461	117	19	then	then	ADV
ejpam-4461	117	20	g	g	PROPN
ejpam-4461	117	21	=	=	PUNCT
ejpam-4461	118	1	k1,n2	k1,n2	PROPN
ejpam-4461	118	2	,	,	PUNCT
ejpam-4461	118	3	a	a	DET
ejpam-4461	118	4	star	star	NOUN
ejpam-4461	118	5	of	of	ADP
ejpam-4461	118	6	order	order	NOUN
ejpam-4461	118	7	n	n	PRON
ejpam-4461	118	8	≥	≥	NOUN
ejpam-4461	118	9	3	3	NUM
ejpam-4461	118	10	.	.	PUNCT
ejpam-4461	119	1	if	if	SCONJ
ejpam-4461	119	2	s	s	VERB
ejpam-4461	119	3	⊆	⊆	NUM
ejpam-4461	119	4	v	v	NOUN
ejpam-4461	119	5	(	(	PUNCT
ejpam-4461	119	6	g	g	NOUN
ejpam-4461	119	7	)	)	PUNCT
ejpam-4461	119	8	is	be	AUX
ejpam-4461	119	9	an	an	DET
ejpam-4461	119	10	outer	outer	ADV
ejpam-4461	119	11	-	-	PUNCT
ejpam-4461	119	12	connected	connect	VERB
ejpam-4461	119	13	semitotal	semitotal	ADJ
ejpam-4461	119	14	dominating	dominating	NOUN
ejpam-4461	119	15	set	set	NOUN
ejpam-4461	119	16	of	of	ADP
ejpam-4461	119	17	g	g	NOUN
ejpam-4461	119	18	,	,	PUNCT
ejpam-4461	119	19	then	then	ADV
ejpam-4461	119	20	either	either	CCONJ
ejpam-4461	119	21	|s|	|s|	PROPN
ejpam-4461	119	22	=	=	SYM
ejpam-4461	119	23	n	n	CCONJ
ejpam-4461	119	24	−	−	PROPN
ejpam-4461	119	25	1	1	NUM
ejpam-4461	119	26	=	=	NOUN
ejpam-4461	119	27	n2	n2	ADJ
ejpam-4461	119	28	or	or	CCONJ
ejpam-4461	119	29	|s|	|s|	PROPN
ejpam-4461	119	30	=	=	SYM
ejpam-4461	119	31	n.	n.	PROPN
ejpam-4461	119	32	thus	thus	ADV
ejpam-4461	119	33	,	,	PUNCT
ejpam-4461	119	34	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	119	35	)	)	PUNCT
ejpam-4461	119	36	=	=	SYM
ejpam-4461	119	37	n2	n2	PROPN
ejpam-4461	119	38	.	.	PUNCT
ejpam-4461	119	39	subcase	subcase	PROPN
ejpam-4461	119	40	1.2	1.2	NUM
ejpam-4461	119	41	:	:	PUNCT
ejpam-4461	119	42	suppose	suppose	VERB
ejpam-4461	119	43	that	that	SCONJ
ejpam-4461	119	44	t	t	PROPN
ejpam-4461	119	45	≥	≥	NUM
ejpam-4461	119	46	3	3	NUM
ejpam-4461	119	47	and	and	CCONJ
ejpam-4461	119	48	n1	n1	NOUN
ejpam-4461	119	49	=	=	SYM
ejpam-4461	119	50	n2	n2	NOUN
ejpam-4461	119	51	=	=	PROPN
ejpam-4461	119	52	1	1	NUM
ejpam-4461	119	53	such	such	ADJ
ejpam-4461	119	54	that	that	SCONJ
ejpam-4461	119	55	g	g	PROPN
ejpam-4461	119	56	is	be	AUX
ejpam-4461	119	57	not	not	PART
ejpam-4461	119	58	a	a	DET
ejpam-4461	119	59	path	path	NOUN
ejpam-4461	119	60	.	.	PUNCT
ejpam-4461	120	1	pick	pick	VERB
ejpam-4461	120	2	u	u	PRON
ejpam-4461	120	3	∈	∈	PROPN
ejpam-4461	120	4	u2	u2	NOUN
ejpam-4461	120	5	and	and	CCONJ
ejpam-4461	120	6	v	v	NOUN
ejpam-4461	120	7	∈	∈	PROPN
ejpam-4461	120	8	u3	u3	NOUN
ejpam-4461	120	9	.	.	PUNCT
ejpam-4461	121	1	then	then	ADV
ejpam-4461	121	2	s	s	VERB
ejpam-4461	121	3	=	=	SYM
ejpam-4461	121	4	{	{	PUNCT
ejpam-4461	121	5	u	u	NOUN
ejpam-4461	121	6	,	,	PUNCT
ejpam-4461	121	7	v	v	NOUN
ejpam-4461	121	8	}	}	PUNCT
ejpam-4461	121	9	is	be	AUX
ejpam-4461	121	10	an	an	DET
ejpam-4461	121	11	outer	outer	ADV
ejpam-4461	121	12	-	-	PUNCT
ejpam-4461	121	13	connected	connect	VERB
ejpam-4461	121	14	semitotal	semitotal	ADJ
ejpam-4461	121	15	dominating	dominating	NOUN
ejpam-4461	121	16	set	set	NOUN
ejpam-4461	121	17	of	of	ADP
ejpam-4461	121	18	g.	g.	PROPN
ejpam-4461	121	19	thus	thus	ADV
ejpam-4461	121	20	,	,	PUNCT
ejpam-4461	121	21	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	121	22	)	)	PUNCT
ejpam-4461	121	23	=	=	SYM
ejpam-4461	122	1	2	2	X
ejpam-4461	122	2	.	.	X
ejpam-4461	122	3	subcase	subcase	PROPN
ejpam-4461	122	4	1.3	1.3	NUM
ejpam-4461	122	5	:	:	PUNCT
ejpam-4461	122	6	suppose	suppose	VERB
ejpam-4461	122	7	that	that	SCONJ
ejpam-4461	122	8	t	t	PROPN
ejpam-4461	122	9	≥	≥	NUM
ejpam-4461	122	10	3	3	NUM
ejpam-4461	122	11	and	and	CCONJ
ejpam-4461	122	12	n2	n2	ADJ
ejpam-4461	122	13	≥	≥	NOUN
ejpam-4461	122	14	2	2	NUM
ejpam-4461	122	15	.	.	PUNCT
ejpam-4461	122	16	pick	pick	VERB
ejpam-4461	122	17	u	u	PRON
ejpam-4461	122	18	∈	∈	PROPN
ejpam-4461	122	19	u1	u1	NOUN
ejpam-4461	122	20	and	and	CCONJ
ejpam-4461	122	21	v	v	ADP
ejpam-4461	122	22	∈	∈	PROPN
ejpam-4461	122	23	u2	u2	NOUN
ejpam-4461	122	24	.	.	PUNCT
ejpam-4461	123	1	then	then	ADV
ejpam-4461	123	2	s	s	VERB
ejpam-4461	123	3	=	=	SYM
ejpam-4461	123	4	{	{	PUNCT
ejpam-4461	123	5	u	u	NOUN
ejpam-4461	123	6	,	,	PUNCT
ejpam-4461	123	7	v	v	NOUN
ejpam-4461	123	8	}	}	PUNCT
ejpam-4461	123	9	is	be	AUX
ejpam-4461	123	10	an	an	DET
ejpam-4461	123	11	outer	outer	ADV
ejpam-4461	123	12	-	-	PUNCT
ejpam-4461	123	13	connected	connect	VERB
ejpam-4461	123	14	semitotal	semitotal	ADJ
ejpam-4461	123	15	dominating	dominating	NOUN
ejpam-4461	123	16	set	set	NOUN
ejpam-4461	123	17	of	of	ADP
ejpam-4461	123	18	g.	g.	PROPN
ejpam-4461	123	19	thus	thus	ADV
ejpam-4461	123	20	,	,	PUNCT
ejpam-4461	123	21	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	123	22	)	)	PUNCT
ejpam-4461	123	23	=	=	SYM
ejpam-4461	123	24	2	2	X
ejpam-4461	123	25	.	.	X
ejpam-4461	123	26	case	case	NOUN
ejpam-4461	123	27	2	2	NUM
ejpam-4461	123	28	:	:	PUNCT
ejpam-4461	123	29	suppose	suppose	VERB
ejpam-4461	123	30	that	that	SCONJ
ejpam-4461	123	31	t	t	PROPN
ejpam-4461	123	32	≥	≥	NUM
ejpam-4461	123	33	2	2	NUM
ejpam-4461	123	34	and	and	CCONJ
ejpam-4461	123	35	nk	nk	PROPN
ejpam-4461	123	36	≥	≥	PROPN
ejpam-4461	123	37	2	2	NUM
ejpam-4461	123	38	for	for	ADP
ejpam-4461	123	39	all	all	DET
ejpam-4461	123	40	k	k	PROPN
ejpam-4461	123	41	∈	∈	PROPN
ejpam-4461	123	42	{	{	PUNCT
ejpam-4461	123	43	1	1	NUM
ejpam-4461	123	44	,	,	PUNCT
ejpam-4461	123	45	2	2	NUM
ejpam-4461	123	46	,	,	PUNCT
ejpam-4461	123	47	.	.	PUNCT
ejpam-4461	123	48	.	.	PUNCT
ejpam-4461	124	1	.	.	PUNCT
ejpam-4461	125	1	,	,	PUNCT
ejpam-4461	125	2	t	t	PROPN
ejpam-4461	125	3	}	}	PUNCT
ejpam-4461	125	4	.	.	PUNCT
ejpam-4461	126	1	pick	pick	VERB
ejpam-4461	126	2	u	u	PRON
ejpam-4461	126	3	∈	∈	PROPN
ejpam-4461	126	4	u1	u1	NOUN
ejpam-4461	126	5	and	and	CCONJ
ejpam-4461	126	6	v	v	ADP
ejpam-4461	126	7	∈	∈	PROPN
ejpam-4461	126	8	u2	u2	NOUN
ejpam-4461	126	9	.	.	PUNCT
ejpam-4461	127	1	then	then	ADV
ejpam-4461	127	2	s	s	VERB
ejpam-4461	127	3	=	=	SYM
ejpam-4461	127	4	{	{	PUNCT
ejpam-4461	127	5	u	u	NOUN
ejpam-4461	127	6	,	,	PUNCT
ejpam-4461	127	7	v	v	NOUN
ejpam-4461	127	8	}	}	PUNCT
ejpam-4461	127	9	is	be	AUX
ejpam-4461	127	10	an	an	DET
ejpam-4461	127	11	outer	outer	ADV
ejpam-4461	127	12	-	-	PUNCT
ejpam-4461	127	13	connected	connect	VERB
ejpam-4461	127	14	semitotal	semitotal	ADJ
ejpam-4461	127	15	dominating	dominating	NOUN
ejpam-4461	127	16	set	set	NOUN
ejpam-4461	127	17	of	of	ADP
ejpam-4461	127	18	g.	g.	PROPN
ejpam-4461	127	19	proposition	proposition	PROPN
ejpam-4461	127	20	4	4	NUM
ejpam-4461	127	21	.	.	PUNCT
ejpam-4461	128	1	let	let	VERB
ejpam-4461	128	2	g	g	PRON
ejpam-4461	128	3	be	be	AUX
ejpam-4461	128	4	a	a	DET
ejpam-4461	128	5	connected	connected	ADJ
ejpam-4461	128	6	graph	graph	NOUN
ejpam-4461	128	7	of	of	ADP
ejpam-4461	128	8	order	order	NOUN
ejpam-4461	128	9	n	n	PRON
ejpam-4461	128	10	≥	≥	NOUN
ejpam-4461	128	11	2	2	NUM
ejpam-4461	128	12	.	.	PUNCT
ejpam-4461	129	1	then	then	ADV
ejpam-4461	129	2	(	(	PUNCT
ejpam-4461	129	3	i	i	NOUN
ejpam-4461	129	4	)	)	PUNCT
ejpam-4461	129	5	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	129	6	)	)	PUNCT
ejpam-4461	129	7	=	=	SYM
ejpam-4461	129	8	2	2	NUM
ejpam-4461	129	9	if	if	SCONJ
ejpam-4461	129	10	and	and	CCONJ
ejpam-4461	129	11	only	only	ADV
ejpam-4461	129	12	if	if	SCONJ
ejpam-4461	129	13	g	g	PROPN
ejpam-4461	129	14	can	can	AUX
ejpam-4461	129	15	be	be	AUX
ejpam-4461	129	16	obtained	obtain	VERB
ejpam-4461	129	17	from	from	ADP
ejpam-4461	129	18	a	a	DET
ejpam-4461	129	19	connected	connected	ADJ
ejpam-4461	129	20	graph	graph	NOUN
ejpam-4461	129	21	h	h	NOUN
ejpam-4461	129	22	of	of	ADP
ejpam-4461	129	23	order	order	NOUN
ejpam-4461	129	24	n−	n−	NOUN
ejpam-4461	129	25	2	2	NUM
ejpam-4461	129	26	by	by	ADP
ejpam-4461	129	27	adding	add	VERB
ejpam-4461	129	28	to	to	ADP
ejpam-4461	129	29	h	h	PROPN
ejpam-4461	129	30	vertices	vertex	NOUN
ejpam-4461	129	31	u	u	NOUN
ejpam-4461	129	32	and	and	CCONJ
ejpam-4461	129	33	v	v	ADP
ejpam-4461	129	34	such	such	ADJ
ejpam-4461	129	35	that	that	DET
ejpam-4461	129	36	dg(u	dg(u	ADJ
ejpam-4461	129	37	,	,	PUNCT
ejpam-4461	129	38	v	v	NOUN
ejpam-4461	129	39	)	)	PUNCT
ejpam-4461	129	40	=	=	SYM
ejpam-4461	129	41	1	1	NUM
ejpam-4461	129	42	or	or	CCONJ
ejpam-4461	129	43	2	2	NUM
ejpam-4461	129	44	and	and	CCONJ
ejpam-4461	129	45	{	{	PUNCT
ejpam-4461	129	46	u	u	NOUN
ejpam-4461	129	47	,	,	PUNCT
ejpam-4461	129	48	v	v	NOUN
ejpam-4461	129	49	}	}	PUNCT
ejpam-4461	129	50	dominates	dominate	VERB
ejpam-4461	129	51	v	v	NOUN
ejpam-4461	129	52	(	(	PUNCT
ejpam-4461	129	53	h	h	NOUN
ejpam-4461	129	54	)	)	PUNCT
ejpam-4461	129	55	.	.	PUNCT
ejpam-4461	130	1	a.	a.	PROPN
ejpam-4461	130	2	aradais	aradais	PROPN
ejpam-4461	130	3	,	,	PUNCT
ejpam-4461	130	4	f.	f.	PROPN
ejpam-4461	130	5	jamil	jamil	PROPN
ejpam-4461	130	6	/	/	SYM
ejpam-4461	130	7	eur	eur	PROPN
ejpam-4461	130	8	.	.	PUNCT
ejpam-4461	131	1	j.	j.	PROPN
ejpam-4461	131	2	pure	pure	PROPN
ejpam-4461	131	3	appl	appl	PROPN
ejpam-4461	131	4	.	.	PROPN
ejpam-4461	131	5	math	math	PROPN
ejpam-4461	131	6	,	,	PUNCT
ejpam-4461	131	7	15	15	NUM
ejpam-4461	131	8	(	(	PUNCT
ejpam-4461	131	9	3	3	NUM
ejpam-4461	131	10	)	)	PUNCT
ejpam-4461	131	11	(	(	PUNCT
ejpam-4461	131	12	2022	2022	NUM
ejpam-4461	131	13	)	)	PUNCT
ejpam-4461	131	14	,	,	PUNCT
ejpam-4461	131	15	1265	1265	NUM
ejpam-4461	131	16	-	-	SYM
ejpam-4461	131	17	1279	1279	NUM
ejpam-4461	131	18	1269	1269	NUM
ejpam-4461	131	19	(	(	PUNCT
ejpam-4461	131	20	ii	ii	NOUN
ejpam-4461	131	21	)	)	PUNCT
ejpam-4461	131	22	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	131	23	)	)	PUNCT
ejpam-4461	131	24	=	=	SYM
ejpam-4461	132	1	n	n	NOUN
ejpam-4461	132	2	if	if	SCONJ
ejpam-4461	132	3	and	and	CCONJ
ejpam-4461	132	4	only	only	ADV
ejpam-4461	132	5	if	if	SCONJ
ejpam-4461	132	6	g	g	PROPN
ejpam-4461	132	7	=	=	SYM
ejpam-4461	132	8	k2	k2	PROPN
ejpam-4461	132	9	.	.	PUNCT
ejpam-4461	133	1	proof	proof	NOUN
ejpam-4461	133	2	.	.	PUNCT
ejpam-4461	134	1	statement	statement	NOUN
ejpam-4461	134	2	(	(	PUNCT
ejpam-4461	134	3	i	i	NOUN
ejpam-4461	134	4	)	)	PUNCT
ejpam-4461	134	5	is	be	AUX
ejpam-4461	134	6	clear	clear	ADJ
ejpam-4461	134	7	.	.	PUNCT
ejpam-4461	135	1	by	by	ADP
ejpam-4461	135	2	proposition	proposition	NOUN
ejpam-4461	135	3	3	3	NUM
ejpam-4461	135	4	,	,	PUNCT
ejpam-4461	135	5	if	if	SCONJ
ejpam-4461	135	6	n	n	NOUN
ejpam-4461	135	7	=	=	SYM
ejpam-4461	135	8	2	2	NUM
ejpam-4461	135	9	,	,	PUNCT
ejpam-4461	135	10	then	then	ADV
ejpam-4461	135	11	γ̃t2(kn	γ̃t2(kn	PROPN
ejpam-4461	135	12	)	)	PUNCT
ejpam-4461	136	1	=	=	SYM
ejpam-4461	136	2	2	2	NUM
ejpam-4461	136	3	=	=	SYM
ejpam-4461	136	4	n.	n.	NOUN
ejpam-4461	136	5	assume	assume	VERB
ejpam-4461	136	6	that	that	SCONJ
ejpam-4461	136	7	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	136	8	)	)	PUNCT
ejpam-4461	136	9	=	=	SYM
ejpam-4461	136	10	n.	n.	NOUN
ejpam-4461	136	11	suppose	suppose	VERB
ejpam-4461	136	12	that	that	SCONJ
ejpam-4461	136	13	n	n	PROPN
ejpam-4461	136	14	≥	≥	NUM
ejpam-4461	136	15	3	3	NUM
ejpam-4461	136	16	.	.	PUNCT
ejpam-4461	136	17	by	by	ADP
ejpam-4461	136	18	proposition	proposition	NOUN
ejpam-4461	136	19	3	3	NUM
ejpam-4461	136	20	,	,	PUNCT
ejpam-4461	136	21	g	g	PROPN
ejpam-4461	136	22	̸=	̸=	PROPN
ejpam-4461	136	23	kn	kn	PROPN
ejpam-4461	136	24	.	.	PUNCT
ejpam-4461	137	1	let	let	VERB
ejpam-4461	137	2	[	[	X
ejpam-4461	137	3	u	u	NOUN
ejpam-4461	137	4	,	,	PUNCT
ejpam-4461	137	5	v	v	ADP
ejpam-4461	137	6	,	,	PUNCT
ejpam-4461	137	7	z	z	X
ejpam-4461	137	8	]	]	X
ejpam-4461	137	9	be	be	AUX
ejpam-4461	137	10	a	a	DET
ejpam-4461	137	11	geodesic	geodesic	NOUN
ejpam-4461	137	12	in	in	ADP
ejpam-4461	137	13	g.	g.	PROPN
ejpam-4461	137	14	put	put	VERB
ejpam-4461	137	15	s	s	PART
ejpam-4461	137	16	=	=	X
ejpam-4461	137	17	v	v	ADJ
ejpam-4461	137	18	(	(	PUNCT
ejpam-4461	137	19	g	g	NOUN
ejpam-4461	137	20	)	)	PUNCT
ejpam-4461	137	21	\	\	NOUN
ejpam-4461	137	22	{	{	PUNCT
ejpam-4461	137	23	v	v	NOUN
ejpam-4461	137	24	}	}	PUNCT
ejpam-4461	137	25	.	.	PUNCT
ejpam-4461	138	1	then	then	ADV
ejpam-4461	138	2	s	s	VERB
ejpam-4461	138	3	is	be	AUX
ejpam-4461	138	4	a	a	DET
ejpam-4461	138	5	semitotal	semitotal	ADJ
ejpam-4461	138	6	dominating	dominating	NOUN
ejpam-4461	138	7	set	set	VERB
ejpam-4461	138	8	with	with	ADP
ejpam-4461	138	9	v	v	PROPN
ejpam-4461	138	10	(	(	PUNCT
ejpam-4461	138	11	g	g	NOUN
ejpam-4461	138	12	)	)	PUNCT
ejpam-4461	138	13	\	\	PART
ejpam-4461	139	1	s	s	PART
ejpam-4461	139	2	=	=	SYM
ejpam-4461	139	3	{	{	PUNCT
ejpam-4461	139	4	v	v	NOUN
ejpam-4461	139	5	}	}	PUNCT
ejpam-4461	139	6	.	.	PUNCT
ejpam-4461	140	1	thus	thus	ADV
ejpam-4461	140	2	s	s	X
ejpam-4461	140	3	is	be	AUX
ejpam-4461	140	4	an	an	DET
ejpam-4461	140	5	outer	outer	ADV
ejpam-4461	140	6	-	-	PUNCT
ejpam-4461	140	7	connected	connect	VERB
ejpam-4461	140	8	semitotal	semitotal	ADJ
ejpam-4461	140	9	dominating	dominating	NOUN
ejpam-4461	140	10	set	set	NOUN
ejpam-4461	140	11	of	of	ADP
ejpam-4461	140	12	g.	g.	PROPN
ejpam-4461	140	13	consequently	consequently	ADV
ejpam-4461	140	14	,	,	PUNCT
ejpam-4461	140	15	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	140	16	)	)	PUNCT
ejpam-4461	140	17	≤	≤	NUM
ejpam-4461	140	18	n−	n−	NOUN
ejpam-4461	140	19	1	1	NUM
ejpam-4461	140	20	,	,	PUNCT
ejpam-4461	140	21	a	a	DET
ejpam-4461	140	22	contradiction	contradiction	NOUN
ejpam-4461	140	23	.	.	PUNCT
ejpam-4461	141	1	therefore	therefore	ADV
ejpam-4461	141	2	,	,	PUNCT
ejpam-4461	141	3	n	n	PROPN
ejpam-4461	141	4	=	=	SYM
ejpam-4461	141	5	2	2	X
ejpam-4461	141	6	.	.	PUNCT
ejpam-4461	142	1	this	this	PRON
ejpam-4461	142	2	proves	prove	VERB
ejpam-4461	142	3	(	(	PUNCT
ejpam-4461	142	4	ii	ii	NOUN
ejpam-4461	142	5	)	)	PUNCT
ejpam-4461	142	6	.	.	PUNCT
ejpam-4461	143	1	proposition	proposition	NOUN
ejpam-4461	143	2	5	5	NUM
ejpam-4461	143	3	.	.	PUNCT
ejpam-4461	144	1	let	let	VERB
ejpam-4461	144	2	g	g	NOUN
ejpam-4461	144	3	be	be	AUX
ejpam-4461	144	4	any	any	DET
ejpam-4461	144	5	graph	graph	NOUN
ejpam-4461	144	6	with	with	ADP
ejpam-4461	144	7	nontrivial	nontrivial	ADJ
ejpam-4461	144	8	components	component	NOUN
ejpam-4461	144	9	c1	c1	PROPN
ejpam-4461	144	10	,	,	PUNCT
ejpam-4461	144	11	c2	c2	PROPN
ejpam-4461	144	12	,	,	PUNCT
ejpam-4461	144	13	.	.	PUNCT
ejpam-4461	144	14	.	.	PUNCT
ejpam-4461	145	1	.	.	PUNCT
ejpam-4461	146	1	,	,	PUNCT
ejpam-4461	146	2	ck	ck	PROPN
ejpam-4461	146	3	of	of	ADP
ejpam-4461	146	4	orders	order	NOUN
ejpam-4461	146	5	n1	n1	NOUN
ejpam-4461	146	6	,	,	PUNCT
ejpam-4461	146	7	n2	n2	NOUN
ejpam-4461	146	8	,	,	PUNCT
ejpam-4461	146	9	.	.	PUNCT
ejpam-4461	146	10	.	.	PUNCT
ejpam-4461	147	1	.	.	PUNCT
ejpam-4461	147	2	,	,	PUNCT
ejpam-4461	147	3	nk	nk	PROPN
ejpam-4461	147	4	,	,	PUNCT
ejpam-4461	147	5	respectively	respectively	ADV
ejpam-4461	147	6	.	.	PUNCT
ejpam-4461	148	1	then	then	ADV
ejpam-4461	148	2	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	148	3	)	)	PUNCT
ejpam-4461	148	4	=	=	SYM
ejpam-4461	148	5	min{γ̃t2(cj	min{γ̃t2(cj	X
ejpam-4461	148	6	)	)	PUNCT
ejpam-4461	148	7	+	+	CCONJ
ejpam-4461	148	8	k∑	k∑	ADJ
ejpam-4461	148	9	i=1,i	i=1,i	ADP
ejpam-4461	148	10	̸=j	̸=j	PROPN
ejpam-4461	148	11	ni	ni	PROPN
ejpam-4461	148	12	:	:	PUNCT
ejpam-4461	148	13	j	j	PROPN
ejpam-4461	148	14	=	=	SYM
ejpam-4461	148	15	1	1	NUM
ejpam-4461	148	16	,	,	PUNCT
ejpam-4461	148	17	2	2	NUM
ejpam-4461	148	18	,	,	PUNCT
ejpam-4461	148	19	.	.	PUNCT
ejpam-4461	148	20	.	.	PUNCT
ejpam-4461	148	21	.	.	PUNCT
ejpam-4461	149	1	,	,	PUNCT
ejpam-4461	149	2	k	k	X
ejpam-4461	149	3	}	}	PUNCT
ejpam-4461	149	4	.	.	PUNCT
ejpam-4461	150	1	proof	proof	NOUN
ejpam-4461	150	2	.	.	PUNCT
ejpam-4461	151	1	put	put	VERB
ejpam-4461	151	2	α	α	NOUN
ejpam-4461	151	3	=	=	SYM
ejpam-4461	151	4	min{γ̃t2(cj	min{γ̃t2(cj	X
ejpam-4461	151	5	)	)	PUNCT
ejpam-4461	152	1	+	+	CCONJ
ejpam-4461	152	2	∑k	∑k	PROPN
ejpam-4461	152	3	i=1,i	i=1,i	ADP
ejpam-4461	152	4	̸=j	̸=j	PROPN
ejpam-4461	152	5	ni	ni	PROPN
ejpam-4461	152	6	:	:	PUNCT
ejpam-4461	152	7	j	j	PROPN
ejpam-4461	152	8	=	=	SYM
ejpam-4461	152	9	1	1	NUM
ejpam-4461	152	10	,	,	PUNCT
ejpam-4461	152	11	2	2	NUM
ejpam-4461	152	12	,	,	PUNCT
ejpam-4461	152	13	.	.	PUNCT
ejpam-4461	152	14	.	.	PUNCT
ejpam-4461	152	15	.	.	PUNCT
ejpam-4461	153	1	,	,	PUNCT
ejpam-4461	153	2	k	k	X
ejpam-4461	153	3	}	}	PUNCT
ejpam-4461	153	4	.	.	PUNCT
ejpam-4461	154	1	let	let	VERB
ejpam-4461	154	2	j	j	PROPN
ejpam-4461	154	3	∈	∈	PROPN
ejpam-4461	154	4	{	{	PUNCT
ejpam-4461	154	5	1	1	NUM
ejpam-4461	154	6	,	,	PUNCT
ejpam-4461	154	7	2	2	NUM
ejpam-4461	154	8	,	,	PUNCT
ejpam-4461	154	9	.	.	PUNCT
ejpam-4461	154	10	.	.	PUNCT
ejpam-4461	155	1	.	.	PUNCT
ejpam-4461	156	1	,	,	PUNCT
ejpam-4461	156	2	k	k	X
ejpam-4461	156	3	}	}	PUNCT
ejpam-4461	156	4	,	,	PUNCT
ejpam-4461	156	5	and	and	CCONJ
ejpam-4461	156	6	choose	choose	VERB
ejpam-4461	156	7	a	a	DET
ejpam-4461	156	8	γ̃t2	γ̃t2	PROPN
ejpam-4461	156	9	-	-	PUNCT
ejpam-4461	156	10	set	set	VERB
ejpam-4461	156	11	sj	sj	NOUN
ejpam-4461	156	12	of	of	ADP
ejpam-4461	156	13	cj	cj	NOUN
ejpam-4461	156	14	.	.	PUNCT
ejpam-4461	157	1	since	since	SCONJ
ejpam-4461	157	2	s	s	PART
ejpam-4461	157	3	=	=	PUNCT
ejpam-4461	157	4	(	(	PUNCT
ejpam-4461	157	5	∪k	∪k	X
ejpam-4461	157	6	i=1;i	i=1;i	PROPN
ejpam-4461	157	7	̸=jv	̸=jv	NOUN
ejpam-4461	157	8	(	(	PUNCT
ejpam-4461	157	9	ci	ci	NOUN
ejpam-4461	157	10	)	)	PUNCT
ejpam-4461	157	11	)	)	PUNCT
ejpam-4461	157	12	∪	∪	ADP
ejpam-4461	157	13	sj	sj	X
ejpam-4461	157	14	is	be	AUX
ejpam-4461	157	15	an	an	DET
ejpam-4461	157	16	outer	outer	ADV
ejpam-4461	157	17	-	-	PUNCT
ejpam-4461	157	18	connected	connect	VERB
ejpam-4461	157	19	semitotal	semitotal	ADJ
ejpam-4461	157	20	dominating	dominating	NOUN
ejpam-4461	157	21	set	set	NOUN
ejpam-4461	157	22	of	of	ADP
ejpam-4461	157	23	g	g	PROPN
ejpam-4461	157	24	,	,	PUNCT
ejpam-4461	157	25	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	157	26	)	)	PUNCT
ejpam-4461	157	27	≤	≤	NUM
ejpam-4461	157	28	|s|	|s|	PROPN
ejpam-4461	157	29	=	=	PUNCT
ejpam-4461	157	30	γ̃t2(cj	γ̃t2(cj	PROPN
ejpam-4461	157	31	)	)	PUNCT
ejpam-4461	158	1	+	+	CCONJ
ejpam-4461	159	1	∑k	∑k	PROPN
ejpam-4461	159	2	i=1,i	i=1,i	ADP
ejpam-4461	159	3	̸=j	̸=j	PROPN
ejpam-4461	159	4	ni	ni	PROPN
ejpam-4461	159	5	.	.	PROPN
ejpam-4461	160	1	since	since	SCONJ
ejpam-4461	160	2	j	j	PROPN
ejpam-4461	160	3	is	be	AUX
ejpam-4461	160	4	arbitrary	arbitrary	ADJ
ejpam-4461	160	5	,	,	PUNCT
ejpam-4461	160	6	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	160	7	)	)	PUNCT
ejpam-4461	160	8	≤	≤	NOUN
ejpam-4461	161	1	α	α	X
ejpam-4461	161	2	.	.	PUNCT
ejpam-4461	162	1	let	let	VERB
ejpam-4461	162	2	s	s	PRON
ejpam-4461	162	3	⊆	⊆	NUM
ejpam-4461	162	4	v	v	NOUN
ejpam-4461	162	5	(	(	PUNCT
ejpam-4461	162	6	g	g	NOUN
ejpam-4461	162	7	)	)	PUNCT
ejpam-4461	162	8	be	be	AUX
ejpam-4461	162	9	an	an	DET
ejpam-4461	162	10	outer	outer	ADV
ejpam-4461	162	11	-	-	PUNCT
ejpam-4461	162	12	connected	connect	VERB
ejpam-4461	162	13	semitotal	semitotal	ADJ
ejpam-4461	162	14	dominating	dominating	NOUN
ejpam-4461	162	15	set	set	NOUN
ejpam-4461	162	16	of	of	ADP
ejpam-4461	162	17	g.	g.	PROPN
ejpam-4461	162	18	since	since	SCONJ
ejpam-4461	162	19	s	s	PROPN
ejpam-4461	162	20	is	be	AUX
ejpam-4461	162	21	a	a	DET
ejpam-4461	162	22	semitotal	semitotal	ADJ
ejpam-4461	162	23	dominating	dominating	NOUN
ejpam-4461	162	24	set	set	NOUN
ejpam-4461	162	25	of	of	ADP
ejpam-4461	162	26	g	g	NOUN
ejpam-4461	162	27	,	,	PUNCT
ejpam-4461	162	28	sj	sj	X
ejpam-4461	162	29	=	=	NOUN
ejpam-4461	162	30	s	s	PROPN
ejpam-4461	162	31	∩	∩	ADJ
ejpam-4461	162	32	v	v	X
ejpam-4461	162	33	(	(	PUNCT
ejpam-4461	162	34	cj	cj	NOUN
ejpam-4461	162	35	)	)	PUNCT
ejpam-4461	162	36	is	be	AUX
ejpam-4461	162	37	a	a	DET
ejpam-4461	162	38	semitotal	semitotal	ADJ
ejpam-4461	162	39	dominating	dominating	NOUN
ejpam-4461	162	40	set	set	NOUN
ejpam-4461	162	41	of	of	ADP
ejpam-4461	162	42	cj	cj	NOUN
ejpam-4461	162	43	for	for	ADP
ejpam-4461	162	44	all	all	DET
ejpam-4461	162	45	j	j	NOUN
ejpam-4461	162	46	=	=	SYM
ejpam-4461	162	47	1	1	NUM
ejpam-4461	162	48	,	,	PUNCT
ejpam-4461	162	49	2	2	NUM
ejpam-4461	162	50	,	,	PUNCT
ejpam-4461	162	51	.	.	PUNCT
ejpam-4461	162	52	.	.	PUNCT
ejpam-4461	163	1	.	.	PUNCT
ejpam-4461	164	1	,	,	PUNCT
ejpam-4461	164	2	k.	k.	PROPN
ejpam-4461	165	1	first	first	ADV
ejpam-4461	165	2	,	,	PUNCT
ejpam-4461	165	3	we	we	PRON
ejpam-4461	165	4	claim	claim	VERB
ejpam-4461	165	5	that	that	SCONJ
ejpam-4461	165	6	there	there	PRON
ejpam-4461	165	7	exists	exist	VERB
ejpam-4461	165	8	j	j	PROPN
ejpam-4461	165	9	∈	∈	PROPN
ejpam-4461	165	10	{	{	PUNCT
ejpam-4461	165	11	1	1	NUM
ejpam-4461	165	12	,	,	PUNCT
ejpam-4461	165	13	2	2	NUM
ejpam-4461	165	14	,	,	PUNCT
ejpam-4461	165	15	.	.	PUNCT
ejpam-4461	165	16	.	.	PUNCT
ejpam-4461	165	17	.	.	PUNCT
ejpam-4461	166	1	,	,	PUNCT
ejpam-4461	166	2	k	k	X
ejpam-4461	166	3	}	}	PUNCT
ejpam-4461	166	4	for	for	ADP
ejpam-4461	166	5	which	which	PRON
ejpam-4461	166	6	si	si	NOUN
ejpam-4461	166	7	=	=	SYM
ejpam-4461	166	8	v	v	PROPN
ejpam-4461	166	9	(	(	PUNCT
ejpam-4461	166	10	ci	ci	NOUN
ejpam-4461	166	11	)	)	PUNCT
ejpam-4461	166	12	for	for	ADP
ejpam-4461	166	13	all	all	PRON
ejpam-4461	166	14	i	i	PRON
ejpam-4461	166	15	except	except	SCONJ
ejpam-4461	166	16	possibly	possibly	ADV
ejpam-4461	166	17	when	when	SCONJ
ejpam-4461	166	18	i	i	PRON
ejpam-4461	166	19	=	=	PUNCT
ejpam-4461	166	20	j.	j.	PROPN
ejpam-4461	166	21	suppose	suppose	VERB
ejpam-4461	166	22	that	that	SCONJ
ejpam-4461	166	23	,	,	PUNCT
ejpam-4461	166	24	to	to	ADP
ejpam-4461	166	25	the	the	DET
ejpam-4461	166	26	contrary	contrary	NOUN
ejpam-4461	166	27	,	,	PUNCT
ejpam-4461	166	28	there	there	PRON
ejpam-4461	166	29	exist	exist	VERB
ejpam-4461	166	30	distinct	distinct	ADJ
ejpam-4461	166	31	i	i	PRON
ejpam-4461	166	32	,	,	PUNCT
ejpam-4461	166	33	j	j	PROPN
ejpam-4461	166	34	∈	∈	PROPN
ejpam-4461	166	35	{	{	PUNCT
ejpam-4461	166	36	1	1	NUM
ejpam-4461	166	37	,	,	PUNCT
ejpam-4461	166	38	2	2	NUM
ejpam-4461	166	39	,	,	PUNCT
ejpam-4461	166	40	.	.	PUNCT
ejpam-4461	166	41	.	.	PUNCT
ejpam-4461	167	1	.	.	PUNCT
ejpam-4461	168	1	,	,	PUNCT
ejpam-4461	168	2	k	k	X
ejpam-4461	168	3	}	}	PUNCT
ejpam-4461	168	4	such	such	ADJ
ejpam-4461	168	5	that	that	SCONJ
ejpam-4461	168	6	si	si	PROPN
ejpam-4461	168	7	̸=	̸=	PROPN
ejpam-4461	168	8	v	v	PROPN
ejpam-4461	168	9	(	(	PUNCT
ejpam-4461	168	10	ci	ci	NOUN
ejpam-4461	168	11	)	)	PUNCT
ejpam-4461	168	12	and	and	CCONJ
ejpam-4461	168	13	sj	sj	INTJ
ejpam-4461	168	14	̸=	̸=	PROPN
ejpam-4461	168	15	v	v	PROPN
ejpam-4461	168	16	(	(	PUNCT
ejpam-4461	168	17	cj	cj	NOUN
ejpam-4461	168	18	)	)	PUNCT
ejpam-4461	168	19	.	.	PUNCT
ejpam-4461	169	1	pick	pick	VERB
ejpam-4461	169	2	u	u	PRON
ejpam-4461	169	3	∈	∈	PROPN
ejpam-4461	169	4	v	v	ADP
ejpam-4461	169	5	(	(	PUNCT
ejpam-4461	169	6	ci	ci	NOUN
ejpam-4461	169	7	)	)	PUNCT
ejpam-4461	169	8	\	\	NOUN
ejpam-4461	170	1	si	si	NOUN
ejpam-4461	171	1	and	and	CCONJ
ejpam-4461	171	2	v	v	ADP
ejpam-4461	171	3	∈	∈	PROPN
ejpam-4461	171	4	v	v	NOUN
ejpam-4461	171	5	(	(	PUNCT
ejpam-4461	171	6	cj	cj	NOUN
ejpam-4461	171	7	)	)	PUNCT
ejpam-4461	171	8	\	\	PROPN
ejpam-4461	172	1	sj	sj	INTJ
ejpam-4461	172	2	.	.	PUNCT
ejpam-4461	173	1	observe	observe	VERB
ejpam-4461	173	2	that	that	PRON
ejpam-4461	173	3	⟨v	⟨v	NOUN
ejpam-4461	173	4	(	(	PUNCT
ejpam-4461	173	5	g	g	NOUN
ejpam-4461	173	6	)	)	PUNCT
ejpam-4461	173	7	\	\	NOUN
ejpam-4461	173	8	s⟩	s⟩	NOUN
ejpam-4461	173	9	does	do	AUX
ejpam-4461	173	10	not	not	PART
ejpam-4461	173	11	have	have	VERB
ejpam-4461	173	12	a	a	DET
ejpam-4461	173	13	path	path	NOUN
ejpam-4461	173	14	joining	join	VERB
ejpam-4461	173	15	u	u	NOUN
ejpam-4461	173	16	and	and	CCONJ
ejpam-4461	173	17	v	v	NOUN
ejpam-4461	173	18	,	,	PUNCT
ejpam-4461	173	19	a	a	DET
ejpam-4461	173	20	contradiction	contradiction	NOUN
ejpam-4461	173	21	and	and	CCONJ
ejpam-4461	173	22	thus	thus	ADV
ejpam-4461	173	23	,	,	PUNCT
ejpam-4461	173	24	the	the	DET
ejpam-4461	173	25	claim	claim	NOUN
ejpam-4461	173	26	is	be	AUX
ejpam-4461	173	27	established	establish	VERB
ejpam-4461	173	28	.	.	PUNCT
ejpam-4461	174	1	this	this	PRON
ejpam-4461	174	2	means	mean	VERB
ejpam-4461	174	3	that	that	SCONJ
ejpam-4461	174	4	,	,	PUNCT
ejpam-4461	174	5	s	s	VERB
ejpam-4461	174	6	=	=	PUNCT
ejpam-4461	174	7	sj	sj	X
ejpam-4461	174	8	∪	∪	NOUN
ejpam-4461	174	9	(	(	PUNCT
ejpam-4461	174	10	∪k	∪k	X
ejpam-4461	174	11	i=1,i	i=1,i	ADP
ejpam-4461	174	12	̸=jv	̸=jv	NOUN
ejpam-4461	174	13	(	(	PUNCT
ejpam-4461	174	14	ci	ci	NOUN
ejpam-4461	174	15	)	)	PUNCT
ejpam-4461	174	16	)	)	PUNCT
ejpam-4461	174	17	for	for	ADP
ejpam-4461	174	18	some	some	DET
ejpam-4461	174	19	j.	j.	PROPN
ejpam-4461	174	20	next	next	ADV
ejpam-4461	174	21	,	,	PUNCT
ejpam-4461	174	22	we	we	PRON
ejpam-4461	174	23	claim	claim	VERB
ejpam-4461	174	24	that	that	SCONJ
ejpam-4461	174	25	sj	sj	PROPN
ejpam-4461	174	26	is	be	AUX
ejpam-4461	174	27	an	an	DET
ejpam-4461	174	28	outer	outer	ADV
ejpam-4461	174	29	-	-	PUNCT
ejpam-4461	174	30	connected	connect	VERB
ejpam-4461	174	31	semitotal	semitotal	ADJ
ejpam-4461	174	32	dominating	dominating	NOUN
ejpam-4461	174	33	set	set	NOUN
ejpam-4461	174	34	of	of	ADP
ejpam-4461	174	35	cj	cj	NOUN
ejpam-4461	174	36	.	.	PUNCT
ejpam-4461	175	1	if	if	SCONJ
ejpam-4461	175	2	s	s	VERB
ejpam-4461	175	3	=	=	SYM
ejpam-4461	175	4	v	v	X
ejpam-4461	175	5	(	(	PUNCT
ejpam-4461	175	6	g	g	NOUN
ejpam-4461	175	7	)	)	PUNCT
ejpam-4461	175	8	,	,	PUNCT
ejpam-4461	175	9	then	then	ADV
ejpam-4461	175	10	sj	sj	INTJ
ejpam-4461	175	11	=	=	SYM
ejpam-4461	175	12	v	v	PROPN
ejpam-4461	175	13	(	(	PUNCT
ejpam-4461	175	14	cj	cj	NOUN
ejpam-4461	175	15	)	)	PUNCT
ejpam-4461	175	16	and	and	CCONJ
ejpam-4461	175	17	we	we	PRON
ejpam-4461	175	18	are	be	AUX
ejpam-4461	175	19	done	do	VERB
ejpam-4461	175	20	.	.	PUNCT
ejpam-4461	176	1	suppose	suppose	VERB
ejpam-4461	176	2	that	that	SCONJ
ejpam-4461	176	3	s	s	VERB
ejpam-4461	176	4	̸=	̸=	PROPN
ejpam-4461	176	5	v	v	NOUN
ejpam-4461	176	6	(	(	PUNCT
ejpam-4461	176	7	g	g	NOUN
ejpam-4461	176	8	)	)	PUNCT
ejpam-4461	176	9	.	.	PUNCT
ejpam-4461	177	1	since	since	SCONJ
ejpam-4461	177	2	sj	sj	PROPN
ejpam-4461	177	3	is	be	AUX
ejpam-4461	177	4	a	a	DET
ejpam-4461	177	5	semitotal	semitotal	ADJ
ejpam-4461	177	6	dominating	dominating	NOUN
ejpam-4461	177	7	set	set	NOUN
ejpam-4461	177	8	,	,	PUNCT
ejpam-4461	177	9	it	it	PRON
ejpam-4461	177	10	is	be	AUX
ejpam-4461	177	11	left	leave	VERB
ejpam-4461	177	12	to	to	PART
ejpam-4461	177	13	verify	verify	VERB
ejpam-4461	177	14	that	that	DET
ejpam-4461	177	15	⟨v	⟨v	NOUN
ejpam-4461	177	16	(	(	PUNCT
ejpam-4461	177	17	cj	cj	NOUN
ejpam-4461	177	18	)	)	PUNCT
ejpam-4461	177	19	\	\	NOUN
ejpam-4461	177	20	sj⟩	sj⟩	PROPN
ejpam-4461	177	21	is	be	AUX
ejpam-4461	177	22	connected	connect	VERB
ejpam-4461	177	23	.	.	PUNCT
ejpam-4461	178	1	but	but	CCONJ
ejpam-4461	178	2	since	since	SCONJ
ejpam-4461	178	3	v	v	NUM
ejpam-4461	178	4	(	(	PUNCT
ejpam-4461	178	5	cj	cj	NOUN
ejpam-4461	178	6	)	)	PUNCT
ejpam-4461	178	7	\	\	NOUN
ejpam-4461	178	8	sj	sj	PROPN
ejpam-4461	178	9	=	=	SYM
ejpam-4461	178	10	v	v	PROPN
ejpam-4461	178	11	(	(	PUNCT
ejpam-4461	178	12	g	g	NOUN
ejpam-4461	178	13	)	)	PUNCT
ejpam-4461	178	14	\	\	PROPN
ejpam-4461	179	1	s	s	X
ejpam-4461	179	2	,	,	PUNCT
ejpam-4461	179	3	the	the	DET
ejpam-4461	179	4	conclusion	conclusion	NOUN
ejpam-4461	179	5	follows	follow	VERB
ejpam-4461	179	6	.	.	PUNCT
ejpam-4461	180	1	thus	thus	ADV
ejpam-4461	180	2	,	,	PUNCT
ejpam-4461	180	3	|s|	|s|	VERB
ejpam-4461	180	4	=	=	SYM
ejpam-4461	180	5	|sj	|sj	PROPN
ejpam-4461	180	6	|+	|+	X
ejpam-4461	180	7	k∑	k∑	ADJ
ejpam-4461	180	8	i=1,i	i=1,i	ADP
ejpam-4461	180	9	̸=j	̸=j	PROPN
ejpam-4461	180	10	ni	ni	PROPN
ejpam-4461	180	11	≥	≥	NOUN
ejpam-4461	180	12	γ̃t2(cj	γ̃t2(cj	PROPN
ejpam-4461	180	13	)	)	PUNCT
ejpam-4461	181	1	+	+	CCONJ
ejpam-4461	181	2	k∑	k∑	VERB
ejpam-4461	181	3	i=1,i	i=1,i	ADP
ejpam-4461	181	4	̸=j	̸=j	PROPN
ejpam-4461	181	5	ni	ni	PROPN
ejpam-4461	181	6	≥	≥	PROPN
ejpam-4461	181	7	α	α	NOUN
ejpam-4461	181	8	.	.	PUNCT
ejpam-4461	182	1	since	since	SCONJ
ejpam-4461	182	2	s	s	NOUN
ejpam-4461	182	3	is	be	AUX
ejpam-4461	182	4	arbitrary	arbitrary	ADJ
ejpam-4461	182	5	,	,	PUNCT
ejpam-4461	182	6	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	182	7	)	)	PUNCT
ejpam-4461	182	8	≥	≥	NUM
ejpam-4461	183	1	α	α	NOUN
ejpam-4461	183	2	.	.	PUNCT
ejpam-4461	183	3	proposition	proposition	NOUN
ejpam-4461	183	4	6	6	NUM
ejpam-4461	183	5	.	.	PUNCT
ejpam-4461	184	1	let	let	VERB
ejpam-4461	184	2	g	g	PRON
ejpam-4461	184	3	be	be	AUX
ejpam-4461	184	4	a	a	DET
ejpam-4461	184	5	nontrivial	nontrivial	ADJ
ejpam-4461	184	6	graph	graph	NOUN
ejpam-4461	184	7	.	.	PUNCT
ejpam-4461	185	1	(	(	PUNCT
ejpam-4461	185	2	i	i	NOUN
ejpam-4461	185	3	)	)	PUNCT
ejpam-4461	185	4	if	if	SCONJ
ejpam-4461	185	5	g	g	PROPN
ejpam-4461	185	6	is	be	AUX
ejpam-4461	185	7	connected	connect	VERB
ejpam-4461	185	8	,	,	PUNCT
ejpam-4461	185	9	then	then	ADV
ejpam-4461	185	10	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	185	11	)	)	PUNCT
ejpam-4461	186	1	=	=	SYM
ejpam-4461	187	1	2	2	X
ejpam-4461	187	2	.	.	PUNCT
ejpam-4461	187	3	(	(	PUNCT
ejpam-4461	187	4	ii	ii	NOUN
ejpam-4461	187	5	)	)	PUNCT
ejpam-4461	187	6	if	if	SCONJ
ejpam-4461	187	7	g	g	PROPN
ejpam-4461	187	8	is	be	AUX
ejpam-4461	187	9	disconnected	disconnect	VERB
ejpam-4461	187	10	with	with	ADP
ejpam-4461	187	11	components	component	NOUN
ejpam-4461	187	12	c1	c1	PROPN
ejpam-4461	187	13	,	,	PUNCT
ejpam-4461	187	14	c2	c2	PROPN
ejpam-4461	187	15	,	,	PUNCT
ejpam-4461	187	16	.	.	PUNCT
ejpam-4461	187	17	.	.	PUNCT
ejpam-4461	188	1	.	.	PUNCT
ejpam-4461	189	1	,	,	PUNCT
ejpam-4461	189	2	ck	ck	PROPN
ejpam-4461	189	3	of	of	ADP
ejpam-4461	189	4	orders	order	NOUN
ejpam-4461	189	5	n1	n1	NOUN
ejpam-4461	189	6	,	,	PUNCT
ejpam-4461	189	7	n2	n2	NOUN
ejpam-4461	189	8	,	,	PUNCT
ejpam-4461	189	9	.	.	PUNCT
ejpam-4461	189	10	.	.	PUNCT
ejpam-4461	190	1	.	.	PUNCT
ejpam-4461	190	2	,	,	PUNCT
ejpam-4461	190	3	nk	nk	PROPN
ejpam-4461	190	4	,	,	PUNCT
ejpam-4461	190	5	a.	a.	PROPN
ejpam-4461	190	6	aradais	aradais	PROPN
ejpam-4461	190	7	,	,	PUNCT
ejpam-4461	190	8	f.	f.	PROPN
ejpam-4461	190	9	jamil	jamil	PROPN
ejpam-4461	190	10	/	/	SYM
ejpam-4461	190	11	eur	eur	PROPN
ejpam-4461	190	12	.	.	PUNCT
ejpam-4461	191	1	j.	j.	PROPN
ejpam-4461	191	2	pure	pure	PROPN
ejpam-4461	191	3	appl	appl	PROPN
ejpam-4461	191	4	.	.	PROPN
ejpam-4461	191	5	math	math	PROPN
ejpam-4461	191	6	,	,	PUNCT
ejpam-4461	191	7	15	15	NUM
ejpam-4461	191	8	(	(	PUNCT
ejpam-4461	191	9	3	3	NUM
ejpam-4461	191	10	)	)	PUNCT
ejpam-4461	191	11	(	(	PUNCT
ejpam-4461	191	12	2022	2022	NUM
ejpam-4461	191	13	)	)	PUNCT
ejpam-4461	191	14	,	,	PUNCT
ejpam-4461	191	15	1265	1265	NUM
ejpam-4461	191	16	-	-	SYM
ejpam-4461	191	17	1279	1279	NUM
ejpam-4461	191	18	1270	1270	NUM
ejpam-4461	191	19	respectively	respectively	ADV
ejpam-4461	191	20	,	,	PUNCT
ejpam-4461	191	21	satisfying	satisfy	VERB
ejpam-4461	191	22	that	that	SCONJ
ejpam-4461	191	23	n1	n1	PROPN
ejpam-4461	191	24	≤	≤	NOUN
ejpam-4461	191	25	n2	n2	NOUN
ejpam-4461	191	26	≤	≤	NOUN
ejpam-4461	191	27	·	·	PUNCT
ejpam-4461	191	28	·	·	PUNCT
ejpam-4461	191	29	·	·	PUNCT
ejpam-4461	192	1	≤	≤	NUM
ejpam-4461	192	2	nk	nk	PROPN
ejpam-4461	192	3	,	,	PUNCT
ejpam-4461	192	4	then	then	ADV
ejpam-4461	192	5	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	192	6	)	)	PUNCT
ejpam-4461	192	7	=	=	SYM
ejpam-4461	192	8	min	min	PROPN
ejpam-4461	192	9	{	{	PUNCT
ejpam-4461	192	10	k∑	k∑	NOUN
ejpam-4461	192	11	j=1	j=1	PROPN
ejpam-4461	192	12	γ(cj	γ(cj	PROPN
ejpam-4461	192	13	)	)	PUNCT
ejpam-4461	192	14	,	,	PUNCT
ejpam-4461	192	15	2	2	NUM
ejpam-4461	192	16	+	+	CCONJ
ejpam-4461	192	17	k−1∑	k−1∑	PROPN
ejpam-4461	192	18	j=1	j=1	PROPN
ejpam-4461	192	19	nj	nj	PROPN
ejpam-4461	192	20	}	}	PUNCT
ejpam-4461	192	21	.	.	PUNCT
ejpam-4461	193	1	proof	proof	NOUN
ejpam-4461	193	2	.	.	PUNCT
ejpam-4461	194	1	put	put	VERB
ejpam-4461	194	2	v	v	NOUN
ejpam-4461	194	3	(	(	PUNCT
ejpam-4461	194	4	k1	k1	NOUN
ejpam-4461	194	5	)	)	PUNCT
ejpam-4461	194	6	=	=	SYM
ejpam-4461	194	7	{	{	PUNCT
ejpam-4461	194	8	u	u	NOUN
ejpam-4461	194	9	}	}	PUNCT
ejpam-4461	194	10	.	.	PUNCT
ejpam-4461	195	1	to	to	PART
ejpam-4461	195	2	prove	prove	VERB
ejpam-4461	195	3	(	(	PUNCT
ejpam-4461	195	4	i	i	NOUN
ejpam-4461	195	5	)	)	PUNCT
ejpam-4461	195	6	,	,	PUNCT
ejpam-4461	195	7	suppose	suppose	VERB
ejpam-4461	195	8	that	that	SCONJ
ejpam-4461	195	9	g	g	PROPN
ejpam-4461	195	10	is	be	AUX
ejpam-4461	195	11	connected	connect	VERB
ejpam-4461	195	12	.	.	PUNCT
ejpam-4461	196	1	since	since	SCONJ
ejpam-4461	196	2	g	g	PROPN
ejpam-4461	196	3	is	be	AUX
ejpam-4461	196	4	nontrivial	nontrivial	ADJ
ejpam-4461	196	5	,	,	PUNCT
ejpam-4461	196	6	g	g	PROPN
ejpam-4461	196	7	contains	contain	VERB
ejpam-4461	196	8	at	at	ADP
ejpam-4461	196	9	least	least	ADV
ejpam-4461	196	10	two	two	NUM
ejpam-4461	196	11	vertices	vertex	NOUN
ejpam-4461	196	12	which	which	PRON
ejpam-4461	196	13	are	be	AUX
ejpam-4461	196	14	not	not	PART
ejpam-4461	196	15	cutvertices	cutvertice	NOUN
ejpam-4461	196	16	.	.	PUNCT
ejpam-4461	197	1	pick	pick	VERB
ejpam-4461	197	2	a	a	DET
ejpam-4461	197	3	non	non	ADJ
ejpam-4461	197	4	-	-	NOUN
ejpam-4461	197	5	cutvertex	cutvertex	ADJ
ejpam-4461	197	6	v	v	NOUN
ejpam-4461	197	7	of	of	ADP
ejpam-4461	197	8	g.	g.	PROPN
ejpam-4461	197	9	then	then	ADV
ejpam-4461	197	10	s	s	VERB
ejpam-4461	197	11	=	=	SYM
ejpam-4461	197	12	{	{	PUNCT
ejpam-4461	197	13	u	u	NOUN
ejpam-4461	197	14	,	,	PUNCT
ejpam-4461	197	15	v	v	NOUN
ejpam-4461	197	16	}	}	PUNCT
ejpam-4461	197	17	is	be	AUX
ejpam-4461	197	18	an	an	DET
ejpam-4461	197	19	outer	outer	ADV
ejpam-4461	197	20	-	-	PUNCT
ejpam-4461	197	21	connected	connect	VERB
ejpam-4461	197	22	semitotal	semitotal	ADJ
ejpam-4461	197	23	dominating	dominating	NOUN
ejpam-4461	197	24	set	set	NOUN
ejpam-4461	197	25	of	of	ADP
ejpam-4461	197	26	g	g	PROPN
ejpam-4461	197	27	+	+	NOUN
ejpam-4461	197	28	k1	k1	NOUN
ejpam-4461	197	29	.	.	PUNCT
ejpam-4461	198	1	by	by	ADP
ejpam-4461	198	2	equation	equation	NOUN
ejpam-4461	198	3	1	1	NUM
ejpam-4461	198	4	,	,	PUNCT
ejpam-4461	198	5	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	198	6	)	)	PUNCT
ejpam-4461	198	7	=	=	SYM
ejpam-4461	198	8	2	2	X
ejpam-4461	198	9	.	.	PUNCT
ejpam-4461	198	10	to	to	PART
ejpam-4461	198	11	prove	prove	VERB
ejpam-4461	198	12	(	(	PUNCT
ejpam-4461	198	13	ii	ii	NOUN
ejpam-4461	198	14	)	)	PUNCT
ejpam-4461	198	15	,	,	PUNCT
ejpam-4461	198	16	suppose	suppose	VERB
ejpam-4461	198	17	that	that	SCONJ
ejpam-4461	198	18	g	g	PROPN
ejpam-4461	198	19	is	be	AUX
ejpam-4461	198	20	disconnected	disconnect	VERB
ejpam-4461	198	21	with	with	ADP
ejpam-4461	198	22	components	component	NOUN
ejpam-4461	198	23	c1	c1	PROPN
ejpam-4461	198	24	,	,	PUNCT
ejpam-4461	198	25	c2	c2	PROPN
ejpam-4461	198	26	,	,	PUNCT
ejpam-4461	198	27	.	.	PUNCT
ejpam-4461	198	28	.	.	PUNCT
ejpam-4461	199	1	.	.	PUNCT
ejpam-4461	200	1	,	,	PUNCT
ejpam-4461	200	2	ck	ck	PROPN
ejpam-4461	200	3	of	of	ADP
ejpam-4461	200	4	orders	order	NOUN
ejpam-4461	200	5	n1	n1	NOUN
ejpam-4461	200	6	,	,	PUNCT
ejpam-4461	200	7	n2	n2	NOUN
ejpam-4461	200	8	,	,	PUNCT
ejpam-4461	200	9	.	.	PUNCT
ejpam-4461	200	10	.	.	PUNCT
ejpam-4461	201	1	.	.	PUNCT
ejpam-4461	201	2	,	,	PUNCT
ejpam-4461	201	3	nk	nk	PROPN
ejpam-4461	201	4	,	,	PUNCT
ejpam-4461	201	5	respectively	respectively	ADV
ejpam-4461	201	6	,	,	PUNCT
ejpam-4461	201	7	and	and	CCONJ
ejpam-4461	201	8	satisfying	satisfy	VERB
ejpam-4461	201	9	that	that	SCONJ
ejpam-4461	201	10	n1	n1	PROPN
ejpam-4461	201	11	≤	≤	NOUN
ejpam-4461	201	12	n2	n2	NOUN
ejpam-4461	201	13	≤	≤	NOUN
ejpam-4461	201	14	·	·	PUNCT
ejpam-4461	202	1	·	·	PUNCT
ejpam-4461	202	2	·	·	PUNCT
ejpam-4461	202	3	≤	≤	NUM
ejpam-4461	203	1	nk	nk	INTJ
ejpam-4461	203	2	.	.	PUNCT
ejpam-4461	204	1	if	if	SCONJ
ejpam-4461	204	2	nk	nk	PROPN
ejpam-4461	204	3	=	=	NOUN
ejpam-4461	204	4	1	1	NUM
ejpam-4461	204	5	,	,	PUNCT
ejpam-4461	204	6	then	then	ADV
ejpam-4461	204	7	g+k1	g+k1	NOUN
ejpam-4461	204	8	is	be	AUX
ejpam-4461	204	9	a	a	DET
ejpam-4461	204	10	star	star	NOUN
ejpam-4461	204	11	,	,	PUNCT
ejpam-4461	204	12	and	and	CCONJ
ejpam-4461	204	13	the	the	DET
ejpam-4461	204	14	result	result	NOUN
ejpam-4461	204	15	follows	follow	VERB
ejpam-4461	204	16	from	from	ADP
ejpam-4461	204	17	(	(	PUNCT
ejpam-4461	204	18	i	i	NOUN
ejpam-4461	204	19	)	)	PUNCT
ejpam-4461	204	20	.	.	PUNCT
ejpam-4461	205	1	it	it	PRON
ejpam-4461	205	2	is	be	AUX
ejpam-4461	205	3	worth	worth	ADJ
ejpam-4461	205	4	noting	note	VERB
ejpam-4461	205	5	that	that	SCONJ
ejpam-4461	205	6	in	in	ADP
ejpam-4461	205	7	this	this	DET
ejpam-4461	205	8	case	case	NOUN
ejpam-4461	205	9	,	,	PUNCT
ejpam-4461	205	10	k∑	k∑	VERB
ejpam-4461	205	11	j=1	j=1	PROPN
ejpam-4461	205	12	γ(cj	γ(cj	PROPN
ejpam-4461	205	13	)	)	PUNCT
ejpam-4461	205	14	=	=	SYM
ejpam-4461	206	1	k	k	X
ejpam-4461	206	2	=	=	X
ejpam-4461	206	3	|v	|v	PROPN
ejpam-4461	206	4	(	(	PUNCT
ejpam-4461	206	5	g)|	g)|	PROPN
ejpam-4461	206	6	.	.	PUNCT
ejpam-4461	206	7	assume	assume	VERB
ejpam-4461	206	8	nk	nk	PROPN
ejpam-4461	206	9	≥	≥	NUM
ejpam-4461	206	10	2	2	NUM
ejpam-4461	206	11	.	.	PUNCT
ejpam-4461	207	1	first	first	ADV
ejpam-4461	207	2	,	,	PUNCT
ejpam-4461	207	3	let	let	VERB
ejpam-4461	207	4	sj	sj	PRON
ejpam-4461	207	5	⊆	⊆	NUM
ejpam-4461	207	6	v	v	ADP
ejpam-4461	207	7	(	(	PUNCT
ejpam-4461	207	8	cj	cj	NOUN
ejpam-4461	207	9	)	)	PUNCT
ejpam-4461	207	10	be	be	AUX
ejpam-4461	207	11	a	a	DET
ejpam-4461	207	12	γ	γ	NOUN
ejpam-4461	207	13	-	-	PUNCT
ejpam-4461	207	14	set	set	NOUN
ejpam-4461	207	15	of	of	ADP
ejpam-4461	207	16	cj	cj	NOUN
ejpam-4461	207	17	for	for	ADP
ejpam-4461	207	18	all	all	DET
ejpam-4461	207	19	j	j	NOUN
ejpam-4461	207	20	=	=	SYM
ejpam-4461	207	21	1	1	NUM
ejpam-4461	207	22	,	,	PUNCT
ejpam-4461	207	23	2	2	NUM
ejpam-4461	207	24	,	,	PUNCT
ejpam-4461	207	25	.	.	PUNCT
ejpam-4461	207	26	.	.	PUNCT
ejpam-4461	208	1	.	.	PUNCT
ejpam-4461	209	1	,	,	PUNCT
ejpam-4461	209	2	k.	k.	PROPN
ejpam-4461	209	3	then	then	ADV
ejpam-4461	209	4	s	s	VERB
ejpam-4461	209	5	=	=	SYM
ejpam-4461	209	6	∪k	∪k	PROPN
ejpam-4461	209	7	j=1sj	j=1sj	NUM
ejpam-4461	209	8	is	be	AUX
ejpam-4461	209	9	a	a	DET
ejpam-4461	209	10	semitotal	semitotal	ADJ
ejpam-4461	209	11	dominating	dominating	NOUN
ejpam-4461	209	12	set	set	NOUN
ejpam-4461	209	13	of	of	ADP
ejpam-4461	209	14	g	g	PROPN
ejpam-4461	209	15	+	+	NOUN
ejpam-4461	209	16	k1	k1	NOUN
ejpam-4461	209	17	.	.	PUNCT
ejpam-4461	210	1	since	since	SCONJ
ejpam-4461	210	2	u	u	PROPN
ejpam-4461	210	3	∈	∈	PROPN
ejpam-4461	210	4	v	v	NOUN
ejpam-4461	210	5	(	(	PUNCT
ejpam-4461	210	6	g	g	PROPN
ejpam-4461	210	7	+	+	NOUN
ejpam-4461	210	8	k1	k1	NOUN
ejpam-4461	210	9	)	)	PUNCT
ejpam-4461	210	10	\	\	PROPN
ejpam-4461	210	11	s	s	X
ejpam-4461	210	12	,	,	PUNCT
ejpam-4461	210	13	s	s	VERB
ejpam-4461	210	14	is	be	AUX
ejpam-4461	210	15	an	an	DET
ejpam-4461	210	16	outer	outer	ADV
ejpam-4461	210	17	-	-	PUNCT
ejpam-4461	210	18	connected	connect	VERB
ejpam-4461	210	19	semitotal	semitotal	ADJ
ejpam-4461	210	20	dominating	dominating	NOUN
ejpam-4461	210	21	set	set	NOUN
ejpam-4461	210	22	of	of	ADP
ejpam-4461	210	23	g+k1	g+k1	NOUN
ejpam-4461	210	24	.	.	PUNCT
ejpam-4461	211	1	thus	thus	ADV
ejpam-4461	211	2	,	,	PUNCT
ejpam-4461	211	3	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	211	4	)	)	PUNCT
ejpam-4461	211	5	≤	≤	NUM
ejpam-4461	211	6	|s|	|s|	PROPN
ejpam-4461	211	7	=	=	SYM
ejpam-4461	211	8	k∑	k∑	NOUN
ejpam-4461	211	9	j=1	j=1	PROPN
ejpam-4461	211	10	γ(cj	γ(cj	PROPN
ejpam-4461	211	11	)	)	PUNCT
ejpam-4461	211	12	.	.	PUNCT
ejpam-4461	212	1	next	next	ADV
ejpam-4461	212	2	,	,	PUNCT
ejpam-4461	212	3	let	let	VERB
ejpam-4461	212	4	s	s	PRON
ejpam-4461	212	5	=	=	PUNCT
ejpam-4461	212	6	(	(	PUNCT
ejpam-4461	212	7	∪k−1	∪k−1	NUM
ejpam-4461	212	8	j=1v	j=1v	PROPN
ejpam-4461	212	9	(	(	PUNCT
ejpam-4461	212	10	cj	cj	NOUN
ejpam-4461	212	11	)	)	PUNCT
ejpam-4461	212	12	)	)	PUNCT
ejpam-4461	212	13	∪	∪	ADP
ejpam-4461	212	14	{	{	PUNCT
ejpam-4461	212	15	u	u	NOUN
ejpam-4461	212	16	,	,	PUNCT
ejpam-4461	212	17	v	v	NOUN
ejpam-4461	212	18	}	}	PUNCT
ejpam-4461	212	19	,	,	PUNCT
ejpam-4461	212	20	where	where	SCONJ
ejpam-4461	212	21	v	v	X
ejpam-4461	212	22	∈	∈	PROPN
ejpam-4461	212	23	v	v	NOUN
ejpam-4461	212	24	(	(	PUNCT
ejpam-4461	212	25	ck	ck	PROPN
ejpam-4461	212	26	)	)	PUNCT
ejpam-4461	212	27	which	which	PRON
ejpam-4461	212	28	is	be	AUX
ejpam-4461	212	29	a	a	DET
ejpam-4461	212	30	non	non	ADJ
ejpam-4461	212	31	-	-	NOUN
ejpam-4461	212	32	cutvertex	cutvertex	NOUN
ejpam-4461	212	33	of	of	ADP
ejpam-4461	212	34	ck	ck	PROPN
ejpam-4461	212	35	.	.	PUNCT
ejpam-4461	213	1	then	then	ADV
ejpam-4461	213	2	s	s	VERB
ejpam-4461	213	3	is	be	AUX
ejpam-4461	213	4	an	an	DET
ejpam-4461	213	5	outer	outer	ADV
ejpam-4461	213	6	-	-	PUNCT
ejpam-4461	213	7	connected	connect	VERB
ejpam-4461	213	8	dominating	dominating	NOUN
ejpam-4461	213	9	set	set	NOUN
ejpam-4461	213	10	of	of	ADP
ejpam-4461	213	11	g+k1	g+k1	NOUN
ejpam-4461	213	12	.	.	PUNCT
ejpam-4461	214	1	this	this	PRON
ejpam-4461	214	2	means	mean	VERB
ejpam-4461	214	3	that	that	SCONJ
ejpam-4461	214	4	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	214	5	)	)	PUNCT
ejpam-4461	214	6	≤	≤	NUM
ejpam-4461	214	7	2	2	NUM
ejpam-4461	214	8	+	+	CCONJ
ejpam-4461	214	9	k−1∑	k−1∑	PROPN
ejpam-4461	214	10	j=1	j=1	PROPN
ejpam-4461	214	11	nj	nj	PROPN
ejpam-4461	214	12	.	.	PUNCT
ejpam-4461	215	1	thus	thus	ADV
ejpam-4461	215	2	,	,	PUNCT
ejpam-4461	215	3	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	215	4	)	)	PUNCT
ejpam-4461	215	5	≤	≤	NUM
ejpam-4461	215	6	min	min	PROPN
ejpam-4461	215	7	{	{	PUNCT
ejpam-4461	215	8	k∑	k∑	NOUN
ejpam-4461	215	9	j=1	j=1	PROPN
ejpam-4461	215	10	γ(cj	γ(cj	PROPN
ejpam-4461	215	11	)	)	PUNCT
ejpam-4461	215	12	,	,	PUNCT
ejpam-4461	215	13	2	2	NUM
ejpam-4461	215	14	+	+	CCONJ
ejpam-4461	215	15	k−1∑	k−1∑	PROPN
ejpam-4461	215	16	j=1	j=1	PROPN
ejpam-4461	215	17	nj	nj	PROPN
ejpam-4461	215	18	}	}	PUNCT
ejpam-4461	215	19	.	.	PUNCT
ejpam-4461	216	1	now	now	ADV
ejpam-4461	216	2	,	,	PUNCT
ejpam-4461	216	3	to	to	PART
ejpam-4461	216	4	get	get	VERB
ejpam-4461	216	5	the	the	DET
ejpam-4461	216	6	other	other	ADJ
ejpam-4461	216	7	inequality	inequality	NOUN
ejpam-4461	216	8	,	,	PUNCT
ejpam-4461	216	9	let	let	VERB
ejpam-4461	216	10	s	s	PRON
ejpam-4461	216	11	⊆	⊆	NUM
ejpam-4461	216	12	v	v	NOUN
ejpam-4461	216	13	(	(	PUNCT
ejpam-4461	216	14	g	g	PROPN
ejpam-4461	216	15	+	+	CCONJ
ejpam-4461	216	16	k1	k1	NOUN
ejpam-4461	216	17	)	)	PUNCT
ejpam-4461	216	18	be	be	VERB
ejpam-4461	216	19	a	a	DET
ejpam-4461	216	20	γ̃t2	γ̃t2	NOUN
ejpam-4461	216	21	-	-	PUNCT
ejpam-4461	216	22	set	set	NOUN
ejpam-4461	216	23	of	of	ADP
ejpam-4461	216	24	g	g	PROPN
ejpam-4461	216	25	+	+	CCONJ
ejpam-4461	216	26	k1	k1	NOUN
ejpam-4461	216	27	.	.	PUNCT
ejpam-4461	217	1	then	then	ADV
ejpam-4461	217	2	sj	sj	VERB
ejpam-4461	217	3	=	=	SYM
ejpam-4461	217	4	s	s	PROPN
ejpam-4461	217	5	∩	∩	ADJ
ejpam-4461	217	6	v	v	X
ejpam-4461	217	7	(	(	PUNCT
ejpam-4461	217	8	cj	cj	NOUN
ejpam-4461	217	9	)	)	PUNCT
ejpam-4461	217	10	is	be	AUX
ejpam-4461	217	11	a	a	DET
ejpam-4461	217	12	dominating	dominating	NOUN
ejpam-4461	217	13	set	set	NOUN
ejpam-4461	217	14	of	of	ADP
ejpam-4461	217	15	cj	cj	NOUN
ejpam-4461	217	16	for	for	ADP
ejpam-4461	217	17	all	all	DET
ejpam-4461	217	18	j	j	PROPN
ejpam-4461	217	19	∈	∈	PROPN
ejpam-4461	217	20	{	{	PUNCT
ejpam-4461	217	21	1	1	NUM
ejpam-4461	217	22	,	,	PUNCT
ejpam-4461	217	23	2	2	NUM
ejpam-4461	217	24	,	,	PUNCT
ejpam-4461	217	25	.	.	PUNCT
ejpam-4461	217	26	.	.	PUNCT
ejpam-4461	218	1	.	.	PUNCT
ejpam-4461	219	1	,	,	PUNCT
ejpam-4461	219	2	k	k	X
ejpam-4461	219	3	}	}	PUNCT
ejpam-4461	219	4	.	.	PUNCT
ejpam-4461	220	1	if	if	SCONJ
ejpam-4461	220	2	u	u	PROPN
ejpam-4461	220	3	/∈	/∈	PUNCT
ejpam-4461	220	4	s	s	PART
ejpam-4461	220	5	,	,	PUNCT
ejpam-4461	220	6	then	then	ADV
ejpam-4461	220	7	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	220	8	)	)	PUNCT
ejpam-4461	220	9	=	=	SYM
ejpam-4461	220	10	|s|	|s|	PROPN
ejpam-4461	220	11	=	=	SYM
ejpam-4461	220	12	k∑	k∑	NOUN
ejpam-4461	220	13	j=1	j=1	PROPN
ejpam-4461	220	14	|sj	|sj	X
ejpam-4461	220	15	|	|	ADV
ejpam-4461	220	16	≥	≥	NOUN
ejpam-4461	220	17	k∑	k∑	VERB
ejpam-4461	220	18	j=1	j=1	PROPN
ejpam-4461	220	19	γ(cj	γ(cj	PROPN
ejpam-4461	220	20	)	)	PUNCT
ejpam-4461	220	21	.	.	PUNCT
ejpam-4461	221	1	suppose	suppose	VERB
ejpam-4461	221	2	that	that	SCONJ
ejpam-4461	221	3	u	u	PROPN
ejpam-4461	221	4	∈	∈	PROPN
ejpam-4461	221	5	s.	s.	PROPN
ejpam-4461	221	6	since	since	SCONJ
ejpam-4461	221	7	⟨v	⟨v	PROPN
ejpam-4461	221	8	(	(	PUNCT
ejpam-4461	221	9	g+k1	g+k1	NOUN
ejpam-4461	221	10	)	)	PUNCT
ejpam-4461	221	11	\	\	PROPN
ejpam-4461	221	12	s⟩	s⟩	PROPN
ejpam-4461	221	13	is	be	AUX
ejpam-4461	221	14	connected	connect	VERB
ejpam-4461	221	15	,	,	PUNCT
ejpam-4461	221	16	v	v	INTJ
ejpam-4461	221	17	(	(	PUNCT
ejpam-4461	221	18	g+k1	g+k1	NOUN
ejpam-4461	221	19	)	)	PUNCT
ejpam-4461	221	20	\	\	PROPN
ejpam-4461	221	21	s	s	PART
ejpam-4461	221	22	=	=	SYM
ejpam-4461	221	23	v	v	PROPN
ejpam-4461	221	24	(	(	PUNCT
ejpam-4461	221	25	cj	cj	NOUN
ejpam-4461	221	26	)	)	PUNCT
ejpam-4461	221	27	\	\	PROPN
ejpam-4461	222	1	sj	sj	PROPN
ejpam-4461	222	2	for	for	ADP
ejpam-4461	222	3	a.	a.	PROPN
ejpam-4461	222	4	aradais	aradais	PROPN
ejpam-4461	222	5	,	,	PUNCT
ejpam-4461	222	6	f.	f.	PROPN
ejpam-4461	222	7	jamil	jamil	PROPN
ejpam-4461	222	8	/	/	SYM
ejpam-4461	222	9	eur	eur	PROPN
ejpam-4461	222	10	.	.	PUNCT
ejpam-4461	223	1	j.	j.	PROPN
ejpam-4461	223	2	pure	pure	PROPN
ejpam-4461	223	3	appl	appl	PROPN
ejpam-4461	223	4	.	.	PROPN
ejpam-4461	223	5	math	math	PROPN
ejpam-4461	223	6	,	,	PUNCT
ejpam-4461	223	7	15	15	NUM
ejpam-4461	223	8	(	(	PUNCT
ejpam-4461	223	9	3	3	NUM
ejpam-4461	223	10	)	)	PUNCT
ejpam-4461	223	11	(	(	PUNCT
ejpam-4461	223	12	2022	2022	NUM
ejpam-4461	223	13	)	)	PUNCT
ejpam-4461	223	14	,	,	PUNCT
ejpam-4461	223	15	1265	1265	NUM
ejpam-4461	223	16	-	-	SYM
ejpam-4461	223	17	1279	1279	NUM
ejpam-4461	223	18	1271	1271	NUM
ejpam-4461	223	19	some	some	DET
ejpam-4461	223	20	j.	j.	PROPN
ejpam-4461	223	21	moreover	moreover	ADV
ejpam-4461	223	22	,	,	PUNCT
ejpam-4461	223	23	since	since	SCONJ
ejpam-4461	223	24	s	s	NOUN
ejpam-4461	223	25	is	be	AUX
ejpam-4461	223	26	a	a	DET
ejpam-4461	223	27	γ̃t2	γ̃t2	PROPN
ejpam-4461	223	28	-	-	PUNCT
ejpam-4461	223	29	set	set	NOUN
ejpam-4461	223	30	of	of	ADP
ejpam-4461	223	31	g	g	PROPN
ejpam-4461	223	32	,	,	PUNCT
ejpam-4461	223	33	j	j	PROPN
ejpam-4461	223	34	=	=	PROPN
ejpam-4461	223	35	k.	k.	PROPN
ejpam-4461	224	1	thus	thus	ADV
ejpam-4461	224	2	,	,	PUNCT
ejpam-4461	224	3	s	s	VERB
ejpam-4461	224	4	=	=	PUNCT
ejpam-4461	224	5	(	(	PUNCT
ejpam-4461	224	6	∪k−1	∪k−1	PROPN
ejpam-4461	224	7	i=1	i=1	PROPN
ejpam-4461	224	8	v	v	PROPN
ejpam-4461	224	9	(	(	PUNCT
ejpam-4461	224	10	ci	ci	NOUN
ejpam-4461	224	11	)	)	PUNCT
ejpam-4461	224	12	)	)	PUNCT
ejpam-4461	224	13	∪	∪	ADP
ejpam-4461	224	14	sk	sk	X
ejpam-4461	224	15	∪	∪	X
ejpam-4461	224	16	{	{	PUNCT
ejpam-4461	224	17	u	u	NOUN
ejpam-4461	224	18	}	}	PUNCT
ejpam-4461	224	19	so	so	SCONJ
ejpam-4461	224	20	that	that	SCONJ
ejpam-4461	224	21	γ̃t2(g+k1	γ̃t2(g+k1	NOUN
ejpam-4461	224	22	)	)	PUNCT
ejpam-4461	225	1	=	=	SYM
ejpam-4461	225	2	|s|	|s|	NOUN
ejpam-4461	225	3	=	=	SYM
ejpam-4461	225	4	1	1	NUM
ejpam-4461	225	5	+	+	NUM
ejpam-4461	225	6	|sk|+	|sk|+	VERB
ejpam-4461	225	7	k−1∑	k−1∑	PROPN
ejpam-4461	225	8	j=1	j=1	PROPN
ejpam-4461	225	9	nj	nj	PROPN
ejpam-4461	225	10	≥	≥	PROPN
ejpam-4461	225	11	2	2	NUM
ejpam-4461	225	12	+	+	CCONJ
ejpam-4461	225	13	k−1∑	k−1∑	PROPN
ejpam-4461	225	14	j=1	j=1	PROPN
ejpam-4461	225	15	nj	nj	PROPN
ejpam-4461	225	16	.	.	PUNCT
ejpam-4461	226	1	therefore	therefore	ADV
ejpam-4461	226	2	,	,	PUNCT
ejpam-4461	226	3	γ̃t2(g+k1	γ̃t2(g+k1	PROPN
ejpam-4461	226	4	)	)	PUNCT
ejpam-4461	226	5	≥	≥	PROPN
ejpam-4461	226	6	min	min	PROPN
ejpam-4461	226	7	{	{	PUNCT
ejpam-4461	226	8	k∑	k∑	NOUN
ejpam-4461	226	9	j=1	j=1	PROPN
ejpam-4461	226	10	γ(cj	γ(cj	PROPN
ejpam-4461	226	11	)	)	PUNCT
ejpam-4461	226	12	,	,	PUNCT
ejpam-4461	226	13	2	2	NUM
ejpam-4461	226	14	+	+	CCONJ
ejpam-4461	226	15	k−1∑	k−1∑	PROPN
ejpam-4461	226	16	j=1	j=1	PROPN
ejpam-4461	226	17	nj	nj	PROPN
ejpam-4461	226	18	}	}	PUNCT
ejpam-4461	226	19	.	.	PUNCT
ejpam-4461	227	1	suppose	suppose	VERB
ejpam-4461	227	2	that	that	SCONJ
ejpam-4461	227	3	cj	cj	VERB
ejpam-4461	227	4	=	=	SYM
ejpam-4461	227	5	k1	k1	PROPN
ejpam-4461	227	6	for	for	ADP
ejpam-4461	227	7	all	all	DET
ejpam-4461	227	8	j	j	PROPN
ejpam-4461	227	9	∈	∈	PROPN
ejpam-4461	227	10	{	{	PUNCT
ejpam-4461	227	11	1	1	NUM
ejpam-4461	227	12	,	,	PUNCT
ejpam-4461	227	13	2	2	NUM
ejpam-4461	227	14	,	,	PUNCT
ejpam-4461	227	15	.	.	PUNCT
ejpam-4461	227	16	.	.	PUNCT
ejpam-4461	228	1	.	.	PUNCT
ejpam-4461	229	1	,	,	PUNCT
ejpam-4461	229	2	k−	k−	PROPN
ejpam-4461	229	3	1	1	NUM
ejpam-4461	229	4	}	}	PUNCT
ejpam-4461	229	5	in	in	ADP
ejpam-4461	229	6	proposition	proposition	NOUN
ejpam-4461	229	7	3	3	X
ejpam-4461	229	8	.	.	PUNCT
ejpam-4461	230	1	if	if	SCONJ
ejpam-4461	230	2	γ(ck	γ(ck	NUM
ejpam-4461	230	3	)	)	PUNCT
ejpam-4461	230	4	=	=	SYM
ejpam-4461	230	5	1	1	NUM
ejpam-4461	230	6	,	,	PUNCT
ejpam-4461	230	7	then	then	ADV
ejpam-4461	230	8	k∑	k∑	VERB
ejpam-4461	230	9	j=1	j=1	PROPN
ejpam-4461	230	10	γ(cj	γ(cj	PROPN
ejpam-4461	230	11	)	)	PUNCT
ejpam-4461	230	12	<	<	X
ejpam-4461	230	13	2	2	NUM
ejpam-4461	230	14	+	+	CCONJ
ejpam-4461	230	15	k−1∑	k−1∑	PROPN
ejpam-4461	230	16	j=1	j=1	PROPN
ejpam-4461	230	17	nj	nj	PROPN
ejpam-4461	230	18	.	.	PUNCT
ejpam-4461	231	1	on	on	ADP
ejpam-4461	231	2	the	the	DET
ejpam-4461	231	3	other	other	ADJ
ejpam-4461	231	4	hand	hand	NOUN
ejpam-4461	231	5	,	,	PUNCT
ejpam-4461	231	6	if	if	SCONJ
ejpam-4461	231	7	γ(ck	γ(ck	NOUN
ejpam-4461	231	8	)	)	PUNCT
ejpam-4461	231	9	≥	≥	NOUN
ejpam-4461	231	10	3	3	NUM
ejpam-4461	231	11	,	,	PUNCT
ejpam-4461	231	12	then	then	ADV
ejpam-4461	231	13	k∑	k∑	VERB
ejpam-4461	231	14	j=1	j=1	PROPN
ejpam-4461	231	15	γ(cj	γ(cj	PROPN
ejpam-4461	231	16	)	)	PUNCT
ejpam-4461	231	17	>	>	X
ejpam-4461	232	1	2	2	NUM
ejpam-4461	233	1	+	+	CCONJ
ejpam-4461	233	2	k−1∑	k−1∑	PROPN
ejpam-4461	233	3	j=1	j=1	PROPN
ejpam-4461	233	4	nj	nj	PROPN
ejpam-4461	233	5	,	,	PUNCT
ejpam-4461	233	6	and	and	CCONJ
ejpam-4461	233	7	attain	attain	VERB
ejpam-4461	233	8	equality	equality	NOUN
ejpam-4461	233	9	if	if	SCONJ
ejpam-4461	233	10	γ(ck	γ(ck	NUM
ejpam-4461	233	11	)	)	PUNCT
ejpam-4461	233	12	=	=	SYM
ejpam-4461	233	13	2	2	X
ejpam-4461	233	14	.	.	X
ejpam-4461	233	15	theorem	theorem	NOUN
ejpam-4461	233	16	1	1	NUM
ejpam-4461	233	17	.	.	PUNCT
ejpam-4461	234	1	[	[	X
ejpam-4461	234	2	1	1	X
ejpam-4461	234	3	]	]	PUNCT
ejpam-4461	234	4	let	let	VERB
ejpam-4461	234	5	g	g	NOUN
ejpam-4461	234	6	and	and	CCONJ
ejpam-4461	234	7	h	h	NOUN
ejpam-4461	234	8	be	be	AUX
ejpam-4461	234	9	nontrivial	nontrivial	ADJ
ejpam-4461	234	10	graphs	graph	NOUN
ejpam-4461	234	11	,	,	PUNCT
ejpam-4461	234	12	and	and	CCONJ
ejpam-4461	234	13	s	s	VERB
ejpam-4461	234	14	⊆	⊆	NUM
ejpam-4461	234	15	v	v	NOUN
ejpam-4461	234	16	(	(	PUNCT
ejpam-4461	234	17	g	g	PROPN
ejpam-4461	234	18	+	+	NOUN
ejpam-4461	234	19	h	h	NOUN
ejpam-4461	234	20	)	)	PUNCT
ejpam-4461	234	21	.	.	PUNCT
ejpam-4461	235	1	then	then	ADV
ejpam-4461	235	2	s	s	VERB
ejpam-4461	235	3	is	be	AUX
ejpam-4461	235	4	a	a	DET
ejpam-4461	235	5	semitotal	semitotal	ADJ
ejpam-4461	235	6	dominating	dominating	NOUN
ejpam-4461	235	7	set	set	VERB
ejpam-4461	235	8	in	in	ADP
ejpam-4461	235	9	g+h	g+h	PROPN
ejpam-4461	236	1	if	if	SCONJ
ejpam-4461	236	2	and	and	CCONJ
ejpam-4461	236	3	only	only	ADV
ejpam-4461	236	4	if	if	SCONJ
ejpam-4461	236	5	one	one	NUM
ejpam-4461	236	6	of	of	ADP
ejpam-4461	236	7	the	the	DET
ejpam-4461	236	8	following	follow	VERB
ejpam-4461	236	9	holds	hold	VERB
ejpam-4461	236	10	:	:	PUNCT
ejpam-4461	236	11	(	(	PUNCT
ejpam-4461	236	12	i	i	NOUN
ejpam-4461	236	13	)	)	PUNCT
ejpam-4461	236	14	s	s	VERB
ejpam-4461	236	15	⊆	⊆	NUM
ejpam-4461	236	16	v	v	NOUN
ejpam-4461	236	17	(	(	PUNCT
ejpam-4461	236	18	g	g	NOUN
ejpam-4461	236	19	)	)	PUNCT
ejpam-4461	236	20	is	be	AUX
ejpam-4461	236	21	a	a	DET
ejpam-4461	236	22	nonsingleton	nonsingleton	NOUN
ejpam-4461	236	23	dominating	dominating	NOUN
ejpam-4461	236	24	set	set	VERB
ejpam-4461	236	25	in	in	ADP
ejpam-4461	236	26	g	g	NOUN
ejpam-4461	236	27	;	;	PUNCT
ejpam-4461	236	28	(	(	PUNCT
ejpam-4461	236	29	ii	ii	NOUN
ejpam-4461	236	30	)	)	PUNCT
ejpam-4461	236	31	s	s	PART
ejpam-4461	236	32	⊆	⊆	NUM
ejpam-4461	236	33	v	v	NOUN
ejpam-4461	236	34	(	(	PUNCT
ejpam-4461	236	35	h	h	NOUN
ejpam-4461	236	36	)	)	PUNCT
ejpam-4461	236	37	is	be	AUX
ejpam-4461	236	38	a	a	DET
ejpam-4461	236	39	nonsingleton	nonsingleton	NOUN
ejpam-4461	236	40	dominating	dominating	NOUN
ejpam-4461	236	41	set	set	VERB
ejpam-4461	236	42	in	in	ADP
ejpam-4461	236	43	h	h	NOUN
ejpam-4461	236	44	;	;	PUNCT
ejpam-4461	236	45	(	(	PUNCT
ejpam-4461	236	46	iii	iii	X
ejpam-4461	236	47	)	)	PUNCT
ejpam-4461	236	48	s	s	PART
ejpam-4461	236	49	∩	∩	ADJ
ejpam-4461	236	50	v	v	ADJ
ejpam-4461	236	51	(	(	PUNCT
ejpam-4461	236	52	g	g	NOUN
ejpam-4461	236	53	)	)	PUNCT
ejpam-4461	236	54	̸=	̸=	PROPN
ejpam-4461	236	55	∅	∅	NOUN
ejpam-4461	236	56	and	and	CCONJ
ejpam-4461	236	57	s	s	VERB
ejpam-4461	236	58	∩v(g	∩v(g	ADJ
ejpam-4461	236	59	)	)	PUNCT
ejpam-4461	236	60	̸=	̸=	PROPN
ejpam-4461	236	61	∅.	∅.	ADV
ejpam-4461	236	62	theorem	theorem	VERB
ejpam-4461	236	63	2	2	NUM
ejpam-4461	236	64	.	.	PUNCT
ejpam-4461	237	1	let	let	VERB
ejpam-4461	237	2	g	g	NOUN
ejpam-4461	238	1	and	and	CCONJ
ejpam-4461	238	2	h	h	NOUN
ejpam-4461	238	3	be	be	VERB
ejpam-4461	238	4	any	any	DET
ejpam-4461	238	5	nontrivial	nontrivial	ADJ
ejpam-4461	238	6	graphs	graph	NOUN
ejpam-4461	238	7	,	,	PUNCT
ejpam-4461	238	8	and	and	CCONJ
ejpam-4461	238	9	s	s	VERB
ejpam-4461	238	10	⊆	⊆	NUM
ejpam-4461	238	11	v	v	NOUN
ejpam-4461	238	12	(	(	PUNCT
ejpam-4461	238	13	g	g	PROPN
ejpam-4461	238	14	+	+	NOUN
ejpam-4461	238	15	h	h	NOUN
ejpam-4461	238	16	)	)	PUNCT
ejpam-4461	238	17	,	,	PUNCT
ejpam-4461	238	18	then	then	ADV
ejpam-4461	238	19	s	s	VERB
ejpam-4461	238	20	is	be	AUX
ejpam-4461	238	21	an	an	DET
ejpam-4461	238	22	outer	outer	ADV
ejpam-4461	238	23	-	-	PUNCT
ejpam-4461	238	24	connected	connect	VERB
ejpam-4461	238	25	semitotal	semitotal	ADJ
ejpam-4461	238	26	dominating	dominating	NOUN
ejpam-4461	238	27	set	set	VERB
ejpam-4461	238	28	in	in	ADP
ejpam-4461	238	29	g+h	g+h	PROPN
ejpam-4461	239	1	if	if	SCONJ
ejpam-4461	239	2	and	and	CCONJ
ejpam-4461	239	3	only	only	ADV
ejpam-4461	239	4	if	if	SCONJ
ejpam-4461	239	5	one	one	NUM
ejpam-4461	239	6	of	of	ADP
ejpam-4461	239	7	the	the	DET
ejpam-4461	239	8	following	follow	VERB
ejpam-4461	239	9	holds	hold	VERB
ejpam-4461	239	10	:	:	PUNCT
ejpam-4461	239	11	(	(	PUNCT
ejpam-4461	239	12	i	i	NOUN
ejpam-4461	239	13	)	)	PUNCT
ejpam-4461	239	14	s	s	VERB
ejpam-4461	239	15	⊆	⊆	NUM
ejpam-4461	239	16	v	v	NOUN
ejpam-4461	239	17	(	(	PUNCT
ejpam-4461	239	18	g	g	NOUN
ejpam-4461	239	19	)	)	PUNCT
ejpam-4461	239	20	and	and	CCONJ
ejpam-4461	239	21	one	one	NUM
ejpam-4461	239	22	of	of	ADP
ejpam-4461	239	23	the	the	DET
ejpam-4461	239	24	following	following	NOUN
ejpam-4461	239	25	holds	hold	VERB
ejpam-4461	239	26	:	:	PUNCT
ejpam-4461	239	27	(	(	PUNCT
ejpam-4461	239	28	a	a	X
ejpam-4461	239	29	)	)	PUNCT
ejpam-4461	239	30	s	s	PART
ejpam-4461	239	31	=	=	SYM
ejpam-4461	239	32	v	v	X
ejpam-4461	239	33	(	(	PUNCT
ejpam-4461	239	34	g	g	NOUN
ejpam-4461	239	35	)	)	PUNCT
ejpam-4461	239	36	and	and	CCONJ
ejpam-4461	239	37	h	h	NOUN
ejpam-4461	239	38	is	be	AUX
ejpam-4461	239	39	connected	connect	VERB
ejpam-4461	239	40	;	;	PUNCT
ejpam-4461	239	41	(	(	PUNCT
ejpam-4461	239	42	b	b	X
ejpam-4461	239	43	)	)	PUNCT
ejpam-4461	239	44	s	s	PART
ejpam-4461	239	45	̸=	̸=	PROPN
ejpam-4461	239	46	v	v	NOUN
ejpam-4461	239	47	(	(	PUNCT
ejpam-4461	239	48	g	g	NOUN
ejpam-4461	239	49	)	)	PUNCT
ejpam-4461	239	50	and	and	CCONJ
ejpam-4461	239	51	s	s	VERB
ejpam-4461	239	52	is	be	AUX
ejpam-4461	239	53	a	a	DET
ejpam-4461	239	54	nonsingleton	nonsingleton	NOUN
ejpam-4461	239	55	dominating	dominating	NOUN
ejpam-4461	239	56	set	set	VERB
ejpam-4461	239	57	in	in	ADP
ejpam-4461	239	58	g.	g.	PROPN
ejpam-4461	239	59	(	(	PUNCT
ejpam-4461	239	60	ii	ii	PROPN
ejpam-4461	239	61	)	)	PUNCT
ejpam-4461	239	62	s	s	PART
ejpam-4461	239	63	⊆	⊆	NUM
ejpam-4461	239	64	v	v	NOUN
ejpam-4461	239	65	(	(	PUNCT
ejpam-4461	239	66	h	h	NOUN
ejpam-4461	239	67	)	)	PUNCT
ejpam-4461	239	68	and	and	CCONJ
ejpam-4461	239	69	one	one	NUM
ejpam-4461	239	70	of	of	ADP
ejpam-4461	239	71	the	the	DET
ejpam-4461	239	72	following	following	NOUN
ejpam-4461	239	73	holds	hold	VERB
ejpam-4461	239	74	:	:	PUNCT
ejpam-4461	239	75	(	(	PUNCT
ejpam-4461	239	76	a	a	X
ejpam-4461	239	77	)	)	PUNCT
ejpam-4461	239	78	s	s	PART
ejpam-4461	239	79	=	=	SYM
ejpam-4461	239	80	v	v	PROPN
ejpam-4461	239	81	(	(	PUNCT
ejpam-4461	239	82	h	h	NOUN
ejpam-4461	239	83	)	)	PUNCT
ejpam-4461	239	84	and	and	CCONJ
ejpam-4461	239	85	g	g	PROPN
ejpam-4461	239	86	is	be	AUX
ejpam-4461	239	87	connected	connect	VERB
ejpam-4461	239	88	;	;	PUNCT
ejpam-4461	239	89	a.	a.	PROPN
ejpam-4461	239	90	aradais	aradais	PROPN
ejpam-4461	239	91	,	,	PUNCT
ejpam-4461	239	92	f.	f.	PROPN
ejpam-4461	239	93	jamil	jamil	PROPN
ejpam-4461	239	94	/	/	SYM
ejpam-4461	239	95	eur	eur	PROPN
ejpam-4461	239	96	.	.	PUNCT
ejpam-4461	240	1	j.	j.	PROPN
ejpam-4461	240	2	pure	pure	PROPN
ejpam-4461	240	3	appl	appl	PROPN
ejpam-4461	240	4	.	.	PROPN
ejpam-4461	240	5	math	math	PROPN
ejpam-4461	240	6	,	,	PUNCT
ejpam-4461	240	7	15	15	NUM
ejpam-4461	240	8	(	(	PUNCT
ejpam-4461	240	9	3	3	NUM
ejpam-4461	240	10	)	)	PUNCT
ejpam-4461	240	11	(	(	PUNCT
ejpam-4461	240	12	2022	2022	NUM
ejpam-4461	240	13	)	)	PUNCT
ejpam-4461	240	14	,	,	PUNCT
ejpam-4461	240	15	1265	1265	NUM
ejpam-4461	240	16	-	-	SYM
ejpam-4461	240	17	1279	1279	NUM
ejpam-4461	240	18	1272	1272	NUM
ejpam-4461	240	19	(	(	PUNCT
ejpam-4461	240	20	b	b	NOUN
ejpam-4461	240	21	)	)	PUNCT
ejpam-4461	240	22	s	s	PART
ejpam-4461	240	23	̸=	̸=	PROPN
ejpam-4461	240	24	v	v	NOUN
ejpam-4461	240	25	(	(	PUNCT
ejpam-4461	240	26	h	h	NOUN
ejpam-4461	240	27	)	)	PUNCT
ejpam-4461	240	28	and	and	CCONJ
ejpam-4461	240	29	s	s	VERB
ejpam-4461	240	30	is	be	AUX
ejpam-4461	240	31	a	a	DET
ejpam-4461	240	32	nonsingleton	nonsingleton	NOUN
ejpam-4461	240	33	dominating	dominating	NOUN
ejpam-4461	240	34	set	set	VERB
ejpam-4461	240	35	in	in	ADP
ejpam-4461	240	36	h.	h.	PROPN
ejpam-4461	240	37	(	(	PUNCT
ejpam-4461	240	38	iii	iii	NOUN
ejpam-4461	240	39	)	)	PUNCT
ejpam-4461	240	40	s	s	PART
ejpam-4461	240	41	∩	∩	ADJ
ejpam-4461	240	42	v	v	ADJ
ejpam-4461	240	43	(	(	PUNCT
ejpam-4461	240	44	g	g	NOUN
ejpam-4461	240	45	)	)	PUNCT
ejpam-4461	240	46	̸=	̸=	PROPN
ejpam-4461	240	47	∅	∅	NOUN
ejpam-4461	240	48	and	and	CCONJ
ejpam-4461	240	49	s	s	VERB
ejpam-4461	240	50	∩	∩	ADJ
ejpam-4461	240	51	v	v	ADJ
ejpam-4461	240	52	(	(	PUNCT
ejpam-4461	240	53	h	h	NOUN
ejpam-4461	240	54	)	)	PUNCT
ejpam-4461	240	55	̸=	̸=	PROPN
ejpam-4461	240	56	∅	∅	NOUN
ejpam-4461	240	57	such	such	ADJ
ejpam-4461	240	58	that	that	SCONJ
ejpam-4461	240	59	if	if	SCONJ
ejpam-4461	240	60	s	s	VERB
ejpam-4461	240	61	̸=	̸=	PROPN
ejpam-4461	240	62	v	v	NOUN
ejpam-4461	240	63	(	(	PUNCT
ejpam-4461	240	64	g	g	PROPN
ejpam-4461	240	65	+	+	NOUN
ejpam-4461	240	66	h	h	NOUN
ejpam-4461	240	67	)	)	PUNCT
ejpam-4461	240	68	,	,	PUNCT
ejpam-4461	240	69	then	then	ADV
ejpam-4461	240	70	one	one	NUM
ejpam-4461	240	71	of	of	ADP
ejpam-4461	240	72	the	the	DET
ejpam-4461	240	73	following	following	NOUN
ejpam-4461	240	74	holds	hold	VERB
ejpam-4461	240	75	:	:	PUNCT
ejpam-4461	240	76	(	(	PUNCT
ejpam-4461	240	77	a	a	X
ejpam-4461	240	78	)	)	PUNCT
ejpam-4461	240	79	v	v	NOUN
ejpam-4461	240	80	(	(	PUNCT
ejpam-4461	240	81	g	g	NOUN
ejpam-4461	240	82	)	)	PUNCT
ejpam-4461	240	83	⊆	⊆	NUM
ejpam-4461	240	84	s	s	NOUN
ejpam-4461	240	85	and	and	CCONJ
ejpam-4461	240	86	⟨v	⟨v	NUM
ejpam-4461	240	87	(	(	PUNCT
ejpam-4461	240	88	h	h	NOUN
ejpam-4461	240	89	)	)	PUNCT
ejpam-4461	240	90	\	\	PROPN
ejpam-4461	241	1	s⟩	s⟩	PROPN
ejpam-4461	241	2	is	be	AUX
ejpam-4461	241	3	connected	connect	VERB
ejpam-4461	241	4	;	;	PUNCT
ejpam-4461	241	5	(	(	PUNCT
ejpam-4461	241	6	b	b	X
ejpam-4461	241	7	)	)	PUNCT
ejpam-4461	241	8	v	v	NOUN
ejpam-4461	241	9	(	(	PUNCT
ejpam-4461	241	10	h	h	NOUN
ejpam-4461	241	11	)	)	PUNCT
ejpam-4461	241	12	⊆	⊆	NUM
ejpam-4461	241	13	s	s	NOUN
ejpam-4461	241	14	and	and	CCONJ
ejpam-4461	241	15	⟨v	⟨v	NUM
ejpam-4461	241	16	(	(	PUNCT
ejpam-4461	241	17	g	g	NOUN
ejpam-4461	241	18	)	)	PUNCT
ejpam-4461	241	19	\	\	PROPN
ejpam-4461	242	1	s	s	PART
ejpam-4461	242	2	is	be	AUX
ejpam-4461	242	3	a	a	DET
ejpam-4461	242	4	connected	connect	VERB
ejpam-4461	242	5	;	;	PUNCT
ejpam-4461	242	6	(	(	PUNCT
ejpam-4461	242	7	c	c	X
ejpam-4461	242	8	)	)	PUNCT
ejpam-4461	242	9	v	v	NOUN
ejpam-4461	242	10	(	(	PUNCT
ejpam-4461	242	11	g	g	NOUN
ejpam-4461	242	12	)	)	PUNCT
ejpam-4461	242	13	\	\	PUNCT
ejpam-4461	243	1	s	s	PART
ejpam-4461	243	2	̸=	̸=	PROPN
ejpam-4461	243	3	∅	∅	NOUN
ejpam-4461	243	4	and	and	CCONJ
ejpam-4461	243	5	v	v	NOUN
ejpam-4461	243	6	(	(	PUNCT
ejpam-4461	243	7	h	h	NOUN
ejpam-4461	243	8	)	)	PUNCT
ejpam-4461	243	9	\	\	PUNCT
ejpam-4461	244	1	s	s	PART
ejpam-4461	244	2	̸=	̸=	PROPN
ejpam-4461	244	3	∅.	∅.	PRON
ejpam-4461	244	4	proof	proof	NOUN
ejpam-4461	244	5	.	.	PUNCT
ejpam-4461	245	1	assume	assume	VERB
ejpam-4461	245	2	that	that	SCONJ
ejpam-4461	245	3	s	s	VERB
ejpam-4461	245	4	is	be	AUX
ejpam-4461	245	5	an	an	DET
ejpam-4461	245	6	outer	outer	ADV
ejpam-4461	245	7	-	-	PUNCT
ejpam-4461	245	8	connected	connect	VERB
ejpam-4461	245	9	semitotal	semitotal	ADJ
ejpam-4461	245	10	dominating	dominating	NOUN
ejpam-4461	245	11	set	set	NOUN
ejpam-4461	245	12	of	of	ADP
ejpam-4461	245	13	g	g	PROPN
ejpam-4461	245	14	+	+	CCONJ
ejpam-4461	245	15	h.	h.	PROPN
ejpam-4461	245	16	suppose	suppose	VERB
ejpam-4461	245	17	that	that	SCONJ
ejpam-4461	245	18	s	s	VERB
ejpam-4461	245	19	⊆	⊆	NUM
ejpam-4461	245	20	v	v	NOUN
ejpam-4461	245	21	(	(	PUNCT
ejpam-4461	245	22	g	g	NOUN
ejpam-4461	245	23	)	)	PUNCT
ejpam-4461	245	24	.	.	PUNCT
ejpam-4461	246	1	if	if	SCONJ
ejpam-4461	246	2	s	s	VERB
ejpam-4461	246	3	=	=	SYM
ejpam-4461	246	4	v	v	X
ejpam-4461	246	5	(	(	PUNCT
ejpam-4461	246	6	g	g	NOUN
ejpam-4461	246	7	)	)	PUNCT
ejpam-4461	246	8	,	,	PUNCT
ejpam-4461	246	9	then	then	ADV
ejpam-4461	246	10	h	h	PROPN
ejpam-4461	246	11	=	=	SYM
ejpam-4461	247	1	⟨v	⟨v	PROPN
ejpam-4461	247	2	(	(	PUNCT
ejpam-4461	247	3	g+h	g+h	NOUN
ejpam-4461	247	4	)	)	PUNCT
ejpam-4461	247	5	\	\	PROPN
ejpam-4461	248	1	s⟩	s⟩	PROPN
ejpam-4461	248	2	is	be	AUX
ejpam-4461	248	3	connected	connect	VERB
ejpam-4461	248	4	,	,	PUNCT
ejpam-4461	248	5	and	and	CCONJ
ejpam-4461	248	6	(	(	PUNCT
ejpam-4461	248	7	i)(a	i)(a	NOUN
ejpam-4461	248	8	)	)	PUNCT
ejpam-4461	248	9	holds	hold	VERB
ejpam-4461	248	10	.	.	PUNCT
ejpam-4461	249	1	suppose	suppose	VERB
ejpam-4461	249	2	that	that	SCONJ
ejpam-4461	249	3	s	s	VERB
ejpam-4461	249	4	̸=	̸=	PROPN
ejpam-4461	249	5	v	v	NOUN
ejpam-4461	249	6	(	(	PUNCT
ejpam-4461	249	7	g	g	NOUN
ejpam-4461	249	8	)	)	PUNCT
ejpam-4461	249	9	.	.	PUNCT
ejpam-4461	250	1	since	since	SCONJ
ejpam-4461	250	2	s	s	PROPN
ejpam-4461	250	3	is	be	AUX
ejpam-4461	250	4	a	a	DET
ejpam-4461	250	5	semitotal	semitotal	ADJ
ejpam-4461	250	6	dominating	dominating	NOUN
ejpam-4461	250	7	set	set	NOUN
ejpam-4461	250	8	of	of	ADP
ejpam-4461	250	9	g	g	PROPN
ejpam-4461	250	10	+	+	CCONJ
ejpam-4461	250	11	h	h	NOUN
ejpam-4461	250	12	,	,	PUNCT
ejpam-4461	250	13	s	s	PART
ejpam-4461	250	14	is	be	AUX
ejpam-4461	250	15	a	a	DET
ejpam-4461	250	16	nonsingleton	nonsingleton	NOUN
ejpam-4461	250	17	dominating	dominating	NOUN
ejpam-4461	250	18	set	set	NOUN
ejpam-4461	250	19	of	of	ADP
ejpam-4461	250	20	g	g	NOUN
ejpam-4461	250	21	,	,	PUNCT
ejpam-4461	250	22	and	and	CCONJ
ejpam-4461	250	23	(	(	PUNCT
ejpam-4461	250	24	i)(b	i)(b	NUM
ejpam-4461	250	25	)	)	PUNCT
ejpam-4461	250	26	holds	hold	NOUN
ejpam-4461	250	27	.	.	PUNCT
ejpam-4461	251	1	similarly	similarly	ADV
ejpam-4461	251	2	,	,	PUNCT
ejpam-4461	251	3	if	if	SCONJ
ejpam-4461	251	4	s	s	VERB
ejpam-4461	251	5	⊆	⊆	NUM
ejpam-4461	251	6	v	v	NOUN
ejpam-4461	251	7	(	(	PUNCT
ejpam-4461	251	8	h	h	NOUN
ejpam-4461	251	9	)	)	PUNCT
ejpam-4461	251	10	,	,	PUNCT
ejpam-4461	251	11	then	then	ADV
ejpam-4461	251	12	(	(	PUNCT
ejpam-4461	251	13	ii	ii	NOUN
ejpam-4461	251	14	)	)	PUNCT
ejpam-4461	251	15	holds	hold	VERB
ejpam-4461	251	16	.	.	PUNCT
ejpam-4461	252	1	now	now	ADV
ejpam-4461	252	2	,	,	PUNCT
ejpam-4461	252	3	assume	assume	VERB
ejpam-4461	252	4	that	that	SCONJ
ejpam-4461	252	5	sg	sg	VERB
ejpam-4461	252	6	=	=	SYM
ejpam-4461	252	7	s	s	PROPN
ejpam-4461	252	8	∩	∩	ADJ
ejpam-4461	252	9	v	v	X
ejpam-4461	252	10	(	(	PUNCT
ejpam-4461	252	11	g	g	NOUN
ejpam-4461	252	12	)	)	PUNCT
ejpam-4461	252	13	̸=	̸=	PROPN
ejpam-4461	252	14	∅	∅	NOUN
ejpam-4461	252	15	and	and	CCONJ
ejpam-4461	252	16	sh	sh	INTJ
ejpam-4461	252	17	=	=	SYM
ejpam-4461	252	18	s	s	PROPN
ejpam-4461	252	19	∩	∩	ADJ
ejpam-4461	252	20	v	v	ADJ
ejpam-4461	252	21	(	(	PUNCT
ejpam-4461	252	22	h	h	NOUN
ejpam-4461	252	23	)	)	PUNCT
ejpam-4461	252	24	̸=	̸=	PROPN
ejpam-4461	252	25	∅.	∅.	ADV
ejpam-4461	252	26	suppose	suppose	VERB
ejpam-4461	252	27	further	far	ADV
ejpam-4461	252	28	that	that	PRON
ejpam-4461	252	29	s	s	VERB
ejpam-4461	252	30	̸=	̸=	PROPN
ejpam-4461	252	31	v	v	NOUN
ejpam-4461	252	32	(	(	PUNCT
ejpam-4461	252	33	g	g	PROPN
ejpam-4461	252	34	+	+	NOUN
ejpam-4461	252	35	h	h	NOUN
ejpam-4461	252	36	)	)	PUNCT
ejpam-4461	252	37	.	.	PUNCT
ejpam-4461	253	1	statement	statement	NOUN
ejpam-4461	253	2	(	(	PUNCT
ejpam-4461	253	3	iii)(a	iii)(a	PROPN
ejpam-4461	253	4	)	)	PUNCT
ejpam-4461	253	5	follows	follow	VERB
ejpam-4461	253	6	from	from	ADP
ejpam-4461	253	7	the	the	DET
ejpam-4461	253	8	fact	fact	NOUN
ejpam-4461	253	9	that	that	SCONJ
ejpam-4461	253	10	if	if	SCONJ
ejpam-4461	253	11	v	v	X
ejpam-4461	253	12	(	(	PUNCT
ejpam-4461	253	13	g	g	NOUN
ejpam-4461	253	14	)	)	PUNCT
ejpam-4461	253	15	⊆	⊆	NUM
ejpam-4461	253	16	s	s	NOUN
ejpam-4461	253	17	,	,	PUNCT
ejpam-4461	253	18	then	then	ADV
ejpam-4461	253	19	⟨v	⟨v	NUM
ejpam-4461	253	20	(	(	PUNCT
ejpam-4461	253	21	g+h	g+h	NOUN
ejpam-4461	253	22	)	)	PUNCT
ejpam-4461	253	23	\	\	NOUN
ejpam-4461	253	24	s⟩	s⟩	NOUN
ejpam-4461	254	1	=	=	SYM
ejpam-4461	254	2	⟨v	⟨v	NUM
ejpam-4461	254	3	(	(	PUNCT
ejpam-4461	254	4	h	h	NOUN
ejpam-4461	254	5	)	)	PUNCT
ejpam-4461	254	6	\	\	PROPN
ejpam-4461	254	7	sh⟩	sh⟩	NOUN
ejpam-4461	254	8	is	be	AUX
ejpam-4461	254	9	connected	connect	VERB
ejpam-4461	254	10	.	.	PUNCT
ejpam-4461	255	1	similarly	similarly	ADV
ejpam-4461	255	2	,	,	PUNCT
ejpam-4461	255	3	if	if	SCONJ
ejpam-4461	255	4	v	v	X
ejpam-4461	255	5	(	(	PUNCT
ejpam-4461	255	6	h	h	NOUN
ejpam-4461	255	7	)	)	PUNCT
ejpam-4461	255	8	⊆	⊆	NUM
ejpam-4461	255	9	s	s	NOUN
ejpam-4461	255	10	,	,	PUNCT
ejpam-4461	255	11	then	then	ADV
ejpam-4461	255	12	(	(	PUNCT
ejpam-4461	255	13	iii)(b	iii)(b	ADJ
ejpam-4461	255	14	)	)	PUNCT
ejpam-4461	255	15	holds	hold	VERB
ejpam-4461	255	16	.	.	PUNCT
ejpam-4461	256	1	if	if	SCONJ
ejpam-4461	256	2	both	both	PRON
ejpam-4461	256	3	(	(	PUNCT
ejpam-4461	256	4	iii)(a	iii)(a	PROPN
ejpam-4461	256	5	)	)	PUNCT
ejpam-4461	256	6	and	and	CCONJ
ejpam-4461	256	7	(	(	PUNCT
ejpam-4461	256	8	iii)(b	iii)(b	NOUN
ejpam-4461	256	9	)	)	PUNCT
ejpam-4461	256	10	do	do	AUX
ejpam-4461	256	11	not	not	PART
ejpam-4461	256	12	hold	hold	VERB
ejpam-4461	256	13	,	,	PUNCT
ejpam-4461	256	14	then	then	ADV
ejpam-4461	256	15	necessarily	necessarily	ADV
ejpam-4461	256	16	,	,	PUNCT
ejpam-4461	256	17	(	(	PUNCT
ejpam-4461	256	18	iii)(c	iii)(c	NOUN
ejpam-4461	256	19	)	)	PUNCT
ejpam-4461	256	20	holds	hold	VERB
ejpam-4461	256	21	.	.	PUNCT
ejpam-4461	257	1	conversely	conversely	ADV
ejpam-4461	257	2	,	,	PUNCT
ejpam-4461	257	3	suppose	suppose	VERB
ejpam-4461	257	4	that	that	SCONJ
ejpam-4461	257	5	s	s	VERB
ejpam-4461	257	6	̸=	̸=	PROPN
ejpam-4461	257	7	v	v	NOUN
ejpam-4461	257	8	(	(	PUNCT
ejpam-4461	257	9	g+h	g+h	NOUN
ejpam-4461	257	10	)	)	PUNCT
ejpam-4461	257	11	satisfying	satisfy	VERB
ejpam-4461	257	12	condition	condition	NOUN
ejpam-4461	257	13	(	(	PUNCT
ejpam-4461	257	14	i	i	NOUN
ejpam-4461	257	15	)	)	PUNCT
ejpam-4461	257	16	.	.	PUNCT
ejpam-4461	258	1	then	then	ADV
ejpam-4461	258	2	s	s	VERB
ejpam-4461	258	3	⊆	⊆	NUM
ejpam-4461	258	4	v	v	NOUN
ejpam-4461	258	5	(	(	PUNCT
ejpam-4461	258	6	g	g	NOUN
ejpam-4461	258	7	)	)	PUNCT
ejpam-4461	258	8	and	and	CCONJ
ejpam-4461	258	9	is	be	AUX
ejpam-4461	258	10	a	a	DET
ejpam-4461	258	11	nonsingleton	nonsingleton	NOUN
ejpam-4461	258	12	dominating	dominating	NOUN
ejpam-4461	258	13	set	set	NOUN
ejpam-4461	258	14	of	of	ADP
ejpam-4461	258	15	g.	g.	PROPN
ejpam-4461	258	16	by	by	ADP
ejpam-4461	258	17	theorem	theorem	NOUN
ejpam-4461	258	18	1	1	NUM
ejpam-4461	258	19	,	,	PUNCT
ejpam-4461	258	20	s	s	VERB
ejpam-4461	258	21	is	be	AUX
ejpam-4461	258	22	semitotal	semitotal	ADJ
ejpam-4461	258	23	dominating	dominating	NOUN
ejpam-4461	258	24	set	set	NOUN
ejpam-4461	258	25	of	of	ADP
ejpam-4461	258	26	g	g	PROPN
ejpam-4461	258	27	+	+	PROPN
ejpam-4461	258	28	h.	h.	PROPN
ejpam-4461	258	29	if	if	SCONJ
ejpam-4461	258	30	s	s	VERB
ejpam-4461	258	31	=	=	SYM
ejpam-4461	258	32	v	v	X
ejpam-4461	258	33	(	(	PUNCT
ejpam-4461	258	34	g	g	NOUN
ejpam-4461	258	35	)	)	PUNCT
ejpam-4461	258	36	,	,	PUNCT
ejpam-4461	258	37	then	then	ADV
ejpam-4461	258	38	⟨v	⟨v	CCONJ
ejpam-4461	258	39	(	(	PUNCT
ejpam-4461	258	40	g	g	PROPN
ejpam-4461	258	41	+	+	NOUN
ejpam-4461	258	42	h	h	NOUN
ejpam-4461	258	43	)	)	PUNCT
ejpam-4461	258	44	\	\	NOUN
ejpam-4461	258	45	s⟩	s⟩	NOUN
ejpam-4461	259	1	=	=	SYM
ejpam-4461	259	2	h	h	NOUN
ejpam-4461	259	3	,	,	PUNCT
ejpam-4461	259	4	which	which	PRON
ejpam-4461	259	5	by	by	ADP
ejpam-4461	259	6	(	(	PUNCT
ejpam-4461	259	7	i)(a	i)(a	NOUN
ejpam-4461	259	8	)	)	PUNCT
ejpam-4461	259	9	is	be	AUX
ejpam-4461	259	10	connected	connect	VERB
ejpam-4461	259	11	.	.	PUNCT
ejpam-4461	259	12	suppose	suppose	VERB
ejpam-4461	259	13	that	that	SCONJ
ejpam-4461	259	14	s	s	VERB
ejpam-4461	259	15	̸=	̸=	PROPN
ejpam-4461	259	16	v	v	NOUN
ejpam-4461	259	17	(	(	PUNCT
ejpam-4461	259	18	g	g	NOUN
ejpam-4461	259	19	)	)	PUNCT
ejpam-4461	259	20	.	.	PUNCT
ejpam-4461	260	1	then	then	ADV
ejpam-4461	260	2	⟨v	⟨v	CCONJ
ejpam-4461	260	3	(	(	PUNCT
ejpam-4461	260	4	g+h	g+h	NOUN
ejpam-4461	260	5	)	)	PUNCT
ejpam-4461	260	6	\	\	NOUN
ejpam-4461	260	7	s⟩	s⟩	NOUN
ejpam-4461	261	1	=	=	X
ejpam-4461	261	2	⟨(v	⟨(v	NOUN
ejpam-4461	261	3	(	(	PUNCT
ejpam-4461	261	4	g	g	NOUN
ejpam-4461	261	5	)	)	PUNCT
ejpam-4461	261	6	\	\	PROPN
ejpam-4461	261	7	s	s	X
ejpam-4461	261	8	)	)	PUNCT
ejpam-4461	261	9	∪	∪	NOUN
ejpam-4461	261	10	v	v	NOUN
ejpam-4461	261	11	(	(	PUNCT
ejpam-4461	261	12	h)⟩	h)⟩	PROPN
ejpam-4461	261	13	is	be	AUX
ejpam-4461	261	14	clearly	clearly	ADV
ejpam-4461	261	15	connected	connect	VERB
ejpam-4461	261	16	.	.	PUNCT
ejpam-4461	262	1	this	this	PRON
ejpam-4461	262	2	makes	make	VERB
ejpam-4461	262	3	s	s	PRON
ejpam-4461	262	4	an	an	DET
ejpam-4461	262	5	outer	outer	ADV
ejpam-4461	262	6	-	-	PUNCT
ejpam-4461	262	7	connected	connect	VERB
ejpam-4461	262	8	semitotal	semitotal	ADJ
ejpam-4461	262	9	dominating	dominating	NOUN
ejpam-4461	262	10	set	set	NOUN
ejpam-4461	262	11	of	of	ADP
ejpam-4461	262	12	g	g	PROPN
ejpam-4461	262	13	+	+	PROPN
ejpam-4461	262	14	h.	h.	PROPN
ejpam-4461	262	15	similarly	similarly	ADV
ejpam-4461	262	16	,	,	PUNCT
ejpam-4461	262	17	if	if	SCONJ
ejpam-4461	262	18	(	(	PUNCT
ejpam-4461	262	19	ii	ii	NOUN
ejpam-4461	262	20	)	)	PUNCT
ejpam-4461	262	21	holds	hold	VERB
ejpam-4461	262	22	,	,	PUNCT
ejpam-4461	262	23	then	then	ADV
ejpam-4461	262	24	s	s	VERB
ejpam-4461	262	25	is	be	AUX
ejpam-4461	262	26	an	an	DET
ejpam-4461	262	27	outer	outer	ADV
ejpam-4461	262	28	-	-	PUNCT
ejpam-4461	262	29	connected	connect	VERB
ejpam-4461	262	30	semitotal	semitotal	ADJ
ejpam-4461	262	31	dominating	dominating	NOUN
ejpam-4461	262	32	set	set	NOUN
ejpam-4461	262	33	of	of	ADP
ejpam-4461	262	34	g	g	PROPN
ejpam-4461	262	35	+	+	CCONJ
ejpam-4461	262	36	h.	h.	PROPN
ejpam-4461	262	37	finally	finally	ADV
ejpam-4461	262	38	,	,	PUNCT
ejpam-4461	262	39	suppose	suppose	VERB
ejpam-4461	262	40	that	that	SCONJ
ejpam-4461	262	41	(	(	PUNCT
ejpam-4461	262	42	iii	iii	NOUN
ejpam-4461	262	43	)	)	PUNCT
ejpam-4461	262	44	holds	hold	VERB
ejpam-4461	262	45	.	.	PUNCT
ejpam-4461	263	1	by	by	ADP
ejpam-4461	263	2	theorem	theorem	NOUN
ejpam-4461	263	3	1	1	NUM
ejpam-4461	263	4	,	,	PUNCT
ejpam-4461	263	5	s	s	VERB
ejpam-4461	263	6	is	be	AUX
ejpam-4461	263	7	a	a	DET
ejpam-4461	263	8	semitotal	semitotal	ADJ
ejpam-4461	263	9	dominating	dominating	NOUN
ejpam-4461	263	10	set	set	NOUN
ejpam-4461	263	11	of	of	ADP
ejpam-4461	263	12	g	g	PROPN
ejpam-4461	263	13	+	+	CCONJ
ejpam-4461	263	14	h.	h.	NOUN
ejpam-4461	263	15	if	if	SCONJ
ejpam-4461	263	16	v	v	INTJ
ejpam-4461	263	17	(	(	PUNCT
ejpam-4461	263	18	g	g	NOUN
ejpam-4461	263	19	)	)	PUNCT
ejpam-4461	263	20	⊆	⊆	NUM
ejpam-4461	263	21	s	s	NOUN
ejpam-4461	263	22	,	,	PUNCT
ejpam-4461	263	23	then	then	ADV
ejpam-4461	263	24	⟨v	⟨v	CCONJ
ejpam-4461	263	25	(	(	PUNCT
ejpam-4461	263	26	g	g	PROPN
ejpam-4461	263	27	+	+	NOUN
ejpam-4461	263	28	h	h	NOUN
ejpam-4461	263	29	)	)	PUNCT
ejpam-4461	263	30	\	\	NOUN
ejpam-4461	263	31	s⟩	s⟩	NOUN
ejpam-4461	264	1	=	=	SYM
ejpam-4461	264	2	⟨v	⟨v	NUM
ejpam-4461	264	3	(	(	PUNCT
ejpam-4461	264	4	h	h	NOUN
ejpam-4461	264	5	)	)	PUNCT
ejpam-4461	264	6	\	\	PROPN
ejpam-4461	264	7	s⟩	s⟩	PROPN
ejpam-4461	264	8	,	,	PUNCT
ejpam-4461	264	9	which	which	PRON
ejpam-4461	264	10	is	be	AUX
ejpam-4461	264	11	connected	connect	VERB
ejpam-4461	264	12	by	by	ADP
ejpam-4461	264	13	(	(	PUNCT
ejpam-4461	264	14	iii)(a	iii)(a	PROPN
ejpam-4461	264	15	)	)	PUNCT
ejpam-4461	264	16	.	.	PUNCT
ejpam-4461	265	1	similarly	similarly	ADV
ejpam-4461	265	2	,	,	PUNCT
ejpam-4461	265	3	if	if	SCONJ
ejpam-4461	265	4	(	(	PUNCT
ejpam-4461	265	5	iii)(b	iii)(b	ADJ
ejpam-4461	265	6	)	)	PUNCT
ejpam-4461	265	7	holds	hold	VERB
ejpam-4461	265	8	,	,	PUNCT
ejpam-4461	265	9	then	then	ADV
ejpam-4461	265	10	s	s	VERB
ejpam-4461	265	11	is	be	AUX
ejpam-4461	265	12	an	an	DET
ejpam-4461	265	13	outer	outer	ADV
ejpam-4461	265	14	-	-	PUNCT
ejpam-4461	265	15	connected	connect	VERB
ejpam-4461	265	16	semitotal	semitotal	ADJ
ejpam-4461	265	17	dominating	dominating	NOUN
ejpam-4461	265	18	set	set	NOUN
ejpam-4461	265	19	of	of	ADP
ejpam-4461	265	20	g+h	g+h	PROPN
ejpam-4461	265	21	.	.	PUNCT
ejpam-4461	266	1	following	follow	VERB
ejpam-4461	266	2	similar	similar	ADJ
ejpam-4461	266	3	arguments	argument	NOUN
ejpam-4461	266	4	as	as	ADP
ejpam-4461	266	5	above	above	ADV
ejpam-4461	266	6	,	,	PUNCT
ejpam-4461	266	7	if	if	SCONJ
ejpam-4461	266	8	(	(	PUNCT
ejpam-4461	266	9	iii)(c	iii)(c	NOUN
ejpam-4461	266	10	)	)	PUNCT
ejpam-4461	266	11	holds	hold	VERB
ejpam-4461	266	12	then	then	ADV
ejpam-4461	266	13	s	s	VERB
ejpam-4461	266	14	is	be	AUX
ejpam-4461	266	15	an	an	DET
ejpam-4461	266	16	outer	outer	ADV
ejpam-4461	266	17	-	-	PUNCT
ejpam-4461	266	18	connected	connect	VERB
ejpam-4461	266	19	semitotal	semitotal	ADJ
ejpam-4461	266	20	dominating	dominating	NOUN
ejpam-4461	266	21	set	set	NOUN
ejpam-4461	266	22	of	of	ADP
ejpam-4461	266	23	g+h	g+h	PROPN
ejpam-4461	266	24	.	.	PUNCT
ejpam-4461	267	1	corollary	corollary	ADJ
ejpam-4461	267	2	1	1	NUM
ejpam-4461	267	3	.	.	PUNCT
ejpam-4461	268	1	for	for	ADP
ejpam-4461	268	2	all	all	DET
ejpam-4461	268	3	nontrivial	nontrivial	ADJ
ejpam-4461	268	4	graphs	graph	NOUN
ejpam-4461	268	5	g	g	NOUN
ejpam-4461	268	6	and	and	CCONJ
ejpam-4461	268	7	h	h	NOUN
ejpam-4461	268	8	,	,	PUNCT
ejpam-4461	268	9	γ̃t2(g+h	γ̃t2(g+h	NOUN
ejpam-4461	268	10	)	)	PUNCT
ejpam-4461	269	1	=	=	SYM
ejpam-4461	269	2	2	2	X
ejpam-4461	269	3	.	.	X
ejpam-4461	269	4	proof	proof	NOUN
ejpam-4461	269	5	.	.	PUNCT
ejpam-4461	270	1	pick	pick	VERB
ejpam-4461	270	2	u	u	PRON
ejpam-4461	270	3	∈	∈	PROPN
ejpam-4461	270	4	v	v	ADP
ejpam-4461	270	5	(	(	PUNCT
ejpam-4461	270	6	g	g	NOUN
ejpam-4461	270	7	)	)	PUNCT
ejpam-4461	270	8	and	and	CCONJ
ejpam-4461	270	9	v	v	ADP
ejpam-4461	270	10	∈	∈	PROPN
ejpam-4461	270	11	v	v	NOUN
ejpam-4461	270	12	(	(	PUNCT
ejpam-4461	270	13	h	h	NOUN
ejpam-4461	270	14	)	)	PUNCT
ejpam-4461	270	15	.	.	PUNCT
ejpam-4461	271	1	by	by	ADP
ejpam-4461	271	2	theorem	theorem	NOUN
ejpam-4461	271	3	2	2	NUM
ejpam-4461	271	4	,	,	PUNCT
ejpam-4461	271	5	s	s	PART
ejpam-4461	271	6	=	=	PUNCT
ejpam-4461	271	7	{	{	PUNCT
ejpam-4461	271	8	u	u	NOUN
ejpam-4461	271	9	,	,	PUNCT
ejpam-4461	271	10	v	v	NOUN
ejpam-4461	271	11	}	}	PUNCT
ejpam-4461	271	12	is	be	AUX
ejpam-4461	271	13	an	an	DET
ejpam-4461	271	14	outerconnected	outerconnected	ADJ
ejpam-4461	271	15	semitotal	semitotal	ADJ
ejpam-4461	271	16	dominating	dominating	NOUN
ejpam-4461	271	17	set	set	NOUN
ejpam-4461	271	18	of	of	ADP
ejpam-4461	271	19	g	g	PROPN
ejpam-4461	271	20	+	+	PROPN
ejpam-4461	271	21	h.	h.	PROPN
ejpam-4461	272	1	thus	thus	ADV
ejpam-4461	272	2	,	,	PUNCT
ejpam-4461	272	3	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	272	4	+	+	NUM
ejpam-4461	272	5	h	h	NOUN
ejpam-4461	272	6	)	)	PUNCT
ejpam-4461	272	7	≤	≤	NUM
ejpam-4461	272	8	2	2	NUM
ejpam-4461	272	9	.	.	PUNCT
ejpam-4461	273	1	finally	finally	ADV
ejpam-4461	273	2	,	,	PUNCT
ejpam-4461	273	3	by	by	ADP
ejpam-4461	273	4	(	(	PUNCT
ejpam-4461	273	5	1	1	NUM
ejpam-4461	273	6	)	)	PUNCT
ejpam-4461	273	7	,	,	PUNCT
ejpam-4461	273	8	γ̃t2(g+h	γ̃t2(g+h	NOUN
ejpam-4461	273	9	)	)	PUNCT
ejpam-4461	273	10	=	=	SYM
ejpam-4461	273	11	2	2	X
ejpam-4461	273	12	.	.	X
ejpam-4461	273	13	theorem	theorem	NOUN
ejpam-4461	273	14	3	3	X
ejpam-4461	273	15	.	.	PUNCT
ejpam-4461	274	1	let	let	VERB
ejpam-4461	274	2	g	g	PRON
ejpam-4461	274	3	be	be	AUX
ejpam-4461	274	4	a	a	DET
ejpam-4461	274	5	nontrivial	nontrivial	ADJ
ejpam-4461	274	6	connected	connect	VERB
ejpam-4461	274	7	graph	graph	NOUN
ejpam-4461	274	8	and	and	CCONJ
ejpam-4461	274	9	s	s	VERB
ejpam-4461	274	10	⊆	⊆	NUM
ejpam-4461	274	11	v	v	NOUN
ejpam-4461	274	12	(	(	PUNCT
ejpam-4461	274	13	g	g	PROPN
ejpam-4461	274	14	◦	◦	NOUN
ejpam-4461	274	15	k1	k1	NOUN
ejpam-4461	274	16	)	)	PUNCT
ejpam-4461	274	17	.	.	PUNCT
ejpam-4461	275	1	then	then	ADV
ejpam-4461	275	2	s	s	VERB
ejpam-4461	275	3	is	be	AUX
ejpam-4461	275	4	an	an	DET
ejpam-4461	275	5	outer	outer	ADV
ejpam-4461	275	6	-	-	PUNCT
ejpam-4461	275	7	connected	connect	VERB
ejpam-4461	275	8	semitotal	semitotal	ADJ
ejpam-4461	275	9	dominating	dominating	NOUN
ejpam-4461	275	10	set	set	NOUN
ejpam-4461	275	11	of	of	ADP
ejpam-4461	275	12	g	g	NOUN
ejpam-4461	275	13	◦	◦	NOUN
ejpam-4461	275	14	k1	k1	NOUN
ejpam-4461	275	15	if	if	SCONJ
ejpam-4461	275	16	and	and	CCONJ
ejpam-4461	275	17	only	only	ADV
ejpam-4461	275	18	if	if	SCONJ
ejpam-4461	275	19	one	one	NUM
ejpam-4461	275	20	of	of	ADP
ejpam-4461	275	21	the	the	DET
ejpam-4461	275	22	following	following	NOUN
ejpam-4461	275	23	holds	hold	VERB
ejpam-4461	275	24	for	for	ADP
ejpam-4461	275	25	s	s	PRON
ejpam-4461	275	26	:	:	PUNCT
ejpam-4461	275	27	(	(	PUNCT
ejpam-4461	275	28	i	i	NOUN
ejpam-4461	275	29	)	)	PUNCT
ejpam-4461	275	30	s	s	PART
ejpam-4461	275	31	=	=	SYM
ejpam-4461	275	32	v	v	NOUN
ejpam-4461	275	33	(	(	PUNCT
ejpam-4461	275	34	g	g	PROPN
ejpam-4461	275	35	◦	◦	NOUN
ejpam-4461	275	36	k1	k1	NOUN
ejpam-4461	275	37	)	)	PUNCT
ejpam-4461	275	38	\	\	PROPN
ejpam-4461	275	39	v	v	X
ejpam-4461	275	40	(	(	PUNCT
ejpam-4461	275	41	kv	kv	PROPN
ejpam-4461	275	42	1	1	NUM
ejpam-4461	275	43	)	)	PUNCT
ejpam-4461	275	44	for	for	ADP
ejpam-4461	275	45	some	some	DET
ejpam-4461	275	46	v	v	ADP
ejpam-4461	275	47	∈	∈	PROPN
ejpam-4461	275	48	v	v	NOUN
ejpam-4461	275	49	(	(	PUNCT
ejpam-4461	275	50	g	g	NOUN
ejpam-4461	275	51	)	)	PUNCT
ejpam-4461	275	52	;	;	PUNCT
ejpam-4461	275	53	(	(	PUNCT
ejpam-4461	275	54	ii	ii	NOUN
ejpam-4461	275	55	)	)	PUNCT
ejpam-4461	275	56	s	s	PART
ejpam-4461	275	57	=	=	PUNCT
ejpam-4461	275	58	a∪	a∪	PROPN
ejpam-4461	275	59	(	(	PUNCT
ejpam-4461	275	60	∪v∈v	∪v∈v	X
ejpam-4461	275	61	(	(	PUNCT
ejpam-4461	275	62	g)v	g)v	X
ejpam-4461	275	63	(	(	PUNCT
ejpam-4461	275	64	kv	kv	PROPN
ejpam-4461	275	65	1	1	NUM
ejpam-4461	275	66	)	)	PUNCT
ejpam-4461	275	67	)	)	PUNCT
ejpam-4461	275	68	,	,	PUNCT
ejpam-4461	275	69	where	where	SCONJ
ejpam-4461	275	70	a	a	DET
ejpam-4461	275	71	⊆	⊆	NUM
ejpam-4461	275	72	v	v	NOUN
ejpam-4461	275	73	(	(	PUNCT
ejpam-4461	275	74	g	g	NOUN
ejpam-4461	275	75	)	)	PUNCT
ejpam-4461	275	76	is	be	AUX
ejpam-4461	275	77	an	an	DET
ejpam-4461	275	78	outer	outer	ADV
ejpam-4461	275	79	-	-	PUNCT
ejpam-4461	275	80	connected	connect	VERB
ejpam-4461	275	81	dominating	dominating	NOUN
ejpam-4461	275	82	set	set	NOUN
ejpam-4461	275	83	of	of	ADP
ejpam-4461	275	84	g.	g.	PROPN
ejpam-4461	275	85	a.	a.	PROPN
ejpam-4461	275	86	aradais	aradais	PROPN
ejpam-4461	275	87	,	,	PUNCT
ejpam-4461	275	88	f.	f.	PROPN
ejpam-4461	275	89	jamil	jamil	PROPN
ejpam-4461	275	90	/	/	SYM
ejpam-4461	275	91	eur	eur	PROPN
ejpam-4461	275	92	.	.	PUNCT
ejpam-4461	276	1	j.	j.	PROPN
ejpam-4461	276	2	pure	pure	PROPN
ejpam-4461	276	3	appl	appl	PROPN
ejpam-4461	276	4	.	.	PROPN
ejpam-4461	276	5	math	math	PROPN
ejpam-4461	276	6	,	,	PUNCT
ejpam-4461	276	7	15	15	NUM
ejpam-4461	276	8	(	(	PUNCT
ejpam-4461	276	9	3	3	NUM
ejpam-4461	276	10	)	)	PUNCT
ejpam-4461	276	11	(	(	PUNCT
ejpam-4461	276	12	2022	2022	NUM
ejpam-4461	276	13	)	)	PUNCT
ejpam-4461	276	14	,	,	PUNCT
ejpam-4461	276	15	1265	1265	NUM
ejpam-4461	276	16	-	-	SYM
ejpam-4461	276	17	1279	1279	NUM
ejpam-4461	276	18	1273	1273	NUM
ejpam-4461	276	19	proof	proof	NOUN
ejpam-4461	276	20	.	.	PUNCT
ejpam-4461	277	1	put	put	VERB
ejpam-4461	277	2	v	v	NOUN
ejpam-4461	277	3	(	(	PUNCT
ejpam-4461	277	4	k1	k1	NOUN
ejpam-4461	277	5	)	)	PUNCT
ejpam-4461	277	6	=	=	SYM
ejpam-4461	277	7	{	{	PUNCT
ejpam-4461	277	8	x	x	NOUN
ejpam-4461	277	9	}	}	PUNCT
ejpam-4461	277	10	.	.	PUNCT
ejpam-4461	278	1	then	then	ADV
ejpam-4461	278	2	v	v	X
ejpam-4461	278	3	(	(	PUNCT
ejpam-4461	278	4	kv	kv	PROPN
ejpam-4461	278	5	1	1	NUM
ejpam-4461	278	6	)	)	PUNCT
ejpam-4461	278	7	=	=	PRON
ejpam-4461	278	8	{	{	PUNCT
ejpam-4461	278	9	xv	xv	PROPN
ejpam-4461	278	10	}	}	PUNCT
ejpam-4461	278	11	.	.	PUNCT
ejpam-4461	279	1	assume	assume	VERB
ejpam-4461	279	2	that	that	SCONJ
ejpam-4461	279	3	s	s	VERB
ejpam-4461	279	4	is	be	AUX
ejpam-4461	279	5	an	an	DET
ejpam-4461	279	6	outer	outer	ADV
ejpam-4461	279	7	-	-	PUNCT
ejpam-4461	279	8	connected	connect	VERB
ejpam-4461	279	9	semitotal	semitotal	ADJ
ejpam-4461	279	10	dominating	dominating	NOUN
ejpam-4461	279	11	set	set	NOUN
ejpam-4461	279	12	of	of	ADP
ejpam-4461	279	13	g	g	PROPN
ejpam-4461	279	14	◦	◦	NOUN
ejpam-4461	279	15	k1	k1	NOUN
ejpam-4461	279	16	.	.	PUNCT
ejpam-4461	280	1	we	we	PRON
ejpam-4461	280	2	consider	consider	VERB
ejpam-4461	280	3	two	two	NUM
ejpam-4461	280	4	cases	case	NOUN
ejpam-4461	280	5	:	:	PUNCT
ejpam-4461	280	6	case	case	NOUN
ejpam-4461	280	7	1	1	NUM
ejpam-4461	280	8	:	:	PUNCT
ejpam-4461	280	9	suppose	suppose	VERB
ejpam-4461	280	10	that	that	SCONJ
ejpam-4461	280	11	xv	xv	PROPN
ejpam-4461	280	12	/∈	/∈	PROPN
ejpam-4461	280	13	s	s	PART
ejpam-4461	280	14	for	for	ADP
ejpam-4461	280	15	some	some	DET
ejpam-4461	280	16	v	v	ADP
ejpam-4461	280	17	∈	∈	PROPN
ejpam-4461	280	18	v	v	NOUN
ejpam-4461	280	19	(	(	PUNCT
ejpam-4461	280	20	g	g	NOUN
ejpam-4461	280	21	)	)	PUNCT
ejpam-4461	280	22	.	.	PUNCT
ejpam-4461	281	1	since	since	SCONJ
ejpam-4461	281	2	s	s	PROPN
ejpam-4461	281	3	is	be	AUX
ejpam-4461	281	4	a	a	DET
ejpam-4461	281	5	dominating	dominating	NOUN
ejpam-4461	281	6	set	set	NOUN
ejpam-4461	281	7	of	of	ADP
ejpam-4461	281	8	g	g	PROPN
ejpam-4461	281	9	◦	◦	NOUN
ejpam-4461	281	10	k1	k1	NOUN
ejpam-4461	281	11	,	,	PUNCT
ejpam-4461	281	12	v	v	ADP
ejpam-4461	281	13	∈	∈	NOUN
ejpam-4461	281	14	s.	s.	PROPN
ejpam-4461	281	15	since	since	SCONJ
ejpam-4461	281	16	xv	xv	PROPN
ejpam-4461	281	17	∈	∈	PROPN
ejpam-4461	281	18	v	v	PROPN
ejpam-4461	281	19	(	(	PUNCT
ejpam-4461	281	20	g	g	PROPN
ejpam-4461	281	21	◦	◦	NOUN
ejpam-4461	281	22	k1	k1	NOUN
ejpam-4461	281	23	)	)	PUNCT
ejpam-4461	281	24	\s	\s	NOUN
ejpam-4461	281	25	and	and	CCONJ
ejpam-4461	281	26	⟨v	⟨v	NUM
ejpam-4461	281	27	(	(	PUNCT
ejpam-4461	281	28	g	g	PROPN
ejpam-4461	281	29	◦	◦	NOUN
ejpam-4461	281	30	k1	k1	NOUN
ejpam-4461	281	31	)	)	PUNCT
ejpam-4461	282	1	\s⟩	\s⟩	PROPN
ejpam-4461	282	2	is	be	AUX
ejpam-4461	282	3	connected	connect	VERB
ejpam-4461	282	4	,	,	PUNCT
ejpam-4461	282	5	v	v	INTJ
ejpam-4461	282	6	(	(	PUNCT
ejpam-4461	282	7	g	g	PROPN
ejpam-4461	282	8	◦	◦	NOUN
ejpam-4461	282	9	k1	k1	NOUN
ejpam-4461	282	10	)	)	PUNCT
ejpam-4461	282	11	\s	\s	NOUN
ejpam-4461	282	12	=	=	PUNCT
ejpam-4461	282	13	{	{	PUNCT
ejpam-4461	282	14	xv	xv	PROPN
ejpam-4461	282	15	}	}	PUNCT
ejpam-4461	282	16	.	.	PUNCT
ejpam-4461	283	1	that	that	PRON
ejpam-4461	283	2	is	be	AUX
ejpam-4461	283	3	,	,	PUNCT
ejpam-4461	283	4	s	s	PART
ejpam-4461	283	5	=	=	SYM
ejpam-4461	283	6	v	v	X
ejpam-4461	283	7	(	(	PUNCT
ejpam-4461	283	8	g	g	PROPN
ejpam-4461	283	9	◦	◦	NOUN
ejpam-4461	283	10	k1	k1	NOUN
ejpam-4461	283	11	)	)	PUNCT
ejpam-4461	283	12	\	\	NOUN
ejpam-4461	283	13	{	{	PUNCT
ejpam-4461	283	14	xv	xv	PROPN
ejpam-4461	283	15	}	}	PUNCT
ejpam-4461	283	16	.	.	PUNCT
ejpam-4461	284	1	in	in	ADP
ejpam-4461	284	2	this	this	DET
ejpam-4461	284	3	case	case	NOUN
ejpam-4461	284	4	,	,	PUNCT
ejpam-4461	284	5	(	(	PUNCT
ejpam-4461	284	6	i	i	NOUN
ejpam-4461	284	7	)	)	PUNCT
ejpam-4461	284	8	holds	hold	VERB
ejpam-4461	284	9	.	.	PUNCT
ejpam-4461	285	1	case	case	NOUN
ejpam-4461	285	2	2	2	NUM
ejpam-4461	285	3	:	:	PUNCT
ejpam-4461	285	4	suppose	suppose	VERB
ejpam-4461	285	5	that	that	SCONJ
ejpam-4461	285	6	xv	xv	PROPN
ejpam-4461	285	7	∈	∈	PROPN
ejpam-4461	285	8	s	s	PROPN
ejpam-4461	285	9	for	for	ADP
ejpam-4461	285	10	all	all	PRON
ejpam-4461	285	11	v	v	ADP
ejpam-4461	285	12	∈	∈	NUM
ejpam-4461	285	13	v	v	NOUN
ejpam-4461	285	14	(	(	PUNCT
ejpam-4461	285	15	g	g	NOUN
ejpam-4461	285	16	)	)	PUNCT
ejpam-4461	285	17	.	.	PUNCT
ejpam-4461	286	1	define	define	VERB
ejpam-4461	286	2	a	a	DET
ejpam-4461	286	3	=	=	SYM
ejpam-4461	286	4	s	s	NOUN
ejpam-4461	286	5	∩	∩	ADJ
ejpam-4461	286	6	v	v	X
ejpam-4461	286	7	(	(	PUNCT
ejpam-4461	286	8	g	g	NOUN
ejpam-4461	286	9	)	)	PUNCT
ejpam-4461	286	10	.	.	PUNCT
ejpam-4461	287	1	then	then	ADV
ejpam-4461	287	2	s	s	VERB
ejpam-4461	287	3	=	=	PUNCT
ejpam-4461	287	4	a	a	DET
ejpam-4461	287	5	∪	∪	X
ejpam-4461	287	6	(	(	PUNCT
ejpam-4461	287	7	∪v∈v	∪v∈v	X
ejpam-4461	287	8	(	(	PUNCT
ejpam-4461	287	9	g){xv	g){xv	NOUN
ejpam-4461	287	10	}	}	PUNCT
ejpam-4461	287	11	)	)	PUNCT
ejpam-4461	287	12	.	.	PUNCT
ejpam-4461	288	1	we	we	PRON
ejpam-4461	288	2	claim	claim	VERB
ejpam-4461	288	3	that	that	SCONJ
ejpam-4461	288	4	a	a	PRON
ejpam-4461	288	5	is	be	AUX
ejpam-4461	288	6	an	an	DET
ejpam-4461	288	7	outer	outer	ADV
ejpam-4461	288	8	-	-	PUNCT
ejpam-4461	288	9	connected	connect	VERB
ejpam-4461	288	10	dominating	dominating	NOUN
ejpam-4461	288	11	set	set	NOUN
ejpam-4461	288	12	of	of	ADP
ejpam-4461	288	13	g.	g.	PROPN
ejpam-4461	288	14	first	first	ADV
ejpam-4461	288	15	,	,	PUNCT
ejpam-4461	288	16	let	let	VERB
ejpam-4461	288	17	v	v	NUM
ejpam-4461	288	18	∈	∈	PROPN
ejpam-4461	288	19	v	v	NOUN
ejpam-4461	288	20	(	(	PUNCT
ejpam-4461	288	21	g)\a	g)\a	NOUN
ejpam-4461	288	22	.	.	PUNCT
ejpam-4461	289	1	then	then	ADV
ejpam-4461	289	2	xv	xv	PROPN
ejpam-4461	289	3	∈	∈	PROPN
ejpam-4461	289	4	s.	s.	PROPN
ejpam-4461	289	5	since	since	SCONJ
ejpam-4461	289	6	s	s	PROPN
ejpam-4461	289	7	is	be	AUX
ejpam-4461	289	8	a	a	DET
ejpam-4461	289	9	semitotal	semitotal	ADJ
ejpam-4461	289	10	dominating	dominating	NOUN
ejpam-4461	289	11	set	set	NOUN
ejpam-4461	289	12	of	of	ADP
ejpam-4461	289	13	g	g	PROPN
ejpam-4461	289	14	◦	◦	NOUN
ejpam-4461	289	15	k1	k1	NOUN
ejpam-4461	289	16	,	,	PUNCT
ejpam-4461	289	17	there	there	PRON
ejpam-4461	289	18	exists	exist	VERB
ejpam-4461	289	19	u	u	PROPN
ejpam-4461	289	20	∈	∈	PROPN
ejpam-4461	289	21	s	s	X
ejpam-4461	289	22	for	for	ADP
ejpam-4461	289	23	which	which	PRON
ejpam-4461	289	24	dg	dg	VERB
ejpam-4461	289	25	◦	◦	NOUN
ejpam-4461	289	26	k1(x	k1(x	NOUN
ejpam-4461	289	27	v	v	NOUN
ejpam-4461	289	28	,	,	PUNCT
ejpam-4461	289	29	u	u	NOUN
ejpam-4461	289	30	)	)	PUNCT
ejpam-4461	289	31	≤	≤	NUM
ejpam-4461	289	32	2	2	NUM
ejpam-4461	289	33	.	.	PUNCT
ejpam-4461	290	1	because	because	SCONJ
ejpam-4461	290	2	v	v	NUM
ejpam-4461	290	3	/∈	/∈	SYM
ejpam-4461	290	4	s	s	X
ejpam-4461	290	5	,	,	PUNCT
ejpam-4461	290	6	u	u	PROPN
ejpam-4461	290	7	∈	∈	PROPN
ejpam-4461	290	8	a	a	DET
ejpam-4461	290	9	∩ng(v	∩ng(v	PROPN
ejpam-4461	290	10	)	)	PUNCT
ejpam-4461	290	11	.	.	PUNCT
ejpam-4461	291	1	since	since	SCONJ
ejpam-4461	291	2	v	v	NOUN
ejpam-4461	291	3	is	be	AUX
ejpam-4461	291	4	arbitrary	arbitrary	ADJ
ejpam-4461	291	5	,	,	PUNCT
ejpam-4461	291	6	a	a	PRON
ejpam-4461	291	7	is	be	AUX
ejpam-4461	291	8	a	a	DET
ejpam-4461	291	9	dominating	dominating	NOUN
ejpam-4461	291	10	set	set	NOUN
ejpam-4461	291	11	of	of	ADP
ejpam-4461	291	12	g.	g.	PROPN
ejpam-4461	291	13	note	note	VERB
ejpam-4461	291	14	further	far	ADV
ejpam-4461	291	15	that	that	SCONJ
ejpam-4461	291	16	,	,	PUNCT
ejpam-4461	291	17	v	v	X
ejpam-4461	291	18	(	(	PUNCT
ejpam-4461	291	19	g	g	NOUN
ejpam-4461	291	20	)	)	PUNCT
ejpam-4461	291	21	\	\	NOUN
ejpam-4461	292	1	a	a	DET
ejpam-4461	292	2	=	=	SYM
ejpam-4461	292	3	v	v	NOUN
ejpam-4461	292	4	(	(	PUNCT
ejpam-4461	292	5	g	g	PROPN
ejpam-4461	292	6	◦	◦	NOUN
ejpam-4461	292	7	k1	k1	NOUN
ejpam-4461	292	8	)	)	PUNCT
ejpam-4461	292	9	\	\	PROPN
ejpam-4461	292	10	s.	s.	PROPN
ejpam-4461	292	11	thus	thus	ADV
ejpam-4461	292	12	,	,	PUNCT
ejpam-4461	292	13	a	a	PRON
ejpam-4461	292	14	is	be	AUX
ejpam-4461	292	15	an	an	DET
ejpam-4461	292	16	outer	outer	ADV
ejpam-4461	292	17	-	-	PUNCT
ejpam-4461	292	18	connected	connect	VERB
ejpam-4461	292	19	dominating	dominating	NOUN
ejpam-4461	292	20	set	set	NOUN
ejpam-4461	292	21	of	of	ADP
ejpam-4461	292	22	g.	g.	PROPN
ejpam-4461	292	23	in	in	ADP
ejpam-4461	292	24	this	this	DET
ejpam-4461	292	25	case	case	NOUN
ejpam-4461	292	26	,	,	PUNCT
ejpam-4461	292	27	(	(	PUNCT
ejpam-4461	292	28	ii	ii	NOUN
ejpam-4461	292	29	)	)	PUNCT
ejpam-4461	292	30	holds	hold	VERB
ejpam-4461	292	31	.	.	PUNCT
ejpam-4461	293	1	conversely	conversely	ADV
ejpam-4461	293	2	,	,	PUNCT
ejpam-4461	293	3	obviously	obviously	ADV
ejpam-4461	293	4	,	,	PUNCT
ejpam-4461	293	5	if	if	SCONJ
ejpam-4461	293	6	condition	condition	NOUN
ejpam-4461	293	7	(	(	PUNCT
ejpam-4461	293	8	i	i	NOUN
ejpam-4461	293	9	)	)	PUNCT
ejpam-4461	293	10	holds	hold	VERB
ejpam-4461	293	11	for	for	ADP
ejpam-4461	293	12	s	s	PROPN
ejpam-4461	293	13	,	,	PUNCT
ejpam-4461	293	14	then	then	ADV
ejpam-4461	293	15	s	s	VERB
ejpam-4461	293	16	is	be	AUX
ejpam-4461	293	17	an	an	DET
ejpam-4461	293	18	outer	outer	ADV
ejpam-4461	293	19	-	-	PUNCT
ejpam-4461	293	20	connected	connect	VERB
ejpam-4461	293	21	semitotal	semitotal	ADJ
ejpam-4461	293	22	dominating	dominating	NOUN
ejpam-4461	293	23	set	set	NOUN
ejpam-4461	293	24	of	of	ADP
ejpam-4461	293	25	g	g	PROPN
ejpam-4461	293	26	◦	◦	NOUN
ejpam-4461	293	27	k1	k1	NOUN
ejpam-4461	293	28	.	.	PUNCT
ejpam-4461	294	1	now	now	ADV
ejpam-4461	294	2	,	,	PUNCT
ejpam-4461	294	3	suppose	suppose	VERB
ejpam-4461	294	4	that	that	SCONJ
ejpam-4461	294	5	condition	condition	NOUN
ejpam-4461	294	6	(	(	PUNCT
ejpam-4461	294	7	ii	ii	NOUN
ejpam-4461	294	8	)	)	PUNCT
ejpam-4461	294	9	holds	hold	VERB
ejpam-4461	294	10	for	for	ADP
ejpam-4461	294	11	s.	s.	PROPN
ejpam-4461	294	12	since	since	SCONJ
ejpam-4461	294	13	∪v∈v	∪v∈v	X
ejpam-4461	294	14	(	(	PUNCT
ejpam-4461	294	15	g){xv	g){xv	NOUN
ejpam-4461	294	16	}	}	PUNCT
ejpam-4461	294	17	is	be	AUX
ejpam-4461	294	18	a	a	DET
ejpam-4461	294	19	dominating	dominating	NOUN
ejpam-4461	294	20	set	set	NOUN
ejpam-4461	294	21	of	of	ADP
ejpam-4461	294	22	g	g	PROPN
ejpam-4461	294	23	◦	◦	NOUN
ejpam-4461	294	24	k1	k1	NOUN
ejpam-4461	294	25	,	,	PUNCT
ejpam-4461	294	26	s	s	PART
ejpam-4461	294	27	is	be	AUX
ejpam-4461	294	28	a	a	DET
ejpam-4461	294	29	dominating	dominating	NOUN
ejpam-4461	294	30	set	set	NOUN
ejpam-4461	294	31	of	of	ADP
ejpam-4461	294	32	g	g	PROPN
ejpam-4461	294	33	◦	◦	NOUN
ejpam-4461	294	34	k1	k1	NOUN
ejpam-4461	294	35	.	.	PUNCT
ejpam-4461	295	1	let	let	VERB
ejpam-4461	295	2	u	u	PRON
ejpam-4461	295	3	∈	∈	PROPN
ejpam-4461	295	4	s.	s.	PROPN
ejpam-4461	295	5	we	we	PRON
ejpam-4461	295	6	consider	consider	VERB
ejpam-4461	295	7	the	the	DET
ejpam-4461	295	8	following	follow	VERB
ejpam-4461	295	9	cases	case	NOUN
ejpam-4461	295	10	:	:	PUNCT
ejpam-4461	295	11	case	case	NOUN
ejpam-4461	295	12	1	1	NUM
ejpam-4461	295	13	:	:	PUNCT
ejpam-4461	295	14	suppose	suppose	VERB
ejpam-4461	295	15	that	that	SCONJ
ejpam-4461	295	16	u	u	PRON
ejpam-4461	295	17	=	=	X
ejpam-4461	295	18	xv	xv	PROPN
ejpam-4461	295	19	for	for	ADP
ejpam-4461	295	20	some	some	DET
ejpam-4461	295	21	v	v	ADP
ejpam-4461	295	22	∈	∈	PROPN
ejpam-4461	295	23	v	v	NOUN
ejpam-4461	295	24	(	(	PUNCT
ejpam-4461	295	25	g	g	NOUN
ejpam-4461	295	26	)	)	PUNCT
ejpam-4461	295	27	.	.	PUNCT
ejpam-4461	296	1	if	if	SCONJ
ejpam-4461	296	2	v	v	NUM
ejpam-4461	296	3	∈	∈	PROPN
ejpam-4461	296	4	s	s	NOUN
ejpam-4461	296	5	,	,	PUNCT
ejpam-4461	296	6	then	then	ADV
ejpam-4461	296	7	we	we	PRON
ejpam-4461	296	8	pick	pick	VERB
ejpam-4461	296	9	v	v	NOUN
ejpam-4461	296	10	for	for	ADP
ejpam-4461	296	11	dg(u	dg(u	ADJ
ejpam-4461	296	12	,	,	PUNCT
ejpam-4461	296	13	v	v	NOUN
ejpam-4461	296	14	)	)	PUNCT
ejpam-4461	296	15	≤	≤	NOUN
ejpam-4461	296	16	2	2	NUM
ejpam-4461	296	17	.	.	PUNCT
ejpam-4461	296	18	suppose	suppose	VERB
ejpam-4461	296	19	that	that	SCONJ
ejpam-4461	296	20	v	v	NOUN
ejpam-4461	296	21	/∈	/∈	PUNCT
ejpam-4461	296	22	s.	s.	PROPN
ejpam-4461	296	23	since	since	SCONJ
ejpam-4461	296	24	a	a	PRON
ejpam-4461	296	25	is	be	AUX
ejpam-4461	296	26	a	a	DET
ejpam-4461	296	27	dominating	dominating	NOUN
ejpam-4461	296	28	set	set	NOUN
ejpam-4461	296	29	of	of	ADP
ejpam-4461	296	30	g	g	PROPN
ejpam-4461	296	31	and	and	CCONJ
ejpam-4461	296	32	v	v	ADP
ejpam-4461	296	33	∈	∈	PROPN
ejpam-4461	296	34	v	v	NOUN
ejpam-4461	296	35	(	(	PUNCT
ejpam-4461	296	36	g	g	NOUN
ejpam-4461	296	37	)	)	PUNCT
ejpam-4461	296	38	\	\	PROPN
ejpam-4461	297	1	a	a	PRON
ejpam-4461	297	2	,	,	PUNCT
ejpam-4461	297	3	there	there	PRON
ejpam-4461	297	4	exists	exist	VERB
ejpam-4461	297	5	w	w	PROPN
ejpam-4461	297	6	∈	∈	PROPN
ejpam-4461	297	7	a	a	DET
ejpam-4461	297	8	⊆	⊆	NUM
ejpam-4461	297	9	s	s	NOUN
ejpam-4461	297	10	such	such	ADJ
ejpam-4461	297	11	that	that	SCONJ
ejpam-4461	297	12	wv	wv	PROPN
ejpam-4461	297	13	∈	∈	PROPN
ejpam-4461	297	14	e(g	e(g	PROPN
ejpam-4461	297	15	)	)	PUNCT
ejpam-4461	297	16	⊆	⊆	NUM
ejpam-4461	297	17	e(g	e(g	PROPN
ejpam-4461	297	18	◦	◦	NOUN
ejpam-4461	297	19	k1	k1	NOUN
ejpam-4461	297	20	)	)	PUNCT
ejpam-4461	297	21	.	.	PUNCT
ejpam-4461	298	1	since	since	SCONJ
ejpam-4461	298	2	dg	dg	PROPN
ejpam-4461	298	3	◦	◦	NOUN
ejpam-4461	298	4	k1(u	k1(u	PROPN
ejpam-4461	298	5	,	,	PUNCT
ejpam-4461	298	6	w	w	NOUN
ejpam-4461	298	7	)	)	PUNCT
ejpam-4461	298	8	=	=	SYM
ejpam-4461	298	9	2	2	NUM
ejpam-4461	298	10	,	,	PUNCT
ejpam-4461	298	11	w	w	NOUN
ejpam-4461	298	12	is	be	AUX
ejpam-4461	298	13	the	the	DET
ejpam-4461	298	14	desired	desire	VERB
ejpam-4461	298	15	vertex	vertex	NOUN
ejpam-4461	298	16	.	.	PUNCT
ejpam-4461	299	1	case	case	NOUN
ejpam-4461	299	2	2	2	NUM
ejpam-4461	299	3	:	:	PUNCT
ejpam-4461	299	4	suppose	suppose	VERB
ejpam-4461	299	5	that	that	SCONJ
ejpam-4461	299	6	u	u	PROPN
ejpam-4461	299	7	∈	∈	PROPN
ejpam-4461	299	8	v	v	ADP
ejpam-4461	299	9	(	(	PUNCT
ejpam-4461	299	10	g	g	NOUN
ejpam-4461	299	11	)	)	PUNCT
ejpam-4461	299	12	.	.	PUNCT
ejpam-4461	300	1	in	in	ADP
ejpam-4461	300	2	this	this	DET
ejpam-4461	300	3	case	case	NOUN
ejpam-4461	300	4	,	,	PUNCT
ejpam-4461	300	5	we	we	PRON
ejpam-4461	300	6	pick	pick	VERB
ejpam-4461	300	7	xu	xu	PROPN
ejpam-4461	300	8	∈	∈	PROPN
ejpam-4461	300	9	s.	s.	PROPN
ejpam-4461	300	10	note	note	VERB
ejpam-4461	300	11	that	that	SCONJ
ejpam-4461	300	12	uxu	uxu	PROPN
ejpam-4461	300	13	∈	∈	PROPN
ejpam-4461	300	14	e(g	e(g	PROPN
ejpam-4461	300	15	◦	◦	NOUN
ejpam-4461	300	16	k1	k1	NOUN
ejpam-4461	300	17	)	)	PUNCT
ejpam-4461	300	18	.	.	PUNCT
ejpam-4461	301	1	the	the	DET
ejpam-4461	301	2	above	above	ADJ
ejpam-4461	301	3	cases	case	NOUN
ejpam-4461	301	4	show	show	VERB
ejpam-4461	301	5	that	that	SCONJ
ejpam-4461	301	6	s	s	VERB
ejpam-4461	301	7	is	be	AUX
ejpam-4461	301	8	a	a	DET
ejpam-4461	301	9	semitotal	semitotal	ADJ
ejpam-4461	301	10	dominating	dominating	NOUN
ejpam-4461	301	11	set	set	NOUN
ejpam-4461	301	12	of	of	ADP
ejpam-4461	301	13	g	g	PROPN
ejpam-4461	301	14	◦	◦	NOUN
ejpam-4461	301	15	k1	k1	NOUN
ejpam-4461	301	16	.	.	PUNCT
ejpam-4461	302	1	finally	finally	ADV
ejpam-4461	302	2	,	,	PUNCT
ejpam-4461	302	3	since	since	SCONJ
ejpam-4461	302	4	a	a	PRON
ejpam-4461	302	5	is	be	AUX
ejpam-4461	302	6	an	an	DET
ejpam-4461	302	7	outer	outer	ADV
ejpam-4461	302	8	-	-	PUNCT
ejpam-4461	302	9	connected	connect	VERB
ejpam-4461	302	10	dominating	dominating	NOUN
ejpam-4461	302	11	set	set	NOUN
ejpam-4461	302	12	of	of	ADP
ejpam-4461	302	13	g	g	NOUN
ejpam-4461	302	14	,	,	PUNCT
ejpam-4461	302	15	⟨v	⟨v	NOUN
ejpam-4461	302	16	(	(	PUNCT
ejpam-4461	302	17	g	g	NOUN
ejpam-4461	302	18	)	)	PUNCT
ejpam-4461	302	19	\	\	NOUN
ejpam-4461	302	20	a⟩	a⟩	NOUN
ejpam-4461	302	21	=	=	PUNCT
ejpam-4461	302	22	⟨v	⟨v	X
ejpam-4461	302	23	(	(	PUNCT
ejpam-4461	302	24	g	g	PROPN
ejpam-4461	302	25	◦	◦	NOUN
ejpam-4461	302	26	k1	k1	NOUN
ejpam-4461	302	27	)	)	PUNCT
ejpam-4461	302	28	\	\	PROPN
ejpam-4461	302	29	s⟩	s⟩	PROPN
ejpam-4461	302	30	is	be	AUX
ejpam-4461	302	31	connected	connect	VERB
ejpam-4461	302	32	.	.	PUNCT
ejpam-4461	303	1	therefore	therefore	ADV
ejpam-4461	303	2	,	,	PUNCT
ejpam-4461	303	3	s	s	VERB
ejpam-4461	303	4	is	be	AUX
ejpam-4461	303	5	an	an	DET
ejpam-4461	303	6	outer	outer	ADV
ejpam-4461	303	7	-	-	PUNCT
ejpam-4461	303	8	connected	connect	VERB
ejpam-4461	303	9	semitotal	semitotal	ADJ
ejpam-4461	303	10	dominating	dominating	NOUN
ejpam-4461	303	11	set	set	NOUN
ejpam-4461	303	12	of	of	ADP
ejpam-4461	303	13	g	g	PROPN
ejpam-4461	303	14	◦	◦	NOUN
ejpam-4461	303	15	k1	k1	NOUN
ejpam-4461	303	16	.	.	PUNCT
ejpam-4461	304	1	corollary	corollary	ADJ
ejpam-4461	304	2	2	2	NUM
ejpam-4461	304	3	.	.	PUNCT
ejpam-4461	305	1	for	for	ADP
ejpam-4461	305	2	nontrivial	nontrivial	ADJ
ejpam-4461	305	3	connected	connect	VERB
ejpam-4461	305	4	graph	graph	NOUN
ejpam-4461	305	5	g	g	NOUN
ejpam-4461	305	6	of	of	ADP
ejpam-4461	305	7	order	order	NOUN
ejpam-4461	305	8	n	n	CCONJ
ejpam-4461	305	9	,	,	PUNCT
ejpam-4461	305	10	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	305	11	◦	◦	NOUN
ejpam-4461	305	12	k1	k1	NOUN
ejpam-4461	305	13	)	)	PUNCT
ejpam-4461	305	14	=	=	SYM
ejpam-4461	305	15	n+	n+	PUNCT
ejpam-4461	305	16	γ̃(g	γ̃(g	NOUN
ejpam-4461	305	17	)	)	PUNCT
ejpam-4461	305	18	.	.	PUNCT
ejpam-4461	306	1	proof	proof	NOUN
ejpam-4461	306	2	.	.	PUNCT
ejpam-4461	307	1	in	in	ADP
ejpam-4461	307	2	view	view	NOUN
ejpam-4461	307	3	of	of	ADP
ejpam-4461	307	4	theorem	theorem	NOUN
ejpam-4461	307	5	3	3	NUM
ejpam-4461	307	6	,	,	PUNCT
ejpam-4461	307	7	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	307	8	◦	◦	NOUN
ejpam-4461	307	9	k1	k1	NOUN
ejpam-4461	307	10	)	)	PUNCT
ejpam-4461	307	11	=	=	PUNCT
ejpam-4461	307	12	min{2n−	min{2n−	ADJ
ejpam-4461	307	13	1	1	NUM
ejpam-4461	307	14	,	,	PUNCT
ejpam-4461	307	15	n+	n+	AUX
ejpam-4461	307	16	γ̃(g	γ̃(g	NOUN
ejpam-4461	307	17	)	)	PUNCT
ejpam-4461	307	18	}	}	PUNCT
ejpam-4461	307	19	=	=	SYM
ejpam-4461	307	20	n+	n+	PUNCT
ejpam-4461	307	21	γ̃(g	γ̃(g	NOUN
ejpam-4461	307	22	)	)	PUNCT
ejpam-4461	307	23	.	.	PUNCT
ejpam-4461	308	1	theorem	theorem	ADJ
ejpam-4461	308	2	4	4	NUM
ejpam-4461	308	3	.	.	PUNCT
ejpam-4461	309	1	let	let	VERB
ejpam-4461	309	2	g	g	NOUN
ejpam-4461	309	3	and	and	CCONJ
ejpam-4461	309	4	h	h	NOUN
ejpam-4461	309	5	be	be	AUX
ejpam-4461	309	6	nontrivial	nontrivial	ADJ
ejpam-4461	309	7	connected	connected	ADJ
ejpam-4461	309	8	graphs	graph	NOUN
ejpam-4461	309	9	,	,	PUNCT
ejpam-4461	309	10	and	and	CCONJ
ejpam-4461	309	11	let	let	VERB
ejpam-4461	309	12	s	s	PRON
ejpam-4461	309	13	⊆	⊆	NUM
ejpam-4461	309	14	v	v	NOUN
ejpam-4461	309	15	(	(	PUNCT
ejpam-4461	309	16	g	g	PROPN
ejpam-4461	309	17	◦	◦	NOUN
ejpam-4461	309	18	h	h	NOUN
ejpam-4461	309	19	)	)	PUNCT
ejpam-4461	309	20	.	.	PUNCT
ejpam-4461	310	1	then	then	ADV
ejpam-4461	310	2	s	s	VERB
ejpam-4461	310	3	is	be	AUX
ejpam-4461	310	4	an	an	DET
ejpam-4461	310	5	outer	outer	ADV
ejpam-4461	310	6	-	-	PUNCT
ejpam-4461	310	7	connected	connect	VERB
ejpam-4461	310	8	semitotal	semitotal	ADJ
ejpam-4461	310	9	dominating	dominating	NOUN
ejpam-4461	310	10	set	set	NOUN
ejpam-4461	310	11	of	of	ADP
ejpam-4461	310	12	g	g	PROPN
ejpam-4461	310	13	◦	◦	NOUN
ejpam-4461	310	14	h	h	NOUN
ejpam-4461	310	15	if	if	SCONJ
ejpam-4461	311	1	and	and	CCONJ
ejpam-4461	311	2	only	only	ADV
ejpam-4461	311	3	if	if	SCONJ
ejpam-4461	311	4	one	one	NUM
ejpam-4461	311	5	of	of	ADP
ejpam-4461	311	6	the	the	DET
ejpam-4461	311	7	following	following	NOUN
ejpam-4461	311	8	holds	hold	VERB
ejpam-4461	311	9	for	for	ADP
ejpam-4461	311	10	s	s	PRON
ejpam-4461	311	11	:	:	PUNCT
ejpam-4461	311	12	a.	a.	PROPN
ejpam-4461	311	13	aradais	aradais	PROPN
ejpam-4461	311	14	,	,	PUNCT
ejpam-4461	311	15	f.	f.	PROPN
ejpam-4461	311	16	jamil	jamil	PROPN
ejpam-4461	311	17	/	/	SYM
ejpam-4461	311	18	eur	eur	PROPN
ejpam-4461	311	19	.	.	PUNCT
ejpam-4461	312	1	j.	j.	PROPN
ejpam-4461	312	2	pure	pure	PROPN
ejpam-4461	312	3	appl	appl	PROPN
ejpam-4461	312	4	.	.	PROPN
ejpam-4461	312	5	math	math	PROPN
ejpam-4461	312	6	,	,	PUNCT
ejpam-4461	312	7	15	15	NUM
ejpam-4461	312	8	(	(	PUNCT
ejpam-4461	312	9	3	3	NUM
ejpam-4461	312	10	)	)	PUNCT
ejpam-4461	312	11	(	(	PUNCT
ejpam-4461	312	12	2022	2022	NUM
ejpam-4461	312	13	)	)	PUNCT
ejpam-4461	312	14	,	,	PUNCT
ejpam-4461	312	15	1265	1265	NUM
ejpam-4461	312	16	-	-	SYM
ejpam-4461	312	17	1279	1279	NUM
ejpam-4461	312	18	1274	1274	NUM
ejpam-4461	312	19	(	(	PUNCT
ejpam-4461	312	20	i	i	NOUN
ejpam-4461	312	21	)	)	PUNCT
ejpam-4461	312	22	there	there	PRON
ejpam-4461	312	23	exists	exist	VERB
ejpam-4461	312	24	v	v	ADP
ejpam-4461	312	25	∈	∈	PROPN
ejpam-4461	312	26	v	v	NOUN
ejpam-4461	312	27	(	(	PUNCT
ejpam-4461	312	28	g	g	NOUN
ejpam-4461	312	29	)	)	PUNCT
ejpam-4461	312	30	and	and	CCONJ
ejpam-4461	312	31	b	b	X
ejpam-4461	312	32	⊆	⊆	NUM
ejpam-4461	312	33	v	v	NOUN
ejpam-4461	312	34	(	(	PUNCT
ejpam-4461	312	35	hv	hv	NOUN
ejpam-4461	312	36	)	)	PUNCT
ejpam-4461	312	37	such	such	ADJ
ejpam-4461	313	1	that	that	PRON
ejpam-4461	313	2	s	s	PART
ejpam-4461	313	3	=	=	X
ejpam-4461	313	4	(	(	PUNCT
ejpam-4461	313	5	v	v	NOUN
ejpam-4461	313	6	(	(	PUNCT
ejpam-4461	313	7	g	g	PROPN
ejpam-4461	313	8	◦	◦	NOUN
ejpam-4461	313	9	h	h	NOUN
ejpam-4461	313	10	)	)	PUNCT
ejpam-4461	313	11	\	\	PROPN
ejpam-4461	313	12	v	v	X
ejpam-4461	313	13	(	(	PUNCT
ejpam-4461	313	14	hv	hv	NOUN
ejpam-4461	313	15	)	)	PUNCT
ejpam-4461	313	16	)	)	PUNCT
ejpam-4461	313	17	∪b	∪b	VERB
ejpam-4461	313	18	,	,	PUNCT
ejpam-4461	313	19	where	where	SCONJ
ejpam-4461	313	20	either	either	CCONJ
ejpam-4461	313	21	b	b	X
ejpam-4461	313	22	=	=	SYM
ejpam-4461	313	23	v	v	PROPN
ejpam-4461	313	24	(	(	PUNCT
ejpam-4461	313	25	hv	hv	NOUN
ejpam-4461	313	26	)	)	PUNCT
ejpam-4461	313	27	or	or	CCONJ
ejpam-4461	313	28	⟨v	⟨v	NUM
ejpam-4461	313	29	(	(	PUNCT
ejpam-4461	313	30	hv	hv	NOUN
ejpam-4461	313	31	)	)	PUNCT
ejpam-4461	313	32	\b⟩	\b⟩	PRON
ejpam-4461	313	33	is	be	AUX
ejpam-4461	313	34	connected	connect	VERB
ejpam-4461	313	35	.	.	PUNCT
ejpam-4461	314	1	(	(	PUNCT
ejpam-4461	314	2	ii	ii	X
ejpam-4461	314	3	)	)	PUNCT
ejpam-4461	314	4	s	s	PART
ejpam-4461	314	5	=	=	PUNCT
ejpam-4461	314	6	a	a	DET
ejpam-4461	314	7	∪	∪	X
ejpam-4461	314	8	(	(	PUNCT
ejpam-4461	314	9	∪x∈av	∪x∈av	PROPN
ejpam-4461	314	10	(	(	PUNCT
ejpam-4461	314	11	hx	hx	PROPN
ejpam-4461	314	12	)	)	PUNCT
ejpam-4461	314	13	)	)	PUNCT
ejpam-4461	314	14	∪	∪	ADP
ejpam-4461	314	15	(	(	PUNCT
ejpam-4461	314	16	∪x∈v	∪x∈v	X
ejpam-4461	314	17	(	(	PUNCT
ejpam-4461	314	18	g)\asx	g)\asx	PROPN
ejpam-4461	314	19	)	)	PUNCT
ejpam-4461	314	20	,	,	PUNCT
ejpam-4461	314	21	(	(	PUNCT
ejpam-4461	314	22	2	2	X
ejpam-4461	314	23	)	)	PUNCT
ejpam-4461	314	24	where	where	SCONJ
ejpam-4461	314	25	a	a	DET
ejpam-4461	314	26	⊆	⊆	NUM
ejpam-4461	314	27	v	v	NOUN
ejpam-4461	314	28	(	(	PUNCT
ejpam-4461	314	29	g	g	NOUN
ejpam-4461	314	30	)	)	PUNCT
ejpam-4461	314	31	and	and	CCONJ
ejpam-4461	314	32	sx	sx	PROPN
ejpam-4461	314	33	⊆	⊆	NUM
ejpam-4461	314	34	v	v	NOUN
ejpam-4461	314	35	(	(	PUNCT
ejpam-4461	314	36	hx	hx	PROPN
ejpam-4461	314	37	)	)	PUNCT
ejpam-4461	314	38	for	for	ADP
ejpam-4461	314	39	all	all	PRON
ejpam-4461	314	40	x	x	SYM
ejpam-4461	314	41	∈	∈	PROPN
ejpam-4461	314	42	v	v	NOUN
ejpam-4461	314	43	(	(	PUNCT
ejpam-4461	314	44	g	g	NOUN
ejpam-4461	314	45	)	)	PUNCT
ejpam-4461	314	46	\a	\a	VERB
ejpam-4461	314	47	satisfying	satisfy	VERB
ejpam-4461	314	48	the	the	DET
ejpam-4461	314	49	following	following	NOUN
ejpam-4461	314	50	:	:	PUNCT
ejpam-4461	314	51	(	(	PUNCT
ejpam-4461	314	52	a	a	NOUN
ejpam-4461	314	53	)	)	PUNCT
ejpam-4461	314	54	⟨v	⟨v	NOUN
ejpam-4461	314	55	(	(	PUNCT
ejpam-4461	314	56	g	g	NOUN
ejpam-4461	314	57	)	)	PUNCT
ejpam-4461	314	58	\a⟩	\a⟩	PROPN
ejpam-4461	314	59	is	be	AUX
ejpam-4461	314	60	connected	connect	VERB
ejpam-4461	314	61	;	;	PUNCT
ejpam-4461	314	62	(	(	PUNCT
ejpam-4461	314	63	b	b	X
ejpam-4461	314	64	)	)	PUNCT
ejpam-4461	314	65	for	for	ADP
ejpam-4461	314	66	each	each	DET
ejpam-4461	314	67	x	x	SYM
ejpam-4461	314	68	∈	∈	PROPN
ejpam-4461	314	69	v	v	ADP
ejpam-4461	314	70	(	(	PUNCT
ejpam-4461	314	71	g	g	NOUN
ejpam-4461	314	72	)	)	PUNCT
ejpam-4461	314	73	\	\	PROPN
ejpam-4461	315	1	a	a	PRON
ejpam-4461	315	2	,	,	PUNCT
ejpam-4461	315	3	sx	sx	PROPN
ejpam-4461	315	4	is	be	AUX
ejpam-4461	315	5	a	a	DET
ejpam-4461	315	6	dominating	dominating	NOUN
ejpam-4461	315	7	set	set	NOUN
ejpam-4461	315	8	of	of	ADP
ejpam-4461	315	9	hx	hx	PROPN
ejpam-4461	315	10	.	.	PUNCT
ejpam-4461	316	1	moreover	moreover	ADV
ejpam-4461	316	2	,	,	PUNCT
ejpam-4461	316	3	if	if	SCONJ
ejpam-4461	316	4	|sx|	|sx|	NUM
ejpam-4461	316	5	=	=	SYM
ejpam-4461	316	6	1	1	NUM
ejpam-4461	316	7	,	,	PUNCT
ejpam-4461	316	8	then	then	ADV
ejpam-4461	316	9	a	a	DET
ejpam-4461	316	10	∩ng(x	∩ng(x	NOUN
ejpam-4461	316	11	)	)	PUNCT
ejpam-4461	316	12	̸=	̸=	PROPN
ejpam-4461	316	13	∅.	∅.	ADP
ejpam-4461	316	14	proof	proof	NOUN
ejpam-4461	316	15	.	.	PUNCT
ejpam-4461	317	1	assume	assume	VERB
ejpam-4461	317	2	that	that	SCONJ
ejpam-4461	317	3	s	s	VERB
ejpam-4461	317	4	is	be	AUX
ejpam-4461	317	5	an	an	DET
ejpam-4461	317	6	outer	outer	ADV
ejpam-4461	317	7	-	-	PUNCT
ejpam-4461	317	8	connected	connect	VERB
ejpam-4461	317	9	semitotal	semitotal	ADJ
ejpam-4461	317	10	dominating	dominating	NOUN
ejpam-4461	317	11	set	set	NOUN
ejpam-4461	317	12	of	of	ADP
ejpam-4461	317	13	g	g	PROPN
ejpam-4461	317	14	◦	◦	PROPN
ejpam-4461	317	15	h.	h.	NOUN
ejpam-4461	317	16	if	if	SCONJ
ejpam-4461	317	17	s	s	VERB
ejpam-4461	317	18	=	=	SYM
ejpam-4461	317	19	v	v	ADJ
ejpam-4461	317	20	(	(	PUNCT
ejpam-4461	317	21	g	g	PROPN
ejpam-4461	317	22	◦	◦	NOUN
ejpam-4461	317	23	h	h	NOUN
ejpam-4461	317	24	)	)	PUNCT
ejpam-4461	317	25	,	,	PUNCT
ejpam-4461	317	26	then	then	ADV
ejpam-4461	317	27	(	(	PUNCT
ejpam-4461	317	28	i	i	NOUN
ejpam-4461	317	29	)	)	PUNCT
ejpam-4461	317	30	holds	hold	VERB
ejpam-4461	317	31	.	.	PUNCT
ejpam-4461	318	1	in	in	ADP
ejpam-4461	318	2	what	what	PRON
ejpam-4461	318	3	follows	follow	VERB
ejpam-4461	318	4	,	,	PUNCT
ejpam-4461	318	5	we	we	PRON
ejpam-4461	318	6	assume	assume	VERB
ejpam-4461	318	7	that	that	SCONJ
ejpam-4461	318	8	s	s	VERB
ejpam-4461	318	9	̸=	̸=	PROPN
ejpam-4461	318	10	v	v	NOUN
ejpam-4461	318	11	(	(	PUNCT
ejpam-4461	318	12	g	g	PROPN
ejpam-4461	318	13	◦	◦	NOUN
ejpam-4461	318	14	h	h	NOUN
ejpam-4461	318	15	)	)	PUNCT
ejpam-4461	318	16	.	.	PUNCT
ejpam-4461	319	1	we	we	PRON
ejpam-4461	319	2	consider	consider	VERB
ejpam-4461	319	3	two	two	NUM
ejpam-4461	319	4	cases	case	NOUN
ejpam-4461	319	5	:	:	PUNCT
ejpam-4461	319	6	case	case	NOUN
ejpam-4461	319	7	1	1	NUM
ejpam-4461	319	8	:	:	PUNCT
ejpam-4461	319	9	suppose	suppose	VERB
ejpam-4461	319	10	that	that	SCONJ
ejpam-4461	319	11	v	v	X
ejpam-4461	319	12	(	(	PUNCT
ejpam-4461	319	13	g	g	NOUN
ejpam-4461	319	14	)	)	PUNCT
ejpam-4461	319	15	⊆	⊆	NUM
ejpam-4461	319	16	s.	s.	PROPN
ejpam-4461	319	17	since	since	SCONJ
ejpam-4461	319	18	⟨v	⟨v	PROPN
ejpam-4461	319	19	(	(	PUNCT
ejpam-4461	319	20	g	g	ADP
ejpam-4461	319	21	◦	◦	NOUN
ejpam-4461	319	22	h)\s⟩	h)\s⟩	PROPN
ejpam-4461	319	23	is	be	AUX
ejpam-4461	319	24	connected	connect	VERB
ejpam-4461	319	25	,	,	PUNCT
ejpam-4461	319	26	there	there	PRON
ejpam-4461	319	27	exists	exist	VERB
ejpam-4461	319	28	v	v	ADP
ejpam-4461	319	29	∈	∈	PROPN
ejpam-4461	319	30	v	v	NOUN
ejpam-4461	319	31	(	(	PUNCT
ejpam-4461	319	32	g	g	NOUN
ejpam-4461	319	33	)	)	PUNCT
ejpam-4461	319	34	and	and	CCONJ
ejpam-4461	319	35	b	b	X
ejpam-4461	319	36	⊆	⊆	NUM
ejpam-4461	319	37	v	v	NOUN
ejpam-4461	319	38	(	(	PUNCT
ejpam-4461	319	39	hv	hv	NOUN
ejpam-4461	319	40	)	)	PUNCT
ejpam-4461	319	41	such	such	ADJ
ejpam-4461	319	42	that	that	PRON
ejpam-4461	319	43	v	v	NOUN
ejpam-4461	319	44	(	(	PUNCT
ejpam-4461	319	45	g	g	PROPN
ejpam-4461	319	46	◦	◦	NOUN
ejpam-4461	319	47	h	h	NOUN
ejpam-4461	319	48	)	)	PUNCT
ejpam-4461	319	49	\	\	PROPN
ejpam-4461	319	50	s	s	PART
ejpam-4461	319	51	=	=	SYM
ejpam-4461	319	52	v	v	PROPN
ejpam-4461	319	53	(	(	PUNCT
ejpam-4461	319	54	hv	hv	NOUN
ejpam-4461	319	55	)	)	PUNCT
ejpam-4461	319	56	\b	\b	NOUN
ejpam-4461	319	57	.	.	PUNCT
ejpam-4461	320	1	that	that	PRON
ejpam-4461	320	2	is	be	AUX
ejpam-4461	320	3	,	,	PUNCT
ejpam-4461	320	4	s	s	PART
ejpam-4461	320	5	=	=	PUNCT
ejpam-4461	320	6	(	(	PUNCT
ejpam-4461	320	7	v	v	NOUN
ejpam-4461	320	8	(	(	PUNCT
ejpam-4461	320	9	g	g	PROPN
ejpam-4461	320	10	◦	◦	NOUN
ejpam-4461	320	11	h	h	NOUN
ejpam-4461	320	12	)	)	PUNCT
ejpam-4461	320	13	\	\	PROPN
ejpam-4461	320	14	v	v	X
ejpam-4461	320	15	(	(	PUNCT
ejpam-4461	320	16	hv	hv	NOUN
ejpam-4461	320	17	)	)	PUNCT
ejpam-4461	320	18	)	)	PUNCT
ejpam-4461	320	19	∪b	∪b	PUNCT
ejpam-4461	320	20	and	and	CCONJ
ejpam-4461	320	21	⟨v	⟨v	NUM
ejpam-4461	320	22	(	(	PUNCT
ejpam-4461	320	23	hv	hv	NOUN
ejpam-4461	320	24	)	)	PUNCT
ejpam-4461	320	25	\b⟩	\b⟩	PRON
ejpam-4461	320	26	is	be	AUX
ejpam-4461	320	27	connected	connect	VERB
ejpam-4461	320	28	.	.	PUNCT
ejpam-4461	321	1	case	case	NOUN
ejpam-4461	321	2	2	2	NUM
ejpam-4461	321	3	:	:	PUNCT
ejpam-4461	321	4	suppose	suppose	VERB
ejpam-4461	321	5	that	that	SCONJ
ejpam-4461	321	6	v	v	X
ejpam-4461	321	7	(	(	PUNCT
ejpam-4461	321	8	g	g	NOUN
ejpam-4461	321	9	)	)	PUNCT
ejpam-4461	321	10	⊈	⊈	PROPN
ejpam-4461	321	11	s.	s.	PROPN
ejpam-4461	321	12	put	put	VERB
ejpam-4461	321	13	a	a	DET
ejpam-4461	321	14	=	=	SYM
ejpam-4461	321	15	s	s	NOUN
ejpam-4461	321	16	∩	∩	ADJ
ejpam-4461	321	17	v	v	X
ejpam-4461	321	18	(	(	PUNCT
ejpam-4461	321	19	g	g	NOUN
ejpam-4461	321	20	)	)	PUNCT
ejpam-4461	321	21	.	.	PUNCT
ejpam-4461	322	1	if	if	SCONJ
ejpam-4461	322	2	a	a	DET
ejpam-4461	322	3	=	=	NOUN
ejpam-4461	322	4	∅	∅	NOUN
ejpam-4461	322	5	,	,	PUNCT
ejpam-4461	322	6	then	then	ADV
ejpam-4461	322	7	(	(	PUNCT
ejpam-4461	322	8	2	2	X
ejpam-4461	322	9	)	)	PUNCT
ejpam-4461	322	10	trivially	trivially	ADV
ejpam-4461	322	11	holds	hold	VERB
ejpam-4461	322	12	with	with	ADP
ejpam-4461	322	13	sx	sx	PROPN
ejpam-4461	322	14	=	=	SYM
ejpam-4461	322	15	s	s	PROPN
ejpam-4461	322	16	∩	∩	ADJ
ejpam-4461	322	17	v	v	X
ejpam-4461	322	18	(	(	PUNCT
ejpam-4461	322	19	hx	hx	PROPN
ejpam-4461	322	20	)	)	PUNCT
ejpam-4461	322	21	for	for	ADP
ejpam-4461	322	22	all	all	PRON
ejpam-4461	322	23	x	x	SYM
ejpam-4461	322	24	∈	∈	PROPN
ejpam-4461	322	25	v	v	NOUN
ejpam-4461	322	26	(	(	PUNCT
ejpam-4461	322	27	g	g	NOUN
ejpam-4461	322	28	)	)	PUNCT
ejpam-4461	322	29	.	.	PUNCT
ejpam-4461	323	1	suppose	suppose	VERB
ejpam-4461	323	2	that	that	SCONJ
ejpam-4461	323	3	a	a	DET
ejpam-4461	323	4	̸=	̸=	PROPN
ejpam-4461	323	5	∅.	∅.	NOUN
ejpam-4461	323	6	since	since	SCONJ
ejpam-4461	323	7	⟨v	⟨v	PROPN
ejpam-4461	323	8	(	(	PUNCT
ejpam-4461	323	9	g	g	PROPN
ejpam-4461	323	10	◦	◦	NOUN
ejpam-4461	323	11	h	h	NOUN
ejpam-4461	323	12	)	)	PUNCT
ejpam-4461	323	13	\	\	PROPN
ejpam-4461	323	14	s⟩	s⟩	PROPN
ejpam-4461	323	15	is	be	AUX
ejpam-4461	323	16	connected	connect	VERB
ejpam-4461	323	17	and	and	CCONJ
ejpam-4461	323	18	v	v	ADJ
ejpam-4461	323	19	(	(	PUNCT
ejpam-4461	323	20	g	g	NOUN
ejpam-4461	323	21	)	)	PUNCT
ejpam-4461	323	22	\	\	NOUN
ejpam-4461	324	1	a	a	DET
ejpam-4461	324	2	̸=	̸=	PROPN
ejpam-4461	324	3	∅	∅	NOUN
ejpam-4461	324	4	,	,	PUNCT
ejpam-4461	324	5	v	v	PROPN
ejpam-4461	324	6	(	(	PUNCT
ejpam-4461	324	7	hx	hx	PROPN
ejpam-4461	324	8	)	)	PUNCT
ejpam-4461	324	9	⊆	⊆	NUM
ejpam-4461	324	10	s	s	NOUN
ejpam-4461	324	11	for	for	ADP
ejpam-4461	324	12	all	all	DET
ejpam-4461	324	13	x	x	SYM
ejpam-4461	324	14	∈	∈	NOUN
ejpam-4461	324	15	a.	a.	NOUN
ejpam-4461	324	16	put	put	VERB
ejpam-4461	324	17	sx	sx	PROPN
ejpam-4461	324	18	=	=	SYM
ejpam-4461	324	19	s	s	PROPN
ejpam-4461	324	20	∩	∩	ADJ
ejpam-4461	324	21	v	v	X
ejpam-4461	324	22	(	(	PUNCT
ejpam-4461	324	23	hx	hx	PROPN
ejpam-4461	324	24	)	)	PUNCT
ejpam-4461	324	25	for	for	ADP
ejpam-4461	324	26	all	all	PRON
ejpam-4461	324	27	x	x	SYM
ejpam-4461	324	28	∈	∈	PROPN
ejpam-4461	324	29	v	v	NOUN
ejpam-4461	324	30	(	(	PUNCT
ejpam-4461	324	31	g)\a	g)\a	NOUN
ejpam-4461	324	32	.	.	PUNCT
ejpam-4461	325	1	then	then	ADV
ejpam-4461	325	2	equation	equation	NOUN
ejpam-4461	325	3	(	(	PUNCT
ejpam-4461	325	4	2	2	X
ejpam-4461	325	5	)	)	PUNCT
ejpam-4461	325	6	holds	hold	VERB
ejpam-4461	325	7	for	for	ADP
ejpam-4461	325	8	s.	s.	PROPN
ejpam-4461	325	9	statement	statement	PROPN
ejpam-4461	325	10	(	(	PUNCT
ejpam-4461	325	11	ii)(a	ii)(a	PROPN
ejpam-4461	325	12	)	)	PUNCT
ejpam-4461	325	13	follows	follow	VERB
ejpam-4461	325	14	immediately	immediately	ADV
ejpam-4461	325	15	from	from	ADP
ejpam-4461	325	16	the	the	DET
ejpam-4461	325	17	connectedness	connectedness	NOUN
ejpam-4461	325	18	of	of	ADP
ejpam-4461	325	19	⟨v	⟨v	PROPN
ejpam-4461	325	20	(	(	PUNCT
ejpam-4461	325	21	g	g	PROPN
ejpam-4461	325	22	◦	◦	NOUN
ejpam-4461	325	23	h	h	NOUN
ejpam-4461	325	24	)	)	PUNCT
ejpam-4461	326	1	\s⟩.	\s⟩.	PROPN
ejpam-4461	326	2	now	now	ADV
ejpam-4461	326	3	,	,	PUNCT
ejpam-4461	326	4	let	let	VERB
ejpam-4461	326	5	x	x	PUNCT
ejpam-4461	326	6	∈	∈	PROPN
ejpam-4461	326	7	v	v	X
ejpam-4461	326	8	(	(	PUNCT
ejpam-4461	326	9	g	g	NOUN
ejpam-4461	326	10	)	)	PUNCT
ejpam-4461	326	11	\a	\a	ADJ
ejpam-4461	326	12	and	and	CCONJ
ejpam-4461	326	13	u	u	PROPN
ejpam-4461	326	14	∈	∈	PROPN
ejpam-4461	326	15	v	v	PROPN
ejpam-4461	326	16	(	(	PUNCT
ejpam-4461	326	17	hx	hx	PROPN
ejpam-4461	326	18	)	)	PUNCT
ejpam-4461	326	19	\sx	\sx	PROPN
ejpam-4461	326	20	.	.	PUNCT
ejpam-4461	327	1	since	since	SCONJ
ejpam-4461	327	2	s	s	NOUN
ejpam-4461	327	3	is	be	AUX
ejpam-4461	327	4	a	a	DET
ejpam-4461	327	5	dominating	dominating	NOUN
ejpam-4461	327	6	set	set	NOUN
ejpam-4461	327	7	of	of	ADP
ejpam-4461	327	8	g	g	NOUN
ejpam-4461	327	9	◦	◦	NOUN
ejpam-4461	327	10	h	h	NOUN
ejpam-4461	327	11	and	and	CCONJ
ejpam-4461	327	12	u	u	NOUN
ejpam-4461	327	13	/∈	/∈	PROPN
ejpam-4461	327	14	s	s	PART
ejpam-4461	327	15	,	,	PUNCT
ejpam-4461	327	16	there	there	PRON
ejpam-4461	327	17	exists	exist	VERB
ejpam-4461	327	18	w	w	PROPN
ejpam-4461	327	19	∈	∈	PROPN
ejpam-4461	327	20	s	s	NOUN
ejpam-4461	327	21	for	for	ADP
ejpam-4461	327	22	which	which	PRON
ejpam-4461	327	23	uw	uw	PROPN
ejpam-4461	327	24	∈	∈	PROPN
ejpam-4461	327	25	e(g	e(g	PROPN
ejpam-4461	327	26	◦	◦	NOUN
ejpam-4461	327	27	h	h	NOUN
ejpam-4461	327	28	)	)	PUNCT
ejpam-4461	327	29	.	.	PUNCT
ejpam-4461	328	1	since	since	SCONJ
ejpam-4461	328	2	x	x	PROPN
ejpam-4461	328	3	/∈	/∈	PROPN
ejpam-4461	328	4	s	s	X
ejpam-4461	328	5	,	,	PUNCT
ejpam-4461	328	6	w	w	PROPN
ejpam-4461	328	7	̸=	̸=	PROPN
ejpam-4461	328	8	x	x	PUNCT
ejpam-4461	328	9	so	so	SCONJ
ejpam-4461	328	10	that	that	SCONJ
ejpam-4461	328	11	w	w	PROPN
ejpam-4461	328	12	∈	∈	PROPN
ejpam-4461	328	13	sx	sx	PROPN
ejpam-4461	328	14	.	.	PUNCT
ejpam-4461	329	1	this	this	PRON
ejpam-4461	329	2	means	mean	VERB
ejpam-4461	329	3	that	that	SCONJ
ejpam-4461	329	4	sx	sx	PROPN
ejpam-4461	329	5	is	be	AUX
ejpam-4461	329	6	a	a	DET
ejpam-4461	329	7	dominating	dominating	NOUN
ejpam-4461	329	8	set	set	NOUN
ejpam-4461	329	9	of	of	ADP
ejpam-4461	329	10	hx	hx	PROPN
ejpam-4461	329	11	.	.	PUNCT
ejpam-4461	329	12	suppose	suppose	VERB
ejpam-4461	329	13	further	far	ADV
ejpam-4461	329	14	that	that	PRON
ejpam-4461	329	15	|sx|	|sx|	NOUN
ejpam-4461	329	16	=	=	SYM
ejpam-4461	329	17	1	1	NUM
ejpam-4461	329	18	,	,	PUNCT
ejpam-4461	329	19	say	say	VERB
ejpam-4461	329	20	sx	sx	PROPN
ejpam-4461	329	21	=	=	PUNCT
ejpam-4461	329	22	{	{	PUNCT
ejpam-4461	329	23	u	u	NOUN
ejpam-4461	329	24	}	}	PUNCT
ejpam-4461	329	25	.	.	PUNCT
ejpam-4461	330	1	because	because	SCONJ
ejpam-4461	330	2	s	s	NOUN
ejpam-4461	330	3	is	be	AUX
ejpam-4461	330	4	a	a	DET
ejpam-4461	330	5	semitotal	semitotal	ADJ
ejpam-4461	330	6	dominating	dominating	NOUN
ejpam-4461	330	7	set	set	NOUN
ejpam-4461	330	8	of	of	ADP
ejpam-4461	330	9	g	g	PROPN
ejpam-4461	330	10	◦	◦	NOUN
ejpam-4461	330	11	h	h	NOUN
ejpam-4461	330	12	,	,	PUNCT
ejpam-4461	330	13	there	there	PRON
ejpam-4461	330	14	exists	exist	VERB
ejpam-4461	330	15	w	w	PROPN
ejpam-4461	330	16	∈	∈	PROPN
ejpam-4461	330	17	s	s	PART
ejpam-4461	330	18	\	\	X
ejpam-4461	330	19	{	{	PUNCT
ejpam-4461	330	20	u	u	NOUN
ejpam-4461	330	21	}	}	PUNCT
ejpam-4461	330	22	such	such	ADJ
ejpam-4461	330	23	that	that	SCONJ
ejpam-4461	330	24	dg	dg	PROPN
ejpam-4461	330	25	◦	◦	PROPN
ejpam-4461	330	26	h(u	h(u	PROPN
ejpam-4461	330	27	,	,	PUNCT
ejpam-4461	330	28	w	w	NOUN
ejpam-4461	330	29	)	)	PUNCT
ejpam-4461	330	30	≤	≤	NOUN
ejpam-4461	330	31	2	2	NUM
ejpam-4461	330	32	.	.	PUNCT
ejpam-4461	331	1	since	since	SCONJ
ejpam-4461	331	2	w	w	PROPN
ejpam-4461	331	3	/∈	/∈	PROPN
ejpam-4461	331	4	sx	sx	PROPN
ejpam-4461	331	5	,	,	PUNCT
ejpam-4461	331	6	w	w	PROPN
ejpam-4461	331	7	∈	∈	PROPN
ejpam-4461	331	8	a	a	DET
ejpam-4461	331	9	∩	∩	NOUN
ejpam-4461	331	10	ng(x	ng(x	NUM
ejpam-4461	331	11	)	)	PUNCT
ejpam-4461	331	12	,	,	PUNCT
ejpam-4461	331	13	and	and	CCONJ
ejpam-4461	331	14	statement	statement	NOUN
ejpam-4461	331	15	(	(	PUNCT
ejpam-4461	331	16	ii)(b	ii)(b	ADJ
ejpam-4461	331	17	)	)	PUNCT
ejpam-4461	331	18	holds	hold	VERB
ejpam-4461	331	19	.	.	PUNCT
ejpam-4461	332	1	conversely	conversely	ADV
ejpam-4461	332	2	,	,	PUNCT
ejpam-4461	332	3	suppose	suppose	VERB
ejpam-4461	332	4	that	that	SCONJ
ejpam-4461	332	5	condition	condition	NOUN
ejpam-4461	332	6	(	(	PUNCT
ejpam-4461	332	7	i	i	NOUN
ejpam-4461	332	8	)	)	PUNCT
ejpam-4461	332	9	holds	hold	VERB
ejpam-4461	332	10	.	.	PUNCT
ejpam-4461	333	1	since	since	SCONJ
ejpam-4461	333	2	v	v	NOUN
ejpam-4461	333	3	(	(	PUNCT
ejpam-4461	333	4	g	g	NOUN
ejpam-4461	333	5	)	)	PUNCT
ejpam-4461	333	6	⊆	⊆	NUM
ejpam-4461	333	7	s	s	NOUN
ejpam-4461	333	8	,	,	PUNCT
ejpam-4461	333	9	s	s	VERB
ejpam-4461	333	10	is	be	AUX
ejpam-4461	333	11	a	a	DET
ejpam-4461	333	12	semitotal	semitotal	ADJ
ejpam-4461	333	13	dominating	dominating	NOUN
ejpam-4461	333	14	set	set	NOUN
ejpam-4461	333	15	of	of	ADP
ejpam-4461	333	16	g	g	PROPN
ejpam-4461	333	17	◦	◦	NOUN
ejpam-4461	333	18	h.	h.	NOUN
ejpam-4461	333	19	moreover	moreover	ADV
ejpam-4461	333	20	,	,	PUNCT
ejpam-4461	333	21	v	v	INTJ
ejpam-4461	333	22	(	(	PUNCT
ejpam-4461	333	23	g	g	PROPN
ejpam-4461	333	24	◦	◦	NOUN
ejpam-4461	333	25	h	h	NOUN
ejpam-4461	333	26	)	)	PUNCT
ejpam-4461	334	1	\	\	PROPN
ejpam-4461	334	2	s	s	PART
ejpam-4461	334	3	=	=	SYM
ejpam-4461	334	4	v	v	PROPN
ejpam-4461	334	5	(	(	PUNCT
ejpam-4461	334	6	hv	hv	PROPN
ejpam-4461	334	7	)	)	PUNCT
ejpam-4461	334	8	\	\	PROPN
ejpam-4461	335	1	b	b	PROPN
ejpam-4461	336	1	so	so	ADV
ejpam-4461	336	2	that	that	PRON
ejpam-4461	336	3	s	s	VERB
ejpam-4461	336	4	is	be	AUX
ejpam-4461	336	5	an	an	DET
ejpam-4461	336	6	outer	outer	ADV
ejpam-4461	336	7	-	-	PUNCT
ejpam-4461	336	8	connected	connect	VERB
ejpam-4461	336	9	semitotal	semitotal	ADJ
ejpam-4461	336	10	dominating	dominating	NOUN
ejpam-4461	336	11	set	set	NOUN
ejpam-4461	336	12	of	of	ADP
ejpam-4461	336	13	g	g	PROPN
ejpam-4461	336	14	◦	◦	NOUN
ejpam-4461	336	15	h.	h.	PROPN
ejpam-4461	336	16	now	now	ADV
ejpam-4461	336	17	,	,	PUNCT
ejpam-4461	336	18	suppose	suppose	VERB
ejpam-4461	336	19	that	that	SCONJ
ejpam-4461	336	20	condition	condition	NOUN
ejpam-4461	336	21	(	(	PUNCT
ejpam-4461	336	22	ii	ii	NOUN
ejpam-4461	336	23	)	)	PUNCT
ejpam-4461	336	24	holds	hold	VERB
ejpam-4461	336	25	for	for	ADP
ejpam-4461	336	26	s.	s.	PROPN
ejpam-4461	336	27	by	by	ADP
ejpam-4461	336	28	condition	condition	NOUN
ejpam-4461	336	29	(	(	PUNCT
ejpam-4461	336	30	ii)(b	ii)(b	PROPN
ejpam-4461	336	31	)	)	PUNCT
ejpam-4461	336	32	,	,	PUNCT
ejpam-4461	336	33	s	s	VERB
ejpam-4461	336	34	is	be	AUX
ejpam-4461	336	35	a	a	DET
ejpam-4461	336	36	dominating	dominating	NOUN
ejpam-4461	336	37	set	set	NOUN
ejpam-4461	336	38	of	of	ADP
ejpam-4461	336	39	g	g	PROPN
ejpam-4461	336	40	◦	◦	PROPN
ejpam-4461	336	41	h.	h.	PROPN
ejpam-4461	336	42	suppose	suppose	VERB
ejpam-4461	336	43	that	that	SCONJ
ejpam-4461	336	44	a	a	DET
ejpam-4461	336	45	=	=	SYM
ejpam-4461	336	46	∅.	∅.	NOUN
ejpam-4461	336	47	then	then	ADV
ejpam-4461	336	48	s	s	PART
ejpam-4461	336	49	=	=	PUNCT
ejpam-4461	336	50	⋃	⋃	PROPN
ejpam-4461	336	51	x∈v	x∈v	PROPN
ejpam-4461	336	52	(	(	PUNCT
ejpam-4461	336	53	g	g	NOUN
ejpam-4461	336	54	)	)	PUNCT
ejpam-4461	336	55	sx	sx	PROPN
ejpam-4461	336	56	,	,	PUNCT
ejpam-4461	336	57	and	and	CCONJ
ejpam-4461	336	58	by	by	ADP
ejpam-4461	336	59	condition	condition	NOUN
ejpam-4461	336	60	(	(	PUNCT
ejpam-4461	336	61	ii)(b	ii)(b	PROPN
ejpam-4461	336	62	)	)	PUNCT
ejpam-4461	336	63	,	,	PUNCT
ejpam-4461	336	64	sx	sx	PROPN
ejpam-4461	336	65	is	be	AUX
ejpam-4461	336	66	a	a	DET
ejpam-4461	336	67	nonsingleton	nonsingleton	NOUN
ejpam-4461	336	68	dominating	dominating	NOUN
ejpam-4461	336	69	set	set	NOUN
ejpam-4461	336	70	of	of	ADP
ejpam-4461	336	71	hx	hx	PROPN
ejpam-4461	336	72	for	for	ADP
ejpam-4461	336	73	all	all	PRON
ejpam-4461	336	74	x	x	SYM
ejpam-4461	336	75	∈	∈	PROPN
ejpam-4461	336	76	v	v	NOUN
ejpam-4461	336	77	(	(	PUNCT
ejpam-4461	336	78	g	g	NOUN
ejpam-4461	336	79	)	)	PUNCT
ejpam-4461	336	80	.	.	PUNCT
ejpam-4461	337	1	note	note	VERB
ejpam-4461	337	2	that	that	SCONJ
ejpam-4461	337	3	for	for	ADP
ejpam-4461	337	4	each	each	DET
ejpam-4461	337	5	x	x	SYM
ejpam-4461	337	6	∈	∈	PROPN
ejpam-4461	337	7	v	v	NOUN
ejpam-4461	337	8	(	(	PUNCT
ejpam-4461	337	9	g	g	NOUN
ejpam-4461	337	10	)	)	PUNCT
ejpam-4461	337	11	,	,	PUNCT
ejpam-4461	337	12	dg	dg	PROPN
ejpam-4461	337	13	◦	◦	PROPN
ejpam-4461	337	14	h(u	h(u	PROPN
ejpam-4461	337	15	,	,	PUNCT
ejpam-4461	337	16	v	v	NOUN
ejpam-4461	337	17	)	)	PUNCT
ejpam-4461	337	18	≤	≤	NUM
ejpam-4461	337	19	2	2	NUM
ejpam-4461	337	20	for	for	ADP
ejpam-4461	337	21	all	all	DET
ejpam-4461	337	22	u	u	NOUN
ejpam-4461	337	23	,	,	PUNCT
ejpam-4461	337	24	v	v	PROPN
ejpam-4461	337	25	∈	∈	PROPN
ejpam-4461	337	26	sx	sx	NOUN
ejpam-4461	337	27	.	.	PUNCT
ejpam-4461	338	1	it	it	PRON
ejpam-4461	338	2	follows	follow	VERB
ejpam-4461	338	3	that	that	SCONJ
ejpam-4461	338	4	s	s	VERB
ejpam-4461	338	5	is	be	AUX
ejpam-4461	338	6	a	a	DET
ejpam-4461	338	7	semitotal	semitotal	ADJ
ejpam-4461	338	8	dominating	dominating	NOUN
ejpam-4461	338	9	set	set	NOUN
ejpam-4461	338	10	of	of	ADP
ejpam-4461	338	11	g	g	PROPN
ejpam-4461	338	12	◦	◦	NOUN
ejpam-4461	338	13	h.	h.	NOUN
ejpam-4461	338	14	further	far	ADV
ejpam-4461	338	15	,	,	PUNCT
ejpam-4461	338	16	since	since	SCONJ
ejpam-4461	338	17	v	v	NOUN
ejpam-4461	338	18	(	(	PUNCT
ejpam-4461	338	19	g	g	NOUN
ejpam-4461	338	20	)	)	PUNCT
ejpam-4461	338	21	⊆	⊆	NUM
ejpam-4461	338	22	v	v	NOUN
ejpam-4461	338	23	(	(	PUNCT
ejpam-4461	338	24	g	g	NOUN
ejpam-4461	338	25	◦	◦	NOUN
ejpam-4461	338	26	h)\s	h)\s	NOUN
ejpam-4461	338	27	,	,	PUNCT
ejpam-4461	338	28	⟨v	⟨v	NOUN
ejpam-4461	338	29	(	(	PUNCT
ejpam-4461	338	30	g	g	NOUN
ejpam-4461	338	31	◦	◦	NOUN
ejpam-4461	338	32	h)\s⟩	h)\s⟩	PROPN
ejpam-4461	338	33	is	be	AUX
ejpam-4461	338	34	connected	connect	VERB
ejpam-4461	338	35	.	.	PUNCT
ejpam-4461	339	1	finally	finally	ADV
ejpam-4461	339	2	,	,	PUNCT
ejpam-4461	339	3	suppose	suppose	VERB
ejpam-4461	339	4	that	that	SCONJ
ejpam-4461	339	5	a	a	DET
ejpam-4461	339	6	̸=	̸=	PROPN
ejpam-4461	339	7	∅.	∅.	ADV
ejpam-4461	339	8	let	let	VERB
ejpam-4461	339	9	x	x	PROPN
ejpam-4461	339	10	∈	∈	PROPN
ejpam-4461	339	11	s.	s.	PROPN
ejpam-4461	339	12	if	if	SCONJ
ejpam-4461	339	13	x	x	PROPN
ejpam-4461	339	14	∈	∈	PROPN
ejpam-4461	339	15	a	a	PRON
ejpam-4461	339	16	,	,	PUNCT
ejpam-4461	339	17	then	then	ADV
ejpam-4461	339	18	v	v	INTJ
ejpam-4461	339	19	(	(	PUNCT
ejpam-4461	339	20	hx	hx	PROPN
ejpam-4461	339	21	)	)	PUNCT
ejpam-4461	339	22	⊆	⊆	NUM
ejpam-4461	339	23	s.	s.	PROPN
ejpam-4461	339	24	pick	pick	VERB
ejpam-4461	339	25	u	u	PRON
ejpam-4461	339	26	∈	∈	PROPN
ejpam-4461	339	27	v	v	NOUN
ejpam-4461	339	28	(	(	PUNCT
ejpam-4461	339	29	hx	hx	PROPN
ejpam-4461	339	30	)	)	PUNCT
ejpam-4461	339	31	.	.	PUNCT
ejpam-4461	340	1	a.	a.	PROPN
ejpam-4461	340	2	aradais	aradais	PROPN
ejpam-4461	340	3	,	,	PUNCT
ejpam-4461	340	4	f.	f.	PROPN
ejpam-4461	340	5	jamil	jamil	PROPN
ejpam-4461	340	6	/	/	SYM
ejpam-4461	340	7	eur	eur	PROPN
ejpam-4461	340	8	.	.	PUNCT
ejpam-4461	341	1	j.	j.	PROPN
ejpam-4461	341	2	pure	pure	PROPN
ejpam-4461	341	3	appl	appl	PROPN
ejpam-4461	341	4	.	.	PROPN
ejpam-4461	341	5	math	math	PROPN
ejpam-4461	341	6	,	,	PUNCT
ejpam-4461	341	7	15	15	NUM
ejpam-4461	341	8	(	(	PUNCT
ejpam-4461	341	9	3	3	NUM
ejpam-4461	341	10	)	)	PUNCT
ejpam-4461	341	11	(	(	PUNCT
ejpam-4461	341	12	2022	2022	NUM
ejpam-4461	341	13	)	)	PUNCT
ejpam-4461	341	14	,	,	PUNCT
ejpam-4461	341	15	1265	1265	NUM
ejpam-4461	341	16	-	-	SYM
ejpam-4461	341	17	1279	1279	NUM
ejpam-4461	341	18	1275	1275	NUM
ejpam-4461	341	19	then	then	ADV
ejpam-4461	341	20	we	we	PRON
ejpam-4461	341	21	have	have	VERB
ejpam-4461	341	22	u	u	PROPN
ejpam-4461	341	23	∈	∈	PROPN
ejpam-4461	341	24	s	s	PART
ejpam-4461	341	25	and	and	CCONJ
ejpam-4461	341	26	dg	dg	NOUN
ejpam-4461	341	27	◦	◦	NOUN
ejpam-4461	341	28	h(x	h(x	PROPN
ejpam-4461	341	29	,	,	PUNCT
ejpam-4461	341	30	u	u	NOUN
ejpam-4461	341	31	)	)	PUNCT
ejpam-4461	341	32	=	=	SYM
ejpam-4461	342	1	1	1	X
ejpam-4461	342	2	.	.	PUNCT
ejpam-4461	343	1	if	if	SCONJ
ejpam-4461	343	2	x	x	SYM
ejpam-4461	343	3	∈	∈	PROPN
ejpam-4461	343	4	v	v	X
ejpam-4461	343	5	(	(	PUNCT
ejpam-4461	343	6	hv	hv	PROPN
ejpam-4461	343	7	)	)	PUNCT
ejpam-4461	343	8	for	for	ADP
ejpam-4461	343	9	some	some	DET
ejpam-4461	343	10	v	v	ADP
ejpam-4461	343	11	∈	∈	PRON
ejpam-4461	343	12	a	a	PRON
ejpam-4461	343	13	,	,	PUNCT
ejpam-4461	343	14	then	then	ADV
ejpam-4461	343	15	v	v	NOUN
ejpam-4461	343	16	is	be	AUX
ejpam-4461	343	17	the	the	DET
ejpam-4461	343	18	desired	desire	VERB
ejpam-4461	343	19	vertex	vertex	NOUN
ejpam-4461	343	20	in	in	ADP
ejpam-4461	343	21	s	s	PRON
ejpam-4461	343	22	for	for	ADP
ejpam-4461	343	23	which	which	PRON
ejpam-4461	343	24	dg	dg	VERB
ejpam-4461	343	25	◦	◦	NOUN
ejpam-4461	343	26	h(x	h(x	PROPN
ejpam-4461	343	27	,	,	PUNCT
ejpam-4461	343	28	v	v	NOUN
ejpam-4461	343	29	)	)	PUNCT
ejpam-4461	343	30	≤	≤	NOUN
ejpam-4461	343	31	2	2	NUM
ejpam-4461	343	32	.	.	PUNCT
ejpam-4461	344	1	next	next	ADV
ejpam-4461	344	2	,	,	PUNCT
ejpam-4461	344	3	suppose	suppose	VERB
ejpam-4461	344	4	that	that	SCONJ
ejpam-4461	344	5	x	x	SYM
ejpam-4461	344	6	∈	∈	PROPN
ejpam-4461	344	7	v	v	ADP
ejpam-4461	344	8	(	(	PUNCT
ejpam-4461	344	9	hv	hv	PROPN
ejpam-4461	344	10	)	)	PUNCT
ejpam-4461	344	11	for	for	ADP
ejpam-4461	344	12	some	some	DET
ejpam-4461	344	13	v	v	ADP
ejpam-4461	344	14	∈	∈	PROPN
ejpam-4461	344	15	v	v	NOUN
ejpam-4461	344	16	(	(	PUNCT
ejpam-4461	344	17	g	g	NOUN
ejpam-4461	344	18	)	)	PUNCT
ejpam-4461	344	19	\a	\a	ADJ
ejpam-4461	344	20	.	.	PUNCT
ejpam-4461	345	1	if	if	SCONJ
ejpam-4461	345	2	|sv|	|sv|	PROPN
ejpam-4461	345	3	≥	≥	NOUN
ejpam-4461	345	4	2	2	NUM
ejpam-4461	345	5	,	,	PUNCT
ejpam-4461	345	6	then	then	ADV
ejpam-4461	345	7	pick	pick	VERB
ejpam-4461	345	8	u	u	PRON
ejpam-4461	345	9	∈	∈	NOUN
ejpam-4461	345	10	sv	sv	ADP
ejpam-4461	345	11	\	\	PROPN
ejpam-4461	345	12	{	{	PUNCT
ejpam-4461	345	13	x	x	NOUN
ejpam-4461	345	14	}	}	PUNCT
ejpam-4461	345	15	.	.	PUNCT
ejpam-4461	346	1	then	then	ADV
ejpam-4461	346	2	u	u	PROPN
ejpam-4461	346	3	∈	∈	PROPN
ejpam-4461	346	4	s	s	PART
ejpam-4461	346	5	and	and	CCONJ
ejpam-4461	346	6	dg	dg	NOUN
ejpam-4461	346	7	◦	◦	NOUN
ejpam-4461	346	8	h(x	h(x	PROPN
ejpam-4461	346	9	,	,	PUNCT
ejpam-4461	346	10	u	u	NOUN
ejpam-4461	346	11	)	)	PUNCT
ejpam-4461	346	12	≤	≤	NUM
ejpam-4461	346	13	2	2	NUM
ejpam-4461	346	14	.	.	PUNCT
ejpam-4461	347	1	lastly	lastly	ADV
ejpam-4461	347	2	,	,	PUNCT
ejpam-4461	347	3	suppose	suppose	VERB
ejpam-4461	347	4	that	that	SCONJ
ejpam-4461	347	5	|sv|	|sv|	PROPN
ejpam-4461	347	6	=	=	SYM
ejpam-4461	347	7	1	1	NUM
ejpam-4461	347	8	,	,	PUNCT
ejpam-4461	347	9	i.e.	i.e.	X
ejpam-4461	347	10	,	,	PUNCT
ejpam-4461	347	11	sv	sv	INTJ
ejpam-4461	347	12	=	=	SYM
ejpam-4461	347	13	{	{	PUNCT
ejpam-4461	347	14	x	x	NOUN
ejpam-4461	347	15	}	}	PUNCT
ejpam-4461	347	16	.	.	PUNCT
ejpam-4461	348	1	by	by	ADP
ejpam-4461	348	2	condition	condition	NOUN
ejpam-4461	348	3	(	(	PUNCT
ejpam-4461	348	4	ii)(b	ii)(b	PROPN
ejpam-4461	348	5	)	)	PUNCT
ejpam-4461	348	6	,	,	PUNCT
ejpam-4461	348	7	the	the	DET
ejpam-4461	348	8	exists	exist	NOUN
ejpam-4461	348	9	z	z	PROPN
ejpam-4461	348	10	∈	∈	PROPN
ejpam-4461	348	11	a∩ng(v	a∩ng(v	PROPN
ejpam-4461	348	12	)	)	PUNCT
ejpam-4461	348	13	.	.	PUNCT
ejpam-4461	349	1	then	then	ADV
ejpam-4461	349	2	z	z	PROPN
ejpam-4461	349	3	∈	∈	PROPN
ejpam-4461	349	4	s	s	PART
ejpam-4461	349	5	and	and	CCONJ
ejpam-4461	349	6	dg	dg	NOUN
ejpam-4461	349	7	◦	◦	NOUN
ejpam-4461	349	8	h(x	h(x	PROPN
ejpam-4461	349	9	,	,	PUNCT
ejpam-4461	349	10	z	z	NOUN
ejpam-4461	349	11	)	)	PUNCT
ejpam-4461	349	12	=	=	SYM
ejpam-4461	350	1	2	2	X
ejpam-4461	350	2	.	.	X
ejpam-4461	350	3	we	we	PRON
ejpam-4461	350	4	have	have	AUX
ejpam-4461	350	5	shown	show	VERB
ejpam-4461	350	6	that	that	SCONJ
ejpam-4461	350	7	s	s	NOUN
ejpam-4461	350	8	is	be	AUX
ejpam-4461	350	9	a	a	DET
ejpam-4461	350	10	semitotal	semitotal	ADJ
ejpam-4461	350	11	dominating	dominating	NOUN
ejpam-4461	350	12	set	set	NOUN
ejpam-4461	350	13	of	of	ADP
ejpam-4461	350	14	g	g	PROPN
ejpam-4461	350	15	◦	◦	NOUN
ejpam-4461	350	16	h.	h.	NOUN
ejpam-4461	350	17	condition	condition	NOUN
ejpam-4461	350	18	(	(	PUNCT
ejpam-4461	350	19	ii)(a	ii)(a	PROPN
ejpam-4461	350	20	)	)	PUNCT
ejpam-4461	350	21	implies	imply	VERB
ejpam-4461	350	22	further	far	ADV
ejpam-4461	350	23	that	that	PRON
ejpam-4461	350	24	s	s	VERB
ejpam-4461	350	25	is	be	AUX
ejpam-4461	350	26	an	an	DET
ejpam-4461	350	27	outer	outer	ADV
ejpam-4461	350	28	-	-	PUNCT
ejpam-4461	350	29	connected	connect	VERB
ejpam-4461	350	30	semtiotal	semtiotal	ADJ
ejpam-4461	350	31	dominating	dominating	NOUN
ejpam-4461	350	32	set	set	NOUN
ejpam-4461	350	33	of	of	ADP
ejpam-4461	350	34	g	g	PROPN
ejpam-4461	350	35	◦	◦	NOUN
ejpam-4461	350	36	h.	h.	PROPN
ejpam-4461	350	37	corollary	corollary	ADJ
ejpam-4461	350	38	3	3	X
ejpam-4461	350	39	.	.	PUNCT
ejpam-4461	351	1	let	let	VERB
ejpam-4461	351	2	g	g	NOUN
ejpam-4461	351	3	and	and	CCONJ
ejpam-4461	351	4	h	h	NOUN
ejpam-4461	351	5	be	be	AUX
ejpam-4461	351	6	nontrivial	nontrivial	ADJ
ejpam-4461	351	7	connected	connect	VERB
ejpam-4461	351	8	graphs	graph	NOUN
ejpam-4461	351	9	of	of	ADP
ejpam-4461	351	10	orders	order	NOUN
ejpam-4461	351	11	n	n	PRON
ejpam-4461	351	12	and	and	CCONJ
ejpam-4461	351	13	m	m	PROPN
ejpam-4461	351	14	,	,	PUNCT
ejpam-4461	351	15	respectively	respectively	ADV
ejpam-4461	351	16	.	.	PUNCT
ejpam-4461	352	1	(	(	PUNCT
ejpam-4461	352	2	i	i	NOUN
ejpam-4461	352	3	)	)	PUNCT
ejpam-4461	352	4	if	if	SCONJ
ejpam-4461	352	5	γ(h	γ(h	NOUN
ejpam-4461	352	6	)	)	PUNCT
ejpam-4461	352	7	=	=	SYM
ejpam-4461	352	8	1	1	NUM
ejpam-4461	352	9	,	,	PUNCT
ejpam-4461	352	10	then	then	ADV
ejpam-4461	352	11	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	352	12	◦	◦	NOUN
ejpam-4461	352	13	h	h	NOUN
ejpam-4461	352	14	)	)	PUNCT
ejpam-4461	352	15	≤	≤	NOUN
ejpam-4461	352	16	min{2n	min{2n	NOUN
ejpam-4461	352	17	,	,	PUNCT
ejpam-4461	352	18	n+mγ̃(g	n+mγ̃(g	NOUN
ejpam-4461	352	19	)	)	PUNCT
ejpam-4461	352	20	}	}	PUNCT
ejpam-4461	352	21	.	.	PUNCT
ejpam-4461	353	1	(	(	PUNCT
ejpam-4461	353	2	ii	ii	NOUN
ejpam-4461	353	3	)	)	PUNCT
ejpam-4461	353	4	if	if	SCONJ
ejpam-4461	353	5	γ(h	γ(h	NOUN
ejpam-4461	353	6	)	)	PUNCT
ejpam-4461	353	7	≥	≥	NOUN
ejpam-4461	353	8	2	2	NUM
ejpam-4461	353	9	,	,	PUNCT
ejpam-4461	353	10	then	then	ADV
ejpam-4461	353	11	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	353	12	◦	◦	NOUN
ejpam-4461	353	13	h	h	NOUN
ejpam-4461	353	14	)	)	PUNCT
ejpam-4461	353	15	≤	≤	NUM
ejpam-4461	353	16	min{nγ(h	min{nγ(h	NOUN
ejpam-4461	353	17	)	)	PUNCT
ejpam-4461	353	18	,	,	PUNCT
ejpam-4461	353	19	γ̃(g	γ̃(g	NOUN
ejpam-4461	353	20	)	)	PUNCT
ejpam-4461	353	21	(	(	PUNCT
ejpam-4461	353	22	1	1	NUM
ejpam-4461	353	23	+	+	NOUN
ejpam-4461	353	24	m−	m−	PROPN
ejpam-4461	353	25	γ(h	γ(h	NOUN
ejpam-4461	353	26	)	)	PUNCT
ejpam-4461	353	27	)	)	PUNCT
ejpam-4461	354	1	+	+	CCONJ
ejpam-4461	354	2	nγ(h	nγ(h	X
ejpam-4461	354	3	)	)	PUNCT
ejpam-4461	354	4	}	}	PUNCT
ejpam-4461	354	5	proof	proof	NOUN
ejpam-4461	354	6	.	.	PUNCT
ejpam-4461	355	1	let	let	VERB
ejpam-4461	355	2	a	a	DET
ejpam-4461	355	3	⊆	⊆	NUM
ejpam-4461	355	4	v	v	NOUN
ejpam-4461	355	5	(	(	PUNCT
ejpam-4461	355	6	g	g	NOUN
ejpam-4461	355	7	)	)	PUNCT
ejpam-4461	355	8	be	be	AUX
ejpam-4461	355	9	a	a	DET
ejpam-4461	355	10	γ̃-set	γ̃-set	NOUN
ejpam-4461	355	11	of	of	ADP
ejpam-4461	355	12	g.	g.	NOUN
ejpam-4461	355	13	for	for	ADP
ejpam-4461	355	14	each	each	DET
ejpam-4461	355	15	v	v	NOUN
ejpam-4461	355	16	/∈	/∈	PUNCT
ejpam-4461	356	1	a	a	PRON
ejpam-4461	356	2	,	,	PUNCT
ejpam-4461	356	3	let	let	VERB
ejpam-4461	356	4	sv	sv	PROPN
ejpam-4461	356	5	⊆	⊆	NUM
ejpam-4461	356	6	v	v	NOUN
ejpam-4461	356	7	(	(	PUNCT
ejpam-4461	356	8	h	h	NOUN
ejpam-4461	356	9	)	)	PUNCT
ejpam-4461	356	10	be	be	AUX
ejpam-4461	356	11	a	a	DET
ejpam-4461	356	12	γ	γ	NOUN
ejpam-4461	356	13	-	-	PUNCT
ejpam-4461	356	14	set	set	NOUN
ejpam-4461	356	15	of	of	ADP
ejpam-4461	356	16	hv	hv	PROPN
ejpam-4461	356	17	.	.	PUNCT
ejpam-4461	357	1	define	define	PROPN
ejpam-4461	357	2	s	s	PART
ejpam-4461	357	3	=	=	PUNCT
ejpam-4461	357	4	a	a	DET
ejpam-4461	357	5	∪	∪	ADJ
ejpam-4461	357	6	(	(	PUNCT
ejpam-4461	357	7	⋃	⋃	PROPN
ejpam-4461	357	8	v∈a	v∈a	NOUN
ejpam-4461	357	9	v	v	NOUN
ejpam-4461	357	10	(	(	PUNCT
ejpam-4461	357	11	hv	hv	PROPN
ejpam-4461	357	12	)	)	PUNCT
ejpam-4461	357	13	)	)	PUNCT
ejpam-4461	357	14	∪	∪	ADP
ejpam-4461	357	15			PROPN
ejpam-4461	357	16	⋃	⋃	PROPN
ejpam-4461	357	17	v∈v	v∈v	NOUN
ejpam-4461	357	18	(	(	PUNCT
ejpam-4461	357	19	g)\a	g)\a	NOUN
ejpam-4461	357	20	sv	sv	PROPN
ejpam-4461	357	21			PROPN
ejpam-4461	357	22	.	.	PUNCT
ejpam-4461	358	1	since	since	SCONJ
ejpam-4461	358	2	s	s	PART
ejpam-4461	358	3	satisfies	satisfie	NOUN
ejpam-4461	358	4	theorem	theorem	VERB
ejpam-4461	358	5	4(ii	4(ii	NUM
ejpam-4461	358	6	)	)	PUNCT
ejpam-4461	358	7	,	,	PUNCT
ejpam-4461	358	8	s	s	VERB
ejpam-4461	358	9	is	be	AUX
ejpam-4461	358	10	an	an	DET
ejpam-4461	358	11	outer	outer	ADV
ejpam-4461	358	12	-	-	PUNCT
ejpam-4461	358	13	connected	connect	VERB
ejpam-4461	358	14	semitotal	semitotal	ADJ
ejpam-4461	358	15	dominating	dominating	NOUN
ejpam-4461	358	16	set	set	NOUN
ejpam-4461	358	17	of	of	ADP
ejpam-4461	358	18	g	g	PROPN
ejpam-4461	358	19	◦	◦	NOUN
ejpam-4461	358	20	h.	h.	NOUN
ejpam-4461	358	21	thus	thus	ADV
ejpam-4461	358	22	,	,	PUNCT
ejpam-4461	358	23	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	358	24	◦	◦	NOUN
ejpam-4461	358	25	h	h	NOUN
ejpam-4461	358	26	)	)	PUNCT
ejpam-4461	358	27	≤	≤	NUM
ejpam-4461	358	28	|s|	|s|	PROPN
ejpam-4461	358	29	=	=	SYM
ejpam-4461	358	30	|a|+m|a|+	|a|+m|a|+	X
ejpam-4461	358	31	(	(	PUNCT
ejpam-4461	358	32	n−	n−	NOUN
ejpam-4461	358	33	|a|	|a|	NOUN
ejpam-4461	358	34	)	)	PUNCT
ejpam-4461	358	35	γ(h	γ(h	NOUN
ejpam-4461	358	36	)	)	PUNCT
ejpam-4461	358	37	=	=	PUNCT
ejpam-4461	358	38	γ̃(g	γ̃(g	PROPN
ejpam-4461	358	39	)	)	PUNCT
ejpam-4461	358	40	+	+	NOUN
ejpam-4461	358	41	mγ̃(g	mγ̃(g	NOUN
ejpam-4461	358	42	)	)	PUNCT
ejpam-4461	358	43	+	+	CCONJ
ejpam-4461	358	44	(	(	PUNCT
ejpam-4461	358	45	n−	n−	NOUN
ejpam-4461	358	46	γ̃(g))γ(h	γ̃(g))γ(h	PUNCT
ejpam-4461	358	47	)	)	PUNCT
ejpam-4461	358	48	=	=	SYM
ejpam-4461	358	49	γ̃(g	γ̃(g	NOUN
ejpam-4461	358	50	)	)	PUNCT
ejpam-4461	358	51	(	(	PUNCT
ejpam-4461	358	52	1	1	NUM
ejpam-4461	358	53	+	+	NOUN
ejpam-4461	358	54	m−	m−	PROPN
ejpam-4461	358	55	γ(h	γ(h	NOUN
ejpam-4461	358	56	)	)	PUNCT
ejpam-4461	358	57	)	)	PUNCT
ejpam-4461	359	1	+	+	CCONJ
ejpam-4461	359	2	nγ(h	nγ(h	NOUN
ejpam-4461	359	3	)	)	PUNCT
ejpam-4461	359	4	.	.	PUNCT
ejpam-4461	360	1	in	in	ADP
ejpam-4461	360	2	particular	particular	ADJ
ejpam-4461	360	3	,	,	PUNCT
ejpam-4461	360	4	if	if	SCONJ
ejpam-4461	360	5	γ(h	γ(h	NOUN
ejpam-4461	360	6	)	)	PUNCT
ejpam-4461	360	7	=	=	SYM
ejpam-4461	360	8	1	1	NUM
ejpam-4461	360	9	,	,	PUNCT
ejpam-4461	360	10	then	then	ADV
ejpam-4461	360	11	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	360	12	◦	◦	NOUN
ejpam-4461	360	13	h	h	NOUN
ejpam-4461	360	14	)	)	PUNCT
ejpam-4461	360	15	≤	≤	NOUN
ejpam-4461	360	16	n+mγ̃(g	n+mγ̃(g	NOUN
ejpam-4461	360	17	)	)	PUNCT
ejpam-4461	360	18	.	.	PUNCT
ejpam-4461	361	1	to	to	PART
ejpam-4461	361	2	complete	complete	VERB
ejpam-4461	361	3	the	the	DET
ejpam-4461	361	4	desired	desire	VERB
ejpam-4461	361	5	results	result	NOUN
ejpam-4461	361	6	,	,	PUNCT
ejpam-4461	361	7	for	for	ADP
ejpam-4461	361	8	the	the	DET
ejpam-4461	361	9	case	case	NOUN
ejpam-4461	361	10	where	where	SCONJ
ejpam-4461	361	11	γ(h	γ(h	NOUN
ejpam-4461	361	12	)	)	PUNCT
ejpam-4461	361	13	=	=	SYM
ejpam-4461	362	1	1	1	NUM
ejpam-4461	362	2	,	,	PUNCT
ejpam-4461	362	3	let	let	VERB
ejpam-4461	362	4	y	y	PROPN
ejpam-4461	362	5	∈	∈	PROPN
ejpam-4461	362	6	v	v	ADP
ejpam-4461	362	7	(	(	PUNCT
ejpam-4461	362	8	h	h	NOUN
ejpam-4461	362	9	)	)	PUNCT
ejpam-4461	362	10	for	for	ADP
ejpam-4461	362	11	which	which	PRON
ejpam-4461	362	12	nh	nh	NOUN
ejpam-4461	363	1	[	[	X
ejpam-4461	363	2	y	y	X
ejpam-4461	363	3	]	]	X
ejpam-4461	363	4	=	=	SYM
ejpam-4461	363	5	v	v	X
ejpam-4461	363	6	(	(	PUNCT
ejpam-4461	363	7	h	h	NOUN
ejpam-4461	363	8	)	)	PUNCT
ejpam-4461	363	9	.	.	PUNCT
ejpam-4461	364	1	pick	pick	VERB
ejpam-4461	364	2	a	a	DET
ejpam-4461	364	3	z	z	NOUN
ejpam-4461	364	4	∈	∈	PROPN
ejpam-4461	364	5	v	v	ADP
ejpam-4461	364	6	(	(	PUNCT
ejpam-4461	364	7	h	h	NOUN
ejpam-4461	364	8	)	)	PUNCT
ejpam-4461	364	9	\	\	NOUN
ejpam-4461	364	10	{	{	PUNCT
ejpam-4461	364	11	y	y	NOUN
ejpam-4461	364	12	}	}	PUNCT
ejpam-4461	364	13	and	and	CCONJ
ejpam-4461	364	14	define	define	VERB
ejpam-4461	364	15	sv	sv	X
ejpam-4461	364	16	=	=	PUNCT
ejpam-4461	364	17	{	{	PUNCT
ejpam-4461	364	18	z	z	PROPN
ejpam-4461	364	19	,	,	PUNCT
ejpam-4461	364	20	y	y	NOUN
ejpam-4461	364	21	}	}	PUNCT
ejpam-4461	364	22	for	for	ADP
ejpam-4461	364	23	all	all	PRON
ejpam-4461	364	24	v	v	ADP
ejpam-4461	364	25	∈	∈	NOUN
ejpam-4461	364	26	v	v	NOUN
ejpam-4461	364	27	(	(	PUNCT
ejpam-4461	364	28	g	g	NOUN
ejpam-4461	364	29	)	)	PUNCT
ejpam-4461	364	30	.	.	PUNCT
ejpam-4461	365	1	on	on	ADP
ejpam-4461	365	2	the	the	DET
ejpam-4461	365	3	other	other	ADJ
ejpam-4461	365	4	hand	hand	NOUN
ejpam-4461	365	5	,	,	PUNCT
ejpam-4461	365	6	if	if	SCONJ
ejpam-4461	365	7	γ(h	γ(h	NOUN
ejpam-4461	365	8	)	)	PUNCT
ejpam-4461	365	9	≥	≥	NOUN
ejpam-4461	365	10	2	2	NUM
ejpam-4461	365	11	,	,	PUNCT
ejpam-4461	365	12	then	then	ADV
ejpam-4461	365	13	choose	choose	VERB
ejpam-4461	365	14	sv	sv	PROPN
ejpam-4461	365	15	⊆	⊆	NUM
ejpam-4461	365	16	v	v	PROPN
ejpam-4461	365	17	(	(	PUNCT
ejpam-4461	365	18	hv	hv	NOUN
ejpam-4461	365	19	)	)	PUNCT
ejpam-4461	365	20	to	to	PART
ejpam-4461	365	21	be	be	AUX
ejpam-4461	365	22	a	a	DET
ejpam-4461	365	23	γ	γ	NOUN
ejpam-4461	365	24	-	-	PUNCT
ejpam-4461	365	25	set	set	NOUN
ejpam-4461	365	26	of	of	ADP
ejpam-4461	365	27	hv	hv	NOUN
ejpam-4461	365	28	for	for	ADP
ejpam-4461	365	29	all	all	DET
ejpam-4461	365	30	v	v	ADP
ejpam-4461	365	31	∈	∈	NUM
ejpam-4461	365	32	v	v	NOUN
ejpam-4461	365	33	(	(	PUNCT
ejpam-4461	365	34	g	g	NOUN
ejpam-4461	365	35	)	)	PUNCT
ejpam-4461	365	36	.	.	PUNCT
ejpam-4461	366	1	in	in	ADP
ejpam-4461	366	2	any	any	DET
ejpam-4461	366	3	case	case	NOUN
ejpam-4461	366	4	,	,	PUNCT
ejpam-4461	366	5	s	s	NOUN
ejpam-4461	366	6	=	=	PUNCT
ejpam-4461	366	7	⋃	⋃	NOUN
ejpam-4461	366	8	v∈v	v∈v	NOUN
ejpam-4461	366	9	(	(	PUNCT
ejpam-4461	366	10	g	g	NOUN
ejpam-4461	366	11	)	)	PUNCT
ejpam-4461	366	12	sv	sv	PROPN
ejpam-4461	366	13	satisfies	satisfie	NOUN
ejpam-4461	366	14	theorem	theorem	VERB
ejpam-4461	366	15	4(ii	4(ii	NUM
ejpam-4461	366	16	)	)	PUNCT
ejpam-4461	366	17	.	.	PUNCT
ejpam-4461	367	1	thus	thus	ADV
ejpam-4461	367	2	,	,	PUNCT
ejpam-4461	367	3	s	s	VERB
ejpam-4461	367	4	is	be	AUX
ejpam-4461	367	5	an	an	DET
ejpam-4461	367	6	outer	outer	ADV
ejpam-4461	367	7	-	-	PUNCT
ejpam-4461	367	8	connected	connect	VERB
ejpam-4461	367	9	semitotal	semitotal	ADJ
ejpam-4461	367	10	dominating	dominating	NOUN
ejpam-4461	367	11	set	set	NOUN
ejpam-4461	367	12	of	of	ADP
ejpam-4461	367	13	g	g	PROPN
ejpam-4461	367	14	◦	◦	NOUN
ejpam-4461	367	15	h.	h.	NOUN
ejpam-4461	367	16	this	this	PRON
ejpam-4461	367	17	means	mean	VERB
ejpam-4461	367	18	that	that	SCONJ
ejpam-4461	367	19	if	if	SCONJ
ejpam-4461	367	20	γ(h	γ(h	NOUN
ejpam-4461	367	21	)	)	PUNCT
ejpam-4461	367	22	=	=	SYM
ejpam-4461	367	23	1	1	NUM
ejpam-4461	367	24	,	,	PUNCT
ejpam-4461	367	25	then	then	ADV
ejpam-4461	367	26	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	367	27	◦	◦	NOUN
ejpam-4461	367	28	h	h	NOUN
ejpam-4461	367	29	)	)	PUNCT
ejpam-4461	367	30	≤	≤	NUM
ejpam-4461	367	31	|s|	|s|	PROPN
ejpam-4461	367	32	=	=	PUNCT
ejpam-4461	367	33	2n	2n	NUM
ejpam-4461	367	34	.	.	PUNCT
ejpam-4461	368	1	for	for	ADP
ejpam-4461	368	2	γ(h	γ(h	NOUN
ejpam-4461	368	3	)	)	PUNCT
ejpam-4461	368	4	≥	≥	NOUN
ejpam-4461	368	5	2	2	NUM
ejpam-4461	368	6	,	,	PUNCT
ejpam-4461	368	7	γ̃t2(g	γ̃t2(g	PROPN
ejpam-4461	368	8	◦	◦	NOUN
ejpam-4461	368	9	h	h	NOUN
ejpam-4461	368	10	)	)	PUNCT
ejpam-4461	368	11	≤	≤	NUM
ejpam-4461	368	12	|s|	|s|	PROPN
ejpam-4461	368	13	=	=	NOUN
ejpam-4461	368	14	nγ(h	nγ(h	NOUN
ejpam-4461	368	15	)	)	PUNCT
ejpam-4461	368	16	.	.	PUNCT
ejpam-4461	369	1	corollary	corollary	ADJ
ejpam-4461	369	2	4	4	NUM
ejpam-4461	369	3	.	.	PUNCT
ejpam-4461	370	1	let	let	VERB
ejpam-4461	370	2	g	g	NOUN
ejpam-4461	370	3	and	and	CCONJ
ejpam-4461	370	4	h	h	NOUN
ejpam-4461	370	5	be	be	AUX
ejpam-4461	370	6	nontrivial	nontrivial	ADJ
ejpam-4461	370	7	connected	connect	VERB
ejpam-4461	370	8	graphs	graph	NOUN
ejpam-4461	370	9	of	of	ADP
ejpam-4461	370	10	orders	order	NOUN
ejpam-4461	370	11	n	n	PRON
ejpam-4461	370	12	and	and	CCONJ
ejpam-4461	370	13	m	m	PROPN
ejpam-4461	370	14	,	,	PUNCT
ejpam-4461	370	15	respectively	respectively	ADV
ejpam-4461	370	16	.	.	PUNCT
ejpam-4461	371	1	a.	a.	PROPN
ejpam-4461	371	2	aradais	aradais	PROPN
ejpam-4461	371	3	,	,	PUNCT
ejpam-4461	371	4	f.	f.	PROPN
ejpam-4461	371	5	jamil	jamil	PROPN
ejpam-4461	371	6	/	/	SYM
ejpam-4461	371	7	eur	eur	PROPN
ejpam-4461	371	8	.	.	PUNCT
ejpam-4461	372	1	j.	j.	PROPN
ejpam-4461	372	2	pure	pure	PROPN
ejpam-4461	372	3	appl	appl	PROPN
ejpam-4461	372	4	.	.	PROPN
ejpam-4461	372	5	math	math	PROPN
ejpam-4461	372	6	,	,	PUNCT
ejpam-4461	372	7	15	15	NUM
ejpam-4461	372	8	(	(	PUNCT
ejpam-4461	372	9	3	3	NUM
ejpam-4461	372	10	)	)	PUNCT
ejpam-4461	372	11	(	(	PUNCT
ejpam-4461	372	12	2022	2022	NUM
ejpam-4461	372	13	)	)	PUNCT
ejpam-4461	372	14	,	,	PUNCT
ejpam-4461	372	15	1265	1265	NUM
ejpam-4461	372	16	-	-	SYM
ejpam-4461	372	17	1279	1279	NUM
ejpam-4461	372	18	1276	1276	NUM
ejpam-4461	372	19	(	(	PUNCT
ejpam-4461	372	20	i	i	NOUN
ejpam-4461	372	21	)	)	PUNCT
ejpam-4461	372	22	if	if	SCONJ
ejpam-4461	372	23	γ(h	γ(h	NOUN
ejpam-4461	372	24	)	)	PUNCT
ejpam-4461	372	25	=	=	SYM
ejpam-4461	373	1	1	1	NUM
ejpam-4461	373	2	,	,	PUNCT
ejpam-4461	373	3	then	then	ADV
ejpam-4461	373	4	γ̃t2	γ̃t2	PROPN
ejpam-4461	373	5	(	(	PUNCT
ejpam-4461	373	6	(	(	PUNCT
ejpam-4461	373	7	g+k1	g+k1	NOUN
ejpam-4461	373	8	)	)	PUNCT
ejpam-4461	373	9	◦	◦	NOUN
ejpam-4461	373	10	h	h	NOUN
ejpam-4461	373	11	)	)	PUNCT
ejpam-4461	373	12	=	=	NOUN
ejpam-4461	374	1	min{2n+	min{2n+	PROPN
ejpam-4461	374	2	2	2	NUM
ejpam-4461	374	3	,	,	PUNCT
ejpam-4461	374	4	n+m+	n+m+	X
ejpam-4461	374	5	1	1	NUM
ejpam-4461	374	6	}	}	PUNCT
ejpam-4461	374	7	.	.	PUNCT
ejpam-4461	375	1	(	(	PUNCT
ejpam-4461	375	2	ii	ii	NOUN
ejpam-4461	375	3	)	)	PUNCT
ejpam-4461	375	4	if	if	SCONJ
ejpam-4461	375	5	γ(h	γ(h	NOUN
ejpam-4461	375	6	)	)	PUNCT
ejpam-4461	375	7	≥	≥	NOUN
ejpam-4461	375	8	2	2	NUM
ejpam-4461	375	9	,	,	PUNCT
ejpam-4461	375	10	then	then	ADV
ejpam-4461	375	11	γ̃t2	γ̃t2	PROPN
ejpam-4461	375	12	(	(	PUNCT
ejpam-4461	375	13	(	(	PUNCT
ejpam-4461	375	14	g+k1	g+k1	NOUN
ejpam-4461	375	15	)	)	PUNCT
ejpam-4461	375	16	◦	◦	NOUN
ejpam-4461	375	17	h	h	NOUN
ejpam-4461	375	18	)	)	PUNCT
ejpam-4461	375	19	=	=	SYM
ejpam-4461	375	20	min{(n+	min{(n+	PROPN
ejpam-4461	375	21	1)γ(h	1)γ(h	NUM
ejpam-4461	375	22	)	)	PUNCT
ejpam-4461	375	23	,	,	PUNCT
ejpam-4461	375	24	γ̃(g	γ̃(g	NOUN
ejpam-4461	375	25	)	)	PUNCT
ejpam-4461	375	26	(	(	PUNCT
ejpam-4461	375	27	1	1	NUM
ejpam-4461	375	28	+	+	NOUN
ejpam-4461	375	29	m−	m−	PROPN
ejpam-4461	375	30	γ(h	γ(h	NOUN
ejpam-4461	375	31	)	)	PUNCT
ejpam-4461	375	32	)	)	PUNCT
ejpam-4461	376	1	+	+	CCONJ
ejpam-4461	376	2	nγ(h	nγ(h	X
ejpam-4461	376	3	)	)	PUNCT
ejpam-4461	376	4	}	}	PUNCT
ejpam-4461	376	5	proof	proof	NOUN
ejpam-4461	376	6	.	.	PUNCT
ejpam-4461	377	1	put	put	VERB
ejpam-4461	377	2	k	k	PROPN
ejpam-4461	377	3	=	=	PUNCT
ejpam-4461	377	4	(	(	PUNCT
ejpam-4461	377	5	g+k1	g+k1	NOUN
ejpam-4461	377	6	)	)	PUNCT
ejpam-4461	377	7	◦	◦	NOUN
ejpam-4461	377	8	h	h	NOUN
ejpam-4461	377	9	,	,	PUNCT
ejpam-4461	377	10	and	and	CCONJ
ejpam-4461	377	11	α	α	NOUN
ejpam-4461	377	12	=	=	PUNCT
ejpam-4461	377	13	min{2n+2	min{2n+2	PROPN
ejpam-4461	377	14	,	,	PUNCT
ejpam-4461	377	15	n+m+1	n+m+1	PROPN
ejpam-4461	377	16	}	}	PUNCT
ejpam-4461	377	17	.	.	PUNCT
ejpam-4461	378	1	by	by	ADP
ejpam-4461	378	2	corollary	corollary	ADJ
ejpam-4461	378	3	3	3	NUM
ejpam-4461	378	4	,	,	PUNCT
ejpam-4461	378	5	with	with	ADP
ejpam-4461	378	6	γ̃(g+k1	γ̃(g+k1	NOUN
ejpam-4461	378	7	)	)	PUNCT
ejpam-4461	378	8	=	=	SYM
ejpam-4461	378	9	1	1	NUM
ejpam-4461	378	10	,	,	PUNCT
ejpam-4461	378	11	we	we	PRON
ejpam-4461	378	12	have	have	VERB
ejpam-4461	378	13	γ̃t2(k	γ̃t2(k	NOUN
ejpam-4461	378	14	)	)	PUNCT
ejpam-4461	378	15	≤	≤	NOUN
ejpam-4461	379	1	α	α	X
ejpam-4461	379	2	.	.	PUNCT
ejpam-4461	380	1	now	now	ADV
ejpam-4461	380	2	,	,	PUNCT
ejpam-4461	380	3	let	let	VERB
ejpam-4461	380	4	s	s	PRON
ejpam-4461	380	5	⊆	⊆	NUM
ejpam-4461	380	6	v	v	NOUN
ejpam-4461	380	7	(	(	PUNCT
ejpam-4461	380	8	k	k	NOUN
ejpam-4461	380	9	)	)	PUNCT
ejpam-4461	380	10	be	be	AUX
ejpam-4461	380	11	an	an	DET
ejpam-4461	380	12	outer	outer	ADV
ejpam-4461	380	13	-	-	PUNCT
ejpam-4461	380	14	connected	connect	VERB
ejpam-4461	380	15	semitotal	semitotal	ADJ
ejpam-4461	380	16	dominating	dominating	NOUN
ejpam-4461	380	17	set	set	NOUN
ejpam-4461	380	18	of	of	ADP
ejpam-4461	380	19	k.	k.	PROPN
ejpam-4461	380	20	since	since	SCONJ
ejpam-4461	380	21	s	s	PROPN
ejpam-4461	380	22	is	be	AUX
ejpam-4461	380	23	a	a	DET
ejpam-4461	380	24	dominating	dominating	NOUN
ejpam-4461	380	25	set	set	NOUN
ejpam-4461	380	26	of	of	ADP
ejpam-4461	380	27	k	k	PROPN
ejpam-4461	380	28	,	,	PUNCT
ejpam-4461	380	29	s	s	PART
ejpam-4461	380	30	∩	∩	ADJ
ejpam-4461	380	31	v	v	NOUN
ejpam-4461	380	32	(	(	PUNCT
ejpam-4461	380	33	hx	hx	PROPN
ejpam-4461	380	34	+	+	CCONJ
ejpam-4461	380	35	x	x	X
ejpam-4461	380	36	)	)	PUNCT
ejpam-4461	380	37	̸=	̸=	NOUN
ejpam-4461	380	38	∅	∅	NOUN
ejpam-4461	380	39	for	for	ADP
ejpam-4461	380	40	all	all	PRON
ejpam-4461	380	41	x	x	SYM
ejpam-4461	380	42	∈	∈	PROPN
ejpam-4461	380	43	v	v	NOUN
ejpam-4461	380	44	(	(	PUNCT
ejpam-4461	380	45	g	g	PROPN
ejpam-4461	380	46	+	+	CCONJ
ejpam-4461	380	47	k1	k1	NOUN
ejpam-4461	380	48	)	)	PUNCT
ejpam-4461	380	49	.	.	PUNCT
ejpam-4461	381	1	first	first	ADV
ejpam-4461	381	2	,	,	PUNCT
ejpam-4461	381	3	suppose	suppose	VERB
ejpam-4461	381	4	that	that	SCONJ
ejpam-4461	381	5	s	s	VERB
ejpam-4461	381	6	∩	∩	ADJ
ejpam-4461	381	7	v	v	ADJ
ejpam-4461	381	8	(	(	PUNCT
ejpam-4461	381	9	g	g	PROPN
ejpam-4461	381	10	+	+	NOUN
ejpam-4461	381	11	k1	k1	NOUN
ejpam-4461	381	12	)	)	PUNCT
ejpam-4461	381	13	=	=	PUNCT
ejpam-4461	381	14	∅.	∅.	NOUN
ejpam-4461	381	15	by	by	ADP
ejpam-4461	381	16	theorem	theorem	ADJ
ejpam-4461	381	17	4(ii	4(ii	NUM
ejpam-4461	381	18	)	)	PUNCT
ejpam-4461	381	19	,	,	PUNCT
ejpam-4461	381	20	s	s	VERB
ejpam-4461	381	21	∩	∩	ADJ
ejpam-4461	381	22	v	v	X
ejpam-4461	381	23	(	(	PUNCT
ejpam-4461	381	24	hx	hx	PROPN
ejpam-4461	381	25	)	)	PUNCT
ejpam-4461	381	26	is	be	AUX
ejpam-4461	381	27	a	a	DET
ejpam-4461	381	28	nonsingleton	nonsingleton	NOUN
ejpam-4461	381	29	dominating	dominating	NOUN
ejpam-4461	381	30	set	set	NOUN
ejpam-4461	381	31	of	of	ADP
ejpam-4461	381	32	hx	hx	PROPN
ejpam-4461	381	33	+	+	CCONJ
ejpam-4461	381	34	x	x	X
ejpam-4461	381	35	for	for	ADP
ejpam-4461	381	36	all	all	PRON
ejpam-4461	381	37	x	x	SYM
ejpam-4461	381	38	∈	∈	PROPN
ejpam-4461	381	39	v	v	NOUN
ejpam-4461	381	40	(	(	PUNCT
ejpam-4461	381	41	g	g	PROPN
ejpam-4461	381	42	+	+	CCONJ
ejpam-4461	381	43	k1	k1	NOUN
ejpam-4461	381	44	)	)	PUNCT
ejpam-4461	381	45	.	.	PUNCT
ejpam-4461	382	1	this	this	PRON
ejpam-4461	382	2	means	mean	VERB
ejpam-4461	382	3	that	that	SCONJ
ejpam-4461	382	4	|s|	|s|	VERB
ejpam-4461	382	5	≥	≥	NOUN
ejpam-4461	382	6	2(n	2(n	NUM
ejpam-4461	382	7	+	+	CCONJ
ejpam-4461	382	8	1	1	X
ejpam-4461	382	9	)	)	PUNCT
ejpam-4461	382	10	=	=	NOUN
ejpam-4461	382	11	2n	2n	NUM
ejpam-4461	383	1	+	+	CCONJ
ejpam-4461	383	2	2	2	NUM
ejpam-4461	383	3	≥	≥	NOUN
ejpam-4461	383	4	α	α	NOUN
ejpam-4461	383	5	.	.	PUNCT
ejpam-4461	384	1	next	next	ADV
ejpam-4461	384	2	,	,	PUNCT
ejpam-4461	384	3	suppose	suppose	VERB
ejpam-4461	384	4	that	that	SCONJ
ejpam-4461	384	5	s	s	VERB
ejpam-4461	384	6	∩	∩	ADJ
ejpam-4461	384	7	v	v	X
ejpam-4461	384	8	(	(	PUNCT
ejpam-4461	384	9	g+k1	g+k1	NOUN
ejpam-4461	384	10	)	)	PUNCT
ejpam-4461	384	11	̸=	̸=	PROPN
ejpam-4461	384	12	∅.	∅.	VERB
ejpam-4461	384	13	clearly	clearly	ADV
ejpam-4461	384	14	,	,	PUNCT
ejpam-4461	384	15	if	if	SCONJ
ejpam-4461	384	16	v	v	X
ejpam-4461	384	17	(	(	PUNCT
ejpam-4461	384	18	g+k1	g+k1	NOUN
ejpam-4461	384	19	)	)	PUNCT
ejpam-4461	384	20	⊆	⊆	NUM
ejpam-4461	384	21	s	s	NOUN
ejpam-4461	384	22	,	,	PUNCT
ejpam-4461	384	23	then	then	ADV
ejpam-4461	384	24	|s|	|s|	PROPN
ejpam-4461	384	25	≥	≥	PROPN
ejpam-4461	384	26	2n+	2n+	NUM
ejpam-4461	384	27	2	2	NUM
ejpam-4461	384	28	.	.	PUNCT
ejpam-4461	384	29	assume	assume	VERB
ejpam-4461	384	30	that	that	SCONJ
ejpam-4461	384	31	v	v	INTJ
ejpam-4461	384	32	(	(	PUNCT
ejpam-4461	384	33	g+k1)\s	g+k1)\s	AUX
ejpam-4461	384	34	̸=	̸=	PROPN
ejpam-4461	384	35	∅.	∅.	ADV
ejpam-4461	384	36	let	let	VERB
ejpam-4461	384	37	w	w	PROPN
ejpam-4461	384	38	∈	∈	PROPN
ejpam-4461	384	39	s∩v	s∩v	PROPN
ejpam-4461	384	40	(	(	PUNCT
ejpam-4461	384	41	g+k1	g+k1	NOUN
ejpam-4461	384	42	)	)	PUNCT
ejpam-4461	384	43	.	.	PUNCT
ejpam-4461	385	1	since	since	SCONJ
ejpam-4461	385	2	s	s	PROPN
ejpam-4461	385	3	is	be	AUX
ejpam-4461	385	4	an	an	DET
ejpam-4461	385	5	outer	outer	ADV
ejpam-4461	385	6	-	-	PUNCT
ejpam-4461	385	7	connected	connect	VERB
ejpam-4461	385	8	semitotal	semitotal	ADJ
ejpam-4461	385	9	dominating	dominating	NOUN
ejpam-4461	385	10	set	set	NOUN
ejpam-4461	385	11	of	of	ADP
ejpam-4461	385	12	k	k	PROPN
ejpam-4461	385	13	and	and	CCONJ
ejpam-4461	385	14	v	v	PROPN
ejpam-4461	385	15	(	(	PUNCT
ejpam-4461	385	16	g+k1	g+k1	NOUN
ejpam-4461	385	17	)	)	PUNCT
ejpam-4461	385	18	\	\	PROPN
ejpam-4461	385	19	s	s	PART
ejpam-4461	385	20	⊆	⊆	NUM
ejpam-4461	385	21	v	v	NOUN
ejpam-4461	385	22	(	(	PUNCT
ejpam-4461	385	23	k	k	NOUN
ejpam-4461	385	24	)	)	PUNCT
ejpam-4461	385	25	\	\	PROPN
ejpam-4461	386	1	s	s	PROPN
ejpam-4461	386	2	,	,	PUNCT
ejpam-4461	386	3	v	v	PROPN
ejpam-4461	386	4	(	(	PUNCT
ejpam-4461	386	5	hw	hw	NOUN
ejpam-4461	386	6	)	)	PUNCT
ejpam-4461	386	7	⊆	⊆	NUM
ejpam-4461	386	8	s.	s.	PROPN
ejpam-4461	386	9	this	this	PRON
ejpam-4461	386	10	means	mean	VERB
ejpam-4461	386	11	that	that	SCONJ
ejpam-4461	386	12	|s|	|s|	VERB
ejpam-4461	386	13	≥	≥	NUM
ejpam-4461	386	14	|v	|v	PROPN
ejpam-4461	386	15	(	(	PUNCT
ejpam-4461	386	16	hw	hw	X
ejpam-4461	386	17	+	+	CCONJ
ejpam-4461	386	18	w)|+	w)|+	ADJ
ejpam-4461	386	19	∑	∑	PUNCT
ejpam-4461	386	20	x∈v	x∈v	PROPN
ejpam-4461	386	21	(	(	PUNCT
ejpam-4461	386	22	g+k1)\{w	g+k1)\{w	PROPN
ejpam-4461	386	23	}	}	PUNCT
ejpam-4461	386	24	|s	|s	PROPN
ejpam-4461	386	25	∩	∩	PROPN
ejpam-4461	386	26	v	v	X
ejpam-4461	386	27	(	(	PUNCT
ejpam-4461	386	28	hx	hx	PROPN
ejpam-4461	386	29	+	+	PROPN
ejpam-4461	386	30	x)|	x)|	PROPN
ejpam-4461	386	31	≥	≥	NUM
ejpam-4461	386	32	m+	m+	NUM
ejpam-4461	386	33	1	1	NUM
ejpam-4461	386	34	+	+	CCONJ
ejpam-4461	386	35	n	n	CCONJ
ejpam-4461	386	36	≥	≥	NOUN
ejpam-4461	386	37	α	α	NOUN
ejpam-4461	386	38	.	.	PUNCT
ejpam-4461	387	1	since	since	SCONJ
ejpam-4461	387	2	s	s	NOUN
ejpam-4461	387	3	is	be	AUX
ejpam-4461	387	4	arbitrary	arbitrary	ADJ
ejpam-4461	387	5	,	,	PUNCT
ejpam-4461	387	6	γ̃t2(k	γ̃t2(k	PROPN
ejpam-4461	387	7	)	)	PUNCT
ejpam-4461	387	8	≥	≥	NOUN
ejpam-4461	387	9	α	α	X
ejpam-4461	387	10	.	.	PUNCT
ejpam-4461	388	1	similar	similar	ADJ
ejpam-4461	388	2	arguments	argument	NOUN
ejpam-4461	388	3	will	will	AUX
ejpam-4461	388	4	prove	prove	VERB
ejpam-4461	388	5	(	(	PUNCT
ejpam-4461	388	6	ii	ii	NOUN
ejpam-4461	388	7	)	)	PUNCT
ejpam-4461	388	8	.	.	PUNCT
ejpam-4461	389	1	it	it	PRON
ejpam-4461	389	2	is	be	AUX
ejpam-4461	389	3	worth	worth	ADJ
ejpam-4461	389	4	noting	note	VERB
ejpam-4461	389	5	that	that	SCONJ
ejpam-4461	389	6	the	the	DET
ejpam-4461	389	7	wheel	wheel	NOUN
ejpam-4461	389	8	graphs	graph	NOUN
ejpam-4461	389	9	and	and	CCONJ
ejpam-4461	389	10	the	the	DET
ejpam-4461	389	11	fan	fan	NOUN
ejpam-4461	389	12	graphs	graph	NOUN
ejpam-4461	389	13	are	be	AUX
ejpam-4461	389	14	among	among	ADP
ejpam-4461	389	15	the	the	DET
ejpam-4461	389	16	graphs	graph	NOUN
ejpam-4461	389	17	represented	represent	VERB
ejpam-4461	389	18	by	by	ADP
ejpam-4461	389	19	g+k1	g+k1	NOUN
ejpam-4461	389	20	in	in	ADP
ejpam-4461	389	21	corollary	corollary	ADJ
ejpam-4461	389	22	4	4	NUM
ejpam-4461	389	23	.	.	PUNCT
ejpam-4461	389	24	theorem	theorem	NOUN
ejpam-4461	389	25	5	5	NUM
ejpam-4461	389	26	.	.	PUNCT
ejpam-4461	390	1	[	[	X
ejpam-4461	390	2	1	1	X
ejpam-4461	390	3	]	]	PUNCT
ejpam-4461	390	4	let	let	VERB
ejpam-4461	390	5	g	g	NOUN
ejpam-4461	390	6	and	and	CCONJ
ejpam-4461	390	7	h	h	NOUN
ejpam-4461	390	8	be	be	AUX
ejpam-4461	390	9	nontrivial	nontrivial	ADJ
ejpam-4461	390	10	connected	connected	ADJ
ejpam-4461	390	11	graphs	graph	NOUN
ejpam-4461	390	12	,	,	PUNCT
ejpam-4461	390	13	and	and	CCONJ
ejpam-4461	390	14	let	let	VERB
ejpam-4461	390	15	c	c	NOUN
ejpam-4461	390	16	=	=	SYM
ejpam-4461	390	17	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4461	390	18	}	}	PUNCT
ejpam-4461	390	19	×	×	NOUN
ejpam-4461	390	20	tx	tx	PROPN
ejpam-4461	390	21	)	)	PUNCT
ejpam-4461	390	22	⊆	⊆	NUM
ejpam-4461	390	23	v	v	NOUN
ejpam-4461	390	24	(	(	PUNCT
ejpam-4461	390	25	g[h	g[h	PROPN
ejpam-4461	390	26	]	]	PUNCT
ejpam-4461	390	27	)	)	PUNCT
ejpam-4461	390	28	.	.	PUNCT
ejpam-4461	391	1	then	then	ADV
ejpam-4461	391	2	c	c	PROPN
ejpam-4461	391	3	is	be	AUX
ejpam-4461	391	4	a	a	DET
ejpam-4461	391	5	semitotal	semitotal	ADJ
ejpam-4461	391	6	dominating	dominating	NOUN
ejpam-4461	391	7	set	set	VERB
ejpam-4461	391	8	in	in	ADP
ejpam-4461	391	9	g[h	g[h	PROPN
ejpam-4461	391	10	]	]	PUNCT
ejpam-4461	391	11	if	if	SCONJ
ejpam-4461	391	12	and	and	CCONJ
ejpam-4461	391	13	only	only	ADV
ejpam-4461	391	14	if	if	SCONJ
ejpam-4461	391	15	one	one	NUM
ejpam-4461	391	16	of	of	ADP
ejpam-4461	391	17	the	the	DET
ejpam-4461	391	18	following	follow	VERB
ejpam-4461	391	19	holds	hold	VERB
ejpam-4461	391	20	:	:	PUNCT
ejpam-4461	391	21	(	(	PUNCT
ejpam-4461	391	22	i	i	NOUN
ejpam-4461	391	23	)	)	PUNCT
ejpam-4461	391	24	s	s	VERB
ejpam-4461	391	25	is	be	AUX
ejpam-4461	391	26	a	a	DET
ejpam-4461	391	27	total	total	ADJ
ejpam-4461	391	28	dominating	dominating	NOUN
ejpam-4461	391	29	set	set	NOUN
ejpam-4461	391	30	in	in	ADP
ejpam-4461	391	31	g	g	NOUN
ejpam-4461	391	32	;	;	PUNCT
ejpam-4461	391	33	(	(	PUNCT
ejpam-4461	391	34	ii	ii	NOUN
ejpam-4461	391	35	)	)	PUNCT
ejpam-4461	391	36	s	s	VERB
ejpam-4461	391	37	is	be	AUX
ejpam-4461	391	38	a	a	DET
ejpam-4461	391	39	semitotal	semitotal	ADJ
ejpam-4461	391	40	dominating	dominating	NOUN
ejpam-4461	391	41	set	set	NOUN
ejpam-4461	391	42	in	in	ADP
ejpam-4461	391	43	g	g	PROPN
ejpam-4461	391	44	and	and	CCONJ
ejpam-4461	391	45	for	for	ADP
ejpam-4461	391	46	each	each	DET
ejpam-4461	391	47	x	x	X
ejpam-4461	391	48	∈	∈	PROPN
ejpam-4461	391	49	s	s	PART
ejpam-4461	391	50	\ng(s	\ng(s	NOUN
ejpam-4461	391	51	)	)	PUNCT
ejpam-4461	391	52	,	,	PUNCT
ejpam-4461	391	53	tx	tx	PROPN
ejpam-4461	391	54	is	be	AUX
ejpam-4461	391	55	a	a	DET
ejpam-4461	391	56	dominating	dominating	NOUN
ejpam-4461	391	57	set	set	VERB
ejpam-4461	391	58	in	in	ADP
ejpam-4461	391	59	h	h	NOUN
ejpam-4461	391	60	;	;	PUNCT
ejpam-4461	391	61	(	(	PUNCT
ejpam-4461	391	62	iii	iii	X
ejpam-4461	391	63	)	)	PUNCT
ejpam-4461	391	64	s	s	VERB
ejpam-4461	391	65	is	be	AUX
ejpam-4461	391	66	a	a	DET
ejpam-4461	391	67	dominating	dominating	NOUN
ejpam-4461	391	68	set	set	NOUN
ejpam-4461	391	69	in	in	ADP
ejpam-4461	391	70	g	g	NOUN
ejpam-4461	391	71	,	,	PUNCT
ejpam-4461	391	72	such	such	ADJ
ejpam-4461	391	73	that	that	SCONJ
ejpam-4461	391	74	,	,	PUNCT
ejpam-4461	391	75	tx	tx	PROPN
ejpam-4461	391	76	is	be	AUX
ejpam-4461	391	77	a	a	DET
ejpam-4461	391	78	dominating	dominating	NOUN
ejpam-4461	391	79	set	set	VERB
ejpam-4461	391	80	in	in	ADP
ejpam-4461	391	81	h	h	NOUN
ejpam-4461	391	82	for	for	ADP
ejpam-4461	391	83	each	each	DET
ejpam-4461	391	84	x	x	SYM
ejpam-4461	391	85	∈	∈	PROPN
ejpam-4461	391	86	s	s	PART
ejpam-4461	391	87	\ng(s	\ng(s	NOUN
ejpam-4461	391	88	)	)	PUNCT
ejpam-4461	391	89	,	,	PUNCT
ejpam-4461	391	90	and	and	CCONJ
ejpam-4461	391	91	|tx|	|tx|	NOUN
ejpam-4461	391	92	≥	≥	NUM
ejpam-4461	391	93	2	2	NUM
ejpam-4461	391	94	for	for	ADP
ejpam-4461	391	95	each	each	DET
ejpam-4461	391	96	x	x	SYM
ejpam-4461	391	97	∈	∈	PROPN
ejpam-4461	391	98	s	s	PART
ejpam-4461	391	99	\n2	\n2	ADJ
ejpam-4461	391	100	g(s	g(	NOUN
ejpam-4461	391	101	)	)	PUNCT
ejpam-4461	391	102	.	.	PUNCT
ejpam-4461	392	1	for	for	ADP
ejpam-4461	392	2	c	c	PROPN
ejpam-4461	392	3	⊆	⊆	NUM
ejpam-4461	392	4	v	v	NOUN
ejpam-4461	392	5	(	(	PUNCT
ejpam-4461	392	6	g[h	g[h	PROPN
ejpam-4461	392	7	]	]	PUNCT
ejpam-4461	392	8	)	)	PUNCT
ejpam-4461	392	9	,	,	PUNCT
ejpam-4461	392	10	define	define	VERB
ejpam-4461	392	11	cg	cg	NOUN
ejpam-4461	392	12	=	=	SYM
ejpam-4461	392	13	{	{	PUNCT
ejpam-4461	392	14	x	x	PROPN
ejpam-4461	392	15	∈	∈	PROPN
ejpam-4461	392	16	v	v	NOUN
ejpam-4461	392	17	(	(	PUNCT
ejpam-4461	392	18	g	g	NOUN
ejpam-4461	392	19	)	)	PUNCT
ejpam-4461	392	20	:	:	PUNCT
ejpam-4461	392	21	(	(	PUNCT
ejpam-4461	392	22	x	x	X
ejpam-4461	392	23	,	,	PUNCT
ejpam-4461	392	24	y	y	PROPN
ejpam-4461	392	25	)	)	PUNCT
ejpam-4461	392	26	/∈	/∈	PUNCT
ejpam-4461	393	1	c	c	NOUN
ejpam-4461	393	2	for	for	ADP
ejpam-4461	393	3	some	some	PRON
ejpam-4461	393	4	y	y	PROPN
ejpam-4461	393	5	∈	∈	PROPN
ejpam-4461	393	6	v	v	ADP
ejpam-4461	393	7	(	(	PUNCT
ejpam-4461	393	8	h	h	NOUN
ejpam-4461	393	9	)	)	PUNCT
ejpam-4461	393	10	}	}	PUNCT
ejpam-4461	393	11	.	.	PUNCT
ejpam-4461	394	1	theorem	theorem	NOUN
ejpam-4461	394	2	6	6	NUM
ejpam-4461	394	3	.	.	PUNCT
ejpam-4461	395	1	let	let	VERB
ejpam-4461	395	2	g	g	PRON
ejpam-4461	395	3	be	be	AUX
ejpam-4461	395	4	a	a	DET
ejpam-4461	395	5	nontrivial	nontrivial	ADJ
ejpam-4461	395	6	connected	connect	VERB
ejpam-4461	395	7	graph	graph	NOUN
ejpam-4461	395	8	and	and	CCONJ
ejpam-4461	395	9	n	n	PRON
ejpam-4461	395	10	≥	≥	NOUN
ejpam-4461	395	11	2	2	NUM
ejpam-4461	395	12	,	,	PUNCT
ejpam-4461	395	13	and	and	CCONJ
ejpam-4461	395	14	c	c	X
ejpam-4461	395	15	=	=	SYM
ejpam-4461	395	16	∪x∈s	∪x∈s	PROPN
ejpam-4461	395	17	(	(	PUNCT
ejpam-4461	395	18	{	{	PUNCT
ejpam-4461	395	19	x	x	NOUN
ejpam-4461	395	20	}	}	PUNCT
ejpam-4461	395	21	×	×	PROPN
ejpam-4461	395	22	tx	tx	PROPN
ejpam-4461	395	23	)	)	PUNCT
ejpam-4461	395	24	̸=	̸=	PROPN
ejpam-4461	395	25	v	v	NOUN
ejpam-4461	395	26	(	(	PUNCT
ejpam-4461	395	27	g[kn	g[kn	PROPN
ejpam-4461	395	28	]	]	PUNCT
ejpam-4461	395	29	)	)	PUNCT
ejpam-4461	395	30	.	.	PUNCT
ejpam-4461	396	1	then	then	ADV
ejpam-4461	396	2	c	c	PROPN
ejpam-4461	396	3	is	be	AUX
ejpam-4461	396	4	an	an	DET
ejpam-4461	396	5	outer	outer	ADV
ejpam-4461	396	6	-	-	PUNCT
ejpam-4461	396	7	connected	connect	VERB
ejpam-4461	396	8	semitotal	semitotal	ADJ
ejpam-4461	396	9	dominating	dominating	NOUN
ejpam-4461	396	10	set	set	NOUN
ejpam-4461	396	11	of	of	ADP
ejpam-4461	396	12	g[kn	g[kn	PROPN
ejpam-4461	396	13	]	]	PUNCT
ejpam-4461	396	14	if	if	SCONJ
ejpam-4461	396	15	and	and	CCONJ
ejpam-4461	396	16	only	only	ADV
ejpam-4461	396	17	if	if	SCONJ
ejpam-4461	396	18	each	each	PRON
ejpam-4461	396	19	of	of	ADP
ejpam-4461	396	20	the	the	DET
ejpam-4461	396	21	following	follow	VERB
ejpam-4461	396	22	holds	hold	VERB
ejpam-4461	396	23	:	:	PUNCT
ejpam-4461	396	24	(	(	PUNCT
ejpam-4461	396	25	i	i	NOUN
ejpam-4461	396	26	)	)	PUNCT
ejpam-4461	396	27	one	one	NUM
ejpam-4461	396	28	of	of	ADP
ejpam-4461	396	29	the	the	DET
ejpam-4461	396	30	following	following	NOUN
ejpam-4461	396	31	holds	hold	VERB
ejpam-4461	396	32	:	:	PUNCT
ejpam-4461	396	33	(	(	PUNCT
ejpam-4461	396	34	a	a	X
ejpam-4461	396	35	)	)	PUNCT
ejpam-4461	396	36	s	s	VERB
ejpam-4461	396	37	is	be	AUX
ejpam-4461	396	38	a	a	DET
ejpam-4461	396	39	semitotal	semitotal	ADJ
ejpam-4461	396	40	dominating	dominating	NOUN
ejpam-4461	396	41	set	set	VERB
ejpam-4461	396	42	in	in	ADP
ejpam-4461	396	43	g.	g.	PROPN
ejpam-4461	396	44	a.	a.	PROPN
ejpam-4461	396	45	aradais	aradais	PROPN
ejpam-4461	396	46	,	,	PUNCT
ejpam-4461	396	47	f.	f.	PROPN
ejpam-4461	396	48	jamil	jamil	PROPN
ejpam-4461	396	49	/	/	SYM
ejpam-4461	396	50	eur	eur	PROPN
ejpam-4461	396	51	.	.	PUNCT
ejpam-4461	397	1	j.	j.	PROPN
ejpam-4461	397	2	pure	pure	PROPN
ejpam-4461	397	3	appl	appl	PROPN
ejpam-4461	397	4	.	.	PROPN
ejpam-4461	397	5	math	math	PROPN
ejpam-4461	397	6	,	,	PUNCT
ejpam-4461	397	7	15	15	NUM
ejpam-4461	397	8	(	(	PUNCT
ejpam-4461	397	9	3	3	NUM
ejpam-4461	397	10	)	)	PUNCT
ejpam-4461	397	11	(	(	PUNCT
ejpam-4461	397	12	2022	2022	NUM
ejpam-4461	397	13	)	)	PUNCT
ejpam-4461	397	14	,	,	PUNCT
ejpam-4461	397	15	1265	1265	NUM
ejpam-4461	397	16	-	-	SYM
ejpam-4461	397	17	1279	1279	NUM
ejpam-4461	397	18	1277	1277	NUM
ejpam-4461	397	19	(	(	PUNCT
ejpam-4461	397	20	b	b	X
ejpam-4461	397	21	)	)	PUNCT
ejpam-4461	397	22	s	s	AUX
ejpam-4461	397	23	is	be	AUX
ejpam-4461	397	24	a	a	DET
ejpam-4461	397	25	dominating	dominating	NOUN
ejpam-4461	397	26	set	set	VERB
ejpam-4461	397	27	in	in	ADP
ejpam-4461	397	28	g	g	PROPN
ejpam-4461	397	29	such	such	ADJ
ejpam-4461	397	30	that	that	SCONJ
ejpam-4461	397	31	|tx|	|tx|	PROPN
ejpam-4461	397	32	≥	≥	NUM
ejpam-4461	397	33	2	2	NUM
ejpam-4461	397	34	for	for	ADP
ejpam-4461	397	35	each	each	DET
ejpam-4461	397	36	x	x	SYM
ejpam-4461	397	37	∈	∈	PROPN
ejpam-4461	397	38	s	s	PART
ejpam-4461	397	39	\	\	PROPN
ejpam-4461	397	40	n2	n2	ADJ
ejpam-4461	397	41	g(s	g(s	PROPN
ejpam-4461	397	42	)	)	PUNCT
ejpam-4461	397	43	.	.	PUNCT
ejpam-4461	398	1	(	(	PUNCT
ejpam-4461	398	2	ii	ii	NOUN
ejpam-4461	398	3	)	)	PUNCT
ejpam-4461	398	4	exactly	exactly	ADV
ejpam-4461	398	5	one	one	NUM
ejpam-4461	398	6	of	of	ADP
ejpam-4461	398	7	the	the	DET
ejpam-4461	398	8	following	following	NOUN
ejpam-4461	398	9	holds	hold	VERB
ejpam-4461	398	10	:	:	PUNCT
ejpam-4461	398	11	(	(	PUNCT
ejpam-4461	398	12	a	a	X
ejpam-4461	398	13	)	)	PUNCT
ejpam-4461	398	14	cg	cg	NOUN
ejpam-4461	398	15	=	=	SYM
ejpam-4461	398	16	{	{	PUNCT
ejpam-4461	398	17	x	x	NOUN
ejpam-4461	398	18	}	}	PUNCT
ejpam-4461	398	19	for	for	ADP
ejpam-4461	398	20	some	some	DET
ejpam-4461	398	21	x	x	SYM
ejpam-4461	398	22	∈	∈	PROPN
ejpam-4461	398	23	v	v	NOUN
ejpam-4461	398	24	(	(	PUNCT
ejpam-4461	398	25	g	g	NOUN
ejpam-4461	398	26	)	)	PUNCT
ejpam-4461	398	27	.	.	PUNCT
ejpam-4461	399	1	(	(	PUNCT
ejpam-4461	399	2	b	b	X
ejpam-4461	399	3	)	)	PUNCT
ejpam-4461	399	4	|cg|	|cg|	PROPN
ejpam-4461	399	5	≥	≥	NOUN
ejpam-4461	399	6	2	2	NUM
ejpam-4461	399	7	and	and	CCONJ
ejpam-4461	399	8	for	for	ADP
ejpam-4461	399	9	each	each	DET
ejpam-4461	399	10	distinct	distinct	PROPN
ejpam-4461	399	11	u	u	NOUN
ejpam-4461	399	12	,	,	PUNCT
ejpam-4461	399	13	v	v	PROPN
ejpam-4461	399	14	∈	∈	PROPN
ejpam-4461	399	15	cg	cg	NOUN
ejpam-4461	399	16	,	,	PUNCT
ejpam-4461	399	17	g	g	PROPN
ejpam-4461	399	18	has	have	VERB
ejpam-4461	399	19	a	a	DET
ejpam-4461	399	20	u	u	NOUN
ejpam-4461	399	21	-	-	NOUN
ejpam-4461	399	22	v	v	ADJ
ejpam-4461	399	23	geodesic	geodesic	NOUN
ejpam-4461	399	24	p	p	NOUN
ejpam-4461	399	25	for	for	ADP
ejpam-4461	399	26	which	which	PRON
ejpam-4461	399	27	either	either	CCONJ
ejpam-4461	399	28	s	s	VERB
ejpam-4461	399	29	∩	∩	ADJ
ejpam-4461	399	30	v	v	ADJ
ejpam-4461	399	31	(	(	PUNCT
ejpam-4461	399	32	p	p	NOUN
ejpam-4461	399	33	)	)	PUNCT
ejpam-4461	399	34	=	=	NOUN
ejpam-4461	399	35	∅	∅	NOUN
ejpam-4461	399	36	or	or	CCONJ
ejpam-4461	399	37	|tx|	|tx|	NOUN
ejpam-4461	399	38	<	<	X
ejpam-4461	399	39	n	n	X
ejpam-4461	399	40	for	for	ADP
ejpam-4461	399	41	each	each	DET
ejpam-4461	399	42	x	x	SYM
ejpam-4461	399	43	∈	∈	PROPN
ejpam-4461	399	44	s	s	PART
ejpam-4461	399	45	∩	∩	NOUN
ejpam-4461	399	46	v	v	X
ejpam-4461	399	47	(	(	PUNCT
ejpam-4461	399	48	p	p	NOUN
ejpam-4461	399	49	)	)	PUNCT
ejpam-4461	399	50	.	.	PUNCT
ejpam-4461	400	1	proof	proof	NOUN
ejpam-4461	400	2	.	.	PUNCT
ejpam-4461	401	1	assume	assume	VERB
ejpam-4461	401	2	that	that	SCONJ
ejpam-4461	401	3	c	c	PROPN
ejpam-4461	401	4	is	be	AUX
ejpam-4461	401	5	an	an	DET
ejpam-4461	401	6	outer	outer	ADV
ejpam-4461	401	7	-	-	PUNCT
ejpam-4461	401	8	connected	connect	VERB
ejpam-4461	401	9	semitotal	semitotal	ADJ
ejpam-4461	401	10	dominating	dominating	NOUN
ejpam-4461	401	11	set	set	NOUN
ejpam-4461	401	12	of	of	ADP
ejpam-4461	401	13	g[kn	g[kn	PROPN
ejpam-4461	401	14	]	]	PUNCT
ejpam-4461	401	15	.	.	PUNCT
ejpam-4461	402	1	since	since	SCONJ
ejpam-4461	402	2	c	c	PROPN
ejpam-4461	402	3	is	be	AUX
ejpam-4461	402	4	a	a	DET
ejpam-4461	402	5	semitotal	semitotal	ADJ
ejpam-4461	402	6	dominating	dominating	NOUN
ejpam-4461	402	7	set	set	NOUN
ejpam-4461	402	8	of	of	ADP
ejpam-4461	402	9	g[kn	g[kn	PROPN
ejpam-4461	402	10	]	]	PUNCT
ejpam-4461	402	11	and	and	CCONJ
ejpam-4461	402	12	every	every	DET
ejpam-4461	402	13	nonempty	nonempty	NOUN
ejpam-4461	402	14	subset	subset	NOUN
ejpam-4461	402	15	of	of	ADP
ejpam-4461	402	16	v	v	PROPN
ejpam-4461	402	17	(	(	PUNCT
ejpam-4461	402	18	kn	kn	PROPN
ejpam-4461	402	19	)	)	PUNCT
ejpam-4461	402	20	is	be	AUX
ejpam-4461	402	21	a	a	DET
ejpam-4461	402	22	dominating	dominating	NOUN
ejpam-4461	402	23	set	set	NOUN
ejpam-4461	402	24	of	of	ADP
ejpam-4461	402	25	kn	kn	PROPN
ejpam-4461	402	26	,	,	PUNCT
ejpam-4461	402	27	(	(	PUNCT
ejpam-4461	402	28	i	i	NOUN
ejpam-4461	402	29	)	)	PUNCT
ejpam-4461	402	30	holds	hold	VERB
ejpam-4461	402	31	by	by	ADP
ejpam-4461	402	32	theorem	theorem	NOUN
ejpam-4461	402	33	5	5	NUM
ejpam-4461	402	34	.	.	PUNCT
ejpam-4461	402	35	to	to	PART
ejpam-4461	402	36	show	show	VERB
ejpam-4461	402	37	(	(	PUNCT
ejpam-4461	402	38	ii	ii	NOUN
ejpam-4461	402	39	)	)	PUNCT
ejpam-4461	402	40	,	,	PUNCT
ejpam-4461	402	41	if	if	SCONJ
ejpam-4461	402	42	|cg|	|cg|	PROPN
ejpam-4461	402	43	=	=	SYM
ejpam-4461	402	44	1	1	NUM
ejpam-4461	402	45	,	,	PUNCT
ejpam-4461	402	46	then	then	ADV
ejpam-4461	402	47	(	(	PUNCT
ejpam-4461	402	48	ii)(a	ii)(a	NOUN
ejpam-4461	402	49	)	)	PUNCT
ejpam-4461	402	50	holds	hold	VERB
ejpam-4461	402	51	.	.	PUNCT
ejpam-4461	403	1	suppose	suppose	VERB
ejpam-4461	403	2	that	that	SCONJ
ejpam-4461	403	3	|cg|	|cg|	PROPN
ejpam-4461	403	4	≥	≥	NOUN
ejpam-4461	403	5	2	2	NUM
ejpam-4461	403	6	,	,	PUNCT
ejpam-4461	403	7	and	and	CCONJ
ejpam-4461	403	8	let	let	VERB
ejpam-4461	403	9	u	u	NOUN
ejpam-4461	403	10	,	,	PUNCT
ejpam-4461	403	11	v	v	PROPN
ejpam-4461	403	12	∈	∈	PROPN
ejpam-4461	403	13	cg	cg	NOUN
ejpam-4461	403	14	with	with	ADP
ejpam-4461	403	15	u	u	NOUN
ejpam-4461	403	16	̸=	̸=	PROPN
ejpam-4461	403	17	v.	v.	ADP
ejpam-4461	403	18	pick	pick	VERB
ejpam-4461	403	19	z	z	PROPN
ejpam-4461	403	20	,	,	PUNCT
ejpam-4461	403	21	w	w	PROPN
ejpam-4461	403	22	∈	∈	PROPN
ejpam-4461	403	23	v	v	X
ejpam-4461	403	24	(	(	PUNCT
ejpam-4461	403	25	kn	kn	PROPN
ejpam-4461	403	26	)	)	PUNCT
ejpam-4461	403	27	such	such	ADJ
ejpam-4461	403	28	that	that	SCONJ
ejpam-4461	403	29	(	(	PUNCT
ejpam-4461	403	30	u	u	NOUN
ejpam-4461	403	31	,	,	PUNCT
ejpam-4461	403	32	z	z	NOUN
ejpam-4461	403	33	)	)	PUNCT
ejpam-4461	403	34	,	,	PUNCT
ejpam-4461	403	35	(	(	PUNCT
ejpam-4461	403	36	v	v	NOUN
ejpam-4461	403	37	,	,	PUNCT
ejpam-4461	403	38	w	w	NOUN
ejpam-4461	403	39	)	)	PUNCT
ejpam-4461	403	40	/∈	/∈	PUNCT
ejpam-4461	403	41	c.	c.	NOUN
ejpam-4461	403	42	since	since	SCONJ
ejpam-4461	403	43	⟨v	⟨v	PROPN
ejpam-4461	403	44	(	(	PUNCT
ejpam-4461	403	45	g[kn	g[kn	PROPN
ejpam-4461	403	46	]	]	PUNCT
ejpam-4461	403	47	)	)	PUNCT
ejpam-4461	403	48	\	\	NOUN
ejpam-4461	403	49	c⟩	c⟩	PUNCT
ejpam-4461	403	50	is	be	AUX
ejpam-4461	403	51	connected	connect	VERB
ejpam-4461	403	52	,	,	PUNCT
ejpam-4461	403	53	there	there	PRON
ejpam-4461	403	54	exists	exist	VERB
ejpam-4461	403	55	a	a	DET
ejpam-4461	403	56	(	(	PUNCT
ejpam-4461	403	57	u	u	NOUN
ejpam-4461	403	58	,	,	PUNCT
ejpam-4461	403	59	z)-(v	z)-(v	PROPN
ejpam-4461	403	60	,	,	PUNCT
ejpam-4461	403	61	w	w	NOUN
ejpam-4461	403	62	)	)	PUNCT
ejpam-4461	403	63	geodesic	geodesic	NOUN
ejpam-4461	403	64	[	[	X
ejpam-4461	403	65	(	(	PUNCT
ejpam-4461	403	66	u	u	NOUN
ejpam-4461	403	67	,	,	PUNCT
ejpam-4461	403	68	z	z	NOUN
ejpam-4461	403	69	)	)	PUNCT
ejpam-4461	403	70	=	=	SYM
ejpam-4461	403	71	(	(	PUNCT
ejpam-4461	403	72	x1	x1	PROPN
ejpam-4461	403	73	,	,	PUNCT
ejpam-4461	403	74	y1	y1	PROPN
ejpam-4461	403	75	)	)	PUNCT
ejpam-4461	403	76	,	,	PUNCT
ejpam-4461	403	77	(	(	PUNCT
ejpam-4461	403	78	x2	x2	PROPN
ejpam-4461	403	79	,	,	PUNCT
ejpam-4461	403	80	y2	y2	PROPN
ejpam-4461	403	81	)	)	PUNCT
ejpam-4461	403	82	,	,	PUNCT
ejpam-4461	403	83	.	.	PUNCT
ejpam-4461	403	84	.	.	PUNCT
ejpam-4461	403	85	.	.	PUNCT
ejpam-4461	404	1	,	,	PUNCT
ejpam-4461	404	2	(	(	PUNCT
ejpam-4461	404	3	xn	xn	PROPN
ejpam-4461	404	4	,	,	PUNCT
ejpam-4461	404	5	yn	yn	PROPN
ejpam-4461	404	6	)	)	PUNCT
ejpam-4461	404	7	=	=	SYM
ejpam-4461	404	8	(	(	PUNCT
ejpam-4461	404	9	v	v	NOUN
ejpam-4461	404	10	,	,	PUNCT
ejpam-4461	404	11	w	w	NOUN
ejpam-4461	404	12	)	)	PUNCT
ejpam-4461	404	13	]	]	PUNCT
ejpam-4461	405	1	in	in	ADP
ejpam-4461	405	2	g[kn	g[kn	PROPN
ejpam-4461	405	3	]	]	PUNCT
ejpam-4461	405	4	such	such	ADJ
ejpam-4461	405	5	that	that	SCONJ
ejpam-4461	405	6	(	(	PUNCT
ejpam-4461	405	7	xk	xk	PROPN
ejpam-4461	405	8	,	,	PUNCT
ejpam-4461	405	9	yk	yk	PROPN
ejpam-4461	405	10	)	)	PUNCT
ejpam-4461	405	11	/∈	/∈	PUNCT
ejpam-4461	405	12	c	c	NOUN
ejpam-4461	406	1	for	for	ADP
ejpam-4461	406	2	all	all	PRON
ejpam-4461	406	3	k	k	NOUN
ejpam-4461	406	4	=	=	SYM
ejpam-4461	406	5	1	1	NUM
ejpam-4461	406	6	,	,	PUNCT
ejpam-4461	406	7	2	2	NUM
ejpam-4461	406	8	,	,	PUNCT
ejpam-4461	406	9	.	.	PUNCT
ejpam-4461	406	10	.	.	PUNCT
ejpam-4461	406	11	.	.	PUNCT
ejpam-4461	407	1	,	,	PUNCT
ejpam-4461	407	2	n.	n.	PROPN
ejpam-4461	407	3	it	it	PRON
ejpam-4461	407	4	implies	imply	VERB
ejpam-4461	407	5	that	that	SCONJ
ejpam-4461	407	6	for	for	ADP
ejpam-4461	407	7	some	some	DET
ejpam-4461	407	8	k1	k1	NOUN
ejpam-4461	407	9	<	<	X
ejpam-4461	407	10	k2	k2	X
ejpam-4461	407	11	<	<	X
ejpam-4461	407	12	·	·	PUNCT
ejpam-4461	407	13	·	·	PUNCT
ejpam-4461	407	14	·	·	PUNCT
ejpam-4461	408	1	<	<	X
ejpam-4461	408	2	kr	kr	PROPN
ejpam-4461	408	3	in	in	ADP
ejpam-4461	408	4	{	{	PUNCT
ejpam-4461	408	5	1	1	NUM
ejpam-4461	408	6	,	,	PUNCT
ejpam-4461	408	7	2	2	NUM
ejpam-4461	408	8	,	,	PUNCT
ejpam-4461	408	9	.	.	PUNCT
ejpam-4461	408	10	.	.	PUNCT
ejpam-4461	408	11	.	.	PUNCT
ejpam-4461	408	12	,	,	PUNCT
ejpam-4461	408	13	n	n	CCONJ
ejpam-4461	408	14	}	}	PUNCT
ejpam-4461	408	15	,	,	PUNCT
ejpam-4461	408	16	p	p	X
ejpam-4461	408	17	=	=	PUNCT
ejpam-4461	408	18	[	[	X
ejpam-4461	408	19	u	u	X
ejpam-4461	408	20	=	=	PROPN
ejpam-4461	408	21	xk−1	xk−1	PROPN
ejpam-4461	408	22	,	,	PUNCT
ejpam-4461	408	23	xk2	xk2	NOUN
ejpam-4461	408	24	,	,	PUNCT
ejpam-4461	408	25	.	.	PUNCT
ejpam-4461	408	26	.	.	PUNCT
ejpam-4461	408	27	.	.	PUNCT
ejpam-4461	409	1	,	,	PUNCT
ejpam-4461	409	2	xkr	xkr	PROPN
ejpam-4461	409	3	=	=	SYM
ejpam-4461	409	4	v	v	PROPN
ejpam-4461	409	5	]	]	PUNCT
ejpam-4461	409	6	is	be	AUX
ejpam-4461	409	7	a	a	DET
ejpam-4461	409	8	u	u	NOUN
ejpam-4461	409	9	-	-	NOUN
ejpam-4461	409	10	v	v	ADJ
ejpam-4461	409	11	geodesic	geodesic	NOUN
ejpam-4461	409	12	in	in	ADP
ejpam-4461	409	13	g.	g.	PROPN
ejpam-4461	410	1	if	if	SCONJ
ejpam-4461	410	2	v	v	INTJ
ejpam-4461	410	3	(	(	PUNCT
ejpam-4461	410	4	p	p	NOUN
ejpam-4461	410	5	)	)	PUNCT
ejpam-4461	410	6	∩	∩	PROPN
ejpam-4461	410	7	s	s	PART
ejpam-4461	410	8	=	=	SYM
ejpam-4461	410	9	∅	∅	NOUN
ejpam-4461	410	10	,	,	PUNCT
ejpam-4461	410	11	then	then	ADV
ejpam-4461	410	12	we	we	PRON
ejpam-4461	410	13	are	be	AUX
ejpam-4461	410	14	done	do	VERB
ejpam-4461	410	15	.	.	PUNCT
ejpam-4461	411	1	suppose	suppose	VERB
ejpam-4461	411	2	that	that	SCONJ
ejpam-4461	411	3	v	v	INTJ
ejpam-4461	411	4	(	(	PUNCT
ejpam-4461	411	5	p	p	NOUN
ejpam-4461	411	6	)	)	PUNCT
ejpam-4461	411	7	∩s	∩s	PROPN
ejpam-4461	411	8	̸=	̸=	PROPN
ejpam-4461	411	9	∅	∅	NOUN
ejpam-4461	411	10	,	,	PUNCT
ejpam-4461	411	11	and	and	CCONJ
ejpam-4461	411	12	let	let	VERB
ejpam-4461	411	13	xkj	xkj	PROPN
ejpam-4461	411	14	∈	∈	PROPN
ejpam-4461	411	15	s	s	PART
ejpam-4461	411	16	∩v	∩v	NOUN
ejpam-4461	411	17	(	(	PUNCT
ejpam-4461	411	18	p	p	NOUN
ejpam-4461	411	19	)	)	PUNCT
ejpam-4461	411	20	.	.	PUNCT
ejpam-4461	412	1	necessarily	necessarily	ADV
ejpam-4461	412	2	,	,	PUNCT
ejpam-4461	412	3	ykj	ykj	PROPN
ejpam-4461	412	4	/∈	/∈	PUNCT
ejpam-4461	412	5	txkj	txkj	PROPN
ejpam-4461	412	6	.	.	PUNCT
ejpam-4461	413	1	thus	thus	ADV
ejpam-4461	413	2	,	,	PUNCT
ejpam-4461	413	3	txkj	txkj	ADP
ejpam-4461	413	4	̸=	̸=	PROPN
ejpam-4461	413	5	v	v	PROPN
ejpam-4461	413	6	(	(	PUNCT
ejpam-4461	413	7	kn	kn	PROPN
ejpam-4461	413	8	)	)	PUNCT
ejpam-4461	413	9	.	.	PUNCT
ejpam-4461	414	1	this	this	PRON
ejpam-4461	414	2	shows	show	VERB
ejpam-4461	414	3	that	that	SCONJ
ejpam-4461	414	4	(	(	PUNCT
ejpam-4461	414	5	ii)(b	ii)(b	ADJ
ejpam-4461	414	6	)	)	PUNCT
ejpam-4461	414	7	holds	hold	VERB
ejpam-4461	414	8	.	.	PUNCT
ejpam-4461	415	1	conversely	conversely	ADV
ejpam-4461	415	2	,	,	PUNCT
ejpam-4461	415	3	condition	condition	NOUN
ejpam-4461	415	4	(	(	PUNCT
ejpam-4461	415	5	i	i	NOUN
ejpam-4461	415	6	)	)	PUNCT
ejpam-4461	415	7	implies	imply	VERB
ejpam-4461	415	8	that	that	SCONJ
ejpam-4461	415	9	c	c	PROPN
ejpam-4461	415	10	is	be	AUX
ejpam-4461	415	11	a	a	DET
ejpam-4461	415	12	semitotal	semitotal	ADJ
ejpam-4461	415	13	dominating	dominating	NOUN
ejpam-4461	415	14	set	set	NOUN
ejpam-4461	415	15	of	of	ADP
ejpam-4461	415	16	g[kn	g[kn	PROPN
ejpam-4461	415	17	]	]	PUNCT
ejpam-4461	415	18	by	by	ADP
ejpam-4461	415	19	theorem	theorem	NOUN
ejpam-4461	415	20	5	5	NUM
ejpam-4461	415	21	.	.	PUNCT
ejpam-4461	416	1	if	if	SCONJ
ejpam-4461	416	2	condition	condition	NOUN
ejpam-4461	416	3	(	(	PUNCT
ejpam-4461	416	4	ii)(a	ii)(a	NOUN
ejpam-4461	416	5	)	)	PUNCT
ejpam-4461	416	6	holds	hold	VERB
ejpam-4461	416	7	,	,	PUNCT
ejpam-4461	416	8	then	then	ADV
ejpam-4461	416	9	v	v	X
ejpam-4461	416	10	(	(	PUNCT
ejpam-4461	416	11	g[kn	g[kn	PROPN
ejpam-4461	416	12	]	]	PUNCT
ejpam-4461	416	13	)	)	PUNCT
ejpam-4461	416	14	\	\	X
ejpam-4461	417	1	c	c	NOUN
ejpam-4461	417	2	=	=	PRON
ejpam-4461	417	3	{	{	PUNCT
ejpam-4461	417	4	{	{	PUNCT
ejpam-4461	417	5	x	x	NOUN
ejpam-4461	417	6	}	}	PUNCT
ejpam-4461	417	7	×	×	NOUN
ejpam-4461	417	8	v	v	NOUN
ejpam-4461	417	9	(	(	PUNCT
ejpam-4461	417	10	kn	kn	PROPN
ejpam-4461	417	11	)	)	PUNCT
ejpam-4461	417	12	,	,	PUNCT
ejpam-4461	417	13	if	if	SCONJ
ejpam-4461	417	14	x	x	X
ejpam-4461	417	15	/∈	/∈	PRON
ejpam-4461	417	16	s	s	PART
ejpam-4461	417	17	{	{	PUNCT
ejpam-4461	417	18	x	x	NOUN
ejpam-4461	417	19	}	}	PUNCT
ejpam-4461	417	20	×	×	NOUN
ejpam-4461	417	21	(	(	PUNCT
ejpam-4461	417	22	v	v	NOUN
ejpam-4461	417	23	(	(	PUNCT
ejpam-4461	417	24	kn	kn	PROPN
ejpam-4461	417	25	)	)	PUNCT
ejpam-4461	417	26	\	\	PROPN
ejpam-4461	417	27	tx	tx	PROPN
ejpam-4461	417	28	)	)	PUNCT
ejpam-4461	417	29	,	,	PUNCT
ejpam-4461	417	30	if	if	SCONJ
ejpam-4461	417	31	x	x	PUNCT
ejpam-4461	417	32	∈	∈	PROPN
ejpam-4461	417	33	s	s	PART
ejpam-4461	417	34	,	,	PUNCT
ejpam-4461	417	35	and	and	CCONJ
ejpam-4461	417	36	c	c	NOUN
ejpam-4461	417	37	is	be	AUX
ejpam-4461	417	38	an	an	DET
ejpam-4461	417	39	outer	outer	ADV
ejpam-4461	417	40	-	-	PUNCT
ejpam-4461	417	41	connected	connect	VERB
ejpam-4461	417	42	semitotal	semitotal	ADJ
ejpam-4461	417	43	dominating	dominating	NOUN
ejpam-4461	417	44	set	set	NOUN
ejpam-4461	417	45	of	of	ADP
ejpam-4461	417	46	g[h	g[h	NOUN
ejpam-4461	417	47	]	]	PUNCT
ejpam-4461	417	48	.	.	PUNCT
ejpam-4461	418	1	now	now	ADV
ejpam-4461	418	2	,	,	PUNCT
ejpam-4461	418	3	suppose	suppose	VERB
ejpam-4461	418	4	that	that	SCONJ
ejpam-4461	418	5	condition	condition	NOUN
ejpam-4461	418	6	(	(	PUNCT
ejpam-4461	418	7	ii)(b	ii)(b	ADJ
ejpam-4461	418	8	)	)	PUNCT
ejpam-4461	418	9	holds	hold	VERB
ejpam-4461	418	10	.	.	PUNCT
ejpam-4461	419	1	let	let	VERB
ejpam-4461	419	2	(	(	PUNCT
ejpam-4461	419	3	u	u	NOUN
ejpam-4461	419	4	,	,	PUNCT
ejpam-4461	419	5	z	z	NOUN
ejpam-4461	419	6	)	)	PUNCT
ejpam-4461	419	7	,	,	PUNCT
ejpam-4461	419	8	(	(	PUNCT
ejpam-4461	419	9	v	v	NOUN
ejpam-4461	419	10	,	,	PUNCT
ejpam-4461	419	11	w	w	NOUN
ejpam-4461	419	12	)	)	PUNCT
ejpam-4461	419	13	∈	∈	NOUN
ejpam-4461	419	14	v	v	NOUN
ejpam-4461	419	15	(	(	PUNCT
ejpam-4461	419	16	g[kn	g[kn	PROPN
ejpam-4461	419	17	]	]	PUNCT
ejpam-4461	419	18	)	)	PUNCT
ejpam-4461	419	19	\	\	PUNCT
ejpam-4461	420	1	c	c	NOUN
ejpam-4461	420	2	be	be	AUX
ejpam-4461	420	3	distinct	distinct	ADJ
ejpam-4461	420	4	.	.	PUNCT
ejpam-4461	421	1	case	case	NOUN
ejpam-4461	421	2	1	1	NUM
ejpam-4461	421	3	:	:	PUNCT
ejpam-4461	421	4	u	u	PROPN
ejpam-4461	421	5	̸=	̸=	PROPN
ejpam-4461	421	6	v	v	NOUN
ejpam-4461	421	7	since	since	SCONJ
ejpam-4461	421	8	u	u	NOUN
ejpam-4461	421	9	,	,	PUNCT
ejpam-4461	421	10	v	v	PROPN
ejpam-4461	421	11	∈	∈	PROPN
ejpam-4461	421	12	cg	cg	NOUN
ejpam-4461	421	13	,	,	PUNCT
ejpam-4461	421	14	g	g	PROPN
ejpam-4461	421	15	has	have	VERB
ejpam-4461	421	16	a	a	DET
ejpam-4461	421	17	u	u	NOUN
ejpam-4461	421	18	-	-	NOUN
ejpam-4461	421	19	v	v	ADJ
ejpam-4461	421	20	geodesic	geodesic	NOUN
ejpam-4461	421	21	p	p	NOUN
ejpam-4461	422	1	=	=	PUNCT
ejpam-4461	423	1	[	[	X
ejpam-4461	423	2	u	u	X
ejpam-4461	423	3	=	=	SYM
ejpam-4461	423	4	x1	x1	PROPN
ejpam-4461	423	5	,	,	PUNCT
ejpam-4461	423	6	x2	x2	PROPN
ejpam-4461	423	7	,	,	PUNCT
ejpam-4461	423	8	.	.	PUNCT
ejpam-4461	423	9	.	.	PUNCT
ejpam-4461	423	10	.	.	PUNCT
ejpam-4461	424	1	,	,	PUNCT
ejpam-4461	424	2	xn	xn	PUNCT
ejpam-4461	425	1	=	=	SYM
ejpam-4461	425	2	v	v	NOUN
ejpam-4461	425	3	]	]	PUNCT
ejpam-4461	425	4	as	as	ADP
ejpam-4461	425	5	being	be	AUX
ejpam-4461	425	6	described	describe	VERB
ejpam-4461	425	7	in	in	ADP
ejpam-4461	425	8	(	(	PUNCT
ejpam-4461	425	9	ii)(b	ii)(b	ADJ
ejpam-4461	425	10	)	)	PUNCT
ejpam-4461	425	11	.	.	PUNCT
ejpam-4461	426	1	if	if	SCONJ
ejpam-4461	426	2	s∩v	s∩v	PROPN
ejpam-4461	426	3	(	(	PUNCT
ejpam-4461	426	4	p	p	NOUN
ejpam-4461	426	5	)	)	PUNCT
ejpam-4461	426	6	=	=	NOUN
ejpam-4461	426	7	∅	∅	NOUN
ejpam-4461	426	8	,	,	PUNCT
ejpam-4461	426	9	then	then	ADV
ejpam-4461	426	10	for	for	ADP
ejpam-4461	426	11	any	any	DET
ejpam-4461	426	12	y	y	PROPN
ejpam-4461	426	13	∈	∈	PROPN
ejpam-4461	426	14	v	v	PROPN
ejpam-4461	426	15	(	(	PUNCT
ejpam-4461	426	16	kn	kn	PROPN
ejpam-4461	426	17	)	)	PUNCT
ejpam-4461	426	18	,	,	PUNCT
ejpam-4461	427	1	[	[	X
ejpam-4461	427	2	(	(	PUNCT
ejpam-4461	427	3	u	u	NOUN
ejpam-4461	427	4	,	,	PUNCT
ejpam-4461	427	5	z	z	NOUN
ejpam-4461	427	6	)	)	PUNCT
ejpam-4461	427	7	,	,	PUNCT
ejpam-4461	427	8	(	(	PUNCT
ejpam-4461	427	9	x2	x2	PROPN
ejpam-4461	427	10	,	,	PUNCT
ejpam-4461	427	11	y	y	PROPN
ejpam-4461	427	12	)	)	PUNCT
ejpam-4461	427	13	,	,	PUNCT
ejpam-4461	427	14	(	(	PUNCT
ejpam-4461	427	15	x3	x3	ADJ
ejpam-4461	427	16	,	,	PUNCT
ejpam-4461	427	17	y	y	NOUN
ejpam-4461	427	18	)	)	PUNCT
ejpam-4461	427	19	,	,	PUNCT
ejpam-4461	427	20	.	.	PUNCT
ejpam-4461	427	21	.	.	PUNCT
ejpam-4461	428	1	.	.	PUNCT
ejpam-4461	429	1	,	,	PUNCT
ejpam-4461	429	2	(	(	PUNCT
ejpam-4461	429	3	xn−1	xn−1	PROPN
ejpam-4461	429	4	,	,	PUNCT
ejpam-4461	429	5	y	y	PROPN
ejpam-4461	429	6	)	)	PUNCT
ejpam-4461	429	7	,	,	PUNCT
ejpam-4461	429	8	(	(	PUNCT
ejpam-4461	429	9	v	v	NOUN
ejpam-4461	429	10	,	,	PUNCT
ejpam-4461	429	11	w	w	NOUN
ejpam-4461	429	12	)	)	PUNCT
ejpam-4461	429	13	]	]	PUNCT
ejpam-4461	429	14	is	be	AUX
ejpam-4461	429	15	a	a	DET
ejpam-4461	429	16	(	(	PUNCT
ejpam-4461	429	17	u	u	NOUN
ejpam-4461	429	18	,	,	PUNCT
ejpam-4461	429	19	z)-(v	z)-(v	PROPN
ejpam-4461	429	20	,	,	PUNCT
ejpam-4461	429	21	w	w	NOUN
ejpam-4461	429	22	)	)	PUNCT
ejpam-4461	429	23	path	path	NOUN
ejpam-4461	429	24	in	in	ADP
ejpam-4461	429	25	⟨v	⟨v	PROPN
ejpam-4461	429	26	(	(	PUNCT
ejpam-4461	429	27	g[kn	g[kn	PROPN
ejpam-4461	429	28	]	]	PUNCT
ejpam-4461	429	29	)	)	PUNCT
ejpam-4461	429	30	\	\	PROPN
ejpam-4461	429	31	c⟩.	c⟩.	PROPN
ejpam-4461	429	32	suppose	suppose	VERB
ejpam-4461	429	33	that	that	SCONJ
ejpam-4461	429	34	s	s	VERB
ejpam-4461	429	35	∩	∩	ADJ
ejpam-4461	429	36	v	v	ADJ
ejpam-4461	429	37	(	(	PUNCT
ejpam-4461	429	38	p	p	NOUN
ejpam-4461	429	39	)	)	PUNCT
ejpam-4461	429	40	̸=	̸=	PROPN
ejpam-4461	429	41	∅.	∅.	ADV
ejpam-4461	429	42	put	put	VERB
ejpam-4461	429	43	y1	y1	NOUN
ejpam-4461	429	44	=	=	SYM
ejpam-4461	429	45	z	z	NOUN
ejpam-4461	429	46	and	and	CCONJ
ejpam-4461	429	47	w	w	PROPN
ejpam-4461	429	48	=	=	SYM
ejpam-4461	429	49	yn	yn	PROPN
ejpam-4461	429	50	.	.	PUNCT
ejpam-4461	430	1	for	for	ADP
ejpam-4461	430	2	each	each	DET
ejpam-4461	430	3	k	k	PROPN
ejpam-4461	430	4	∈	∈	PROPN
ejpam-4461	430	5	{	{	PUNCT
ejpam-4461	430	6	2	2	NUM
ejpam-4461	430	7	,	,	PUNCT
ejpam-4461	430	8	.	.	PUNCT
ejpam-4461	430	9	.	.	PUNCT
ejpam-4461	430	10	.	.	PUNCT
ejpam-4461	431	1	,	,	PUNCT
ejpam-4461	431	2	n	n	CCONJ
ejpam-4461	431	3	−	−	PROPN
ejpam-4461	431	4	1	1	NUM
ejpam-4461	431	5	}	}	PUNCT
ejpam-4461	431	6	,	,	PUNCT
ejpam-4461	431	7	pick	pick	VERB
ejpam-4461	431	8	any	any	DET
ejpam-4461	431	9	yk	yk	PROPN
ejpam-4461	431	10	∈	∈	PROPN
ejpam-4461	431	11	v	v	PROPN
ejpam-4461	431	12	(	(	PUNCT
ejpam-4461	431	13	kn	kn	PROPN
ejpam-4461	431	14	)	)	PUNCT
ejpam-4461	432	1	whenever	whenever	SCONJ
ejpam-4461	432	2	xk	xk	PROPN
ejpam-4461	432	3	/∈	/∈	PUNCT
ejpam-4461	432	4	s	s	PART
ejpam-4461	432	5	;	;	PUNCT
ejpam-4461	432	6	otherwise	otherwise	ADV
ejpam-4461	432	7	,	,	PUNCT
ejpam-4461	432	8	pick	pick	VERB
ejpam-4461	432	9	yk	yk	PROPN
ejpam-4461	432	10	∈	∈	PROPN
ejpam-4461	432	11	v	v	PROPN
ejpam-4461	432	12	(	(	PUNCT
ejpam-4461	432	13	kn	kn	PROPN
ejpam-4461	432	14	)	)	PUNCT
ejpam-4461	432	15	\	\	PROPN
ejpam-4461	432	16	txk	txk	NOUN
ejpam-4461	432	17	.	.	PUNCT
ejpam-4461	433	1	then	then	ADV
ejpam-4461	433	2	[	[	X
ejpam-4461	433	3	(	(	PUNCT
ejpam-4461	433	4	u	u	NOUN
ejpam-4461	433	5	,	,	PUNCT
ejpam-4461	433	6	z	z	NOUN
ejpam-4461	433	7	)	)	PUNCT
ejpam-4461	433	8	=	=	SYM
ejpam-4461	433	9	(	(	PUNCT
ejpam-4461	433	10	x1	x1	PROPN
ejpam-4461	433	11	,	,	PUNCT
ejpam-4461	433	12	y1	y1	PROPN
ejpam-4461	433	13	)	)	PUNCT
ejpam-4461	433	14	,	,	PUNCT
ejpam-4461	433	15	(	(	PUNCT
ejpam-4461	433	16	x2	x2	PROPN
ejpam-4461	433	17	,	,	PUNCT
ejpam-4461	433	18	y2	y2	PROPN
ejpam-4461	433	19	)	)	PUNCT
ejpam-4461	433	20	,	,	PUNCT
ejpam-4461	433	21	.	.	PUNCT
ejpam-4461	433	22	.	.	PUNCT
ejpam-4461	433	23	.	.	PUNCT
ejpam-4461	434	1	,	,	PUNCT
ejpam-4461	434	2	(	(	PUNCT
ejpam-4461	434	3	xn−1	xn−1	PROPN
ejpam-4461	434	4	,	,	PUNCT
ejpam-4461	434	5	yn−1	yn−1	NOUN
ejpam-4461	434	6	)	)	PUNCT
ejpam-4461	434	7	,	,	PUNCT
ejpam-4461	434	8	(	(	PUNCT
ejpam-4461	434	9	xn	xn	PROPN
ejpam-4461	434	10	,	,	PUNCT
ejpam-4461	434	11	yn	yn	PROPN
ejpam-4461	434	12	)	)	PUNCT
ejpam-4461	434	13	=	=	SYM
ejpam-4461	434	14	(	(	PUNCT
ejpam-4461	434	15	v	v	NOUN
ejpam-4461	434	16	,	,	PUNCT
ejpam-4461	434	17	w	w	NOUN
ejpam-4461	434	18	)	)	PUNCT
ejpam-4461	434	19	]	]	PUNCT
ejpam-4461	434	20	is	be	AUX
ejpam-4461	434	21	a	a	DET
ejpam-4461	434	22	(	(	PUNCT
ejpam-4461	434	23	u	u	NOUN
ejpam-4461	434	24	,	,	PUNCT
ejpam-4461	434	25	z)-(v	z)-(v	PROPN
ejpam-4461	434	26	,	,	PUNCT
ejpam-4461	434	27	w	w	NOUN
ejpam-4461	434	28	)	)	PUNCT
ejpam-4461	434	29	path	path	NOUN
ejpam-4461	434	30	in	in	ADP
ejpam-4461	434	31	⟨v	⟨v	PROPN
ejpam-4461	434	32	(	(	PUNCT
ejpam-4461	434	33	g[kn	g[kn	PROPN
ejpam-4461	434	34	]	]	PUNCT
ejpam-4461	434	35	)	)	PUNCT
ejpam-4461	434	36	\	\	PROPN
ejpam-4461	434	37	c⟩.	c⟩.	ADJ
ejpam-4461	434	38	case	case	NOUN
ejpam-4461	434	39	2	2	NUM
ejpam-4461	434	40	:	:	PUNCT
ejpam-4461	434	41	u	u	NOUN
ejpam-4461	434	42	=	=	PROPN
ejpam-4461	434	43	v	v	PART
ejpam-4461	434	44	pick	pick	VERB
ejpam-4461	434	45	x	x	PUNCT
ejpam-4461	434	46	∈	∈	PROPN
ejpam-4461	434	47	cg	cg	NOUN
ejpam-4461	434	48	\	\	NOUN
ejpam-4461	434	49	{	{	PUNCT
ejpam-4461	434	50	u	u	NOUN
ejpam-4461	434	51	}	}	PUNCT
ejpam-4461	434	52	.	.	PUNCT
ejpam-4461	435	1	let	let	VERB
ejpam-4461	435	2	p	p	NOUN
ejpam-4461	435	3	=	=	PUNCT
ejpam-4461	436	1	[	[	X
ejpam-4461	436	2	x	x	X
ejpam-4461	436	3	=	=	SYM
ejpam-4461	436	4	x1	x1	PROPN
ejpam-4461	436	5	,	,	PUNCT
ejpam-4461	436	6	x2	x2	PROPN
ejpam-4461	436	7	,	,	PUNCT
ejpam-4461	436	8	.	.	PUNCT
ejpam-4461	436	9	.	.	PUNCT
ejpam-4461	436	10	.	.	PUNCT
ejpam-4461	437	1	,	,	PUNCT
ejpam-4461	437	2	xn−1	xn−1	PROPN
ejpam-4461	437	3	,	,	PUNCT
ejpam-4461	437	4	xn	xn	PUNCT
ejpam-4461	438	1	=	=	SYM
ejpam-4461	438	2	u	u	NOUN
ejpam-4461	438	3	]	]	PUNCT
ejpam-4461	438	4	be	be	AUX
ejpam-4461	438	5	a	a	DET
ejpam-4461	438	6	x	x	NOUN
ejpam-4461	438	7	-	-	PUNCT
ejpam-4461	438	8	u	u	NOUN
ejpam-4461	438	9	geodesic	geodesic	NOUN
ejpam-4461	438	10	in	in	ADP
ejpam-4461	438	11	g	g	PROPN
ejpam-4461	438	12	as	as	SCONJ
ejpam-4461	438	13	described	describe	VERB
ejpam-4461	438	14	in	in	ADP
ejpam-4461	438	15	condition	condition	NOUN
ejpam-4461	438	16	(	(	PUNCT
ejpam-4461	438	17	ii)(b	ii)(b	PROPN
ejpam-4461	438	18	)	)	PUNCT
ejpam-4461	438	19	.	.	PUNCT
ejpam-4461	439	1	in	in	ADP
ejpam-4461	439	2	particular	particular	ADJ
ejpam-4461	439	3	,	,	PUNCT
ejpam-4461	439	4	xn−1	xn−1	PROPN
ejpam-4461	439	5	∈	∈	PROPN
ejpam-4461	439	6	cg	cg	INTJ
ejpam-4461	439	7	.	.	PUNCT
ejpam-4461	440	1	pick	pick	VERB
ejpam-4461	440	2	y	y	PROPN
ejpam-4461	440	3	∈	∈	PROPN
ejpam-4461	440	4	v	v	PROPN
ejpam-4461	440	5	(	(	PUNCT
ejpam-4461	440	6	kn	kn	PROPN
ejpam-4461	440	7	)	)	PUNCT
ejpam-4461	440	8	such	such	ADJ
ejpam-4461	440	9	that	that	SCONJ
ejpam-4461	440	10	(	(	PUNCT
ejpam-4461	440	11	xn−1	xn−1	PROPN
ejpam-4461	440	12	,	,	PUNCT
ejpam-4461	440	13	y	y	PROPN
ejpam-4461	440	14	)	)	PUNCT
ejpam-4461	440	15	/∈	/∈	PUNCT
ejpam-4461	441	1	c.	c.	NOUN
ejpam-4461	442	1	then	then	ADV
ejpam-4461	442	2	[	[	X
ejpam-4461	442	3	(	(	PUNCT
ejpam-4461	442	4	u	u	NOUN
ejpam-4461	442	5	,	,	PUNCT
ejpam-4461	442	6	z	z	NOUN
ejpam-4461	442	7	)	)	PUNCT
ejpam-4461	442	8	,	,	PUNCT
ejpam-4461	442	9	(	(	PUNCT
ejpam-4461	442	10	xn−1	xn−1	PROPN
ejpam-4461	442	11	,	,	PUNCT
ejpam-4461	442	12	y	y	PROPN
ejpam-4461	442	13	)	)	PUNCT
ejpam-4461	442	14	,	,	PUNCT
ejpam-4461	442	15	(	(	PUNCT
ejpam-4461	442	16	v	v	NOUN
ejpam-4461	442	17	,	,	PUNCT
ejpam-4461	442	18	w	w	NOUN
ejpam-4461	442	19	)	)	PUNCT
ejpam-4461	442	20	]	]	PUNCT
ejpam-4461	442	21	is	be	AUX
ejpam-4461	442	22	a	a	DET
ejpam-4461	442	23	(	(	PUNCT
ejpam-4461	442	24	u	u	NOUN
ejpam-4461	442	25	,	,	PUNCT
ejpam-4461	442	26	z)-(v	z)-(v	PROPN
ejpam-4461	442	27	,	,	PUNCT
ejpam-4461	442	28	w	w	NOUN
ejpam-4461	442	29	)	)	PUNCT
ejpam-4461	442	30	path	path	NOUN
ejpam-4461	442	31	in	in	ADP
ejpam-4461	442	32	⟨v	⟨v	PROPN
ejpam-4461	442	33	(	(	PUNCT
ejpam-4461	442	34	g[kn	g[kn	PROPN
ejpam-4461	442	35	]	]	PUNCT
ejpam-4461	442	36	)	)	PUNCT
ejpam-4461	442	37	\	\	PROPN
ejpam-4461	443	1	c⟩.	c⟩.	PROPN
ejpam-4461	443	2	the	the	DET
ejpam-4461	443	3	above	above	ADJ
ejpam-4461	443	4	cases	case	NOUN
ejpam-4461	443	5	imply	imply	VERB
ejpam-4461	443	6	that	that	DET
ejpam-4461	443	7	⟨v	⟨v	NOUN
ejpam-4461	443	8	(	(	PUNCT
ejpam-4461	443	9	g[kn	g[kn	PROPN
ejpam-4461	443	10	]	]	PUNCT
ejpam-4461	443	11	)	)	PUNCT
ejpam-4461	443	12	\	\	NOUN
ejpam-4461	443	13	c⟩	c⟩	PUNCT
ejpam-4461	443	14	is	be	AUX
ejpam-4461	443	15	connected	connect	VERB
ejpam-4461	443	16	.	.	PUNCT
ejpam-4461	444	1	therefore	therefore	ADV
ejpam-4461	444	2	,	,	PUNCT
ejpam-4461	444	3	c	c	PROPN
ejpam-4461	444	4	is	be	AUX
ejpam-4461	444	5	an	an	DET
ejpam-4461	444	6	outerconnected	outerconnected	ADJ
ejpam-4461	444	7	semitotal	semitotal	ADJ
ejpam-4461	444	8	dominating	dominating	NOUN
ejpam-4461	444	9	set	set	NOUN
ejpam-4461	444	10	of	of	ADP
ejpam-4461	444	11	g[kn	g[kn	PROPN
ejpam-4461	444	12	]	]	PUNCT
ejpam-4461	444	13	.	.	PUNCT
ejpam-4461	445	1	now	now	ADV
ejpam-4461	445	2	,	,	PUNCT
ejpam-4461	445	3	we	we	PRON
ejpam-4461	445	4	provide	provide	VERB
ejpam-4461	445	5	proof	proof	NOUN
ejpam-4461	445	6	for	for	ADP
ejpam-4461	445	7	the	the	DET
ejpam-4461	445	8	following	follow	VERB
ejpam-4461	445	9	lemma	lemma	PROPN
ejpam-4461	445	10	,	,	PUNCT
ejpam-4461	445	11	which	which	PRON
ejpam-4461	445	12	is	be	AUX
ejpam-4461	445	13	very	very	ADV
ejpam-4461	445	14	useful	useful	ADJ
ejpam-4461	445	15	to	to	PART
ejpam-4461	445	16	get	get	VERB
ejpam-4461	445	17	the	the	DET
ejpam-4461	445	18	desired	desire	VERB
ejpam-4461	445	19	result	result	NOUN
ejpam-4461	445	20	in	in	ADP
ejpam-4461	445	21	this	this	DET
ejpam-4461	445	22	section	section	NOUN
ejpam-4461	445	23	.	.	PUNCT
ejpam-4461	446	1	the	the	DET
ejpam-4461	446	2	lemma	lemma	PROPN
ejpam-4461	446	3	is	be	AUX
ejpam-4461	446	4	given	give	VERB
ejpam-4461	446	5	without	without	ADP
ejpam-4461	446	6	proof	proof	NOUN
ejpam-4461	446	7	in	in	ADP
ejpam-4461	446	8	[	[	X
ejpam-4461	446	9	1	1	NUM
ejpam-4461	446	10	]	]	PUNCT
ejpam-4461	446	11	.	.	PUNCT
ejpam-4461	447	1	a.	a.	PROPN
ejpam-4461	447	2	aradais	aradais	PROPN
ejpam-4461	447	3	,	,	PUNCT
ejpam-4461	447	4	f.	f.	PROPN
ejpam-4461	447	5	jamil	jamil	PROPN
ejpam-4461	447	6	/	/	SYM
ejpam-4461	447	7	eur	eur	PROPN
ejpam-4461	447	8	.	.	PUNCT
ejpam-4461	448	1	j.	j.	PROPN
ejpam-4461	448	2	pure	pure	PROPN
ejpam-4461	448	3	appl	appl	PROPN
ejpam-4461	448	4	.	.	PROPN
ejpam-4461	448	5	math	math	PROPN
ejpam-4461	448	6	,	,	PUNCT
ejpam-4461	448	7	15	15	NUM
ejpam-4461	448	8	(	(	PUNCT
ejpam-4461	448	9	3	3	NUM
ejpam-4461	448	10	)	)	PUNCT
ejpam-4461	448	11	(	(	PUNCT
ejpam-4461	448	12	2022	2022	NUM
ejpam-4461	448	13	)	)	PUNCT
ejpam-4461	448	14	,	,	PUNCT
ejpam-4461	448	15	1265	1265	NUM
ejpam-4461	448	16	-	-	SYM
ejpam-4461	448	17	1279	1279	NUM
ejpam-4461	448	18	1278	1278	NUM
ejpam-4461	448	19	lemma	lemma	PROPN
ejpam-4461	448	20	1	1	NUM
ejpam-4461	448	21	.	.	PUNCT
ejpam-4461	449	1	[	[	X
ejpam-4461	449	2	1	1	X
ejpam-4461	449	3	]	]	X
ejpam-4461	449	4	if	if	SCONJ
ejpam-4461	449	5	g	g	PROPN
ejpam-4461	449	6	is	be	AUX
ejpam-4461	449	7	a	a	DET
ejpam-4461	449	8	nontrival	nontrival	ADJ
ejpam-4461	449	9	connected	connect	VERB
ejpam-4461	449	10	graph	graph	NOUN
ejpam-4461	449	11	and	and	CCONJ
ejpam-4461	449	12	s	s	VERB
ejpam-4461	449	13	⊆	⊆	NUM
ejpam-4461	449	14	v	v	NOUN
ejpam-4461	449	15	(	(	PUNCT
ejpam-4461	449	16	g	g	NOUN
ejpam-4461	449	17	)	)	PUNCT
ejpam-4461	449	18	is	be	AUX
ejpam-4461	449	19	a	a	DET
ejpam-4461	449	20	dominating	dominating	NOUN
ejpam-4461	449	21	set	set	NOUN
ejpam-4461	449	22	in	in	ADP
ejpam-4461	449	23	g	g	PROPN
ejpam-4461	449	24	,	,	PUNCT
ejpam-4461	449	25	then	then	ADV
ejpam-4461	449	26	γt2(g	γt2(g	NUM
ejpam-4461	449	27	)	)	PUNCT
ejpam-4461	449	28	≤	≤	NOUN
ejpam-4461	449	29	2|s	2|s	PUNCT
ejpam-4461	449	30	\n2	\n2	PROPN
ejpam-4461	449	31	g(s)|+	g(s)|+	PROPN
ejpam-4461	449	32	|s	|s	PROPN
ejpam-4461	449	33	∩n2	∩n2	PROPN
ejpam-4461	449	34	g(s)|	g(s)|	PROPN
ejpam-4461	449	35	.	.	PUNCT
ejpam-4461	450	1	proof	proof	NOUN
ejpam-4461	450	2	.	.	PUNCT
ejpam-4461	451	1	let	let	VERB
ejpam-4461	451	2	s	s	PRON
ejpam-4461	451	3	⊆	⊆	NUM
ejpam-4461	451	4	v	v	NOUN
ejpam-4461	451	5	(	(	PUNCT
ejpam-4461	451	6	g	g	NOUN
ejpam-4461	451	7	)	)	PUNCT
ejpam-4461	451	8	be	be	VERB
ejpam-4461	451	9	a	a	DET
ejpam-4461	451	10	dominating	dominating	NOUN
ejpam-4461	451	11	set	set	NOUN
ejpam-4461	451	12	of	of	ADP
ejpam-4461	451	13	g.	g.	PROPN
ejpam-4461	451	14	for	for	ADP
ejpam-4461	451	15	each	each	DET
ejpam-4461	451	16	x	x	SYM
ejpam-4461	451	17	∈	∈	PROPN
ejpam-4461	451	18	s	s	PART
ejpam-4461	451	19	\	\	PROPN
ejpam-4461	451	20	n2	n2	ADJ
ejpam-4461	451	21	g(s	g(s	PROPN
ejpam-4461	451	22	)	)	PUNCT
ejpam-4461	451	23	,	,	PUNCT
ejpam-4461	451	24	pick	pick	VERB
ejpam-4461	451	25	ux	ux	PROPN
ejpam-4461	451	26	∈	∈	PROPN
ejpam-4461	451	27	v	v	ADP
ejpam-4461	451	28	(	(	PUNCT
ejpam-4461	451	29	g	g	NOUN
ejpam-4461	451	30	)	)	PUNCT
ejpam-4461	451	31	such	such	ADJ
ejpam-4461	451	32	that	that	SCONJ
ejpam-4461	451	33	xux	xux	PROPN
ejpam-4461	451	34	∈	∈	PROPN
ejpam-4461	451	35	e(g	e(g	PROPN
ejpam-4461	451	36	)	)	PUNCT
ejpam-4461	451	37	.	.	PUNCT
ejpam-4461	452	1	then	then	ADV
ejpam-4461	452	2	s∗	s∗	PROPN
ejpam-4461	452	3	=	=	SYM
ejpam-4461	452	4	s	s	PART
ejpam-4461	452	5	∪	∪	X
ejpam-4461	452	6	{	{	PUNCT
ejpam-4461	452	7	ux	ux	NOUN
ejpam-4461	452	8	:	:	PUNCT
ejpam-4461	452	9	x	x	PUNCT
ejpam-4461	452	10	∈	∈	PROPN
ejpam-4461	452	11	s	s	PART
ejpam-4461	452	12	\	\	PROPN
ejpam-4461	452	13	n2	n2	ADJ
ejpam-4461	452	14	g(g	g(g	PROPN
ejpam-4461	452	15	)	)	PUNCT
ejpam-4461	452	16	}	}	PUNCT
ejpam-4461	452	17	is	be	AUX
ejpam-4461	452	18	a	a	DET
ejpam-4461	452	19	semitotal	semitotal	ADJ
ejpam-4461	452	20	dominating	dominating	NOUN
ejpam-4461	452	21	set	set	NOUN
ejpam-4461	452	22	of	of	ADP
ejpam-4461	452	23	g.	g.	PROPN
ejpam-4461	452	24	thus	thus	ADV
ejpam-4461	452	25	,	,	PUNCT
ejpam-4461	452	26	γt2(g	γt2(g	NOUN
ejpam-4461	452	27	)	)	PUNCT
ejpam-4461	452	28	≤	≤	NOUN
ejpam-4461	452	29	|s∗|	|s∗|	NUM
ejpam-4461	453	1	=	=	SYM
ejpam-4461	453	2	|s	|s	PROPN
ejpam-4461	453	3	∩n2	∩n2	PROPN
ejpam-4461	453	4	g(s)|+	g(s)|+	PROPN
ejpam-4461	453	5	2|s	2|s	PROPN
ejpam-4461	453	6	\n2	\n2	PROPN
ejpam-4461	453	7	g(s)|	g(s)|	PROPN
ejpam-4461	453	8	.	.	PUNCT
ejpam-4461	454	1	corollary	corollary	PROPN
ejpam-4461	454	2	5	5	NUM
ejpam-4461	454	3	.	.	PUNCT
ejpam-4461	455	1	let	let	VERB
ejpam-4461	455	2	g	g	PRON
ejpam-4461	455	3	be	be	AUX
ejpam-4461	455	4	a	a	DET
ejpam-4461	455	5	nontrivial	nontrivial	ADJ
ejpam-4461	455	6	connected	connect	VERB
ejpam-4461	455	7	graph	graph	NOUN
ejpam-4461	455	8	and	and	CCONJ
ejpam-4461	455	9	n	n	PRON
ejpam-4461	455	10	≥	≥	NOUN
ejpam-4461	455	11	2	2	NUM
ejpam-4461	455	12	.	.	PUNCT
ejpam-4461	456	1	then	then	ADV
ejpam-4461	456	2	γ̃t2(g[kn	γ̃t2(g[kn	PROPN
ejpam-4461	456	3	]	]	PUNCT
ejpam-4461	456	4	)	)	PUNCT
ejpam-4461	456	5	=	=	PUNCT
ejpam-4461	456	6	γt2(g	γt2(g	NOUN
ejpam-4461	456	7	)	)	PUNCT
ejpam-4461	456	8	.	.	PUNCT
ejpam-4461	457	1	proof	proof	NOUN
ejpam-4461	457	2	.	.	PUNCT
ejpam-4461	458	1	let	let	VERB
ejpam-4461	458	2	s	s	PRON
ejpam-4461	458	3	⊆	⊆	NUM
ejpam-4461	458	4	v	v	NOUN
ejpam-4461	458	5	(	(	PUNCT
ejpam-4461	458	6	g	g	NOUN
ejpam-4461	458	7	)	)	PUNCT
ejpam-4461	458	8	be	be	AUX
ejpam-4461	458	9	a	a	DET
ejpam-4461	458	10	γt2	γt2	NOUN
ejpam-4461	458	11	-	-	PUNCT
ejpam-4461	458	12	set	set	NOUN
ejpam-4461	458	13	of	of	ADP
ejpam-4461	458	14	g.	g.	PROPN
ejpam-4461	458	15	choose	choose	VERB
ejpam-4461	458	16	v	v	NUM
ejpam-4461	458	17	∈	∈	PROPN
ejpam-4461	458	18	v	v	NOUN
ejpam-4461	458	19	(	(	PUNCT
ejpam-4461	458	20	kn	kn	PROPN
ejpam-4461	458	21	)	)	PUNCT
ejpam-4461	458	22	and	and	CCONJ
ejpam-4461	458	23	define	define	VERB
ejpam-4461	458	24	c	c	NOUN
ejpam-4461	458	25	=	=	SYM
ejpam-4461	458	26	s	s	PROPN
ejpam-4461	458	27	×	×	NOUN
ejpam-4461	458	28	{	{	PUNCT
ejpam-4461	458	29	v	v	NOUN
ejpam-4461	458	30	}	}	PUNCT
ejpam-4461	458	31	.	.	PUNCT
ejpam-4461	459	1	since	since	SCONJ
ejpam-4461	459	2	conditions	condition	NOUN
ejpam-4461	459	3	(	(	PUNCT
ejpam-4461	459	4	i)(a	i)(a	NOUN
ejpam-4461	459	5	)	)	PUNCT
ejpam-4461	459	6	and	and	CCONJ
ejpam-4461	459	7	(	(	PUNCT
ejpam-4461	459	8	ii)(b	ii)(b	PROPN
ejpam-4461	459	9	)	)	PUNCT
ejpam-4461	459	10	of	of	ADP
ejpam-4461	459	11	theorem	theorem	NOUN
ejpam-4461	459	12	6	6	NUM
ejpam-4461	459	13	hold	hold	NOUN
ejpam-4461	459	14	for	for	ADP
ejpam-4461	459	15	c	c	NOUN
ejpam-4461	459	16	,	,	PUNCT
ejpam-4461	459	17	c	c	PROPN
ejpam-4461	459	18	is	be	AUX
ejpam-4461	459	19	an	an	DET
ejpam-4461	459	20	outer	outer	ADV
ejpam-4461	459	21	-	-	PUNCT
ejpam-4461	459	22	connected	connect	VERB
ejpam-4461	459	23	semitotal	semitotal	ADJ
ejpam-4461	459	24	dominating	dominating	NOUN
ejpam-4461	459	25	set	set	NOUN
ejpam-4461	459	26	of	of	ADP
ejpam-4461	459	27	g[kn	g[kn	PROPN
ejpam-4461	459	28	]	]	PUNCT
ejpam-4461	459	29	.	.	PUNCT
ejpam-4461	460	1	consequently	consequently	ADV
ejpam-4461	460	2	,	,	PUNCT
ejpam-4461	460	3	γ̃t2(g[kn	γ̃t2(g[kn	PROPN
ejpam-4461	460	4	]	]	PUNCT
ejpam-4461	460	5	)	)	PUNCT
ejpam-4461	460	6	≤	≤	NUM
ejpam-4461	460	7	|s|	|s|	PROPN
ejpam-4461	460	8	=	=	SYM
ejpam-4461	460	9	γt2(g	γt2(g	PROPN
ejpam-4461	460	10	)	)	PUNCT
ejpam-4461	460	11	.	.	PUNCT
ejpam-4461	461	1	let	let	VERB
ejpam-4461	461	2	c	c	NOUN
ejpam-4461	461	3	=	=	PUNCT
ejpam-4461	461	4	⋃	⋃	PROPN
ejpam-4461	461	5	x∈s	x∈s	NOUN
ejpam-4461	461	6	(	(	PUNCT
ejpam-4461	461	7	{	{	PUNCT
ejpam-4461	461	8	x	x	NOUN
ejpam-4461	461	9	}	}	PUNCT
ejpam-4461	461	10	×	×	PROPN
ejpam-4461	461	11	tx	tx	PROPN
ejpam-4461	461	12	)	)	PUNCT
ejpam-4461	461	13	⊆	⊆	NUM
ejpam-4461	461	14	v	v	NOUN
ejpam-4461	461	15	(	(	PUNCT
ejpam-4461	461	16	g[kn	g[kn	PROPN
ejpam-4461	461	17	]	]	PUNCT
ejpam-4461	461	18	)	)	PUNCT
ejpam-4461	461	19	be	be	AUX
ejpam-4461	461	20	an	an	DET
ejpam-4461	461	21	outer	outer	ADV
ejpam-4461	461	22	-	-	PUNCT
ejpam-4461	461	23	connected	connect	VERB
ejpam-4461	461	24	semitotal	semitotal	ADJ
ejpam-4461	461	25	dominating	dominating	NOUN
ejpam-4461	461	26	set	set	NOUN
ejpam-4461	461	27	of	of	ADP
ejpam-4461	461	28	g[kn	g[kn	PROPN
ejpam-4461	461	29	]	]	PUNCT
ejpam-4461	461	30	.	.	PUNCT
ejpam-4461	462	1	by	by	ADP
ejpam-4461	462	2	theorem	theorem	NOUN
ejpam-4461	462	3	6	6	NUM
ejpam-4461	462	4	,	,	PUNCT
ejpam-4461	462	5	s	s	VERB
ejpam-4461	462	6	is	be	AUX
ejpam-4461	462	7	a	a	DET
ejpam-4461	462	8	dominating	dominating	NOUN
ejpam-4461	462	9	set	set	NOUN
ejpam-4461	462	10	of	of	ADP
ejpam-4461	462	11	g.	g.	PROPN
ejpam-4461	462	12	if	if	SCONJ
ejpam-4461	462	13	s	s	VERB
ejpam-4461	462	14	is	be	AUX
ejpam-4461	462	15	a	a	DET
ejpam-4461	462	16	semitotal	semitotal	ADJ
ejpam-4461	462	17	dominating	dominating	NOUN
ejpam-4461	462	18	set	set	NOUN
ejpam-4461	462	19	of	of	ADP
ejpam-4461	462	20	g	g	NOUN
ejpam-4461	462	21	,	,	PUNCT
ejpam-4461	462	22	then	then	ADV
ejpam-4461	462	23	γt2(g	γt2(g	NUM
ejpam-4461	462	24	)	)	PUNCT
ejpam-4461	462	25	≤	≤	NOUN
ejpam-4461	462	26	|s|	|s|	NOUN
ejpam-4461	462	27	≤	≤	PROPN
ejpam-4461	462	28	∑	∑	PUNCT
ejpam-4461	462	29	x∈s	x∈s	PROPN
ejpam-4461	462	30	|tx|	|tx|	PROPN
ejpam-4461	462	31	=	=	PUNCT
ejpam-4461	462	32	|c|	|c|	PROPN
ejpam-4461	462	33	.	.	PUNCT
ejpam-4461	462	34	suppose	suppose	VERB
ejpam-4461	462	35	that	that	SCONJ
ejpam-4461	462	36	s	s	VERB
ejpam-4461	462	37	is	be	AUX
ejpam-4461	462	38	not	not	PART
ejpam-4461	462	39	a	a	DET
ejpam-4461	462	40	semitotal	semitotal	ADJ
ejpam-4461	462	41	dominating	dominating	NOUN
ejpam-4461	462	42	set	set	VERB
ejpam-4461	462	43	in	in	ADP
ejpam-4461	462	44	g.	g.	PROPN
ejpam-4461	462	45	let	let	VERB
ejpam-4461	462	46	s1	s1	PROPN
ejpam-4461	462	47	=	=	PUNCT
ejpam-4461	462	48	s	s	PART
ejpam-4461	462	49	\	\	PROPN
ejpam-4461	462	50	n2	n2	ADJ
ejpam-4461	462	51	g(s	g(s	PROPN
ejpam-4461	462	52	)	)	PUNCT
ejpam-4461	462	53	and	and	CCONJ
ejpam-4461	462	54	s2	s2	VERB
ejpam-4461	462	55	=	=	SYM
ejpam-4461	462	56	s	s	PROPN
ejpam-4461	462	57	∩n2	∩n2	PROPN
ejpam-4461	462	58	g(s	g(s	PROPN
ejpam-4461	462	59	)	)	PUNCT
ejpam-4461	462	60	.	.	PUNCT
ejpam-4461	463	1	by	by	ADP
ejpam-4461	463	2	theorem	theorem	NOUN
ejpam-4461	463	3	6	6	NUM
ejpam-4461	463	4	,	,	PUNCT
ejpam-4461	463	5	c	c	NOUN
ejpam-4461	463	6	=	=	SYM
ejpam-4461	463	7			PROPN
ejpam-4461	463	8	⋃	⋃	PROPN
ejpam-4461	463	9	x∈s1	x∈s1	PROPN
ejpam-4461	463	10	(	(	PUNCT
ejpam-4461	463	11	{	{	PUNCT
ejpam-4461	463	12	x	x	NOUN
ejpam-4461	463	13	}	}	PUNCT
ejpam-4461	463	14	×	×	PROPN
ejpam-4461	463	15	tx	tx	PROPN
ejpam-4461	463	16	)	)	PUNCT
ejpam-4461	463	17			PROPN
ejpam-4461	463	18	∪	∪	ADP
ejpam-4461	463	19			PROPN
ejpam-4461	463	20	⋃	⋃	PROPN
ejpam-4461	463	21	x∈s2	x∈s2	NOUN
ejpam-4461	463	22	(	(	PUNCT
ejpam-4461	463	23	{	{	PUNCT
ejpam-4461	463	24	x	x	NOUN
ejpam-4461	463	25	}	}	PUNCT
ejpam-4461	463	26	×	×	PROPN
ejpam-4461	463	27	tx	tx	PROPN
ejpam-4461	463	28	)	)	PUNCT
ejpam-4461	463	29			PROPN
ejpam-4461	463	30	,	,	PUNCT
ejpam-4461	463	31	where	where	SCONJ
ejpam-4461	463	32	|tx|	|tx|	NOUN
ejpam-4461	463	33	≥	≥	NUM
ejpam-4461	463	34	2	2	NUM
ejpam-4461	463	35	for	for	ADP
ejpam-4461	463	36	all	all	DET
ejpam-4461	463	37	x	x	SYM
ejpam-4461	463	38	∈	∈	PROPN
ejpam-4461	463	39	s1	s1	NOUN
ejpam-4461	463	40	.	.	PUNCT
ejpam-4461	464	1	thus	thus	ADV
ejpam-4461	464	2	,	,	PUNCT
ejpam-4461	464	3	|c|	|c|	PROPN
ejpam-4461	464	4	=	=	PUNCT
ejpam-4461	464	5	∑	∑	PUNCT
ejpam-4461	464	6	x∈s1	x∈s1	PROPN
ejpam-4461	464	7	|tx|+	|tx|+	PROPN
ejpam-4461	464	8	∑	∑	PROPN
ejpam-4461	464	9	x∈s2	x∈s2	PROPN
ejpam-4461	464	10	|tx|	|tx|	PROPN
ejpam-4461	464	11	≥	≥	NOUN
ejpam-4461	464	12	2|s1|+	2|s1|+	NUM
ejpam-4461	464	13	|s2|	|s2|	NOUN
ejpam-4461	464	14	=	=	SYM
ejpam-4461	464	15	2|s	2|s	PROPN
ejpam-4461	464	16	\n2	\n2	VERB
ejpam-4461	464	17	g(s)|+	g(s)|+	PROPN
ejpam-4461	464	18	|s	|s	PROPN
ejpam-4461	464	19	∩n2	∩n2	PROPN
ejpam-4461	464	20	g(s)|	g(s)|	PROPN
ejpam-4461	464	21	.	.	PUNCT
ejpam-4461	465	1	by	by	ADP
ejpam-4461	465	2	lemma	lemma	PROPN
ejpam-4461	465	3	1	1	NUM
ejpam-4461	465	4	,	,	PUNCT
ejpam-4461	465	5	γt2(g	γt2(g	NOUN
ejpam-4461	465	6	)	)	PUNCT
ejpam-4461	465	7	≤	≤	NUM
ejpam-4461	465	8	|c|	|c|	PROPN
ejpam-4461	465	9	.	.	PUNCT
ejpam-4461	466	1	since	since	SCONJ
ejpam-4461	466	2	c	c	PROPN
ejpam-4461	466	3	is	be	AUX
ejpam-4461	466	4	arbitrary	arbitrary	ADJ
ejpam-4461	466	5	,	,	PUNCT
ejpam-4461	466	6	γt2(g	γt2(g	NOUN
ejpam-4461	466	7	)	)	PUNCT
ejpam-4461	466	8	≤	≤	NUM
ejpam-4461	466	9	γt2(g[kn	γt2(g[kn	PROPN
ejpam-4461	466	10	]	]	PUNCT
ejpam-4461	466	11	)	)	PUNCT
ejpam-4461	466	12	.	.	PUNCT
ejpam-4461	467	1	references	reference	NOUN
ejpam-4461	467	2	1279	1279	NUM
ejpam-4461	467	3	acknowledgements	acknowledgement	NOUN
ejpam-4461	467	4	the	the	DET
ejpam-4461	467	5	authors	author	NOUN
ejpam-4461	467	6	would	would	AUX
ejpam-4461	467	7	like	like	VERB
ejpam-4461	467	8	to	to	PART
ejpam-4461	467	9	thank	thank	VERB
ejpam-4461	467	10	the	the	DET
ejpam-4461	467	11	referees	referee	NOUN
ejpam-4461	467	12	for	for	ADP
ejpam-4461	467	13	the	the	DET
ejpam-4461	467	14	invaluable	invaluable	ADJ
ejpam-4461	467	15	assistance	assistance	NOUN
ejpam-4461	467	16	they	they	PRON
ejpam-4461	467	17	gave	give	VERB
ejpam-4461	467	18	us	we	PRON
ejpam-4461	467	19	through	through	ADP
ejpam-4461	467	20	their	their	PRON
ejpam-4461	467	21	comments	comment	NOUN
ejpam-4461	467	22	and	and	CCONJ
ejpam-4461	467	23	suggestions	suggestion	NOUN
ejpam-4461	467	24	which	which	PRON
ejpam-4461	467	25	led	lead	VERB
ejpam-4461	467	26	to	to	ADP
ejpam-4461	467	27	the	the	DET
ejpam-4461	467	28	improvement	improvement	NOUN
ejpam-4461	467	29	of	of	ADP
ejpam-4461	467	30	the	the	DET
ejpam-4461	467	31	paper	paper	NOUN
ejpam-4461	467	32	.	.	PUNCT
ejpam-4461	468	1	also	also	ADV
ejpam-4461	468	2	,	,	PUNCT
ejpam-4461	468	3	the	the	DET
ejpam-4461	468	4	authors	author	NOUN
ejpam-4461	468	5	would	would	AUX
ejpam-4461	468	6	like	like	VERB
ejpam-4461	468	7	to	to	PART
ejpam-4461	468	8	thank	thank	VERB
ejpam-4461	468	9	the	the	DET
ejpam-4461	468	10	department	department	NOUN
ejpam-4461	468	11	of	of	ADP
ejpam-4461	468	12	science	science	NOUN
ejpam-4461	468	13	and	and	CCONJ
ejpam-4461	468	14	technology	technology	NOUN
ejpam-4461	468	15	accelerated	accelerate	VERB
ejpam-4461	468	16	science	science	NOUN
ejpam-4461	468	17	and	and	CCONJ
ejpam-4461	468	18	technology	technology	NOUN
ejpam-4461	468	19	human	human	ADJ
ejpam-4461	468	20	resource	resource	NOUN
ejpam-4461	468	21	development	development	NOUN
ejpam-4461	468	22	program	program	NOUN
ejpam-4461	468	23	(	(	PUNCT
ejpam-4461	468	24	dostasthrdp)-philippines	dostasthrdp)-philippine	NOUN
ejpam-4461	468	25	,	,	PUNCT
ejpam-4461	468	26	and	and	CCONJ
ejpam-4461	468	27	msu	msu	PROPN
ejpam-4461	468	28	-	-	PUNCT
ejpam-4461	468	29	iligan	iligan	PROPN
ejpam-4461	468	30	institute	institute	PROPN
ejpam-4461	468	31	of	of	ADP
ejpam-4461	468	32	technology	technology	NOUN
ejpam-4461	468	33	for	for	ADP
ejpam-4461	468	34	funding	fund	VERB
ejpam-4461	468	35	this	this	DET
ejpam-4461	468	36	research	research	NOUN
ejpam-4461	468	37	.	.	PUNCT
ejpam-4461	469	1	furthermore	furthermore	ADV
ejpam-4461	469	2	,	,	PUNCT
ejpam-4461	469	3	the	the	DET
ejpam-4461	469	4	researchers	researcher	NOUN
ejpam-4461	469	5	are	be	AUX
ejpam-4461	469	6	grateful	grateful	ADJ
ejpam-4461	469	7	to	to	ADP
ejpam-4461	469	8	msu	msu	PROPN
ejpam-4461	469	9	-	-	PUNCT
ejpam-4461	469	10	iit	iit	PROPN
ejpam-4461	469	11	and	and	CCONJ
ejpam-4461	469	12	msu	msu	PROPN
ejpam-4461	469	13	-	-	PUNCT
ejpam-4461	469	14	tcto	tcto	NOUN
ejpam-4461	469	15	for	for	ADP
ejpam-4461	469	16	the	the	DET
ejpam-4461	469	17	support	support	NOUN
ejpam-4461	469	18	in	in	ADP
ejpam-4461	469	19	doing	do	VERB
ejpam-4461	469	20	this	this	DET
ejpam-4461	469	21	research	research	NOUN
ejpam-4461	469	22	.	.	PUNCT
ejpam-4461	470	1	references	reference	NOUN
ejpam-4461	470	2	[	[	X
ejpam-4461	470	3	1	1	NUM
ejpam-4461	470	4	]	]	X
ejpam-4461	470	5	i.	i.	NOUN
ejpam-4461	470	6	aniversario	aniversario	PROPN
ejpam-4461	470	7	,	,	PUNCT
ejpam-4461	470	8	jr	jr	PROPN
ejpam-4461	470	9	.	.	PROPN
ejpam-4461	470	10	s.	s.	PROPN
ejpam-4461	470	11	canoy	canoy	PROPN
ejpam-4461	470	12	,	,	PUNCT
ejpam-4461	470	13	and	and	CCONJ
ejpam-4461	470	14	f.p	f.p	PROPN
ejpam-4461	470	15	jamil	jamil	PROPN
ejpam-4461	470	16	.	.	PUNCT
ejpam-4461	471	1	semitotal	semitotal	ADJ
ejpam-4461	471	2	domination	domination	NOUN
ejpam-4461	471	3	in	in	ADP
ejpam-4461	471	4	graphs	graph	NOUN
ejpam-4461	471	5	.	.	PUNCT
ejpam-4461	472	1	european	european	ADJ
ejpam-4461	472	2	journal	journal	PROPN
ejpam-4461	472	3	of	of	ADP
ejpam-4461	472	4	pure	pure	ADJ
ejpam-4461	472	5	and	and	CCONJ
ejpam-4461	472	6	applied	applied	ADJ
ejpam-4461	472	7	mathematics	mathematic	NOUN
ejpam-4461	472	8	.	.	PUNCT
ejpam-4461	472	9	,	,	PUNCT
ejpam-4461	472	10	12(4):1410–1425	12(4):1410–1425	NUM
ejpam-4461	472	11	,	,	PUNCT
ejpam-4461	472	12	2019	2019	NUM
ejpam-4461	472	13	.	.	PUNCT
ejpam-4461	473	1	[	[	X
ejpam-4461	473	2	2	2	NUM
ejpam-4461	473	3	]	]	X
ejpam-4461	473	4	f.	f.	PROPN
ejpam-4461	473	5	buckley	buckley	PROPN
ejpam-4461	473	6	and	and	CCONJ
ejpam-4461	473	7	f.	f.	PROPN
ejpam-4461	473	8	harary	harary	PROPN
ejpam-4461	473	9	.	.	PUNCT
ejpam-4461	474	1	distance	distance	NOUN
ejpam-4461	474	2	in	in	ADP
ejpam-4461	474	3	graphs	graph	NOUN
ejpam-4461	474	4	.	.	PUNCT
ejpam-4461	475	1	redwood	redwood	NOUN
ejpam-4461	475	2	city	city	NOUN
ejpam-4461	475	3	,	,	PUNCT
ejpam-4461	475	4	ca	ca	PROPN
ejpam-4461	475	5	:	:	PUNCT
ejpam-4461	475	6	addison	addison	PROPN
ejpam-4461	475	7	-	-	PUNCT
ejpam-4461	475	8	wesley	wesley	PROPN
ejpam-4461	475	9	.	.	PUNCT
ejpam-4461	475	10	,	,	PUNCT
ejpam-4461	475	11	1990	1990	NUM
ejpam-4461	475	12	.	.	PUNCT
ejpam-4461	476	1	[	[	X
ejpam-4461	476	2	3	3	NUM
ejpam-4461	476	3	]	]	X
ejpam-4461	476	4	e.j	e.j	PROPN
ejpam-4461	476	5	.	.	PROPN
ejpam-4461	476	6	cockayne	cockayne	PROPN
ejpam-4461	476	7	and	and	CCONJ
ejpam-4461	476	8	s.t	s.t	PROPN
ejpam-4461	476	9	.	.	PROPN
ejpam-4461	476	10	hedetniemi	hedetniemi	PROPN
ejpam-4461	476	11	.	.	PUNCT
ejpam-4461	477	1	towards	towards	ADP
ejpam-4461	477	2	a	a	DET
ejpam-4461	477	3	theory	theory	NOUN
ejpam-4461	477	4	of	of	ADP
ejpam-4461	477	5	domination	domination	NOUN
ejpam-4461	477	6	in	in	ADP
ejpam-4461	477	7	graphs	graph	NOUN
ejpam-4461	477	8	.	.	PUNCT
ejpam-4461	478	1	networks	network	NOUN
ejpam-4461	478	2	.	.	PUNCT
ejpam-4461	478	3	,	,	PUNCT
ejpam-4461	478	4	7:247–261	7:247–261	NUM
ejpam-4461	478	5	,	,	PUNCT
ejpam-4461	478	6	1997	1997	NUM
ejpam-4461	478	7	.	.	PUNCT
ejpam-4461	479	1	[	[	X
ejpam-4461	479	2	4	4	X
ejpam-4461	479	3	]	]	PUNCT
ejpam-4461	479	4	j.	j.	PROPN
ejpam-4461	479	5	cyman	cyman	PROPN
ejpam-4461	479	6	.	.	PUNCT
ejpam-4461	480	1	the	the	DET
ejpam-4461	480	2	outer	outer	ADV
ejpam-4461	480	3	-	-	PUNCT
ejpam-4461	480	4	connected	connect	VERB
ejpam-4461	480	5	domination	domination	NOUN
ejpam-4461	480	6	number	number	NOUN
ejpam-4461	480	7	of	of	ADP
ejpam-4461	480	8	a	a	DET
ejpam-4461	480	9	graph	graph	NOUN
ejpam-4461	480	10	.	.	PUNCT
ejpam-4461	481	1	australas	australas	PROPN
ejpam-4461	481	2	j.	j.	PROPN
ejpam-4461	481	3	combin	combin	PROPN
ejpam-4461	481	4	,	,	PUNCT
ejpam-4461	481	5	38:35–46	38:35–46	NUM
ejpam-4461	481	6	,	,	PUNCT
ejpam-4461	481	7	2007	2007	NUM
ejpam-4461	481	8	.	.	PUNCT
ejpam-4461	482	1	[	[	X
ejpam-4461	482	2	5	5	X
ejpam-4461	482	3	]	]	PUNCT
ejpam-4461	482	4	j.	j.	PROPN
ejpam-4461	482	5	cyman	cyman	PROPN
ejpam-4461	482	6	and	and	CCONJ
ejpam-4461	482	7	j.	j.	PROPN
ejpam-4461	482	8	raczek	raczek	PROPN
ejpam-4461	482	9	.	.	PUNCT
ejpam-4461	483	1	total	total	ADJ
ejpam-4461	483	2	outer	outer	ADV
ejpam-4461	483	3	-	-	PUNCT
ejpam-4461	483	4	connected	connect	VERB
ejpam-4461	483	5	domination	domination	NOUN
ejpam-4461	483	6	numbers	number	NOUN
ejpam-4461	483	7	of	of	ADP
ejpam-4461	483	8	trees	tree	NOUN
ejpam-4461	483	9	.	.	PUNCT
ejpam-4461	484	1	discrete	discrete	ADJ
ejpam-4461	484	2	applied	apply	VERB
ejpam-4461	484	3	mathematics	mathematic	NOUN
ejpam-4461	484	4	.	.	PUNCT
ejpam-4461	484	5	,	,	PUNCT
ejpam-4461	484	6	157:3198–3202	157:3198–3202	NUM
ejpam-4461	484	7	,	,	PUNCT
ejpam-4461	484	8	2009	2009	NUM
ejpam-4461	484	9	.	.	PUNCT
ejpam-4461	485	1	[	[	X
ejpam-4461	485	2	6	6	NUM
ejpam-4461	485	3	]	]	PUNCT
ejpam-4461	485	4	w.	w.	PROPN
ejpam-4461	485	5	goddard	goddard	PROPN
ejpam-4461	485	6	,	,	PUNCT
ejpam-4461	485	7	m.	m.	NOUN
ejpam-4461	485	8	henning	henning	PROPN
ejpam-4461	485	9	,	,	PUNCT
ejpam-4461	485	10	and	and	CCONJ
ejpam-4461	485	11	c.	c.	PROPN
ejpam-4461	485	12	mcpil	mcpil	PROPN
ejpam-4461	485	13	.	.	PUNCT
ejpam-4461	486	1	semitotal	semitotal	ADJ
ejpam-4461	486	2	domination	domination	NOUN
ejpam-4461	486	3	in	in	ADP
ejpam-4461	486	4	graphs	graph	NOUN
ejpam-4461	486	5	.	.	PUNCT
ejpam-4461	487	1	utilitas	utilitas	PROPN
ejpam-4461	487	2	mathematica	mathematica	PROPN
ejpam-4461	487	3	.	.	PROPN
ejpam-4461	487	4	,	,	PUNCT
ejpam-4461	487	5	94:67–81	94:67–81	NUM
ejpam-4461	487	6	,	,	PUNCT
ejpam-4461	487	7	2004	2004	NUM
ejpam-4461	487	8	.	.	PUNCT
ejpam-4461	488	1	[	[	X
ejpam-4461	488	2	7	7	X
ejpam-4461	488	3	]	]	X
ejpam-4461	488	4	g.	g.	PROPN
ejpam-4461	488	5	hao	hao	PROPN
ejpam-4461	488	6	and	and	CCONJ
ejpam-4461	488	7	w.	w.	PROPN
ejpam-4461	488	8	zhuang	zhuang	PROPN
ejpam-4461	488	9	.	.	PUNCT
ejpam-4461	489	1	semitotal	semitotal	ADJ
ejpam-4461	489	2	domination	domination	NOUN
ejpam-4461	489	3	in	in	ADP
ejpam-4461	489	4	trees	tree	NOUN
ejpam-4461	489	5	.	.	PUNCT
ejpam-4461	490	1	discrete	discrete	ADJ
ejpam-4461	490	2	mathematics	mathematic	NOUN
ejpam-4461	490	3	and	and	CCONJ
ejpam-4461	490	4	theoretical	theoretical	ADJ
ejpam-4461	490	5	computer	computer	NOUN
ejpam-4461	490	6	science	science	NOUN
ejpam-4461	490	7	.	.	PUNCT
ejpam-4461	490	8	,	,	PUNCT
ejpam-4461	490	9	20(2):1–11	20(2):1–11	PROPN
ejpam-4461	490	10	,	,	PUNCT
ejpam-4461	490	11	2018	2018	NUM
ejpam-4461	490	12	.	.	PUNCT
ejpam-4461	491	1	[	[	X
ejpam-4461	491	2	8	8	NUM
ejpam-4461	491	3	]	]	X
ejpam-4461	491	4	h.	h.	PROPN
ejpam-4461	491	5	henning	henning	PROPN
ejpam-4461	491	6	and	and	CCONJ
ejpam-4461	491	7	a.	a.	PROPN
ejpam-4461	491	8	marcon	marcon	PROPN
ejpam-4461	491	9	.	.	PUNCT
ejpam-4461	492	1	semitotal	semitotal	ADJ
ejpam-4461	492	2	domination	domination	NOUN
ejpam-4461	492	3	in	in	ADP
ejpam-4461	492	4	claw	claw	NOUN
ejpam-4461	492	5	-	-	PUNCT
ejpam-4461	492	6	free	free	ADJ
ejpam-4461	492	7	cubic	cubic	ADJ
ejpam-4461	492	8	graphs	graph	NOUN
ejpam-4461	492	9	.	.	PUNCT
ejpam-4461	493	1	annals	annal	NOUN
ejpam-4461	493	2	of	of	ADP
ejpam-4461	493	3	combinatorics	combinatoric	NOUN
ejpam-4461	493	4	.	.	PUNCT
ejpam-4461	493	5	,	,	PUNCT
ejpam-4461	493	6	20(4):799–813	20(4):799–813	NUM
ejpam-4461	493	7	,	,	PUNCT
ejpam-4461	493	8	2016	2016	NUM
ejpam-4461	493	9	.	.	PUNCT