id	sid	tid	token	lemma	pos
ejpam-3485	1	1	european	european	PROPN
ejpam-3485	1	2	journal	journal	PROPN
ejpam-3485	1	3	of	of	ADP
ejpam-3485	1	4	pure	pure	ADJ
ejpam-3485	1	5	and	and	CCONJ
ejpam-3485	1	6	applied	apply	VERB
ejpam-3485	1	7	mathematics	mathematic	NOUN
ejpam-3485	1	8	vol	vol	NOUN
ejpam-3485	1	9	.	.	PROPN
ejpam-3485	2	1	12	12	NUM
ejpam-3485	2	2	,	,	PUNCT
ejpam-3485	2	3	no	no	INTJ
ejpam-3485	2	4	.	.	NOUN
ejpam-3485	2	5	4	4	NUM
ejpam-3485	2	6	,	,	PUNCT
ejpam-3485	2	7	2019	2019	NUM
ejpam-3485	2	8	,	,	PUNCT
ejpam-3485	2	9	1779	1779	NUM
ejpam-3485	2	10	-	-	SYM
ejpam-3485	2	11	1786	1786	NUM
ejpam-3485	2	12	issn	issn	PROPN
ejpam-3485	2	13	1307	1307	NUM
ejpam-3485	2	14	-	-	SYM
ejpam-3485	2	15	5543	5543	NUM
ejpam-3485	2	16	–	–	PUNCT
ejpam-3485	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3485	2	18	published	publish	VERB
ejpam-3485	2	19	by	by	ADP
ejpam-3485	2	20	new	new	PROPN
ejpam-3485	2	21	york	york	PROPN
ejpam-3485	2	22	business	business	PROPN
ejpam-3485	2	23	global	global	ADJ
ejpam-3485	2	24	forcing	force	VERB
ejpam-3485	2	25	subsets	subset	NOUN
ejpam-3485	2	26	for	for	ADP
ejpam-3485	2	27	γc	γc	NOUN
ejpam-3485	2	28	-	-	PUNCT
ejpam-3485	2	29	sets	set	NOUN
ejpam-3485	2	30	and	and	CCONJ
ejpam-3485	2	31	γt	γt	NOUN
ejpam-3485	2	32	-	-	NOUN
ejpam-3485	2	33	sets	set	NOUN
ejpam-3485	2	34	in	in	ADP
ejpam-3485	2	35	the	the	DET
ejpam-3485	2	36	lexicographic	lexicographic	ADJ
ejpam-3485	2	37	product	product	NOUN
ejpam-3485	2	38	of	of	ADP
ejpam-3485	2	39	graphs	graph	NOUN
ejpam-3485	2	40	cris	cris	PROPN
ejpam-3485	2	41	l.	l.	PROPN
ejpam-3485	2	42	armada1	armada1	PROPN
ejpam-3485	2	43	,	,	PUNCT
ejpam-3485	2	44	sergio	sergio	PROPN
ejpam-3485	2	45	r.	r.	PROPN
ejpam-3485	2	46	canoy	canoy	PROPN
ejpam-3485	2	47	,	,	PUNCT
ejpam-3485	2	48	jr.2,∗	jr.2,∗	NUM
ejpam-3485	2	49	,	,	PUNCT
ejpam-3485	2	50	carmelito	carmelito	PROPN
ejpam-3485	2	51	e.	e.	PROPN
ejpam-3485	2	52	go3	go3	PROPN
ejpam-3485	2	53	1	1	NUM
ejpam-3485	2	54	mathematics	mathematics	PROPN
ejpam-3485	2	55	department	department	NOUN
ejpam-3485	2	56	,	,	PUNCT
ejpam-3485	2	57	cebu	cebu	NOUN
ejpam-3485	2	58	normal	normal	ADJ
ejpam-3485	2	59	university	university	NOUN
ejpam-3485	2	60	,	,	PUNCT
ejpam-3485	2	61	6000	6000	NUM
ejpam-3485	2	62	cebu	cebu	NOUN
ejpam-3485	2	63	city	city	NOUN
ejpam-3485	2	64	,	,	PUNCT
ejpam-3485	2	65	philippines	philippines	PROPN
ejpam-3485	2	66	2	2	NUM
ejpam-3485	2	67	department	department	NOUN
ejpam-3485	2	68	of	of	ADP
ejpam-3485	2	69	mathematics	mathematic	NOUN
ejpam-3485	2	70	and	and	CCONJ
ejpam-3485	2	71	statistics	statistic	NOUN
ejpam-3485	2	72	,	,	PUNCT
ejpam-3485	2	73	college	college	NOUN
ejpam-3485	2	74	of	of	ADP
ejpam-3485	2	75	sciences	science	NOUN
ejpam-3485	2	76	and	and	CCONJ
ejpam-3485	2	77	mathematics	mathematic	NOUN
ejpam-3485	2	78	,	,	PUNCT
ejpam-3485	2	79	center	center	NOUN
ejpam-3485	2	80	for	for	ADP
ejpam-3485	2	81	graph	graph	NOUN
ejpam-3485	2	82	theory	theory	NOUN
ejpam-3485	2	83	,	,	PUNCT
ejpam-3485	2	84	algebra	algebra	NOUN
ejpam-3485	2	85	,	,	PUNCT
ejpam-3485	2	86	and	and	CCONJ
ejpam-3485	2	87	analysis	analysis	NOUN
ejpam-3485	2	88	,	,	PUNCT
ejpam-3485	2	89	premier	premier	PROPN
ejpam-3485	2	90	research	research	PROPN
ejpam-3485	2	91	institute	institute	PROPN
ejpam-3485	2	92	in	in	ADP
ejpam-3485	2	93	science	science	NOUN
ejpam-3485	2	94	and	and	CCONJ
ejpam-3485	2	95	mathematics	mathematic	NOUN
ejpam-3485	2	96	,	,	PUNCT
ejpam-3485	2	97	mindanao	mindanao	PROPN
ejpam-3485	2	98	state	state	PROPN
ejpam-3485	2	99	university	university	PROPN
ejpam-3485	2	100	-	-	PUNCT
ejpam-3485	2	101	iligan	iligan	PROPN
ejpam-3485	2	102	institute	institute	PROPN
ejpam-3485	2	103	of	of	ADP
ejpam-3485	2	104	technology	technology	PROPN
ejpam-3485	2	105	,	,	PUNCT
ejpam-3485	2	106	9200	9200	NUM
ejpam-3485	2	107	iligan	iligan	ADJ
ejpam-3485	2	108	city	city	NOUN
ejpam-3485	2	109	,	,	PUNCT
ejpam-3485	2	110	philippines	philippines	PROPN
ejpam-3485	2	111	3	3	NUM
ejpam-3485	2	112	department	department	NOUN
ejpam-3485	2	113	of	of	ADP
ejpam-3485	2	114	mathematics	mathematics	PROPN
ejpam-3485	2	115	,	,	PUNCT
ejpam-3485	2	116	college	college	NOUN
ejpam-3485	2	117	of	of	ADP
ejpam-3485	2	118	natural	natural	ADJ
ejpam-3485	2	119	sciences	science	NOUN
ejpam-3485	2	120	and	and	CCONJ
ejpam-3485	2	121	mathematics	mathematic	NOUN
ejpam-3485	2	122	,	,	PUNCT
ejpam-3485	2	123	mindanao	mindanao	PROPN
ejpam-3485	2	124	state	state	PROPN
ejpam-3485	2	125	university	university	PROPN
ejpam-3485	2	126	main	main	ADJ
ejpam-3485	2	127	campus	campus	NOUN
ejpam-3485	2	128	,	,	PUNCT
ejpam-3485	2	129	9700	9700	NUM
ejpam-3485	2	130	marawi	marawi	PROPN
ejpam-3485	2	131	city	city	PROPN
ejpam-3485	2	132	,	,	PUNCT
ejpam-3485	2	133	philippines	philippine	NOUN
ejpam-3485	2	134	abstract	abstract	ADJ
ejpam-3485	2	135	.	.	PUNCT
ejpam-3485	3	1	in	in	ADP
ejpam-3485	3	2	this	this	DET
ejpam-3485	3	3	paper	paper	NOUN
ejpam-3485	3	4	,	,	PUNCT
ejpam-3485	3	5	the	the	DET
ejpam-3485	3	6	connected	connected	ADJ
ejpam-3485	3	7	dominating	dominating	NOUN
ejpam-3485	3	8	sets	set	NOUN
ejpam-3485	3	9	and	and	CCONJ
ejpam-3485	3	10	total	total	ADJ
ejpam-3485	3	11	dominating	dominating	NOUN
ejpam-3485	3	12	sets	set	NOUN
ejpam-3485	3	13	in	in	ADP
ejpam-3485	3	14	the	the	DET
ejpam-3485	3	15	lexicographic	lexicographic	ADJ
ejpam-3485	3	16	product	product	NOUN
ejpam-3485	3	17	of	of	ADP
ejpam-3485	3	18	two	two	NUM
ejpam-3485	3	19	graphs	graph	NOUN
ejpam-3485	3	20	are	be	AUX
ejpam-3485	3	21	characterized	characterize	VERB
ejpam-3485	3	22	.	.	PUNCT
ejpam-3485	4	1	further	far	ADV
ejpam-3485	4	2	,	,	PUNCT
ejpam-3485	4	3	the	the	DET
ejpam-3485	4	4	connected	connected	ADJ
ejpam-3485	4	5	domination	domination	NOUN
ejpam-3485	4	6	,	,	PUNCT
ejpam-3485	4	7	total	total	ADJ
ejpam-3485	4	8	domination	domination	NOUN
ejpam-3485	4	9	,	,	PUNCT
ejpam-3485	4	10	forcing	force	VERB
ejpam-3485	4	11	connected	connected	ADJ
ejpam-3485	4	12	domination	domination	NOUN
ejpam-3485	4	13	and	and	CCONJ
ejpam-3485	4	14	forcing	force	VERB
ejpam-3485	4	15	total	total	ADJ
ejpam-3485	4	16	domination	domination	NOUN
ejpam-3485	4	17	numbers	number	NOUN
ejpam-3485	4	18	of	of	ADP
ejpam-3485	4	19	these	these	DET
ejpam-3485	4	20	graphs	graph	NOUN
ejpam-3485	4	21	are	be	AUX
ejpam-3485	4	22	determined	determine	VERB
ejpam-3485	4	23	.	.	PUNCT
ejpam-3485	5	1	2010	2010	NUM
ejpam-3485	5	2	mathematics	mathematic	NOUN
ejpam-3485	5	3	subject	subject	NOUN
ejpam-3485	5	4	classifications	classification	NOUN
ejpam-3485	5	5	:	:	PUNCT
ejpam-3485	5	6	05c69	05c69	X
ejpam-3485	5	7	key	key	ADJ
ejpam-3485	5	8	words	word	NOUN
ejpam-3485	5	9	and	and	CCONJ
ejpam-3485	5	10	phrases	phrase	NOUN
ejpam-3485	5	11	:	:	PUNCT
ejpam-3485	5	12	connected	connected	ADJ
ejpam-3485	5	13	domination	domination	NOUN
ejpam-3485	5	14	,	,	PUNCT
ejpam-3485	5	15	total	total	ADJ
ejpam-3485	5	16	domination	domination	NOUN
ejpam-3485	5	17	,	,	PUNCT
ejpam-3485	5	18	forcing	force	VERB
ejpam-3485	5	19	subset	subset	NOUN
ejpam-3485	5	20	,	,	PUNCT
ejpam-3485	5	21	lexicographic	lexicographic	ADJ
ejpam-3485	5	22	product	product	NOUN
ejpam-3485	5	23	1	1	NUM
ejpam-3485	5	24	.	.	PUNCT
ejpam-3485	6	1	introduction	introduction	NOUN
ejpam-3485	6	2	let	let	VERB
ejpam-3485	6	3	g	g	NOUN
ejpam-3485	6	4	=	=	SYM
ejpam-3485	6	5	(	(	PUNCT
ejpam-3485	6	6	v	v	NOUN
ejpam-3485	6	7	(	(	PUNCT
ejpam-3485	6	8	g	g	NOUN
ejpam-3485	6	9	)	)	PUNCT
ejpam-3485	6	10	,	,	PUNCT
ejpam-3485	6	11	e(g	e(g	PROPN
ejpam-3485	6	12	)	)	PUNCT
ejpam-3485	6	13	)	)	PUNCT
ejpam-3485	6	14	be	be	AUX
ejpam-3485	6	15	a	a	DET
ejpam-3485	6	16	connected	connected	ADJ
ejpam-3485	6	17	graph	graph	NOUN
ejpam-3485	6	18	.	.	PUNCT
ejpam-3485	7	1	a	a	DET
ejpam-3485	7	2	set	set	NOUN
ejpam-3485	7	3	d	d	NOUN
ejpam-3485	7	4	⊆	⊆	NUM
ejpam-3485	7	5	v	v	ADP
ejpam-3485	7	6	(	(	PUNCT
ejpam-3485	7	7	g	g	NOUN
ejpam-3485	7	8	)	)	PUNCT
ejpam-3485	7	9	is	be	AUX
ejpam-3485	7	10	a	a	DET
ejpam-3485	7	11	dominating	dominating	NOUN
ejpam-3485	7	12	set	set	NOUN
ejpam-3485	7	13	of	of	ADP
ejpam-3485	7	14	g	g	PROPN
ejpam-3485	7	15	if	if	SCONJ
ejpam-3485	7	16	every	every	DET
ejpam-3485	7	17	vertex	vertex	NOUN
ejpam-3485	7	18	in	in	ADP
ejpam-3485	7	19	v	v	NOUN
ejpam-3485	7	20	(	(	PUNCT
ejpam-3485	7	21	g)\d	g)\d	NOUN
ejpam-3485	7	22	is	be	AUX
ejpam-3485	7	23	adjacent	adjacent	ADJ
ejpam-3485	7	24	to	to	ADP
ejpam-3485	7	25	at	at	ADV
ejpam-3485	7	26	least	least	ADV
ejpam-3485	7	27	one	one	NUM
ejpam-3485	7	28	vertex	vertex	NOUN
ejpam-3485	7	29	in	in	ADP
ejpam-3485	7	30	d.	d.	PROPN
ejpam-3485	7	31	a	a	DET
ejpam-3485	7	32	set	set	NOUN
ejpam-3485	7	33	s	s	PROPN
ejpam-3485	7	34	⊆	⊆	NUM
ejpam-3485	7	35	v	v	NOUN
ejpam-3485	7	36	(	(	PUNCT
ejpam-3485	7	37	g	g	NOUN
ejpam-3485	7	38	)	)	PUNCT
ejpam-3485	7	39	is	be	AUX
ejpam-3485	7	40	a	a	DET
ejpam-3485	7	41	total	total	ADJ
ejpam-3485	7	42	dominating	dominating	NOUN
ejpam-3485	7	43	set	set	NOUN
ejpam-3485	7	44	(	(	PUNCT
ejpam-3485	7	45	resp	resp	NOUN
ejpam-3485	7	46	.	.	PUNCT
ejpam-3485	8	1	connected	connect	VERB
ejpam-3485	8	2	dominating	dominating	NOUN
ejpam-3485	8	3	set	set	NOUN
ejpam-3485	8	4	)	)	PUNCT
ejpam-3485	8	5	of	of	ADP
ejpam-3485	8	6	g	g	PROPN
ejpam-3485	8	7	if	if	SCONJ
ejpam-3485	8	8	each	each	DET
ejpam-3485	8	9	vertex	vertex	NOUN
ejpam-3485	8	10	in	in	ADP
ejpam-3485	8	11	v	v	NOUN
ejpam-3485	8	12	(	(	PUNCT
ejpam-3485	8	13	g	g	NOUN
ejpam-3485	8	14	)	)	PUNCT
ejpam-3485	8	15	is	be	AUX
ejpam-3485	8	16	adjacent	adjacent	ADJ
ejpam-3485	8	17	to	to	ADP
ejpam-3485	8	18	some	some	DET
ejpam-3485	8	19	vertex	vertex	NOUN
ejpam-3485	8	20	in	in	ADP
ejpam-3485	8	21	s	s	PROPN
ejpam-3485	8	22	(	(	PUNCT
ejpam-3485	8	23	resp	resp	NOUN
ejpam-3485	8	24	.	.	PUNCT
ejpam-3485	9	1	s	s	PART
ejpam-3485	9	2	is	be	AUX
ejpam-3485	9	3	a	a	DET
ejpam-3485	9	4	dominating	dominating	NOUN
ejpam-3485	9	5	set	set	NOUN
ejpam-3485	9	6	and	and	CCONJ
ejpam-3485	9	7	the	the	DET
ejpam-3485	9	8	subgraph	subgraph	NOUN
ejpam-3485	9	9	〈	〈	PROPN
ejpam-3485	9	10	s	s	PROPN
ejpam-3485	9	11	〉	〉	NOUN
ejpam-3485	9	12	induced	induce	VERB
ejpam-3485	9	13	by	by	ADP
ejpam-3485	9	14	s	s	PROPN
ejpam-3485	9	15	is	be	AUX
ejpam-3485	9	16	connected	connect	VERB
ejpam-3485	9	17	in	in	ADP
ejpam-3485	9	18	g	g	NOUN
ejpam-3485	9	19	)	)	PUNCT
ejpam-3485	9	20	.	.	PUNCT
ejpam-3485	10	1	the	the	DET
ejpam-3485	10	2	total	total	ADJ
ejpam-3485	10	3	domination	domination	NOUN
ejpam-3485	10	4	number	number	NOUN
ejpam-3485	10	5	γt(g	γt(g	NUM
ejpam-3485	10	6	)	)	PUNCT
ejpam-3485	10	7	(	(	PUNCT
ejpam-3485	10	8	resp	resp	NOUN
ejpam-3485	10	9	.	.	PUNCT
ejpam-3485	11	1	connected	connected	ADJ
ejpam-3485	11	2	domination	domination	NOUN
ejpam-3485	11	3	number	number	NOUN
ejpam-3485	11	4	γc(g	γc(g	NUM
ejpam-3485	11	5	)	)	PUNCT
ejpam-3485	11	6	)	)	PUNCT
ejpam-3485	11	7	of	of	ADP
ejpam-3485	11	8	g	g	PROPN
ejpam-3485	11	9	is	be	AUX
ejpam-3485	11	10	the	the	DET
ejpam-3485	11	11	minimum	minimum	ADJ
ejpam-3485	11	12	cardinality	cardinality	NOUN
ejpam-3485	11	13	of	of	ADP
ejpam-3485	11	14	a	a	DET
ejpam-3485	11	15	total	total	ADJ
ejpam-3485	11	16	dominating	dominating	NOUN
ejpam-3485	11	17	set	set	NOUN
ejpam-3485	11	18	(	(	PUNCT
ejpam-3485	11	19	resp	resp	NOUN
ejpam-3485	11	20	.	.	PUNCT
ejpam-3485	12	1	connected	connect	VERB
ejpam-3485	12	2	dominating	dominating	NOUN
ejpam-3485	12	3	set	set	NOUN
ejpam-3485	12	4	)	)	PUNCT
ejpam-3485	12	5	.	.	PUNCT
ejpam-3485	13	1	if	if	SCONJ
ejpam-3485	13	2	s	s	NOUN
ejpam-3485	13	3	is	be	AUX
ejpam-3485	13	4	a	a	DET
ejpam-3485	13	5	total	total	ADJ
ejpam-3485	13	6	dominating	dominating	NOUN
ejpam-3485	13	7	set	set	NOUN
ejpam-3485	13	8	(	(	PUNCT
ejpam-3485	13	9	resp	resp	NOUN
ejpam-3485	13	10	.	.	PUNCT
ejpam-3485	14	1	connected	connect	VERB
ejpam-3485	14	2	dominating	dominating	NOUN
ejpam-3485	14	3	set	set	NOUN
ejpam-3485	14	4	)	)	PUNCT
ejpam-3485	14	5	with	with	ADP
ejpam-3485	14	6	|s|	|s|	NOUN
ejpam-3485	14	7	=	=	SYM
ejpam-3485	14	8	γt(g	γt(g	NUM
ejpam-3485	14	9	)	)	PUNCT
ejpam-3485	14	10	(	(	PUNCT
ejpam-3485	14	11	resp	resp	NOUN
ejpam-3485	14	12	.	.	PUNCT
ejpam-3485	14	13	|s|	|s|	PROPN
ejpam-3485	14	14	=	=	NOUN
ejpam-3485	14	15	γc(g	γc(g	X
ejpam-3485	14	16	)	)	PUNCT
ejpam-3485	14	17	)	)	PUNCT
ejpam-3485	14	18	,	,	PUNCT
ejpam-3485	14	19	then	then	ADV
ejpam-3485	14	20	we	we	PRON
ejpam-3485	14	21	call	call	VERB
ejpam-3485	14	22	s	s	PRON
ejpam-3485	14	23	a	a	DET
ejpam-3485	14	24	minimum	minimum	ADJ
ejpam-3485	14	25	total	total	ADJ
ejpam-3485	14	26	dominating	dominating	NOUN
ejpam-3485	14	27	set	set	NOUN
ejpam-3485	14	28	(	(	PUNCT
ejpam-3485	14	29	resp	resp	NOUN
ejpam-3485	14	30	.	.	PUNCT
ejpam-3485	15	1	minimum	minimum	ADJ
ejpam-3485	15	2	connected	connect	VERB
ejpam-3485	15	3	dominating	dominating	NOUN
ejpam-3485	15	4	set	set	NOUN
ejpam-3485	15	5	)	)	PUNCT
ejpam-3485	15	6	of	of	ADP
ejpam-3485	15	7	g	g	PROPN
ejpam-3485	15	8	or	or	CCONJ
ejpam-3485	15	9	a	a	DET
ejpam-3485	15	10	γt	γt	NOUN
ejpam-3485	15	11	-	-	ADJ
ejpam-3485	15	12	set	set	ADJ
ejpam-3485	15	13	(	(	PUNCT
ejpam-3485	15	14	resp	resp	NOUN
ejpam-3485	15	15	.	.	PUNCT
ejpam-3485	16	1	γc	γc	VERB
ejpam-3485	16	2	-	-	PUNCT
ejpam-3485	16	3	set	set	NOUN
ejpam-3485	16	4	)	)	PUNCT
ejpam-3485	16	5	in	in	ADP
ejpam-3485	16	6	g.	g.	PROPN
ejpam-3485	16	7	∗corresponding	∗corresponde	VERB
ejpam-3485	16	8	author	author	NOUN
ejpam-3485	16	9	.	.	PUNCT
ejpam-3485	17	1	doi	doi	NOUN
ejpam-3485	17	2	:	:	PUNCT
ejpam-3485	17	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3485	https://doi.org/10.29020/nybg.ejpam.v12i4.3485	PROPN
ejpam-3485	17	4	email	email	NOUN
ejpam-3485	17	5	addresses	address	NOUN
ejpam-3485	17	6	:	:	PUNCT
ejpam-3485	18	1	cris.armada@g.msuiit.edu.ph	cris.armada@g.msuiit.edu.ph	ADJ
ejpam-3485	18	2	,	,	PUNCT
ejpam-3485	18	3	invictuscris@yahoo.com	invictuscris@yahoo.com	PROPN
ejpam-3485	18	4	(	(	PUNCT
ejpam-3485	18	5	c.	c.	PROPN
ejpam-3485	18	6	armada	armada	PROPN
ejpam-3485	18	7	)	)	PUNCT
ejpam-3485	18	8	,	,	PUNCT
ejpam-3485	18	9	serge_canoy@yahoo.com	serge_canoy@yahoo.com	X
ejpam-3485	18	10	(	(	PUNCT
ejpam-3485	18	11	s.	s.	PROPN
ejpam-3485	18	12	canoy	canoy	PROPN
ejpam-3485	18	13	)	)	PUNCT
ejpam-3485	18	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3485	18	15	1779	1779	NUM
ejpam-3485	18	16	c	c	X
ejpam-3485	18	17	©	©	PROPN
ejpam-3485	18	18	2019	2019	NUM
ejpam-3485	18	19	ejpam	ejpam	NOUN
ejpam-3485	18	20	all	all	DET
ejpam-3485	18	21	rights	right	NOUN
ejpam-3485	18	22	reserved	reserve	VERB
ejpam-3485	18	23	.	.	PUNCT
ejpam-3485	19	1	c.	c.	PROPN
ejpam-3485	19	2	armada	armada	PROPN
ejpam-3485	19	3	,	,	PUNCT
ejpam-3485	19	4	s.	s.	PROPN
ejpam-3485	19	5	canoy	canoy	PROPN
ejpam-3485	19	6	jr	jr	PROPN
ejpam-3485	19	7	.	.	PROPN
ejpam-3485	19	8	,	,	PUNCT
ejpam-3485	19	9	c.	c.	PROPN
ejpam-3485	19	10	go	go	VERB
ejpam-3485	19	11	/	/	SYM
ejpam-3485	19	12	eur	eur	PROPN
ejpam-3485	19	13	.	.	PUNCT
ejpam-3485	20	1	j.	j.	PROPN
ejpam-3485	20	2	pure	pure	PROPN
ejpam-3485	20	3	appl	appl	PROPN
ejpam-3485	20	4	.	.	PROPN
ejpam-3485	20	5	math	math	PROPN
ejpam-3485	20	6	,	,	PUNCT
ejpam-3485	20	7	12	12	NUM
ejpam-3485	20	8	(	(	PUNCT
ejpam-3485	20	9	4	4	NUM
ejpam-3485	20	10	)	)	PUNCT
ejpam-3485	20	11	(	(	PUNCT
ejpam-3485	20	12	2019	2019	NUM
ejpam-3485	20	13	)	)	PUNCT
ejpam-3485	20	14	,	,	PUNCT
ejpam-3485	20	15	1779	1779	NUM
ejpam-3485	20	16	-	-	SYM
ejpam-3485	20	17	1786	1786	NUM
ejpam-3485	20	18	1780	1780	NUM
ejpam-3485	20	19	let	let	VERB
ejpam-3485	20	20	t	t	PROPN
ejpam-3485	20	21	be	be	AUX
ejpam-3485	20	22	a	a	DET
ejpam-3485	20	23	γt	γt	NOUN
ejpam-3485	20	24	-	-	NOUN
ejpam-3485	20	25	set	set	NOUN
ejpam-3485	20	26	of	of	ADP
ejpam-3485	20	27	a	a	DET
ejpam-3485	20	28	graph	graph	NOUN
ejpam-3485	20	29	g.	g.	NOUN
ejpam-3485	20	30	a	a	DET
ejpam-3485	20	31	subset	subset	NOUN
ejpam-3485	20	32	s	s	NOUN
ejpam-3485	20	33	of	of	ADP
ejpam-3485	20	34	t	t	PROPN
ejpam-3485	20	35	is	be	AUX
ejpam-3485	20	36	said	say	VERB
ejpam-3485	20	37	to	to	PART
ejpam-3485	20	38	be	be	AUX
ejpam-3485	20	39	a	a	DET
ejpam-3485	20	40	forcing	forcing	NOUN
ejpam-3485	20	41	subset	subset	NOUN
ejpam-3485	20	42	for	for	ADP
ejpam-3485	20	43	t	t	PROPN
ejpam-3485	20	44	if	if	SCONJ
ejpam-3485	20	45	t	t	PROPN
ejpam-3485	20	46	is	be	AUX
ejpam-3485	20	47	the	the	DET
ejpam-3485	20	48	unique	unique	ADJ
ejpam-3485	20	49	γt	γt	NOUN
ejpam-3485	20	50	-	-	ADJ
ejpam-3485	20	51	set	set	ADJ
ejpam-3485	20	52	containing	contain	VERB
ejpam-3485	20	53	s.	s.	PROPN
ejpam-3485	20	54	the	the	DET
ejpam-3485	20	55	forcing	force	VERB
ejpam-3485	20	56	total	total	ADJ
ejpam-3485	20	57	domination	domination	NOUN
ejpam-3485	20	58	number	number	NOUN
ejpam-3485	20	59	of	of	ADP
ejpam-3485	20	60	t	t	PROPN
ejpam-3485	20	61	is	be	AUX
ejpam-3485	20	62	given	give	VERB
ejpam-3485	20	63	by	by	ADP
ejpam-3485	20	64	fγt(t	fγt(t	PROPN
ejpam-3485	20	65	)	)	PUNCT
ejpam-3485	21	1	=	=	NOUN
ejpam-3485	21	2	min{|s|	min{|s|	NOUN
ejpam-3485	21	3	:	:	PUNCT
ejpam-3485	21	4	s	s	VERB
ejpam-3485	21	5	is	be	AUX
ejpam-3485	21	6	a	a	DET
ejpam-3485	21	7	forcing	forcing	NOUN
ejpam-3485	21	8	subset	subset	NOUN
ejpam-3485	21	9	for	for	ADP
ejpam-3485	21	10	t	t	PROPN
ejpam-3485	21	11	}	}	PUNCT
ejpam-3485	21	12	.	.	PUNCT
ejpam-3485	22	1	the	the	DET
ejpam-3485	22	2	forcing	force	VERB
ejpam-3485	22	3	total	total	ADJ
ejpam-3485	22	4	domination	domination	NOUN
ejpam-3485	22	5	number	number	NOUN
ejpam-3485	22	6	of	of	ADP
ejpam-3485	22	7	g	g	PROPN
ejpam-3485	22	8	is	be	AUX
ejpam-3485	22	9	given	give	VERB
ejpam-3485	22	10	by	by	ADP
ejpam-3485	22	11	fγt(g	fγt(g	PROPN
ejpam-3485	22	12	)	)	PUNCT
ejpam-3485	22	13	=	=	SYM
ejpam-3485	22	14	min{fγt(t	min{fγt(t	PROPN
ejpam-3485	22	15	)	)	PUNCT
ejpam-3485	22	16	:	:	PUNCT
ejpam-3485	22	17	t	t	PROPN
ejpam-3485	22	18	is	be	AUX
ejpam-3485	22	19	a	a	DET
ejpam-3485	22	20	γt	γt	NOUN
ejpam-3485	22	21	-	-	NOUN
ejpam-3485	22	22	set	set	NOUN
ejpam-3485	22	23	of	of	ADP
ejpam-3485	22	24	g	g	NOUN
ejpam-3485	22	25	}	}	PUNCT
ejpam-3485	22	26	.	.	PUNCT
ejpam-3485	23	1	let	let	VERB
ejpam-3485	23	2	c	c	PRON
ejpam-3485	23	3	be	be	AUX
ejpam-3485	23	4	a	a	DET
ejpam-3485	23	5	γc	γc	NOUN
ejpam-3485	23	6	-	-	PUNCT
ejpam-3485	23	7	set	set	NOUN
ejpam-3485	23	8	of	of	ADP
ejpam-3485	23	9	a	a	DET
ejpam-3485	23	10	graph	graph	NOUN
ejpam-3485	23	11	g.	g.	NOUN
ejpam-3485	23	12	a	a	DET
ejpam-3485	23	13	subset	subset	NOUN
ejpam-3485	23	14	d	d	NOUN
ejpam-3485	23	15	of	of	ADP
ejpam-3485	23	16	c	c	PROPN
ejpam-3485	23	17	is	be	AUX
ejpam-3485	23	18	said	say	VERB
ejpam-3485	23	19	to	to	PART
ejpam-3485	23	20	be	be	AUX
ejpam-3485	23	21	a	a	DET
ejpam-3485	23	22	forcing	forcing	NOUN
ejpam-3485	23	23	subset	subset	NOUN
ejpam-3485	23	24	for	for	ADP
ejpam-3485	23	25	c	c	PROPN
ejpam-3485	23	26	if	if	SCONJ
ejpam-3485	23	27	c	c	PROPN
ejpam-3485	23	28	is	be	AUX
ejpam-3485	23	29	the	the	DET
ejpam-3485	23	30	unique	unique	ADJ
ejpam-3485	23	31	γc	γc	NOUN
ejpam-3485	23	32	-	-	PUNCT
ejpam-3485	23	33	set	set	ADJ
ejpam-3485	23	34	containing	contain	VERB
ejpam-3485	23	35	d.	d.	NOUN
ejpam-3485	23	36	the	the	DET
ejpam-3485	23	37	forcing	force	VERB
ejpam-3485	23	38	connected	connect	VERB
ejpam-3485	23	39	domination	domination	NOUN
ejpam-3485	23	40	number	number	NOUN
ejpam-3485	23	41	of	of	ADP
ejpam-3485	23	42	c	c	PROPN
ejpam-3485	23	43	is	be	AUX
ejpam-3485	23	44	given	give	VERB
ejpam-3485	23	45	by	by	ADP
ejpam-3485	23	46	fγc(c	fγc(c	PROPN
ejpam-3485	23	47	)	)	PUNCT
ejpam-3485	23	48	=	=	X
ejpam-3485	23	49	min{|d|	min{|d|	NOUN
ejpam-3485	23	50	:	:	PUNCT
ejpam-3485	24	1	d	d	X
ejpam-3485	24	2	is	be	AUX
ejpam-3485	24	3	a	a	DET
ejpam-3485	24	4	forcing	forcing	NOUN
ejpam-3485	24	5	subset	subset	NOUN
ejpam-3485	24	6	for	for	ADP
ejpam-3485	24	7	c	c	NOUN
ejpam-3485	24	8	}	}	PUNCT
ejpam-3485	24	9	.	.	PUNCT
ejpam-3485	25	1	the	the	DET
ejpam-3485	25	2	forcing	force	VERB
ejpam-3485	25	3	connected	connect	VERB
ejpam-3485	25	4	domination	domination	NOUN
ejpam-3485	25	5	number	number	NOUN
ejpam-3485	25	6	of	of	ADP
ejpam-3485	25	7	g	g	PROPN
ejpam-3485	25	8	is	be	AUX
ejpam-3485	25	9	given	give	VERB
ejpam-3485	25	10	by	by	ADP
ejpam-3485	25	11	fγc(g	fγc(g	PROPN
ejpam-3485	25	12	)	)	PUNCT
ejpam-3485	25	13	=	=	SYM
ejpam-3485	25	14	min{fγc(c	min{fγc(c	PROPN
ejpam-3485	25	15	)	)	PUNCT
ejpam-3485	25	16	:	:	PUNCT
ejpam-3485	26	1	c	c	NOUN
ejpam-3485	26	2	is	be	AUX
ejpam-3485	26	3	a	a	DET
ejpam-3485	26	4	γc	γc	NOUN
ejpam-3485	26	5	-	-	PUNCT
ejpam-3485	26	6	set	set	NOUN
ejpam-3485	26	7	of	of	ADP
ejpam-3485	26	8	g	g	NOUN
ejpam-3485	26	9	}	}	PUNCT
ejpam-3485	26	10	.	.	PUNCT
ejpam-3485	27	1	chartrand	chartrand	PROPN
ejpam-3485	27	2	et	et	PROPN
ejpam-3485	27	3	.	.	PUNCT
ejpam-3485	28	1	al	al	PROPN
ejpam-3485	29	1	[	[	X
ejpam-3485	29	2	2	2	NUM
ejpam-3485	29	3	]	]	PUNCT
ejpam-3485	29	4	initiated	initiate	VERB
ejpam-3485	29	5	the	the	DET
ejpam-3485	29	6	investigation	investigation	NOUN
ejpam-3485	29	7	on	on	ADP
ejpam-3485	29	8	the	the	DET
ejpam-3485	29	9	relation	relation	NOUN
ejpam-3485	29	10	between	between	ADP
ejpam-3485	29	11	forcing	force	VERB
ejpam-3485	29	12	and	and	CCONJ
ejpam-3485	29	13	domination	domination	NOUN
ejpam-3485	29	14	concepts	concept	NOUN
ejpam-3485	29	15	in	in	ADP
ejpam-3485	29	16	1997	1997	NUM
ejpam-3485	29	17	and	and	CCONJ
ejpam-3485	29	18	used	use	VERB
ejpam-3485	29	19	the	the	DET
ejpam-3485	29	20	term	term	NOUN
ejpam-3485	29	21	"	"	PUNCT
ejpam-3485	29	22	forcing	force	VERB
ejpam-3485	29	23	domination	domination	NOUN
ejpam-3485	29	24	number	number	NOUN
ejpam-3485	29	25	"	"	PUNCT
ejpam-3485	29	26	.	.	PUNCT
ejpam-3485	30	1	in	in	ADP
ejpam-3485	30	2	2017	2017	NUM
ejpam-3485	30	3	,	,	PUNCT
ejpam-3485	30	4	john	john	PROPN
ejpam-3485	30	5	et	et	PROPN
ejpam-3485	30	6	.	.	PUNCT
ejpam-3485	31	1	al	al	PROPN
ejpam-3485	32	1	[	[	X
ejpam-3485	32	2	3	3	NUM
ejpam-3485	32	3	]	]	PUNCT
ejpam-3485	32	4	investigated	investigate	VERB
ejpam-3485	32	5	the	the	DET
ejpam-3485	32	6	forcing	force	VERB
ejpam-3485	32	7	connected	connected	ADJ
ejpam-3485	32	8	domination	domination	NOUN
ejpam-3485	32	9	of	of	ADP
ejpam-3485	32	10	a	a	DET
ejpam-3485	32	11	graph	graph	NOUN
ejpam-3485	32	12	.	.	PUNCT
ejpam-3485	33	1	in	in	ADP
ejpam-3485	33	2	2018	2018	NUM
ejpam-3485	33	3	,	,	PUNCT
ejpam-3485	33	4	canoy	canoy	ADJ
ejpam-3485	33	5	et	et	PROPN
ejpam-3485	33	6	.	.	PUNCT
ejpam-3485	34	1	al	al	PROPN
ejpam-3485	35	1	[	[	X
ejpam-3485	35	2	1	1	NUM
ejpam-3485	35	3	]	]	PUNCT
ejpam-3485	35	4	investigated	investigate	VERB
ejpam-3485	35	5	the	the	DET
ejpam-3485	35	6	forcing	force	VERB
ejpam-3485	35	7	domination	domination	NOUN
ejpam-3485	35	8	number	number	NOUN
ejpam-3485	35	9	of	of	ADP
ejpam-3485	35	10	graphs	graph	NOUN
ejpam-3485	35	11	under	under	ADP
ejpam-3485	35	12	some	some	DET
ejpam-3485	35	13	binary	binary	ADJ
ejpam-3485	35	14	operations	operation	NOUN
ejpam-3485	35	15	.	.	PUNCT
ejpam-3485	36	1	the	the	DET
ejpam-3485	36	2	lexicographic	lexicographic	ADJ
ejpam-3485	36	3	product	product	NOUN
ejpam-3485	36	4	(	(	PUNCT
ejpam-3485	36	5	composition	composition	NOUN
ejpam-3485	36	6	)	)	PUNCT
ejpam-3485	36	7	g[h	g[h	PROPN
ejpam-3485	36	8	]	]	PUNCT
ejpam-3485	36	9	of	of	ADP
ejpam-3485	36	10	two	two	NUM
ejpam-3485	36	11	graphs	graph	NOUN
ejpam-3485	36	12	g	g	NOUN
ejpam-3485	36	13	and	and	CCONJ
ejpam-3485	36	14	h	h	NOUN
ejpam-3485	36	15	is	be	AUX
ejpam-3485	36	16	the	the	DET
ejpam-3485	36	17	graph	graph	NOUN
ejpam-3485	36	18	with	with	ADP
ejpam-3485	36	19	v	v	NOUN
ejpam-3485	36	20	(	(	PUNCT
ejpam-3485	36	21	g[h	g[h	PROPN
ejpam-3485	36	22	]	]	PUNCT
ejpam-3485	36	23	)	)	PUNCT
ejpam-3485	36	24	=	=	SYM
ejpam-3485	36	25	v	v	X
ejpam-3485	36	26	(	(	PUNCT
ejpam-3485	36	27	g)×	g)×	NOUN
ejpam-3485	36	28	v	v	NOUN
ejpam-3485	36	29	(	(	PUNCT
ejpam-3485	36	30	h	h	NOUN
ejpam-3485	36	31	)	)	PUNCT
ejpam-3485	36	32	,	,	PUNCT
ejpam-3485	36	33	and	and	CCONJ
ejpam-3485	36	34	(	(	PUNCT
ejpam-3485	36	35	u	u	NOUN
ejpam-3485	36	36	,	,	PUNCT
ejpam-3485	36	37	u′)(v	u′)(v	NOUN
ejpam-3485	36	38	,	,	PUNCT
ejpam-3485	36	39	v′	v′	NOUN
ejpam-3485	36	40	)	)	PUNCT
ejpam-3485	36	41	∈	∈	NOUN
ejpam-3485	36	42	e(g[h	e(g[h	NOUN
ejpam-3485	36	43	]	]	PUNCT
ejpam-3485	36	44	)	)	PUNCT
ejpam-3485	36	45	if	if	SCONJ
ejpam-3485	36	46	and	and	CCONJ
ejpam-3485	36	47	only	only	ADV
ejpam-3485	36	48	if	if	SCONJ
ejpam-3485	36	49	either	either	DET
ejpam-3485	36	50	uv	uv	PROPN
ejpam-3485	36	51	∈	∈	PROPN
ejpam-3485	36	52	e(g	e(g	PROPN
ejpam-3485	36	53	)	)	PUNCT
ejpam-3485	36	54	or	or	CCONJ
ejpam-3485	36	55	u	u	X
ejpam-3485	36	56	=	=	NOUN
ejpam-3485	36	57	v	v	PROPN
ejpam-3485	36	58	and	and	CCONJ
ejpam-3485	36	59	u′v′	u′v′	PROPN
ejpam-3485	36	60	∈	∈	PROPN
ejpam-3485	36	61	e(h	e(h	PROPN
ejpam-3485	36	62	)	)	PUNCT
ejpam-3485	36	63	.	.	PUNCT
ejpam-3485	37	1	for	for	ADP
ejpam-3485	37	2	each	each	DET
ejpam-3485	37	3	∅	∅	NOUN
ejpam-3485	37	4	6=	6=	ADP
ejpam-3485	37	5	c	c	PROPN
ejpam-3485	37	6	⊆	⊆	NUM
ejpam-3485	37	7	v	v	NOUN
ejpam-3485	37	8	(	(	PUNCT
ejpam-3485	37	9	g)×	g)×	NOUN
ejpam-3485	37	10	v	v	NOUN
ejpam-3485	37	11	(	(	PUNCT
ejpam-3485	37	12	h	h	NOUN
ejpam-3485	37	13	)	)	PUNCT
ejpam-3485	37	14	,	,	PUNCT
ejpam-3485	37	15	the	the	DET
ejpam-3485	37	16	g	g	NOUN
ejpam-3485	37	17	-	-	PUNCT
ejpam-3485	37	18	projection	projection	NOUN
ejpam-3485	37	19	and	and	CCONJ
ejpam-3485	37	20	h	h	NOUN
ejpam-3485	37	21	-	-	PUNCT
ejpam-3485	37	22	projection	projection	NOUN
ejpam-3485	37	23	of	of	ADP
ejpam-3485	37	24	c	c	PROPN
ejpam-3485	37	25	are	be	AUX
ejpam-3485	37	26	,	,	PUNCT
ejpam-3485	37	27	respectively	respectively	ADV
ejpam-3485	37	28	,	,	PUNCT
ejpam-3485	37	29	the	the	DET
ejpam-3485	37	30	sets	set	NOUN
ejpam-3485	38	1	cg	cg	NOUN
ejpam-3485	38	2	=	=	SYM
ejpam-3485	38	3	{	{	PUNCT
ejpam-3485	38	4	x	x	PROPN
ejpam-3485	38	5	∈	∈	PROPN
ejpam-3485	38	6	v	v	NOUN
ejpam-3485	38	7	(	(	PUNCT
ejpam-3485	38	8	g	g	NOUN
ejpam-3485	38	9	)	)	PUNCT
ejpam-3485	38	10	:	:	PUNCT
ejpam-3485	38	11	(	(	PUNCT
ejpam-3485	38	12	x	x	X
ejpam-3485	38	13	,	,	PUNCT
ejpam-3485	38	14	a	a	PRON
ejpam-3485	38	15	)	)	PUNCT
ejpam-3485	38	16	∈	∈	PROPN
ejpam-3485	38	17	c	c	NOUN
ejpam-3485	38	18	for	for	ADP
ejpam-3485	38	19	some	some	PRON
ejpam-3485	38	20	a	a	DET
ejpam-3485	38	21	∈	∈	PROPN
ejpam-3485	38	22	v	v	NOUN
ejpam-3485	38	23	(	(	PUNCT
ejpam-3485	38	24	h	h	NOUN
ejpam-3485	38	25	)	)	PUNCT
ejpam-3485	38	26	}	}	PUNCT
ejpam-3485	38	27	and	and	CCONJ
ejpam-3485	38	28	ch	ch	NOUN
ejpam-3485	38	29	=	=	SYM
ejpam-3485	38	30	{	{	PUNCT
ejpam-3485	38	31	a	a	DET
ejpam-3485	38	32	∈	∈	PROPN
ejpam-3485	38	33	v	v	ADP
ejpam-3485	38	34	(	(	PUNCT
ejpam-3485	38	35	h	h	NOUN
ejpam-3485	38	36	)	)	PUNCT
ejpam-3485	38	37	:	:	PUNCT
ejpam-3485	38	38	(	(	PUNCT
ejpam-3485	38	39	y	y	NOUN
ejpam-3485	38	40	,	,	PUNCT
ejpam-3485	38	41	a	a	PRON
ejpam-3485	38	42	)	)	PUNCT
ejpam-3485	38	43	∈	∈	PROPN
ejpam-3485	38	44	c	c	NOUN
ejpam-3485	38	45	for	for	ADP
ejpam-3485	38	46	some	some	DET
ejpam-3485	38	47	y	y	PROPN
ejpam-3485	38	48	∈	∈	PROPN
ejpam-3485	38	49	v	v	ADP
ejpam-3485	38	50	(	(	PUNCT
ejpam-3485	38	51	g	g	NOUN
ejpam-3485	38	52	)	)	PUNCT
ejpam-3485	38	53	}	}	PUNCT
ejpam-3485	38	54	.	.	PUNCT
ejpam-3485	39	1	observe	observe	VERB
ejpam-3485	39	2	that	that	SCONJ
ejpam-3485	39	3	any	any	DET
ejpam-3485	39	4	non	non	ADJ
ejpam-3485	39	5	-	-	ADJ
ejpam-3485	39	6	empty	empty	ADJ
ejpam-3485	39	7	subset	subset	NOUN
ejpam-3485	39	8	c	c	NOUN
ejpam-3485	39	9	of	of	ADP
ejpam-3485	39	10	v	v	PROPN
ejpam-3485	39	11	(	(	PUNCT
ejpam-3485	39	12	g)×	g)×	NOUN
ejpam-3485	39	13	v	v	NOUN
ejpam-3485	39	14	(	(	PUNCT
ejpam-3485	39	15	h	h	NOUN
ejpam-3485	39	16	)	)	PUNCT
ejpam-3485	39	17	can	can	AUX
ejpam-3485	39	18	be	be	AUX
ejpam-3485	39	19	written	write	VERB
ejpam-3485	39	20	as	as	ADP
ejpam-3485	39	21	c	c	NOUN
ejpam-3485	39	22	=	=	SYM
ejpam-3485	39	23	∪x∈s({x	∪x∈s({x	NOUN
ejpam-3485	39	24	}	}	PUNCT
ejpam-3485	39	25	×	×	NOUN
ejpam-3485	39	26	tx	tx	PROPN
ejpam-3485	39	27	)	)	PUNCT
ejpam-3485	39	28	⊆	⊆	NUM
ejpam-3485	39	29	v	v	NOUN
ejpam-3485	39	30	(	(	PUNCT
ejpam-3485	39	31	g[h	g[h	PROPN
ejpam-3485	39	32	]	]	PUNCT
ejpam-3485	39	33	)	)	PUNCT
ejpam-3485	39	34	,	,	PUNCT
ejpam-3485	39	35	where	where	SCONJ
ejpam-3485	39	36	s	s	VERB
ejpam-3485	39	37	⊆	⊆	NUM
ejpam-3485	39	38	v	v	NOUN
ejpam-3485	39	39	(	(	PUNCT
ejpam-3485	39	40	g	g	NOUN
ejpam-3485	39	41	)	)	PUNCT
ejpam-3485	39	42	and	and	CCONJ
ejpam-3485	39	43	tx	tx	VERB
ejpam-3485	39	44	=	=	PUNCT
ejpam-3485	39	45	{	{	PUNCT
ejpam-3485	39	46	a	a	DET
ejpam-3485	39	47	∈	∈	PROPN
ejpam-3485	39	48	ch	ch	NOUN
ejpam-3485	39	49	:	:	PUNCT
ejpam-3485	39	50	(	(	PUNCT
ejpam-3485	39	51	x	x	X
ejpam-3485	39	52	,	,	PUNCT
ejpam-3485	39	53	a	a	PRON
ejpam-3485	39	54	)	)	PUNCT
ejpam-3485	39	55	∈	∈	PROPN
ejpam-3485	39	56	c	c	NOUN
ejpam-3485	39	57	}	}	PUNCT
ejpam-3485	39	58	for	for	ADP
ejpam-3485	39	59	all	all	DET
ejpam-3485	39	60	x	x	SYM
ejpam-3485	39	61	∈	∈	PROPN
ejpam-3485	39	62	s.	s.	PROPN
ejpam-3485	39	63	2	2	NUM
ejpam-3485	39	64	.	.	PUNCT
ejpam-3485	39	65	total	total	ADJ
ejpam-3485	39	66	domination	domination	NOUN
ejpam-3485	39	67	in	in	ADP
ejpam-3485	39	68	the	the	DET
ejpam-3485	39	69	lexicographic	lexicographic	ADJ
ejpam-3485	39	70	product	product	NOUN
ejpam-3485	39	71	of	of	ADP
ejpam-3485	39	72	graphs	graph	NOUN
ejpam-3485	39	73	we	we	PRON
ejpam-3485	39	74	shall	shall	AUX
ejpam-3485	39	75	use	use	VERB
ejpam-3485	39	76	the	the	DET
ejpam-3485	39	77	following	follow	VERB
ejpam-3485	39	78	well	well	ADV
ejpam-3485	39	79	-	-	PUNCT
ejpam-3485	39	80	known	know	VERB
ejpam-3485	39	81	result	result	NOUN
ejpam-3485	39	82	.	.	PUNCT
ejpam-3485	40	1	lemma	lemma	PROPN
ejpam-3485	40	2	2.1	2.1	NUM
ejpam-3485	40	3	.	.	PUNCT
ejpam-3485	41	1	[	[	X
ejpam-3485	41	2	1	1	X
ejpam-3485	41	3	]	]	PUNCT
ejpam-3485	41	4	let	let	VERB
ejpam-3485	41	5	g	g	PRON
ejpam-3485	41	6	be	be	AUX
ejpam-3485	41	7	a	a	DET
ejpam-3485	41	8	connected	connected	ADJ
ejpam-3485	41	9	graph	graph	NOUN
ejpam-3485	41	10	and	and	CCONJ
ejpam-3485	41	11	s	s	VERB
ejpam-3485	41	12	a	a	DET
ejpam-3485	41	13	dominating	dominating	NOUN
ejpam-3485	41	14	set	set	NOUN
ejpam-3485	41	15	of	of	ADP
ejpam-3485	41	16	g.	g.	PROPN
ejpam-3485	41	17	then	then	ADV
ejpam-3485	41	18	γt(g	γt(g	PUNCT
ejpam-3485	41	19	)	)	PUNCT
ejpam-3485	41	20	≤	≤	NUM
ejpam-3485	41	21	|s	|s	PROPN
ejpam-3485	41	22	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3485	41	23	2|s	2|s	NUM
ejpam-3485	41	24	\ng(s)|	\ng(s)|	NOUN
ejpam-3485	41	25	.	.	PUNCT
ejpam-3485	42	1	in	in	ADP
ejpam-3485	42	2	particular	particular	ADJ
ejpam-3485	42	3	,	,	PUNCT
ejpam-3485	42	4	γt(g	γt(g	PUNCT
ejpam-3485	42	5	)	)	PUNCT
ejpam-3485	42	6	≤	≤	NUM
ejpam-3485	42	7	2γ(g	2γ(g	NUM
ejpam-3485	42	8	)	)	PUNCT
ejpam-3485	42	9	.	.	PUNCT
ejpam-3485	43	1	c.	c.	PROPN
ejpam-3485	43	2	armada	armada	PROPN
ejpam-3485	43	3	,	,	PUNCT
ejpam-3485	43	4	s.	s.	PROPN
ejpam-3485	43	5	canoy	canoy	PROPN
ejpam-3485	43	6	jr	jr	PROPN
ejpam-3485	43	7	.	.	PROPN
ejpam-3485	43	8	,	,	PUNCT
ejpam-3485	43	9	c.	c.	PROPN
ejpam-3485	43	10	go	go	VERB
ejpam-3485	43	11	/	/	SYM
ejpam-3485	43	12	eur	eur	PROPN
ejpam-3485	43	13	.	.	PUNCT
ejpam-3485	44	1	j.	j.	PROPN
ejpam-3485	44	2	pure	pure	PROPN
ejpam-3485	44	3	appl	appl	PROPN
ejpam-3485	44	4	.	.	PROPN
ejpam-3485	44	5	math	math	PROPN
ejpam-3485	44	6	,	,	PUNCT
ejpam-3485	44	7	12	12	NUM
ejpam-3485	44	8	(	(	PUNCT
ejpam-3485	44	9	4	4	NUM
ejpam-3485	44	10	)	)	PUNCT
ejpam-3485	44	11	(	(	PUNCT
ejpam-3485	44	12	2019	2019	NUM
ejpam-3485	44	13	)	)	PUNCT
ejpam-3485	44	14	,	,	PUNCT
ejpam-3485	44	15	1779	1779	NUM
ejpam-3485	44	16	-	-	SYM
ejpam-3485	44	17	1786	1786	NUM
ejpam-3485	44	18	1781	1781	NUM
ejpam-3485	44	19	theorem	theorem	VERB
ejpam-3485	44	20	2.2	2.2	NUM
ejpam-3485	44	21	.	.	PUNCT
ejpam-3485	45	1	let	let	VERB
ejpam-3485	45	2	g	g	NOUN
ejpam-3485	45	3	and	and	CCONJ
ejpam-3485	45	4	h	h	NOUN
ejpam-3485	45	5	be	be	VERB
ejpam-3485	45	6	both	both	PRON
ejpam-3485	45	7	nontrivial	nontrivial	ADJ
ejpam-3485	45	8	connected	connected	ADJ
ejpam-3485	45	9	graphs	graph	NOUN
ejpam-3485	45	10	.	.	PUNCT
ejpam-3485	46	1	then	then	ADV
ejpam-3485	46	2	c	c	X
ejpam-3485	46	3	=	=	SYM
ejpam-3485	46	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	46	5	}	}	PUNCT
ejpam-3485	46	6	×	×	NOUN
ejpam-3485	46	7	tx	tx	PROPN
ejpam-3485	46	8	)	)	PUNCT
ejpam-3485	46	9	⊆	⊆	NUM
ejpam-3485	46	10	v	v	NOUN
ejpam-3485	46	11	(	(	PUNCT
ejpam-3485	46	12	g[h	g[h	PROPN
ejpam-3485	46	13	]	]	PUNCT
ejpam-3485	46	14	)	)	PUNCT
ejpam-3485	46	15	,	,	PUNCT
ejpam-3485	46	16	where	where	SCONJ
ejpam-3485	46	17	s	s	VERB
ejpam-3485	46	18	⊆	⊆	NUM
ejpam-3485	46	19	v	v	NOUN
ejpam-3485	46	20	(	(	PUNCT
ejpam-3485	46	21	g	g	NOUN
ejpam-3485	46	22	)	)	PUNCT
ejpam-3485	46	23	and	and	CCONJ
ejpam-3485	46	24	tx	tx	VERB
ejpam-3485	46	25	⊆	⊆	NUM
ejpam-3485	46	26	v	v	NOUN
ejpam-3485	46	27	(	(	PUNCT
ejpam-3485	46	28	h	h	NOUN
ejpam-3485	46	29	)	)	PUNCT
ejpam-3485	46	30	for	for	ADP
ejpam-3485	46	31	every	every	DET
ejpam-3485	46	32	x	x	SYM
ejpam-3485	46	33	∈	∈	PROPN
ejpam-3485	46	34	s	s	NOUN
ejpam-3485	46	35	,	,	PUNCT
ejpam-3485	46	36	is	be	AUX
ejpam-3485	46	37	a	a	DET
ejpam-3485	46	38	total	total	ADJ
ejpam-3485	46	39	dominating	dominating	NOUN
ejpam-3485	46	40	set	set	NOUN
ejpam-3485	46	41	of	of	ADP
ejpam-3485	46	42	g[h	g[h	PROPN
ejpam-3485	46	43	]	]	PUNCT
ejpam-3485	46	44	if	if	SCONJ
ejpam-3485	46	45	and	and	CCONJ
ejpam-3485	46	46	only	only	ADV
ejpam-3485	46	47	if	if	SCONJ
ejpam-3485	46	48	either	either	CCONJ
ejpam-3485	46	49	(	(	PUNCT
ejpam-3485	46	50	i	i	NOUN
ejpam-3485	46	51	)	)	PUNCT
ejpam-3485	46	52	s	s	VERB
ejpam-3485	46	53	is	be	AUX
ejpam-3485	46	54	a	a	DET
ejpam-3485	46	55	total	total	ADJ
ejpam-3485	46	56	dominating	dominating	NOUN
ejpam-3485	46	57	set	set	NOUN
ejpam-3485	46	58	of	of	ADP
ejpam-3485	46	59	g	g	PROPN
ejpam-3485	46	60	or	or	CCONJ
ejpam-3485	46	61	(	(	PUNCT
ejpam-3485	46	62	ii	ii	NOUN
ejpam-3485	46	63	)	)	PUNCT
ejpam-3485	47	1	s	s	AUX
ejpam-3485	47	2	is	be	AUX
ejpam-3485	47	3	a	a	DET
ejpam-3485	47	4	dominating	dominating	NOUN
ejpam-3485	47	5	set	set	NOUN
ejpam-3485	47	6	of	of	ADP
ejpam-3485	47	7	g	g	PROPN
ejpam-3485	47	8	and	and	CCONJ
ejpam-3485	47	9	tx	tx	PROPN
ejpam-3485	47	10	is	be	AUX
ejpam-3485	47	11	a	a	DET
ejpam-3485	47	12	total	total	ADJ
ejpam-3485	47	13	dominating	dominating	NOUN
ejpam-3485	47	14	set	set	NOUN
ejpam-3485	47	15	of	of	ADP
ejpam-3485	47	16	h	h	NOUN
ejpam-3485	47	17	for	for	ADP
ejpam-3485	47	18	every	every	DET
ejpam-3485	47	19	x	x	SYM
ejpam-3485	47	20	∈	∈	PROPN
ejpam-3485	47	21	s\ng(s	s\ng(s	NOUN
ejpam-3485	47	22	)	)	PUNCT
ejpam-3485	47	23	.	.	PUNCT
ejpam-3485	48	1	proof	proof	NOUN
ejpam-3485	48	2	.	.	PUNCT
ejpam-3485	49	1	suppose	suppose	VERB
ejpam-3485	49	2	that	that	SCONJ
ejpam-3485	49	3	c	c	NOUN
ejpam-3485	49	4	=	=	SYM
ejpam-3485	49	5	∪x∈s({x	∪x∈s({x	PROPN
ejpam-3485	49	6	}	}	PUNCT
ejpam-3485	49	7	×	×	PROPN
ejpam-3485	49	8	tx	tx	PROPN
ejpam-3485	49	9	)	)	PUNCT
ejpam-3485	49	10	,	,	PUNCT
ejpam-3485	49	11	where	where	SCONJ
ejpam-3485	49	12	s	s	VERB
ejpam-3485	49	13	⊆	⊆	NUM
ejpam-3485	49	14	v	v	NOUN
ejpam-3485	49	15	(	(	PUNCT
ejpam-3485	49	16	g	g	NOUN
ejpam-3485	49	17	)	)	PUNCT
ejpam-3485	49	18	and	and	CCONJ
ejpam-3485	49	19	tx	tx	VERB
ejpam-3485	49	20	⊆	⊆	NUM
ejpam-3485	49	21	v	v	NOUN
ejpam-3485	49	22	(	(	PUNCT
ejpam-3485	49	23	h	h	NOUN
ejpam-3485	49	24	)	)	PUNCT
ejpam-3485	49	25	for	for	ADP
ejpam-3485	49	26	each	each	DET
ejpam-3485	49	27	x	x	SYM
ejpam-3485	49	28	∈	∈	PROPN
ejpam-3485	49	29	s	s	NOUN
ejpam-3485	49	30	,	,	PUNCT
ejpam-3485	49	31	is	be	AUX
ejpam-3485	49	32	a	a	DET
ejpam-3485	49	33	total	total	ADJ
ejpam-3485	49	34	dominating	dominating	NOUN
ejpam-3485	49	35	set	set	NOUN
ejpam-3485	49	36	of	of	ADP
ejpam-3485	49	37	g[h	g[h	PROPN
ejpam-3485	49	38	]	]	PUNCT
ejpam-3485	49	39	.	.	PUNCT
ejpam-3485	50	1	let	let	VERB
ejpam-3485	50	2	u	u	PRON
ejpam-3485	50	3	∈	∈	PROPN
ejpam-3485	50	4	v	v	NOUN
ejpam-3485	50	5	(	(	PUNCT
ejpam-3485	50	6	g)\s	g)\s	VERB
ejpam-3485	50	7	and	and	CCONJ
ejpam-3485	50	8	pick	pick	VERB
ejpam-3485	50	9	any	any	DET
ejpam-3485	50	10	b	b	PROPN
ejpam-3485	50	11	∈	∈	PROPN
ejpam-3485	50	12	v	v	NOUN
ejpam-3485	50	13	(	(	PUNCT
ejpam-3485	50	14	h	h	NOUN
ejpam-3485	50	15	)	)	PUNCT
ejpam-3485	50	16	.	.	PUNCT
ejpam-3485	51	1	since	since	SCONJ
ejpam-3485	51	2	(	(	PUNCT
ejpam-3485	51	3	u	u	NOUN
ejpam-3485	51	4	,	,	PUNCT
ejpam-3485	51	5	b	b	NOUN
ejpam-3485	51	6	)	)	PUNCT
ejpam-3485	51	7	∈	∈	NOUN
ejpam-3485	51	8	v	v	NOUN
ejpam-3485	51	9	(	(	PUNCT
ejpam-3485	51	10	g[h	g[h	PROPN
ejpam-3485	51	11	]	]	PUNCT
ejpam-3485	51	12	)	)	PUNCT
ejpam-3485	51	13	\	\	PROPN
ejpam-3485	51	14	c	c	PROPN
ejpam-3485	51	15	and	and	CCONJ
ejpam-3485	51	16	c	c	PROPN
ejpam-3485	51	17	is	be	AUX
ejpam-3485	51	18	a	a	DET
ejpam-3485	51	19	dominating	dominating	NOUN
ejpam-3485	51	20	set	set	NOUN
ejpam-3485	51	21	of	of	ADP
ejpam-3485	51	22	g[h	g[h	PROPN
ejpam-3485	51	23	]	]	PUNCT
ejpam-3485	51	24	,	,	PUNCT
ejpam-3485	51	25	there	there	PRON
ejpam-3485	51	26	exists	exist	VERB
ejpam-3485	51	27	(	(	PUNCT
ejpam-3485	51	28	y	y	NOUN
ejpam-3485	51	29	,	,	PUNCT
ejpam-3485	51	30	c	c	NOUN
ejpam-3485	51	31	)	)	PUNCT
ejpam-3485	51	32	∈	∈	PROPN
ejpam-3485	51	33	c	c	NOUN
ejpam-3485	51	34	such	such	ADJ
ejpam-3485	51	35	that	that	PRON
ejpam-3485	51	36	(	(	PUNCT
ejpam-3485	51	37	y	y	NOUN
ejpam-3485	51	38	,	,	PUNCT
ejpam-3485	51	39	c)(u	c)(u	PROPN
ejpam-3485	51	40	,	,	PUNCT
ejpam-3485	51	41	b	b	X
ejpam-3485	51	42	)	)	PUNCT
ejpam-3485	51	43	∈	∈	NOUN
ejpam-3485	51	44	e(g[h	e(g[h	NOUN
ejpam-3485	51	45	]	]	PUNCT
ejpam-3485	51	46	)	)	PUNCT
ejpam-3485	51	47	.	.	PUNCT
ejpam-3485	52	1	this	this	PRON
ejpam-3485	52	2	implies	imply	VERB
ejpam-3485	52	3	that	that	SCONJ
ejpam-3485	52	4	y	y	PROPN
ejpam-3485	52	5	∈	∈	PROPN
ejpam-3485	52	6	s	s	PART
ejpam-3485	52	7	and	and	CCONJ
ejpam-3485	52	8	u	u	NOUN
ejpam-3485	52	9	∈	∈	PROPN
ejpam-3485	52	10	ng(y	ng(y	NOUN
ejpam-3485	52	11	)	)	PUNCT
ejpam-3485	52	12	.	.	PUNCT
ejpam-3485	53	1	this	this	PRON
ejpam-3485	53	2	shows	show	VERB
ejpam-3485	53	3	that	that	SCONJ
ejpam-3485	53	4	s	s	VERB
ejpam-3485	53	5	is	be	AUX
ejpam-3485	53	6	a	a	DET
ejpam-3485	53	7	dominating	dominating	NOUN
ejpam-3485	53	8	set	set	NOUN
ejpam-3485	53	9	of	of	ADP
ejpam-3485	53	10	g.	g.	PROPN
ejpam-3485	53	11	if	if	SCONJ
ejpam-3485	53	12	s	s	VERB
ejpam-3485	53	13	is	be	AUX
ejpam-3485	53	14	a	a	DET
ejpam-3485	53	15	total	total	ADJ
ejpam-3485	53	16	dominating	dominating	NOUN
ejpam-3485	53	17	set	set	NOUN
ejpam-3485	53	18	of	of	ADP
ejpam-3485	53	19	g	g	PROPN
ejpam-3485	53	20	,	,	PUNCT
ejpam-3485	53	21	then	then	ADV
ejpam-3485	53	22	we	we	PRON
ejpam-3485	53	23	are	be	AUX
ejpam-3485	53	24	done	do	VERB
ejpam-3485	53	25	.	.	PUNCT
ejpam-3485	54	1	so	so	ADV
ejpam-3485	54	2	suppose	suppose	VERB
ejpam-3485	54	3	s	s	NOUN
ejpam-3485	54	4	is	be	AUX
ejpam-3485	54	5	not	not	PART
ejpam-3485	54	6	a	a	DET
ejpam-3485	54	7	total	total	ADJ
ejpam-3485	54	8	dominating	dominating	NOUN
ejpam-3485	54	9	set	set	NOUN
ejpam-3485	54	10	of	of	ADP
ejpam-3485	54	11	g.	g.	PROPN
ejpam-3485	54	12	then	then	ADV
ejpam-3485	54	13	s	s	VERB
ejpam-3485	54	14	\	\	PROPN
ejpam-3485	54	15	ng(s	ng(s	NUM
ejpam-3485	54	16	)	)	PUNCT
ejpam-3485	54	17	6=	6=	ADP
ejpam-3485	54	18	∅.	∅.	AUX
ejpam-3485	54	19	let	let	VERB
ejpam-3485	54	20	x	x	PUNCT
ejpam-3485	54	21	∈	∈	PROPN
ejpam-3485	54	22	s	s	PART
ejpam-3485	54	23	\	\	NOUN
ejpam-3485	54	24	ng(s	ng(s	NUM
ejpam-3485	54	25	)	)	PUNCT
ejpam-3485	54	26	.	.	PUNCT
ejpam-3485	55	1	suppose	suppose	VERB
ejpam-3485	55	2	there	there	PRON
ejpam-3485	55	3	exists	exist	VERB
ejpam-3485	55	4	y	y	PROPN
ejpam-3485	55	5	∈	∈	PROPN
ejpam-3485	55	6	v	v	PROPN
ejpam-3485	55	7	(	(	PUNCT
ejpam-3485	55	8	h	h	NOUN
ejpam-3485	55	9	)	)	PUNCT
ejpam-3485	55	10	\	\	PUNCT
ejpam-3485	56	1	nh(tx	nh(tx	NOUN
ejpam-3485	56	2	)	)	PUNCT
ejpam-3485	56	3	.	.	PUNCT
ejpam-3485	57	1	then	then	ADV
ejpam-3485	57	2	yz	yz	PROPN
ejpam-3485	57	3	/∈	/∈	PUNCT
ejpam-3485	57	4	e(h	e(h	PROPN
ejpam-3485	57	5	)	)	PUNCT
ejpam-3485	57	6	for	for	ADP
ejpam-3485	57	7	all	all	DET
ejpam-3485	57	8	z	z	NOUN
ejpam-3485	57	9	∈	∈	PROPN
ejpam-3485	57	10	tx	tx	PROPN
ejpam-3485	57	11	.	.	PUNCT
ejpam-3485	58	1	this	this	PRON
ejpam-3485	58	2	implies	imply	VERB
ejpam-3485	58	3	that	that	SCONJ
ejpam-3485	58	4	(	(	PUNCT
ejpam-3485	58	5	x	x	X
ejpam-3485	58	6	,	,	PUNCT
ejpam-3485	58	7	y	y	PROPN
ejpam-3485	58	8	)	)	PUNCT
ejpam-3485	58	9	/∈	/∈	PUNCT
ejpam-3485	59	1	ng[h](c	ng[h](c	ADJ
ejpam-3485	59	2	)	)	PUNCT
ejpam-3485	60	1	,	,	PUNCT
ejpam-3485	60	2	contrary	contrary	ADV
ejpam-3485	60	3	to	to	ADP
ejpam-3485	60	4	our	our	PRON
ejpam-3485	60	5	assumption	assumption	NOUN
ejpam-3485	60	6	that	that	SCONJ
ejpam-3485	60	7	c	c	PROPN
ejpam-3485	60	8	is	be	AUX
ejpam-3485	60	9	a	a	DET
ejpam-3485	60	10	total	total	ADJ
ejpam-3485	60	11	dominating	dominating	NOUN
ejpam-3485	60	12	set	set	NOUN
ejpam-3485	60	13	of	of	ADP
ejpam-3485	60	14	g[h	g[h	PROPN
ejpam-3485	60	15	]	]	PUNCT
ejpam-3485	60	16	.	.	PUNCT
ejpam-3485	61	1	therefore	therefore	ADV
ejpam-3485	61	2	,	,	PUNCT
ejpam-3485	61	3	nh(tx	nh(tx	NOUN
ejpam-3485	61	4	)	)	PUNCT
ejpam-3485	62	1	=	=	SYM
ejpam-3485	62	2	v	v	X
ejpam-3485	62	3	(	(	PUNCT
ejpam-3485	62	4	h	h	NOUN
ejpam-3485	62	5	)	)	PUNCT
ejpam-3485	62	6	,	,	PUNCT
ejpam-3485	62	7	i.e.	i.e.	X
ejpam-3485	62	8	,	,	PUNCT
ejpam-3485	62	9	tx	tx	PROPN
ejpam-3485	62	10	is	be	AUX
ejpam-3485	62	11	a	a	DET
ejpam-3485	62	12	total	total	ADJ
ejpam-3485	62	13	dominating	dominating	NOUN
ejpam-3485	62	14	set	set	NOUN
ejpam-3485	62	15	of	of	ADP
ejpam-3485	62	16	h.	h.	PROPN
ejpam-3485	62	17	for	for	ADP
ejpam-3485	62	18	the	the	DET
ejpam-3485	62	19	converse	converse	NOUN
ejpam-3485	62	20	,	,	PUNCT
ejpam-3485	62	21	let	let	VERB
ejpam-3485	62	22	c	c	NOUN
ejpam-3485	62	23	=	=	SYM
ejpam-3485	62	24	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	62	25	}	}	PUNCT
ejpam-3485	62	26	×	×	NOUN
ejpam-3485	62	27	tx	tx	PROPN
ejpam-3485	62	28	)	)	PUNCT
ejpam-3485	62	29	and	and	CCONJ
ejpam-3485	62	30	(	(	PUNCT
ejpam-3485	62	31	u	u	NOUN
ejpam-3485	62	32	,	,	PUNCT
ejpam-3485	62	33	t	t	PROPN
ejpam-3485	62	34	)	)	PUNCT
ejpam-3485	62	35	∈	∈	PROPN
ejpam-3485	62	36	v	v	NOUN
ejpam-3485	62	37	(	(	PUNCT
ejpam-3485	62	38	g[h	g[h	PROPN
ejpam-3485	62	39	]	]	PUNCT
ejpam-3485	62	40	)	)	PUNCT
ejpam-3485	62	41	.	.	PUNCT
ejpam-3485	63	1	assume	assume	VERB
ejpam-3485	63	2	first	first	ADV
ejpam-3485	63	3	that	that	SCONJ
ejpam-3485	63	4	s	s	VERB
ejpam-3485	63	5	is	be	AUX
ejpam-3485	63	6	a	a	DET
ejpam-3485	63	7	total	total	ADJ
ejpam-3485	63	8	dominating	dominating	NOUN
ejpam-3485	63	9	set	set	NOUN
ejpam-3485	63	10	of	of	ADP
ejpam-3485	63	11	g.	g.	PROPN
ejpam-3485	63	12	then	then	ADV
ejpam-3485	63	13	there	there	PRON
ejpam-3485	63	14	exists	exist	VERB
ejpam-3485	63	15	x	x	X
ejpam-3485	63	16	∈	∈	PROPN
ejpam-3485	63	17	s	s	PART
ejpam-3485	63	18	\	\	X
ejpam-3485	63	19	{	{	PUNCT
ejpam-3485	63	20	u	u	NOUN
ejpam-3485	63	21	}	}	PUNCT
ejpam-3485	63	22	such	such	ADJ
ejpam-3485	63	23	that	that	SCONJ
ejpam-3485	63	24	u	u	PROPN
ejpam-3485	63	25	∈	∈	PROPN
ejpam-3485	63	26	ng(x	ng(x	NUM
ejpam-3485	63	27	)	)	PUNCT
ejpam-3485	63	28	.	.	PUNCT
ejpam-3485	64	1	choose	choose	VERB
ejpam-3485	64	2	d	d	PROPN
ejpam-3485	64	3	∈	∈	PROPN
ejpam-3485	64	4	tx	tx	PROPN
ejpam-3485	64	5	.	.	PUNCT
ejpam-3485	65	1	then	then	ADV
ejpam-3485	65	2	(	(	PUNCT
ejpam-3485	65	3	x	x	X
ejpam-3485	65	4	,	,	PUNCT
ejpam-3485	65	5	d	d	NOUN
ejpam-3485	65	6	)	)	PUNCT
ejpam-3485	65	7	∈	∈	PROPN
ejpam-3485	65	8	c	c	PROPN
ejpam-3485	65	9	and	and	CCONJ
ejpam-3485	65	10	(	(	PUNCT
ejpam-3485	65	11	u	u	NOUN
ejpam-3485	65	12	,	,	PUNCT
ejpam-3485	65	13	t)(x	t)(x	PROPN
ejpam-3485	65	14	,	,	PUNCT
ejpam-3485	65	15	d	d	X
ejpam-3485	65	16	)	)	PUNCT
ejpam-3485	65	17	∈	∈	NOUN
ejpam-3485	65	18	e(g[h	e(g[h	NOUN
ejpam-3485	65	19	]	]	PUNCT
ejpam-3485	65	20	)	)	PUNCT
ejpam-3485	65	21	.	.	PUNCT
ejpam-3485	66	1	hence	hence	ADV
ejpam-3485	66	2	,	,	PUNCT
ejpam-3485	66	3	(	(	PUNCT
ejpam-3485	66	4	u	u	NOUN
ejpam-3485	66	5	,	,	PUNCT
ejpam-3485	66	6	t	t	PROPN
ejpam-3485	66	7	)	)	PUNCT
ejpam-3485	66	8	∈	∈	PROPN
ejpam-3485	66	9	ng[h](c	ng[h](c	PROPN
ejpam-3485	66	10	)	)	PUNCT
ejpam-3485	66	11	.	.	PUNCT
ejpam-3485	66	12	suppose	suppose	VERB
ejpam-3485	66	13	now	now	ADV
ejpam-3485	66	14	that	that	SCONJ
ejpam-3485	66	15	(	(	PUNCT
ejpam-3485	66	16	ii	ii	NOUN
ejpam-3485	66	17	)	)	PUNCT
ejpam-3485	66	18	holds	hold	VERB
ejpam-3485	66	19	.	.	PUNCT
ejpam-3485	67	1	if	if	SCONJ
ejpam-3485	67	2	u	u	PROPN
ejpam-3485	67	3	∈	∈	PROPN
ejpam-3485	67	4	v	v	ADP
ejpam-3485	67	5	(	(	PUNCT
ejpam-3485	67	6	g	g	NOUN
ejpam-3485	67	7	)	)	PUNCT
ejpam-3485	67	8	\	\	PROPN
ejpam-3485	67	9	s	s	X
ejpam-3485	67	10	,	,	PUNCT
ejpam-3485	67	11	then	then	ADV
ejpam-3485	67	12	because	because	SCONJ
ejpam-3485	67	13	s	s	NOUN
ejpam-3485	67	14	is	be	AUX
ejpam-3485	67	15	a	a	DET
ejpam-3485	67	16	dominating	dominating	NOUN
ejpam-3485	67	17	set	set	NOUN
ejpam-3485	67	18	of	of	ADP
ejpam-3485	67	19	g	g	NOUN
ejpam-3485	67	20	,	,	PUNCT
ejpam-3485	67	21	there	there	PRON
ejpam-3485	67	22	exists	exist	VERB
ejpam-3485	67	23	y	y	PROPN
ejpam-3485	67	24	∈	∈	PROPN
ejpam-3485	67	25	s	s	VERB
ejpam-3485	67	26	such	such	ADJ
ejpam-3485	67	27	that	that	SCONJ
ejpam-3485	67	28	u	u	PROPN
ejpam-3485	67	29	∈	∈	PROPN
ejpam-3485	67	30	ng(y	ng(y	NOUN
ejpam-3485	67	31	)	)	PUNCT
ejpam-3485	67	32	.	.	PUNCT
ejpam-3485	68	1	pick	pick	VERB
ejpam-3485	68	2	a	a	DET
ejpam-3485	68	3	∈	∈	PROPN
ejpam-3485	68	4	ty	ty	PRON
ejpam-3485	68	5	.	.	PUNCT
ejpam-3485	69	1	then	then	ADV
ejpam-3485	69	2	(	(	PUNCT
ejpam-3485	69	3	y	y	NOUN
ejpam-3485	69	4	,	,	PUNCT
ejpam-3485	69	5	a	a	PRON
ejpam-3485	69	6	)	)	PUNCT
ejpam-3485	69	7	∈	∈	PROPN
ejpam-3485	69	8	c	c	NOUN
ejpam-3485	69	9	and	and	CCONJ
ejpam-3485	69	10	(	(	PUNCT
ejpam-3485	69	11	u	u	NOUN
ejpam-3485	69	12	,	,	PUNCT
ejpam-3485	69	13	t)(y	t)(y	PROPN
ejpam-3485	69	14	,	,	PUNCT
ejpam-3485	69	15	a	a	DET
ejpam-3485	69	16	)	)	PUNCT
ejpam-3485	69	17	∈	∈	NOUN
ejpam-3485	69	18	e(g[h	e(g[h	NOUN
ejpam-3485	69	19	]	]	PUNCT
ejpam-3485	69	20	)	)	PUNCT
ejpam-3485	69	21	.	.	PUNCT
ejpam-3485	69	22	suppose	suppose	VERB
ejpam-3485	69	23	that	that	SCONJ
ejpam-3485	69	24	u	u	PROPN
ejpam-3485	69	25	∈	∈	PROPN
ejpam-3485	69	26	s.	s.	PROPN
ejpam-3485	69	27	if	if	SCONJ
ejpam-3485	69	28	u	u	PROPN
ejpam-3485	69	29	∈	∈	PROPN
ejpam-3485	69	30	ng(z	ng(z	NUM
ejpam-3485	69	31	)	)	PUNCT
ejpam-3485	69	32	for	for	ADP
ejpam-3485	69	33	some	some	DET
ejpam-3485	69	34	z	z	NOUN
ejpam-3485	69	35	∈	∈	PROPN
ejpam-3485	69	36	s	s	PART
ejpam-3485	69	37	\	\	X
ejpam-3485	69	38	{	{	PUNCT
ejpam-3485	69	39	u	u	NOUN
ejpam-3485	69	40	}	}	PUNCT
ejpam-3485	69	41	,	,	PUNCT
ejpam-3485	69	42	then	then	ADV
ejpam-3485	69	43	there	there	PRON
ejpam-3485	69	44	exists	exist	VERB
ejpam-3485	69	45	(	(	PUNCT
ejpam-3485	69	46	z	z	NOUN
ejpam-3485	69	47	,	,	PUNCT
ejpam-3485	69	48	b	b	NOUN
ejpam-3485	69	49	)	)	PUNCT
ejpam-3485	69	50	∈	∈	PROPN
ejpam-3485	69	51	c	c	NOUN
ejpam-3485	69	52	such	such	ADJ
ejpam-3485	69	53	that	that	PRON
ejpam-3485	69	54	(	(	PUNCT
ejpam-3485	69	55	u	u	NOUN
ejpam-3485	69	56	,	,	PUNCT
ejpam-3485	69	57	t)(z	t)(z	ADP
ejpam-3485	69	58	,	,	PUNCT
ejpam-3485	69	59	b	b	X
ejpam-3485	69	60	)	)	PUNCT
ejpam-3485	69	61	∈	∈	NOUN
ejpam-3485	69	62	e(g[h	e(g[h	NOUN
ejpam-3485	69	63	]	]	PUNCT
ejpam-3485	69	64	)	)	PUNCT
ejpam-3485	69	65	.	.	PUNCT
ejpam-3485	70	1	if	if	SCONJ
ejpam-3485	70	2	u	u	PROPN
ejpam-3485	70	3	/∈	/∈	PROPN
ejpam-3485	70	4	ng(z	ng(z	NUM
ejpam-3485	70	5	)	)	PUNCT
ejpam-3485	70	6	for	for	ADP
ejpam-3485	70	7	all	all	DET
ejpam-3485	70	8	z	z	NOUN
ejpam-3485	70	9	∈	∈	PROPN
ejpam-3485	70	10	s	s	PART
ejpam-3485	70	11	\	\	X
ejpam-3485	70	12	{	{	PUNCT
ejpam-3485	70	13	u	u	NOUN
ejpam-3485	70	14	}	}	PUNCT
ejpam-3485	70	15	,	,	PUNCT
ejpam-3485	70	16	then	then	ADV
ejpam-3485	70	17	by	by	ADP
ejpam-3485	70	18	assumption	assumption	NOUN
ejpam-3485	70	19	,	,	PUNCT
ejpam-3485	70	20	tu	tu	PROPN
ejpam-3485	70	21	is	be	AUX
ejpam-3485	70	22	a	a	DET
ejpam-3485	70	23	total	total	ADJ
ejpam-3485	70	24	dominating	dominating	NOUN
ejpam-3485	70	25	set	set	NOUN
ejpam-3485	70	26	of	of	ADP
ejpam-3485	70	27	h.	h.	PROPN
ejpam-3485	70	28	since	since	SCONJ
ejpam-3485	70	29	(	(	PUNCT
ejpam-3485	70	30	u	u	NOUN
ejpam-3485	70	31	,	,	PUNCT
ejpam-3485	70	32	t	t	PROPN
ejpam-3485	70	33	)	)	PUNCT
ejpam-3485	70	34	/∈	/∈	PUNCT
ejpam-3485	71	1	c	c	X
ejpam-3485	71	2	,	,	PUNCT
ejpam-3485	71	3	t	t	PROPN
ejpam-3485	71	4	/∈	/∈	PUNCT
ejpam-3485	72	1	tu	tu	PROPN
ejpam-3485	72	2	.	.	PUNCT
ejpam-3485	73	1	this	this	PRON
ejpam-3485	73	2	implies	imply	VERB
ejpam-3485	73	3	that	that	SCONJ
ejpam-3485	73	4	there	there	PRON
ejpam-3485	73	5	exists	exist	VERB
ejpam-3485	73	6	s	s	PROPN
ejpam-3485	73	7	∈	∈	PROPN
ejpam-3485	73	8	tu	tu	PROPN
ejpam-3485	73	9	such	such	ADJ
ejpam-3485	73	10	that	that	PRON
ejpam-3485	73	11	ts	ts	ADP
ejpam-3485	73	12	∈	∈	PROPN
ejpam-3485	73	13	e(h	e(h	PROPN
ejpam-3485	73	14	)	)	PUNCT
ejpam-3485	73	15	.	.	PUNCT
ejpam-3485	74	1	it	it	PRON
ejpam-3485	74	2	follows	follow	VERB
ejpam-3485	74	3	that	that	SCONJ
ejpam-3485	74	4	(	(	PUNCT
ejpam-3485	74	5	u	u	NOUN
ejpam-3485	74	6	,	,	PUNCT
ejpam-3485	74	7	s	s	PART
ejpam-3485	74	8	)	)	PUNCT
ejpam-3485	74	9	∈	∈	PROPN
ejpam-3485	74	10	c	c	PROPN
ejpam-3485	74	11	and	and	CCONJ
ejpam-3485	74	12	(	(	PUNCT
ejpam-3485	74	13	u	u	NOUN
ejpam-3485	74	14	,	,	PUNCT
ejpam-3485	74	15	t)(u	t)(u	ADJ
ejpam-3485	74	16	,	,	PUNCT
ejpam-3485	74	17	s	s	NOUN
ejpam-3485	74	18	)	)	PUNCT
ejpam-3485	74	19	∈	∈	NOUN
ejpam-3485	74	20	e(g[h	e(g[h	NOUN
ejpam-3485	74	21	]	]	PUNCT
ejpam-3485	74	22	)	)	PUNCT
ejpam-3485	74	23	.	.	PUNCT
ejpam-3485	75	1	thus	thus	ADV
ejpam-3485	75	2	,	,	PUNCT
ejpam-3485	75	3	(	(	PUNCT
ejpam-3485	75	4	u	u	NOUN
ejpam-3485	75	5	,	,	PUNCT
ejpam-3485	75	6	t	t	PROPN
ejpam-3485	75	7	)	)	PUNCT
ejpam-3485	75	8	∈	∈	PROPN
ejpam-3485	75	9	ng[h](c	ng[h](c	PROPN
ejpam-3485	75	10	)	)	PUNCT
ejpam-3485	75	11	.	.	PUNCT
ejpam-3485	76	1	in	in	ADP
ejpam-3485	76	2	both	both	DET
ejpam-3485	76	3	cases	case	NOUN
ejpam-3485	76	4	,	,	PUNCT
ejpam-3485	76	5	we	we	PRON
ejpam-3485	76	6	have	have	AUX
ejpam-3485	76	7	shown	show	VERB
ejpam-3485	76	8	that	that	SCONJ
ejpam-3485	76	9	(	(	PUNCT
ejpam-3485	76	10	u	u	NOUN
ejpam-3485	76	11	,	,	PUNCT
ejpam-3485	76	12	t	t	PROPN
ejpam-3485	76	13	)	)	PUNCT
ejpam-3485	76	14	∈	∈	PROPN
ejpam-3485	76	15	ng[h](c	ng[h](c	PROPN
ejpam-3485	76	16	)	)	PUNCT
ejpam-3485	76	17	.	.	PUNCT
ejpam-3485	77	1	therefore	therefore	ADV
ejpam-3485	77	2	,	,	PUNCT
ejpam-3485	77	3	ng[h](c	ng[h](c	NUM
ejpam-3485	77	4	)	)	PUNCT
ejpam-3485	77	5	=	=	SYM
ejpam-3485	77	6	v	v	X
ejpam-3485	77	7	(	(	PUNCT
ejpam-3485	77	8	g[h	g[h	PROPN
ejpam-3485	77	9	]	]	PUNCT
ejpam-3485	77	10	)	)	PUNCT
ejpam-3485	77	11	,	,	PUNCT
ejpam-3485	77	12	i.e.	i.e.	X
ejpam-3485	77	13	,	,	PUNCT
ejpam-3485	77	14	c	c	PROPN
ejpam-3485	77	15	is	be	AUX
ejpam-3485	77	16	a	a	DET
ejpam-3485	77	17	total	total	ADJ
ejpam-3485	77	18	dominating	dominating	NOUN
ejpam-3485	77	19	set	set	NOUN
ejpam-3485	77	20	of	of	ADP
ejpam-3485	77	21	g[h	g[h	PROPN
ejpam-3485	77	22	]	]	PUNCT
ejpam-3485	77	23	.	.	PUNCT
ejpam-3485	78	1	�	�	PROPN
ejpam-3485	78	2	corollary	corollary	ADJ
ejpam-3485	78	3	2.3	2.3	NUM
ejpam-3485	78	4	.	.	PUNCT
ejpam-3485	79	1	let	let	VERB
ejpam-3485	79	2	g	g	NOUN
ejpam-3485	79	3	and	and	CCONJ
ejpam-3485	79	4	h	h	NOUN
ejpam-3485	79	5	be	be	AUX
ejpam-3485	79	6	nontrivial	nontrivial	ADJ
ejpam-3485	79	7	connected	connect	VERB
ejpam-3485	79	8	graphs	graph	NOUN
ejpam-3485	79	9	with	with	ADP
ejpam-3485	79	10	γt(h	γt(h	NUM
ejpam-3485	79	11	)	)	PUNCT
ejpam-3485	79	12	=	=	SYM
ejpam-3485	80	1	2	2	X
ejpam-3485	80	2	.	.	PUNCT
ejpam-3485	80	3	then	then	ADV
ejpam-3485	80	4	c	c	X
ejpam-3485	80	5	=	=	SYM
ejpam-3485	80	6	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	80	7	}	}	PUNCT
ejpam-3485	80	8	×	×	NOUN
ejpam-3485	80	9	tx	tx	PROPN
ejpam-3485	80	10	)	)	PUNCT
ejpam-3485	80	11	⊆	⊆	NUM
ejpam-3485	80	12	v	v	NOUN
ejpam-3485	80	13	(	(	PUNCT
ejpam-3485	80	14	g[h	g[h	PROPN
ejpam-3485	80	15	]	]	PUNCT
ejpam-3485	80	16	)	)	PUNCT
ejpam-3485	80	17	,	,	PUNCT
ejpam-3485	80	18	where	where	SCONJ
ejpam-3485	80	19	s	s	VERB
ejpam-3485	80	20	⊆	⊆	NUM
ejpam-3485	80	21	v	v	NOUN
ejpam-3485	80	22	(	(	PUNCT
ejpam-3485	80	23	g	g	NOUN
ejpam-3485	80	24	)	)	PUNCT
ejpam-3485	80	25	and	and	CCONJ
ejpam-3485	80	26	tx	tx	VERB
ejpam-3485	80	27	⊆	⊆	NUM
ejpam-3485	80	28	v	v	NOUN
ejpam-3485	80	29	(	(	PUNCT
ejpam-3485	80	30	h	h	NOUN
ejpam-3485	80	31	)	)	PUNCT
ejpam-3485	80	32	∀x	∀x	VERB
ejpam-3485	80	33	∈	∈	PROPN
ejpam-3485	80	34	s	s	NOUN
ejpam-3485	80	35	,	,	PUNCT
ejpam-3485	80	36	is	be	AUX
ejpam-3485	80	37	a	a	DET
ejpam-3485	80	38	γt	γt	NOUN
ejpam-3485	80	39	-	-	NOUN
ejpam-3485	80	40	set	set	NOUN
ejpam-3485	80	41	of	of	ADP
ejpam-3485	80	42	g[h	g[h	NOUN
ejpam-3485	80	43	]	]	PUNCT
ejpam-3485	80	44	if	if	SCONJ
ejpam-3485	80	45	and	and	CCONJ
ejpam-3485	80	46	only	only	ADV
ejpam-3485	80	47	if	if	SCONJ
ejpam-3485	80	48	either	either	CCONJ
ejpam-3485	80	49	(	(	PUNCT
ejpam-3485	80	50	i	i	NOUN
ejpam-3485	80	51	)	)	PUNCT
ejpam-3485	80	52	s	s	VERB
ejpam-3485	80	53	is	be	AUX
ejpam-3485	80	54	a	a	DET
ejpam-3485	80	55	γt	γt	NOUN
ejpam-3485	80	56	-	-	NOUN
ejpam-3485	80	57	set	set	NOUN
ejpam-3485	80	58	of	of	ADP
ejpam-3485	80	59	g	g	NOUN
ejpam-3485	80	60	and	and	CCONJ
ejpam-3485	80	61	|tx|	|tx|	NUM
ejpam-3485	80	62	=	=	SYM
ejpam-3485	80	63	1	1	NUM
ejpam-3485	80	64	for	for	ADP
ejpam-3485	81	1	all	all	DET
ejpam-3485	81	2	x	x	SYM
ejpam-3485	81	3	∈	∈	PROPN
ejpam-3485	81	4	s	s	X
ejpam-3485	81	5	;	;	PUNCT
ejpam-3485	81	6	or	or	CCONJ
ejpam-3485	81	7	(	(	PUNCT
ejpam-3485	81	8	ii	ii	NOUN
ejpam-3485	81	9	)	)	PUNCT
ejpam-3485	81	10	s	s	VERB
ejpam-3485	81	11	is	be	AUX
ejpam-3485	81	12	a	a	DET
ejpam-3485	81	13	dominating	dominating	NOUN
ejpam-3485	81	14	set	set	NOUN
ejpam-3485	81	15	of	of	ADP
ejpam-3485	81	16	g	g	PROPN
ejpam-3485	81	17	such	such	ADJ
ejpam-3485	81	18	that	that	DET
ejpam-3485	81	19	|s	|s	PROPN
ejpam-3485	82	1	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3485	83	1	2|s\ng(s)|	2|s\ng(s)|	NUM
ejpam-3485	83	2	=	=	PUNCT
ejpam-3485	83	3	γt(g	γt(g	NUM
ejpam-3485	83	4	)	)	PUNCT
ejpam-3485	83	5	,	,	PUNCT
ejpam-3485	83	6	|tx|	|tx|	X
ejpam-3485	83	7	=	=	SYM
ejpam-3485	83	8	1	1	NUM
ejpam-3485	83	9	for	for	ADP
ejpam-3485	83	10	all	all	DET
ejpam-3485	83	11	x	x	SYM
ejpam-3485	83	12	∈	∈	NOUN
ejpam-3485	83	13	s	s	NOUN
ejpam-3485	83	14	∩ng(s	∩ng(s	NOUN
ejpam-3485	83	15	)	)	PUNCT
ejpam-3485	83	16	,	,	PUNCT
ejpam-3485	83	17	and	and	CCONJ
ejpam-3485	83	18	tx	tx	PROPN
ejpam-3485	83	19	is	be	AUX
ejpam-3485	83	20	a	a	DET
ejpam-3485	83	21	γt	γt	NOUN
ejpam-3485	83	22	-	-	NOUN
ejpam-3485	83	23	set	set	NOUN
ejpam-3485	83	24	of	of	ADP
ejpam-3485	83	25	h	h	NOUN
ejpam-3485	83	26	(	(	PUNCT
ejpam-3485	83	27	hence	hence	ADV
ejpam-3485	83	28	|tx|	|tx|	NOUN
ejpam-3485	83	29	=	=	SYM
ejpam-3485	83	30	2	2	NUM
ejpam-3485	83	31	)	)	PUNCT
ejpam-3485	83	32	for	for	ADP
ejpam-3485	83	33	every	every	DET
ejpam-3485	83	34	x	x	SYM
ejpam-3485	83	35	∈	∈	PROPN
ejpam-3485	83	36	s\ng(s	s\ng(s	NOUN
ejpam-3485	83	37	)	)	PUNCT
ejpam-3485	83	38	.	.	PUNCT
ejpam-3485	84	1	proof	proof	NOUN
ejpam-3485	84	2	.	.	PUNCT
ejpam-3485	85	1	suppose	suppose	VERB
ejpam-3485	85	2	c	c	NOUN
ejpam-3485	85	3	=	=	SYM
ejpam-3485	85	4	∪x∈s({x	∪x∈s({x	PROPN
ejpam-3485	85	5	}	}	PUNCT
ejpam-3485	85	6	×	×	NOUN
ejpam-3485	85	7	tx	tx	PROPN
ejpam-3485	85	8	)	)	PUNCT
ejpam-3485	85	9	is	be	AUX
ejpam-3485	85	10	a	a	DET
ejpam-3485	85	11	γt	γt	NOUN
ejpam-3485	85	12	-	-	NOUN
ejpam-3485	85	13	set	set	NOUN
ejpam-3485	85	14	of	of	ADP
ejpam-3485	85	15	g[h	g[h	NOUN
ejpam-3485	85	16	]	]	PUNCT
ejpam-3485	85	17	.	.	PUNCT
ejpam-3485	86	1	by	by	ADP
ejpam-3485	86	2	theorem	theorem	NOUN
ejpam-3485	86	3	2.2	2.2	NUM
ejpam-3485	86	4	,	,	PUNCT
ejpam-3485	86	5	s	s	PART
ejpam-3485	86	6	is	be	AUX
ejpam-3485	86	7	a	a	DET
ejpam-3485	86	8	total	total	ADJ
ejpam-3485	86	9	dominating	dominating	NOUN
ejpam-3485	86	10	set	set	NOUN
ejpam-3485	86	11	of	of	ADP
ejpam-3485	86	12	g	g	PROPN
ejpam-3485	86	13	or	or	CCONJ
ejpam-3485	86	14	s	s	NOUN
ejpam-3485	86	15	is	be	AUX
ejpam-3485	86	16	a	a	DET
ejpam-3485	86	17	dominating	dominating	NOUN
ejpam-3485	86	18	set	set	NOUN
ejpam-3485	86	19	of	of	ADP
ejpam-3485	86	20	g	g	PROPN
ejpam-3485	86	21	and	and	CCONJ
ejpam-3485	86	22	tx	tx	PROPN
ejpam-3485	86	23	is	be	AUX
ejpam-3485	86	24	a	a	DET
ejpam-3485	86	25	total	total	ADJ
ejpam-3485	86	26	dominating	dominating	NOUN
ejpam-3485	86	27	set	set	NOUN
ejpam-3485	86	28	of	of	ADP
ejpam-3485	86	29	h	h	NOUN
ejpam-3485	86	30	for	for	ADP
ejpam-3485	86	31	every	every	DET
ejpam-3485	86	32	x	x	SYM
ejpam-3485	86	33	∈	∈	PROPN
ejpam-3485	86	34	s	s	PART
ejpam-3485	86	35	\	\	NOUN
ejpam-3485	86	36	ng(s	ng(s	NUM
ejpam-3485	86	37	)	)	PUNCT
ejpam-3485	86	38	.	.	PUNCT
ejpam-3485	87	1	suppose	suppose	VERB
ejpam-3485	87	2	first	first	ADV
ejpam-3485	87	3	that	that	SCONJ
ejpam-3485	87	4	s	s	VERB
ejpam-3485	87	5	is	be	AUX
ejpam-3485	87	6	total	total	ADJ
ejpam-3485	87	7	dominating	dominating	NOUN
ejpam-3485	87	8	set	set	NOUN
ejpam-3485	87	9	.	.	PUNCT
ejpam-3485	88	1	suppose	suppose	VERB
ejpam-3485	88	2	further	far	ADV
ejpam-3485	88	3	that	that	SCONJ
ejpam-3485	88	4	that	that	PRON
ejpam-3485	88	5	|tz|	|tz|	VERB
ejpam-3485	88	6	≥	≥	NOUN
ejpam-3485	88	7	2	2	NUM
ejpam-3485	88	8	for	for	ADP
ejpam-3485	88	9	some	some	DET
ejpam-3485	88	10	z	z	PROPN
ejpam-3485	88	11	∈	∈	PROPN
ejpam-3485	88	12	s.	s.	PROPN
ejpam-3485	88	13	let	let	VERB
ejpam-3485	88	14	a	a	DET
ejpam-3485	88	15	∈	∈	NOUN
ejpam-3485	88	16	tz	tz	NOUN
ejpam-3485	88	17	and	and	CCONJ
ejpam-3485	88	18	define	define	VERB
ejpam-3485	88	19	t	t	PROPN
ejpam-3485	88	20	∗z	∗z	PROPN
ejpam-3485	89	1	=	=	SYM
ejpam-3485	89	2	{	{	PUNCT
ejpam-3485	89	3	a	a	NOUN
ejpam-3485	89	4	}	}	PUNCT
ejpam-3485	89	5	.	.	PUNCT
ejpam-3485	90	1	then	then	ADV
ejpam-3485	90	2	c∗	c∗	PROPN
ejpam-3485	90	3	=	=	PUNCT
ejpam-3485	91	1	[	[	X
ejpam-3485	91	2	∪x∈s\{z}({x	∪x∈s\{z}({x	ADJ
ejpam-3485	91	3	}	}	PUNCT
ejpam-3485	91	4	×	×	PROPN
ejpam-3485	91	5	tx	tx	PROPN
ejpam-3485	91	6	)	)	PUNCT
ejpam-3485	91	7	]	]	PUNCT
ejpam-3485	91	8	∪	∪	X
ejpam-3485	91	9	(	(	PUNCT
ejpam-3485	91	10	{	{	PUNCT
ejpam-3485	91	11	z	z	NOUN
ejpam-3485	91	12	}	}	PUNCT
ejpam-3485	91	13	×	×	PROPN
ejpam-3485	91	14	t	t	PROPN
ejpam-3485	91	15	∗z	∗z	PROPN
ejpam-3485	91	16	)	)	PUNCT
ejpam-3485	91	17	is	be	AUX
ejpam-3485	91	18	a	a	DET
ejpam-3485	91	19	total	total	ADJ
ejpam-3485	91	20	dominating	dominating	NOUN
ejpam-3485	91	21	set	set	VERB
ejpam-3485	91	22	by	by	ADP
ejpam-3485	91	23	theorem	theorem	NOUN
ejpam-3485	91	24	2.2(i	2.2(i	NUM
ejpam-3485	91	25	)	)	PUNCT
ejpam-3485	91	26	.	.	PUNCT
ejpam-3485	92	1	this	this	PRON
ejpam-3485	92	2	,	,	PUNCT
ejpam-3485	92	3	however	however	ADV
ejpam-3485	92	4	,	,	PUNCT
ejpam-3485	92	5	is	be	AUX
ejpam-3485	92	6	impossible	impossible	ADJ
ejpam-3485	92	7	because	because	SCONJ
ejpam-3485	92	8	|c∗|	|c∗|	VERB
ejpam-3485	92	9	<	<	X
ejpam-3485	92	10	|c|	|c|	PROPN
ejpam-3485	92	11	.	.	PUNCT
ejpam-3485	93	1	thus	thus	ADV
ejpam-3485	93	2	,	,	PUNCT
ejpam-3485	93	3	|tx|	|tx|	X
ejpam-3485	93	4	=	=	SYM
ejpam-3485	93	5	1	1	NUM
ejpam-3485	93	6	for	for	ADP
ejpam-3485	93	7	all	all	DET
ejpam-3485	93	8	x	x	PROPN
ejpam-3485	93	9	∈	∈	PROPN
ejpam-3485	93	10	s.	s.	PROPN
ejpam-3485	93	11	thus	thus	ADV
ejpam-3485	93	12	,	,	PUNCT
ejpam-3485	93	13	(	(	PUNCT
ejpam-3485	93	14	i	i	NOUN
ejpam-3485	93	15	)	)	PUNCT
ejpam-3485	93	16	holds	hold	VERB
ejpam-3485	93	17	.	.	PUNCT
ejpam-3485	94	1	suppose	suppose	VERB
ejpam-3485	94	2	now	now	ADV
ejpam-3485	94	3	that	that	PRON
ejpam-3485	94	4	s	s	VERB
ejpam-3485	94	5	is	be	AUX
ejpam-3485	94	6	a	a	DET
ejpam-3485	94	7	dominating	dominating	NOUN
ejpam-3485	94	8	(	(	PUNCT
ejpam-3485	94	9	not	not	PART
ejpam-3485	94	10	a	a	DET
ejpam-3485	94	11	total	total	ADJ
ejpam-3485	94	12	dominating	dominating	NOUN
ejpam-3485	94	13	)	)	PUNCT
ejpam-3485	94	14	set	set	NOUN
ejpam-3485	94	15	of	of	ADP
ejpam-3485	94	16	g.	g.	PROPN
ejpam-3485	94	17	suppose	suppose	VERB
ejpam-3485	94	18	first	first	ADV
ejpam-3485	94	19	that	that	PRON
ejpam-3485	94	20	γt(g	γt(g	PUNCT
ejpam-3485	94	21	)	)	PUNCT
ejpam-3485	94	22	<	<	X
ejpam-3485	94	23	|s	|s	PROPN
ejpam-3485	94	24	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3485	95	1	2|s	2|s	NUM
ejpam-3485	95	2	\ng(s)|	\ng(s)|	NUM
ejpam-3485	95	3	≤	≤	NUM
ejpam-3485	95	4	|c|	|c|	PROPN
ejpam-3485	95	5	.	.	PUNCT
ejpam-3485	96	1	choose	choose	VERB
ejpam-3485	96	2	a	a	DET
ejpam-3485	96	3	γt	γt	NOUN
ejpam-3485	96	4	-	-	ADJ
ejpam-3485	96	5	set	set	ADJ
ejpam-3485	96	6	r	r	NOUN
ejpam-3485	96	7	in	in	ADP
ejpam-3485	96	8	g	g	NOUN
ejpam-3485	96	9	and	and	CCONJ
ejpam-3485	96	10	set	set	VERB
ejpam-3485	96	11	sx	sx	PROPN
ejpam-3485	96	12	=	=	PUNCT
ejpam-3485	96	13	{	{	PUNCT
ejpam-3485	96	14	v	v	NOUN
ejpam-3485	96	15	}	}	PUNCT
ejpam-3485	96	16	c.	c.	PROPN
ejpam-3485	96	17	armada	armada	PROPN
ejpam-3485	96	18	,	,	PUNCT
ejpam-3485	96	19	s.	s.	PROPN
ejpam-3485	96	20	canoy	canoy	PROPN
ejpam-3485	96	21	jr	jr	PROPN
ejpam-3485	96	22	.	.	PROPN
ejpam-3485	96	23	,	,	PUNCT
ejpam-3485	96	24	c.	c.	PROPN
ejpam-3485	96	25	go	go	VERB
ejpam-3485	96	26	/	/	SYM
ejpam-3485	96	27	eur	eur	PROPN
ejpam-3485	96	28	.	.	PUNCT
ejpam-3485	97	1	j.	j.	PROPN
ejpam-3485	97	2	pure	pure	PROPN
ejpam-3485	97	3	appl	appl	PROPN
ejpam-3485	97	4	.	.	PROPN
ejpam-3485	97	5	math	math	PROPN
ejpam-3485	97	6	,	,	PUNCT
ejpam-3485	97	7	12	12	NUM
ejpam-3485	97	8	(	(	PUNCT
ejpam-3485	97	9	4	4	NUM
ejpam-3485	97	10	)	)	PUNCT
ejpam-3485	97	11	(	(	PUNCT
ejpam-3485	97	12	2019	2019	NUM
ejpam-3485	97	13	)	)	PUNCT
ejpam-3485	97	14	,	,	PUNCT
ejpam-3485	97	15	1779	1779	NUM
ejpam-3485	97	16	-	-	SYM
ejpam-3485	97	17	1786	1786	NUM
ejpam-3485	97	18	1782	1782	NUM
ejpam-3485	97	19	for	for	ADP
ejpam-3485	97	20	every	every	DET
ejpam-3485	97	21	x	x	SYM
ejpam-3485	97	22	∈	∈	PROPN
ejpam-3485	97	23	r	r	NOUN
ejpam-3485	97	24	,	,	PUNCT
ejpam-3485	97	25	where	where	SCONJ
ejpam-3485	97	26	v	v	X
ejpam-3485	97	27	∈	∈	PROPN
ejpam-3485	97	28	v	v	NOUN
ejpam-3485	97	29	(	(	PUNCT
ejpam-3485	97	30	h	h	NOUN
ejpam-3485	97	31	)	)	PUNCT
ejpam-3485	97	32	.	.	PUNCT
ejpam-3485	98	1	then	then	ADV
ejpam-3485	98	2	y	y	PROPN
ejpam-3485	98	3	=	=	SYM
ejpam-3485	98	4	∪x∈r({x	∪x∈r({x	PROPN
ejpam-3485	98	5	}	}	PUNCT
ejpam-3485	98	6	×	×	PROPN
ejpam-3485	98	7	sx	sx	PROPN
ejpam-3485	98	8	)	)	PUNCT
ejpam-3485	98	9	is	be	AUX
ejpam-3485	98	10	a	a	DET
ejpam-3485	98	11	total	total	ADJ
ejpam-3485	98	12	dominating	dominating	NOUN
ejpam-3485	98	13	set	set	VERB
ejpam-3485	98	14	by	by	ADP
ejpam-3485	98	15	theorem	theorem	NOUN
ejpam-3485	98	16	2.2(i	2.2(i	NUM
ejpam-3485	98	17	)	)	PUNCT
ejpam-3485	98	18	.	.	PUNCT
ejpam-3485	99	1	it	it	PRON
ejpam-3485	99	2	follows	follow	VERB
ejpam-3485	99	3	that	that	PRON
ejpam-3485	99	4	γt(g	γt(g	PUNCT
ejpam-3485	99	5	)	)	PUNCT
ejpam-3485	99	6	=	=	SYM
ejpam-3485	99	7	|r|	|r|	NOUN
ejpam-3485	99	8	=	=	NOUN
ejpam-3485	99	9	|y	|y	NOUN
ejpam-3485	99	10	|	|	ADV
ejpam-3485	99	11	<	<	X
ejpam-3485	99	12	|c|	|c|	PROPN
ejpam-3485	99	13	,	,	PUNCT
ejpam-3485	99	14	contrary	contrary	ADJ
ejpam-3485	99	15	to	to	ADP
ejpam-3485	99	16	our	our	PRON
ejpam-3485	99	17	assumption	assumption	NOUN
ejpam-3485	99	18	of	of	ADP
ejpam-3485	99	19	c.	c.	PROPN
ejpam-3485	99	20	thus	thus	ADV
ejpam-3485	99	21	,	,	PUNCT
ejpam-3485	99	22	by	by	ADP
ejpam-3485	99	23	lemma	lemma	PROPN
ejpam-3485	99	24	2.1	2.1	NUM
ejpam-3485	99	25	,	,	PUNCT
ejpam-3485	99	26	γt(g	γt(g	NUM
ejpam-3485	99	27	)	)	PUNCT
ejpam-3485	99	28	=	=	SYM
ejpam-3485	99	29	|s	|s	PROPN
ejpam-3485	99	30	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3485	99	31	2|s	2|s	NUM
ejpam-3485	100	1	\ng(s)|	\ng(s)|	NUM
ejpam-3485	100	2	.	.	PUNCT
ejpam-3485	101	1	next	next	ADV
ejpam-3485	101	2	,	,	PUNCT
ejpam-3485	101	3	suppose	suppose	VERB
ejpam-3485	101	4	that	that	SCONJ
ejpam-3485	101	5	there	there	PRON
ejpam-3485	101	6	exists	exist	VERB
ejpam-3485	101	7	z	z	PROPN
ejpam-3485	101	8	∈	∈	PROPN
ejpam-3485	101	9	s	s	VERB
ejpam-3485	101	10	∩ng(s	∩ng(s	NOUN
ejpam-3485	101	11	)	)	PUNCT
ejpam-3485	101	12	with	with	ADP
ejpam-3485	101	13	|tz|	|tz|	NOUN
ejpam-3485	101	14	≥	≥	NOUN
ejpam-3485	101	15	2	2	NUM
ejpam-3485	101	16	.	.	PUNCT
ejpam-3485	102	1	let	let	VERB
ejpam-3485	102	2	a	a	DET
ejpam-3485	102	3	∈	∈	NOUN
ejpam-3485	102	4	tz	tz	NOUN
ejpam-3485	102	5	and	and	CCONJ
ejpam-3485	102	6	define	define	VERB
ejpam-3485	102	7	t	t	PROPN
ejpam-3485	102	8	∗z	∗z	PROPN
ejpam-3485	103	1	=	=	SYM
ejpam-3485	103	2	{	{	PUNCT
ejpam-3485	103	3	a	a	NOUN
ejpam-3485	103	4	}	}	PUNCT
ejpam-3485	103	5	.	.	PUNCT
ejpam-3485	104	1	then	then	ADV
ejpam-3485	104	2	c∗	c∗	PROPN
ejpam-3485	104	3	=	=	PUNCT
ejpam-3485	105	1	[	[	X
ejpam-3485	105	2	∪x∈s\{z}({x	∪x∈s\{z}({x	ADJ
ejpam-3485	105	3	}	}	PUNCT
ejpam-3485	105	4	×	×	PROPN
ejpam-3485	105	5	tx	tx	PROPN
ejpam-3485	105	6	)	)	PUNCT
ejpam-3485	105	7	]	]	PUNCT
ejpam-3485	105	8	∪	∪	X
ejpam-3485	105	9	(	(	PUNCT
ejpam-3485	105	10	{	{	PUNCT
ejpam-3485	105	11	z	z	NOUN
ejpam-3485	105	12	}	}	PUNCT
ejpam-3485	105	13	×	×	PROPN
ejpam-3485	105	14	t	t	PROPN
ejpam-3485	105	15	∗z	∗z	PROPN
ejpam-3485	105	16	)	)	PUNCT
ejpam-3485	105	17	is	be	AUX
ejpam-3485	105	18	a	a	DET
ejpam-3485	105	19	total	total	ADJ
ejpam-3485	105	20	dominating	dominating	NOUN
ejpam-3485	105	21	set	set	VERB
ejpam-3485	105	22	by	by	ADP
ejpam-3485	105	23	theorem	theorem	NOUN
ejpam-3485	105	24	2.2(ii	2.2(ii	NUM
ejpam-3485	105	25	)	)	PUNCT
ejpam-3485	105	26	.	.	PUNCT
ejpam-3485	106	1	this	this	PRON
ejpam-3485	106	2	is	be	AUX
ejpam-3485	106	3	not	not	PART
ejpam-3485	106	4	possible	possible	ADJ
ejpam-3485	106	5	because	because	SCONJ
ejpam-3485	106	6	|c∗|	|c∗|	VERB
ejpam-3485	106	7	<	<	X
ejpam-3485	106	8	|c|	|c|	PROPN
ejpam-3485	106	9	therefore	therefore	ADV
ejpam-3485	106	10	|tx|	|tx|	X
ejpam-3485	106	11	=	=	SYM
ejpam-3485	106	12	1	1	NUM
ejpam-3485	106	13	for	for	ADP
ejpam-3485	106	14	all	all	DET
ejpam-3485	106	15	x	x	SYM
ejpam-3485	106	16	∈	∈	NOUN
ejpam-3485	106	17	s	s	NOUN
ejpam-3485	106	18	∩ng(s	∩ng(s	NOUN
ejpam-3485	106	19	)	)	PUNCT
ejpam-3485	106	20	.	.	PUNCT
ejpam-3485	107	1	finally	finally	ADV
ejpam-3485	107	2	,	,	PUNCT
ejpam-3485	107	3	suppose	suppose	VERB
ejpam-3485	107	4	there	there	PRON
ejpam-3485	107	5	exists	exist	VERB
ejpam-3485	107	6	w	w	PROPN
ejpam-3485	107	7	∈	∈	PROPN
ejpam-3485	107	8	s	s	PART
ejpam-3485	107	9	\ng(s	\ng(s	NOUN
ejpam-3485	107	10	)	)	PUNCT
ejpam-3485	107	11	such	such	ADJ
ejpam-3485	107	12	that	that	SCONJ
ejpam-3485	107	13	tw	tw	PROPN
ejpam-3485	107	14	is	be	AUX
ejpam-3485	107	15	not	not	PART
ejpam-3485	107	16	a	a	DET
ejpam-3485	107	17	γt	γt	NOUN
ejpam-3485	107	18	-	-	NOUN
ejpam-3485	107	19	set	set	NOUN
ejpam-3485	107	20	of	of	ADP
ejpam-3485	107	21	h.	h.	NOUN
ejpam-3485	107	22	since	since	SCONJ
ejpam-3485	107	23	tw	tw	NOUN
ejpam-3485	107	24	is	be	AUX
ejpam-3485	107	25	a	a	DET
ejpam-3485	107	26	dominating	dominating	NOUN
ejpam-3485	107	27	set	set	NOUN
ejpam-3485	107	28	and	and	CCONJ
ejpam-3485	107	29	γt(h	γt(h	NUM
ejpam-3485	107	30	)	)	PUNCT
ejpam-3485	107	31	=	=	SYM
ejpam-3485	107	32	2	2	NUM
ejpam-3485	107	33	,	,	PUNCT
ejpam-3485	107	34	|tw|	|tw|	PROPN
ejpam-3485	107	35	>	>	X
ejpam-3485	108	1	2	2	X
ejpam-3485	108	2	.	.	PUNCT
ejpam-3485	108	3	let	let	VERB
ejpam-3485	108	4	lw	lw	NOUN
ejpam-3485	108	5	=	=	PRON
ejpam-3485	108	6	{	{	PUNCT
ejpam-3485	108	7	a	a	PRON
ejpam-3485	108	8	,	,	PUNCT
ejpam-3485	108	9	b	b	X
ejpam-3485	108	10	}	}	PUNCT
ejpam-3485	108	11	be	be	AUX
ejpam-3485	108	12	a	a	DET
ejpam-3485	108	13	γt	γt	NOUN
ejpam-3485	108	14	-	-	NOUN
ejpam-3485	108	15	set	set	NOUN
ejpam-3485	108	16	of	of	ADP
ejpam-3485	108	17	h.	h.	PROPN
ejpam-3485	108	18	then	then	ADV
ejpam-3485	108	19	c1	c1	PROPN
ejpam-3485	108	20	=	=	PUNCT
ejpam-3485	109	1	[	[	X
ejpam-3485	109	2	∪x∈s\{w}({x	∪x∈s\{w}({x	X
ejpam-3485	109	3	}	}	PUNCT
ejpam-3485	109	4	×	×	PROPN
ejpam-3485	109	5	tx	tx	PROPN
ejpam-3485	109	6	)	)	PUNCT
ejpam-3485	109	7	]	]	PUNCT
ejpam-3485	109	8	∪	∪	X
ejpam-3485	109	9	(	(	PUNCT
ejpam-3485	109	10	{	{	PUNCT
ejpam-3485	109	11	w	w	NOUN
ejpam-3485	109	12	}	}	PUNCT
ejpam-3485	109	13	×	×	PROPN
ejpam-3485	109	14	lw	lw	NOUN
ejpam-3485	109	15	)	)	PUNCT
ejpam-3485	109	16	is	be	AUX
ejpam-3485	109	17	a	a	DET
ejpam-3485	109	18	total	total	ADJ
ejpam-3485	109	19	dominating	dominating	NOUN
ejpam-3485	109	20	set	set	VERB
ejpam-3485	109	21	by	by	ADP
ejpam-3485	109	22	theorem	theorem	NOUN
ejpam-3485	109	23	2.2(ii	2.2(ii	NUM
ejpam-3485	109	24	)	)	PUNCT
ejpam-3485	109	25	.	.	PUNCT
ejpam-3485	110	1	again	again	ADV
ejpam-3485	110	2	,	,	PUNCT
ejpam-3485	110	3	this	this	PRON
ejpam-3485	110	4	is	be	AUX
ejpam-3485	110	5	not	not	PART
ejpam-3485	110	6	possible	possible	ADJ
ejpam-3485	110	7	because	because	SCONJ
ejpam-3485	110	8	|c1|	|c1|	PROPN
ejpam-3485	110	9	<	<	X
ejpam-3485	110	10	|c|	|c|	PROPN
ejpam-3485	110	11	.	.	PUNCT
ejpam-3485	111	1	therefore	therefore	ADV
ejpam-3485	111	2	,	,	PUNCT
ejpam-3485	111	3	tx	tx	PROPN
ejpam-3485	111	4	is	be	AUX
ejpam-3485	111	5	a	a	DET
ejpam-3485	111	6	γt	γt	NOUN
ejpam-3485	111	7	-	-	NOUN
ejpam-3485	111	8	set	set	NOUN
ejpam-3485	111	9	of	of	ADP
ejpam-3485	111	10	h	h	NOUN
ejpam-3485	111	11	for	for	ADP
ejpam-3485	111	12	every	every	DET
ejpam-3485	111	13	x	x	SYM
ejpam-3485	111	14	∈	∈	PROPN
ejpam-3485	111	15	s	s	PART
ejpam-3485	111	16	\ng(s	\ng(s	NOUN
ejpam-3485	111	17	)	)	PUNCT
ejpam-3485	111	18	.	.	PUNCT
ejpam-3485	112	1	the	the	DET
ejpam-3485	112	2	converse	converse	NOUN
ejpam-3485	112	3	is	be	AUX
ejpam-3485	112	4	easy	easy	ADJ
ejpam-3485	112	5	.	.	PUNCT
ejpam-3485	113	1	�	�	PROPN
ejpam-3485	113	2	corollary	corollary	ADJ
ejpam-3485	113	3	2.4	2.4	NUM
ejpam-3485	113	4	.	.	PUNCT
ejpam-3485	114	1	let	let	VERB
ejpam-3485	114	2	g	g	NOUN
ejpam-3485	114	3	and	and	CCONJ
ejpam-3485	114	4	h	h	NOUN
ejpam-3485	114	5	be	be	AUX
ejpam-3485	114	6	nontrivial	nontrivial	ADJ
ejpam-3485	114	7	connected	connect	VERB
ejpam-3485	114	8	graphs	graph	NOUN
ejpam-3485	114	9	with	with	ADP
ejpam-3485	114	10	γt(h	γt(h	NUM
ejpam-3485	114	11	)	)	PUNCT
ejpam-3485	114	12	6=	6=	ADP
ejpam-3485	115	1	2	2	X
ejpam-3485	115	2	.	.	PUNCT
ejpam-3485	115	3	then	then	ADV
ejpam-3485	115	4	a	a	DET
ejpam-3485	115	5	subset	subset	NOUN
ejpam-3485	115	6	c	c	NOUN
ejpam-3485	115	7	=	=	SYM
ejpam-3485	115	8	∪x∈s({x}×	∪x∈s({x}×	PROPN
ejpam-3485	115	9	tx	tx	PROPN
ejpam-3485	115	10	)	)	PUNCT
ejpam-3485	115	11	of	of	ADP
ejpam-3485	115	12	v	v	NOUN
ejpam-3485	115	13	(	(	PUNCT
ejpam-3485	115	14	g[h	g[h	PROPN
ejpam-3485	115	15	]	]	PUNCT
ejpam-3485	115	16	)	)	PUNCT
ejpam-3485	115	17	,	,	PUNCT
ejpam-3485	115	18	where	where	SCONJ
ejpam-3485	115	19	s	s	VERB
ejpam-3485	115	20	⊆	⊆	NUM
ejpam-3485	115	21	v	v	NOUN
ejpam-3485	115	22	(	(	PUNCT
ejpam-3485	115	23	g	g	NOUN
ejpam-3485	115	24	)	)	PUNCT
ejpam-3485	115	25	and	and	CCONJ
ejpam-3485	115	26	tx	tx	VERB
ejpam-3485	115	27	⊆	⊆	NUM
ejpam-3485	115	28	v	v	NOUN
ejpam-3485	115	29	(	(	PUNCT
ejpam-3485	115	30	h	h	NOUN
ejpam-3485	115	31	)	)	PUNCT
ejpam-3485	115	32	for	for	ADP
ejpam-3485	115	33	every	every	DET
ejpam-3485	115	34	x	x	SYM
ejpam-3485	115	35	∈	∈	PROPN
ejpam-3485	115	36	s	s	NOUN
ejpam-3485	115	37	,	,	PUNCT
ejpam-3485	115	38	is	be	AUX
ejpam-3485	115	39	a	a	DET
ejpam-3485	115	40	γt	γt	NOUN
ejpam-3485	115	41	-	-	NOUN
ejpam-3485	115	42	set	set	NOUN
ejpam-3485	115	43	of	of	ADP
ejpam-3485	115	44	g[h	g[h	NOUN
ejpam-3485	115	45	]	]	PUNCT
ejpam-3485	115	46	if	if	SCONJ
ejpam-3485	115	47	and	and	CCONJ
ejpam-3485	115	48	only	only	ADV
ejpam-3485	115	49	if	if	SCONJ
ejpam-3485	115	50	s	s	NOUN
ejpam-3485	115	51	is	be	AUX
ejpam-3485	115	52	a	a	DET
ejpam-3485	115	53	γt	γt	NOUN
ejpam-3485	115	54	-	-	NOUN
ejpam-3485	115	55	set	set	NOUN
ejpam-3485	115	56	of	of	ADP
ejpam-3485	115	57	g	g	NOUN
ejpam-3485	115	58	and	and	CCONJ
ejpam-3485	115	59	|tx|	|tx|	NUM
ejpam-3485	115	60	=	=	SYM
ejpam-3485	115	61	1	1	NUM
ejpam-3485	115	62	for	for	ADP
ejpam-3485	115	63	all	all	DET
ejpam-3485	115	64	x	x	SYM
ejpam-3485	115	65	∈	∈	PROPN
ejpam-3485	115	66	s.	s.	PROPN
ejpam-3485	115	67	proof	proof	PROPN
ejpam-3485	115	68	.	.	PUNCT
ejpam-3485	116	1	suppose	suppose	VERB
ejpam-3485	116	2	c	c	NOUN
ejpam-3485	116	3	=	=	SYM
ejpam-3485	116	4	∪x∈s({x	∪x∈s({x	PROPN
ejpam-3485	116	5	}	}	PUNCT
ejpam-3485	116	6	×	×	NOUN
ejpam-3485	116	7	tx	tx	PROPN
ejpam-3485	116	8	)	)	PUNCT
ejpam-3485	116	9	is	be	AUX
ejpam-3485	116	10	a	a	DET
ejpam-3485	116	11	γt	γt	NOUN
ejpam-3485	116	12	-	-	NOUN
ejpam-3485	116	13	set	set	NOUN
ejpam-3485	116	14	of	of	ADP
ejpam-3485	116	15	g[h	g[h	NOUN
ejpam-3485	116	16	]	]	PUNCT
ejpam-3485	116	17	.	.	PUNCT
ejpam-3485	117	1	suppose	suppose	VERB
ejpam-3485	117	2	s	s	NOUN
ejpam-3485	117	3	is	be	AUX
ejpam-3485	117	4	not	not	PART
ejpam-3485	117	5	a	a	DET
ejpam-3485	117	6	total	total	ADJ
ejpam-3485	117	7	dominating	dominating	NOUN
ejpam-3485	117	8	set	set	NOUN
ejpam-3485	117	9	.	.	PUNCT
ejpam-3485	118	1	then	then	ADV
ejpam-3485	118	2	s	s	VERB
ejpam-3485	118	3	is	be	AUX
ejpam-3485	118	4	a	a	DET
ejpam-3485	118	5	dominating	dominating	NOUN
ejpam-3485	118	6	set	set	NOUN
ejpam-3485	118	7	of	of	ADP
ejpam-3485	118	8	g	g	PROPN
ejpam-3485	118	9	and	and	CCONJ
ejpam-3485	118	10	tx	tx	PROPN
ejpam-3485	118	11	is	be	AUX
ejpam-3485	118	12	a	a	DET
ejpam-3485	118	13	total	total	ADJ
ejpam-3485	118	14	dominating	dominating	NOUN
ejpam-3485	118	15	set	set	NOUN
ejpam-3485	118	16	of	of	ADP
ejpam-3485	118	17	h	h	NOUN
ejpam-3485	118	18	for	for	ADP
ejpam-3485	118	19	every	every	DET
ejpam-3485	118	20	x	x	SYM
ejpam-3485	118	21	∈	∈	PROPN
ejpam-3485	118	22	s	s	PART
ejpam-3485	118	23	\	\	NOUN
ejpam-3485	118	24	ng(s	ng(s	NUM
ejpam-3485	118	25	)	)	PUNCT
ejpam-3485	118	26	,	,	PUNCT
ejpam-3485	118	27	by	by	ADP
ejpam-3485	118	28	theorem	theorem	NOUN
ejpam-3485	118	29	2.2	2.2	NUM
ejpam-3485	118	30	.	.	PUNCT
ejpam-3485	119	1	since	since	SCONJ
ejpam-3485	119	2	γt(h	γt(h	NUM
ejpam-3485	119	3	)	)	PUNCT
ejpam-3485	119	4	6=	6=	ADP
ejpam-3485	119	5	2	2	NUM
ejpam-3485	119	6	,	,	PUNCT
ejpam-3485	119	7	it	it	PRON
ejpam-3485	119	8	follows	follow	VERB
ejpam-3485	119	9	that	that	SCONJ
ejpam-3485	119	10	|tx|	|tx|	NOUN
ejpam-3485	119	11	>	>	X
ejpam-3485	119	12	2	2	NUM
ejpam-3485	119	13	for	for	ADP
ejpam-3485	119	14	every	every	DET
ejpam-3485	119	15	x	x	SYM
ejpam-3485	119	16	∈	∈	PROPN
ejpam-3485	119	17	s	s	PART
ejpam-3485	119	18	\ng(s	\ng(s	NOUN
ejpam-3485	119	19	)	)	PUNCT
ejpam-3485	119	20	.	.	PUNCT
ejpam-3485	120	1	by	by	ADP
ejpam-3485	120	2	lemma	lemma	PROPN
ejpam-3485	120	3	2.1	2.1	NUM
ejpam-3485	120	4	and	and	CCONJ
ejpam-3485	120	5	since	since	SCONJ
ejpam-3485	120	6	|c|	|c|	PROPN
ejpam-3485	120	7	=	=	SYM
ejpam-3485	120	8	∑	∑	NOUN
ejpam-3485	120	9	x∈s∩ng(s	x∈s∩ng(s	NOUN
ejpam-3485	120	10	)	)	PUNCT
ejpam-3485	120	11	|tx|+	|tx|+	X
ejpam-3485	120	12	∑	∑	PUNCT
ejpam-3485	120	13	x∈s\ng(s	x∈s\ng(s	NUM
ejpam-3485	120	14	)	)	PUNCT
ejpam-3485	120	15	|tx|	|tx|	NOUN
ejpam-3485	120	16	,	,	PUNCT
ejpam-3485	120	17	it	it	PRON
ejpam-3485	120	18	follows	follow	VERB
ejpam-3485	120	19	that	that	PRON
ejpam-3485	120	20	γt(g	γt(g	PUNCT
ejpam-3485	120	21	)	)	PUNCT
ejpam-3485	120	22	<	<	X
ejpam-3485	120	23	|c|	|c|	PROPN
ejpam-3485	120	24	.	.	PUNCT
ejpam-3485	121	1	let	let	VERB
ejpam-3485	121	2	s1	s1	NOUN
ejpam-3485	121	3	be	be	AUX
ejpam-3485	121	4	a	a	DET
ejpam-3485	121	5	γt	γt	NOUN
ejpam-3485	121	6	-	-	NOUN
ejpam-3485	121	7	set	set	NOUN
ejpam-3485	121	8	of	of	ADP
ejpam-3485	121	9	g	g	NOUN
ejpam-3485	121	10	and	and	CCONJ
ejpam-3485	121	11	set	set	VERB
ejpam-3485	121	12	qx	qx	PROPN
ejpam-3485	121	13	=	=	X
ejpam-3485	121	14	{	{	PUNCT
ejpam-3485	121	15	a	a	NOUN
ejpam-3485	121	16	}	}	PUNCT
ejpam-3485	121	17	for	for	ADP
ejpam-3485	121	18	every	every	DET
ejpam-3485	121	19	x	x	PROPN
ejpam-3485	121	20	∈	∈	PROPN
ejpam-3485	121	21	s1	s1	NOUN
ejpam-3485	121	22	,	,	PUNCT
ejpam-3485	121	23	where	where	SCONJ
ejpam-3485	121	24	a	a	DET
ejpam-3485	121	25	∈	∈	PROPN
ejpam-3485	121	26	v	v	NOUN
ejpam-3485	121	27	(	(	PUNCT
ejpam-3485	121	28	h	h	NOUN
ejpam-3485	121	29	)	)	PUNCT
ejpam-3485	121	30	.	.	PUNCT
ejpam-3485	122	1	put	put	VERB
ejpam-3485	122	2	q	q	NOUN
ejpam-3485	122	3	=	=	PUNCT
ejpam-3485	122	4	∪x∈s1({x	∪x∈s1({x	NOUN
ejpam-3485	122	5	}	}	PUNCT
ejpam-3485	122	6	×qx	×qx	NOUN
ejpam-3485	122	7	)	)	PUNCT
ejpam-3485	122	8	.	.	PUNCT
ejpam-3485	123	1	then	then	ADV
ejpam-3485	123	2	q	q	X
ejpam-3485	123	3	is	be	AUX
ejpam-3485	123	4	a	a	DET
ejpam-3485	123	5	total	total	ADJ
ejpam-3485	123	6	dominating	dominating	NOUN
ejpam-3485	123	7	set	set	NOUN
ejpam-3485	123	8	of	of	ADP
ejpam-3485	123	9	g[h	g[h	PROPN
ejpam-3485	123	10	]	]	PUNCT
ejpam-3485	123	11	by	by	ADP
ejpam-3485	123	12	theorem	theorem	NOUN
ejpam-3485	123	13	2.2(i	2.2(i	NUM
ejpam-3485	123	14	)	)	PUNCT
ejpam-3485	123	15	.	.	PUNCT
ejpam-3485	124	1	moreover	moreover	ADV
ejpam-3485	124	2	,	,	PUNCT
ejpam-3485	124	3	|q|	|q|	X
ejpam-3485	124	4	=	=	SYM
ejpam-3485	124	5	|s1|	|s1|	NOUN
ejpam-3485	124	6	=	=	SYM
ejpam-3485	124	7	γt(g	γt(g	NUM
ejpam-3485	124	8	)	)	PUNCT
ejpam-3485	124	9	.	.	PUNCT
ejpam-3485	125	1	thus	thus	ADV
ejpam-3485	125	2	,	,	PUNCT
ejpam-3485	125	3	|q|	|q|	VERB
ejpam-3485	125	4	<	<	X
ejpam-3485	125	5	|c|	|c|	PROPN
ejpam-3485	125	6	,	,	PUNCT
ejpam-3485	125	7	contrary	contrary	ADJ
ejpam-3485	125	8	to	to	ADP
ejpam-3485	125	9	our	our	PRON
ejpam-3485	125	10	assumption	assumption	NOUN
ejpam-3485	125	11	of	of	ADP
ejpam-3485	125	12	c.	c.	PROPN
ejpam-3485	125	13	therefore	therefore	ADV
ejpam-3485	125	14	,	,	PUNCT
ejpam-3485	125	15	s	s	VERB
ejpam-3485	125	16	is	be	AUX
ejpam-3485	125	17	a	a	DET
ejpam-3485	125	18	total	total	ADJ
ejpam-3485	125	19	dominating	dominating	NOUN
ejpam-3485	125	20	set	set	NOUN
ejpam-3485	125	21	of	of	ADP
ejpam-3485	125	22	g.	g.	PROPN
ejpam-3485	125	23	using	use	VERB
ejpam-3485	125	24	a	a	DET
ejpam-3485	125	25	similar	similar	ADJ
ejpam-3485	125	26	argument	argument	NOUN
ejpam-3485	125	27	,	,	PUNCT
ejpam-3485	125	28	it	it	PRON
ejpam-3485	125	29	can	can	AUX
ejpam-3485	125	30	be	be	AUX
ejpam-3485	125	31	shown	show	VERB
ejpam-3485	125	32	that	that	SCONJ
ejpam-3485	125	33	s	s	NOUN
ejpam-3485	125	34	is	be	AUX
ejpam-3485	125	35	a	a	DET
ejpam-3485	125	36	γt	γt	NOUN
ejpam-3485	125	37	-	-	NOUN
ejpam-3485	125	38	set	set	NOUN
ejpam-3485	125	39	of	of	ADP
ejpam-3485	125	40	g	g	NOUN
ejpam-3485	125	41	and	and	CCONJ
ejpam-3485	125	42	|tx|	|tx|	NUM
ejpam-3485	125	43	=	=	SYM
ejpam-3485	125	44	1	1	NUM
ejpam-3485	125	45	for	for	ADP
ejpam-3485	125	46	all	all	DET
ejpam-3485	125	47	x	x	SYM
ejpam-3485	125	48	∈	∈	PROPN
ejpam-3485	125	49	s.	s.	PROPN
ejpam-3485	125	50	for	for	ADP
ejpam-3485	125	51	the	the	DET
ejpam-3485	125	52	converse	converse	NOUN
ejpam-3485	125	53	,	,	PUNCT
ejpam-3485	125	54	suppose	suppose	VERB
ejpam-3485	125	55	that	that	SCONJ
ejpam-3485	125	56	c	c	AUX
ejpam-3485	125	57	=	=	SYM
ejpam-3485	125	58	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-3485	125	59	)	)	PUNCT
ejpam-3485	125	60	and	and	CCONJ
ejpam-3485	125	61	s	s	VERB
ejpam-3485	125	62	is	be	AUX
ejpam-3485	125	63	a	a	DET
ejpam-3485	125	64	γt	γt	NOUN
ejpam-3485	125	65	-	-	NOUN
ejpam-3485	125	66	set	set	NOUN
ejpam-3485	125	67	of	of	ADP
ejpam-3485	125	68	g	g	NOUN
ejpam-3485	125	69	with	with	ADP
ejpam-3485	125	70	|tx|	|tx|	NOUN
ejpam-3485	125	71	=	=	SYM
ejpam-3485	125	72	1	1	NUM
ejpam-3485	125	73	for	for	ADP
ejpam-3485	125	74	all	all	DET
ejpam-3485	125	75	x	x	SYM
ejpam-3485	125	76	∈	∈	PROPN
ejpam-3485	125	77	s.	s.	PROPN
ejpam-3485	125	78	by	by	ADP
ejpam-3485	125	79	theorem	theorem	NOUN
ejpam-3485	125	80	2.2	2.2	NUM
ejpam-3485	125	81	,	,	PUNCT
ejpam-3485	125	82	c	c	PROPN
ejpam-3485	125	83	is	be	AUX
ejpam-3485	125	84	a	a	DET
ejpam-3485	125	85	total	total	ADJ
ejpam-3485	125	86	dominating	dominating	NOUN
ejpam-3485	125	87	set	set	NOUN
ejpam-3485	125	88	of	of	ADP
ejpam-3485	125	89	g[h	g[h	NOUN
ejpam-3485	125	90	]	]	PUNCT
ejpam-3485	125	91	.	.	PUNCT
ejpam-3485	126	1	if	if	SCONJ
ejpam-3485	126	2	c1	c1	PROPN
ejpam-3485	126	3	=	=	SYM
ejpam-3485	126	4	∪x∈s1({x}×lx	∪x∈s1({x}×lx	PROPN
ejpam-3485	126	5	)	)	PUNCT
ejpam-3485	126	6	is	be	AUX
ejpam-3485	126	7	another	another	DET
ejpam-3485	126	8	total	total	ADJ
ejpam-3485	126	9	dominating	dominating	NOUN
ejpam-3485	126	10	set	set	NOUN
ejpam-3485	126	11	of	of	ADP
ejpam-3485	126	12	g[h	g[h	PROPN
ejpam-3485	126	13	]	]	PUNCT
ejpam-3485	126	14	,	,	PUNCT
ejpam-3485	126	15	then	then	ADV
ejpam-3485	126	16	,	,	PUNCT
ejpam-3485	126	17	by	by	ADP
ejpam-3485	126	18	theorem	theorem	NOUN
ejpam-3485	126	19	2.2	2.2	NUM
ejpam-3485	126	20	,	,	PUNCT
ejpam-3485	126	21	s1	s1	PROPN
ejpam-3485	126	22	is	be	AUX
ejpam-3485	126	23	dominating	dominate	VERB
ejpam-3485	126	24	set	set	NOUN
ejpam-3485	126	25	of	of	ADP
ejpam-3485	126	26	g	g	PROPN
ejpam-3485	126	27	and	and	CCONJ
ejpam-3485	126	28	lx	lx	NOUN
ejpam-3485	126	29	is	be	AUX
ejpam-3485	126	30	a	a	DET
ejpam-3485	126	31	total	total	ADJ
ejpam-3485	126	32	dominating	dominating	NOUN
ejpam-3485	126	33	set	set	NOUN
ejpam-3485	126	34	of	of	ADP
ejpam-3485	126	35	hx	hx	PROPN
ejpam-3485	126	36	for	for	ADP
ejpam-3485	126	37	each	each	DET
ejpam-3485	126	38	x	x	SYM
ejpam-3485	126	39	∈	∈	PROPN
ejpam-3485	126	40	s1	s1	NOUN
ejpam-3485	126	41	\ng(s1	\ng(s1	NUM
ejpam-3485	126	42	)	)	PUNCT
ejpam-3485	126	43	.	.	PUNCT
ejpam-3485	127	1	let	let	VERB
ejpam-3485	127	2	d1	d1	PROPN
ejpam-3485	127	3	=	=	SYM
ejpam-3485	127	4	s1	s1	PROPN
ejpam-3485	127	5	∩ng(s1	∩ng(s1	X
ejpam-3485	127	6	)	)	PUNCT
ejpam-3485	127	7	and	and	CCONJ
ejpam-3485	127	8	d2	d2	PROPN
ejpam-3485	127	9	=	=	PROPN
ejpam-3485	127	10	s1	s1	PROPN
ejpam-3485	127	11	\ng(s1	\ng(s1	NUM
ejpam-3485	127	12	)	)	PUNCT
ejpam-3485	127	13	.	.	PUNCT
ejpam-3485	128	1	by	by	ADP
ejpam-3485	128	2	theorem	theorem	ADJ
ejpam-3485	128	3	2.2	2.2	NUM
ejpam-3485	128	4	,	,	PUNCT
ejpam-3485	128	5	|d1|+	|d1|+	PRON
ejpam-3485	128	6	2|d2|	2|d2|	NUM
ejpam-3485	128	7	≤	≤	NUM
ejpam-3485	128	8	∑	∑	PUNCT
ejpam-3485	128	9	x∈d1	x∈d1	NOUN
ejpam-3485	128	10	|lx|+	|lx|+	PROPN
ejpam-3485	128	11	∑	∑	PUNCT
ejpam-3485	128	12	x∈d2	x∈d2	ADJ
ejpam-3485	128	13	|lx|	|lx|	PROPN
ejpam-3485	128	14	=	=	PUNCT
ejpam-3485	128	15	|c1|	|c1|	PROPN
ejpam-3485	128	16	.	.	PUNCT
ejpam-3485	129	1	thus	thus	ADV
ejpam-3485	129	2	,	,	PUNCT
ejpam-3485	129	3	by	by	ADP
ejpam-3485	129	4	lemma	lemma	PROPN
ejpam-3485	129	5	2.1	2.1	NUM
ejpam-3485	129	6	,	,	PUNCT
ejpam-3485	129	7	γt(g	γt(g	NUM
ejpam-3485	129	8	)	)	PUNCT
ejpam-3485	129	9	=	=	SYM
ejpam-3485	129	10	|c|	|c|	PROPN
ejpam-3485	129	11	≤	≤	NUM
ejpam-3485	129	12	|c1|	|c1|	NOUN
ejpam-3485	129	13	.	.	PUNCT
ejpam-3485	130	1	this	this	PRON
ejpam-3485	130	2	implies	imply	VERB
ejpam-3485	130	3	that	that	SCONJ
ejpam-3485	130	4	c	c	PROPN
ejpam-3485	130	5	is	be	AUX
ejpam-3485	130	6	a	a	DET
ejpam-3485	130	7	γt	γt	NOUN
ejpam-3485	130	8	-	-	NOUN
ejpam-3485	130	9	set	set	NOUN
ejpam-3485	130	10	of	of	ADP
ejpam-3485	130	11	g[h	g[h	NOUN
ejpam-3485	130	12	]	]	PUNCT
ejpam-3485	130	13	.	.	PUNCT
ejpam-3485	131	1	�	�	PROPN
ejpam-3485	131	2	corollary	corollary	ADJ
ejpam-3485	131	3	2.5	2.5	NUM
ejpam-3485	131	4	.	.	PUNCT
ejpam-3485	132	1	let	let	VERB
ejpam-3485	132	2	g	g	NOUN
ejpam-3485	132	3	and	and	CCONJ
ejpam-3485	132	4	h	h	NOUN
ejpam-3485	132	5	be	be	AUX
ejpam-3485	132	6	nontrivial	nontrivial	ADJ
ejpam-3485	132	7	connected	connected	ADJ
ejpam-3485	132	8	graphs	graph	NOUN
ejpam-3485	132	9	.	.	PUNCT
ejpam-3485	133	1	then	then	ADV
ejpam-3485	133	2	γt(g[h	γt(g[h	NOUN
ejpam-3485	133	3	]	]	X
ejpam-3485	133	4	)	)	PUNCT
ejpam-3485	133	5	=	=	SYM
ejpam-3485	133	6	γt(g	γt(g	NUM
ejpam-3485	133	7	)	)	PUNCT
ejpam-3485	133	8	.	.	PUNCT
ejpam-3485	134	1	proof	proof	NOUN
ejpam-3485	134	2	.	.	PUNCT
ejpam-3485	135	1	let	let	VERB
ejpam-3485	135	2	s	s	PRON
ejpam-3485	135	3	be	be	AUX
ejpam-3485	135	4	a	a	DET
ejpam-3485	135	5	γt	γt	NOUN
ejpam-3485	135	6	-	-	NOUN
ejpam-3485	135	7	set	set	NOUN
ejpam-3485	135	8	of	of	ADP
ejpam-3485	135	9	g.	g.	PROPN
ejpam-3485	135	10	pick	pick	VERB
ejpam-3485	135	11	a	a	DET
ejpam-3485	135	12	∈	∈	PROPN
ejpam-3485	135	13	v	v	ADP
ejpam-3485	135	14	(	(	PUNCT
ejpam-3485	135	15	h	h	NOUN
ejpam-3485	135	16	)	)	PUNCT
ejpam-3485	135	17	and	and	CCONJ
ejpam-3485	135	18	set	set	VERB
ejpam-3485	135	19	tx	tx	PROPN
ejpam-3485	135	20	=	=	PUNCT
ejpam-3485	135	21	{	{	PUNCT
ejpam-3485	135	22	a	a	NOUN
ejpam-3485	135	23	}	}	PUNCT
ejpam-3485	135	24	and	and	CCONJ
ejpam-3485	135	25	c	c	NOUN
ejpam-3485	135	26	=	=	SYM
ejpam-3485	135	27	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	135	28	}	}	PUNCT
ejpam-3485	135	29	×	×	PROPN
ejpam-3485	135	30	tx	tx	PROPN
ejpam-3485	135	31	)	)	PUNCT
ejpam-3485	135	32	.	.	PUNCT
ejpam-3485	136	1	by	by	ADP
ejpam-3485	136	2	corollary	corollary	ADJ
ejpam-3485	136	3	2.3	2.3	NUM
ejpam-3485	136	4	and	and	CCONJ
ejpam-3485	136	5	corollary	corollary	ADJ
ejpam-3485	136	6	2.4	2.4	NUM
ejpam-3485	136	7	,	,	PUNCT
ejpam-3485	136	8	c	c	PROPN
ejpam-3485	136	9	is	be	AUX
ejpam-3485	136	10	γt	γt	NOUN
ejpam-3485	136	11	-	-	ADJ
ejpam-3485	136	12	set	set	NOUN
ejpam-3485	136	13	of	of	ADP
ejpam-3485	136	14	g[h	g[h	NOUN
ejpam-3485	136	15	]	]	PUNCT
ejpam-3485	136	16	.	.	PUNCT
ejpam-3485	137	1	thus	thus	ADV
ejpam-3485	137	2	,	,	PUNCT
ejpam-3485	137	3	γt(g[h	γt(g[h	NOUN
ejpam-3485	137	4	]	]	X
ejpam-3485	137	5	)	)	PUNCT
ejpam-3485	138	1	=	=	SYM
ejpam-3485	138	2	|c|	|c|	PROPN
ejpam-3485	138	3	=	=	SYM
ejpam-3485	138	4	|s|	|s|	PROPN
ejpam-3485	138	5	=	=	SYM
ejpam-3485	138	6	γt(g	γt(g	NUM
ejpam-3485	138	7	)	)	PUNCT
ejpam-3485	138	8	.	.	PUNCT
ejpam-3485	139	1	�	�	PROPN
ejpam-3485	139	2	theorem	theorem	VERB
ejpam-3485	139	3	2.6	2.6	NUM
ejpam-3485	139	4	.	.	PUNCT
ejpam-3485	140	1	let	let	VERB
ejpam-3485	140	2	g	g	NOUN
ejpam-3485	140	3	and	and	CCONJ
ejpam-3485	140	4	h	h	NOUN
ejpam-3485	140	5	be	be	AUX
ejpam-3485	140	6	nontrivial	nontrivial	ADJ
ejpam-3485	140	7	connected	connected	ADJ
ejpam-3485	140	8	graphs	graph	NOUN
ejpam-3485	140	9	.	.	PUNCT
ejpam-3485	141	1	then	then	ADV
ejpam-3485	141	2	fγt(g[h	fγt(g[h	NUM
ejpam-3485	141	3	]	]	PUNCT
ejpam-3485	141	4	)	)	PUNCT
ejpam-3485	141	5	=	=	SYM
ejpam-3485	141	6	γt(g	γt(g	NUM
ejpam-3485	141	7	)	)	PUNCT
ejpam-3485	141	8	.	.	PUNCT
ejpam-3485	142	1	c.	c.	PROPN
ejpam-3485	142	2	armada	armada	PROPN
ejpam-3485	142	3	,	,	PUNCT
ejpam-3485	142	4	s.	s.	PROPN
ejpam-3485	142	5	canoy	canoy	PROPN
ejpam-3485	142	6	jr	jr	PROPN
ejpam-3485	142	7	.	.	PROPN
ejpam-3485	142	8	,	,	PUNCT
ejpam-3485	142	9	c.	c.	PROPN
ejpam-3485	142	10	go	go	VERB
ejpam-3485	142	11	/	/	SYM
ejpam-3485	142	12	eur	eur	PROPN
ejpam-3485	142	13	.	.	PUNCT
ejpam-3485	143	1	j.	j.	PROPN
ejpam-3485	143	2	pure	pure	PROPN
ejpam-3485	143	3	appl	appl	PROPN
ejpam-3485	143	4	.	.	PROPN
ejpam-3485	143	5	math	math	PROPN
ejpam-3485	143	6	,	,	PUNCT
ejpam-3485	143	7	12	12	NUM
ejpam-3485	143	8	(	(	PUNCT
ejpam-3485	143	9	4	4	NUM
ejpam-3485	143	10	)	)	PUNCT
ejpam-3485	143	11	(	(	PUNCT
ejpam-3485	143	12	2019	2019	NUM
ejpam-3485	143	13	)	)	PUNCT
ejpam-3485	143	14	,	,	PUNCT
ejpam-3485	143	15	1779	1779	NUM
ejpam-3485	143	16	-	-	SYM
ejpam-3485	143	17	1786	1786	NUM
ejpam-3485	143	18	1783	1783	NUM
ejpam-3485	143	19	proof	proof	NOUN
ejpam-3485	143	20	.	.	PUNCT
ejpam-3485	144	1	let	let	VERB
ejpam-3485	144	2	c	c	NOUN
ejpam-3485	144	3	=	=	PUNCT
ejpam-3485	144	4	∪x∈s	∪x∈s	PROPN
ejpam-3485	144	5	[	[	X
ejpam-3485	144	6	{	{	PUNCT
ejpam-3485	144	7	x	x	NOUN
ejpam-3485	144	8	}	}	PUNCT
ejpam-3485	144	9	×	×	PROPN
ejpam-3485	144	10	tx	tx	PROPN
ejpam-3485	144	11	]	]	PUNCT
ejpam-3485	144	12	be	be	AUX
ejpam-3485	144	13	a	a	DET
ejpam-3485	144	14	γt	γt	NOUN
ejpam-3485	144	15	-	-	NOUN
ejpam-3485	144	16	set	set	NOUN
ejpam-3485	144	17	of	of	ADP
ejpam-3485	144	18	g[h	g[h	PROPN
ejpam-3485	144	19	]	]	PUNCT
ejpam-3485	144	20	and	and	CCONJ
ejpam-3485	144	21	let	let	VERB
ejpam-3485	144	22	rc	rc	PROPN
ejpam-3485	144	23	=	=	PROPN
ejpam-3485	144	24	∪x∈d[{x	∪x∈d[{x	PROPN
ejpam-3485	144	25	}	}	PUNCT
ejpam-3485	144	26	×rx	×rx	PROPN
ejpam-3485	144	27	]	]	PUNCT
ejpam-3485	144	28	be	be	VERB
ejpam-3485	144	29	a	a	DET
ejpam-3485	144	30	forcing	forcing	NOUN
ejpam-3485	144	31	subset	subset	NOUN
ejpam-3485	144	32	for	for	ADP
ejpam-3485	144	33	c.	c.	PROPN
ejpam-3485	144	34	first	first	ADV
ejpam-3485	144	35	,	,	PUNCT
ejpam-3485	144	36	suppose	suppose	VERB
ejpam-3485	144	37	that	that	SCONJ
ejpam-3485	144	38	s	s	VERB
ejpam-3485	144	39	is	be	AUX
ejpam-3485	144	40	a	a	DET
ejpam-3485	144	41	γt	γt	NOUN
ejpam-3485	144	42	-	-	NOUN
ejpam-3485	144	43	set	set	NOUN
ejpam-3485	144	44	of	of	ADP
ejpam-3485	144	45	g.	g.	PROPN
ejpam-3485	144	46	then	then	ADV
ejpam-3485	144	47	|tx|	|tx|	PROPN
ejpam-3485	144	48	=	=	PUNCT
ejpam-3485	144	49	1	1	NUM
ejpam-3485	144	50	for	for	ADP
ejpam-3485	144	51	all	all	DET
ejpam-3485	144	52	x	x	SYM
ejpam-3485	144	53	∈	∈	NOUN
ejpam-3485	144	54	s	s	X
ejpam-3485	144	55	by	by	ADP
ejpam-3485	144	56	corollaries	corollary	NOUN
ejpam-3485	144	57	2.3	2.3	NUM
ejpam-3485	144	58	(	(	PUNCT
ejpam-3485	144	59	i	i	NOUN
ejpam-3485	144	60	)	)	PUNCT
ejpam-3485	144	61	and	and	CCONJ
ejpam-3485	144	62	2.4	2.4	NUM
ejpam-3485	144	63	.	.	PUNCT
ejpam-3485	145	1	hence	hence	ADV
ejpam-3485	145	2	,	,	PUNCT
ejpam-3485	145	3	rx	rx	VERB
ejpam-3485	145	4	=	=	SYM
ejpam-3485	145	5	tx	tx	PROPN
ejpam-3485	145	6	for	for	ADP
ejpam-3485	145	7	all	all	DET
ejpam-3485	145	8	x	x	SYM
ejpam-3485	145	9	∈	∈	PROPN
ejpam-3485	145	10	d.	d.	NOUN
ejpam-3485	145	11	if	if	SCONJ
ejpam-3485	145	12	d	d	PROPN
ejpam-3485	145	13	6=	6=	PROPN
ejpam-3485	145	14	s	s	PART
ejpam-3485	145	15	,	,	PUNCT
ejpam-3485	145	16	say	say	VERB
ejpam-3485	145	17	y	y	PROPN
ejpam-3485	145	18	∈	∈	PROPN
ejpam-3485	145	19	s\d	s\d	NOUN
ejpam-3485	145	20	,	,	PUNCT
ejpam-3485	145	21	then	then	ADV
ejpam-3485	145	22	rc	rc	PROPN
ejpam-3485	145	23	⊆	⊆	NUM
ejpam-3485	145	24	c∗	c∗	PROPN
ejpam-3485	145	25	=	=	SYM
ejpam-3485	145	26	∪x∈s	∪x∈s	PROPN
ejpam-3485	145	27	[	[	X
ejpam-3485	145	28	{	{	PUNCT
ejpam-3485	145	29	x	x	NOUN
ejpam-3485	145	30	}	}	PUNCT
ejpam-3485	145	31	×	×	NOUN
ejpam-3485	145	32	t	t	NOUN
ejpam-3485	145	33	∗x	∗x	PROPN
ejpam-3485	145	34	]	]	PUNCT
ejpam-3485	145	35	,	,	PUNCT
ejpam-3485	145	36	where	where	SCONJ
ejpam-3485	145	37	t	t	NOUN
ejpam-3485	145	38	∗x	∗x	PROPN
ejpam-3485	145	39	=	=	SYM
ejpam-3485	145	40	tx	tx	VERB
ejpam-3485	145	41	for	for	ADP
ejpam-3485	145	42	x	x	PROPN
ejpam-3485	145	43	∈	∈	PROPN
ejpam-3485	145	44	s\{y	s\{y	X
ejpam-3485	145	45	}	}	PUNCT
ejpam-3485	145	46	and	and	CCONJ
ejpam-3485	145	47	t	t	PROPN
ejpam-3485	145	48	∗y	∗y	PROPN
ejpam-3485	145	49	is	be	AUX
ejpam-3485	145	50	a	a	DET
ejpam-3485	145	51	singleton	singleton	NOUN
ejpam-3485	145	52	subset	subset	NOUN
ejpam-3485	145	53	of	of	ADP
ejpam-3485	145	54	h	h	NOUN
ejpam-3485	145	55	different	different	ADJ
ejpam-3485	145	56	from	from	ADP
ejpam-3485	145	57	ty	ty	PRON
ejpam-3485	145	58	.	.	PUNCT
ejpam-3485	146	1	since	since	SCONJ
ejpam-3485	146	2	c∗	c∗	PROPN
ejpam-3485	146	3	is	be	AUX
ejpam-3485	146	4	a	a	DET
ejpam-3485	146	5	γt	γt	NOUN
ejpam-3485	146	6	-	-	NOUN
ejpam-3485	146	7	set	set	NOUN
ejpam-3485	146	8	of	of	ADP
ejpam-3485	146	9	g[h	g[h	NOUN
ejpam-3485	146	10	]	]	PUNCT
ejpam-3485	146	11	and	and	CCONJ
ejpam-3485	146	12	c∗	c∗	PROPN
ejpam-3485	146	13	6=	6=	PROPN
ejpam-3485	146	14	c	c	PROPN
ejpam-3485	146	15	,	,	PUNCT
ejpam-3485	146	16	rc	rc	PROPN
ejpam-3485	146	17	is	be	AUX
ejpam-3485	146	18	not	not	PART
ejpam-3485	146	19	a	a	DET
ejpam-3485	146	20	forcing	forcing	NOUN
ejpam-3485	146	21	subset	subset	NOUN
ejpam-3485	146	22	for	for	ADP
ejpam-3485	146	23	c	c	PROPN
ejpam-3485	146	24	,	,	PUNCT
ejpam-3485	146	25	contrary	contrary	ADV
ejpam-3485	146	26	to	to	ADP
ejpam-3485	146	27	the	the	DET
ejpam-3485	146	28	assumption	assumption	NOUN
ejpam-3485	146	29	.	.	PUNCT
ejpam-3485	147	1	thus	thus	ADV
ejpam-3485	147	2	,	,	PUNCT
ejpam-3485	147	3	d	d	PROPN
ejpam-3485	147	4	=	=	SYM
ejpam-3485	147	5	s	s	PROPN
ejpam-3485	147	6	,	,	PUNCT
ejpam-3485	147	7	that	that	ADV
ejpam-3485	147	8	is	is	ADV
ejpam-3485	147	9	,	,	PUNCT
ejpam-3485	147	10	rc	rc	PROPN
ejpam-3485	147	11	=	=	PROPN
ejpam-3485	147	12	c.	c.	PROPN
ejpam-3485	147	13	hence	hence	ADV
ejpam-3485	147	14	,	,	PUNCT
ejpam-3485	147	15	fγt(c	fγt(c	ADJ
ejpam-3485	147	16	)	)	PUNCT
ejpam-3485	147	17	=	=	SYM
ejpam-3485	147	18	|c|	|c|	PROPN
ejpam-3485	147	19	=	=	SYM
ejpam-3485	147	20	|s|	|s|	PROPN
ejpam-3485	147	21	=	=	PUNCT
ejpam-3485	147	22	γt(g	γt(g	NUM
ejpam-3485	147	23	)	)	PUNCT
ejpam-3485	147	24	=	=	PUNCT
ejpam-3485	147	25	fγt(g[h	fγt(g[h	NUM
ejpam-3485	147	26	]	]	PUNCT
ejpam-3485	147	27	)	)	PUNCT
ejpam-3485	147	28	.	.	PUNCT
ejpam-3485	148	1	next	next	ADV
ejpam-3485	148	2	,	,	PUNCT
ejpam-3485	148	3	suppose	suppose	VERB
ejpam-3485	148	4	that	that	SCONJ
ejpam-3485	148	5	s	s	VERB
ejpam-3485	148	6	is	be	AUX
ejpam-3485	148	7	a	a	DET
ejpam-3485	148	8	dominating	dominating	NOUN
ejpam-3485	148	9	(	(	PUNCT
ejpam-3485	148	10	not	not	PART
ejpam-3485	148	11	a	a	DET
ejpam-3485	148	12	total	total	ADJ
ejpam-3485	148	13	dominating	dominating	NOUN
ejpam-3485	148	14	)	)	PUNCT
ejpam-3485	148	15	set	set	NOUN
ejpam-3485	148	16	of	of	ADP
ejpam-3485	148	17	g	g	NOUN
ejpam-3485	148	18	such	such	ADJ
ejpam-3485	148	19	that	that	DET
ejpam-3485	148	20	|s	|s	PROPN
ejpam-3485	148	21	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3485	148	22	2|s\ng(s)|	2|s\ng(s)|	NUM
ejpam-3485	148	23	=	=	PUNCT
ejpam-3485	148	24	γt(g	γt(g	NUM
ejpam-3485	148	25	)	)	PUNCT
ejpam-3485	148	26	.	.	PUNCT
ejpam-3485	149	1	then	then	ADV
ejpam-3485	149	2	|tx|	|tx|	X
ejpam-3485	149	3	=	=	PUNCT
ejpam-3485	149	4	1	1	NUM
ejpam-3485	149	5	for	for	ADP
ejpam-3485	149	6	all	all	DET
ejpam-3485	149	7	x	x	SYM
ejpam-3485	149	8	∈	∈	NOUN
ejpam-3485	149	9	s	s	NOUN
ejpam-3485	149	10	∩ng(s	∩ng(s	NOUN
ejpam-3485	149	11	)	)	PUNCT
ejpam-3485	149	12	and	and	CCONJ
ejpam-3485	149	13	tx	tx	PROPN
ejpam-3485	149	14	is	be	AUX
ejpam-3485	149	15	a	a	DET
ejpam-3485	149	16	γt	γt	NOUN
ejpam-3485	149	17	-	-	NOUN
ejpam-3485	149	18	set	set	NOUN
ejpam-3485	149	19	of	of	ADP
ejpam-3485	149	20	h	h	NOUN
ejpam-3485	149	21	for	for	ADP
ejpam-3485	149	22	each	each	DET
ejpam-3485	149	23	x	x	SYM
ejpam-3485	149	24	∈	∈	PROPN
ejpam-3485	149	25	s\ng(s	s\ng(s	NOUN
ejpam-3485	149	26	)	)	PUNCT
ejpam-3485	149	27	by	by	ADP
ejpam-3485	149	28	corollary	corollary	ADJ
ejpam-3485	149	29	2.3(ii	2.3(ii	NUM
ejpam-3485	149	30	)	)	PUNCT
ejpam-3485	149	31	.	.	PUNCT
ejpam-3485	150	1	(	(	PUNCT
ejpam-3485	150	2	note	note	VERB
ejpam-3485	150	3	that	that	SCONJ
ejpam-3485	150	4	in	in	ADP
ejpam-3485	150	5	this	this	DET
ejpam-3485	150	6	case	case	NOUN
ejpam-3485	150	7	,	,	PUNCT
ejpam-3485	150	8	γt(h	γt(h	NUM
ejpam-3485	150	9	)	)	PUNCT
ejpam-3485	150	10	=	=	SYM
ejpam-3485	150	11	2	2	NUM
ejpam-3485	150	12	)	)	PUNCT
ejpam-3485	150	13	.	.	PUNCT
ejpam-3485	151	1	let	let	VERB
ejpam-3485	151	2	c	c	NOUN
ejpam-3485	151	3	=	=	PROPN
ejpam-3485	151	4	c1	c1	PROPN
ejpam-3485	151	5	∪	∪	PROPN
ejpam-3485	151	6	c2	c2	PROPN
ejpam-3485	151	7	where	where	SCONJ
ejpam-3485	151	8	c1	c1	NOUN
ejpam-3485	151	9	=	=	SYM
ejpam-3485	151	10	∪x∈s∩ng(s)[{x	∪x∈s∩ng(s)[{x	NUM
ejpam-3485	151	11	}	}	PUNCT
ejpam-3485	151	12	×	×	PROPN
ejpam-3485	151	13	tx	tx	PROPN
ejpam-3485	151	14	]	]	PUNCT
ejpam-3485	151	15	and	and	CCONJ
ejpam-3485	151	16	c2	c2	PROPN
ejpam-3485	151	17	=	=	SYM
ejpam-3485	151	18	∪x∈s\ng(s)[{x	∪x∈s\ng(s)[{x	PROPN
ejpam-3485	151	19	}	}	PUNCT
ejpam-3485	151	20	×	×	NOUN
ejpam-3485	151	21	tx	tx	PROPN
ejpam-3485	151	22	]	]	PUNCT
ejpam-3485	151	23	.	.	PUNCT
ejpam-3485	152	1	clearly	clearly	ADV
ejpam-3485	152	2	,	,	PUNCT
ejpam-3485	152	3	s	s	NOUN
ejpam-3485	152	4	∩ng(s	∩ng(s	NOUN
ejpam-3485	152	5	)	)	PUNCT
ejpam-3485	152	6	⊆	⊆	NUM
ejpam-3485	152	7	d	d	NOUN
ejpam-3485	152	8	,	,	PUNCT
ejpam-3485	152	9	that	that	ADV
ejpam-3485	152	10	is	is	ADV
ejpam-3485	152	11	,	,	PUNCT
ejpam-3485	152	12	c1	c1	PROPN
ejpam-3485	152	13	⊆	⊆	NUM
ejpam-3485	152	14	rc	rc	PROPN
ejpam-3485	152	15	.	.	PUNCT
ejpam-3485	153	1	now	now	ADV
ejpam-3485	153	2	,	,	PUNCT
ejpam-3485	153	3	choose	choose	VERB
ejpam-3485	153	4	vy	vy	NOUN
ejpam-3485	153	5	∈	∈	PROPN
ejpam-3485	153	6	ng(y	ng(y	NOUN
ejpam-3485	153	7	)	)	PUNCT
ejpam-3485	153	8	for	for	ADP
ejpam-3485	153	9	each	each	DET
ejpam-3485	153	10	y	y	PROPN
ejpam-3485	153	11	∈	∈	PROPN
ejpam-3485	153	12	s	s	PART
ejpam-3485	153	13	\ng(s	\ng(s	NOUN
ejpam-3485	153	14	)	)	PUNCT
ejpam-3485	153	15	and	and	CCONJ
ejpam-3485	153	16	let	let	VERB
ejpam-3485	153	17	fs	fs	VERB
ejpam-3485	153	18	=	=	PUNCT
ejpam-3485	153	19	{	{	PUNCT
ejpam-3485	153	20	vy	vy	X
ejpam-3485	153	21	:	:	PUNCT
ejpam-3485	153	22	y	y	PROPN
ejpam-3485	153	23	∈	∈	PROPN
ejpam-3485	153	24	s	s	PART
ejpam-3485	153	25	\	\	NOUN
ejpam-3485	153	26	ng(s	ng(s	NUM
ejpam-3485	153	27	)	)	PUNCT
ejpam-3485	153	28	}	}	PUNCT
ejpam-3485	153	29	.	.	PUNCT
ejpam-3485	154	1	clearly	clearly	ADV
ejpam-3485	154	2	,	,	PUNCT
ejpam-3485	154	3	s	s	VERB
ejpam-3485	154	4	∩	∩	ADJ
ejpam-3485	154	5	fs	fs	AUX
ejpam-3485	154	6	=	=	PUNCT
ejpam-3485	154	7	∅.	∅.	AUX
ejpam-3485	154	8	suppose	suppose	VERB
ejpam-3485	154	9	that	that	SCONJ
ejpam-3485	154	10	|fs	|fs	PRON
ejpam-3485	154	11	|	|	ADV
ejpam-3485	154	12	<	<	X
ejpam-3485	154	13	|s	|s	PROPN
ejpam-3485	154	14	\	\	PROPN
ejpam-3485	154	15	ng(s)|	ng(s)|	PROPN
ejpam-3485	154	16	.	.	PUNCT
ejpam-3485	155	1	then	then	ADV
ejpam-3485	155	2	there	there	PRON
ejpam-3485	155	3	exist	exist	VERB
ejpam-3485	155	4	distinct	distinct	ADJ
ejpam-3485	155	5	y1	y1	NOUN
ejpam-3485	155	6	,	,	PUNCT
ejpam-3485	155	7	y2	y2	PROPN
ejpam-3485	155	8	∈	∈	PROPN
ejpam-3485	155	9	s	s	PART
ejpam-3485	155	10	\ng(s	\ng(s	NOUN
ejpam-3485	155	11	)	)	PUNCT
ejpam-3485	155	12	such	such	ADJ
ejpam-3485	155	13	that	that	DET
ejpam-3485	155	14	vy1	vy1	NOUN
ejpam-3485	155	15	=	=	SYM
ejpam-3485	155	16	vy2	vy2	NOUN
ejpam-3485	155	17	.	.	PUNCT
ejpam-3485	156	1	let	let	VERB
ejpam-3485	156	2	s0	s0	PROPN
ejpam-3485	156	3	=	=	PUNCT
ejpam-3485	156	4	s	s	PART
ejpam-3485	156	5	∪	∪	NOUN
ejpam-3485	156	6	fs	f	NOUN
ejpam-3485	156	7	.	.	PUNCT
ejpam-3485	157	1	then	then	ADV
ejpam-3485	157	2	|s0|	|s0|	VERB
ejpam-3485	157	3	=	=	SYM
ejpam-3485	157	4	|s|+	|s|+	PROPN
ejpam-3485	157	5	|fs	|fs	X
ejpam-3485	157	6	|	|	ADV
ejpam-3485	157	7	<	<	X
ejpam-3485	157	8	|s	|s	PROPN
ejpam-3485	157	9	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3485	158	1	2|s\ng(s)|	2|s\ng(s)|	NUM
ejpam-3485	158	2	=	=	PUNCT
ejpam-3485	158	3	γt(g	γt(g	NUM
ejpam-3485	158	4	)	)	PUNCT
ejpam-3485	158	5	.	.	PUNCT
ejpam-3485	159	1	this	this	PRON
ejpam-3485	159	2	is	be	AUX
ejpam-3485	159	3	a	a	DET
ejpam-3485	159	4	contradiction	contradiction	NOUN
ejpam-3485	159	5	because	because	SCONJ
ejpam-3485	159	6	s0	s0	PROPN
ejpam-3485	159	7	is	be	AUX
ejpam-3485	159	8	a	a	DET
ejpam-3485	159	9	total	total	ADJ
ejpam-3485	159	10	dominating	dominating	NOUN
ejpam-3485	159	11	set	set	NOUN
ejpam-3485	159	12	of	of	ADP
ejpam-3485	159	13	g.	g.	PROPN
ejpam-3485	159	14	thus	thus	ADV
ejpam-3485	159	15	,	,	PUNCT
ejpam-3485	159	16	|fs	|fs	PRON
ejpam-3485	159	17	|	|	ADV
ejpam-3485	159	18	=	=	SYM
ejpam-3485	159	19	|s	|s	PROPN
ejpam-3485	160	1	\ng(s)|	\ng(s)|	INTJ
ejpam-3485	161	1	(	(	PUNCT
ejpam-3485	161	2	hence	hence	ADV
ejpam-3485	161	3	,	,	PUNCT
ejpam-3485	161	4	the	the	DET
ejpam-3485	161	5	vy	vy	NOUN
ejpam-3485	161	6	’s	’s	PART
ejpam-3485	161	7	are	be	AUX
ejpam-3485	161	8	distinct	distinct	ADJ
ejpam-3485	161	9	)	)	PUNCT
ejpam-3485	161	10	.	.	PUNCT
ejpam-3485	162	1	next	next	ADV
ejpam-3485	162	2	,	,	PUNCT
ejpam-3485	162	3	suppose	suppose	VERB
ejpam-3485	162	4	that	that	SCONJ
ejpam-3485	162	5	there	there	PRON
ejpam-3485	162	6	exists	exist	VERB
ejpam-3485	162	7	q	q	PROPN
ejpam-3485	162	8	∈	∈	PROPN
ejpam-3485	162	9	s	s	PART
ejpam-3485	162	10	\	\	NOUN
ejpam-3485	162	11	ng(s	ng(s	PRON
ejpam-3485	162	12	)	)	PUNCT
ejpam-3485	162	13	such	such	ADJ
ejpam-3485	162	14	that	that	SCONJ
ejpam-3485	162	15	{	{	PUNCT
ejpam-3485	162	16	q	q	NOUN
ejpam-3485	162	17	}	}	PUNCT
ejpam-3485	162	18	×	×	NOUN
ejpam-3485	162	19	tq	tq	ADP
ejpam-3485	162	20	is	be	AUX
ejpam-3485	162	21	not	not	PART
ejpam-3485	162	22	contained	contain	VERB
ejpam-3485	162	23	in	in	ADP
ejpam-3485	162	24	rc	rc	PROPN
ejpam-3485	162	25	.	.	PUNCT
ejpam-3485	163	1	let	let	VERB
ejpam-3485	163	2	tq	tq	INTJ
ejpam-3485	163	3	=	=	VERB
ejpam-3485	163	4	{	{	PUNCT
ejpam-3485	163	5	a	a	DET
ejpam-3485	163	6	,	,	PUNCT
ejpam-3485	163	7	b	b	NOUN
ejpam-3485	163	8	}	}	PUNCT
ejpam-3485	163	9	and	and	CCONJ
ejpam-3485	163	10	suppose	suppose	VERB
ejpam-3485	163	11	,	,	PUNCT
ejpam-3485	163	12	without	without	ADP
ejpam-3485	163	13	loss	loss	NOUN
ejpam-3485	163	14	of	of	ADP
ejpam-3485	163	15	generality	generality	NOUN
ejpam-3485	163	16	,	,	PUNCT
ejpam-3485	163	17	that	that	SCONJ
ejpam-3485	163	18	(	(	PUNCT
ejpam-3485	163	19	q	q	X
ejpam-3485	163	20	,	,	PUNCT
ejpam-3485	163	21	a	a	PRON
ejpam-3485	163	22	)	)	PUNCT
ejpam-3485	163	23	/∈	/∈	PUNCT
ejpam-3485	164	1	rc	rc	PROPN
ejpam-3485	164	2	.	.	PUNCT
ejpam-3485	165	1	let	let	VERB
ejpam-3485	165	2	sq	sq	INTJ
ejpam-3485	165	3	=	=	VERB
ejpam-3485	165	4	s	s	NOUN
ejpam-3485	165	5	∪	∪	X
ejpam-3485	165	6	{	{	PUNCT
ejpam-3485	165	7	vq	vq	NOUN
ejpam-3485	165	8	}	}	PUNCT
ejpam-3485	165	9	and	and	CCONJ
ejpam-3485	165	10	set	set	VERB
ejpam-3485	165	11	rq	rq	NOUN
ejpam-3485	165	12	=	=	PUNCT
ejpam-3485	165	13	{	{	PUNCT
ejpam-3485	165	14	b	b	NOUN
ejpam-3485	165	15	}	}	PUNCT
ejpam-3485	165	16	,	,	PUNCT
ejpam-3485	165	17	rvq	rvq	PROPN
ejpam-3485	165	18	=	=	PUNCT
ejpam-3485	165	19	{	{	PUNCT
ejpam-3485	165	20	a	a	NOUN
ejpam-3485	165	21	}	}	PUNCT
ejpam-3485	165	22	,	,	PUNCT
ejpam-3485	165	23	rx	rx	VERB
ejpam-3485	165	24	=	=	SYM
ejpam-3485	165	25	tx	tx	PROPN
ejpam-3485	165	26	for	for	ADP
ejpam-3485	165	27	each	each	DET
ejpam-3485	165	28	x	x	SYM
ejpam-3485	165	29	∈	∈	PROPN
ejpam-3485	165	30	s	s	PART
ejpam-3485	165	31	{	{	PUNCT
ejpam-3485	165	32	q	q	NOUN
ejpam-3485	165	33	}	}	PUNCT
ejpam-3485	165	34	,	,	PUNCT
ejpam-3485	165	35	and	and	CCONJ
ejpam-3485	165	36	cq	cq	NOUN
ejpam-3485	165	37	=	=	SYM
ejpam-3485	165	38	∪x∈sq	∪x∈sq	PROPN
ejpam-3485	165	39	[	[	X
ejpam-3485	165	40	{	{	PUNCT
ejpam-3485	165	41	x	x	NOUN
ejpam-3485	165	42	}	}	PUNCT
ejpam-3485	165	43	×	×	NOUN
ejpam-3485	165	44	rx	rx	NOUN
ejpam-3485	165	45	]	]	PUNCT
ejpam-3485	165	46	.	.	PUNCT
ejpam-3485	166	1	then	then	ADV
ejpam-3485	166	2	sq	sq	PROPN
ejpam-3485	166	3	∩	∩	ADJ
ejpam-3485	166	4	ng(sq	ng(sq	NOUN
ejpam-3485	166	5	)	)	PUNCT
ejpam-3485	166	6	=	=	PUNCT
ejpam-3485	167	1	[	[	X
ejpam-3485	167	2	s	s	X
ejpam-3485	167	3	∩	∩	NOUN
ejpam-3485	167	4	ng(s	ng(s	NUM
ejpam-3485	167	5	)	)	PUNCT
ejpam-3485	167	6	]	]	PUNCT
ejpam-3485	167	7	∪	∪	X
ejpam-3485	167	8	{	{	PUNCT
ejpam-3485	167	9	q	q	NOUN
ejpam-3485	167	10	,	,	PUNCT
ejpam-3485	167	11	vq	vq	NOUN
ejpam-3485	167	12	}	}	PUNCT
ejpam-3485	167	13	and	and	CCONJ
ejpam-3485	167	14	sq	sq	ADJ
ejpam-3485	167	15	\ng(sq	\ng(sq	NOUN
ejpam-3485	167	16	)	)	PUNCT
ejpam-3485	167	17	=	=	PRON
ejpam-3485	168	1	(	(	PUNCT
ejpam-3485	168	2	s	s	NOUN
ejpam-3485	168	3	\ng(s	\ng(s	NUM
ejpam-3485	168	4	)	)	PUNCT
ejpam-3485	168	5	)	)	PUNCT
ejpam-3485	168	6	\	\	NOUN
ejpam-3485	169	1	{	{	PUNCT
ejpam-3485	169	2	q	q	NOUN
ejpam-3485	169	3	}	}	PUNCT
ejpam-3485	169	4	.	.	PUNCT
ejpam-3485	170	1	hence	hence	ADV
ejpam-3485	170	2	,	,	PUNCT
ejpam-3485	170	3	|sq	|sq	X
ejpam-3485	170	4	∩ng(sq)|+	∩ng(sq)|+	SYM
ejpam-3485	170	5	2|sq\ng(sq)|	2|sq\ng(sq)|	NUM
ejpam-3485	170	6	=	=	SYM
ejpam-3485	170	7	|s	|s	PROPN
ejpam-3485	170	8	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3485	170	9	2	2	NUM
ejpam-3485	171	1	+	+	CCONJ
ejpam-3485	171	2	2|s\ng(s)|	2|s\ng(s)|	NUM
ejpam-3485	171	3	−	−	NOUN
ejpam-3485	171	4	2	2	NUM
ejpam-3485	171	5	=	=	NUM
ejpam-3485	171	6	γt(g	γt(g	NUM
ejpam-3485	171	7	)	)	PUNCT
ejpam-3485	171	8	.	.	PUNCT
ejpam-3485	172	1	thus	thus	ADV
ejpam-3485	172	2	,	,	PUNCT
ejpam-3485	172	3	cq	cq	PROPN
ejpam-3485	172	4	is	be	AUX
ejpam-3485	172	5	a	a	DET
ejpam-3485	172	6	γt	γt	NOUN
ejpam-3485	172	7	-	-	NOUN
ejpam-3485	172	8	set	set	NOUN
ejpam-3485	172	9	of	of	ADP
ejpam-3485	172	10	g[h	g[h	NOUN
ejpam-3485	172	11	]	]	PUNCT
ejpam-3485	172	12	by	by	ADP
ejpam-3485	172	13	corollaries	corollary	NOUN
ejpam-3485	172	14	2.3	2.3	NUM
ejpam-3485	172	15	and	and	CCONJ
ejpam-3485	172	16	2.4	2.4	NUM
ejpam-3485	172	17	,	,	PUNCT
ejpam-3485	172	18	cq	cq	PROPN
ejpam-3485	172	19	6=	6=	PROPN
ejpam-3485	172	20	c	c	X
ejpam-3485	172	21	,	,	PUNCT
ejpam-3485	172	22	and	and	CCONJ
ejpam-3485	172	23	rc	rc	PROPN
ejpam-3485	172	24	⊆	⊆	NUM
ejpam-3485	172	25	cq	cq	PROPN
ejpam-3485	172	26	.	.	PUNCT
ejpam-3485	173	1	this	this	PRON
ejpam-3485	173	2	implies	imply	VERB
ejpam-3485	173	3	that	that	SCONJ
ejpam-3485	173	4	rc	rc	PROPN
ejpam-3485	173	5	is	be	AUX
ejpam-3485	173	6	not	not	PART
ejpam-3485	173	7	a	a	DET
ejpam-3485	173	8	forcing	forcing	NOUN
ejpam-3485	173	9	subset	subset	NOUN
ejpam-3485	173	10	for	for	ADP
ejpam-3485	173	11	c	c	PROPN
ejpam-3485	173	12	,	,	PUNCT
ejpam-3485	173	13	contrary	contrary	ADV
ejpam-3485	173	14	to	to	ADP
ejpam-3485	173	15	the	the	DET
ejpam-3485	173	16	assumption	assumption	NOUN
ejpam-3485	173	17	that	that	SCONJ
ejpam-3485	173	18	it	it	PRON
ejpam-3485	173	19	is	be	AUX
ejpam-3485	173	20	.	.	PUNCT
ejpam-3485	174	1	therefore	therefore	ADV
ejpam-3485	174	2	c2	c2	PROPN
ejpam-3485	174	3	⊆	⊆	NUM
ejpam-3485	174	4	rc	rc	PROPN
ejpam-3485	174	5	,	,	PUNCT
ejpam-3485	174	6	showing	show	VERB
ejpam-3485	174	7	that	that	DET
ejpam-3485	174	8	rc	rc	PROPN
ejpam-3485	174	9	=	=	PROPN
ejpam-3485	174	10	c.	c.	PROPN
ejpam-3485	174	11	accordingly	accordingly	ADV
ejpam-3485	174	12	,	,	PUNCT
ejpam-3485	174	13	fγt(g[h	fγt(g[h	NUM
ejpam-3485	174	14	]	]	PUNCT
ejpam-3485	174	15	)	)	PUNCT
ejpam-3485	174	16	=	=	SYM
ejpam-3485	174	17	|c|	|c|	PROPN
ejpam-3485	174	18	=	=	PUNCT
ejpam-3485	174	19	γt(g	γt(g	NUM
ejpam-3485	174	20	)	)	PUNCT
ejpam-3485	174	21	.	.	PUNCT
ejpam-3485	175	1	�	�	PROPN
ejpam-3485	175	2	3	3	NUM
ejpam-3485	175	3	.	.	PUNCT
ejpam-3485	175	4	connected	connect	VERB
ejpam-3485	175	5	domination	domination	NOUN
ejpam-3485	175	6	in	in	ADP
ejpam-3485	175	7	the	the	DET
ejpam-3485	175	8	lexicographic	lexicographic	ADJ
ejpam-3485	175	9	product	product	NOUN
ejpam-3485	175	10	of	of	ADP
ejpam-3485	175	11	graphs	graph	NOUN
ejpam-3485	175	12	theorem	theorem	VERB
ejpam-3485	175	13	3.1	3.1	NUM
ejpam-3485	175	14	.	.	PUNCT
ejpam-3485	176	1	let	let	VERB
ejpam-3485	176	2	g	g	NOUN
ejpam-3485	176	3	and	and	CCONJ
ejpam-3485	176	4	h	h	NOUN
ejpam-3485	176	5	be	be	AUX
ejpam-3485	176	6	nontrivial	nontrivial	ADJ
ejpam-3485	176	7	connected	connected	ADJ
ejpam-3485	176	8	graphs	graph	NOUN
ejpam-3485	176	9	.	.	PUNCT
ejpam-3485	177	1	then	then	ADV
ejpam-3485	177	2	c	c	X
ejpam-3485	177	3	=	=	SYM
ejpam-3485	177	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	177	5	}	}	PUNCT
ejpam-3485	177	6	×	×	NOUN
ejpam-3485	177	7	tx	tx	PROPN
ejpam-3485	177	8	)	)	PUNCT
ejpam-3485	177	9	⊆	⊆	NUM
ejpam-3485	177	10	v	v	NOUN
ejpam-3485	177	11	(	(	PUNCT
ejpam-3485	177	12	g[h	g[h	PROPN
ejpam-3485	177	13	]	]	PUNCT
ejpam-3485	177	14	)	)	PUNCT
ejpam-3485	177	15	,	,	PUNCT
ejpam-3485	177	16	where	where	SCONJ
ejpam-3485	177	17	s	s	VERB
ejpam-3485	177	18	⊆	⊆	NUM
ejpam-3485	177	19	v	v	NOUN
ejpam-3485	177	20	(	(	PUNCT
ejpam-3485	177	21	g	g	NOUN
ejpam-3485	177	22	)	)	PUNCT
ejpam-3485	177	23	and	and	CCONJ
ejpam-3485	177	24	tx	tx	VERB
ejpam-3485	177	25	⊆	⊆	NUM
ejpam-3485	177	26	v	v	NOUN
ejpam-3485	177	27	(	(	PUNCT
ejpam-3485	177	28	h	h	NOUN
ejpam-3485	177	29	)	)	PUNCT
ejpam-3485	177	30	for	for	ADP
ejpam-3485	177	31	every	every	DET
ejpam-3485	177	32	x	x	SYM
ejpam-3485	177	33	∈	∈	PROPN
ejpam-3485	177	34	s	s	NOUN
ejpam-3485	177	35	,	,	PUNCT
ejpam-3485	177	36	is	be	AUX
ejpam-3485	177	37	a	a	DET
ejpam-3485	177	38	connected	connected	ADJ
ejpam-3485	177	39	dominating	dominating	NOUN
ejpam-3485	177	40	set	set	NOUN
ejpam-3485	177	41	of	of	ADP
ejpam-3485	177	42	g[h	g[h	PROPN
ejpam-3485	177	43	]	]	PUNCT
ejpam-3485	177	44	if	if	SCONJ
ejpam-3485	178	1	and	and	CCONJ
ejpam-3485	178	2	only	only	ADV
ejpam-3485	178	3	if	if	SCONJ
ejpam-3485	178	4	s	s	NOUN
ejpam-3485	178	5	is	be	AUX
ejpam-3485	178	6	a	a	DET
ejpam-3485	178	7	connected	connected	ADJ
ejpam-3485	178	8	dominating	dominating	NOUN
ejpam-3485	178	9	set	set	NOUN
ejpam-3485	178	10	of	of	ADP
ejpam-3485	178	11	g	g	NOUN
ejpam-3485	178	12	,	,	PUNCT
ejpam-3485	178	13	where	where	SCONJ
ejpam-3485	178	14	tx	tx	PROPN
ejpam-3485	178	15	is	be	AUX
ejpam-3485	178	16	a	a	DET
ejpam-3485	178	17	connected	connected	ADJ
ejpam-3485	178	18	dominating	dominating	NOUN
ejpam-3485	178	19	set	set	NOUN
ejpam-3485	178	20	of	of	ADP
ejpam-3485	178	21	h	h	NOUN
ejpam-3485	178	22	whenever	whenever	SCONJ
ejpam-3485	178	23	|s|	|s|	PROPN
ejpam-3485	178	24	=	=	SYM
ejpam-3485	178	25	1	1	NUM
ejpam-3485	178	26	.	.	PUNCT
ejpam-3485	179	1	proof	proof	NOUN
ejpam-3485	179	2	.	.	PUNCT
ejpam-3485	180	1	suppose	suppose	VERB
ejpam-3485	180	2	that	that	SCONJ
ejpam-3485	180	3	c	c	AUX
ejpam-3485	180	4	=	=	SYM
ejpam-3485	180	5	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-3485	180	6	)	)	PUNCT
ejpam-3485	180	7	⊆	⊆	NUM
ejpam-3485	180	8	v	v	NOUN
ejpam-3485	180	9	(	(	PUNCT
ejpam-3485	180	10	g[h	g[h	PROPN
ejpam-3485	180	11	]	]	PUNCT
ejpam-3485	180	12	)	)	PUNCT
ejpam-3485	180	13	,	,	PUNCT
ejpam-3485	180	14	where	where	SCONJ
ejpam-3485	180	15	s	s	VERB
ejpam-3485	180	16	⊆	⊆	NUM
ejpam-3485	180	17	v	v	NOUN
ejpam-3485	180	18	(	(	PUNCT
ejpam-3485	180	19	g	g	NOUN
ejpam-3485	180	20	)	)	PUNCT
ejpam-3485	180	21	and	and	CCONJ
ejpam-3485	180	22	tx	tx	VERB
ejpam-3485	180	23	⊆	⊆	NUM
ejpam-3485	180	24	v	v	NOUN
ejpam-3485	180	25	(	(	PUNCT
ejpam-3485	180	26	h	h	NOUN
ejpam-3485	180	27	)	)	PUNCT
ejpam-3485	180	28	for	for	ADP
ejpam-3485	180	29	every	every	DET
ejpam-3485	180	30	x	x	SYM
ejpam-3485	180	31	∈	∈	PROPN
ejpam-3485	180	32	s	s	NOUN
ejpam-3485	180	33	,	,	PUNCT
ejpam-3485	180	34	is	be	AUX
ejpam-3485	180	35	a	a	DET
ejpam-3485	180	36	connected	connected	ADJ
ejpam-3485	180	37	dominating	dominating	NOUN
ejpam-3485	180	38	set	set	NOUN
ejpam-3485	180	39	of	of	ADP
ejpam-3485	180	40	g[h	g[h	PROPN
ejpam-3485	180	41	]	]	PUNCT
ejpam-3485	180	42	.	.	PUNCT
ejpam-3485	181	1	then	then	ADV
ejpam-3485	181	2	,	,	PUNCT
ejpam-3485	181	3	clearly	clearly	ADV
ejpam-3485	181	4	,	,	PUNCT
ejpam-3485	181	5	s	s	VERB
ejpam-3485	181	6	is	be	AUX
ejpam-3485	181	7	a	a	DET
ejpam-3485	181	8	dominating	dominating	NOUN
ejpam-3485	181	9	set	set	VERB
ejpam-3485	181	10	in	in	ADP
ejpam-3485	181	11	g.	g.	PROPN
ejpam-3485	181	12	let	let	VERB
ejpam-3485	181	13	x	x	PRON
ejpam-3485	181	14	,	,	PUNCT
ejpam-3485	181	15	y	y	PROPN
ejpam-3485	181	16	∈	∈	PROPN
ejpam-3485	181	17	s	s	PROPN
ejpam-3485	181	18	,	,	PUNCT
ejpam-3485	181	19	where	where	SCONJ
ejpam-3485	181	20	x	x	X
ejpam-3485	181	21	6=	6=	ADP
ejpam-3485	181	22	y	y	PROPN
ejpam-3485	181	23	and	and	CCONJ
ejpam-3485	181	24	xy	xy	PROPN
ejpam-3485	181	25	/∈	/∈	PUNCT
ejpam-3485	181	26	e(g	e(g	PROPN
ejpam-3485	181	27	)	)	PUNCT
ejpam-3485	181	28	.	.	PUNCT
ejpam-3485	182	1	let	let	VERB
ejpam-3485	182	2	a	a	DET
ejpam-3485	182	3	∈	∈	PROPN
ejpam-3485	182	4	tx	tx	NOUN
ejpam-3485	182	5	and	and	CCONJ
ejpam-3485	182	6	b	b	X
ejpam-3485	182	7	∈	∈	PROPN
ejpam-3485	183	1	ty	ty	INTJ
ejpam-3485	183	2	.	.	PUNCT
ejpam-3485	184	1	then	then	ADV
ejpam-3485	184	2	(	(	PUNCT
ejpam-3485	184	3	x	x	X
ejpam-3485	184	4	,	,	PUNCT
ejpam-3485	184	5	a	a	PRON
ejpam-3485	184	6	)	)	PUNCT
ejpam-3485	184	7	,	,	PUNCT
ejpam-3485	184	8	(	(	PUNCT
ejpam-3485	184	9	y	y	PROPN
ejpam-3485	184	10	,	,	PUNCT
ejpam-3485	184	11	b	b	NOUN
ejpam-3485	184	12	)	)	PUNCT
ejpam-3485	184	13	∈	∈	PROPN
ejpam-3485	184	14	c	c	NOUN
ejpam-3485	184	15	,	,	PUNCT
ejpam-3485	184	16	(	(	PUNCT
ejpam-3485	184	17	x	x	NOUN
ejpam-3485	184	18	,	,	PUNCT
ejpam-3485	184	19	a	a	PRON
ejpam-3485	184	20	)	)	PUNCT
ejpam-3485	184	21	6=	6=	ADP
ejpam-3485	184	22	(	(	PUNCT
ejpam-3485	184	23	y	y	PROPN
ejpam-3485	184	24	,	,	PUNCT
ejpam-3485	184	25	b	b	NOUN
ejpam-3485	184	26	)	)	PUNCT
ejpam-3485	184	27	and	and	CCONJ
ejpam-3485	184	28	(	(	PUNCT
ejpam-3485	184	29	x	x	X
ejpam-3485	184	30	,	,	PUNCT
ejpam-3485	184	31	a)(y	a)(y	PROPN
ejpam-3485	184	32	,	,	PUNCT
ejpam-3485	184	33	b	b	NOUN
ejpam-3485	184	34	)	)	PUNCT
ejpam-3485	184	35	/∈	/∈	PUNCT
ejpam-3485	184	36	e(g[h	e(g[h	NOUN
ejpam-3485	184	37	]	]	PUNCT
ejpam-3485	184	38	)	)	PUNCT
ejpam-3485	184	39	.	.	PUNCT
ejpam-3485	185	1	since	since	SCONJ
ejpam-3485	185	2	〈	〈	PROPN
ejpam-3485	185	3	c	c	PROPN
ejpam-3485	185	4	〉	〉	PROPN
ejpam-3485	185	5	is	be	AUX
ejpam-3485	185	6	connected	connect	VERB
ejpam-3485	185	7	,	,	PUNCT
ejpam-3485	185	8	there	there	PRON
ejpam-3485	185	9	exists	exist	VERB
ejpam-3485	185	10	an	an	DET
ejpam-3485	185	11	(	(	PUNCT
ejpam-3485	185	12	x	x	NOUN
ejpam-3485	185	13	,	,	PUNCT
ejpam-3485	185	14	a)-(y	a)-(y	PROPN
ejpam-3485	185	15	,	,	PUNCT
ejpam-3485	185	16	b	b	NOUN
ejpam-3485	185	17	)	)	PUNCT
ejpam-3485	185	18	geodesic	geodesic	NOUN
ejpam-3485	186	1	[	[	X
ejpam-3485	186	2	(	(	PUNCT
ejpam-3485	186	3	x1	x1	ADJ
ejpam-3485	186	4	,	,	PUNCT
ejpam-3485	186	5	a1	a1	NOUN
ejpam-3485	186	6	)	)	PUNCT
ejpam-3485	186	7	,	,	PUNCT
ejpam-3485	186	8	(	(	PUNCT
ejpam-3485	186	9	x2	x2	PROPN
ejpam-3485	186	10	,	,	PUNCT
ejpam-3485	186	11	a2	a2	PROPN
ejpam-3485	186	12	)	)	PUNCT
ejpam-3485	186	13	,	,	PUNCT
ejpam-3485	186	14	.	.	PUNCT
ejpam-3485	186	15	.	.	PUNCT
ejpam-3485	186	16	.	.	PUNCT
ejpam-3485	187	1	,	,	PUNCT
ejpam-3485	187	2	(	(	PUNCT
ejpam-3485	187	3	xk	xk	PROPN
ejpam-3485	187	4	,	,	PUNCT
ejpam-3485	187	5	ak	ak	PROPN
ejpam-3485	187	6	)	)	PUNCT
ejpam-3485	187	7	]	]	PUNCT
ejpam-3485	187	8	,	,	PUNCT
ejpam-3485	187	9	where	where	SCONJ
ejpam-3485	187	10	(	(	PUNCT
ejpam-3485	187	11	x1	x1	ADJ
ejpam-3485	187	12	,	,	PUNCT
ejpam-3485	187	13	a1	a1	NOUN
ejpam-3485	187	14	)	)	PUNCT
ejpam-3485	187	15	=	=	SYM
ejpam-3485	187	16	(	(	PUNCT
ejpam-3485	187	17	x	x	X
ejpam-3485	187	18	,	,	PUNCT
ejpam-3485	187	19	a	a	PRON
ejpam-3485	187	20	)	)	PUNCT
ejpam-3485	187	21	,	,	PUNCT
ejpam-3485	187	22	(	(	PUNCT
ejpam-3485	187	23	xk	xk	PROPN
ejpam-3485	187	24	,	,	PUNCT
ejpam-3485	187	25	ak	ak	PROPN
ejpam-3485	187	26	)	)	PUNCT
ejpam-3485	187	27	=	=	PUNCT
ejpam-3485	187	28	(	(	PUNCT
ejpam-3485	187	29	y	y	PROPN
ejpam-3485	187	30	,	,	PUNCT
ejpam-3485	187	31	b	b	NOUN
ejpam-3485	187	32	)	)	PUNCT
ejpam-3485	187	33	,	,	PUNCT
ejpam-3485	187	34	and	and	CCONJ
ejpam-3485	187	35	(	(	PUNCT
ejpam-3485	187	36	xi	xi	INTJ
ejpam-3485	187	37	,	,	PUNCT
ejpam-3485	187	38	ai	ai	VERB
ejpam-3485	187	39	)	)	PUNCT
ejpam-3485	187	40	∈	∈	PROPN
ejpam-3485	187	41	c	c	NOUN
ejpam-3485	187	42	for	for	ADP
ejpam-3485	187	43	all	all	PRON
ejpam-3485	187	44	i	i	PRON
ejpam-3485	187	45	∈	∈	PROPN
ejpam-3485	187	46	{	{	PUNCT
ejpam-3485	187	47	1	1	NUM
ejpam-3485	187	48	,	,	PUNCT
ejpam-3485	187	49	2	2	NUM
ejpam-3485	187	50	,	,	PUNCT
ejpam-3485	187	51	.	.	PUNCT
ejpam-3485	187	52	.	.	PUNCT
ejpam-3485	188	1	.	.	PUNCT
ejpam-3485	189	1	,	,	PUNCT
ejpam-3485	189	2	k	k	X
ejpam-3485	189	3	}	}	PUNCT
ejpam-3485	189	4	(	(	PUNCT
ejpam-3485	189	5	k	k	X
ejpam-3485	189	6	≥	≥	NUM
ejpam-3485	189	7	3	3	NUM
ejpam-3485	189	8	)	)	PUNCT
ejpam-3485	189	9	.	.	PUNCT
ejpam-3485	190	1	c.	c.	PROPN
ejpam-3485	190	2	armada	armada	PROPN
ejpam-3485	190	3	,	,	PUNCT
ejpam-3485	190	4	s.	s.	PROPN
ejpam-3485	190	5	canoy	canoy	PROPN
ejpam-3485	190	6	jr	jr	PROPN
ejpam-3485	190	7	.	.	PROPN
ejpam-3485	190	8	,	,	PUNCT
ejpam-3485	190	9	c.	c.	PROPN
ejpam-3485	190	10	go	go	VERB
ejpam-3485	190	11	/	/	SYM
ejpam-3485	190	12	eur	eur	PROPN
ejpam-3485	190	13	.	.	PUNCT
ejpam-3485	191	1	j.	j.	PROPN
ejpam-3485	191	2	pure	pure	PROPN
ejpam-3485	191	3	appl	appl	PROPN
ejpam-3485	191	4	.	.	PROPN
ejpam-3485	191	5	math	math	PROPN
ejpam-3485	191	6	,	,	PUNCT
ejpam-3485	191	7	12	12	NUM
ejpam-3485	191	8	(	(	PUNCT
ejpam-3485	191	9	4	4	NUM
ejpam-3485	191	10	)	)	PUNCT
ejpam-3485	191	11	(	(	PUNCT
ejpam-3485	191	12	2019	2019	NUM
ejpam-3485	191	13	)	)	PUNCT
ejpam-3485	191	14	,	,	PUNCT
ejpam-3485	191	15	1779	1779	NUM
ejpam-3485	191	16	-	-	SYM
ejpam-3485	191	17	1786	1786	NUM
ejpam-3485	191	18	1784	1784	NUM
ejpam-3485	191	19	it	it	PRON
ejpam-3485	191	20	follows	follow	VERB
ejpam-3485	191	21	that	that	SCONJ
ejpam-3485	192	1	[	[	X
ejpam-3485	192	2	x1	x1	X
ejpam-3485	192	3	,	,	PUNCT
ejpam-3485	192	4	x2	x2	PROPN
ejpam-3485	192	5	,	,	PUNCT
ejpam-3485	192	6	.	.	PUNCT
ejpam-3485	192	7	.	.	PUNCT
ejpam-3485	192	8	.	.	PUNCT
ejpam-3485	193	1	,	,	PUNCT
ejpam-3485	193	2	xk	xk	PROPN
ejpam-3485	193	3	]	]	X
ejpam-3485	193	4	,	,	PUNCT
ejpam-3485	193	5	where	where	SCONJ
ejpam-3485	193	6	x1	x1	ADJ
ejpam-3485	193	7	=	=	PUNCT
ejpam-3485	193	8	x	x	X
ejpam-3485	193	9	and	and	CCONJ
ejpam-3485	193	10	xk	xk	PROPN
ejpam-3485	193	11	=	=	SYM
ejpam-3485	193	12	y	y	PROPN
ejpam-3485	193	13	,	,	PUNCT
ejpam-3485	193	14	is	be	AUX
ejpam-3485	193	15	an	an	DET
ejpam-3485	193	16	x	x	NOUN
ejpam-3485	193	17	-	-	NOUN
ejpam-3485	193	18	y	y	ADJ
ejpam-3485	193	19	geodesic	geodesic	NOUN
ejpam-3485	193	20	and	and	CCONJ
ejpam-3485	193	21	xi	xi	NUM
ejpam-3485	193	22	∈	∈	PROPN
ejpam-3485	193	23	s	s	PROPN
ejpam-3485	193	24	for	for	ADP
ejpam-3485	193	25	all	all	PRON
ejpam-3485	193	26	i	i	PRON
ejpam-3485	193	27	∈	∈	PROPN
ejpam-3485	193	28	{	{	PUNCT
ejpam-3485	193	29	1	1	NUM
ejpam-3485	193	30	,	,	PUNCT
ejpam-3485	193	31	2	2	NUM
ejpam-3485	193	32	,	,	PUNCT
ejpam-3485	193	33	.	.	PUNCT
ejpam-3485	193	34	.	.	PUNCT
ejpam-3485	193	35	.	.	PUNCT
ejpam-3485	194	1	,	,	PUNCT
ejpam-3485	194	2	k	k	X
ejpam-3485	194	3	}	}	PUNCT
ejpam-3485	194	4	.	.	PUNCT
ejpam-3485	195	1	this	this	PRON
ejpam-3485	195	2	implies	imply	VERB
ejpam-3485	195	3	that	that	SCONJ
ejpam-3485	195	4	〈	〈	PROPN
ejpam-3485	195	5	s	s	PART
ejpam-3485	195	6	〉	〉	PROPN
ejpam-3485	195	7	is	be	AUX
ejpam-3485	195	8	connected	connect	VERB
ejpam-3485	195	9	.	.	PUNCT
ejpam-3485	196	1	now	now	ADV
ejpam-3485	196	2	,	,	PUNCT
ejpam-3485	196	3	suppose	suppose	VERB
ejpam-3485	196	4	that	that	SCONJ
ejpam-3485	196	5	|s|	|s|	PROPN
ejpam-3485	196	6	=	=	SYM
ejpam-3485	196	7	1	1	NUM
ejpam-3485	196	8	,	,	PUNCT
ejpam-3485	196	9	say	say	VERB
ejpam-3485	196	10	s	s	X
ejpam-3485	196	11	=	=	PUNCT
ejpam-3485	196	12	{	{	PUNCT
ejpam-3485	196	13	x	x	NOUN
ejpam-3485	196	14	}	}	PUNCT
ejpam-3485	196	15	.	.	PUNCT
ejpam-3485	197	1	let	let	VERB
ejpam-3485	197	2	a	a	DET
ejpam-3485	197	3	,	,	PUNCT
ejpam-3485	197	4	b	b	PROPN
ejpam-3485	197	5	∈	∈	PROPN
ejpam-3485	197	6	tx	tx	PROPN
ejpam-3485	197	7	,	,	PUNCT
ejpam-3485	197	8	where	where	SCONJ
ejpam-3485	197	9	a	a	DET
ejpam-3485	197	10	6=	6=	SYM
ejpam-3485	197	11	b	b	PROPN
ejpam-3485	197	12	and	and	CCONJ
ejpam-3485	197	13	ab	ab	PROPN
ejpam-3485	197	14	/∈	/∈	PUNCT
ejpam-3485	197	15	e(g	e(g	PROPN
ejpam-3485	197	16	)	)	PUNCT
ejpam-3485	197	17	.	.	PUNCT
ejpam-3485	198	1	since	since	SCONJ
ejpam-3485	198	2	(	(	PUNCT
ejpam-3485	198	3	x	x	X
ejpam-3485	198	4	,	,	PUNCT
ejpam-3485	198	5	a	a	PRON
ejpam-3485	198	6	)	)	PUNCT
ejpam-3485	198	7	,	,	PUNCT
ejpam-3485	198	8	(	(	PUNCT
ejpam-3485	198	9	x	x	NOUN
ejpam-3485	198	10	,	,	PUNCT
ejpam-3485	198	11	b	b	NOUN
ejpam-3485	198	12	)	)	PUNCT
ejpam-3485	198	13	∈	∈	PROPN
ejpam-3485	198	14	c	c	NOUN
ejpam-3485	198	15	,	,	PUNCT
ejpam-3485	198	16	(	(	PUNCT
ejpam-3485	198	17	x	x	NOUN
ejpam-3485	198	18	,	,	PUNCT
ejpam-3485	198	19	a	a	PRON
ejpam-3485	198	20	)	)	PUNCT
ejpam-3485	198	21	6=	6=	SYM
ejpam-3485	198	22	(	(	PUNCT
ejpam-3485	198	23	x	x	X
ejpam-3485	198	24	,	,	PUNCT
ejpam-3485	198	25	b	b	NOUN
ejpam-3485	198	26	)	)	PUNCT
ejpam-3485	198	27	and	and	CCONJ
ejpam-3485	198	28	(	(	PUNCT
ejpam-3485	198	29	x	x	NOUN
ejpam-3485	198	30	,	,	PUNCT
ejpam-3485	198	31	a)(x	a)(x	PROPN
ejpam-3485	198	32	,	,	PUNCT
ejpam-3485	198	33	b	b	NOUN
ejpam-3485	198	34	)	)	PUNCT
ejpam-3485	198	35	/∈	/∈	PUNCT
ejpam-3485	198	36	e(g[h	e(g[h	NOUN
ejpam-3485	198	37	]	]	PUNCT
ejpam-3485	198	38	)	)	PUNCT
ejpam-3485	198	39	,	,	PUNCT
ejpam-3485	198	40	there	there	PRON
ejpam-3485	198	41	exists	exist	VERB
ejpam-3485	198	42	an	an	DET
ejpam-3485	198	43	(	(	PUNCT
ejpam-3485	198	44	x	x	NOUN
ejpam-3485	198	45	,	,	PUNCT
ejpam-3485	198	46	a	a	NOUN
ejpam-3485	198	47	)	)	PUNCT
ejpam-3485	198	48	−	−	PROPN
ejpam-3485	198	49	(	(	PUNCT
ejpam-3485	198	50	x	x	NOUN
ejpam-3485	198	51	,	,	PUNCT
ejpam-3485	198	52	b	b	NOUN
ejpam-3485	198	53	)	)	PUNCT
ejpam-3485	198	54	geodesic	geodesic	NOUN
ejpam-3485	199	1	[	[	X
ejpam-3485	199	2	(	(	PUNCT
ejpam-3485	199	3	x	x	NOUN
ejpam-3485	199	4	,	,	PUNCT
ejpam-3485	199	5	a1	a1	NOUN
ejpam-3485	199	6	)	)	PUNCT
ejpam-3485	199	7	,	,	PUNCT
ejpam-3485	199	8	(	(	PUNCT
ejpam-3485	199	9	x	x	NOUN
ejpam-3485	199	10	,	,	PUNCT
ejpam-3485	199	11	a2	a2	PROPN
ejpam-3485	199	12	)	)	PUNCT
ejpam-3485	199	13	,	,	PUNCT
ejpam-3485	199	14	.	.	PUNCT
ejpam-3485	199	15	.	.	PUNCT
ejpam-3485	199	16	.	.	PUNCT
ejpam-3485	200	1	,	,	PUNCT
ejpam-3485	200	2	(	(	PUNCT
ejpam-3485	200	3	x	x	NOUN
ejpam-3485	200	4	,	,	PUNCT
ejpam-3485	200	5	ak	ak	PROPN
ejpam-3485	200	6	)	)	PUNCT
ejpam-3485	200	7	]	]	PUNCT
ejpam-3485	200	8	,	,	PUNCT
ejpam-3485	200	9	where	where	SCONJ
ejpam-3485	200	10	a1	a1	NOUN
ejpam-3485	200	11	=	=	SYM
ejpam-3485	200	12	a	a	PROPN
ejpam-3485	200	13	,	,	PUNCT
ejpam-3485	200	14	ak	ak	PROPN
ejpam-3485	200	15	=	=	SYM
ejpam-3485	200	16	b	b	PROPN
ejpam-3485	200	17	,	,	PUNCT
ejpam-3485	200	18	and	and	CCONJ
ejpam-3485	200	19	(	(	PUNCT
ejpam-3485	200	20	x	x	X
ejpam-3485	200	21	,	,	PUNCT
ejpam-3485	200	22	ai	ai	VERB
ejpam-3485	200	23	)	)	PUNCT
ejpam-3485	200	24	∈	∈	PROPN
ejpam-3485	200	25	c	c	NOUN
ejpam-3485	200	26	for	for	ADP
ejpam-3485	200	27	all	all	PRON
ejpam-3485	200	28	i	i	PRON
ejpam-3485	200	29	∈	∈	PROPN
ejpam-3485	200	30	{	{	PUNCT
ejpam-3485	200	31	1	1	NUM
ejpam-3485	200	32	,	,	PUNCT
ejpam-3485	200	33	2	2	NUM
ejpam-3485	200	34	,	,	PUNCT
ejpam-3485	200	35	.	.	PUNCT
ejpam-3485	200	36	.	.	PUNCT
ejpam-3485	200	37	.	.	PUNCT
ejpam-3485	201	1	,	,	PUNCT
ejpam-3485	201	2	k	k	X
ejpam-3485	201	3	}	}	PUNCT
ejpam-3485	201	4	.	.	PUNCT
ejpam-3485	202	1	it	it	PRON
ejpam-3485	202	2	follows	follow	VERB
ejpam-3485	202	3	that	that	SCONJ
ejpam-3485	202	4	[	[	X
ejpam-3485	202	5	a1	a1	NOUN
ejpam-3485	202	6	,	,	PUNCT
ejpam-3485	202	7	a2	a2	PROPN
ejpam-3485	202	8	,	,	PUNCT
ejpam-3485	202	9	.	.	PUNCT
ejpam-3485	202	10	.	.	PUNCT
ejpam-3485	203	1	.	.	PUNCT
ejpam-3485	204	1	,	,	PUNCT
ejpam-3485	204	2	ak	ak	PROPN
ejpam-3485	204	3	]	]	X
ejpam-3485	204	4	is	be	AUX
ejpam-3485	204	5	an	an	DET
ejpam-3485	204	6	a	a	DET
ejpam-3485	204	7	-	-	PUNCT
ejpam-3485	204	8	b	b	NOUN
ejpam-3485	204	9	geodesic	geodesic	NOUN
ejpam-3485	204	10	and	and	CCONJ
ejpam-3485	204	11	ai	ai	PROPN
ejpam-3485	204	12	∈	∈	PROPN
ejpam-3485	204	13	tx	tx	NOUN
ejpam-3485	204	14	for	for	ADP
ejpam-3485	204	15	all	all	PRON
ejpam-3485	204	16	i	i	PRON
ejpam-3485	204	17	∈	∈	PROPN
ejpam-3485	204	18	{	{	PUNCT
ejpam-3485	204	19	1	1	NUM
ejpam-3485	204	20	,	,	PUNCT
ejpam-3485	204	21	2	2	NUM
ejpam-3485	204	22	,	,	PUNCT
ejpam-3485	204	23	.	.	PUNCT
ejpam-3485	204	24	.	.	PUNCT
ejpam-3485	205	1	.	.	PUNCT
ejpam-3485	206	1	,	,	PUNCT
ejpam-3485	206	2	k	k	X
ejpam-3485	206	3	}	}	PUNCT
ejpam-3485	206	4	.	.	PUNCT
ejpam-3485	207	1	hence	hence	ADV
ejpam-3485	207	2	,	,	PUNCT
ejpam-3485	207	3	〈	〈	PROPN
ejpam-3485	207	4	tx	tx	PROPN
ejpam-3485	207	5	〉	〉	PROPN
ejpam-3485	207	6	is	be	AUX
ejpam-3485	207	7	connected	connect	VERB
ejpam-3485	207	8	.	.	PUNCT
ejpam-3485	208	1	moreover	moreover	ADV
ejpam-3485	208	2	,	,	PUNCT
ejpam-3485	208	3	tx	tx	PROPN
ejpam-3485	208	4	is	be	AUX
ejpam-3485	208	5	a	a	DET
ejpam-3485	208	6	dominating	dominating	NOUN
ejpam-3485	208	7	set	set	VERB
ejpam-3485	208	8	in	in	ADP
ejpam-3485	208	9	h.	h.	PROPN
ejpam-3485	208	10	for	for	ADP
ejpam-3485	208	11	the	the	DET
ejpam-3485	208	12	converse	converse	NOUN
ejpam-3485	208	13	,	,	PUNCT
ejpam-3485	208	14	let	let	VERB
ejpam-3485	208	15	c	c	NOUN
ejpam-3485	208	16	=	=	SYM
ejpam-3485	208	17	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	208	18	}	}	PUNCT
ejpam-3485	208	19	×	×	PROPN
ejpam-3485	208	20	tx	tx	PROPN
ejpam-3485	208	21	)	)	PUNCT
ejpam-3485	208	22	.	.	PUNCT
ejpam-3485	209	1	assume	assume	VERB
ejpam-3485	209	2	that	that	SCONJ
ejpam-3485	209	3	s	s	VERB
ejpam-3485	209	4	is	be	AUX
ejpam-3485	209	5	a	a	DET
ejpam-3485	209	6	connected	connected	ADJ
ejpam-3485	209	7	dominating	dominating	NOUN
ejpam-3485	209	8	set	set	NOUN
ejpam-3485	209	9	of	of	ADP
ejpam-3485	209	10	g	g	NOUN
ejpam-3485	209	11	,	,	PUNCT
ejpam-3485	209	12	and	and	CCONJ
ejpam-3485	209	13	that	that	SCONJ
ejpam-3485	209	14	tx	tx	PROPN
ejpam-3485	209	15	is	be	AUX
ejpam-3485	209	16	a	a	DET
ejpam-3485	209	17	connected	connected	ADJ
ejpam-3485	209	18	dominating	dominating	NOUN
ejpam-3485	209	19	set	set	NOUN
ejpam-3485	209	20	of	of	ADP
ejpam-3485	209	21	h	h	NOUN
ejpam-3485	209	22	whenever	whenever	SCONJ
ejpam-3485	209	23	|s|	|s|	PROPN
ejpam-3485	209	24	=	=	SYM
ejpam-3485	209	25	1	1	X
ejpam-3485	209	26	.	.	X
ejpam-3485	209	27	assume	assume	VERB
ejpam-3485	209	28	first	first	ADV
ejpam-3485	209	29	that	that	PRON
ejpam-3485	209	30	|s|	|s|	VERB
ejpam-3485	209	31	≥	≥	NOUN
ejpam-3485	209	32	2	2	NUM
ejpam-3485	209	33	and	and	CCONJ
ejpam-3485	209	34	let	let	VERB
ejpam-3485	209	35	(	(	PUNCT
ejpam-3485	209	36	z	z	NOUN
ejpam-3485	209	37	,	,	PUNCT
ejpam-3485	209	38	c	c	NOUN
ejpam-3485	209	39	)	)	PUNCT
ejpam-3485	209	40	/∈	/∈	PUNCT
ejpam-3485	210	1	c.	c.	NOUN
ejpam-3485	210	2	since	since	SCONJ
ejpam-3485	210	3	〈	〈	PROPN
ejpam-3485	210	4	s	s	PART
ejpam-3485	210	5	〉	〉	PROPN
ejpam-3485	210	6	is	be	AUX
ejpam-3485	210	7	connected	connect	VERB
ejpam-3485	210	8	,	,	PUNCT
ejpam-3485	210	9	there	there	PRON
ejpam-3485	210	10	exists	exist	VERB
ejpam-3485	210	11	w	w	PROPN
ejpam-3485	210	12	∈	∈	PROPN
ejpam-3485	210	13	s	s	VERB
ejpam-3485	210	14	such	such	ADJ
ejpam-3485	210	15	that	that	SCONJ
ejpam-3485	210	16	wz	wz	PROPN
ejpam-3485	210	17	∈	∈	PROPN
ejpam-3485	210	18	e(g	e(g	PROPN
ejpam-3485	210	19	)	)	PUNCT
ejpam-3485	210	20	.	.	PUNCT
ejpam-3485	211	1	let	let	VERB
ejpam-3485	211	2	d	d	X
ejpam-3485	211	3	∈	∈	PROPN
ejpam-3485	211	4	tw	tw	PROPN
ejpam-3485	211	5	.	.	PUNCT
ejpam-3485	212	1	then	then	ADV
ejpam-3485	212	2	(	(	PUNCT
ejpam-3485	212	3	w	w	PROPN
ejpam-3485	212	4	,	,	PUNCT
ejpam-3485	212	5	d	d	NOUN
ejpam-3485	212	6	)	)	PUNCT
ejpam-3485	212	7	∈	∈	PROPN
ejpam-3485	212	8	c	c	PROPN
ejpam-3485	212	9	and	and	CCONJ
ejpam-3485	212	10	(	(	PUNCT
ejpam-3485	212	11	z	z	NOUN
ejpam-3485	212	12	,	,	PUNCT
ejpam-3485	212	13	c)(w	c)(w	ADJ
ejpam-3485	212	14	,	,	PUNCT
ejpam-3485	212	15	d	d	NOUN
ejpam-3485	212	16	)	)	PUNCT
ejpam-3485	212	17	∈	∈	NOUN
ejpam-3485	212	18	e(g[h	e(g[h	NOUN
ejpam-3485	212	19	]	]	PUNCT
ejpam-3485	212	20	)	)	PUNCT
ejpam-3485	212	21	.	.	PUNCT
ejpam-3485	213	1	thus	thus	ADV
ejpam-3485	213	2	,	,	PUNCT
ejpam-3485	213	3	c	c	PROPN
ejpam-3485	213	4	is	be	AUX
ejpam-3485	213	5	a	a	DET
ejpam-3485	213	6	dominating	dominating	NOUN
ejpam-3485	213	7	set	set	VERB
ejpam-3485	213	8	in	in	ADP
ejpam-3485	213	9	g[h	g[h	PROPN
ejpam-3485	213	10	]	]	PUNCT
ejpam-3485	213	11	.	.	PUNCT
ejpam-3485	214	1	next	next	ADJ
ejpam-3485	214	2	,	,	PUNCT
ejpam-3485	214	3	let	let	VERB
ejpam-3485	214	4	(	(	PUNCT
ejpam-3485	214	5	u	u	NOUN
ejpam-3485	214	6	,	,	PUNCT
ejpam-3485	214	7	s	s	PART
ejpam-3485	214	8	)	)	PUNCT
ejpam-3485	214	9	,	,	PUNCT
ejpam-3485	214	10	(	(	PUNCT
ejpam-3485	214	11	v	v	NOUN
ejpam-3485	214	12	,	,	PUNCT
ejpam-3485	214	13	t	t	PROPN
ejpam-3485	214	14	)	)	PUNCT
ejpam-3485	214	15	∈	∈	PROPN
ejpam-3485	214	16	c	c	NOUN
ejpam-3485	214	17	,	,	PUNCT
ejpam-3485	214	18	where	where	SCONJ
ejpam-3485	214	19	(	(	PUNCT
ejpam-3485	214	20	u	u	NOUN
ejpam-3485	214	21	,	,	PUNCT
ejpam-3485	214	22	s	s	PART
ejpam-3485	214	23	)	)	PUNCT
ejpam-3485	214	24	6=	6=	ADP
ejpam-3485	214	25	(	(	PUNCT
ejpam-3485	214	26	v	v	NOUN
ejpam-3485	214	27	,	,	PUNCT
ejpam-3485	214	28	t	t	PROPN
ejpam-3485	214	29	)	)	PUNCT
ejpam-3485	214	30	and	and	CCONJ
ejpam-3485	214	31	(	(	PUNCT
ejpam-3485	214	32	u	u	NOUN
ejpam-3485	214	33	,	,	PUNCT
ejpam-3485	214	34	s)(v	s)(v	PROPN
ejpam-3485	214	35	,	,	PUNCT
ejpam-3485	214	36	t	t	PROPN
ejpam-3485	214	37	)	)	PUNCT
ejpam-3485	214	38	/∈	/∈	PUNCT
ejpam-3485	215	1	e(g[h	e(g[h	NOUN
ejpam-3485	215	2	]	]	PUNCT
ejpam-3485	215	3	)	)	PUNCT
ejpam-3485	215	4	.	.	PUNCT
ejpam-3485	216	1	if	if	SCONJ
ejpam-3485	216	2	u	u	PROPN
ejpam-3485	216	3	=	=	PROPN
ejpam-3485	216	4	v	v	PROPN
ejpam-3485	216	5	,	,	PUNCT
ejpam-3485	216	6	then	then	ADV
ejpam-3485	216	7	we	we	PRON
ejpam-3485	216	8	choose	choose	VERB
ejpam-3485	216	9	w	w	PROPN
ejpam-3485	216	10	∈	∈	PROPN
ejpam-3485	216	11	s	s	VERB
ejpam-3485	216	12	such	such	ADJ
ejpam-3485	216	13	that	that	SCONJ
ejpam-3485	216	14	uw	uw	PROPN
ejpam-3485	216	15	∈	∈	PROPN
ejpam-3485	216	16	e(g	e(g	PROPN
ejpam-3485	216	17	)	)	PUNCT
ejpam-3485	216	18	.	.	PUNCT
ejpam-3485	217	1	let	let	VERB
ejpam-3485	217	2	q	q	PROPN
ejpam-3485	217	3	∈	∈	PROPN
ejpam-3485	217	4	tw	tw	PROPN
ejpam-3485	217	5	.	.	PUNCT
ejpam-3485	218	1	then	then	ADV
ejpam-3485	218	2	(	(	PUNCT
ejpam-3485	218	3	w	w	PROPN
ejpam-3485	218	4	,	,	PUNCT
ejpam-3485	218	5	q	q	NOUN
ejpam-3485	218	6	)	)	PUNCT
ejpam-3485	218	7	∈	∈	PROPN
ejpam-3485	218	8	c	c	NOUN
ejpam-3485	218	9	and	and	CCONJ
ejpam-3485	218	10	[	[	X
ejpam-3485	218	11	(	(	PUNCT
ejpam-3485	218	12	u	u	NOUN
ejpam-3485	218	13	,	,	PUNCT
ejpam-3485	218	14	s	s	PART
ejpam-3485	218	15	)	)	PUNCT
ejpam-3485	218	16	,	,	PUNCT
ejpam-3485	218	17	(	(	PUNCT
ejpam-3485	218	18	w	w	NOUN
ejpam-3485	218	19	,	,	PUNCT
ejpam-3485	218	20	q	q	NOUN
ejpam-3485	218	21	)	)	PUNCT
ejpam-3485	218	22	,	,	PUNCT
ejpam-3485	218	23	(	(	PUNCT
ejpam-3485	218	24	v	v	NOUN
ejpam-3485	218	25	,	,	PUNCT
ejpam-3485	218	26	t	t	PROPN
ejpam-3485	218	27	)	)	PUNCT
ejpam-3485	218	28	]	]	PUNCT
ejpam-3485	218	29	is	be	AUX
ejpam-3485	218	30	a	a	DET
ejpam-3485	218	31	(	(	PUNCT
ejpam-3485	218	32	u	u	NOUN
ejpam-3485	218	33	,	,	PUNCT
ejpam-3485	218	34	s)−	s)−	PROPN
ejpam-3485	218	35	(	(	PUNCT
ejpam-3485	218	36	v	v	NOUN
ejpam-3485	218	37	,	,	PUNCT
ejpam-3485	218	38	t	t	NOUN
ejpam-3485	218	39	)	)	PUNCT
ejpam-3485	218	40	geodesic	geodesic	NOUN
ejpam-3485	218	41	.	.	PUNCT
ejpam-3485	219	1	if	if	SCONJ
ejpam-3485	219	2	u	u	PROPN
ejpam-3485	219	3	6=	6=	PROPN
ejpam-3485	219	4	v	v	NOUN
ejpam-3485	220	1	,	,	PUNCT
ejpam-3485	220	2	then	then	ADV
ejpam-3485	220	3	there	there	PRON
ejpam-3485	220	4	exists	exist	VERB
ejpam-3485	220	5	a	a	DET
ejpam-3485	220	6	u	u	NOUN
ejpam-3485	220	7	−	−	PROPN
ejpam-3485	220	8	v	v	PRON
ejpam-3485	220	9	geodesic	geodesic	NOUN
ejpam-3485	220	10	[	[	X
ejpam-3485	220	11	u1	u1	NOUN
ejpam-3485	220	12	,	,	PUNCT
ejpam-3485	220	13	u2	u2	NOUN
ejpam-3485	220	14	,	,	PUNCT
ejpam-3485	220	15	.	.	PUNCT
ejpam-3485	220	16	.	.	PUNCT
ejpam-3485	221	1	.	.	PUNCT
ejpam-3485	222	1	,	,	PUNCT
ejpam-3485	222	2	uk	uk	PROPN
ejpam-3485	222	3	]	]	PUNCT
ejpam-3485	222	4	where	where	SCONJ
ejpam-3485	222	5	u1	u1	NOUN
ejpam-3485	222	6	=	=	SYM
ejpam-3485	222	7	u	u	PROPN
ejpam-3485	222	8	,	,	PUNCT
ejpam-3485	222	9	uk	uk	PROPN
ejpam-3485	222	10	=	=	PROPN
ejpam-3485	222	11	v	v	PROPN
ejpam-3485	222	12	and	and	CCONJ
ejpam-3485	222	13	ui	ui	PROPN
ejpam-3485	222	14	∈	∈	PROPN
ejpam-3485	222	15	s	s	PROPN
ejpam-3485	222	16	for	for	ADP
ejpam-3485	222	17	each	each	DET
ejpam-3485	222	18	i	i	PRON
ejpam-3485	222	19	∈	∈	PROPN
ejpam-3485	222	20	{	{	PUNCT
ejpam-3485	222	21	1	1	NUM
ejpam-3485	222	22	,	,	PUNCT
ejpam-3485	222	23	2	2	NUM
ejpam-3485	222	24	,	,	PUNCT
ejpam-3485	222	25	.	.	PUNCT
ejpam-3485	222	26	.	.	PUNCT
ejpam-3485	222	27	.	.	PUNCT
ejpam-3485	223	1	,	,	PUNCT
ejpam-3485	223	2	k	k	X
ejpam-3485	223	3	}	}	PUNCT
ejpam-3485	223	4	,	,	PUNCT
ejpam-3485	223	5	since	since	SCONJ
ejpam-3485	223	6	〈	〈	PROPN
ejpam-3485	223	7	s	s	PART
ejpam-3485	223	8	〉	〉	PROPN
ejpam-3485	223	9	is	be	AUX
ejpam-3485	223	10	connected	connect	VERB
ejpam-3485	223	11	.	.	PUNCT
ejpam-3485	224	1	choose	choose	VERB
ejpam-3485	224	2	si	si	PROPN
ejpam-3485	224	3	∈	∈	PROPN
ejpam-3485	224	4	tui	tui	NOUN
ejpam-3485	224	5	for	for	ADP
ejpam-3485	224	6	each	each	DET
ejpam-3485	224	7	i	i	PRON
ejpam-3485	224	8	∈	∈	PROPN
ejpam-3485	224	9	{	{	PUNCT
ejpam-3485	224	10	1	1	NUM
ejpam-3485	224	11	,	,	PUNCT
ejpam-3485	224	12	2	2	NUM
ejpam-3485	224	13	,	,	PUNCT
ejpam-3485	224	14	.	.	PUNCT
ejpam-3485	224	15	.	.	PUNCT
ejpam-3485	224	16	.	.	PUNCT
ejpam-3485	225	1	,	,	PUNCT
ejpam-3485	225	2	k	k	X
ejpam-3485	225	3	}	}	PUNCT
ejpam-3485	225	4	,	,	PUNCT
ejpam-3485	225	5	where	where	SCONJ
ejpam-3485	225	6	s1	s1	PROPN
ejpam-3485	225	7	=	=	SYM
ejpam-3485	225	8	s	s	PROPN
ejpam-3485	225	9	and	and	CCONJ
ejpam-3485	225	10	sk	sk	INTJ
ejpam-3485	225	11	=	=	PROPN
ejpam-3485	225	12	t.	t.	NOUN
ejpam-3485	225	13	then	then	ADV
ejpam-3485	225	14	[	[	X
ejpam-3485	225	15	(	(	PUNCT
ejpam-3485	225	16	u1	u1	NOUN
ejpam-3485	225	17	,	,	PUNCT
ejpam-3485	225	18	s1	s1	PROPN
ejpam-3485	225	19	)	)	PUNCT
ejpam-3485	225	20	,	,	PUNCT
ejpam-3485	225	21	(	(	PUNCT
ejpam-3485	225	22	u2	u2	NOUN
ejpam-3485	225	23	,	,	PUNCT
ejpam-3485	225	24	s2	s2	PROPN
ejpam-3485	225	25	)	)	PUNCT
ejpam-3485	225	26	,	,	PUNCT
ejpam-3485	225	27	.	.	PUNCT
ejpam-3485	225	28	.	.	PUNCT
ejpam-3485	225	29	.	.	PUNCT
ejpam-3485	226	1	,	,	PUNCT
ejpam-3485	226	2	(	(	PUNCT
ejpam-3485	226	3	uk	uk	PROPN
ejpam-3485	226	4	,	,	PUNCT
ejpam-3485	226	5	sk	sk	VERB
ejpam-3485	226	6	)	)	PUNCT
ejpam-3485	226	7	]	]	PUNCT
ejpam-3485	226	8	is	be	AUX
ejpam-3485	226	9	a	a	DET
ejpam-3485	226	10	(	(	PUNCT
ejpam-3485	226	11	u	u	NOUN
ejpam-3485	226	12	,	,	PUNCT
ejpam-3485	226	13	s)−	s)−	PROPN
ejpam-3485	226	14	(	(	PUNCT
ejpam-3485	226	15	v	v	NOUN
ejpam-3485	226	16	,	,	PUNCT
ejpam-3485	226	17	t	t	PROPN
ejpam-3485	226	18	)	)	PUNCT
ejpam-3485	226	19	geodesic	geodesic	NOUN
ejpam-3485	226	20	and	and	CCONJ
ejpam-3485	226	21	(	(	PUNCT
ejpam-3485	226	22	ui	ui	PROPN
ejpam-3485	226	23	,	,	PUNCT
ejpam-3485	226	24	si	si	NOUN
ejpam-3485	226	25	)	)	PUNCT
ejpam-3485	226	26	∈	∈	PROPN
ejpam-3485	226	27	c	c	PROPN
ejpam-3485	226	28	for	for	ADP
ejpam-3485	226	29	each	each	DET
ejpam-3485	226	30	i	i	PRON
ejpam-3485	226	31	∈	∈	PROPN
ejpam-3485	226	32	{	{	PUNCT
ejpam-3485	226	33	1	1	NUM
ejpam-3485	226	34	,	,	PUNCT
ejpam-3485	226	35	2	2	NUM
ejpam-3485	226	36	,	,	PUNCT
ejpam-3485	226	37	.	.	PUNCT
ejpam-3485	226	38	.	.	PUNCT
ejpam-3485	227	1	.	.	PUNCT
ejpam-3485	228	1	,	,	PUNCT
ejpam-3485	228	2	k	k	X
ejpam-3485	228	3	}	}	PUNCT
ejpam-3485	228	4	.	.	PUNCT
ejpam-3485	229	1	thus	thus	ADV
ejpam-3485	229	2	,	,	PUNCT
ejpam-3485	229	3	〈	〈	PROPN
ejpam-3485	229	4	c	c	PROPN
ejpam-3485	229	5	〉	〉	PROPN
ejpam-3485	229	6	is	be	AUX
ejpam-3485	229	7	connected	connect	VERB
ejpam-3485	229	8	.	.	PUNCT
ejpam-3485	230	1	it	it	PRON
ejpam-3485	230	2	is	be	AUX
ejpam-3485	230	3	easy	easy	ADJ
ejpam-3485	230	4	to	to	PART
ejpam-3485	230	5	show	show	VERB
ejpam-3485	230	6	that	that	SCONJ
ejpam-3485	230	7	c	c	PROPN
ejpam-3485	230	8	is	be	AUX
ejpam-3485	230	9	a	a	DET
ejpam-3485	230	10	connected	connect	VERB
ejpam-3485	230	11	dominating	dominating	NOUN
ejpam-3485	230	12	set	set	NOUN
ejpam-3485	230	13	if	if	SCONJ
ejpam-3485	230	14	s	s	VERB
ejpam-3485	230	15	=	=	PRON
ejpam-3485	230	16	{	{	PUNCT
ejpam-3485	230	17	x	x	NOUN
ejpam-3485	230	18	}	}	PUNCT
ejpam-3485	230	19	is	be	AUX
ejpam-3485	230	20	a	a	DET
ejpam-3485	230	21	dominating	dominating	NOUN
ejpam-3485	230	22	set	set	NOUN
ejpam-3485	230	23	and	and	CCONJ
ejpam-3485	230	24	tx	tx	PROPN
ejpam-3485	230	25	is	be	AUX
ejpam-3485	230	26	a	a	DET
ejpam-3485	230	27	connected	connected	ADJ
ejpam-3485	230	28	dominating	dominating	NOUN
ejpam-3485	230	29	set	set	VERB
ejpam-3485	230	30	in	in	ADP
ejpam-3485	230	31	h.	h.	PROPN
ejpam-3485	230	32	�	�	PROPN
ejpam-3485	230	33	corollary	corollary	ADJ
ejpam-3485	230	34	3.2	3.2	NUM
ejpam-3485	230	35	.	.	PUNCT
ejpam-3485	231	1	let	let	VERB
ejpam-3485	231	2	g	g	NOUN
ejpam-3485	231	3	and	and	CCONJ
ejpam-3485	231	4	h	h	NOUN
ejpam-3485	231	5	be	be	AUX
ejpam-3485	231	6	nontrivial	nontrivial	ADJ
ejpam-3485	231	7	connected	connect	VERB
ejpam-3485	231	8	graphs	graph	NOUN
ejpam-3485	231	9	with	with	ADP
ejpam-3485	231	10	γ(g	γ(g	PROPN
ejpam-3485	231	11	)	)	PUNCT
ejpam-3485	231	12	=	=	SYM
ejpam-3485	232	1	1	1	X
ejpam-3485	232	2	.	.	PUNCT
ejpam-3485	232	3	then	then	ADV
ejpam-3485	232	4	γc(g[h	γc(g[h	ADJ
ejpam-3485	232	5	]	]	PUNCT
ejpam-3485	232	6	)	)	PUNCT
ejpam-3485	233	1	=	=	SYM
ejpam-3485	233	2	{	{	PUNCT
ejpam-3485	233	3	1	1	NUM
ejpam-3485	233	4	,	,	PUNCT
ejpam-3485	233	5	γ(h	γ(h	NOUN
ejpam-3485	233	6	)	)	PUNCT
ejpam-3485	233	7	=	=	SYM
ejpam-3485	233	8	1	1	NUM
ejpam-3485	233	9	2	2	NUM
ejpam-3485	233	10	,	,	PUNCT
ejpam-3485	233	11	otherwise	otherwise	ADV
ejpam-3485	233	12	.	.	PUNCT
ejpam-3485	234	1	proof	proof	NOUN
ejpam-3485	234	2	.	.	PUNCT
ejpam-3485	235	1	let	let	VERB
ejpam-3485	235	2	{	{	PUNCT
ejpam-3485	235	3	x	x	AUX
ejpam-3485	235	4	}	}	PUNCT
ejpam-3485	235	5	be	be	AUX
ejpam-3485	235	6	a	a	DET
ejpam-3485	235	7	dominating	dominating	NOUN
ejpam-3485	235	8	set	set	VERB
ejpam-3485	235	9	in	in	ADP
ejpam-3485	235	10	g.	g.	PROPN
ejpam-3485	235	11	if	if	SCONJ
ejpam-3485	235	12	γ(h	γ(h	PROPN
ejpam-3485	235	13	)	)	PUNCT
ejpam-3485	235	14	=	=	SYM
ejpam-3485	236	1	1	1	NUM
ejpam-3485	236	2	,	,	PUNCT
ejpam-3485	236	3	then	then	ADV
ejpam-3485	236	4	choose	choose	VERB
ejpam-3485	236	5	a	a	DET
ejpam-3485	236	6	dominating	dominating	NOUN
ejpam-3485	236	7	set	set	NOUN
ejpam-3485	236	8	{	{	PUNCT
ejpam-3485	236	9	d	d	NOUN
ejpam-3485	236	10	}	}	PUNCT
ejpam-3485	236	11	in	in	ADP
ejpam-3485	236	12	h.	h.	PROPN
ejpam-3485	236	13	clearly	clearly	ADV
ejpam-3485	236	14	,	,	PUNCT
ejpam-3485	236	15	c0	c0	PROPN
ejpam-3485	236	16	=	=	PUNCT
ejpam-3485	236	17	{	{	PUNCT
ejpam-3485	236	18	(	(	PUNCT
ejpam-3485	236	19	x	x	NOUN
ejpam-3485	236	20	,	,	PUNCT
ejpam-3485	236	21	d	d	NOUN
ejpam-3485	236	22	)	)	PUNCT
ejpam-3485	236	23	}	}	PUNCT
ejpam-3485	236	24	is	be	AUX
ejpam-3485	236	25	a	a	DET
ejpam-3485	236	26	connected	connected	ADJ
ejpam-3485	236	27	dominating	dominating	NOUN
ejpam-3485	236	28	set	set	NOUN
ejpam-3485	236	29	of	of	ADP
ejpam-3485	236	30	g[h	g[h	NOUN
ejpam-3485	236	31	]	]	PUNCT
ejpam-3485	236	32	.	.	PUNCT
ejpam-3485	237	1	hence	hence	ADV
ejpam-3485	237	2	,	,	PUNCT
ejpam-3485	237	3	γc(g[h	γc(g[h	ADJ
ejpam-3485	237	4	]	]	PUNCT
ejpam-3485	237	5	)	)	PUNCT
ejpam-3485	237	6	=	=	SYM
ejpam-3485	238	1	1	1	X
ejpam-3485	238	2	.	.	PUNCT
ejpam-3485	238	3	suppose	suppose	VERB
ejpam-3485	238	4	that	that	SCONJ
ejpam-3485	238	5	γ(h	γ(h	PROPN
ejpam-3485	238	6	)	)	PUNCT
ejpam-3485	238	7	≥	≥	NOUN
ejpam-3485	238	8	2	2	NUM
ejpam-3485	238	9	and	and	CCONJ
ejpam-3485	238	10	let	let	VERB
ejpam-3485	238	11	s	s	PRON
ejpam-3485	238	12	=	=	PUNCT
ejpam-3485	238	13	{	{	PUNCT
ejpam-3485	238	14	x	x	PROPN
ejpam-3485	238	15	,	,	PUNCT
ejpam-3485	238	16	y	y	NOUN
ejpam-3485	238	17	}	}	PUNCT
ejpam-3485	238	18	with	with	ADP
ejpam-3485	238	19	xy	xy	PROPN
ejpam-3485	238	20	∈	∈	PROPN
ejpam-3485	238	21	e(g	e(g	PROPN
ejpam-3485	238	22	)	)	PUNCT
ejpam-3485	238	23	.	.	PUNCT
ejpam-3485	239	1	choose	choose	VERB
ejpam-3485	239	2	any	any	PRON
ejpam-3485	239	3	a	a	DET
ejpam-3485	239	4	∈	∈	PROPN
ejpam-3485	239	5	v	v	NOUN
ejpam-3485	239	6	(	(	PUNCT
ejpam-3485	239	7	h	h	NOUN
ejpam-3485	239	8	)	)	PUNCT
ejpam-3485	239	9	.	.	PUNCT
ejpam-3485	240	1	then	then	ADV
ejpam-3485	240	2	c	c	X
ejpam-3485	240	3	=	=	PRON
ejpam-3485	240	4	{	{	PUNCT
ejpam-3485	240	5	(	(	PUNCT
ejpam-3485	240	6	x	x	NOUN
ejpam-3485	240	7	,	,	PUNCT
ejpam-3485	240	8	a	a	PRON
ejpam-3485	240	9	)	)	PUNCT
ejpam-3485	240	10	,	,	PUNCT
ejpam-3485	240	11	(	(	PUNCT
ejpam-3485	240	12	y	y	NOUN
ejpam-3485	240	13	,	,	PUNCT
ejpam-3485	240	14	a	a	PRON
ejpam-3485	240	15	)	)	PUNCT
ejpam-3485	240	16	}	}	PUNCT
ejpam-3485	240	17	is	be	AUX
ejpam-3485	240	18	a	a	DET
ejpam-3485	240	19	connected	connected	ADJ
ejpam-3485	240	20	dominating	dominating	NOUN
ejpam-3485	240	21	set	set	NOUN
ejpam-3485	240	22	of	of	ADP
ejpam-3485	240	23	g[h	g[h	PROPN
ejpam-3485	240	24	]	]	PUNCT
ejpam-3485	240	25	by	by	ADP
ejpam-3485	240	26	theorem	theorem	NOUN
ejpam-3485	240	27	3.1	3.1	NUM
ejpam-3485	240	28	.	.	PUNCT
ejpam-3485	241	1	since	since	SCONJ
ejpam-3485	241	2	g[h	g[h	NOUN
ejpam-3485	241	3	]	]	PUNCT
ejpam-3485	241	4	can	can	AUX
ejpam-3485	241	5	not	not	PART
ejpam-3485	241	6	be	be	AUX
ejpam-3485	241	7	dominated	dominate	VERB
ejpam-3485	241	8	by	by	ADP
ejpam-3485	241	9	a	a	DET
ejpam-3485	241	10	single	single	ADJ
ejpam-3485	241	11	vertex	vertex	NOUN
ejpam-3485	241	12	,	,	PUNCT
ejpam-3485	241	13	it	it	PRON
ejpam-3485	241	14	follows	follow	VERB
ejpam-3485	241	15	that	that	PRON
ejpam-3485	241	16	γc(g[h	γc(g[h	ADP
ejpam-3485	241	17	]	]	PUNCT
ejpam-3485	241	18	)	)	PUNCT
ejpam-3485	241	19	=	=	SYM
ejpam-3485	241	20	|c|	|c|	PROPN
ejpam-3485	241	21	=	=	SYM
ejpam-3485	241	22	2	2	X
ejpam-3485	241	23	.	.	PUNCT
ejpam-3485	241	24	�	�	PROPN
ejpam-3485	241	25	corollary	corollary	ADJ
ejpam-3485	241	26	3.3	3.3	NUM
ejpam-3485	241	27	.	.	PUNCT
ejpam-3485	242	1	let	let	VERB
ejpam-3485	242	2	g	g	NOUN
ejpam-3485	242	3	and	and	CCONJ
ejpam-3485	242	4	h	h	NOUN
ejpam-3485	242	5	be	be	AUX
ejpam-3485	242	6	nontrivial	nontrivial	ADJ
ejpam-3485	242	7	connected	connect	VERB
ejpam-3485	242	8	graphs	graph	NOUN
ejpam-3485	242	9	with	with	ADP
ejpam-3485	242	10	γ(g	γ(g	PROPN
ejpam-3485	242	11	)	)	PUNCT
ejpam-3485	242	12	6=	6=	ADP
ejpam-3485	243	1	1	1	X
ejpam-3485	243	2	.	.	PUNCT
ejpam-3485	243	3	then	then	ADV
ejpam-3485	243	4	γc(g[h	γc(g[h	ADJ
ejpam-3485	243	5	]	]	PUNCT
ejpam-3485	243	6	)	)	PUNCT
ejpam-3485	243	7	=	=	SYM
ejpam-3485	244	1	γc(g	γc(g	X
ejpam-3485	244	2	)	)	PUNCT
ejpam-3485	244	3	.	.	PUNCT
ejpam-3485	245	1	proof	proof	NOUN
ejpam-3485	245	2	.	.	PUNCT
ejpam-3485	246	1	let	let	VERB
ejpam-3485	246	2	s	s	PRON
ejpam-3485	246	3	be	be	AUX
ejpam-3485	246	4	a	a	DET
ejpam-3485	246	5	minimum	minimum	ADJ
ejpam-3485	246	6	connected	connect	VERB
ejpam-3485	246	7	dominating	dominating	NOUN
ejpam-3485	246	8	set	set	VERB
ejpam-3485	246	9	in	in	ADP
ejpam-3485	246	10	g.	g.	PROPN
ejpam-3485	246	11	choose	choose	VERB
ejpam-3485	246	12	any	any	DET
ejpam-3485	246	13	a	a	DET
ejpam-3485	246	14	∈	∈	PROPN
ejpam-3485	246	15	v	v	NOUN
ejpam-3485	246	16	(	(	PUNCT
ejpam-3485	246	17	h	h	NOUN
ejpam-3485	246	18	)	)	PUNCT
ejpam-3485	246	19	and	and	CCONJ
ejpam-3485	246	20	set	set	VERB
ejpam-3485	246	21	tx	tx	PROPN
ejpam-3485	246	22	=	=	PUNCT
ejpam-3485	246	23	{	{	PUNCT
ejpam-3485	246	24	a	a	NOUN
ejpam-3485	246	25	}	}	PUNCT
ejpam-3485	246	26	for	for	ADP
ejpam-3485	246	27	each	each	DET
ejpam-3485	246	28	x	x	SYM
ejpam-3485	246	29	∈	∈	PROPN
ejpam-3485	246	30	s.	s.	PROPN
ejpam-3485	246	31	then	then	ADV
ejpam-3485	246	32	c	c	X
ejpam-3485	246	33	=	=	SYM
ejpam-3485	246	34	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3485	246	35	}	}	PUNCT
ejpam-3485	246	36	×	×	NOUN
ejpam-3485	246	37	tx	tx	PROPN
ejpam-3485	246	38	)	)	PUNCT
ejpam-3485	246	39	is	be	AUX
ejpam-3485	246	40	a	a	DET
ejpam-3485	246	41	minimum	minimum	ADJ
ejpam-3485	246	42	connected	connect	VERB
ejpam-3485	246	43	dominating	dominating	NOUN
ejpam-3485	246	44	set	set	NOUN
ejpam-3485	246	45	of	of	ADP
ejpam-3485	246	46	g[h	g[h	PROPN
ejpam-3485	246	47	]	]	PUNCT
ejpam-3485	246	48	by	by	ADP
ejpam-3485	246	49	theorem	theorem	NOUN
ejpam-3485	246	50	3.1	3.1	NUM
ejpam-3485	246	51	.	.	PUNCT
ejpam-3485	247	1	therefore	therefore	ADV
ejpam-3485	247	2	,	,	PUNCT
ejpam-3485	247	3	γc(g[h	γc(g[h	ADJ
ejpam-3485	247	4	]	]	PUNCT
ejpam-3485	247	5	)	)	PUNCT
ejpam-3485	248	1	=	=	SYM
ejpam-3485	248	2	|c|	|c|	PROPN
ejpam-3485	248	3	=	=	SYM
ejpam-3485	248	4	|s|	|s|	PROPN
ejpam-3485	248	5	=	=	NOUN
ejpam-3485	248	6	γc(g	γc(g	X
ejpam-3485	248	7	)	)	PUNCT
ejpam-3485	248	8	.	.	PUNCT
ejpam-3485	249	1	�	�	PROPN
ejpam-3485	249	2	theorem	theorem	VERB
ejpam-3485	249	3	3.4	3.4	NUM
ejpam-3485	249	4	.	.	PUNCT
ejpam-3485	250	1	let	let	VERB
ejpam-3485	250	2	g	g	NOUN
ejpam-3485	250	3	and	and	CCONJ
ejpam-3485	250	4	h	h	NOUN
ejpam-3485	250	5	be	be	AUX
ejpam-3485	250	6	nontrivial	nontrivial	ADJ
ejpam-3485	250	7	connected	connect	VERB
ejpam-3485	250	8	graphs	graph	NOUN
ejpam-3485	250	9	with	with	ADP
ejpam-3485	250	10	γ(g	γ(g	PROPN
ejpam-3485	250	11	)	)	PUNCT
ejpam-3485	250	12	=	=	SYM
ejpam-3485	250	13	1	1	NUM
ejpam-3485	250	14	and	and	CCONJ
ejpam-3485	250	15	γ(h	γ(h	NOUN
ejpam-3485	250	16	)	)	PUNCT
ejpam-3485	250	17	=	=	SYM
ejpam-3485	251	1	1	1	X
ejpam-3485	251	2	.	.	PUNCT
ejpam-3485	251	3	then	then	ADV
ejpam-3485	251	4	fγc(g[h	fγc(g[h	NUM
ejpam-3485	251	5	]	]	PUNCT
ejpam-3485	251	6	)	)	PUNCT
ejpam-3485	251	7	=	=	SYM
ejpam-3485	251	8	{	{	PUNCT
ejpam-3485	251	9	0	0	NUM
ejpam-3485	251	10	,	,	PUNCT
ejpam-3485	251	11	both	both	PRON
ejpam-3485	251	12	g	g	PROPN
ejpam-3485	251	13	and	and	CCONJ
ejpam-3485	251	14	h	h	NOUN
ejpam-3485	251	15	have	have	AUX
ejpam-3485	251	16	unique	unique	ADJ
ejpam-3485	251	17	γ	γ	NOUN
ejpam-3485	251	18	-	-	PUNCT
ejpam-3485	251	19	sets	set	NOUN
ejpam-3485	251	20	,	,	PUNCT
ejpam-3485	251	21	1	1	NUM
ejpam-3485	251	22	,	,	PUNCT
ejpam-3485	251	23	otherwise	otherwise	ADV
ejpam-3485	251	24	.	.	PUNCT
ejpam-3485	252	1	references	reference	NOUN
ejpam-3485	252	2	1785	1785	NUM
ejpam-3485	252	3	proof	proof	NOUN
ejpam-3485	252	4	.	.	PUNCT
ejpam-3485	252	5	suppose	suppose	VERB
ejpam-3485	252	6	that	that	SCONJ
ejpam-3485	252	7	both	both	PRON
ejpam-3485	252	8	g	g	PROPN
ejpam-3485	252	9	and	and	CCONJ
ejpam-3485	252	10	h	h	NOUN
ejpam-3485	252	11	have	have	AUX
ejpam-3485	252	12	unique	unique	ADJ
ejpam-3485	252	13	γ	γ	NOUN
ejpam-3485	252	14	-	-	PUNCT
ejpam-3485	252	15	sets	set	NOUN
ejpam-3485	252	16	,	,	PUNCT
ejpam-3485	252	17	say	say	VERB
ejpam-3485	252	18	s	s	NOUN
ejpam-3485	252	19	and	and	CCONJ
ejpam-3485	252	20	t	t	PROPN
ejpam-3485	252	21	,	,	PUNCT
ejpam-3485	252	22	respectively	respectively	ADV
ejpam-3485	252	23	.	.	PUNCT
ejpam-3485	253	1	then	then	ADV
ejpam-3485	253	2	s	s	VERB
ejpam-3485	253	3	and	and	CCONJ
ejpam-3485	253	4	t	t	PROPN
ejpam-3485	253	5	are	be	AUX
ejpam-3485	253	6	also	also	ADV
ejpam-3485	253	7	γc	γc	NOUN
ejpam-3485	253	8	-	-	PUNCT
ejpam-3485	253	9	sets	set	NOUN
ejpam-3485	253	10	.	.	PUNCT
ejpam-3485	254	1	by	by	ADP
ejpam-3485	254	2	theorem	theorem	NOUN
ejpam-3485	254	3	3.1	3.1	NUM
ejpam-3485	254	4	,	,	PUNCT
ejpam-3485	254	5	c	c	NOUN
ejpam-3485	254	6	=	=	SYM
ejpam-3485	254	7	∪x∈s({x	∪x∈s({x	PROPN
ejpam-3485	254	8	}	}	PUNCT
ejpam-3485	254	9	×	×	NOUN
ejpam-3485	254	10	tx	tx	PROPN
ejpam-3485	254	11	)	)	PUNCT
ejpam-3485	254	12	⊆	⊆	NUM
ejpam-3485	254	13	v	v	NOUN
ejpam-3485	254	14	(	(	PUNCT
ejpam-3485	254	15	g[h	g[h	PROPN
ejpam-3485	254	16	]	]	PUNCT
ejpam-3485	254	17	)	)	PUNCT
ejpam-3485	254	18	,	,	PUNCT
ejpam-3485	254	19	where	where	SCONJ
ejpam-3485	254	20	s	s	VERB
ejpam-3485	254	21	⊆	⊆	NUM
ejpam-3485	254	22	v	v	NOUN
ejpam-3485	254	23	(	(	PUNCT
ejpam-3485	254	24	g	g	NOUN
ejpam-3485	254	25	)	)	PUNCT
ejpam-3485	254	26	and	and	CCONJ
ejpam-3485	254	27	tx	tx	VERB
ejpam-3485	254	28	⊆	⊆	NUM
ejpam-3485	254	29	v	v	NOUN
ejpam-3485	254	30	(	(	PUNCT
ejpam-3485	254	31	h	h	NOUN
ejpam-3485	254	32	)	)	PUNCT
ejpam-3485	254	33	for	for	ADP
ejpam-3485	254	34	every	every	DET
ejpam-3485	254	35	x	x	SYM
ejpam-3485	254	36	∈	∈	PROPN
ejpam-3485	254	37	s	s	NOUN
ejpam-3485	254	38	,	,	PUNCT
ejpam-3485	254	39	is	be	AUX
ejpam-3485	254	40	the	the	DET
ejpam-3485	254	41	only	only	ADJ
ejpam-3485	254	42	γc	γc	NOUN
ejpam-3485	254	43	-	-	PUNCT
ejpam-3485	254	44	set	set	NOUN
ejpam-3485	254	45	of	of	ADP
ejpam-3485	254	46	g[h	g[h	NOUN
ejpam-3485	254	47	]	]	PUNCT
ejpam-3485	254	48	,	,	PUNCT
ejpam-3485	254	49	that	that	ADV
ejpam-3485	254	50	is	is	ADV
ejpam-3485	254	51	,	,	PUNCT
ejpam-3485	254	52	∅	∅	NOUN
ejpam-3485	254	53	is	be	AUX
ejpam-3485	254	54	a	a	DET
ejpam-3485	254	55	forcing	forcing	NOUN
ejpam-3485	254	56	subset	subset	NOUN
ejpam-3485	254	57	for	for	ADP
ejpam-3485	254	58	c.	c.	PROPN
ejpam-3485	254	59	thus	thus	ADV
ejpam-3485	254	60	,	,	PUNCT
ejpam-3485	254	61	fγc(g[h	fγc(g[h	ADJ
ejpam-3485	254	62	]	]	PUNCT
ejpam-3485	254	63	)	)	PUNCT
ejpam-3485	254	64	=	=	SYM
ejpam-3485	254	65	fγc(c	fγc(c	X
ejpam-3485	254	66	)	)	PUNCT
ejpam-3485	255	1	=	=	SYM
ejpam-3485	255	2	0	0	X
ejpam-3485	255	3	.	.	PUNCT
ejpam-3485	255	4	suppose	suppose	VERB
ejpam-3485	255	5	that	that	SCONJ
ejpam-3485	255	6	either	either	CCONJ
ejpam-3485	255	7	g	g	PROPN
ejpam-3485	255	8	or	or	CCONJ
ejpam-3485	255	9	h	h	NOUN
ejpam-3485	255	10	has	have	VERB
ejpam-3485	255	11	no	no	DET
ejpam-3485	255	12	unique	unique	ADJ
ejpam-3485	255	13	γ	γ	X
ejpam-3485	255	14	-	-	PUNCT
ejpam-3485	255	15	set	set	ADJ
ejpam-3485	255	16	(	(	PUNCT
ejpam-3485	255	17	γc	γc	NOUN
ejpam-3485	255	18	-	-	PUNCT
ejpam-3485	255	19	set	set	NOUN
ejpam-3485	255	20	)	)	PUNCT
ejpam-3485	255	21	.	.	PUNCT
ejpam-3485	256	1	then	then	ADV
ejpam-3485	256	2	by	by	ADP
ejpam-3485	256	3	theorem	theorem	NOUN
ejpam-3485	256	4	3.1	3.1	NUM
ejpam-3485	256	5	,	,	PUNCT
ejpam-3485	256	6	c	c	NOUN
ejpam-3485	256	7	=	=	PRON
ejpam-3485	256	8	{	{	PUNCT
ejpam-3485	256	9	(	(	PUNCT
ejpam-3485	256	10	x	x	NOUN
ejpam-3485	256	11	,	,	PUNCT
ejpam-3485	256	12	y	y	PROPN
ejpam-3485	256	13	)	)	PUNCT
ejpam-3485	256	14	:	:	PUNCT
ejpam-3485	257	1	x	x	PUNCT
ejpam-3485	257	2	∈	∈	NOUN
ejpam-3485	257	3	s	s	X
ejpam-3485	257	4	and	and	CCONJ
ejpam-3485	257	5	y	y	PROPN
ejpam-3485	257	6	∈	∈	PROPN
ejpam-3485	257	7	tx	tx	PROPN
ejpam-3485	257	8	}	}	PUNCT
ejpam-3485	257	9	,	,	PUNCT
ejpam-3485	257	10	where	where	SCONJ
ejpam-3485	257	11	s	s	NOUN
ejpam-3485	257	12	is	be	AUX
ejpam-3485	257	13	a	a	DET
ejpam-3485	257	14	γc	γc	NOUN
ejpam-3485	257	15	-	-	PUNCT
ejpam-3485	257	16	set	set	NOUN
ejpam-3485	257	17	of	of	ADP
ejpam-3485	257	18	g	g	PROPN
ejpam-3485	257	19	and	and	CCONJ
ejpam-3485	257	20	tx	tx	PROPN
ejpam-3485	257	21	is	be	AUX
ejpam-3485	257	22	a	a	DET
ejpam-3485	257	23	γc	γc	NOUN
ejpam-3485	257	24	-	-	PUNCT
ejpam-3485	257	25	set	set	NOUN
ejpam-3485	257	26	of	of	ADP
ejpam-3485	257	27	h	h	NOUN
ejpam-3485	257	28	,	,	PUNCT
ejpam-3485	257	29	is	be	AUX
ejpam-3485	257	30	not	not	PART
ejpam-3485	257	31	a	a	DET
ejpam-3485	257	32	unique	unique	ADJ
ejpam-3485	257	33	γc	γc	NOUN
ejpam-3485	257	34	-	-	PUNCT
ejpam-3485	257	35	set	set	NOUN
ejpam-3485	257	36	of	of	ADP
ejpam-3485	257	37	g[h	g[h	NOUN
ejpam-3485	257	38	]	]	PUNCT
ejpam-3485	257	39	.	.	PUNCT
ejpam-3485	258	1	by	by	ADP
ejpam-3485	258	2	corollary	corollary	ADJ
ejpam-3485	258	3	3.2	3.2	NUM
ejpam-3485	258	4	,	,	PUNCT
ejpam-3485	258	5	|c|	|c|	PROPN
ejpam-3485	258	6	=	=	SYM
ejpam-3485	258	7	1	1	NUM
ejpam-3485	258	8	,	,	PUNCT
ejpam-3485	258	9	that	that	ADV
ejpam-3485	258	10	is	is	ADV
ejpam-3485	258	11	,	,	PUNCT
ejpam-3485	258	12	c	c	PROPN
ejpam-3485	258	13	is	be	AUX
ejpam-3485	258	14	a	a	DET
ejpam-3485	258	15	forcing	forcing	NOUN
ejpam-3485	258	16	subset	subset	NOUN
ejpam-3485	258	17	for	for	ADP
ejpam-3485	258	18	itself	itself	PRON
ejpam-3485	258	19	.	.	PUNCT
ejpam-3485	259	1	thus	thus	ADV
ejpam-3485	259	2	,	,	PUNCT
ejpam-3485	259	3	fγc(g[h	fγc(g[h	ADJ
ejpam-3485	259	4	]	]	PUNCT
ejpam-3485	259	5	)	)	PUNCT
ejpam-3485	259	6	=	=	SYM
ejpam-3485	259	7	fγc(c	fγc(c	X
ejpam-3485	259	8	)	)	PUNCT
ejpam-3485	259	9	=	=	SYM
ejpam-3485	259	10	1	1	X
ejpam-3485	259	11	.	.	X
ejpam-3485	259	12	�	�	PROPN
ejpam-3485	259	13	theorem	theorem	VERB
ejpam-3485	259	14	3.5	3.5	NUM
ejpam-3485	259	15	.	.	PUNCT
ejpam-3485	260	1	let	let	VERB
ejpam-3485	260	2	g	g	NOUN
ejpam-3485	260	3	and	and	CCONJ
ejpam-3485	260	4	h	h	NOUN
ejpam-3485	260	5	be	be	AUX
ejpam-3485	260	6	nontrivial	nontrivial	ADJ
ejpam-3485	260	7	connected	connect	VERB
ejpam-3485	260	8	graphs	graph	NOUN
ejpam-3485	260	9	with	with	ADP
ejpam-3485	260	10	γ(g	γ(g	PROPN
ejpam-3485	260	11	)	)	PUNCT
ejpam-3485	260	12	=	=	SYM
ejpam-3485	260	13	1	1	NUM
ejpam-3485	260	14	and	and	CCONJ
ejpam-3485	260	15	γ(h	γ(h	NOUN
ejpam-3485	260	16	)	)	PUNCT
ejpam-3485	260	17	>	>	X
ejpam-3485	261	1	1	1	X
ejpam-3485	261	2	.	.	PUNCT
ejpam-3485	262	1	then	then	ADV
ejpam-3485	262	2	fγc(g[h	fγc(g[h	NUM
ejpam-3485	262	3	]	]	PUNCT
ejpam-3485	262	4	)	)	PUNCT
ejpam-3485	262	5	=	=	SYM
ejpam-3485	263	1	2	2	X
ejpam-3485	263	2	.	.	X
ejpam-3485	263	3	proof	proof	NOUN
ejpam-3485	263	4	.	.	PUNCT
ejpam-3485	264	1	note	note	VERB
ejpam-3485	264	2	that	that	SCONJ
ejpam-3485	264	3	by	by	ADP
ejpam-3485	264	4	corollary	corollary	ADJ
ejpam-3485	264	5	3.2	3.2	NUM
ejpam-3485	264	6	,	,	PUNCT
ejpam-3485	264	7	γc(g[h	γc(g[h	ADJ
ejpam-3485	264	8	]	]	PUNCT
ejpam-3485	264	9	)	)	PUNCT
ejpam-3485	264	10	=	=	SYM
ejpam-3485	265	1	2	2	X
ejpam-3485	265	2	.	.	X
ejpam-3485	265	3	let	let	VERB
ejpam-3485	265	4	s	s	VERB
ejpam-3485	265	5	=	=	PUNCT
ejpam-3485	265	6	{	{	PUNCT
ejpam-3485	265	7	x	x	PROPN
ejpam-3485	265	8	,	,	PUNCT
ejpam-3485	265	9	y	y	PROPN
ejpam-3485	265	10	}	}	PUNCT
ejpam-3485	265	11	be	be	AUX
ejpam-3485	265	12	a	a	DET
ejpam-3485	265	13	γc	γc	NOUN
ejpam-3485	265	14	-	-	PUNCT
ejpam-3485	265	15	set	set	NOUN
ejpam-3485	265	16	of	of	ADP
ejpam-3485	265	17	g.	g.	PROPN
ejpam-3485	265	18	choose	choose	VERB
ejpam-3485	265	19	any	any	DET
ejpam-3485	265	20	vertex	vertex	NOUN
ejpam-3485	265	21	a	a	DET
ejpam-3485	265	22	∈	∈	NOUN
ejpam-3485	265	23	v	v	ADP
ejpam-3485	265	24	(	(	PUNCT
ejpam-3485	265	25	h	h	NOUN
ejpam-3485	265	26	)	)	PUNCT
ejpam-3485	265	27	.	.	PUNCT
ejpam-3485	266	1	then	then	ADV
ejpam-3485	266	2	c	c	X
ejpam-3485	266	3	=	=	PRON
ejpam-3485	266	4	{	{	PUNCT
ejpam-3485	266	5	(	(	PUNCT
ejpam-3485	266	6	x	x	NOUN
ejpam-3485	266	7	,	,	PUNCT
ejpam-3485	266	8	a	a	PRON
ejpam-3485	266	9	)	)	PUNCT
ejpam-3485	266	10	,	,	PUNCT
ejpam-3485	266	11	(	(	PUNCT
ejpam-3485	266	12	y	y	NOUN
ejpam-3485	266	13	,	,	PUNCT
ejpam-3485	266	14	a	a	PRON
ejpam-3485	266	15	)	)	PUNCT
ejpam-3485	266	16	}	}	PUNCT
ejpam-3485	266	17	is	be	AUX
ejpam-3485	266	18	a	a	DET
ejpam-3485	266	19	γc	γc	NOUN
ejpam-3485	266	20	-	-	PUNCT
ejpam-3485	266	21	set	set	NOUN
ejpam-3485	266	22	of	of	ADP
ejpam-3485	266	23	g[h	g[h	NOUN
ejpam-3485	266	24	]	]	PUNCT
ejpam-3485	266	25	by	by	ADP
ejpam-3485	266	26	theorem	theorem	NOUN
ejpam-3485	266	27	3.1	3.1	NUM
ejpam-3485	266	28	.	.	PUNCT
ejpam-3485	267	1	pick	pick	VERB
ejpam-3485	267	2	b	b	PROPN
ejpam-3485	267	3	∈	∈	PROPN
ejpam-3485	267	4	v	v	NOUN
ejpam-3485	267	5	(	(	PUNCT
ejpam-3485	267	6	h)\{a	h)\{a	NOUN
ejpam-3485	267	7	}	}	PUNCT
ejpam-3485	267	8	.	.	PUNCT
ejpam-3485	268	1	then	then	ADV
ejpam-3485	268	2	{	{	PUNCT
ejpam-3485	268	3	(	(	PUNCT
ejpam-3485	268	4	x	x	NOUN
ejpam-3485	268	5	,	,	PUNCT
ejpam-3485	268	6	a	a	NOUN
ejpam-3485	268	7	)	)	PUNCT
ejpam-3485	268	8	}	}	PUNCT
ejpam-3485	268	9	⊆	⊆	NUM
ejpam-3485	268	10	c	c	NOUN
ejpam-3485	268	11	′	′	NUM
ejpam-3485	269	1	=	=	SYM
ejpam-3485	270	1	{	{	PUNCT
ejpam-3485	270	2	(	(	PUNCT
ejpam-3485	270	3	x	x	NOUN
ejpam-3485	270	4	,	,	PUNCT
ejpam-3485	270	5	a	a	PRON
ejpam-3485	270	6	)	)	PUNCT
ejpam-3485	270	7	,	,	PUNCT
ejpam-3485	270	8	(	(	PUNCT
ejpam-3485	270	9	y	y	PROPN
ejpam-3485	270	10	,	,	PUNCT
ejpam-3485	270	11	b	b	NOUN
ejpam-3485	270	12	)	)	PUNCT
ejpam-3485	270	13	}	}	PUNCT
ejpam-3485	270	14	and	and	CCONJ
ejpam-3485	270	15	{	{	PUNCT
ejpam-3485	270	16	(	(	PUNCT
ejpam-3485	270	17	y	y	PROPN
ejpam-3485	270	18	,	,	PUNCT
ejpam-3485	270	19	a	a	NOUN
ejpam-3485	270	20	)	)	PUNCT
ejpam-3485	270	21	}	}	PUNCT
ejpam-3485	270	22	⊆	⊆	NUM
ejpam-3485	270	23	c∗	c∗	NOUN
ejpam-3485	270	24	=	=	SYM
ejpam-3485	270	25	{	{	PUNCT
ejpam-3485	270	26	(	(	PUNCT
ejpam-3485	270	27	x	x	NOUN
ejpam-3485	270	28	,	,	PUNCT
ejpam-3485	270	29	b	b	NOUN
ejpam-3485	270	30	)	)	PUNCT
ejpam-3485	270	31	,	,	PUNCT
ejpam-3485	270	32	(	(	PUNCT
ejpam-3485	270	33	y	y	NOUN
ejpam-3485	270	34	,	,	PUNCT
ejpam-3485	270	35	a	a	NOUN
ejpam-3485	270	36	)	)	PUNCT
ejpam-3485	270	37	}	}	PUNCT
ejpam-3485	270	38	,	,	PUNCT
ejpam-3485	270	39	where	where	SCONJ
ejpam-3485	270	40	c	c	NOUN
ejpam-3485	270	41	′	′	NOUN
ejpam-3485	270	42	and	and	CCONJ
ejpam-3485	270	43	c∗	c∗	NOUN
ejpam-3485	270	44	are	be	AUX
ejpam-3485	270	45	also	also	ADV
ejpam-3485	270	46	γc	γc	NOUN
ejpam-3485	270	47	-	-	PUNCT
ejpam-3485	270	48	sets	set	NOUN
ejpam-3485	270	49	of	of	ADP
ejpam-3485	270	50	g[h	g[h	NOUN
ejpam-3485	270	51	]	]	X
ejpam-3485	270	52	different	different	ADJ
ejpam-3485	270	53	from	from	ADP
ejpam-3485	270	54	c.	c.	PROPN
ejpam-3485	270	55	thus	thus	ADV
ejpam-3485	270	56	,	,	PUNCT
ejpam-3485	270	57	fγc(c	fγc(c	PROPN
ejpam-3485	270	58	)	)	PUNCT
ejpam-3485	270	59	=	=	SYM
ejpam-3485	270	60	2	2	NUM
ejpam-3485	270	61	=	=	SYM
ejpam-3485	270	62	fγc(g[h	fγc(g[h	NUM
ejpam-3485	270	63	]	]	PUNCT
ejpam-3485	270	64	)	)	PUNCT
ejpam-3485	270	65	.	.	PUNCT
ejpam-3485	271	1	�	�	PROPN
ejpam-3485	271	2	theorem	theorem	VERB
ejpam-3485	271	3	3.6	3.6	NUM
ejpam-3485	271	4	.	.	PUNCT
ejpam-3485	272	1	let	let	VERB
ejpam-3485	272	2	g	g	NOUN
ejpam-3485	272	3	and	and	CCONJ
ejpam-3485	272	4	h	h	NOUN
ejpam-3485	272	5	be	be	AUX
ejpam-3485	272	6	nontrivial	nontrivial	ADJ
ejpam-3485	272	7	connected	connect	VERB
ejpam-3485	272	8	graphs	graph	NOUN
ejpam-3485	272	9	with	with	ADP
ejpam-3485	272	10	γ(g	γ(g	PROPN
ejpam-3485	272	11	)	)	PUNCT
ejpam-3485	272	12	6=	6=	ADP
ejpam-3485	273	1	1	1	X
ejpam-3485	273	2	.	.	PUNCT
ejpam-3485	274	1	then	then	ADV
ejpam-3485	274	2	fγc(g[h	fγc(g[h	NUM
ejpam-3485	274	3	]	]	PUNCT
ejpam-3485	274	4	)	)	PUNCT
ejpam-3485	274	5	=	=	SYM
ejpam-3485	274	6	γc(g	γc(g	X
ejpam-3485	274	7	)	)	PUNCT
ejpam-3485	274	8	.	.	PUNCT
ejpam-3485	275	1	proof	proof	NOUN
ejpam-3485	275	2	.	.	PUNCT
ejpam-3485	276	1	let	let	VERB
ejpam-3485	276	2	c	c	NOUN
ejpam-3485	276	3	=	=	PUNCT
ejpam-3485	276	4	∪x∈s	∪x∈s	PROPN
ejpam-3485	276	5	[	[	X
ejpam-3485	276	6	{	{	PUNCT
ejpam-3485	276	7	x	x	NOUN
ejpam-3485	276	8	}	}	PUNCT
ejpam-3485	276	9	×	×	PROPN
ejpam-3485	276	10	tx	tx	PROPN
ejpam-3485	276	11	]	]	PUNCT
ejpam-3485	276	12	be	be	AUX
ejpam-3485	276	13	a	a	DET
ejpam-3485	276	14	γc	γc	NOUN
ejpam-3485	276	15	-	-	PUNCT
ejpam-3485	276	16	set	set	NOUN
ejpam-3485	276	17	of	of	ADP
ejpam-3485	276	18	g[h	g[h	PROPN
ejpam-3485	276	19	]	]	PUNCT
ejpam-3485	276	20	and	and	CCONJ
ejpam-3485	276	21	let	let	VERB
ejpam-3485	276	22	pc	pc	NOUN
ejpam-3485	276	23	=	=	NOUN
ejpam-3485	276	24	∪x∈d[{x	∪x∈d[{x	ADJ
ejpam-3485	276	25	}	}	PUNCT
ejpam-3485	276	26	×	×	PROPN
ejpam-3485	276	27	px	px	X
ejpam-3485	276	28	]	]	PUNCT
ejpam-3485	276	29	be	be	AUX
ejpam-3485	276	30	a	a	DET
ejpam-3485	276	31	forcing	forcing	NOUN
ejpam-3485	276	32	subset	subset	NOUN
ejpam-3485	276	33	for	for	ADP
ejpam-3485	276	34	c.	c.	PROPN
ejpam-3485	276	35	first	first	ADV
ejpam-3485	276	36	,	,	PUNCT
ejpam-3485	276	37	suppose	suppose	VERB
ejpam-3485	276	38	that	that	SCONJ
ejpam-3485	276	39	s	s	VERB
ejpam-3485	276	40	is	be	AUX
ejpam-3485	276	41	a	a	DET
ejpam-3485	276	42	γc	γc	NOUN
ejpam-3485	276	43	-	-	PUNCT
ejpam-3485	276	44	set	set	NOUN
ejpam-3485	276	45	of	of	ADP
ejpam-3485	276	46	g.	g.	PROPN
ejpam-3485	276	47	then	then	ADV
ejpam-3485	276	48	|tx|	|tx|	PROPN
ejpam-3485	276	49	=	=	PUNCT
ejpam-3485	276	50	1	1	NUM
ejpam-3485	276	51	for	for	ADP
ejpam-3485	276	52	all	all	DET
ejpam-3485	276	53	x	x	SYM
ejpam-3485	276	54	∈	∈	NOUN
ejpam-3485	276	55	s	s	X
ejpam-3485	276	56	by	by	ADP
ejpam-3485	276	57	theorem	theorem	ADJ
ejpam-3485	276	58	3.1	3.1	NUM
ejpam-3485	276	59	and	and	CCONJ
ejpam-3485	276	60	corollary	corollary	ADJ
ejpam-3485	276	61	3.3	3.3	NUM
ejpam-3485	276	62	.	.	PUNCT
ejpam-3485	277	1	hence	hence	ADV
ejpam-3485	277	2	,	,	PUNCT
ejpam-3485	277	3	px	px	PROPN
ejpam-3485	277	4	=	=	PUNCT
ejpam-3485	277	5	tx	tx	PROPN
ejpam-3485	277	6	for	for	ADP
ejpam-3485	277	7	all	all	DET
ejpam-3485	277	8	x	x	SYM
ejpam-3485	277	9	∈	∈	PROPN
ejpam-3485	277	10	d.	d.	NOUN
ejpam-3485	277	11	if	if	SCONJ
ejpam-3485	277	12	d	d	PROPN
ejpam-3485	277	13	6=	6=	PROPN
ejpam-3485	277	14	s	s	PART
ejpam-3485	277	15	,	,	PUNCT
ejpam-3485	277	16	say	say	VERB
ejpam-3485	277	17	y	y	PROPN
ejpam-3485	277	18	∈	∈	PROPN
ejpam-3485	277	19	s\d	s\d	NOUN
ejpam-3485	277	20	,	,	PUNCT
ejpam-3485	277	21	then	then	ADV
ejpam-3485	277	22	pc	pc	VERB
ejpam-3485	277	23	⊆	⊆	NUM
ejpam-3485	277	24	c∗	c∗	NOUN
ejpam-3485	277	25	=	=	SYM
ejpam-3485	277	26	∪x∈s	∪x∈s	PROPN
ejpam-3485	278	1	[	[	X
ejpam-3485	278	2	{	{	PUNCT
ejpam-3485	278	3	x	x	NOUN
ejpam-3485	278	4	}	}	PUNCT
ejpam-3485	278	5	×	×	NOUN
ejpam-3485	278	6	t	t	NOUN
ejpam-3485	278	7	∗x	∗x	PROPN
ejpam-3485	278	8	]	]	PUNCT
ejpam-3485	278	9	,	,	PUNCT
ejpam-3485	278	10	where	where	SCONJ
ejpam-3485	278	11	t	t	NOUN
ejpam-3485	278	12	∗x	∗x	PROPN
ejpam-3485	278	13	=	=	SYM
ejpam-3485	278	14	tx	tx	VERB
ejpam-3485	278	15	for	for	ADP
ejpam-3485	278	16	x	x	PROPN
ejpam-3485	278	17	∈	∈	PROPN
ejpam-3485	278	18	s\{y	s\{y	X
ejpam-3485	278	19	}	}	PUNCT
ejpam-3485	278	20	and	and	CCONJ
ejpam-3485	278	21	t	t	PROPN
ejpam-3485	278	22	∗y	∗y	PROPN
ejpam-3485	278	23	is	be	AUX
ejpam-3485	278	24	a	a	DET
ejpam-3485	278	25	singleton	singleton	NOUN
ejpam-3485	278	26	subset	subset	NOUN
ejpam-3485	278	27	of	of	ADP
ejpam-3485	278	28	h	h	NOUN
ejpam-3485	278	29	different	different	ADJ
ejpam-3485	278	30	from	from	ADP
ejpam-3485	278	31	ty	ty	PRON
ejpam-3485	278	32	.	.	PUNCT
ejpam-3485	279	1	since	since	SCONJ
ejpam-3485	279	2	c∗	c∗	PROPN
ejpam-3485	279	3	is	be	AUX
ejpam-3485	279	4	a	a	DET
ejpam-3485	279	5	γc	γc	NOUN
ejpam-3485	279	6	-	-	PUNCT
ejpam-3485	279	7	set	set	NOUN
ejpam-3485	279	8	of	of	ADP
ejpam-3485	279	9	g[h	g[h	NOUN
ejpam-3485	279	10	]	]	PUNCT
ejpam-3485	279	11	and	and	CCONJ
ejpam-3485	279	12	c∗	c∗	PROPN
ejpam-3485	279	13	6=	6=	PROPN
ejpam-3485	279	14	c	c	X
ejpam-3485	279	15	,	,	PUNCT
ejpam-3485	279	16	pc	pc	NOUN
ejpam-3485	279	17	is	be	AUX
ejpam-3485	279	18	not	not	PART
ejpam-3485	279	19	a	a	DET
ejpam-3485	279	20	forcing	forcing	NOUN
ejpam-3485	279	21	subset	subset	NOUN
ejpam-3485	279	22	for	for	ADP
ejpam-3485	279	23	c	c	PROPN
ejpam-3485	279	24	,	,	PUNCT
ejpam-3485	279	25	contrary	contrary	ADV
ejpam-3485	279	26	to	to	ADP
ejpam-3485	279	27	the	the	DET
ejpam-3485	279	28	assumption	assumption	NOUN
ejpam-3485	279	29	.	.	PUNCT
ejpam-3485	280	1	thus	thus	ADV
ejpam-3485	280	2	,	,	PUNCT
ejpam-3485	280	3	d	d	PROPN
ejpam-3485	280	4	=	=	SYM
ejpam-3485	280	5	s	s	PROPN
ejpam-3485	280	6	,	,	PUNCT
ejpam-3485	280	7	that	that	ADV
ejpam-3485	280	8	is	is	ADV
ejpam-3485	280	9	,	,	PUNCT
ejpam-3485	280	10	pc	pc	NOUN
ejpam-3485	280	11	=	=	SYM
ejpam-3485	280	12	c.	c.	NOUN
ejpam-3485	280	13	hence	hence	ADV
ejpam-3485	280	14	,	,	PUNCT
ejpam-3485	280	15	fγc(c	fγc(c	PROPN
ejpam-3485	280	16	)	)	PUNCT
ejpam-3485	280	17	=	=	SYM
ejpam-3485	280	18	|c|	|c|	PROPN
ejpam-3485	280	19	=	=	SYM
ejpam-3485	280	20	|s|	|s|	PROPN
ejpam-3485	280	21	=	=	NOUN
ejpam-3485	280	22	γc(g	γc(g	X
ejpam-3485	280	23	)	)	PUNCT
ejpam-3485	280	24	=	=	SYM
ejpam-3485	280	25	fγc(g[h	fγc(g[h	PROPN
ejpam-3485	280	26	]	]	PUNCT
ejpam-3485	280	27	)	)	PUNCT
ejpam-3485	280	28	.	.	PUNCT
ejpam-3485	281	1	�	�	PROPN
ejpam-3485	281	2	acknowledgements	acknowledgement	VERB
ejpam-3485	281	3	the	the	DET
ejpam-3485	281	4	authors	author	NOUN
ejpam-3485	281	5	would	would	AUX
ejpam-3485	281	6	like	like	VERB
ejpam-3485	281	7	to	to	PART
ejpam-3485	281	8	thank	thank	VERB
ejpam-3485	281	9	the	the	DET
ejpam-3485	281	10	referees	referee	NOUN
ejpam-3485	281	11	for	for	ADP
ejpam-3485	281	12	their	their	PRON
ejpam-3485	281	13	invaluable	invaluable	ADJ
ejpam-3485	281	14	suggestions	suggestion	NOUN
ejpam-3485	281	15	and	and	CCONJ
ejpam-3485	281	16	comments	comment	NOUN
ejpam-3485	281	17	which	which	PRON
ejpam-3485	281	18	greatly	greatly	ADV
ejpam-3485	281	19	contributed	contribute	VERB
ejpam-3485	281	20	in	in	ADP
ejpam-3485	281	21	the	the	DET
ejpam-3485	281	22	improvement	improvement	NOUN
ejpam-3485	281	23	of	of	ADP
ejpam-3485	281	24	the	the	DET
ejpam-3485	281	25	paper	paper	NOUN
ejpam-3485	281	26	.	.	PUNCT
ejpam-3485	282	1	the	the	DET
ejpam-3485	282	2	authors	author	NOUN
ejpam-3485	282	3	would	would	AUX
ejpam-3485	282	4	like	like	VERB
ejpam-3485	282	5	to	to	PART
ejpam-3485	282	6	thank	thank	VERB
ejpam-3485	282	7	also	also	ADV
ejpam-3485	282	8	the	the	DET
ejpam-3485	282	9	following	follow	VERB
ejpam-3485	282	10	funding	funding	NOUN
ejpam-3485	282	11	agencies	agency	NOUN
ejpam-3485	282	12	:	:	PUNCT
ejpam-3485	282	13	department	department	NOUN
ejpam-3485	282	14	of	of	ADP
ejpam-3485	282	15	science	science	NOUN
ejpam-3485	282	16	and	and	CCONJ
ejpam-3485	282	17	technology	technology	NOUN
ejpam-3485	282	18	-	-	PUNCT
ejpam-3485	282	19	science	science	NOUN
ejpam-3485	282	20	education	education	PROPN
ejpam-3485	282	21	institute	institute	NOUN
ejpam-3485	282	22	-	-	PUNCT
ejpam-3485	282	23	accelerated	accelerate	VERB
ejpam-3485	282	24	science	science	NOUN
ejpam-3485	282	25	and	and	CCONJ
ejpam-3485	282	26	technology	technology	NOUN
ejpam-3485	282	27	human	human	ADJ
ejpam-3485	282	28	resource	resource	NOUN
ejpam-3485	282	29	development	development	NOUN
ejpam-3485	282	30	program	program	NOUN
ejpam-3485	282	31	(	(	PUNCT
ejpam-3485	282	32	dost	dost	NOUN
ejpam-3485	282	33	-	-	PUNCT
ejpam-3485	282	34	sei	sei	ADJ
ejpam-3485	282	35	-	-	PUNCT
ejpam-3485	282	36	asthrdp	asthrdp	NOUN
ejpam-3485	282	37	)	)	PUNCT
ejpam-3485	282	38	,	,	PUNCT
ejpam-3485	282	39	mindanao	mindanao	PROPN
ejpam-3485	282	40	state	state	PROPN
ejpam-3485	282	41	university	university	PROPN
ejpam-3485	282	42	-	-	PUNCT
ejpam-3485	282	43	iligan	iligan	PROPN
ejpam-3485	282	44	institute	institute	PROPN
ejpam-3485	282	45	of	of	ADP
ejpam-3485	282	46	technology	technology	PROPN
ejpam-3485	282	47	,	,	PUNCT
ejpam-3485	282	48	cebu	cebu	NOUN
ejpam-3485	282	49	normal	normal	ADJ
ejpam-3485	282	50	university	university	NOUN
ejpam-3485	282	51	and	and	CCONJ
ejpam-3485	282	52	commission	commission	NOUN
ejpam-3485	282	53	on	on	ADP
ejpam-3485	282	54	higher	high	ADJ
ejpam-3485	282	55	education	education	NOUN
ejpam-3485	282	56	,	,	PUNCT
ejpam-3485	282	57	philippines	philippine	NOUN
ejpam-3485	282	58	.	.	PUNCT
ejpam-3485	283	1	references	reference	NOUN
ejpam-3485	283	2	[	[	X
ejpam-3485	283	3	1	1	NUM
ejpam-3485	283	4	]	]	X
ejpam-3485	283	5	c.	c.	PROPN
ejpam-3485	283	6	armada	armada	PROPN
ejpam-3485	283	7	,	,	PUNCT
ejpam-3485	283	8	s.	s.	PROPN
ejpam-3485	283	9	canoy	canoy	PROPN
ejpam-3485	283	10	jr	jr	PROPN
ejpam-3485	283	11	.	.	PROPN
ejpam-3485	283	12	,	,	PUNCT
ejpam-3485	283	13	and	and	CCONJ
ejpam-3485	283	14	c.	c.	PROPN
ejpam-3485	283	15	go	go	VERB
ejpam-3485	283	16	,	,	PUNCT
ejpam-3485	283	17	forcing	force	VERB
ejpam-3485	283	18	domination	domination	NOUN
ejpam-3485	283	19	numbers	number	NOUN
ejpam-3485	283	20	of	of	ADP
ejpam-3485	283	21	graphs	graph	NOUN
ejpam-3485	283	22	under	under	ADP
ejpam-3485	283	23	some	some	DET
ejpam-3485	283	24	binary	binary	ADJ
ejpam-3485	283	25	operations	operation	NOUN
ejpam-3485	283	26	,	,	PUNCT
ejpam-3485	283	27	advances	advance	NOUN
ejpam-3485	283	28	and	and	CCONJ
ejpam-3485	283	29	applications	application	NOUN
ejpam-3485	283	30	in	in	ADP
ejpam-3485	283	31	discrete	discrete	ADJ
ejpam-3485	283	32	mathematics	mathematic	NOUN
ejpam-3485	283	33	,	,	PUNCT
ejpam-3485	283	34	19	19	NUM
ejpam-3485	283	35	:	:	SYM
ejpam-3485	283	36	213	213	NUM
ejpam-3485	283	37	-	-	SYM
ejpam-3485	283	38	228	228	NUM
ejpam-3485	283	39	,	,	PUNCT
ejpam-3485	283	40	2018	2018	NUM
ejpam-3485	283	41	references	reference	NOUN
ejpam-3485	283	42	1786	1786	NUM
ejpam-3485	283	43	[	[	X
ejpam-3485	283	44	2	2	NUM
ejpam-3485	283	45	]	]	PUNCT
ejpam-3485	283	46	g.	g.	PROPN
ejpam-3485	283	47	chartrand	chartrand	PROPN
ejpam-3485	283	48	,	,	PUNCT
ejpam-3485	283	49	h.	h.	PROPN
ejpam-3485	283	50	gavlas	gavlas	PROPN
ejpam-3485	283	51	,	,	PUNCT
ejpam-3485	283	52	k.c	k.c	PROPN
ejpam-3485	283	53	.	.	PROPN
ejpam-3485	283	54	vandell	vandell	PROPN
ejpam-3485	283	55	,	,	PUNCT
ejpam-3485	283	56	and	and	CCONJ
ejpam-3485	283	57	f.	f.	PROPN
ejpam-3485	283	58	harary	harary	PROPN
ejpam-3485	283	59	,	,	PUNCT
ejpam-3485	283	60	the	the	DET
ejpam-3485	283	61	forcing	force	VERB
ejpam-3485	283	62	domination	domination	NOUN
ejpam-3485	283	63	number	number	NOUN
ejpam-3485	283	64	of	of	ADP
ejpam-3485	283	65	a	a	DET
ejpam-3485	283	66	graph	graph	NOUN
ejpam-3485	283	67	,	,	PUNCT
ejpam-3485	283	68	j.combin	j.combin	NOUN
ejpam-3485	283	69	.	.	PUNCT
ejpam-3485	284	1	math	math	NOUN
ejpam-3485	284	2	.	.	PUNCT
ejpam-3485	285	1	combin	combin	NOUN
ejpam-3485	285	2	.	.	PUNCT
ejpam-3485	286	1	comput	comput	NOUN
ejpam-3485	286	2	.	.	PUNCT
ejpam-3485	286	3	,	,	PUNCT
ejpam-3485	286	4	25:161	25:161	NUM
ejpam-3485	286	5	-	-	SYM
ejpam-3485	286	6	174	174	NUM
ejpam-3485	286	7	,	,	PUNCT
ejpam-3485	286	8	1997	1997	NUM
ejpam-3485	286	9	[	[	X
ejpam-3485	286	10	3	3	X
ejpam-3485	286	11	]	]	X
ejpam-3485	286	12	j.	j.	PROPN
ejpam-3485	286	13	john	john	PROPN
ejpam-3485	286	14	,	,	PUNCT
ejpam-3485	286	15	s.	s.	PROPN
ejpam-3485	286	16	kavitha	kavitha	PROPN
ejpam-3485	286	17	and	and	CCONJ
ejpam-3485	286	18	s.	s.	PROPN
ejpam-3485	286	19	robinson	robinson	PROPN
ejpam-3485	286	20	chellathurai	chellathurai	PROPN
ejpam-3485	286	21	.	.	PUNCT
ejpam-3485	287	1	on	on	ADP
ejpam-3485	287	2	the	the	DET
ejpam-3485	287	3	forcing	force	VERB
ejpam-3485	287	4	connected	connect	VERB
ejpam-3485	287	5	domination	domination	NOUN
ejpam-3485	287	6	number	number	NOUN
ejpam-3485	287	7	of	of	ADP
ejpam-3485	287	8	a	a	DET
ejpam-3485	287	9	graph	graph	NOUN
ejpam-3485	287	10	.	.	PUNCT
ejpam-3485	287	11	journal	journal	NOUN
ejpam-3485	287	12	of	of	ADP
ejpam-3485	287	13	discrete	discrete	ADJ
ejpam-3485	287	14	mathematical	mathematical	ADJ
ejpam-3485	287	15	sciences	science	NOUN
ejpam-3485	287	16	and	and	CCONJ
ejpam-3485	287	17	cryptography	cryptography	NOUN
ejpam-3485	287	18	,	,	PUNCT
ejpam-3485	287	19	20:611?624	20:611?624	NUM
ejpam-3485	287	20	,	,	PUNCT
ejpam-3485	287	21	2017	2017	NUM
ejpam-3485	287	22	.	.	PUNCT