id	sid	tid	token	lemma	pos
ejpam-3484	1	1	european	european	PROPN
ejpam-3484	1	2	journal	journal	PROPN
ejpam-3484	1	3	of	of	ADP
ejpam-3484	1	4	pure	pure	ADJ
ejpam-3484	1	5	and	and	CCONJ
ejpam-3484	1	6	applied	apply	VERB
ejpam-3484	1	7	mathematics	mathematic	NOUN
ejpam-3484	1	8	vol	vol	NOUN
ejpam-3484	1	9	.	.	PROPN
ejpam-3484	2	1	12	12	NUM
ejpam-3484	2	2	,	,	PUNCT
ejpam-3484	2	3	no	no	INTJ
ejpam-3484	2	4	.	.	NOUN
ejpam-3484	2	5	4	4	NUM
ejpam-3484	2	6	,	,	PUNCT
ejpam-3484	2	7	2019	2019	NUM
ejpam-3484	2	8	,	,	PUNCT
ejpam-3484	2	9	1371	1371	NUM
ejpam-3484	2	10	-	-	SYM
ejpam-3484	2	11	1381	1381	NUM
ejpam-3484	2	12	issn	issn	PROPN
ejpam-3484	2	13	1307	1307	NUM
ejpam-3484	2	14	-	-	SYM
ejpam-3484	2	15	5543	5543	NUM
ejpam-3484	2	16	–	–	PUNCT
ejpam-3484	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3484	2	18	published	publish	VERB
ejpam-3484	2	19	by	by	ADP
ejpam-3484	2	20	new	new	PROPN
ejpam-3484	2	21	york	york	PROPN
ejpam-3484	2	22	business	business	PROPN
ejpam-3484	2	23	global	global	ADJ
ejpam-3484	2	24	forcing	force	VERB
ejpam-3484	2	25	independent	independent	ADJ
ejpam-3484	2	26	domination	domination	NOUN
ejpam-3484	2	27	number	number	NOUN
ejpam-3484	2	28	of	of	ADP
ejpam-3484	2	29	a	a	DET
ejpam-3484	2	30	graph	graph	NOUN
ejpam-3484	2	31	cris	cris	PROPN
ejpam-3484	2	32	l.	l.	PROPN
ejpam-3484	2	33	armada1	armada1	PROPN
ejpam-3484	2	34	,	,	PUNCT
ejpam-3484	2	35	sergio	sergio	PROPN
ejpam-3484	2	36	r.	r.	PROPN
ejpam-3484	2	37	canoy	canoy	PROPN
ejpam-3484	2	38	,	,	PUNCT
ejpam-3484	2	39	jr.2,3,∗	jr.2,3,∗	PROPN
ejpam-3484	2	40	1	1	NUM
ejpam-3484	2	41	mathematics	mathematics	PROPN
ejpam-3484	2	42	department	department	NOUN
ejpam-3484	2	43	,	,	PUNCT
ejpam-3484	2	44	cebu	cebu	NOUN
ejpam-3484	2	45	normal	normal	ADJ
ejpam-3484	2	46	university	university	NOUN
ejpam-3484	2	47	,	,	PUNCT
ejpam-3484	2	48	6000	6000	NUM
ejpam-3484	2	49	cebu	cebu	NOUN
ejpam-3484	2	50	city	city	NOUN
ejpam-3484	2	51	,	,	PUNCT
ejpam-3484	2	52	philippines	philippines	PROPN
ejpam-3484	2	53	2	2	NUM
ejpam-3484	2	54	department	department	NOUN
ejpam-3484	2	55	of	of	ADP
ejpam-3484	2	56	mathematics	mathematic	NOUN
ejpam-3484	2	57	and	and	CCONJ
ejpam-3484	2	58	statistics	statistic	NOUN
ejpam-3484	2	59	,	,	PUNCT
ejpam-3484	2	60	college	college	NOUN
ejpam-3484	2	61	of	of	ADP
ejpam-3484	2	62	sciences	science	NOUN
ejpam-3484	2	63	and	and	CCONJ
ejpam-3484	2	64	mathematics	mathematic	NOUN
ejpam-3484	2	65	,	,	PUNCT
ejpam-3484	2	66	mindanao	mindanao	PROPN
ejpam-3484	2	67	state	state	PROPN
ejpam-3484	2	68	university	university	PROPN
ejpam-3484	2	69	-	-	PUNCT
ejpam-3484	2	70	iligan	iligan	PROPN
ejpam-3484	2	71	institute	institute	PROPN
ejpam-3484	2	72	of	of	ADP
ejpam-3484	2	73	technology	technology	PROPN
ejpam-3484	2	74	,	,	PUNCT
ejpam-3484	2	75	9200	9200	NUM
ejpam-3484	2	76	iligan	iligan	ADJ
ejpam-3484	2	77	city	city	NOUN
ejpam-3484	2	78	,	,	PUNCT
ejpam-3484	2	79	philippines	philippine	NOUN
ejpam-3484	2	80	3	3	NUM
ejpam-3484	2	81	center	center	NOUN
ejpam-3484	2	82	for	for	ADP
ejpam-3484	2	83	graph	graph	NOUN
ejpam-3484	2	84	theory	theory	NOUN
ejpam-3484	2	85	,	,	PUNCT
ejpam-3484	2	86	algebra	algebra	NOUN
ejpam-3484	2	87	,	,	PUNCT
ejpam-3484	2	88	and	and	CCONJ
ejpam-3484	2	89	analysis	analysis	NOUN
ejpam-3484	2	90	,	,	PUNCT
ejpam-3484	2	91	premier	premier	PROPN
ejpam-3484	2	92	research	research	PROPN
ejpam-3484	2	93	institute	institute	PROPN
ejpam-3484	2	94	in	in	ADP
ejpam-3484	2	95	science	science	NOUN
ejpam-3484	2	96	and	and	CCONJ
ejpam-3484	2	97	mathematics	mathematic	NOUN
ejpam-3484	2	98	,	,	PUNCT
ejpam-3484	2	99	mindanao	mindanao	PROPN
ejpam-3484	2	100	state	state	PROPN
ejpam-3484	2	101	university	university	PROPN
ejpam-3484	2	102	-	-	PUNCT
ejpam-3484	2	103	iligan	iligan	PROPN
ejpam-3484	2	104	institute	institute	PROPN
ejpam-3484	2	105	of	of	ADP
ejpam-3484	2	106	technology	technology	PROPN
ejpam-3484	2	107	,	,	PUNCT
ejpam-3484	2	108	9200	9200	NUM
ejpam-3484	2	109	iligan	iligan	ADJ
ejpam-3484	2	110	city	city	NOUN
ejpam-3484	2	111	,	,	PUNCT
ejpam-3484	2	112	philippines	philippine	NOUN
ejpam-3484	2	113	abstract	abstract	ADJ
ejpam-3484	2	114	.	.	PUNCT
ejpam-3484	3	1	in	in	ADP
ejpam-3484	3	2	this	this	DET
ejpam-3484	3	3	paper	paper	NOUN
ejpam-3484	3	4	,	,	PUNCT
ejpam-3484	3	5	we	we	PRON
ejpam-3484	3	6	obtain	obtain	VERB
ejpam-3484	3	7	the	the	DET
ejpam-3484	3	8	forcing	force	VERB
ejpam-3484	3	9	independent	independent	ADJ
ejpam-3484	3	10	domination	domination	NOUN
ejpam-3484	3	11	number	number	NOUN
ejpam-3484	3	12	of	of	ADP
ejpam-3484	3	13	some	some	DET
ejpam-3484	3	14	special	special	ADJ
ejpam-3484	3	15	graphs	graph	NOUN
ejpam-3484	3	16	.	.	PUNCT
ejpam-3484	4	1	further	far	ADV
ejpam-3484	4	2	,	,	PUNCT
ejpam-3484	4	3	we	we	PRON
ejpam-3484	4	4	determine	determine	VERB
ejpam-3484	4	5	the	the	DET
ejpam-3484	4	6	forcing	force	VERB
ejpam-3484	4	7	independent	independent	ADJ
ejpam-3484	4	8	domination	domination	NOUN
ejpam-3484	4	9	number	number	NOUN
ejpam-3484	4	10	of	of	ADP
ejpam-3484	4	11	graphs	graph	NOUN
ejpam-3484	4	12	under	under	ADP
ejpam-3484	4	13	some	some	DET
ejpam-3484	4	14	binary	binary	ADJ
ejpam-3484	4	15	operations	operation	NOUN
ejpam-3484	4	16	such	such	ADJ
ejpam-3484	4	17	join	join	NOUN
ejpam-3484	4	18	,	,	PUNCT
ejpam-3484	4	19	corona	corona	NOUN
ejpam-3484	4	20	and	and	CCONJ
ejpam-3484	4	21	lexicographic	lexicographic	ADJ
ejpam-3484	4	22	product	product	NOUN
ejpam-3484	4	23	of	of	ADP
ejpam-3484	4	24	two	two	NUM
ejpam-3484	4	25	graphs	graph	NOUN
ejpam-3484	4	26	.	.	PUNCT
ejpam-3484	5	1	2010	2010	NUM
ejpam-3484	5	2	mathematics	mathematic	NOUN
ejpam-3484	5	3	subject	subject	NOUN
ejpam-3484	5	4	classifications	classification	NOUN
ejpam-3484	5	5	:	:	PUNCT
ejpam-3484	5	6	05c69	05c69	X
ejpam-3484	5	7	key	key	ADJ
ejpam-3484	5	8	words	word	NOUN
ejpam-3484	5	9	and	and	CCONJ
ejpam-3484	5	10	phrases	phrase	NOUN
ejpam-3484	5	11	:	:	PUNCT
ejpam-3484	5	12	forcing	force	VERB
ejpam-3484	5	13	,	,	PUNCT
ejpam-3484	5	14	independent	independent	ADJ
ejpam-3484	5	15	,	,	PUNCT
ejpam-3484	5	16	domination	domination	NOUN
ejpam-3484	5	17	,	,	PUNCT
ejpam-3484	5	18	join	join	NOUN
ejpam-3484	5	19	,	,	PUNCT
ejpam-3484	5	20	corona	corona	PROPN
ejpam-3484	5	21	,	,	PUNCT
ejpam-3484	5	22	lexicographic	lexicographic	ADJ
ejpam-3484	5	23	product	product	NOUN
ejpam-3484	5	24	1	1	NUM
ejpam-3484	5	25	.	.	PUNCT
ejpam-3484	5	26	introduction	introduction	NOUN
ejpam-3484	5	27	let	let	VERB
ejpam-3484	5	28	g	g	NOUN
ejpam-3484	5	29	=	=	SYM
ejpam-3484	5	30	(	(	PUNCT
ejpam-3484	5	31	v	v	NOUN
ejpam-3484	5	32	(	(	PUNCT
ejpam-3484	5	33	g	g	NOUN
ejpam-3484	5	34	)	)	PUNCT
ejpam-3484	5	35	,	,	PUNCT
ejpam-3484	5	36	e(g	e(g	PROPN
ejpam-3484	5	37	)	)	PUNCT
ejpam-3484	5	38	)	)	PUNCT
ejpam-3484	5	39	be	be	AUX
ejpam-3484	5	40	a	a	DET
ejpam-3484	5	41	graph	graph	NOUN
ejpam-3484	5	42	and	and	CCONJ
ejpam-3484	5	43	v	v	ADP
ejpam-3484	5	44	∈	∈	PROPN
ejpam-3484	5	45	v	v	NOUN
ejpam-3484	5	46	(	(	PUNCT
ejpam-3484	5	47	g	g	NOUN
ejpam-3484	5	48	)	)	PUNCT
ejpam-3484	5	49	.	.	PUNCT
ejpam-3484	6	1	the	the	DET
ejpam-3484	6	2	open	open	ADJ
ejpam-3484	6	3	neighborhood	neighborhood	NOUN
ejpam-3484	6	4	of	of	ADP
ejpam-3484	6	5	v	v	NOUN
ejpam-3484	6	6	in	in	ADP
ejpam-3484	6	7	g	g	PROPN
ejpam-3484	6	8	is	be	AUX
ejpam-3484	6	9	the	the	DET
ejpam-3484	6	10	set	set	NOUN
ejpam-3484	6	11	n(v	n(v	PROPN
ejpam-3484	6	12	)	)	PUNCT
ejpam-3484	6	13	=	=	PRON
ejpam-3484	7	1	{	{	PUNCT
ejpam-3484	7	2	u	u	NOUN
ejpam-3484	7	3	∈	∈	PROPN
ejpam-3484	7	4	v	v	NOUN
ejpam-3484	7	5	(	(	PUNCT
ejpam-3484	7	6	g	g	NOUN
ejpam-3484	7	7	)	)	PUNCT
ejpam-3484	7	8	:	:	PUNCT
ejpam-3484	7	9	uv	uv	PROPN
ejpam-3484	7	10	∈	∈	PROPN
ejpam-3484	7	11	e(g	e(g	PROPN
ejpam-3484	7	12	)	)	PUNCT
ejpam-3484	7	13	}	}	PUNCT
ejpam-3484	7	14	and	and	CCONJ
ejpam-3484	7	15	the	the	DET
ejpam-3484	7	16	closed	closed	ADJ
ejpam-3484	7	17	neighborhood	neighborhood	NOUN
ejpam-3484	7	18	of	of	ADP
ejpam-3484	7	19	v	v	NOUN
ejpam-3484	7	20	is	be	AUX
ejpam-3484	7	21	the	the	DET
ejpam-3484	7	22	set	set	ADJ
ejpam-3484	7	23	n	n	PROPN
ejpam-3484	7	24	[	[	X
ejpam-3484	7	25	v	v	X
ejpam-3484	7	26	]	]	X
ejpam-3484	7	27	=	=	PUNCT
ejpam-3484	7	28	n(v	n(v	PROPN
ejpam-3484	7	29	)	)	PUNCT
ejpam-3484	7	30	∪	∪	NOUN
ejpam-3484	7	31	{	{	PUNCT
ejpam-3484	7	32	v	v	NOUN
ejpam-3484	7	33	}	}	PUNCT
ejpam-3484	7	34	.	.	PUNCT
ejpam-3484	8	1	for	for	ADP
ejpam-3484	8	2	x	x	SYM
ejpam-3484	8	3	⊆	⊆	NUM
ejpam-3484	8	4	v	v	ADP
ejpam-3484	8	5	(	(	PUNCT
ejpam-3484	8	6	g	g	NOUN
ejpam-3484	8	7	)	)	PUNCT
ejpam-3484	8	8	,	,	PUNCT
ejpam-3484	8	9	the	the	DET
ejpam-3484	8	10	open	open	ADJ
ejpam-3484	8	11	neighborhood	neighborhood	NOUN
ejpam-3484	8	12	of	of	ADP
ejpam-3484	8	13	x	x	SYM
ejpam-3484	8	14	is	be	AUX
ejpam-3484	8	15	the	the	DET
ejpam-3484	8	16	set	set	NOUN
ejpam-3484	8	17	n(x	n(x	NOUN
ejpam-3484	8	18	)	)	PUNCT
ejpam-3484	8	19	=	=	PUNCT
ejpam-3484	8	20	∪v∈xng(v	∪v∈xng(v	PROPN
ejpam-3484	8	21	)	)	PUNCT
ejpam-3484	8	22	and	and	CCONJ
ejpam-3484	8	23	its	its	PRON
ejpam-3484	8	24	closed	closed	ADJ
ejpam-3484	8	25	neighborhood	neighborhood	NOUN
ejpam-3484	8	26	is	be	AUX
ejpam-3484	8	27	the	the	DET
ejpam-3484	8	28	set	set	ADJ
ejpam-3484	8	29	n	n	NOUN
ejpam-3484	8	30	[	[	X
ejpam-3484	8	31	x	x	X
ejpam-3484	8	32	]	]	X
ejpam-3484	8	33	=	=	SYM
ejpam-3484	8	34	n(x	n(x	X
ejpam-3484	8	35	)	)	PUNCT
ejpam-3484	8	36	∪x	∪x	NUM
ejpam-3484	8	37	.	.	PUNCT
ejpam-3484	9	1	a	a	DET
ejpam-3484	9	2	set	set	NOUN
ejpam-3484	9	3	i	i	PRON
ejpam-3484	9	4	⊆	⊆	NUM
ejpam-3484	9	5	v	v	ADP
ejpam-3484	9	6	(	(	PUNCT
ejpam-3484	9	7	g	g	NOUN
ejpam-3484	9	8	)	)	PUNCT
ejpam-3484	9	9	is	be	AUX
ejpam-3484	9	10	an	an	DET
ejpam-3484	9	11	independent	independent	ADJ
ejpam-3484	9	12	set	set	NOUN
ejpam-3484	9	13	of	of	ADP
ejpam-3484	9	14	g	g	PROPN
ejpam-3484	9	15	if	if	SCONJ
ejpam-3484	9	16	i	i	PRON
ejpam-3484	9	17	∩	∩	VERB
ejpam-3484	9	18	n(i	n(i	ADJ
ejpam-3484	9	19	)	)	PUNCT
ejpam-3484	10	1	=	=	PUNCT
ejpam-3484	10	2	∅.	∅.	VERB
ejpam-3484	10	3	a	a	DET
ejpam-3484	10	4	set	set	NOUN
ejpam-3484	10	5	d	d	NOUN
ejpam-3484	10	6	⊆	⊆	NUM
ejpam-3484	10	7	v	v	ADP
ejpam-3484	10	8	(	(	PUNCT
ejpam-3484	10	9	g	g	NOUN
ejpam-3484	10	10	)	)	PUNCT
ejpam-3484	10	11	is	be	AUX
ejpam-3484	10	12	a	a	DET
ejpam-3484	10	13	dominating	dominating	NOUN
ejpam-3484	10	14	set	set	NOUN
ejpam-3484	10	15	of	of	ADP
ejpam-3484	10	16	g	g	PROPN
ejpam-3484	10	17	if	if	SCONJ
ejpam-3484	10	18	n	n	PROPN
ejpam-3484	10	19	[	[	X
ejpam-3484	10	20	d	d	X
ejpam-3484	10	21	]	]	X
ejpam-3484	10	22	=	=	SYM
ejpam-3484	10	23	v	v	NOUN
ejpam-3484	10	24	(	(	PUNCT
ejpam-3484	10	25	g	g	NOUN
ejpam-3484	10	26	)	)	PUNCT
ejpam-3484	10	27	.	.	PUNCT
ejpam-3484	11	1	a	a	DET
ejpam-3484	11	2	set	set	NOUN
ejpam-3484	11	3	t	t	PROPN
ejpam-3484	11	4	⊆	⊆	NUM
ejpam-3484	11	5	v	v	NOUN
ejpam-3484	11	6	(	(	PUNCT
ejpam-3484	11	7	g	g	NOUN
ejpam-3484	11	8	)	)	PUNCT
ejpam-3484	11	9	is	be	AUX
ejpam-3484	11	10	an	an	DET
ejpam-3484	11	11	independent	independent	ADJ
ejpam-3484	11	12	dominating	dominating	NOUN
ejpam-3484	11	13	set	set	NOUN
ejpam-3484	11	14	of	of	ADP
ejpam-3484	11	15	g	g	PROPN
ejpam-3484	11	16	if	if	SCONJ
ejpam-3484	11	17	t	t	PROPN
ejpam-3484	11	18	is	be	AUX
ejpam-3484	11	19	both	both	CCONJ
ejpam-3484	11	20	independent	independent	ADJ
ejpam-3484	11	21	and	and	CCONJ
ejpam-3484	11	22	dominating	dominating	NOUN
ejpam-3484	11	23	set	set	NOUN
ejpam-3484	11	24	.	.	PUNCT
ejpam-3484	12	1	the	the	DET
ejpam-3484	12	2	independent	independent	ADJ
ejpam-3484	12	3	domination	domination	NOUN
ejpam-3484	12	4	number	number	NOUN
ejpam-3484	12	5	γi(g	γi(g	NUM
ejpam-3484	12	6	)	)	PUNCT
ejpam-3484	12	7	of	of	ADP
ejpam-3484	12	8	g	g	PROPN
ejpam-3484	12	9	is	be	AUX
ejpam-3484	12	10	the	the	DET
ejpam-3484	12	11	minimum	minimum	ADJ
ejpam-3484	12	12	cardinality	cardinality	NOUN
ejpam-3484	12	13	of	of	ADP
ejpam-3484	12	14	an	an	DET
ejpam-3484	12	15	independent	independent	ADJ
ejpam-3484	12	16	dominating	dominating	NOUN
ejpam-3484	12	17	set	set	NOUN
ejpam-3484	12	18	.	.	PUNCT
ejpam-3484	13	1	if	if	SCONJ
ejpam-3484	13	2	s	s	NOUN
ejpam-3484	13	3	is	be	AUX
ejpam-3484	13	4	an	an	DET
ejpam-3484	13	5	independent	independent	ADJ
ejpam-3484	13	6	dominating	dominating	NOUN
ejpam-3484	13	7	set	set	VERB
ejpam-3484	13	8	with	with	ADP
ejpam-3484	13	9	|s|	|s|	NOUN
ejpam-3484	13	10	=	=	NOUN
ejpam-3484	13	11	γi(g	γi(g	NOUN
ejpam-3484	13	12	)	)	PUNCT
ejpam-3484	13	13	,	,	PUNCT
ejpam-3484	13	14	then	then	ADV
ejpam-3484	13	15	we	we	PRON
ejpam-3484	13	16	call	call	VERB
ejpam-3484	13	17	s	s	PRON
ejpam-3484	13	18	a	a	DET
ejpam-3484	13	19	γi	γi	NOUN
ejpam-3484	13	20	-	-	PUNCT
ejpam-3484	13	21	set	set	NOUN
ejpam-3484	13	22	of	of	ADP
ejpam-3484	13	23	g.	g.	PROPN
ejpam-3484	13	24	a	a	DET
ejpam-3484	13	25	maximum	maximum	ADJ
ejpam-3484	13	26	independent	independent	ADJ
ejpam-3484	13	27	set	set	NOUN
ejpam-3484	13	28	(	(	PUNCT
ejpam-3484	13	29	α	α	NOUN
ejpam-3484	13	30	-	-	PUNCT
ejpam-3484	13	31	set	set	NOUN
ejpam-3484	13	32	)	)	PUNCT
ejpam-3484	13	33	is	be	AUX
ejpam-3484	13	34	an	an	DET
ejpam-3484	13	35	independent	independent	ADJ
ejpam-3484	13	36	set	set	NOUN
ejpam-3484	13	37	of	of	ADP
ejpam-3484	13	38	largest	large	ADJ
ejpam-3484	13	39	possible	possible	ADJ
ejpam-3484	13	40	size	size	NOUN
ejpam-3484	13	41	for	for	ADP
ejpam-3484	13	42	a	a	DET
ejpam-3484	13	43	given	give	VERB
ejpam-3484	13	44	graph	graph	NOUN
ejpam-3484	13	45	g.	g.	NOUN
ejpam-3484	13	46	this	this	DET
ejpam-3484	13	47	size	size	NOUN
ejpam-3484	13	48	,	,	PUNCT
ejpam-3484	13	49	denoted	denote	VERB
ejpam-3484	13	50	by	by	ADP
ejpam-3484	13	51	α(g	α(g	NOUN
ejpam-3484	13	52	)	)	PUNCT
ejpam-3484	13	53	,	,	PUNCT
ejpam-3484	13	54	is	be	AUX
ejpam-3484	13	55	called	call	VERB
ejpam-3484	13	56	the	the	DET
ejpam-3484	13	57	independence	independence	NOUN
ejpam-3484	13	58	number	number	NOUN
ejpam-3484	13	59	of	of	ADP
ejpam-3484	13	60	g.	g.	PROPN
ejpam-3484	13	61	∗corresponding	∗corresponde	VERB
ejpam-3484	13	62	author	author	NOUN
ejpam-3484	13	63	.	.	PUNCT
ejpam-3484	14	1	doi	doi	NOUN
ejpam-3484	14	2	:	:	PUNCT
ejpam-3484	14	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3484	https://doi.org/10.29020/nybg.ejpam.v12i4.3484	PROPN
ejpam-3484	14	4	email	email	NOUN
ejpam-3484	14	5	addresses	address	NOUN
ejpam-3484	14	6	:	:	PUNCT
ejpam-3484	14	7	cris.armada@g.msuiit.edu.ph	cris.armada@g.msuiit.edu.ph	ADJ
ejpam-3484	14	8	,	,	PUNCT
ejpam-3484	14	9	armadac@cnu.edu.ph	armadac@cnu.edu.ph	PROPN
ejpam-3484	14	10	(	(	PUNCT
ejpam-3484	14	11	c.	c.	PROPN
ejpam-3484	14	12	armada	armada	PROPN
ejpam-3484	14	13	)	)	PUNCT
ejpam-3484	14	14	,	,	PUNCT
ejpam-3484	14	15	serge_canoy@yahoo.com	serge_canoy@yahoo.com	X
ejpam-3484	14	16	(	(	PUNCT
ejpam-3484	14	17	s.	s.	PROPN
ejpam-3484	14	18	canoy	canoy	PROPN
ejpam-3484	14	19	)	)	PUNCT
ejpam-3484	14	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3484	14	21	1371	1371	NUM
ejpam-3484	15	1	c	c	X
ejpam-3484	15	2	©	©	PROPN
ejpam-3484	15	3	2019	2019	NUM
ejpam-3484	15	4	ejpam	ejpam	NOUN
ejpam-3484	15	5	all	all	DET
ejpam-3484	15	6	rights	right	NOUN
ejpam-3484	15	7	reserved	reserve	VERB
ejpam-3484	15	8	.	.	PUNCT
ejpam-3484	16	1	c.	c.	PROPN
ejpam-3484	16	2	armada	armada	PROPN
ejpam-3484	16	3	,	,	PUNCT
ejpam-3484	16	4	s.	s.	PROPN
ejpam-3484	16	5	canoy	canoy	PROPN
ejpam-3484	16	6	jr	jr	PROPN
ejpam-3484	16	7	.	.	PROPN
ejpam-3484	16	8	/	/	SYM
ejpam-3484	16	9	eur	eur	PROPN
ejpam-3484	16	10	.	.	PUNCT
ejpam-3484	17	1	j.	j.	PROPN
ejpam-3484	17	2	pure	pure	PROPN
ejpam-3484	17	3	appl	appl	PROPN
ejpam-3484	17	4	.	.	PROPN
ejpam-3484	17	5	math	math	PROPN
ejpam-3484	17	6	,	,	PUNCT
ejpam-3484	17	7	12	12	NUM
ejpam-3484	17	8	(	(	PUNCT
ejpam-3484	17	9	4	4	NUM
ejpam-3484	17	10	)	)	PUNCT
ejpam-3484	17	11	(	(	PUNCT
ejpam-3484	17	12	2019	2019	NUM
ejpam-3484	17	13	)	)	PUNCT
ejpam-3484	17	14	,	,	PUNCT
ejpam-3484	17	15	1371	1371	NUM
ejpam-3484	17	16	-	-	SYM
ejpam-3484	17	17	1381	1381	NUM
ejpam-3484	17	18	1372	1372	NUM
ejpam-3484	17	19	let	let	VERB
ejpam-3484	17	20	i	i	PRON
ejpam-3484	17	21	be	be	AUX
ejpam-3484	17	22	a	a	DET
ejpam-3484	17	23	γi	γi	NOUN
ejpam-3484	17	24	-	-	PUNCT
ejpam-3484	17	25	set	set	NOUN
ejpam-3484	17	26	of	of	ADP
ejpam-3484	17	27	a	a	DET
ejpam-3484	17	28	graph	graph	NOUN
ejpam-3484	17	29	g.	g.	NOUN
ejpam-3484	18	1	a	a	DET
ejpam-3484	18	2	subset	subset	NOUN
ejpam-3484	18	3	d	d	NOUN
ejpam-3484	18	4	of	of	ADP
ejpam-3484	18	5	i	i	PRON
ejpam-3484	18	6	is	be	AUX
ejpam-3484	18	7	said	say	VERB
ejpam-3484	18	8	to	to	PART
ejpam-3484	18	9	be	be	AUX
ejpam-3484	18	10	a	a	DET
ejpam-3484	18	11	forcing	forcing	NOUN
ejpam-3484	18	12	subset	subset	NOUN
ejpam-3484	18	13	for	for	ADP
ejpam-3484	18	14	i	i	PRON
ejpam-3484	18	15	if	if	SCONJ
ejpam-3484	18	16	i	i	PRON
ejpam-3484	18	17	is	be	AUX
ejpam-3484	18	18	the	the	DET
ejpam-3484	18	19	unique	unique	ADJ
ejpam-3484	18	20	γi	γi	NOUN
ejpam-3484	18	21	-	-	PUNCT
ejpam-3484	18	22	set	set	NOUN
ejpam-3484	18	23	containing	contain	VERB
ejpam-3484	18	24	d.	d.	NOUN
ejpam-3484	18	25	the	the	DET
ejpam-3484	18	26	forcing	force	VERB
ejpam-3484	18	27	independent	independent	ADJ
ejpam-3484	18	28	domination	domination	NOUN
ejpam-3484	18	29	number	number	NOUN
ejpam-3484	18	30	of	of	ADP
ejpam-3484	18	31	i	i	PRON
ejpam-3484	18	32	is	be	AUX
ejpam-3484	18	33	given	give	VERB
ejpam-3484	18	34	by	by	ADP
ejpam-3484	18	35	fγi(i	fγi(i	PROPN
ejpam-3484	18	36	)	)	PUNCT
ejpam-3484	18	37	=	=	X
ejpam-3484	19	1	min{|d|	min{|d|	NOUN
ejpam-3484	19	2	:	:	PUNCT
ejpam-3484	20	1	d	d	X
ejpam-3484	20	2	is	be	AUX
ejpam-3484	20	3	a	a	DET
ejpam-3484	20	4	forcing	forcing	NOUN
ejpam-3484	20	5	subset	subset	NOUN
ejpam-3484	20	6	for	for	ADP
ejpam-3484	20	7	i	i	PROPN
ejpam-3484	20	8	}	}	PUNCT
ejpam-3484	20	9	.	.	PUNCT
ejpam-3484	21	1	the	the	DET
ejpam-3484	21	2	forcing	force	VERB
ejpam-3484	21	3	independent	independent	ADJ
ejpam-3484	21	4	domination	domination	NOUN
ejpam-3484	21	5	number	number	NOUN
ejpam-3484	21	6	of	of	ADP
ejpam-3484	21	7	g	g	PROPN
ejpam-3484	21	8	is	be	AUX
ejpam-3484	21	9	given	give	VERB
ejpam-3484	21	10	by	by	ADP
ejpam-3484	21	11	fγi(g	fγi(g	PROPN
ejpam-3484	21	12	)	)	PUNCT
ejpam-3484	21	13	=	=	SYM
ejpam-3484	21	14	min{fγi(i	min{fγi(i	PROPN
ejpam-3484	21	15	)	)	PUNCT
ejpam-3484	21	16	:	:	PUNCT
ejpam-3484	22	1	i	i	PRON
ejpam-3484	22	2	is	be	AUX
ejpam-3484	22	3	a	a	DET
ejpam-3484	22	4	γi	γi	NOUN
ejpam-3484	22	5	-	-	PUNCT
ejpam-3484	22	6	set	set	NOUN
ejpam-3484	22	7	of	of	ADP
ejpam-3484	22	8	g	g	NOUN
ejpam-3484	22	9	}	}	PUNCT
ejpam-3484	22	10	.	.	PUNCT
ejpam-3484	23	1	let	let	VERB
ejpam-3484	23	2	b	b	X
ejpam-3484	23	3	be	be	AUX
ejpam-3484	23	4	an	an	DET
ejpam-3484	23	5	α	α	NOUN
ejpam-3484	23	6	-	-	PUNCT
ejpam-3484	23	7	set	set	NOUN
ejpam-3484	23	8	of	of	ADP
ejpam-3484	23	9	a	a	DET
ejpam-3484	23	10	graph	graph	NOUN
ejpam-3484	23	11	g.	g.	NOUN
ejpam-3484	23	12	a	a	DET
ejpam-3484	23	13	subset	subset	NOUN
ejpam-3484	23	14	p	p	NOUN
ejpam-3484	23	15	of	of	ADP
ejpam-3484	23	16	b	b	NOUN
ejpam-3484	23	17	is	be	AUX
ejpam-3484	23	18	said	say	VERB
ejpam-3484	23	19	to	to	PART
ejpam-3484	23	20	be	be	AUX
ejpam-3484	23	21	a	a	DET
ejpam-3484	23	22	forcing	forcing	NOUN
ejpam-3484	23	23	subset	subset	NOUN
ejpam-3484	23	24	for	for	ADP
ejpam-3484	23	25	b	b	NOUN
ejpam-3484	23	26	if	if	SCONJ
ejpam-3484	23	27	b	b	PROPN
ejpam-3484	23	28	is	be	AUX
ejpam-3484	23	29	the	the	DET
ejpam-3484	23	30	unique	unique	ADJ
ejpam-3484	23	31	α	α	NOUN
ejpam-3484	23	32	-	-	PUNCT
ejpam-3484	23	33	set	set	ADJ
ejpam-3484	23	34	containing	contain	VERB
ejpam-3484	23	35	p	p	NOUN
ejpam-3484	23	36	.	.	PUNCT
ejpam-3484	24	1	the	the	DET
ejpam-3484	24	2	forcing	force	VERB
ejpam-3484	24	3	independence	independence	NOUN
ejpam-3484	24	4	number	number	NOUN
ejpam-3484	24	5	of	of	ADP
ejpam-3484	24	6	b	b	NOUN
ejpam-3484	24	7	is	be	AUX
ejpam-3484	24	8	given	give	VERB
ejpam-3484	24	9	by	by	ADP
ejpam-3484	24	10	fα(b	fα(b	PUNCT
ejpam-3484	24	11	)	)	PUNCT
ejpam-3484	25	1	=	=	SYM
ejpam-3484	25	2	min{|p	min{|p	PROPN
ejpam-3484	26	1	|	|	ADV
ejpam-3484	26	2	:	:	PUNCT
ejpam-3484	26	3	p	p	PRON
ejpam-3484	26	4	is	be	AUX
ejpam-3484	26	5	a	a	DET
ejpam-3484	26	6	forcing	forcing	NOUN
ejpam-3484	26	7	subset	subset	NOUN
ejpam-3484	26	8	for	for	ADP
ejpam-3484	26	9	b	b	NOUN
ejpam-3484	26	10	}	}	PUNCT
ejpam-3484	26	11	.	.	PUNCT
ejpam-3484	27	1	the	the	DET
ejpam-3484	27	2	forcing	force	VERB
ejpam-3484	27	3	independence	independence	NOUN
ejpam-3484	27	4	number	number	NOUN
ejpam-3484	27	5	of	of	ADP
ejpam-3484	27	6	g	g	PROPN
ejpam-3484	27	7	is	be	AUX
ejpam-3484	27	8	given	give	VERB
ejpam-3484	27	9	by	by	ADP
ejpam-3484	27	10	fα(g	fα(g	PUNCT
ejpam-3484	27	11	)	)	PUNCT
ejpam-3484	27	12	=	=	SYM
ejpam-3484	27	13	min{fα(b	min{fα(b	X
ejpam-3484	27	14	)	)	PUNCT
ejpam-3484	27	15	:	:	PUNCT
ejpam-3484	28	1	b	b	X
ejpam-3484	28	2	is	be	AUX
ejpam-3484	28	3	an	an	DET
ejpam-3484	28	4	α	α	NOUN
ejpam-3484	28	5	-	-	PUNCT
ejpam-3484	28	6	set	set	NOUN
ejpam-3484	28	7	of	of	ADP
ejpam-3484	28	8	g	g	NOUN
ejpam-3484	28	9	}	}	PUNCT
ejpam-3484	28	10	.	.	PUNCT
ejpam-3484	29	1	chartrand	chartrand	PROPN
ejpam-3484	29	2	et	et	PROPN
ejpam-3484	29	3	.	.	PUNCT
ejpam-3484	30	1	al	al	PROPN
ejpam-3484	31	1	[	[	X
ejpam-3484	31	2	3	3	NUM
ejpam-3484	31	3	]	]	PUNCT
ejpam-3484	31	4	initiated	initiate	VERB
ejpam-3484	31	5	the	the	DET
ejpam-3484	31	6	investigation	investigation	NOUN
ejpam-3484	31	7	on	on	ADP
ejpam-3484	31	8	the	the	DET
ejpam-3484	31	9	relation	relation	NOUN
ejpam-3484	31	10	between	between	ADP
ejpam-3484	31	11	forcing	force	VERB
ejpam-3484	31	12	and	and	CCONJ
ejpam-3484	31	13	domination	domination	NOUN
ejpam-3484	31	14	concepts	concept	NOUN
ejpam-3484	31	15	in	in	ADP
ejpam-3484	31	16	1997	1997	NUM
ejpam-3484	31	17	and	and	CCONJ
ejpam-3484	31	18	used	use	VERB
ejpam-3484	31	19	the	the	DET
ejpam-3484	31	20	term	term	NOUN
ejpam-3484	31	21	"	"	PUNCT
ejpam-3484	31	22	forcing	force	VERB
ejpam-3484	31	23	domination	domination	NOUN
ejpam-3484	31	24	number	number	NOUN
ejpam-3484	31	25	"	"	PUNCT
ejpam-3484	31	26	.	.	PUNCT
ejpam-3484	32	1	independent	independent	ADJ
ejpam-3484	32	2	domination	domination	NOUN
ejpam-3484	32	3	under	under	ADP
ejpam-3484	32	4	some	some	DET
ejpam-3484	32	5	binary	binary	ADJ
ejpam-3484	32	6	operations	operation	NOUN
ejpam-3484	32	7	such	such	ADJ
ejpam-3484	32	8	as	as	ADP
ejpam-3484	32	9	corona	corona	NOUN
ejpam-3484	32	10	and	and	CCONJ
ejpam-3484	32	11	composition	composition	NOUN
ejpam-3484	32	12	is	be	AUX
ejpam-3484	32	13	studied	study	VERB
ejpam-3484	32	14	by	by	ADP
ejpam-3484	32	15	canoy	canoy	NOUN
ejpam-3484	32	16	[	[	X
ejpam-3484	32	17	2	2	NUM
ejpam-3484	32	18	]	]	PUNCT
ejpam-3484	32	19	.	.	PUNCT
ejpam-3484	33	1	in	in	ADP
ejpam-3484	33	2	2013	2013	NUM
ejpam-3484	33	3	,	,	PUNCT
ejpam-3484	33	4	larson	larson	PROPN
ejpam-3484	33	5	et	et	PROPN
ejpam-3484	33	6	.	.	PUNCT
ejpam-3484	34	1	al	al	PROPN
ejpam-3484	35	1	[	[	X
ejpam-3484	35	2	5	5	NUM
ejpam-3484	35	3	]	]	PUNCT
ejpam-3484	35	4	investigated	investigate	VERB
ejpam-3484	35	5	the	the	DET
ejpam-3484	35	6	forcing	force	VERB
ejpam-3484	35	7	independence	independence	NOUN
ejpam-3484	35	8	number	number	NOUN
ejpam-3484	35	9	.	.	PUNCT
ejpam-3484	36	1	in	in	ADP
ejpam-3484	36	2	2018	2018	NUM
ejpam-3484	36	3	,	,	PUNCT
ejpam-3484	36	4	canoy	canoy	ADJ
ejpam-3484	36	5	et	et	PROPN
ejpam-3484	36	6	.	.	PUNCT
ejpam-3484	37	1	al	al	PROPN
ejpam-3484	38	1	[	[	X
ejpam-3484	38	2	1	1	NUM
ejpam-3484	38	3	]	]	PUNCT
ejpam-3484	38	4	investigated	investigate	VERB
ejpam-3484	38	5	the	the	DET
ejpam-3484	38	6	forcing	force	VERB
ejpam-3484	38	7	domination	domination	NOUN
ejpam-3484	38	8	number	number	NOUN
ejpam-3484	38	9	of	of	ADP
ejpam-3484	38	10	graphs	graph	NOUN
ejpam-3484	38	11	under	under	ADP
ejpam-3484	38	12	some	some	DET
ejpam-3484	38	13	binary	binary	ADJ
ejpam-3484	38	14	operations	operation	NOUN
ejpam-3484	38	15	.	.	PUNCT
ejpam-3484	39	1	let	let	VERB
ejpam-3484	39	2	g	g	NOUN
ejpam-3484	39	3	and	and	CCONJ
ejpam-3484	39	4	h	h	NOUN
ejpam-3484	39	5	be	be	VERB
ejpam-3484	39	6	two	two	NUM
ejpam-3484	39	7	graphs	graph	NOUN
ejpam-3484	39	8	.	.	PUNCT
ejpam-3484	40	1	the	the	DET
ejpam-3484	40	2	join	join	NOUN
ejpam-3484	40	3	of	of	ADP
ejpam-3484	40	4	g	g	PROPN
ejpam-3484	40	5	and	and	CCONJ
ejpam-3484	40	6	h	h	NOUN
ejpam-3484	40	7	,	,	PUNCT
ejpam-3484	40	8	denoted	denote	VERB
ejpam-3484	40	9	by	by	ADP
ejpam-3484	40	10	g	g	PROPN
ejpam-3484	40	11	+	+	CCONJ
ejpam-3484	40	12	h	h	NOUN
ejpam-3484	40	13	is	be	AUX
ejpam-3484	40	14	the	the	DET
ejpam-3484	40	15	graph	graph	NOUN
ejpam-3484	40	16	with	with	ADP
ejpam-3484	40	17	vertex	vertex	NOUN
ejpam-3484	40	18	set	set	VERB
ejpam-3484	40	19	v	v	NOUN
ejpam-3484	40	20	(	(	PUNCT
ejpam-3484	40	21	g	g	PROPN
ejpam-3484	40	22	+	+	NOUN
ejpam-3484	40	23	h	h	NOUN
ejpam-3484	40	24	)	)	PUNCT
ejpam-3484	40	25	=	=	NOUN
ejpam-3484	40	26	v	v	X
ejpam-3484	40	27	(	(	PUNCT
ejpam-3484	40	28	g	g	NOUN
ejpam-3484	40	29	)	)	PUNCT
ejpam-3484	40	30	∪	∪	NOUN
ejpam-3484	40	31	v	v	NOUN
ejpam-3484	40	32	(	(	PUNCT
ejpam-3484	40	33	h	h	NOUN
ejpam-3484	40	34	)	)	PUNCT
ejpam-3484	40	35	and	and	CCONJ
ejpam-3484	40	36	edge	edge	NOUN
ejpam-3484	40	37	set	set	VERB
ejpam-3484	40	38	e(g+h	e(g+h	NUM
ejpam-3484	40	39	)	)	PUNCT
ejpam-3484	41	1	=	=	SYM
ejpam-3484	41	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-3484	41	3	{	{	PUNCT
ejpam-3484	41	4	uv	uv	NOUN
ejpam-3484	41	5	:	:	PUNCT
ejpam-3484	41	6	u	u	PROPN
ejpam-3484	41	7	∈	∈	PROPN
ejpam-3484	41	8	v	v	ADP
ejpam-3484	41	9	(	(	PUNCT
ejpam-3484	41	10	g	g	NOUN
ejpam-3484	41	11	)	)	PUNCT
ejpam-3484	41	12	,	,	PUNCT
ejpam-3484	41	13	v	v	X
ejpam-3484	41	14	∈	∈	PROPN
ejpam-3484	41	15	v	v	NOUN
ejpam-3484	41	16	(	(	PUNCT
ejpam-3484	41	17	h	h	NOUN
ejpam-3484	41	18	)	)	PUNCT
ejpam-3484	41	19	}	}	PUNCT
ejpam-3484	41	20	.	.	PUNCT
ejpam-3484	42	1	the	the	DET
ejpam-3484	42	2	corona	corona	NOUN
ejpam-3484	42	3	g	g	PROPN
ejpam-3484	42	4	◦	◦	NOUN
ejpam-3484	42	5	h	h	NOUN
ejpam-3484	42	6	of	of	ADP
ejpam-3484	42	7	g	g	PROPN
ejpam-3484	42	8	and	and	CCONJ
ejpam-3484	42	9	h	h	NOUN
ejpam-3484	42	10	is	be	AUX
ejpam-3484	42	11	the	the	DET
ejpam-3484	42	12	graph	graph	NOUN
ejpam-3484	42	13	obtained	obtain	VERB
ejpam-3484	42	14	by	by	ADP
ejpam-3484	42	15	taking	take	VERB
ejpam-3484	42	16	one	one	NUM
ejpam-3484	42	17	copy	copy	NOUN
ejpam-3484	42	18	of	of	ADP
ejpam-3484	42	19	g	g	PROPN
ejpam-3484	42	20	and	and	CCONJ
ejpam-3484	42	21	|v	|v	PROPN
ejpam-3484	42	22	(	(	PUNCT
ejpam-3484	42	23	g)|	g)|	NOUN
ejpam-3484	42	24	copies	copy	NOUN
ejpam-3484	42	25	of	of	ADP
ejpam-3484	42	26	h	h	NOUN
ejpam-3484	42	27	,	,	PUNCT
ejpam-3484	42	28	and	and	CCONJ
ejpam-3484	42	29	then	then	ADV
ejpam-3484	42	30	forming	form	VERB
ejpam-3484	42	31	the	the	DET
ejpam-3484	42	32	join	join	NOUN
ejpam-3484	42	33	〈	〈	PROPN
ejpam-3484	42	34	{	{	PUNCT
ejpam-3484	42	35	v}〉+hv	v}〉+hv	PROPN
ejpam-3484	42	36	=	=	SYM
ejpam-3484	42	37	v	v	PROPN
ejpam-3484	42	38	+	+	PROPN
ejpam-3484	42	39	hv	hv	PROPN
ejpam-3484	42	40	,	,	PUNCT
ejpam-3484	42	41	where	where	SCONJ
ejpam-3484	42	42	hv	hv	PROPN
ejpam-3484	42	43	is	be	AUX
ejpam-3484	42	44	a	a	DET
ejpam-3484	42	45	copy	copy	NOUN
ejpam-3484	42	46	of	of	ADP
ejpam-3484	42	47	h	h	NOUN
ejpam-3484	42	48	,	,	PUNCT
ejpam-3484	42	49	for	for	ADP
ejpam-3484	42	50	each	each	DET
ejpam-3484	42	51	v	v	NUM
ejpam-3484	42	52	∈	∈	PROPN
ejpam-3484	42	53	v	v	NOUN
ejpam-3484	42	54	(	(	PUNCT
ejpam-3484	42	55	g	g	NOUN
ejpam-3484	42	56	)	)	PUNCT
ejpam-3484	42	57	.	.	PUNCT
ejpam-3484	43	1	the	the	DET
ejpam-3484	43	2	lexicographic	lexicographic	ADJ
ejpam-3484	43	3	product	product	NOUN
ejpam-3484	43	4	(	(	PUNCT
ejpam-3484	43	5	or	or	CCONJ
ejpam-3484	43	6	composition	composition	NOUN
ejpam-3484	43	7	)	)	PUNCT
ejpam-3484	43	8	g[h	g[h	NOUN
ejpam-3484	43	9	]	]	PUNCT
ejpam-3484	43	10	of	of	ADP
ejpam-3484	43	11	g	g	PROPN
ejpam-3484	43	12	and	and	CCONJ
ejpam-3484	43	13	h	h	NOUN
ejpam-3484	43	14	is	be	AUX
ejpam-3484	43	15	the	the	DET
ejpam-3484	43	16	graph	graph	NOUN
ejpam-3484	43	17	with	with	ADP
ejpam-3484	43	18	v	v	NOUN
ejpam-3484	43	19	(	(	PUNCT
ejpam-3484	43	20	g[h	g[h	PROPN
ejpam-3484	43	21	]	]	PUNCT
ejpam-3484	43	22	)	)	PUNCT
ejpam-3484	43	23	=	=	SYM
ejpam-3484	43	24	v	v	X
ejpam-3484	43	25	(	(	PUNCT
ejpam-3484	43	26	g)×	g)×	NOUN
ejpam-3484	43	27	v	v	NOUN
ejpam-3484	43	28	(	(	PUNCT
ejpam-3484	43	29	h	h	NOUN
ejpam-3484	43	30	)	)	PUNCT
ejpam-3484	43	31	,	,	PUNCT
ejpam-3484	43	32	and	and	CCONJ
ejpam-3484	43	33	(	(	PUNCT
ejpam-3484	43	34	u	u	NOUN
ejpam-3484	43	35	,	,	PUNCT
ejpam-3484	43	36	u′)(v	u′)(v	NOUN
ejpam-3484	43	37	,	,	PUNCT
ejpam-3484	43	38	v′	v′	NOUN
ejpam-3484	43	39	)	)	PUNCT
ejpam-3484	43	40	∈	∈	NOUN
ejpam-3484	43	41	e(g[h	e(g[h	NOUN
ejpam-3484	43	42	]	]	PUNCT
ejpam-3484	43	43	)	)	PUNCT
ejpam-3484	43	44	if	if	SCONJ
ejpam-3484	43	45	and	and	CCONJ
ejpam-3484	43	46	only	only	ADV
ejpam-3484	43	47	if	if	SCONJ
ejpam-3484	43	48	either	either	DET
ejpam-3484	43	49	uv	uv	PROPN
ejpam-3484	43	50	∈	∈	PROPN
ejpam-3484	43	51	e(g	e(g	PROPN
ejpam-3484	43	52	)	)	PUNCT
ejpam-3484	43	53	or	or	CCONJ
ejpam-3484	43	54	u	u	X
ejpam-3484	43	55	=	=	NOUN
ejpam-3484	43	56	v	v	PROPN
ejpam-3484	43	57	and	and	CCONJ
ejpam-3484	43	58	u′v′	u′v′	PROPN
ejpam-3484	43	59	∈	∈	PROPN
ejpam-3484	43	60	e(h	e(h	PROPN
ejpam-3484	43	61	)	)	PUNCT
ejpam-3484	43	62	.	.	PUNCT
ejpam-3484	44	1	note	note	VERB
ejpam-3484	44	2	that	that	SCONJ
ejpam-3484	44	3	for	for	ADP
ejpam-3484	44	4	each	each	DET
ejpam-3484	44	5	∅	∅	NOUN
ejpam-3484	44	6	6=	6=	ADP
ejpam-3484	44	7	c	c	PROPN
ejpam-3484	44	8	⊆	⊆	NUM
ejpam-3484	44	9	v	v	ADP
ejpam-3484	44	10	(	(	PUNCT
ejpam-3484	44	11	g	g	NOUN
ejpam-3484	44	12	)	)	PUNCT
ejpam-3484	44	13	×	×	NOUN
ejpam-3484	44	14	v	v	NOUN
ejpam-3484	44	15	(	(	PUNCT
ejpam-3484	44	16	h	h	NOUN
ejpam-3484	44	17	)	)	PUNCT
ejpam-3484	44	18	,	,	PUNCT
ejpam-3484	44	19	the	the	DET
ejpam-3484	44	20	g	g	NOUN
ejpam-3484	44	21	-	-	PUNCT
ejpam-3484	44	22	projection	projection	NOUN
ejpam-3484	44	23	and	and	CCONJ
ejpam-3484	44	24	h	h	NOUN
ejpam-3484	44	25	-	-	PUNCT
ejpam-3484	44	26	projection	projection	NOUN
ejpam-3484	44	27	of	of	ADP
ejpam-3484	44	28	c	c	PROPN
ejpam-3484	44	29	are	be	AUX
ejpam-3484	44	30	,	,	PUNCT
ejpam-3484	44	31	respectively	respectively	ADV
ejpam-3484	44	32	,	,	PUNCT
ejpam-3484	44	33	the	the	DET
ejpam-3484	44	34	sets	set	NOUN
ejpam-3484	44	35	cg	cg	NOUN
ejpam-3484	44	36	=	=	SYM
ejpam-3484	44	37	{	{	PUNCT
ejpam-3484	44	38	x	x	PROPN
ejpam-3484	44	39	∈	∈	PROPN
ejpam-3484	44	40	v	v	NOUN
ejpam-3484	44	41	(	(	PUNCT
ejpam-3484	44	42	g	g	NOUN
ejpam-3484	44	43	)	)	PUNCT
ejpam-3484	44	44	:	:	PUNCT
ejpam-3484	44	45	(	(	PUNCT
ejpam-3484	44	46	x	x	X
ejpam-3484	44	47	,	,	PUNCT
ejpam-3484	44	48	a	a	PRON
ejpam-3484	44	49	)	)	PUNCT
ejpam-3484	44	50	∈	∈	PROPN
ejpam-3484	44	51	c	c	NOUN
ejpam-3484	44	52	for	for	ADP
ejpam-3484	44	53	some	some	PRON
ejpam-3484	44	54	a	a	DET
ejpam-3484	44	55	∈	∈	PROPN
ejpam-3484	44	56	v	v	NOUN
ejpam-3484	44	57	(	(	PUNCT
ejpam-3484	44	58	h	h	NOUN
ejpam-3484	44	59	)	)	PUNCT
ejpam-3484	44	60	}	}	PUNCT
ejpam-3484	44	61	and	and	CCONJ
ejpam-3484	44	62	ch	ch	NOUN
ejpam-3484	44	63	=	=	SYM
ejpam-3484	44	64	{	{	PUNCT
ejpam-3484	44	65	a	a	DET
ejpam-3484	44	66	∈	∈	PROPN
ejpam-3484	44	67	v	v	ADP
ejpam-3484	44	68	(	(	PUNCT
ejpam-3484	44	69	h	h	NOUN
ejpam-3484	44	70	)	)	PUNCT
ejpam-3484	44	71	:	:	PUNCT
ejpam-3484	44	72	(	(	PUNCT
ejpam-3484	44	73	y	y	NOUN
ejpam-3484	44	74	,	,	PUNCT
ejpam-3484	44	75	a	a	PRON
ejpam-3484	44	76	)	)	PUNCT
ejpam-3484	44	77	∈	∈	PROPN
ejpam-3484	44	78	c	c	NOUN
ejpam-3484	44	79	for	for	ADP
ejpam-3484	44	80	some	some	DET
ejpam-3484	44	81	y	y	PROPN
ejpam-3484	44	82	∈	∈	PROPN
ejpam-3484	44	83	v	v	ADP
ejpam-3484	44	84	(	(	PUNCT
ejpam-3484	44	85	g	g	NOUN
ejpam-3484	44	86	)	)	PUNCT
ejpam-3484	44	87	}	}	PUNCT
ejpam-3484	44	88	.	.	PUNCT
ejpam-3484	45	1	observe	observe	VERB
ejpam-3484	45	2	that	that	SCONJ
ejpam-3484	45	3	any	any	DET
ejpam-3484	45	4	non	non	ADJ
ejpam-3484	45	5	-	-	ADJ
ejpam-3484	45	6	empty	empty	ADJ
ejpam-3484	45	7	subset	subset	NOUN
ejpam-3484	45	8	c	c	NOUN
ejpam-3484	45	9	of	of	ADP
ejpam-3484	45	10	v	v	PROPN
ejpam-3484	45	11	(	(	PUNCT
ejpam-3484	45	12	g)×v	g)×v	PROPN
ejpam-3484	45	13	(	(	PUNCT
ejpam-3484	45	14	h	h	NOUN
ejpam-3484	45	15	)	)	PUNCT
ejpam-3484	45	16	can	can	AUX
ejpam-3484	45	17	be	be	AUX
ejpam-3484	45	18	written	write	VERB
ejpam-3484	45	19	as	as	ADP
ejpam-3484	45	20	c	c	PROPN
ejpam-3484	45	21	=	=	SYM
ejpam-3484	45	22	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-3484	45	23	)	)	PUNCT
ejpam-3484	45	24	⊆	⊆	NUM
ejpam-3484	45	25	v	v	NOUN
ejpam-3484	45	26	(	(	PUNCT
ejpam-3484	45	27	g[h	g[h	PROPN
ejpam-3484	45	28	]	]	PUNCT
ejpam-3484	45	29	)	)	PUNCT
ejpam-3484	45	30	,	,	PUNCT
ejpam-3484	45	31	where	where	SCONJ
ejpam-3484	45	32	s	s	VERB
ejpam-3484	45	33	=	=	PUNCT
ejpam-3484	45	34	cg	cg	NOUN
ejpam-3484	45	35	⊆	⊆	NUM
ejpam-3484	45	36	v	v	NOUN
ejpam-3484	45	37	(	(	PUNCT
ejpam-3484	45	38	g	g	NOUN
ejpam-3484	45	39	)	)	PUNCT
ejpam-3484	45	40	and	and	CCONJ
ejpam-3484	45	41	tx	tx	VERB
ejpam-3484	45	42	=	=	PUNCT
ejpam-3484	45	43	{	{	PUNCT
ejpam-3484	45	44	a	a	DET
ejpam-3484	45	45	∈	∈	PROPN
ejpam-3484	45	46	ch	ch	NOUN
ejpam-3484	45	47	:	:	PUNCT
ejpam-3484	45	48	(	(	PUNCT
ejpam-3484	45	49	x	x	X
ejpam-3484	45	50	,	,	PUNCT
ejpam-3484	45	51	a	a	PRON
ejpam-3484	45	52	)	)	PUNCT
ejpam-3484	45	53	∈	∈	PROPN
ejpam-3484	45	54	c	c	NOUN
ejpam-3484	45	55	}	}	PUNCT
ejpam-3484	45	56	for	for	ADP
ejpam-3484	45	57	each	each	PRON
ejpam-3484	45	58	x	x	SYM
ejpam-3484	45	59	∈	∈	PROPN
ejpam-3484	45	60	s.	s.	PROPN
ejpam-3484	45	61	2	2	NUM
ejpam-3484	45	62	.	.	PUNCT
ejpam-3484	45	63	known	know	VERB
ejpam-3484	45	64	results	result	NOUN
ejpam-3484	45	65	theorem	theorem	VERB
ejpam-3484	45	66	2.1	2.1	NUM
ejpam-3484	45	67	.	.	PUNCT
ejpam-3484	46	1	[	[	X
ejpam-3484	46	2	4	4	X
ejpam-3484	46	3	]	]	PUNCT
ejpam-3484	46	4	for	for	ADP
ejpam-3484	46	5	any	any	DET
ejpam-3484	46	6	graph	graph	NOUN
ejpam-3484	46	7	g	g	NOUN
ejpam-3484	46	8	,	,	PUNCT
ejpam-3484	46	9	d	d	PROPN
ejpam-3484	46	10	n	n	NOUN
ejpam-3484	46	11	1+∆e	1+∆e	NUM
ejpam-3484	46	12	≤	≤	NOUN
ejpam-3484	46	13	γi(g	γi(g	NOUN
ejpam-3484	46	14	)	)	PUNCT
ejpam-3484	46	15	≤	≤	NOUN
ejpam-3484	46	16	n−∆.	n−∆.	NUM
ejpam-3484	46	17	theorem	theorem	VERB
ejpam-3484	46	18	2.2	2.2	NUM
ejpam-3484	46	19	.	.	PUNCT
ejpam-3484	47	1	[	[	X
ejpam-3484	47	2	4	4	X
ejpam-3484	47	3	]	]	PUNCT
ejpam-3484	47	4	the	the	DET
ejpam-3484	47	5	independent	independent	ADJ
ejpam-3484	47	6	domination	domination	NOUN
ejpam-3484	47	7	number	number	NOUN
ejpam-3484	47	8	of	of	ADP
ejpam-3484	47	9	a	a	DET
ejpam-3484	47	10	cycle	cycle	NOUN
ejpam-3484	47	11	cn	cn	NOUN
ejpam-3484	47	12	with	with	ADP
ejpam-3484	47	13	n	n	NUM
ejpam-3484	47	14	≥	≥	NUM
ejpam-3484	47	15	3	3	NUM
ejpam-3484	47	16	,	,	PUNCT
ejpam-3484	47	17	a	a	DET
ejpam-3484	47	18	path	path	NOUN
ejpam-3484	47	19	pn	pn	NOUN
ejpam-3484	47	20	with	with	ADP
ejpam-3484	47	21	n	n	PRON
ejpam-3484	47	22	≥	≥	NUM
ejpam-3484	47	23	1	1	NUM
ejpam-3484	47	24	and	and	CCONJ
ejpam-3484	47	25	complete	complete	ADJ
ejpam-3484	47	26	bipartite	bipartite	PROPN
ejpam-3484	47	27	graph	graph	NOUN
ejpam-3484	47	28	kr	kr	PROPN
ejpam-3484	47	29	,	,	PUNCT
ejpam-3484	47	30	s	s	VERB
ejpam-3484	47	31	are	be	AUX
ejpam-3484	47	32	given	give	VERB
ejpam-3484	47	33	by	by	ADP
ejpam-3484	47	34	i.	i.	NOUN
ejpam-3484	47	35	γi(pn	γi(pn	PROPN
ejpam-3484	47	36	)	)	PUNCT
ejpam-3484	48	1	=	=	SYM
ejpam-3484	48	2	γi(cn	γi(cn	ADJ
ejpam-3484	48	3	)	)	PUNCT
ejpam-3484	48	4	=	=	SYM
ejpam-3484	49	1	dn	dn	NOUN
ejpam-3484	49	2	3	3	NUM
ejpam-3484	49	3	e	e	PROPN
ejpam-3484	49	4	,	,	PUNCT
ejpam-3484	49	5	ii	ii	PROPN
ejpam-3484	49	6	.	.	PUNCT
ejpam-3484	50	1	γi(kr	γi(kr	PROPN
ejpam-3484	50	2	,	,	PUNCT
ejpam-3484	50	3	s	s	NOUN
ejpam-3484	50	4	)	)	PUNCT
ejpam-3484	50	5	=	=	SYM
ejpam-3484	50	6	min{r	min{r	PROPN
ejpam-3484	50	7	,	,	PUNCT
ejpam-3484	50	8	s	s	PART
ejpam-3484	50	9	}	}	PUNCT
ejpam-3484	50	10	.	.	PUNCT
ejpam-3484	51	1	theorem	theorem	VERB
ejpam-3484	51	2	2.3	2.3	NUM
ejpam-3484	51	3	.	.	PUNCT
ejpam-3484	52	1	[	[	X
ejpam-3484	52	2	2	2	X
ejpam-3484	52	3	]	]	PUNCT
ejpam-3484	52	4	let	let	VERB
ejpam-3484	52	5	g	g	PRON
ejpam-3484	52	6	be	be	AUX
ejpam-3484	52	7	a	a	DET
ejpam-3484	52	8	connected	connected	ADJ
ejpam-3484	52	9	graph	graph	NOUN
ejpam-3484	52	10	and	and	CCONJ
ejpam-3484	52	11	h	h	NOUN
ejpam-3484	52	12	be	be	AUX
ejpam-3484	52	13	any	any	DET
ejpam-3484	52	14	graph	graph	NOUN
ejpam-3484	52	15	.	.	PUNCT
ejpam-3484	53	1	then	then	ADV
ejpam-3484	53	2	c	c	PROPN
ejpam-3484	53	3	⊆	⊆	NUM
ejpam-3484	53	4	v	v	NOUN
ejpam-3484	53	5	(	(	PUNCT
ejpam-3484	53	6	g	g	PROPN
ejpam-3484	53	7	◦	◦	NOUN
ejpam-3484	53	8	h	h	NOUN
ejpam-3484	53	9	)	)	PUNCT
ejpam-3484	53	10	is	be	AUX
ejpam-3484	53	11	an	an	DET
ejpam-3484	53	12	independent	independent	ADJ
ejpam-3484	53	13	dominating	dominating	NOUN
ejpam-3484	53	14	set	set	VERB
ejpam-3484	53	15	in	in	ADP
ejpam-3484	53	16	g	g	PROPN
ejpam-3484	53	17	◦	◦	NOUN
ejpam-3484	53	18	h	h	NOUN
ejpam-3484	54	1	if	if	SCONJ
ejpam-3484	55	1	and	and	CCONJ
ejpam-3484	55	2	only	only	ADV
ejpam-3484	55	3	if	if	SCONJ
ejpam-3484	55	4	c	c	PROPN
ejpam-3484	55	5	∩	∩	X
ejpam-3484	55	6	v	v	X
ejpam-3484	55	7	(	(	PUNCT
ejpam-3484	55	8	g	g	NOUN
ejpam-3484	55	9	)	)	PUNCT
ejpam-3484	55	10	is	be	AUX
ejpam-3484	55	11	an	an	DET
ejpam-3484	55	12	independent	independent	ADJ
ejpam-3484	55	13	set	set	NOUN
ejpam-3484	55	14	in	in	ADP
ejpam-3484	55	15	g	g	PROPN
ejpam-3484	55	16	and	and	CCONJ
ejpam-3484	55	17	c	c	PROPN
ejpam-3484	55	18	∩	∩	PROPN
ejpam-3484	55	19	v	v	X
ejpam-3484	55	20	(	(	PUNCT
ejpam-3484	55	21	v+hv	v+hv	NOUN
ejpam-3484	55	22	)	)	PUNCT
ejpam-3484	55	23	is	be	AUX
ejpam-3484	55	24	an	an	DET
ejpam-3484	55	25	independent	independent	ADJ
ejpam-3484	55	26	dominating	dominating	NOUN
ejpam-3484	55	27	set	set	VERB
ejpam-3484	55	28	in	in	ADP
ejpam-3484	55	29	v+hv	v+hv	NOUN
ejpam-3484	55	30	for	for	ADP
ejpam-3484	55	31	every	every	DET
ejpam-3484	55	32	v	v	NUM
ejpam-3484	55	33	∈	∈	PROPN
ejpam-3484	55	34	v	v	NOUN
ejpam-3484	55	35	(	(	PUNCT
ejpam-3484	55	36	g	g	NOUN
ejpam-3484	55	37	)	)	PUNCT
ejpam-3484	55	38	.	.	PUNCT
ejpam-3484	56	1	c.	c.	PROPN
ejpam-3484	56	2	armada	armada	PROPN
ejpam-3484	56	3	,	,	PUNCT
ejpam-3484	56	4	s.	s.	PROPN
ejpam-3484	56	5	canoy	canoy	PROPN
ejpam-3484	56	6	jr	jr	PROPN
ejpam-3484	56	7	.	.	PROPN
ejpam-3484	56	8	/	/	SYM
ejpam-3484	56	9	eur	eur	PROPN
ejpam-3484	56	10	.	.	PUNCT
ejpam-3484	57	1	j.	j.	PROPN
ejpam-3484	57	2	pure	pure	PROPN
ejpam-3484	57	3	appl	appl	PROPN
ejpam-3484	57	4	.	.	PROPN
ejpam-3484	57	5	math	math	PROPN
ejpam-3484	57	6	,	,	PUNCT
ejpam-3484	57	7	12	12	NUM
ejpam-3484	57	8	(	(	PUNCT
ejpam-3484	57	9	4	4	NUM
ejpam-3484	57	10	)	)	PUNCT
ejpam-3484	57	11	(	(	PUNCT
ejpam-3484	57	12	2019	2019	NUM
ejpam-3484	57	13	)	)	PUNCT
ejpam-3484	57	14	,	,	PUNCT
ejpam-3484	57	15	1371	1371	NUM
ejpam-3484	57	16	-	-	SYM
ejpam-3484	57	17	1381	1381	NUM
ejpam-3484	57	18	1373	1373	NUM
ejpam-3484	57	19	theorem	theorem	VERB
ejpam-3484	57	20	2.4	2.4	NUM
ejpam-3484	57	21	.	.	PUNCT
ejpam-3484	58	1	[	[	X
ejpam-3484	58	2	2	2	X
ejpam-3484	58	3	]	]	PUNCT
ejpam-3484	58	4	let	let	VERB
ejpam-3484	58	5	g	g	PRON
ejpam-3484	58	6	be	be	AUX
ejpam-3484	58	7	a	a	DET
ejpam-3484	58	8	connected	connected	ADJ
ejpam-3484	58	9	graph	graph	NOUN
ejpam-3484	58	10	of	of	ADP
ejpam-3484	58	11	order	order	NOUN
ejpam-3484	58	12	n	n	NOUN
ejpam-3484	58	13	and	and	CCONJ
ejpam-3484	58	14	h	h	NOUN
ejpam-3484	58	15	any	any	DET
ejpam-3484	58	16	graph	graph	NOUN
ejpam-3484	58	17	with	with	ADP
ejpam-3484	58	18	γi(h	γi(h	NOUN
ejpam-3484	58	19	)	)	PUNCT
ejpam-3484	58	20	6=	6=	ADP
ejpam-3484	58	21	1	1	X
ejpam-3484	58	22	.	.	PUNCT
ejpam-3484	59	1	if	if	SCONJ
ejpam-3484	59	2	c	c	PROPN
ejpam-3484	59	3	⊆	⊆	NUM
ejpam-3484	59	4	v	v	NOUN
ejpam-3484	59	5	(	(	PUNCT
ejpam-3484	59	6	g	g	PROPN
ejpam-3484	59	7	◦	◦	NOUN
ejpam-3484	59	8	h	h	NOUN
ejpam-3484	59	9	)	)	PUNCT
ejpam-3484	59	10	is	be	AUX
ejpam-3484	59	11	a	a	DET
ejpam-3484	59	12	minimum	minimum	ADJ
ejpam-3484	59	13	independent	independent	ADJ
ejpam-3484	59	14	dominating	dominating	NOUN
ejpam-3484	59	15	set	set	VERB
ejpam-3484	59	16	in	in	ADP
ejpam-3484	59	17	g	g	PROPN
ejpam-3484	59	18	◦	◦	NOUN
ejpam-3484	59	19	h	h	NOUN
ejpam-3484	59	20	,	,	PUNCT
ejpam-3484	59	21	then	then	ADV
ejpam-3484	59	22	c	c	PROPN
ejpam-3484	59	23	∩	∩	PROPN
ejpam-3484	59	24	v	v	X
ejpam-3484	59	25	(	(	PUNCT
ejpam-3484	59	26	g	g	NOUN
ejpam-3484	59	27	)	)	PUNCT
ejpam-3484	59	28	is	be	AUX
ejpam-3484	59	29	a	a	DET
ejpam-3484	59	30	maximum	maximum	ADJ
ejpam-3484	59	31	independent	independent	ADJ
ejpam-3484	59	32	set	set	NOUN
ejpam-3484	59	33	in	in	ADP
ejpam-3484	59	34	g.	g.	PROPN
ejpam-3484	59	35	theorem	theorem	VERB
ejpam-3484	59	36	2.5	2.5	NUM
ejpam-3484	59	37	.	.	PUNCT
ejpam-3484	60	1	[	[	X
ejpam-3484	60	2	2	2	X
ejpam-3484	60	3	]	]	PUNCT
ejpam-3484	60	4	let	let	VERB
ejpam-3484	60	5	g	g	NOUN
ejpam-3484	60	6	and	and	CCONJ
ejpam-3484	60	7	h	h	NOUN
ejpam-3484	60	8	be	be	AUX
ejpam-3484	60	9	nontrivial	nontrivial	ADJ
ejpam-3484	60	10	connected	connected	ADJ
ejpam-3484	60	11	graphs	graph	NOUN
ejpam-3484	60	12	.	.	PUNCT
ejpam-3484	61	1	a	a	DET
ejpam-3484	61	2	subset	subset	NOUN
ejpam-3484	61	3	c	c	NOUN
ejpam-3484	61	4	=	=	SYM
ejpam-3484	61	5	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3484	61	6	}	}	PUNCT
ejpam-3484	61	7	×	×	PROPN
ejpam-3484	61	8	tx	tx	PROPN
ejpam-3484	61	9	)	)	PUNCT
ejpam-3484	61	10	of	of	ADP
ejpam-3484	61	11	v	v	NOUN
ejpam-3484	61	12	(	(	PUNCT
ejpam-3484	61	13	g[h	g[h	PROPN
ejpam-3484	61	14	]	]	PUNCT
ejpam-3484	61	15	)	)	PUNCT
ejpam-3484	61	16	,	,	PUNCT
ejpam-3484	61	17	is	be	AUX
ejpam-3484	61	18	an	an	DET
ejpam-3484	61	19	independent	independent	ADJ
ejpam-3484	61	20	dominating	dominating	NOUN
ejpam-3484	61	21	set	set	VERB
ejpam-3484	61	22	in	in	ADP
ejpam-3484	61	23	g[h	g[h	PROPN
ejpam-3484	61	24	]	]	PUNCT
ejpam-3484	61	25	if	if	SCONJ
ejpam-3484	61	26	and	and	CCONJ
ejpam-3484	61	27	only	only	ADV
ejpam-3484	61	28	if	if	SCONJ
ejpam-3484	61	29	s	s	NOUN
ejpam-3484	61	30	is	be	AUX
ejpam-3484	61	31	an	an	DET
ejpam-3484	61	32	independent	independent	ADJ
ejpam-3484	61	33	dominating	dominating	NOUN
ejpam-3484	61	34	set	set	VERB
ejpam-3484	61	35	in	in	ADP
ejpam-3484	61	36	g	g	PROPN
ejpam-3484	61	37	and	and	CCONJ
ejpam-3484	61	38	tx	tx	PROPN
ejpam-3484	61	39	is	be	AUX
ejpam-3484	61	40	an	an	DET
ejpam-3484	61	41	independent	independent	ADJ
ejpam-3484	61	42	dominating	dominating	NOUN
ejpam-3484	61	43	set	set	VERB
ejpam-3484	61	44	in	in	ADP
ejpam-3484	61	45	h	h	NOUN
ejpam-3484	61	46	for	for	ADP
ejpam-3484	61	47	every	every	DET
ejpam-3484	61	48	x	x	PROPN
ejpam-3484	61	49	∈	∈	PROPN
ejpam-3484	61	50	s.	s.	PROPN
ejpam-3484	61	51	corollary	corollary	PROPN
ejpam-3484	61	52	2.6	2.6	NUM
ejpam-3484	61	53	.	.	PUNCT
ejpam-3484	62	1	[	[	X
ejpam-3484	62	2	2	2	X
ejpam-3484	62	3	]	]	PUNCT
ejpam-3484	62	4	let	let	VERB
ejpam-3484	62	5	g	g	NOUN
ejpam-3484	62	6	and	and	CCONJ
ejpam-3484	62	7	h	h	NOUN
ejpam-3484	62	8	be	be	AUX
ejpam-3484	62	9	nontrivial	nontrivial	ADJ
ejpam-3484	62	10	connected	connected	ADJ
ejpam-3484	62	11	graphs	graph	NOUN
ejpam-3484	62	12	.	.	PUNCT
ejpam-3484	63	1	then	then	ADV
ejpam-3484	63	2	γi(g[h	γi(g[h	VERB
ejpam-3484	63	3	]	]	X
ejpam-3484	63	4	)	)	PUNCT
ejpam-3484	64	1	=	=	SYM
ejpam-3484	64	2	γi(g)γi(h	γi(g)γi(h	NOUN
ejpam-3484	64	3	)	)	PUNCT
ejpam-3484	64	4	.	.	PUNCT
ejpam-3484	65	1	corollary	corollary	ADJ
ejpam-3484	65	2	2.7	2.7	NUM
ejpam-3484	65	3	.	.	PUNCT
ejpam-3484	66	1	[	[	X
ejpam-3484	66	2	2	2	X
ejpam-3484	66	3	]	]	PUNCT
ejpam-3484	66	4	let	let	VERB
ejpam-3484	66	5	g	g	PRON
ejpam-3484	66	6	be	be	AUX
ejpam-3484	66	7	a	a	DET
ejpam-3484	66	8	connected	connected	ADJ
ejpam-3484	66	9	graph	graph	NOUN
ejpam-3484	66	10	and	and	CCONJ
ejpam-3484	66	11	kn	kn	PROPN
ejpam-3484	66	12	the	the	DET
ejpam-3484	66	13	complete	complete	ADJ
ejpam-3484	66	14	graph	graph	NOUN
ejpam-3484	66	15	of	of	ADP
ejpam-3484	66	16	order	order	NOUN
ejpam-3484	66	17	n	n	PRON
ejpam-3484	66	18	≥	≥	NOUN
ejpam-3484	66	19	1	1	NUM
ejpam-3484	66	20	.	.	PUNCT
ejpam-3484	67	1	then	then	ADV
ejpam-3484	67	2	γi(g[kn	γi(g[kn	NUM
ejpam-3484	67	3	]	]	PUNCT
ejpam-3484	67	4	)	)	PUNCT
ejpam-3484	67	5	=	=	SYM
ejpam-3484	67	6	γi(g	γi(g	NOUN
ejpam-3484	67	7	)	)	PUNCT
ejpam-3484	67	8	.	.	PUNCT
ejpam-3484	68	1	3	3	X
ejpam-3484	68	2	.	.	X
ejpam-3484	68	3	main	main	ADJ
ejpam-3484	68	4	results	result	NOUN
ejpam-3484	68	5	the	the	DET
ejpam-3484	68	6	next	next	ADJ
ejpam-3484	68	7	two	two	NUM
ejpam-3484	68	8	results	result	NOUN
ejpam-3484	68	9	follow	follow	VERB
ejpam-3484	68	10	directly	directly	ADV
ejpam-3484	68	11	from	from	ADP
ejpam-3484	68	12	the	the	DET
ejpam-3484	68	13	definition	definition	NOUN
ejpam-3484	68	14	of	of	ADP
ejpam-3484	68	15	forcing	force	VERB
ejpam-3484	68	16	independent	independent	ADJ
ejpam-3484	68	17	domination	domination	NOUN
ejpam-3484	68	18	and	and	CCONJ
ejpam-3484	68	19	theorem	theorem	VERB
ejpam-3484	68	20	2.1	2.1	NUM
ejpam-3484	68	21	.	.	PUNCT
ejpam-3484	68	22	remark	remark	PROPN
ejpam-3484	68	23	3.1	3.1	NUM
ejpam-3484	68	24	.	.	PUNCT
ejpam-3484	69	1	let	let	VERB
ejpam-3484	69	2	g	g	PRON
ejpam-3484	69	3	be	be	AUX
ejpam-3484	69	4	a	a	DET
ejpam-3484	69	5	graph	graph	NOUN
ejpam-3484	69	6	.	.	PUNCT
ejpam-3484	70	1	then	then	ADV
ejpam-3484	70	2	(	(	PUNCT
ejpam-3484	70	3	i	i	NOUN
ejpam-3484	70	4	)	)	PUNCT
ejpam-3484	70	5	fγi(g	fγi(g	PROPN
ejpam-3484	70	6	)	)	PUNCT
ejpam-3484	70	7	=	=	SYM
ejpam-3484	70	8	0	0	PUNCT
ejpam-3484	71	1	if	if	SCONJ
ejpam-3484	71	2	and	and	CCONJ
ejpam-3484	71	3	only	only	ADV
ejpam-3484	71	4	if	if	SCONJ
ejpam-3484	71	5	g	g	PROPN
ejpam-3484	71	6	has	have	VERB
ejpam-3484	71	7	a	a	DET
ejpam-3484	71	8	unique	unique	ADJ
ejpam-3484	71	9	γi	γi	NOUN
ejpam-3484	71	10	-	-	PUNCT
ejpam-3484	71	11	set	set	NOUN
ejpam-3484	71	12	.	.	PUNCT
ejpam-3484	72	1	(	(	PUNCT
ejpam-3484	72	2	ii	ii	NOUN
ejpam-3484	72	3	)	)	PUNCT
ejpam-3484	72	4	fγi(g	fγi(g	PROPN
ejpam-3484	72	5	)	)	PUNCT
ejpam-3484	73	1	=	=	PUNCT
ejpam-3484	73	2	1	1	NUM
ejpam-3484	73	3	if	if	SCONJ
ejpam-3484	73	4	and	and	CCONJ
ejpam-3484	73	5	only	only	ADV
ejpam-3484	73	6	if	if	SCONJ
ejpam-3484	73	7	g	g	PROPN
ejpam-3484	73	8	has	have	VERB
ejpam-3484	73	9	at	at	ADV
ejpam-3484	73	10	least	least	ADV
ejpam-3484	73	11	two	two	NUM
ejpam-3484	73	12	γi	γi	NOUN
ejpam-3484	73	13	-	-	PUNCT
ejpam-3484	73	14	sets	set	NOUN
ejpam-3484	73	15	and	and	CCONJ
ejpam-3484	73	16	there	there	PRON
ejpam-3484	73	17	exists	exist	VERB
ejpam-3484	73	18	a	a	DET
ejpam-3484	73	19	vertex	vertex	NOUN
ejpam-3484	73	20	which	which	PRON
ejpam-3484	73	21	is	be	AUX
ejpam-3484	73	22	contained	contain	VERB
ejpam-3484	73	23	in	in	ADP
ejpam-3484	73	24	exactly	exactly	ADV
ejpam-3484	73	25	one	one	NUM
ejpam-3484	73	26	γi	γi	NOUN
ejpam-3484	73	27	-	-	PUNCT
ejpam-3484	73	28	set	set	NOUN
ejpam-3484	73	29	of	of	ADP
ejpam-3484	73	30	g.	g.	PROPN
ejpam-3484	73	31	remark	remark	PROPN
ejpam-3484	73	32	3.2	3.2	NUM
ejpam-3484	73	33	.	.	PUNCT
ejpam-3484	74	1	let	let	VERB
ejpam-3484	74	2	g	g	NOUN
ejpam-3484	74	3	be	be	AUX
ejpam-3484	74	4	any	any	DET
ejpam-3484	74	5	graph	graph	NOUN
ejpam-3484	74	6	of	of	ADP
ejpam-3484	74	7	order	order	NOUN
ejpam-3484	74	8	n.	n.	NOUN
ejpam-3484	74	9	then	then	ADV
ejpam-3484	74	10	0	0	NUM
ejpam-3484	74	11	≤	≤	NUM
ejpam-3484	74	12	fγi(g	fγi(g	PROPN
ejpam-3484	74	13	)	)	PUNCT
ejpam-3484	74	14	≤	≤	NOUN
ejpam-3484	74	15	n−∆.	n−∆.	NUM
ejpam-3484	74	16	theorem	theorem	VERB
ejpam-3484	74	17	3.3	3.3	NUM
ejpam-3484	74	18	.	.	PUNCT
ejpam-3484	75	1	let	let	VERB
ejpam-3484	75	2	g	g	PRON
ejpam-3484	75	3	be	be	AUX
ejpam-3484	75	4	a	a	DET
ejpam-3484	75	5	connected	connected	ADJ
ejpam-3484	75	6	graph	graph	NOUN
ejpam-3484	75	7	.	.	PUNCT
ejpam-3484	76	1	then	then	ADV
ejpam-3484	76	2	fγi(g	fγi(g	PROPN
ejpam-3484	76	3	)	)	PUNCT
ejpam-3484	76	4	=	=	SYM
ejpam-3484	77	1	γi(g	γi(g	NOUN
ejpam-3484	77	2	)	)	PUNCT
ejpam-3484	78	1	if	if	SCONJ
ejpam-3484	78	2	and	and	CCONJ
ejpam-3484	78	3	only	only	ADV
ejpam-3484	78	4	if	if	SCONJ
ejpam-3484	78	5	for	for	ADP
ejpam-3484	78	6	every	every	DET
ejpam-3484	78	7	γi	γi	NOUN
ejpam-3484	78	8	-	-	PUNCT
ejpam-3484	78	9	set	set	VERB
ejpam-3484	78	10	s	s	NOUN
ejpam-3484	78	11	of	of	ADP
ejpam-3484	78	12	g	g	NOUN
ejpam-3484	78	13	and	and	CCONJ
ejpam-3484	78	14	for	for	ADP
ejpam-3484	78	15	each	each	DET
ejpam-3484	78	16	x	x	SYM
ejpam-3484	78	17	∈	∈	PROPN
ejpam-3484	78	18	s	s	X
ejpam-3484	78	19	,	,	PUNCT
ejpam-3484	78	20	there	there	PRON
ejpam-3484	78	21	exists	exist	VERB
ejpam-3484	78	22	yx	yx	PROPN
ejpam-3484	78	23	∈	∈	PROPN
ejpam-3484	78	24	v	v	X
ejpam-3484	78	25	(	(	PUNCT
ejpam-3484	78	26	g)\s	g)\s	VERB
ejpam-3484	78	27	such	such	ADJ
ejpam-3484	78	28	that	that	SCONJ
ejpam-3484	78	29	[	[	X
ejpam-3484	78	30	s\{x	s\{x	X
ejpam-3484	78	31	}	}	PUNCT
ejpam-3484	78	32	]	]	PUNCT
ejpam-3484	78	33	∪	∪	X
ejpam-3484	78	34	{	{	PUNCT
ejpam-3484	78	35	yx	yx	NOUN
ejpam-3484	78	36	}	}	PUNCT
ejpam-3484	78	37	is	be	AUX
ejpam-3484	78	38	a	a	DET
ejpam-3484	78	39	γi	γi	NOUN
ejpam-3484	78	40	-	-	PUNCT
ejpam-3484	78	41	set	set	NOUN
ejpam-3484	78	42	of	of	ADP
ejpam-3484	78	43	g.	g.	PROPN
ejpam-3484	78	44	proof	proof	PROPN
ejpam-3484	78	45	.	.	PUNCT
ejpam-3484	79	1	suppose	suppose	VERB
ejpam-3484	79	2	that	that	SCONJ
ejpam-3484	79	3	fγi(g	fγi(g	PROPN
ejpam-3484	79	4	)	)	PUNCT
ejpam-3484	79	5	=	=	SYM
ejpam-3484	79	6	γi(g	γi(g	NOUN
ejpam-3484	79	7	)	)	PUNCT
ejpam-3484	79	8	.	.	PUNCT
ejpam-3484	80	1	let	let	VERB
ejpam-3484	80	2	s	s	PRON
ejpam-3484	80	3	be	be	AUX
ejpam-3484	80	4	a	a	DET
ejpam-3484	80	5	γi	γi	NOUN
ejpam-3484	80	6	-	-	PUNCT
ejpam-3484	80	7	set	set	NOUN
ejpam-3484	80	8	of	of	ADP
ejpam-3484	80	9	g.	g.	PROPN
ejpam-3484	80	10	then	then	ADV
ejpam-3484	80	11	,	,	PUNCT
ejpam-3484	80	12	by	by	ADP
ejpam-3484	80	13	assumption	assumption	NOUN
ejpam-3484	80	14	,	,	PUNCT
ejpam-3484	80	15	γi(g	γi(g	X
ejpam-3484	80	16	)	)	PUNCT
ejpam-3484	80	17	=	=	SYM
ejpam-3484	80	18	|s|	|s|	PROPN
ejpam-3484	80	19	=	=	PUNCT
ejpam-3484	80	20	fγi(g	fγi(g	PROPN
ejpam-3484	80	21	)	)	PUNCT
ejpam-3484	80	22	,	,	PUNCT
ejpam-3484	80	23	that	that	ADV
ejpam-3484	80	24	is	is	ADV
ejpam-3484	80	25	,	,	PUNCT
ejpam-3484	80	26	s	s	VERB
ejpam-3484	80	27	is	be	AUX
ejpam-3484	80	28	the	the	DET
ejpam-3484	80	29	only	only	ADJ
ejpam-3484	80	30	forcing	forcing	NOUN
ejpam-3484	80	31	subset	subset	NOUN
ejpam-3484	80	32	for	for	ADP
ejpam-3484	80	33	itself	itself	PRON
ejpam-3484	80	34	.	.	PUNCT
ejpam-3484	81	1	let	let	VERB
ejpam-3484	81	2	x	x	SYM
ejpam-3484	81	3	∈	∈	PROPN
ejpam-3484	81	4	s.	s.	PROPN
ejpam-3484	81	5	since	since	SCONJ
ejpam-3484	81	6	s\{x	s\{x	PROPN
ejpam-3484	81	7	}	}	PUNCT
ejpam-3484	81	8	is	be	AUX
ejpam-3484	81	9	not	not	PART
ejpam-3484	81	10	a	a	DET
ejpam-3484	81	11	forcing	forcing	NOUN
ejpam-3484	81	12	subset	subset	NOUN
ejpam-3484	81	13	for	for	ADP
ejpam-3484	81	14	s	s	PROPN
ejpam-3484	81	15	,	,	PUNCT
ejpam-3484	81	16	there	there	PRON
ejpam-3484	81	17	exists	exist	VERB
ejpam-3484	81	18	a	a	DET
ejpam-3484	81	19	yx	yx	NOUN
ejpam-3484	81	20	∈	∈	PROPN
ejpam-3484	81	21	v	v	NOUN
ejpam-3484	81	22	(	(	PUNCT
ejpam-3484	81	23	g)\s	g)\s	VERB
ejpam-3484	81	24	such	such	ADJ
ejpam-3484	81	25	that	that	SCONJ
ejpam-3484	81	26	[	[	X
ejpam-3484	81	27	s\{x	s\{x	X
ejpam-3484	81	28	}	}	PUNCT
ejpam-3484	81	29	]	]	PUNCT
ejpam-3484	81	30	∪	∪	X
ejpam-3484	81	31	{	{	PUNCT
ejpam-3484	81	32	yx	yx	NOUN
ejpam-3484	81	33	}	}	PUNCT
ejpam-3484	81	34	is	be	AUX
ejpam-3484	81	35	a	a	DET
ejpam-3484	81	36	γi	γi	NOUN
ejpam-3484	81	37	-	-	PUNCT
ejpam-3484	81	38	set	set	NOUN
ejpam-3484	81	39	of	of	ADP
ejpam-3484	81	40	g.	g.	NOUN
ejpam-3484	81	41	conversely	conversely	ADV
ejpam-3484	81	42	,	,	PUNCT
ejpam-3484	81	43	suppose	suppose	VERB
ejpam-3484	81	44	that	that	SCONJ
ejpam-3484	81	45	every	every	DET
ejpam-3484	81	46	γi	γi	NOUN
ejpam-3484	81	47	-	-	PUNCT
ejpam-3484	81	48	set	set	NOUN
ejpam-3484	81	49	s′	s′	NOUN
ejpam-3484	81	50	of	of	ADP
ejpam-3484	81	51	g	g	PROPN
ejpam-3484	81	52	satisfies	satisfy	VERB
ejpam-3484	81	53	the	the	DET
ejpam-3484	81	54	given	give	VERB
ejpam-3484	81	55	condition	condition	NOUN
ejpam-3484	81	56	.	.	PUNCT
ejpam-3484	82	1	let	let	VERB
ejpam-3484	82	2	s	s	PRON
ejpam-3484	82	3	be	be	AUX
ejpam-3484	82	4	a	a	DET
ejpam-3484	82	5	a	a	DET
ejpam-3484	82	6	γi	γi	NOUN
ejpam-3484	82	7	-	-	PUNCT
ejpam-3484	82	8	set	set	NOUN
ejpam-3484	82	9	of	of	ADP
ejpam-3484	82	10	g	g	NOUN
ejpam-3484	82	11	such	such	ADJ
ejpam-3484	82	12	that	that	DET
ejpam-3484	82	13	fγi(g	fγi(g	PROPN
ejpam-3484	82	14	)	)	PUNCT
ejpam-3484	82	15	=	=	SYM
ejpam-3484	82	16	fγi(s	fγi(s	NOUN
ejpam-3484	82	17	)	)	PUNCT
ejpam-3484	82	18	.	.	PUNCT
ejpam-3484	83	1	suppose	suppose	VERB
ejpam-3484	83	2	further	far	ADV
ejpam-3484	83	3	that	that	SCONJ
ejpam-3484	83	4	s	s	VERB
ejpam-3484	83	5	has	have	VERB
ejpam-3484	83	6	a	a	DET
ejpam-3484	83	7	forcing	forcing	NOUN
ejpam-3484	83	8	subset	subset	NOUN
ejpam-3484	83	9	p	p	NOUN
ejpam-3484	83	10	with	with	ADP
ejpam-3484	83	11	|p	|p	NOUN
ejpam-3484	83	12	|	|	ADV
ejpam-3484	83	13	<	<	X
ejpam-3484	83	14	|s|	|s|	NOUN
ejpam-3484	83	15	,	,	PUNCT
ejpam-3484	83	16	that	that	ADV
ejpam-3484	83	17	is	be	AUX
ejpam-3484	83	18	,	,	PUNCT
ejpam-3484	83	19	s	s	PART
ejpam-3484	83	20	=	=	PUNCT
ejpam-3484	83	21	p	p	X
ejpam-3484	83	22	∪k	∪k	PROPN
ejpam-3484	83	23	,	,	PUNCT
ejpam-3484	83	24	where	where	SCONJ
ejpam-3484	83	25	k	k	NOUN
ejpam-3484	83	26	=	=	PRON
ejpam-3484	83	27	{	{	PUNCT
ejpam-3484	83	28	x	x	PUNCT
ejpam-3484	83	29	∈	∈	PROPN
ejpam-3484	83	30	s	s	PART
ejpam-3484	83	31	:	:	PUNCT
ejpam-3484	83	32	x	x	X
ejpam-3484	83	33	/∈	/∈	PUNCT
ejpam-3484	84	1	p	p	X
ejpam-3484	84	2	}	}	PUNCT
ejpam-3484	84	3	.	.	PUNCT
ejpam-3484	85	1	pick	pick	VERB
ejpam-3484	85	2	x	x	PUNCT
ejpam-3484	85	3	∈	∈	PROPN
ejpam-3484	85	4	k.	k.	PROPN
ejpam-3484	85	5	by	by	ADP
ejpam-3484	85	6	assumption	assumption	NOUN
ejpam-3484	85	7	,	,	PUNCT
ejpam-3484	85	8	there	there	PRON
ejpam-3484	85	9	exists	exist	VERB
ejpam-3484	85	10	yx	yx	PROPN
ejpam-3484	85	11	∈	∈	PROPN
ejpam-3484	85	12	v	v	X
ejpam-3484	85	13	(	(	PUNCT
ejpam-3484	85	14	g)\s	g)\s	VERB
ejpam-3484	85	15	such	such	ADJ
ejpam-3484	85	16	that	that	SCONJ
ejpam-3484	85	17	[	[	X
ejpam-3484	85	18	s\{x	s\{x	X
ejpam-3484	85	19	}	}	PUNCT
ejpam-3484	85	20	]	]	PUNCT
ejpam-3484	85	21	∪	∪	X
ejpam-3484	85	22	{	{	PUNCT
ejpam-3484	85	23	yx	yx	NOUN
ejpam-3484	85	24	}	}	PUNCT
ejpam-3484	85	25	=	=	SYM
ejpam-3484	85	26	t	t	NOUN
ejpam-3484	85	27	is	be	AUX
ejpam-3484	85	28	a	a	DET
ejpam-3484	85	29	γi	γi	NOUN
ejpam-3484	85	30	-	-	PUNCT
ejpam-3484	85	31	set	set	NOUN
ejpam-3484	85	32	of	of	ADP
ejpam-3484	85	33	g.	g.	PROPN
ejpam-3484	85	34	hence	hence	ADV
ejpam-3484	85	35	,	,	PUNCT
ejpam-3484	85	36	t	t	PROPN
ejpam-3484	86	1	=	=	PUNCT
ejpam-3484	86	2	p	p	NOUN
ejpam-3484	86	3	∪	∪	ADP
ejpam-3484	86	4	r	r	NOUN
ejpam-3484	86	5	,	,	PUNCT
ejpam-3484	86	6	where	where	SCONJ
ejpam-3484	86	7	r	r	NOUN
ejpam-3484	86	8	=	=	PUNCT
ejpam-3484	87	1	[	[	X
ejpam-3484	87	2	k\{x	k\{x	X
ejpam-3484	87	3	}	}	PUNCT
ejpam-3484	87	4	]	]	PUNCT
ejpam-3484	87	5	∪	∪	X
ejpam-3484	87	6	{	{	PUNCT
ejpam-3484	87	7	yx	yx	NOUN
ejpam-3484	87	8	}	}	PUNCT
ejpam-3484	87	9	,	,	PUNCT
ejpam-3484	87	10	is	be	AUX
ejpam-3484	87	11	a	a	DET
ejpam-3484	87	12	γi	γi	NOUN
ejpam-3484	87	13	-	-	PUNCT
ejpam-3484	87	14	set	set	ADJ
ejpam-3484	87	15	containing	contain	VERB
ejpam-3484	87	16	p	p	NOUN
ejpam-3484	87	17	,	,	PUNCT
ejpam-3484	87	18	a	a	DET
ejpam-3484	87	19	contradiction	contradiction	NOUN
ejpam-3484	87	20	.	.	PUNCT
ejpam-3484	88	1	hence	hence	ADV
ejpam-3484	88	2	,	,	PUNCT
ejpam-3484	88	3	s	s	VERB
ejpam-3484	88	4	is	be	AUX
ejpam-3484	88	5	the	the	DET
ejpam-3484	88	6	only	only	ADJ
ejpam-3484	88	7	forcing	forcing	NOUN
ejpam-3484	88	8	subset	subset	NOUN
ejpam-3484	88	9	for	for	ADP
ejpam-3484	88	10	s.	s.	PROPN
ejpam-3484	88	11	therefore	therefore	ADV
ejpam-3484	88	12	,	,	PUNCT
ejpam-3484	88	13	fγi(g	fγi(g	PROPN
ejpam-3484	88	14	)	)	PUNCT
ejpam-3484	88	15	=	=	SYM
ejpam-3484	88	16	|s|	|s|	NOUN
ejpam-3484	88	17	=	=	NOUN
ejpam-3484	88	18	γi(g	γi(g	NOUN
ejpam-3484	88	19	)	)	PUNCT
ejpam-3484	88	20	.	.	PUNCT
ejpam-3484	89	1	theorem	theorem	VERB
ejpam-3484	89	2	3.4	3.4	NUM
ejpam-3484	89	3	.	.	PUNCT
ejpam-3484	90	1	for	for	ADP
ejpam-3484	90	2	any	any	DET
ejpam-3484	90	3	complete	complete	ADJ
ejpam-3484	90	4	graph	graph	NOUN
ejpam-3484	90	5	kn	kn	PROPN
ejpam-3484	90	6	with	with	ADP
ejpam-3484	90	7	n	n	PRON
ejpam-3484	90	8	≥	≥	NUM
ejpam-3484	90	9	1	1	NUM
ejpam-3484	90	10	vertices	vertex	NOUN
ejpam-3484	90	11	,	,	PUNCT
ejpam-3484	90	12	fγi(kn	fγi(kn	NUM
ejpam-3484	90	13	)	)	PUNCT
ejpam-3484	90	14	=	=	PUNCT
ejpam-3484	90	15	{	{	PUNCT
ejpam-3484	90	16	0	0	NUM
ejpam-3484	90	17	,	,	PUNCT
ejpam-3484	90	18	n	n	NOUN
ejpam-3484	90	19	=	=	SYM
ejpam-3484	90	20	1	1	NUM
ejpam-3484	90	21	,	,	PUNCT
ejpam-3484	90	22	1	1	NUM
ejpam-3484	90	23	,	,	PUNCT
ejpam-3484	90	24	n	n	NOUN
ejpam-3484	90	25	>	>	X
ejpam-3484	90	26	1	1	X
ejpam-3484	90	27	.	.	PUNCT
ejpam-3484	90	28	c.	c.	PROPN
ejpam-3484	90	29	armada	armada	PROPN
ejpam-3484	90	30	,	,	PUNCT
ejpam-3484	90	31	s.	s.	PROPN
ejpam-3484	90	32	canoy	canoy	PROPN
ejpam-3484	90	33	jr	jr	PROPN
ejpam-3484	90	34	.	.	PROPN
ejpam-3484	90	35	/	/	SYM
ejpam-3484	90	36	eur	eur	PROPN
ejpam-3484	90	37	.	.	PUNCT
ejpam-3484	91	1	j.	j.	PROPN
ejpam-3484	91	2	pure	pure	PROPN
ejpam-3484	91	3	appl	appl	PROPN
ejpam-3484	91	4	.	.	PROPN
ejpam-3484	91	5	math	math	PROPN
ejpam-3484	91	6	,	,	PUNCT
ejpam-3484	91	7	12	12	NUM
ejpam-3484	91	8	(	(	PUNCT
ejpam-3484	91	9	4	4	NUM
ejpam-3484	91	10	)	)	PUNCT
ejpam-3484	91	11	(	(	PUNCT
ejpam-3484	91	12	2019	2019	NUM
ejpam-3484	91	13	)	)	PUNCT
ejpam-3484	91	14	,	,	PUNCT
ejpam-3484	91	15	1371	1371	NUM
ejpam-3484	91	16	-	-	SYM
ejpam-3484	91	17	1381	1381	NUM
ejpam-3484	91	18	1374	1374	NUM
ejpam-3484	91	19	proof	proof	NOUN
ejpam-3484	91	20	.	.	PUNCT
ejpam-3484	92	1	each	each	DET
ejpam-3484	92	2	vertex	vertex	NOUN
ejpam-3484	92	3	of	of	ADP
ejpam-3484	92	4	kn	kn	PROPN
ejpam-3484	92	5	forms	form	VERB
ejpam-3484	92	6	a	a	DET
ejpam-3484	92	7	γi	γi	NOUN
ejpam-3484	92	8	-	-	PUNCT
ejpam-3484	92	9	set	set	NOUN
ejpam-3484	92	10	of	of	ADP
ejpam-3484	92	11	kn	kn	PROPN
ejpam-3484	92	12	,	,	PUNCT
ejpam-3484	92	13	so	so	ADV
ejpam-3484	92	14	by	by	ADP
ejpam-3484	92	15	remark	remark	NOUN
ejpam-3484	92	16	3.1	3.1	NUM
ejpam-3484	92	17	,	,	PUNCT
ejpam-3484	92	18	the	the	DET
ejpam-3484	92	19	result	result	NOUN
ejpam-3484	92	20	follows	follow	VERB
ejpam-3484	92	21	.	.	PUNCT
ejpam-3484	93	1	theorem	theorem	VERB
ejpam-3484	93	2	3.5	3.5	NUM
ejpam-3484	93	3	.	.	PUNCT
ejpam-3484	94	1	for	for	ADP
ejpam-3484	94	2	any	any	DET
ejpam-3484	94	3	path	path	NOUN
ejpam-3484	94	4	pn	pn	NOUN
ejpam-3484	94	5	with	with	ADP
ejpam-3484	94	6	n	n	PRON
ejpam-3484	94	7	≥	≥	NUM
ejpam-3484	94	8	1	1	NUM
ejpam-3484	94	9	vertices	vertex	NOUN
ejpam-3484	94	10	,	,	PUNCT
ejpam-3484	94	11	fγi(pn	fγi(pn	NOUN
ejpam-3484	94	12	)	)	PUNCT
ejpam-3484	94	13	=	=	NOUN
ejpam-3484	94	14	{	{	PUNCT
ejpam-3484	94	15	0	0	NUM
ejpam-3484	94	16	,	,	PUNCT
ejpam-3484	94	17	if	if	SCONJ
ejpam-3484	94	18	n	n	NOUN
ejpam-3484	94	19	=	=	SYM
ejpam-3484	94	20	1	1	NUM
ejpam-3484	94	21	or	or	CCONJ
ejpam-3484	94	22	n	n	PRON
ejpam-3484	94	23	≡	≡	PROPN
ejpam-3484	94	24	0(mod	0(mod	NOUN
ejpam-3484	94	25	3	3	NUM
ejpam-3484	94	26	)	)	PUNCT
ejpam-3484	94	27	,	,	PUNCT
ejpam-3484	94	28	1	1	NUM
ejpam-3484	94	29	,	,	PUNCT
ejpam-3484	94	30	otherwise	otherwise	ADV
ejpam-3484	94	31	.	.	PUNCT
ejpam-3484	95	1	proof	proof	NOUN
ejpam-3484	95	2	.	.	PUNCT
ejpam-3484	96	1	suppose	suppose	VERB
ejpam-3484	96	2	that	that	SCONJ
ejpam-3484	96	3	pn	pn	PROPN
ejpam-3484	96	4	=	=	PUNCT
ejpam-3484	97	1	[	[	X
ejpam-3484	97	2	u1	u1	NOUN
ejpam-3484	97	3	,	,	PUNCT
ejpam-3484	97	4	u2	u2	NOUN
ejpam-3484	97	5	,	,	PUNCT
ejpam-3484	97	6	.	.	PUNCT
ejpam-3484	97	7	.	.	PUNCT
ejpam-3484	97	8	.	.	PUNCT
ejpam-3484	98	1	,	,	PUNCT
ejpam-3484	98	2	un	un	PROPN
ejpam-3484	98	3	]	]	X
ejpam-3484	98	4	.	.	PUNCT
ejpam-3484	99	1	by	by	ADP
ejpam-3484	99	2	theorem	theorem	NOUN
ejpam-3484	99	3	2.2(i	2.2(i	NUM
ejpam-3484	99	4	)	)	PUNCT
ejpam-3484	99	5	,	,	PUNCT
ejpam-3484	99	6	γi(pn	γi(pn	PROPN
ejpam-3484	99	7	)	)	PUNCT
ejpam-3484	99	8	=	=	SYM
ejpam-3484	99	9	dn	dn	PROPN
ejpam-3484	99	10	3	3	NUM
ejpam-3484	99	11	e.	e.	PROPN
ejpam-3484	99	12	note	note	VERB
ejpam-3484	99	13	that	that	SCONJ
ejpam-3484	99	14	p1	p1	PROPN
ejpam-3484	99	15	∼=	∼=	PROPN
ejpam-3484	99	16	k1	k1	NOUN
ejpam-3484	99	17	.	.	PUNCT
ejpam-3484	100	1	then	then	ADV
ejpam-3484	100	2	fγi(p1	fγi(p1	NOUN
ejpam-3484	100	3	)	)	PUNCT
ejpam-3484	100	4	=	=	SYM
ejpam-3484	100	5	0	0	NUM
ejpam-3484	100	6	by	by	ADP
ejpam-3484	100	7	theorem	theorem	NOUN
ejpam-3484	100	8	3.4	3.4	NUM
ejpam-3484	100	9	.	.	PUNCT
ejpam-3484	101	1	next	next	ADV
ejpam-3484	101	2	,	,	PUNCT
ejpam-3484	101	3	let	let	VERB
ejpam-3484	101	4	n	n	PRON
ejpam-3484	101	5	≥	≥	X
ejpam-3484	101	6	2	2	NUM
ejpam-3484	101	7	and	and	CCONJ
ejpam-3484	101	8	consider	consider	VERB
ejpam-3484	101	9	the	the	DET
ejpam-3484	101	10	following	follow	VERB
ejpam-3484	101	11	cases	case	NOUN
ejpam-3484	101	12	:	:	PUNCT
ejpam-3484	101	13	case	case	NOUN
ejpam-3484	101	14	1	1	NUM
ejpam-3484	101	15	:	:	PUNCT
ejpam-3484	101	16	n	n	NUM
ejpam-3484	101	17	≡	≡	PROPN
ejpam-3484	101	18	0(mod	0(mod	NOUN
ejpam-3484	101	19	3	3	X
ejpam-3484	101	20	)	)	PUNCT
ejpam-3484	101	21	let	let	VERB
ejpam-3484	101	22	s	s	PRON
ejpam-3484	101	23	=	=	PUNCT
ejpam-3484	101	24	{	{	PUNCT
ejpam-3484	101	25	u2	u2	PROPN
ejpam-3484	101	26	,	,	PUNCT
ejpam-3484	101	27	u5	u5	PROPN
ejpam-3484	101	28	,	,	PUNCT
ejpam-3484	101	29	u8	u8	PROPN
ejpam-3484	101	30	,	,	PUNCT
ejpam-3484	101	31	.	.	PUNCT
ejpam-3484	101	32	.	.	PUNCT
ejpam-3484	102	1	.	.	PUNCT
ejpam-3484	103	1	,	,	PUNCT
ejpam-3484	103	2	un−1	un−1	ADJ
ejpam-3484	103	3	}	}	PUNCT
ejpam-3484	103	4	=	=	SYM
ejpam-3484	103	5	{	{	PUNCT
ejpam-3484	103	6	u3k−1	u3k−1	INTJ
ejpam-3484	103	7	:	:	PUNCT
ejpam-3484	103	8	k	k	X
ejpam-3484	104	1	=	=	SYM
ejpam-3484	104	2	1	1	NUM
ejpam-3484	104	3	,	,	PUNCT
ejpam-3484	104	4	2	2	NUM
ejpam-3484	104	5	,	,	PUNCT
ejpam-3484	104	6	.	.	PUNCT
ejpam-3484	104	7	.	.	PUNCT
ejpam-3484	105	1	.	.	PUNCT
ejpam-3484	106	1	,	,	PUNCT
ejpam-3484	106	2	n	n	ADV
ejpam-3484	106	3	3	3	NUM
ejpam-3484	106	4	}	}	PUNCT
ejpam-3484	106	5	.	.	PUNCT
ejpam-3484	107	1	clearly	clearly	ADV
ejpam-3484	107	2	,	,	PUNCT
ejpam-3484	107	3	s	s	VERB
ejpam-3484	107	4	∩	∩	NOUN
ejpam-3484	107	5	n(s	n(s	NOUN
ejpam-3484	107	6	)	)	PUNCT
ejpam-3484	107	7	=	=	NOUN
ejpam-3484	107	8	∅	∅	NOUN
ejpam-3484	107	9	and	and	CCONJ
ejpam-3484	107	10	|s|	|s|	PROPN
ejpam-3484	107	11	=	=	SYM
ejpam-3484	107	12	dn	dn	PROPN
ejpam-3484	107	13	3	3	NUM
ejpam-3484	107	14	e.	e.	PROPN
ejpam-3484	107	15	since	since	SCONJ
ejpam-3484	107	16	s	s	PROPN
ejpam-3484	107	17	is	be	AUX
ejpam-3484	107	18	the	the	DET
ejpam-3484	107	19	only	only	ADJ
ejpam-3484	107	20	γi	γi	NOUN
ejpam-3484	107	21	-	-	PUNCT
ejpam-3484	107	22	set	set	NOUN
ejpam-3484	107	23	of	of	ADP
ejpam-3484	107	24	pn	pn	PROPN
ejpam-3484	107	25	,	,	PUNCT
ejpam-3484	107	26	fγi(pn	fγi(pn	NOUN
ejpam-3484	107	27	)	)	PUNCT
ejpam-3484	107	28	=	=	SYM
ejpam-3484	107	29	0	0	NUM
ejpam-3484	107	30	by	by	ADP
ejpam-3484	107	31	remark	remark	NOUN
ejpam-3484	107	32	3.1(i	3.1(i	NUM
ejpam-3484	107	33	)	)	PUNCT
ejpam-3484	107	34	.	.	PUNCT
ejpam-3484	108	1	case	case	NOUN
ejpam-3484	108	2	2	2	NUM
ejpam-3484	108	3	:	:	PUNCT
ejpam-3484	108	4	n	n	NUM
ejpam-3484	108	5	≡	≡	PROPN
ejpam-3484	108	6	1(mod	1(mod	NUM
ejpam-3484	108	7	3	3	X
ejpam-3484	108	8	)	)	PUNCT
ejpam-3484	108	9	let	let	VERB
ejpam-3484	108	10	s1	s1	NOUN
ejpam-3484	108	11	=	=	SYM
ejpam-3484	108	12	{	{	PUNCT
ejpam-3484	108	13	u1	u1	NOUN
ejpam-3484	108	14	}	}	PUNCT
ejpam-3484	108	15	∪	∪	NOUN
ejpam-3484	108	16	{	{	PUNCT
ejpam-3484	108	17	u3k	u3k	NOUN
ejpam-3484	108	18	:	:	PUNCT
ejpam-3484	109	1	k	k	X
ejpam-3484	109	2	=	=	SYM
ejpam-3484	109	3	1	1	NUM
ejpam-3484	109	4	,	,	PUNCT
ejpam-3484	109	5	2	2	NUM
ejpam-3484	109	6	,	,	PUNCT
ejpam-3484	109	7	.	.	PUNCT
ejpam-3484	109	8	.	.	PUNCT
ejpam-3484	109	9	.	.	PUNCT
ejpam-3484	110	1	,	,	PUNCT
ejpam-3484	110	2	n−1	n−1	PROPN
ejpam-3484	110	3	3	3	NUM
ejpam-3484	110	4	}	}	PUNCT
ejpam-3484	110	5	,	,	PUNCT
ejpam-3484	110	6	s2	s2	X
ejpam-3484	110	7	=	=	SYM
ejpam-3484	110	8	{	{	PUNCT
ejpam-3484	110	9	u1	u1	NOUN
ejpam-3484	110	10	}	}	PUNCT
ejpam-3484	110	11	∪	∪	NOUN
ejpam-3484	110	12	{	{	PUNCT
ejpam-3484	110	13	u3k+1	u3k+1	NOUN
ejpam-3484	110	14	:	:	PUNCT
ejpam-3484	110	15	k	k	X
ejpam-3484	110	16	=	=	SYM
ejpam-3484	110	17	1	1	NUM
ejpam-3484	110	18	,	,	PUNCT
ejpam-3484	110	19	2	2	NUM
ejpam-3484	110	20	,	,	PUNCT
ejpam-3484	110	21	.	.	PUNCT
ejpam-3484	110	22	.	.	PUNCT
ejpam-3484	111	1	.	.	PUNCT
ejpam-3484	112	1	,	,	PUNCT
ejpam-3484	112	2	n−2	n−2	PROPN
ejpam-3484	112	3	3	3	NUM
ejpam-3484	112	4	}	}	PUNCT
ejpam-3484	112	5	and	and	CCONJ
ejpam-3484	112	6	sk	sk	VERB
ejpam-3484	112	7	,	,	PUNCT
ejpam-3484	112	8	p	p	NOUN
ejpam-3484	112	9	=	=	NOUN
ejpam-3484	112	10	{	{	PUNCT
ejpam-3484	112	11	u1	u1	NOUN
ejpam-3484	112	12	}	}	PUNCT
ejpam-3484	112	13	∪	∪	NOUN
ejpam-3484	112	14	{	{	PUNCT
ejpam-3484	112	15	u3k+1	u3k+1	NOUN
ejpam-3484	112	16	:	:	PUNCT
ejpam-3484	112	17	k	k	X
ejpam-3484	112	18	=	=	SYM
ejpam-3484	112	19	1	1	NUM
ejpam-3484	112	20	,	,	PUNCT
ejpam-3484	112	21	2	2	NUM
ejpam-3484	112	22	,	,	PUNCT
ejpam-3484	112	23	.	.	PUNCT
ejpam-3484	112	24	.	.	PUNCT
ejpam-3484	113	1	.	.	PUNCT
ejpam-3484	114	1	,	,	PUNCT
ejpam-3484	114	2	n−4	n−4	PROPN
ejpam-3484	114	3	3	3	NUM
ejpam-3484	114	4	}	}	PUNCT
ejpam-3484	114	5	∪	∪	NOUN
ejpam-3484	114	6	{	{	PUNCT
ejpam-3484	114	7	u3p	u3p	NOUN
ejpam-3484	114	8	:	:	PUNCT
ejpam-3484	114	9	k	k	X
ejpam-3484	114	10	<	<	X
ejpam-3484	114	11	p	p	X
ejpam-3484	114	12	≤	≤	NUM
ejpam-3484	114	13	n−1	n−1	PROPN
ejpam-3484	114	14	3	3	NUM
ejpam-3484	114	15	}	}	PUNCT
ejpam-3484	114	16	.	.	PUNCT
ejpam-3484	115	1	then	then	ADV
ejpam-3484	115	2	for	for	ADP
ejpam-3484	115	3	all	all	PRON
ejpam-3484	115	4	i	i	PRON
ejpam-3484	115	5	∈	∈	PROPN
ejpam-3484	115	6	{	{	PUNCT
ejpam-3484	115	7	1	1	NUM
ejpam-3484	115	8	,	,	PUNCT
ejpam-3484	115	9	2	2	NUM
ejpam-3484	115	10	}	}	PUNCT
ejpam-3484	115	11	and	and	CCONJ
ejpam-3484	115	12	for	for	ADP
ejpam-3484	115	13	all	all	DET
ejpam-3484	115	14	k	k	NOUN
ejpam-3484	115	15	,	,	PUNCT
ejpam-3484	115	16	p	p	NOUN
ejpam-3484	115	17	with	with	ADP
ejpam-3484	115	18	k	k	PROPN
ejpam-3484	115	19	∈	∈	PROPN
ejpam-3484	115	20	{	{	PUNCT
ejpam-3484	115	21	1	1	NUM
ejpam-3484	115	22	,	,	PUNCT
ejpam-3484	115	23	2	2	NUM
ejpam-3484	115	24	,	,	PUNCT
ejpam-3484	115	25	.	.	PUNCT
ejpam-3484	115	26	.	.	PUNCT
ejpam-3484	115	27	.	.	PUNCT
ejpam-3484	116	1	,	,	PUNCT
ejpam-3484	116	2	n−4	n−4	PROPN
ejpam-3484	116	3	3	3	NUM
ejpam-3484	116	4	}	}	PUNCT
ejpam-3484	116	5	and	and	CCONJ
ejpam-3484	116	6	k	k	X
ejpam-3484	116	7	<	<	X
ejpam-3484	116	8	p	p	X
ejpam-3484	116	9	≤	≤	NUM
ejpam-3484	116	10	n−1	n−1	PROPN
ejpam-3484	116	11	3	3	NUM
ejpam-3484	116	12	,	,	PUNCT
ejpam-3484	116	13	si	si	NOUN
ejpam-3484	116	14	∩n(si	∩n(si	PROPN
ejpam-3484	116	15	)	)	PUNCT
ejpam-3484	117	1	=	=	NOUN
ejpam-3484	117	2	∅	∅	NOUN
ejpam-3484	117	3	and	and	CCONJ
ejpam-3484	117	4	|si|	|si|	PROPN
ejpam-3484	117	5	=	=	PUNCT
ejpam-3484	118	1	dn	dn	NOUN
ejpam-3484	118	2	3	3	NUM
ejpam-3484	118	3	e	e	NOUN
ejpam-3484	118	4	,	,	PUNCT
ejpam-3484	118	5	that	that	ADV
ejpam-3484	118	6	is	is	ADV
ejpam-3484	118	7	,	,	PUNCT
ejpam-3484	118	8	si	si	PROPN
ejpam-3484	118	9	and	and	CCONJ
ejpam-3484	118	10	sk	sk	INTJ
ejpam-3484	118	11	,	,	PUNCT
ejpam-3484	118	12	p	p	NOUN
ejpam-3484	118	13	are	be	AUX
ejpam-3484	118	14	γi	γi	NOUN
ejpam-3484	118	15	-	-	PUNCT
ejpam-3484	118	16	sets	set	NOUN
ejpam-3484	118	17	of	of	ADP
ejpam-3484	118	18	pn	pn	NOUN
ejpam-3484	118	19	and	and	CCONJ
ejpam-3484	118	20	u3	u3	PROPN
ejpam-3484	118	21	∈	∈	PROPN
ejpam-3484	118	22	s1\(s2	s1\(s2	NOUN
ejpam-3484	118	23	∪	∪	NOUN
ejpam-3484	118	24	sk	sk	ADP
ejpam-3484	118	25	,	,	PUNCT
ejpam-3484	118	26	p	p	NOUN
ejpam-3484	118	27	)	)	PUNCT
ejpam-3484	118	28	.	.	PUNCT
ejpam-3484	119	1	let	let	VERB
ejpam-3484	119	2	s	s	PRON
ejpam-3484	119	3	be	be	AUX
ejpam-3484	119	4	a	a	DET
ejpam-3484	119	5	γi	γi	NOUN
ejpam-3484	119	6	-	-	PUNCT
ejpam-3484	119	7	set	set	NOUN
ejpam-3484	119	8	of	of	ADP
ejpam-3484	119	9	pn	pn	NOUN
ejpam-3484	119	10	such	such	ADJ
ejpam-3484	119	11	that	that	SCONJ
ejpam-3484	119	12	u2	u2	PROPN
ejpam-3484	119	13	∈	∈	PROPN
ejpam-3484	119	14	s.	s.	PROPN
ejpam-3484	119	15	then	then	ADV
ejpam-3484	119	16	u3	u3	PROPN
ejpam-3484	119	17	∈	∈	PROPN
ejpam-3484	119	18	s1\s	s1\s	PROPN
ejpam-3484	119	19	.	.	PUNCT
ejpam-3484	120	1	since	since	SCONJ
ejpam-3484	120	2	s1	s1	PROPN
ejpam-3484	120	3	is	be	AUX
ejpam-3484	120	4	the	the	DET
ejpam-3484	120	5	only	only	ADJ
ejpam-3484	120	6	γi	γi	NOUN
ejpam-3484	120	7	-	-	PUNCT
ejpam-3484	120	8	set	set	ADJ
ejpam-3484	120	9	containing	contain	VERB
ejpam-3484	120	10	u3	u3	NOUN
ejpam-3484	120	11	,	,	PUNCT
ejpam-3484	120	12	by	by	ADP
ejpam-3484	120	13	remark	remark	NOUN
ejpam-3484	120	14	3.1(ii	3.1(ii	NUM
ejpam-3484	120	15	)	)	PUNCT
ejpam-3484	120	16	,	,	PUNCT
ejpam-3484	120	17	fγi(s1	fγi(s1	PROPN
ejpam-3484	120	18	)	)	PUNCT
ejpam-3484	120	19	=	=	SYM
ejpam-3484	120	20	1	1	NUM
ejpam-3484	120	21	=	=	SYM
ejpam-3484	120	22	fγi(pn	fγi(pn	NOUN
ejpam-3484	120	23	)	)	PUNCT
ejpam-3484	120	24	.	.	PUNCT
ejpam-3484	121	1	case	case	NOUN
ejpam-3484	121	2	3	3	NUM
ejpam-3484	121	3	:	:	PUNCT
ejpam-3484	121	4	n	n	NUM
ejpam-3484	121	5	≡	≡	PROPN
ejpam-3484	121	6	2(mod	2(mod	NUM
ejpam-3484	121	7	3	3	X
ejpam-3484	121	8	)	)	PUNCT
ejpam-3484	121	9	then	then	ADV
ejpam-3484	121	10	the	the	DET
ejpam-3484	121	11	set	set	NOUN
ejpam-3484	121	12	s1	s1	NOUN
ejpam-3484	121	13	=	=	SYM
ejpam-3484	121	14	{	{	PUNCT
ejpam-3484	121	15	u1	u1	PROPN
ejpam-3484	121	16	,	,	PUNCT
ejpam-3484	121	17	u4	u4	PROPN
ejpam-3484	121	18	,	,	PUNCT
ejpam-3484	121	19	u7	u7	PROPN
ejpam-3484	121	20	,	,	PUNCT
ejpam-3484	121	21	.	.	PUNCT
ejpam-3484	121	22	.	.	PUNCT
ejpam-3484	122	1	.	.	PUNCT
ejpam-3484	123	1	,	,	PUNCT
ejpam-3484	123	2	un−1	un−1	ADJ
ejpam-3484	123	3	}	}	PUNCT
ejpam-3484	123	4	=	=	SYM
ejpam-3484	123	5	{	{	PUNCT
ejpam-3484	123	6	u3k+1	u3k+1	INTJ
ejpam-3484	123	7	:	:	PUNCT
ejpam-3484	124	1	k	k	X
ejpam-3484	124	2	=	=	SYM
ejpam-3484	124	3	0	0	NUM
ejpam-3484	124	4	,	,	PUNCT
ejpam-3484	124	5	1	1	NUM
ejpam-3484	124	6	,	,	PUNCT
ejpam-3484	124	7	.	.	PUNCT
ejpam-3484	124	8	.	.	PUNCT
ejpam-3484	124	9	.	.	PUNCT
ejpam-3484	125	1	,	,	PUNCT
ejpam-3484	125	2	n−2	n−2	PROPN
ejpam-3484	125	3	3	3	NUM
ejpam-3484	125	4	}	}	PUNCT
ejpam-3484	125	5	is	be	AUX
ejpam-3484	125	6	the	the	DET
ejpam-3484	125	7	only	only	ADJ
ejpam-3484	125	8	γi	γi	NOUN
ejpam-3484	125	9	-	-	PUNCT
ejpam-3484	125	10	set	set	NOUN
ejpam-3484	125	11	of	of	ADP
ejpam-3484	125	12	pn	pn	PROPN
ejpam-3484	125	13	that	that	PRON
ejpam-3484	125	14	contains	contain	VERB
ejpam-3484	125	15	u1	u1	NOUN
ejpam-3484	125	16	.	.	PUNCT
ejpam-3484	126	1	since	since	SCONJ
ejpam-3484	126	2	s2	s2	PROPN
ejpam-3484	126	3	=	=	SYM
ejpam-3484	126	4	{	{	PUNCT
ejpam-3484	126	5	u2	u2	PROPN
ejpam-3484	126	6	,	,	PUNCT
ejpam-3484	126	7	u4	u4	PROPN
ejpam-3484	126	8	,	,	PUNCT
ejpam-3484	126	9	u7	u7	PROPN
ejpam-3484	126	10	,	,	PUNCT
ejpam-3484	126	11	.	.	PUNCT
ejpam-3484	126	12	.	.	PUNCT
ejpam-3484	126	13	.	.	PUNCT
ejpam-3484	127	1	,	,	PUNCT
ejpam-3484	127	2	un−1	un−1	ADJ
ejpam-3484	127	3	}	}	PUNCT
ejpam-3484	127	4	is	be	AUX
ejpam-3484	127	5	also	also	ADV
ejpam-3484	127	6	a	a	DET
ejpam-3484	127	7	γi	γi	NOUN
ejpam-3484	127	8	-	-	PUNCT
ejpam-3484	127	9	set	set	NOUN
ejpam-3484	127	10	of	of	ADP
ejpam-3484	127	11	pn	pn	PROPN
ejpam-3484	127	12	,	,	PUNCT
ejpam-3484	127	13	it	it	PRON
ejpam-3484	127	14	follows	follow	VERB
ejpam-3484	127	15	from	from	ADP
ejpam-3484	127	16	remark	remark	NOUN
ejpam-3484	127	17	3.1(ii	3.1(ii	NUM
ejpam-3484	127	18	)	)	PUNCT
ejpam-3484	127	19	that	that	SCONJ
ejpam-3484	127	20	fγi(s1	fγi(s1	VERB
ejpam-3484	127	21	)	)	PUNCT
ejpam-3484	127	22	=	=	SYM
ejpam-3484	127	23	1	1	NUM
ejpam-3484	127	24	=	=	SYM
ejpam-3484	127	25	fγi(pn	fγi(pn	NOUN
ejpam-3484	127	26	)	)	PUNCT
ejpam-3484	127	27	.	.	PUNCT
ejpam-3484	128	1	theorem	theorem	VERB
ejpam-3484	128	2	3.6	3.6	NUM
ejpam-3484	128	3	.	.	PUNCT
ejpam-3484	129	1	for	for	ADP
ejpam-3484	129	2	any	any	DET
ejpam-3484	129	3	cycle	cycle	NOUN
ejpam-3484	129	4	cn	cn	NOUN
ejpam-3484	129	5	with	with	ADP
ejpam-3484	129	6	n	n	NUM
ejpam-3484	129	7	≥	≥	NUM
ejpam-3484	129	8	3	3	NUM
ejpam-3484	129	9	vertices	vertex	NOUN
ejpam-3484	129	10	,	,	PUNCT
ejpam-3484	129	11	fγi(cn	fγi(cn	NUM
ejpam-3484	129	12	)	)	PUNCT
ejpam-3484	129	13	=	=	PRON
ejpam-3484	129	14	{	{	PUNCT
ejpam-3484	129	15	1	1	NUM
ejpam-3484	129	16	,	,	PUNCT
ejpam-3484	129	17	if	if	SCONJ
ejpam-3484	129	18	n	n	CCONJ
ejpam-3484	129	19	=	=	SYM
ejpam-3484	129	20	4	4	NUM
ejpam-3484	129	21	or	or	CCONJ
ejpam-3484	129	22	n	n	PRON
ejpam-3484	129	23	≡	≡	PROPN
ejpam-3484	129	24	0(mod	0(mod	NOUN
ejpam-3484	129	25	3	3	NUM
ejpam-3484	129	26	)	)	PUNCT
ejpam-3484	129	27	,	,	PUNCT
ejpam-3484	129	28	2	2	NUM
ejpam-3484	129	29	,	,	PUNCT
ejpam-3484	129	30	otherwise	otherwise	ADV
ejpam-3484	129	31	.	.	PUNCT
ejpam-3484	130	1	proof	proof	NOUN
ejpam-3484	130	2	.	.	PUNCT
ejpam-3484	131	1	suppose	suppose	VERB
ejpam-3484	131	2	that	that	SCONJ
ejpam-3484	131	3	cn	cn	PROPN
ejpam-3484	131	4	=	=	PUNCT
ejpam-3484	132	1	[	[	X
ejpam-3484	132	2	u1	u1	NOUN
ejpam-3484	132	3	,	,	PUNCT
ejpam-3484	132	4	u2	u2	NOUN
ejpam-3484	132	5	,	,	PUNCT
ejpam-3484	132	6	.	.	PUNCT
ejpam-3484	132	7	.	.	PUNCT
ejpam-3484	132	8	.	.	PUNCT
ejpam-3484	133	1	,	,	PUNCT
ejpam-3484	133	2	un	un	PROPN
ejpam-3484	133	3	,	,	PUNCT
ejpam-3484	133	4	u1	u1	NOUN
ejpam-3484	133	5	]	]	PUNCT
ejpam-3484	133	6	.	.	PUNCT
ejpam-3484	134	1	by	by	ADP
ejpam-3484	134	2	theorem	theorem	NOUN
ejpam-3484	134	3	2.2(i	2.2(i	NUM
ejpam-3484	134	4	)	)	PUNCT
ejpam-3484	134	5	,	,	PUNCT
ejpam-3484	134	6	γi(cn	γi(cn	PROPN
ejpam-3484	134	7	)	)	PUNCT
ejpam-3484	135	1	=	=	SYM
ejpam-3484	135	2	dn	dn	PROPN
ejpam-3484	135	3	3	3	NUM
ejpam-3484	135	4	e.	e.	PROPN
ejpam-3484	135	5	if	if	SCONJ
ejpam-3484	135	6	n	n	PROPN
ejpam-3484	135	7	=	=	SYM
ejpam-3484	135	8	4	4	NUM
ejpam-3484	135	9	,	,	PUNCT
ejpam-3484	135	10	then	then	ADV
ejpam-3484	135	11	s1	s1	PROPN
ejpam-3484	135	12	=	=	SYM
ejpam-3484	135	13	{	{	PUNCT
ejpam-3484	135	14	u1	u1	NOUN
ejpam-3484	135	15	,	,	PUNCT
ejpam-3484	135	16	u3	u3	NOUN
ejpam-3484	135	17	}	}	PUNCT
ejpam-3484	135	18	and	and	CCONJ
ejpam-3484	135	19	s2	s2	PROPN
ejpam-3484	135	20	=	=	SYM
ejpam-3484	135	21	{	{	PUNCT
ejpam-3484	135	22	u2	u2	PROPN
ejpam-3484	135	23	,	,	PUNCT
ejpam-3484	135	24	u4	u4	PROPN
ejpam-3484	135	25	}	}	PUNCT
ejpam-3484	135	26	are	be	AUX
ejpam-3484	135	27	the	the	DET
ejpam-3484	135	28	only	only	ADJ
ejpam-3484	135	29	γi	γi	NOUN
ejpam-3484	135	30	-	-	PUNCT
ejpam-3484	135	31	sets	set	NOUN
ejpam-3484	135	32	of	of	ADP
ejpam-3484	135	33	c4	c4	NOUN
ejpam-3484	135	34	.	.	PUNCT
ejpam-3484	136	1	since	since	SCONJ
ejpam-3484	136	2	s1	s1	PROPN
ejpam-3484	136	3	contains	contain	VERB
ejpam-3484	136	4	an	an	DET
ejpam-3484	136	5	element	element	NOUN
ejpam-3484	136	6	which	which	PRON
ejpam-3484	136	7	is	be	AUX
ejpam-3484	136	8	not	not	PART
ejpam-3484	136	9	in	in	ADP
ejpam-3484	136	10	s2	s2	NOUN
ejpam-3484	136	11	,	,	PUNCT
ejpam-3484	136	12	fγi(s1	fγi(s1	NOUN
ejpam-3484	136	13	)	)	PUNCT
ejpam-3484	136	14	=	=	SYM
ejpam-3484	136	15	fγi(c4	fγi(c4	NOUN
ejpam-3484	136	16	)	)	PUNCT
ejpam-3484	136	17	=	=	SYM
ejpam-3484	136	18	1	1	NUM
ejpam-3484	136	19	by	by	ADP
ejpam-3484	136	20	remark	remark	NOUN
ejpam-3484	136	21	3.1(ii	3.1(ii	NUM
ejpam-3484	136	22	)	)	PUNCT
ejpam-3484	136	23	.	.	PUNCT
ejpam-3484	137	1	next	next	ADV
ejpam-3484	137	2	,	,	PUNCT
ejpam-3484	137	3	let	let	VERB
ejpam-3484	137	4	n	n	PRON
ejpam-3484	137	5	≥	≥	NOUN
ejpam-3484	137	6	3	3	NUM
ejpam-3484	137	7	,	,	PUNCT
ejpam-3484	137	8	where	where	SCONJ
ejpam-3484	137	9	n	n	X
ejpam-3484	137	10	6=	6=	NUM
ejpam-3484	137	11	4	4	NUM
ejpam-3484	137	12	,	,	PUNCT
ejpam-3484	137	13	and	and	CCONJ
ejpam-3484	137	14	consider	consider	VERB
ejpam-3484	137	15	the	the	DET
ejpam-3484	137	16	following	follow	VERB
ejpam-3484	137	17	cases	case	NOUN
ejpam-3484	137	18	:	:	PUNCT
ejpam-3484	137	19	case	case	NOUN
ejpam-3484	137	20	1	1	NUM
ejpam-3484	137	21	:	:	PUNCT
ejpam-3484	137	22	n	n	NUM
ejpam-3484	137	23	≡	≡	PROPN
ejpam-3484	137	24	0(mod	0(mod	NOUN
ejpam-3484	137	25	3	3	X
ejpam-3484	137	26	)	)	PUNCT
ejpam-3484	137	27	let	let	VERB
ejpam-3484	137	28	i1	i1	PROPN
ejpam-3484	137	29	=	=	PUNCT
ejpam-3484	137	30	{	{	PUNCT
ejpam-3484	137	31	u3k	u3k	NOUN
ejpam-3484	137	32	:	:	PUNCT
ejpam-3484	138	1	k	k	X
ejpam-3484	138	2	=	=	SYM
ejpam-3484	138	3	1	1	NUM
ejpam-3484	138	4	,	,	PUNCT
ejpam-3484	138	5	2	2	NUM
ejpam-3484	138	6	,	,	PUNCT
ejpam-3484	138	7	.	.	PUNCT
ejpam-3484	138	8	.	.	PUNCT
ejpam-3484	139	1	.	.	PUNCT
ejpam-3484	140	1	,	,	PUNCT
ejpam-3484	140	2	n	n	ADV
ejpam-3484	140	3	3	3	NUM
ejpam-3484	140	4	}	}	PUNCT
ejpam-3484	140	5	,	,	PUNCT
ejpam-3484	140	6	i2	i2	PROPN
ejpam-3484	140	7	=	=	PUNCT
ejpam-3484	140	8	{	{	PUNCT
ejpam-3484	140	9	u3k+1	u3k+1	INTJ
ejpam-3484	140	10	:	:	PUNCT
ejpam-3484	140	11	k	k	X
ejpam-3484	140	12	=	=	SYM
ejpam-3484	140	13	0	0	NUM
ejpam-3484	140	14	,	,	PUNCT
ejpam-3484	140	15	1	1	NUM
ejpam-3484	140	16	,	,	PUNCT
ejpam-3484	140	17	.	.	PUNCT
ejpam-3484	140	18	.	.	PUNCT
ejpam-3484	141	1	.	.	PUNCT
ejpam-3484	142	1	,	,	PUNCT
ejpam-3484	142	2	n−3	n−3	PROPN
ejpam-3484	142	3	3	3	NUM
ejpam-3484	142	4	}	}	PUNCT
ejpam-3484	142	5	,	,	PUNCT
ejpam-3484	142	6	and	and	CCONJ
ejpam-3484	142	7	i3	i3	NOUN
ejpam-3484	142	8	=	=	SYM
ejpam-3484	142	9	{	{	PUNCT
ejpam-3484	142	10	u3k+2	u3k+2	NOUN
ejpam-3484	142	11	:	:	PUNCT
ejpam-3484	142	12	k	k	X
ejpam-3484	142	13	=	=	SYM
ejpam-3484	142	14	0	0	NUM
ejpam-3484	142	15	,	,	PUNCT
ejpam-3484	142	16	1	1	NUM
ejpam-3484	142	17	,	,	PUNCT
ejpam-3484	142	18	.	.	PUNCT
ejpam-3484	142	19	.	.	PUNCT
ejpam-3484	142	20	.	.	PUNCT
ejpam-3484	143	1	,	,	PUNCT
ejpam-3484	143	2	n−3	n−3	PROPN
ejpam-3484	143	3	3	3	NUM
ejpam-3484	143	4	}	}	PUNCT
ejpam-3484	143	5	.	.	PUNCT
ejpam-3484	144	1	then	then	ADV
ejpam-3484	144	2	for	for	ADP
ejpam-3484	144	3	all	all	DET
ejpam-3484	144	4	j	j	PROPN
ejpam-3484	144	5	∈	∈	PROPN
ejpam-3484	144	6	{	{	PUNCT
ejpam-3484	144	7	1	1	NUM
ejpam-3484	144	8	,	,	PUNCT
ejpam-3484	144	9	2	2	NUM
ejpam-3484	144	10	,	,	PUNCT
ejpam-3484	144	11	3	3	NUM
ejpam-3484	144	12	}	}	PUNCT
ejpam-3484	144	13	,	,	PUNCT
ejpam-3484	144	14	ij	ij	INTJ
ejpam-3484	144	15	∩n(ij	∩n(ij	NOUN
ejpam-3484	144	16	)	)	PUNCT
ejpam-3484	144	17	=	=	NOUN
ejpam-3484	144	18	∅	∅	NOUN
ejpam-3484	144	19	and	and	CCONJ
ejpam-3484	144	20	|ij	|ij	X
ejpam-3484	145	1	|	|	ADV
ejpam-3484	145	2	=	=	SYM
ejpam-3484	145	3	dn	dn	PROPN
ejpam-3484	145	4	3	3	NUM
ejpam-3484	145	5	e.	e.	PROPN
ejpam-3484	145	6	thus	thus	ADV
ejpam-3484	145	7	,	,	PUNCT
ejpam-3484	145	8	i1	i1	PROPN
ejpam-3484	145	9	,	,	PUNCT
ejpam-3484	145	10	i2	i2	PROPN
ejpam-3484	145	11	and	and	CCONJ
ejpam-3484	145	12	i3	i3	NOUN
ejpam-3484	145	13	are	be	AUX
ejpam-3484	145	14	the	the	DET
ejpam-3484	145	15	only	only	ADJ
ejpam-3484	145	16	γi	γi	NOUN
ejpam-3484	145	17	-	-	PUNCT
ejpam-3484	145	18	sets	set	NOUN
ejpam-3484	145	19	of	of	ADP
ejpam-3484	145	20	cn	cn	PROPN
ejpam-3484	145	21	.	.	PUNCT
ejpam-3484	145	22	clearly	clearly	ADV
ejpam-3484	145	23	,	,	PUNCT
ejpam-3484	145	24	i1	i1	PROPN
ejpam-3484	145	25	contains	contain	VERB
ejpam-3484	145	26	an	an	DET
ejpam-3484	145	27	element	element	NOUN
ejpam-3484	145	28	which	which	PRON
ejpam-3484	145	29	is	be	AUX
ejpam-3484	145	30	not	not	PART
ejpam-3484	145	31	in	in	ADP
ejpam-3484	145	32	i2	i2	PROPN
ejpam-3484	145	33	and	and	CCONJ
ejpam-3484	145	34	i3	i3	NOUN
ejpam-3484	145	35	,	,	PUNCT
ejpam-3484	145	36	by	by	ADP
ejpam-3484	145	37	remark	remark	NOUN
ejpam-3484	145	38	3.1(ii	3.1(ii	NUM
ejpam-3484	145	39	)	)	PUNCT
ejpam-3484	145	40	,	,	PUNCT
ejpam-3484	145	41	fγi(i1	fγi(i1	NOUN
ejpam-3484	145	42	)	)	PUNCT
ejpam-3484	145	43	=	=	SYM
ejpam-3484	145	44	fγi(cn	fγi(cn	PROPN
ejpam-3484	145	45	)	)	PUNCT
ejpam-3484	145	46	=	=	SYM
ejpam-3484	145	47	1	1	X
ejpam-3484	145	48	.	.	PUNCT
ejpam-3484	145	49	c.	c.	PROPN
ejpam-3484	145	50	armada	armada	PROPN
ejpam-3484	145	51	,	,	PUNCT
ejpam-3484	145	52	s.	s.	PROPN
ejpam-3484	145	53	canoy	canoy	PROPN
ejpam-3484	145	54	jr	jr	PROPN
ejpam-3484	145	55	.	.	PROPN
ejpam-3484	145	56	/	/	SYM
ejpam-3484	145	57	eur	eur	PROPN
ejpam-3484	145	58	.	.	PUNCT
ejpam-3484	146	1	j.	j.	PROPN
ejpam-3484	146	2	pure	pure	PROPN
ejpam-3484	146	3	appl	appl	PROPN
ejpam-3484	146	4	.	.	PROPN
ejpam-3484	146	5	math	math	PROPN
ejpam-3484	146	6	,	,	PUNCT
ejpam-3484	146	7	12	12	NUM
ejpam-3484	146	8	(	(	PUNCT
ejpam-3484	146	9	4	4	NUM
ejpam-3484	146	10	)	)	PUNCT
ejpam-3484	146	11	(	(	PUNCT
ejpam-3484	146	12	2019	2019	NUM
ejpam-3484	146	13	)	)	PUNCT
ejpam-3484	146	14	,	,	PUNCT
ejpam-3484	146	15	1371	1371	NUM
ejpam-3484	146	16	-	-	SYM
ejpam-3484	146	17	1381	1381	NUM
ejpam-3484	146	18	1375	1375	NUM
ejpam-3484	146	19	case	case	NOUN
ejpam-3484	146	20	2	2	NUM
ejpam-3484	146	21	:	:	PUNCT
ejpam-3484	146	22	n	n	NUM
ejpam-3484	146	23	≡	≡	PROPN
ejpam-3484	146	24	1(mod	1(mod	NUM
ejpam-3484	146	25	3	3	X
ejpam-3484	146	26	)	)	PUNCT
ejpam-3484	146	27	then	then	ADV
ejpam-3484	146	28	clearly	clearly	ADV
ejpam-3484	146	29	,	,	PUNCT
ejpam-3484	146	30	s	s	PART
ejpam-3484	146	31	=	=	PUNCT
ejpam-3484	146	32	{	{	PUNCT
ejpam-3484	146	33	u1	u1	PROPN
ejpam-3484	146	34	,	,	PUNCT
ejpam-3484	146	35	u3}∪{u3k+2	u3}∪{u3k+2	PROPN
ejpam-3484	146	36	:	:	PUNCT
ejpam-3484	147	1	k	k	X
ejpam-3484	147	2	=	=	SYM
ejpam-3484	147	3	1	1	NUM
ejpam-3484	147	4	,	,	PUNCT
ejpam-3484	147	5	2	2	NUM
ejpam-3484	147	6	,	,	PUNCT
ejpam-3484	147	7	.	.	PUNCT
ejpam-3484	147	8	.	.	PUNCT
ejpam-3484	148	1	.	.	PUNCT
ejpam-3484	149	1	,	,	PUNCT
ejpam-3484	149	2	n−4	n−4	PROPN
ejpam-3484	149	3	3	3	NUM
ejpam-3484	149	4	}	}	PUNCT
ejpam-3484	149	5	is	be	AUX
ejpam-3484	149	6	a	a	DET
ejpam-3484	149	7	γi	γi	NOUN
ejpam-3484	149	8	-	-	PUNCT
ejpam-3484	149	9	set	set	NOUN
ejpam-3484	149	10	of	of	ADP
ejpam-3484	149	11	cn	cn	PROPN
ejpam-3484	149	12	.	.	PUNCT
ejpam-3484	149	13	clearly	clearly	ADV
ejpam-3484	149	14	,	,	PUNCT
ejpam-3484	149	15	s	s	NOUN
ejpam-3484	149	16	contains	contain	VERB
ejpam-3484	149	17	u1	u1	NOUN
ejpam-3484	149	18	and	and	CCONJ
ejpam-3484	149	19	u5	u5	PROPN
ejpam-3484	149	20	where	where	SCONJ
ejpam-3484	149	21	d(u1	d(u1	NOUN
ejpam-3484	149	22	,	,	PUNCT
ejpam-3484	149	23	u3	u3	NOUN
ejpam-3484	149	24	)	)	PUNCT
ejpam-3484	149	25	=	=	SYM
ejpam-3484	149	26	d(u3	d(u3	NOUN
ejpam-3484	149	27	,	,	PUNCT
ejpam-3484	149	28	u5	u5	PROPN
ejpam-3484	149	29	)	)	PUNCT
ejpam-3484	149	30	=	=	SYM
ejpam-3484	149	31	2	2	X
ejpam-3484	149	32	.	.	X
ejpam-3484	149	33	replacing	replace	VERB
ejpam-3484	149	34	any	any	PRON
ejpam-3484	149	35	of	of	ADP
ejpam-3484	149	36	the	the	DET
ejpam-3484	149	37	vertices	vertex	NOUN
ejpam-3484	149	38	u3k+2	u3k+2	NOUN
ejpam-3484	149	39	(	(	PUNCT
ejpam-3484	149	40	k	k	PROPN
ejpam-3484	149	41	6=	6=	PROPN
ejpam-3484	149	42	1	1	NUM
ejpam-3484	149	43	)	)	PUNCT
ejpam-3484	149	44	to	to	PART
ejpam-3484	149	45	form	form	VERB
ejpam-3484	149	46	another	another	DET
ejpam-3484	149	47	γi	γi	NOUN
ejpam-3484	149	48	-	-	PUNCT
ejpam-3484	149	49	set	set	NOUN
ejpam-3484	149	50	is	be	AUX
ejpam-3484	149	51	not	not	PART
ejpam-3484	149	52	possible	possible	ADJ
ejpam-3484	149	53	since	since	SCONJ
ejpam-3484	149	54	d(u5	d(u5	NOUN
ejpam-3484	149	55	,	,	PUNCT
ejpam-3484	149	56	u8	u8	PROPN
ejpam-3484	149	57	)	)	PUNCT
ejpam-3484	149	58	=	=	SYM
ejpam-3484	149	59	d(u1	d(u1	NOUN
ejpam-3484	149	60	,	,	PUNCT
ejpam-3484	149	61	un−2	un−2	VERB
ejpam-3484	149	62	)	)	PUNCT
ejpam-3484	149	63	=	=	SYM
ejpam-3484	149	64	d(u3k+2	d(u3k+2	X
ejpam-3484	149	65	,	,	PUNCT
ejpam-3484	149	66	u3k+5	u3k+5	ADJ
ejpam-3484	149	67	)	)	PUNCT
ejpam-3484	149	68	=	=	SYM
ejpam-3484	149	69	3	3	NUM
ejpam-3484	149	70	for	for	ADP
ejpam-3484	149	71	all	all	DET
ejpam-3484	149	72	k	k	PROPN
ejpam-3484	149	73	∈	∈	PROPN
ejpam-3484	149	74	{	{	PUNCT
ejpam-3484	149	75	2	2	NUM
ejpam-3484	149	76	,	,	PUNCT
ejpam-3484	149	77	3	3	NUM
ejpam-3484	149	78	,	,	PUNCT
ejpam-3484	149	79	.	.	PUNCT
ejpam-3484	149	80	.	.	PUNCT
ejpam-3484	150	1	.	.	PUNCT
ejpam-3484	151	1	,	,	PUNCT
ejpam-3484	151	2	n−7	n−7	NOUN
ejpam-3484	151	3	3	3	NUM
ejpam-3484	151	4	}	}	PUNCT
ejpam-3484	151	5	.	.	PUNCT
ejpam-3484	152	1	since	since	SCONJ
ejpam-3484	152	2	u1	u1	NOUN
ejpam-3484	152	3	is	be	AUX
ejpam-3484	152	4	also	also	ADV
ejpam-3484	152	5	contained	contain	VERB
ejpam-3484	152	6	in	in	ADP
ejpam-3484	152	7	the	the	DET
ejpam-3484	152	8	γi	γi	NOUN
ejpam-3484	152	9	-	-	PUNCT
ejpam-3484	152	10	set	set	VERB
ejpam-3484	152	11	s′	s′	ADJ
ejpam-3484	152	12	=	=	PUNCT
ejpam-3484	152	13	{	{	PUNCT
ejpam-3484	152	14	u1	u1	NOUN
ejpam-3484	152	15	,	,	PUNCT
ejpam-3484	152	16	un−1	un−1	ADJ
ejpam-3484	152	17	}	}	PUNCT
ejpam-3484	152	18	∪	∪	NOUN
ejpam-3484	152	19	{	{	PUNCT
ejpam-3484	152	20	u3k	u3k	NOUN
ejpam-3484	152	21	:	:	PUNCT
ejpam-3484	153	1	k	k	X
ejpam-3484	153	2	=	=	SYM
ejpam-3484	153	3	1	1	NUM
ejpam-3484	153	4	,	,	PUNCT
ejpam-3484	153	5	2	2	NUM
ejpam-3484	153	6	,	,	PUNCT
ejpam-3484	153	7	.	.	PUNCT
ejpam-3484	153	8	.	.	PUNCT
ejpam-3484	153	9	.	.	PUNCT
ejpam-3484	154	1	,	,	PUNCT
ejpam-3484	154	2	n−4	n−4	PROPN
ejpam-3484	154	3	3	3	NUM
ejpam-3484	154	4	}	}	PUNCT
ejpam-3484	154	5	,	,	PUNCT
ejpam-3484	154	6	no	no	DET
ejpam-3484	154	7	vertex	vertex	NOUN
ejpam-3484	154	8	of	of	ADP
ejpam-3484	154	9	cn	cn	PROPN
ejpam-3484	154	10	is	be	AUX
ejpam-3484	154	11	contained	contain	VERB
ejpam-3484	154	12	in	in	ADP
ejpam-3484	154	13	a	a	DET
ejpam-3484	154	14	unique	unique	ADJ
ejpam-3484	154	15	γi	γi	NOUN
ejpam-3484	154	16	-	-	PUNCT
ejpam-3484	154	17	set	set	NOUN
ejpam-3484	154	18	.	.	PUNCT
ejpam-3484	155	1	thus	thus	ADV
ejpam-3484	155	2	,	,	PUNCT
ejpam-3484	155	3	fγi(s	fγi(s	PROPN
ejpam-3484	155	4	)	)	PUNCT
ejpam-3484	155	5	≥	≥	NOUN
ejpam-3484	155	6	2	2	NUM
ejpam-3484	155	7	.	.	PUNCT
ejpam-3484	156	1	clearly	clearly	ADV
ejpam-3484	156	2	,	,	PUNCT
ejpam-3484	156	3	{	{	PUNCT
ejpam-3484	156	4	u1	u1	NOUN
ejpam-3484	156	5	,	,	PUNCT
ejpam-3484	156	6	u5	u5	PROPN
ejpam-3484	156	7	}	}	PUNCT
ejpam-3484	156	8	is	be	AUX
ejpam-3484	156	9	uniquely	uniquely	ADV
ejpam-3484	156	10	contained	contain	VERB
ejpam-3484	156	11	in	in	ADP
ejpam-3484	156	12	s.	s.	PROPN
ejpam-3484	156	13	therefore	therefore	ADV
ejpam-3484	156	14	,	,	PUNCT
ejpam-3484	156	15	fγi(s	fγi(s	NOUN
ejpam-3484	156	16	)	)	PUNCT
ejpam-3484	156	17	=	=	SYM
ejpam-3484	156	18	2	2	NUM
ejpam-3484	156	19	=	=	SYM
ejpam-3484	156	20	fγi(cn	fγi(cn	NOUN
ejpam-3484	156	21	)	)	PUNCT
ejpam-3484	156	22	.	.	PUNCT
ejpam-3484	157	1	case	case	NOUN
ejpam-3484	157	2	3	3	NUM
ejpam-3484	157	3	:	:	PUNCT
ejpam-3484	157	4	n	n	NUM
ejpam-3484	157	5	≡	≡	PROPN
ejpam-3484	157	6	2(mod	2(mod	NUM
ejpam-3484	157	7	3	3	X
ejpam-3484	157	8	)	)	PUNCT
ejpam-3484	157	9	suppose	suppose	VERB
ejpam-3484	157	10	that	that	SCONJ
ejpam-3484	157	11	n	n	NOUN
ejpam-3484	157	12	=	=	SYM
ejpam-3484	157	13	5	5	NUM
ejpam-3484	157	14	.	.	PUNCT
ejpam-3484	158	1	the	the	DET
ejpam-3484	158	2	γi	γi	NOUN
ejpam-3484	158	3	-	-	PUNCT
ejpam-3484	158	4	sets	set	NOUN
ejpam-3484	158	5	of	of	ADP
ejpam-3484	158	6	c5	c5	PROPN
ejpam-3484	158	7	are	be	AUX
ejpam-3484	158	8	s1	s1	NOUN
ejpam-3484	158	9	=	=	SYM
ejpam-3484	158	10	{	{	PUNCT
ejpam-3484	158	11	u1	u1	NOUN
ejpam-3484	158	12	,	,	PUNCT
ejpam-3484	158	13	u3	u3	PROPN
ejpam-3484	158	14	}	}	PUNCT
ejpam-3484	158	15	,	,	PUNCT
ejpam-3484	158	16	s2	s2	NOUN
ejpam-3484	158	17	=	=	SYM
ejpam-3484	158	18	{	{	PUNCT
ejpam-3484	158	19	u1	u1	PROPN
ejpam-3484	158	20	,	,	PUNCT
ejpam-3484	158	21	u4	u4	PROPN
ejpam-3484	158	22	}	}	PUNCT
ejpam-3484	158	23	,	,	PUNCT
ejpam-3484	158	24	s3	s3	PROPN
ejpam-3484	158	25	=	=	SYM
ejpam-3484	158	26	{	{	PUNCT
ejpam-3484	158	27	u2	u2	PROPN
ejpam-3484	158	28	,	,	PUNCT
ejpam-3484	158	29	u4	u4	PROPN
ejpam-3484	158	30	}	}	PUNCT
ejpam-3484	158	31	,	,	PUNCT
ejpam-3484	158	32	s4	s4	PROPN
ejpam-3484	158	33	=	=	SYM
ejpam-3484	158	34	{	{	PUNCT
ejpam-3484	158	35	u2	u2	PROPN
ejpam-3484	158	36	,	,	PUNCT
ejpam-3484	158	37	u5	u5	PROPN
ejpam-3484	158	38	}	}	PUNCT
ejpam-3484	158	39	and	and	CCONJ
ejpam-3484	158	40	s5	s5	PROPN
ejpam-3484	158	41	=	=	SYM
ejpam-3484	158	42	{	{	PUNCT
ejpam-3484	158	43	u3	u3	PROPN
ejpam-3484	158	44	,	,	PUNCT
ejpam-3484	158	45	u5	u5	PROPN
ejpam-3484	158	46	}	}	PUNCT
ejpam-3484	158	47	.	.	PUNCT
ejpam-3484	159	1	clearly	clearly	ADV
ejpam-3484	159	2	,	,	PUNCT
ejpam-3484	159	3	for	for	SCONJ
ejpam-3484	159	4	each	each	DET
ejpam-3484	159	5	ui	ui	PROPN
ejpam-3484	159	6	∈	∈	PROPN
ejpam-3484	159	7	sj	sj	INTJ
ejpam-3484	159	8	where	where	SCONJ
ejpam-3484	159	9	i	i	PRON
ejpam-3484	159	10	,	,	PUNCT
ejpam-3484	159	11	j	j	PROPN
ejpam-3484	159	12	∈	∈	PROPN
ejpam-3484	159	13	{	{	PUNCT
ejpam-3484	159	14	1	1	NUM
ejpam-3484	159	15	,	,	PUNCT
ejpam-3484	159	16	2	2	NUM
ejpam-3484	159	17	,	,	PUNCT
ejpam-3484	159	18	3	3	NUM
ejpam-3484	159	19	,	,	PUNCT
ejpam-3484	159	20	4	4	NUM
ejpam-3484	159	21	,	,	PUNCT
ejpam-3484	159	22	5	5	NUM
ejpam-3484	159	23	}	}	PUNCT
ejpam-3484	159	24	,	,	PUNCT
ejpam-3484	159	25	there	there	PRON
ejpam-3484	159	26	exists	exist	VERB
ejpam-3484	159	27	uk	uk	PROPN
ejpam-3484	159	28	∈	∈	PROPN
ejpam-3484	159	29	v	v	NOUN
ejpam-3484	159	30	(	(	PUNCT
ejpam-3484	159	31	c5)\sj	c5)\sj	X
ejpam-3484	159	32	such	such	ADJ
ejpam-3484	159	33	that	that	SCONJ
ejpam-3484	159	34	[	[	X
ejpam-3484	159	35	sj\{ui	sj\{ui	X
ejpam-3484	159	36	}	}	PUNCT
ejpam-3484	159	37	]	]	PUNCT
ejpam-3484	159	38	∪	∪	X
ejpam-3484	159	39	{	{	PUNCT
ejpam-3484	159	40	uk	uk	PROPN
ejpam-3484	159	41	}	}	PUNCT
ejpam-3484	159	42	is	be	AUX
ejpam-3484	159	43	a	a	DET
ejpam-3484	159	44	γi	γi	NOUN
ejpam-3484	159	45	-	-	PUNCT
ejpam-3484	159	46	set	set	NOUN
ejpam-3484	159	47	of	of	ADP
ejpam-3484	159	48	g.	g.	PROPN
ejpam-3484	159	49	by	by	ADP
ejpam-3484	159	50	theorem	theorem	NOUN
ejpam-3484	159	51	3.3	3.3	NUM
ejpam-3484	159	52	,	,	PUNCT
ejpam-3484	159	53	fγi(c5	fγi(c5	NOUN
ejpam-3484	159	54	)	)	PUNCT
ejpam-3484	159	55	=	=	SYM
ejpam-3484	160	1	2	2	X
ejpam-3484	160	2	.	.	PUNCT
ejpam-3484	160	3	now	now	ADV
ejpam-3484	160	4	,	,	PUNCT
ejpam-3484	160	5	suppose	suppose	VERB
ejpam-3484	160	6	that	that	SCONJ
ejpam-3484	160	7	n	n	PROPN
ejpam-3484	160	8	>	>	X
ejpam-3484	160	9	5	5	NUM
ejpam-3484	160	10	.	.	PUNCT
ejpam-3484	160	11	then	then	ADV
ejpam-3484	160	12	s	s	AUX
ejpam-3484	160	13	=	=	SYM
ejpam-3484	160	14	{	{	PUNCT
ejpam-3484	160	15	u1	u1	NOUN
ejpam-3484	160	16	}	}	PUNCT
ejpam-3484	160	17	∪	∪	NOUN
ejpam-3484	160	18	{	{	PUNCT
ejpam-3484	160	19	u3k	u3k	NOUN
ejpam-3484	160	20	:	:	PUNCT
ejpam-3484	160	21	k	k	X
ejpam-3484	160	22	=	=	SYM
ejpam-3484	160	23	1	1	NUM
ejpam-3484	160	24	,	,	PUNCT
ejpam-3484	160	25	2	2	NUM
ejpam-3484	160	26	,	,	PUNCT
ejpam-3484	160	27	.	.	PUNCT
ejpam-3484	160	28	.	.	PUNCT
ejpam-3484	161	1	.	.	PUNCT
ejpam-3484	162	1	,	,	PUNCT
ejpam-3484	162	2	n−2	n−2	PROPN
ejpam-3484	162	3	3	3	NUM
ejpam-3484	162	4	}	}	PUNCT
ejpam-3484	162	5	is	be	AUX
ejpam-3484	162	6	a	a	DET
ejpam-3484	162	7	γi	γi	NOUN
ejpam-3484	162	8	-	-	PUNCT
ejpam-3484	162	9	set	set	NOUN
ejpam-3484	162	10	of	of	ADP
ejpam-3484	162	11	cn	cn	PROPN
ejpam-3484	162	12	.	.	PUNCT
ejpam-3484	162	13	clearly	clearly	ADV
ejpam-3484	162	14	,	,	PUNCT
ejpam-3484	162	15	s	s	NOUN
ejpam-3484	162	16	contains	contain	VERB
ejpam-3484	162	17	u1	u1	NOUN
ejpam-3484	162	18	and	and	CCONJ
ejpam-3484	162	19	u3	u3	NOUN
ejpam-3484	162	20	where	where	SCONJ
ejpam-3484	162	21	d(u1	d(u1	NOUN
ejpam-3484	162	22	,	,	PUNCT
ejpam-3484	162	23	u3	u3	NOUN
ejpam-3484	162	24	)	)	PUNCT
ejpam-3484	162	25	=	=	SYM
ejpam-3484	162	26	2	2	X
ejpam-3484	162	27	.	.	PUNCT
ejpam-3484	162	28	since	since	SCONJ
ejpam-3484	162	29	u1	u1	NOUN
ejpam-3484	162	30	is	be	AUX
ejpam-3484	162	31	also	also	ADV
ejpam-3484	162	32	contained	contain	VERB
ejpam-3484	162	33	in	in	ADP
ejpam-3484	162	34	the	the	DET
ejpam-3484	162	35	γi	γi	NOUN
ejpam-3484	162	36	-	-	PUNCT
ejpam-3484	162	37	set	set	VERB
ejpam-3484	162	38	s′	s′	ADJ
ejpam-3484	162	39	=	=	PUNCT
ejpam-3484	162	40	{	{	PUNCT
ejpam-3484	162	41	u1	u1	NOUN
ejpam-3484	162	42	,	,	PUNCT
ejpam-3484	162	43	u4}∪{u3k	u4}∪{u3k	NUM
ejpam-3484	162	44	:	:	PUNCT
ejpam-3484	163	1	k	k	X
ejpam-3484	163	2	=	=	SYM
ejpam-3484	163	3	2	2	NUM
ejpam-3484	163	4	,	,	PUNCT
ejpam-3484	163	5	3	3	NUM
ejpam-3484	163	6	,	,	PUNCT
ejpam-3484	163	7	.	.	PUNCT
ejpam-3484	163	8	.	.	PUNCT
ejpam-3484	163	9	.	.	PUNCT
ejpam-3484	164	1	,	,	PUNCT
ejpam-3484	164	2	n−2	n−2	PROPN
ejpam-3484	164	3	3	3	NUM
ejpam-3484	164	4	}	}	PUNCT
ejpam-3484	164	5	,	,	PUNCT
ejpam-3484	164	6	no	no	DET
ejpam-3484	164	7	vertex	vertex	NOUN
ejpam-3484	164	8	of	of	ADP
ejpam-3484	164	9	cn	cn	PROPN
ejpam-3484	164	10	is	be	AUX
ejpam-3484	164	11	contained	contain	VERB
ejpam-3484	164	12	in	in	ADP
ejpam-3484	164	13	a	a	DET
ejpam-3484	164	14	unique	unique	ADJ
ejpam-3484	164	15	γi	γi	NOUN
ejpam-3484	164	16	-	-	PUNCT
ejpam-3484	164	17	set	set	NOUN
ejpam-3484	164	18	.	.	PUNCT
ejpam-3484	165	1	thus	thus	ADV
ejpam-3484	165	2	,	,	PUNCT
ejpam-3484	165	3	fγi(s	fγi(s	PROPN
ejpam-3484	165	4	)	)	PUNCT
ejpam-3484	165	5	≥	≥	NOUN
ejpam-3484	165	6	2	2	NUM
ejpam-3484	165	7	.	.	PUNCT
ejpam-3484	166	1	since	since	SCONJ
ejpam-3484	166	2	{	{	PUNCT
ejpam-3484	166	3	u1	u1	NOUN
ejpam-3484	166	4	,	,	PUNCT
ejpam-3484	166	5	u3	u3	PROPN
ejpam-3484	166	6	}	}	PUNCT
ejpam-3484	166	7	is	be	AUX
ejpam-3484	166	8	a	a	DET
ejpam-3484	166	9	forcing	forcing	NOUN
ejpam-3484	166	10	subset	subset	NOUN
ejpam-3484	166	11	for	for	ADP
ejpam-3484	166	12	s	s	PROPN
ejpam-3484	166	13	,	,	PUNCT
ejpam-3484	166	14	fγi(s	fγi(s	NOUN
ejpam-3484	166	15	)	)	PUNCT
ejpam-3484	166	16	=	=	SYM
ejpam-3484	166	17	2	2	NUM
ejpam-3484	166	18	=	=	SYM
ejpam-3484	166	19	fγi(cn	fγi(cn	NOUN
ejpam-3484	166	20	)	)	PUNCT
ejpam-3484	166	21	.	.	PUNCT
ejpam-3484	167	1	theorem	theorem	VERB
ejpam-3484	167	2	3.7	3.7	NUM
ejpam-3484	167	3	.	.	PUNCT
ejpam-3484	168	1	let	let	VERB
ejpam-3484	168	2	g	g	NOUN
ejpam-3484	169	1	and	and	CCONJ
ejpam-3484	169	2	h	h	NOUN
ejpam-3484	169	3	be	be	VERB
ejpam-3484	169	4	any	any	DET
ejpam-3484	169	5	graphs	graph	NOUN
ejpam-3484	169	6	.	.	PUNCT
ejpam-3484	170	1	then	then	ADV
ejpam-3484	170	2	s0	s0	PROPN
ejpam-3484	170	3	⊆	⊆	NUM
ejpam-3484	170	4	v	v	NOUN
ejpam-3484	170	5	(	(	PUNCT
ejpam-3484	170	6	g+h	g+h	PROPN
ejpam-3484	170	7	)	)	PUNCT
ejpam-3484	170	8	is	be	AUX
ejpam-3484	170	9	a	a	DET
ejpam-3484	170	10	γi	γi	NOUN
ejpam-3484	170	11	-	-	PUNCT
ejpam-3484	170	12	set	set	NOUN
ejpam-3484	170	13	of	of	ADP
ejpam-3484	170	14	g+h	g+h	PROPN
ejpam-3484	170	15	if	if	SCONJ
ejpam-3484	170	16	and	and	CCONJ
ejpam-3484	170	17	only	only	ADV
ejpam-3484	170	18	if	if	SCONJ
ejpam-3484	170	19	one	one	NUM
ejpam-3484	170	20	of	of	ADP
ejpam-3484	170	21	the	the	DET
ejpam-3484	170	22	following	follow	VERB
ejpam-3484	170	23	holds	hold	VERB
ejpam-3484	170	24	:	:	PUNCT
ejpam-3484	170	25	(	(	PUNCT
ejpam-3484	170	26	i	i	NOUN
ejpam-3484	170	27	)	)	PUNCT
ejpam-3484	170	28	s0	s0	PROPN
ejpam-3484	170	29	is	be	AUX
ejpam-3484	170	30	a	a	DET
ejpam-3484	170	31	γi	γi	NOUN
ejpam-3484	170	32	-	-	PUNCT
ejpam-3484	170	33	set	set	NOUN
ejpam-3484	170	34	of	of	ADP
ejpam-3484	170	35	g	g	NOUN
ejpam-3484	170	36	and	and	CCONJ
ejpam-3484	170	37	γi(g	γi(g	NOUN
ejpam-3484	170	38	)	)	PUNCT
ejpam-3484	170	39	<	<	X
ejpam-3484	170	40	γi(h	γi(h	NOUN
ejpam-3484	170	41	)	)	PUNCT
ejpam-3484	170	42	(	(	PUNCT
ejpam-3484	170	43	ii	ii	NOUN
ejpam-3484	170	44	)	)	PUNCT
ejpam-3484	170	45	s0	s0	PROPN
ejpam-3484	170	46	is	be	AUX
ejpam-3484	170	47	a	a	DET
ejpam-3484	170	48	γi	γi	NOUN
ejpam-3484	170	49	-	-	PUNCT
ejpam-3484	170	50	set	set	NOUN
ejpam-3484	170	51	of	of	ADP
ejpam-3484	170	52	h	h	NOUN
ejpam-3484	170	53	and	and	CCONJ
ejpam-3484	170	54	γi(h	γi(h	NOUN
ejpam-3484	170	55	)	)	PUNCT
ejpam-3484	170	56	<	<	X
ejpam-3484	170	57	γi(g	γi(g	NOUN
ejpam-3484	170	58	)	)	PUNCT
ejpam-3484	170	59	(	(	PUNCT
ejpam-3484	170	60	iii	iii	X
ejpam-3484	170	61	)	)	PUNCT
ejpam-3484	170	62	s0	s0	PROPN
ejpam-3484	170	63	is	be	AUX
ejpam-3484	170	64	either	either	CCONJ
ejpam-3484	170	65	a	a	DET
ejpam-3484	170	66	γi	γi	NOUN
ejpam-3484	170	67	-	-	PUNCT
ejpam-3484	170	68	set	set	NOUN
ejpam-3484	170	69	of	of	ADP
ejpam-3484	170	70	g	g	NOUN
ejpam-3484	170	71	or	or	CCONJ
ejpam-3484	170	72	h	h	NOUN
ejpam-3484	170	73	,	,	PUNCT
ejpam-3484	170	74	and	and	CCONJ
ejpam-3484	170	75	γi(h	γi(h	NOUN
ejpam-3484	170	76	)	)	PUNCT
ejpam-3484	170	77	=	=	SYM
ejpam-3484	170	78	γi(g	γi(g	NOUN
ejpam-3484	170	79	)	)	PUNCT
ejpam-3484	170	80	.	.	PUNCT
ejpam-3484	171	1	in	in	ADP
ejpam-3484	171	2	particular	particular	ADJ
ejpam-3484	171	3	,	,	PUNCT
ejpam-3484	171	4	γi(g+h	γi(g+h	PROPN
ejpam-3484	171	5	)	)	PUNCT
ejpam-3484	171	6	=	=	SYM
ejpam-3484	171	7	min{γi(g	min{γi(g	PROPN
ejpam-3484	171	8	)	)	PUNCT
ejpam-3484	171	9	,	,	PUNCT
ejpam-3484	171	10	γi(h	γi(h	NOUN
ejpam-3484	171	11	)	)	PUNCT
ejpam-3484	171	12	}	}	PUNCT
ejpam-3484	171	13	.	.	PUNCT
ejpam-3484	172	1	proof	proof	NOUN
ejpam-3484	172	2	.	.	PUNCT
ejpam-3484	173	1	clearly	clearly	ADV
ejpam-3484	173	2	,	,	PUNCT
ejpam-3484	173	3	s	s	VERB
ejpam-3484	173	4	⊆	⊆	NUM
ejpam-3484	173	5	v	v	NOUN
ejpam-3484	173	6	(	(	PUNCT
ejpam-3484	173	7	g+h	g+h	PROPN
ejpam-3484	173	8	)	)	PUNCT
ejpam-3484	173	9	is	be	AUX
ejpam-3484	173	10	an	an	DET
ejpam-3484	173	11	independent	independent	ADJ
ejpam-3484	173	12	dominating	dominating	NOUN
ejpam-3484	173	13	set	set	NOUN
ejpam-3484	173	14	of	of	ADP
ejpam-3484	173	15	g+h	g+h	PROPN
ejpam-3484	174	1	if	if	SCONJ
ejpam-3484	174	2	and	and	CCONJ
ejpam-3484	174	3	only	only	ADV
ejpam-3484	174	4	if	if	SCONJ
ejpam-3484	174	5	either	either	PRON
ejpam-3484	174	6	s	s	VERB
ejpam-3484	174	7	is	be	AUX
ejpam-3484	174	8	an	an	DET
ejpam-3484	174	9	independent	independent	ADJ
ejpam-3484	174	10	dominating	dominating	NOUN
ejpam-3484	174	11	set	set	NOUN
ejpam-3484	174	12	of	of	ADP
ejpam-3484	174	13	g	g	PROPN
ejpam-3484	174	14	or	or	CCONJ
ejpam-3484	174	15	s	s	NOUN
ejpam-3484	174	16	is	be	AUX
ejpam-3484	174	17	an	an	DET
ejpam-3484	174	18	independent	independent	ADJ
ejpam-3484	174	19	dominating	dominating	NOUN
ejpam-3484	174	20	set	set	NOUN
ejpam-3484	174	21	of	of	ADP
ejpam-3484	174	22	h.	h.	PROPN
ejpam-3484	174	23	in	in	ADP
ejpam-3484	174	24	particular	particular	ADJ
ejpam-3484	174	25	,	,	PUNCT
ejpam-3484	174	26	γi(g+h	γi(g+h	PROPN
ejpam-3484	174	27	)	)	PUNCT
ejpam-3484	174	28	=	=	SYM
ejpam-3484	174	29	min{γi(g	min{γi(g	PROPN
ejpam-3484	174	30	)	)	PUNCT
ejpam-3484	174	31	,	,	PUNCT
ejpam-3484	174	32	γi(h	γi(h	NOUN
ejpam-3484	174	33	)	)	PUNCT
ejpam-3484	174	34	}	}	PUNCT
ejpam-3484	174	35	.	.	PUNCT
ejpam-3484	175	1	hence	hence	ADV
ejpam-3484	175	2	,	,	PUNCT
ejpam-3484	175	3	s0	s0	PROPN
ejpam-3484	175	4	is	be	AUX
ejpam-3484	175	5	a	a	DET
ejpam-3484	175	6	γi	γi	NOUN
ejpam-3484	175	7	-	-	PUNCT
ejpam-3484	175	8	set	set	NOUN
ejpam-3484	175	9	of	of	ADP
ejpam-3484	175	10	g+h	g+h	PROPN
ejpam-3484	175	11	if	if	SCONJ
ejpam-3484	175	12	and	and	CCONJ
ejpam-3484	175	13	only	only	ADV
ejpam-3484	175	14	if	if	SCONJ
ejpam-3484	175	15	one	one	NUM
ejpam-3484	175	16	of	of	ADP
ejpam-3484	175	17	(	(	PUNCT
ejpam-3484	175	18	i	i	NOUN
ejpam-3484	175	19	)	)	PUNCT
ejpam-3484	175	20	,	,	PUNCT
ejpam-3484	175	21	(	(	PUNCT
ejpam-3484	175	22	ii	ii	NOUN
ejpam-3484	175	23	)	)	PUNCT
ejpam-3484	175	24	,	,	PUNCT
ejpam-3484	175	25	and	and	CCONJ
ejpam-3484	175	26	(	(	PUNCT
ejpam-3484	175	27	iii	iii	NOUN
ejpam-3484	175	28	)	)	PUNCT
ejpam-3484	175	29	holds	hold	VERB
ejpam-3484	175	30	.	.	PUNCT
ejpam-3484	176	1	theorem	theorem	VERB
ejpam-3484	176	2	3.8	3.8	NUM
ejpam-3484	176	3	.	.	PUNCT
ejpam-3484	177	1	for	for	ADP
ejpam-3484	177	2	any	any	DET
ejpam-3484	177	3	graphs	graph	NOUN
ejpam-3484	177	4	g	g	NOUN
ejpam-3484	177	5	and	and	CCONJ
ejpam-3484	177	6	h	h	NOUN
ejpam-3484	177	7	with	with	ADP
ejpam-3484	177	8	γi(g	γi(g	NOUN
ejpam-3484	177	9	)	)	PUNCT
ejpam-3484	177	10	=	=	SYM
ejpam-3484	177	11	γi(h	γi(h	NOUN
ejpam-3484	177	12	)	)	PUNCT
ejpam-3484	177	13	,	,	PUNCT
ejpam-3484	177	14	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	177	15	)	)	PUNCT
ejpam-3484	177	16	=	=	NOUN
ejpam-3484	177	17	{	{	PUNCT
ejpam-3484	177	18	1	1	NUM
ejpam-3484	177	19	,	,	PUNCT
ejpam-3484	177	20	if	if	SCONJ
ejpam-3484	177	21	either	either	CCONJ
ejpam-3484	177	22	g	g	PROPN
ejpam-3484	177	23	or	or	CCONJ
ejpam-3484	177	24	h	h	NOUN
ejpam-3484	177	25	has	have	VERB
ejpam-3484	177	26	a	a	DET
ejpam-3484	177	27	unique	unique	ADJ
ejpam-3484	177	28	γi	γi	NOUN
ejpam-3484	177	29	-	-	PUNCT
ejpam-3484	177	30	set	set	ADJ
ejpam-3484	177	31	,	,	PUNCT
ejpam-3484	177	32	min{fγi(g	min{fγi(g	PROPN
ejpam-3484	177	33	)	)	PUNCT
ejpam-3484	177	34	,	,	PUNCT
ejpam-3484	177	35	fγi(h	fγi(h	PROPN
ejpam-3484	177	36	)	)	PUNCT
ejpam-3484	177	37	}	}	PUNCT
ejpam-3484	177	38	,	,	PUNCT
ejpam-3484	177	39	otherwise	otherwise	ADV
ejpam-3484	177	40	.	.	PUNCT
ejpam-3484	178	1	proof	proof	NOUN
ejpam-3484	178	2	.	.	PUNCT
ejpam-3484	179	1	by	by	ADP
ejpam-3484	179	2	theorem	theorem	ADJ
ejpam-3484	179	3	3.7	3.7	NUM
ejpam-3484	179	4	,	,	PUNCT
ejpam-3484	179	5	γi(g+h	γi(g+h	PROPN
ejpam-3484	179	6	)	)	PUNCT
ejpam-3484	179	7	=	=	SYM
ejpam-3484	179	8	γi(g	γi(g	X
ejpam-3484	179	9	)	)	PUNCT
ejpam-3484	179	10	=	=	SYM
ejpam-3484	180	1	γi(h	γi(h	NOUN
ejpam-3484	180	2	)	)	PUNCT
ejpam-3484	180	3	.	.	PUNCT
ejpam-3484	181	1	suppose	suppose	VERB
ejpam-3484	181	2	that	that	SCONJ
ejpam-3484	181	3	either	either	CCONJ
ejpam-3484	181	4	g	g	PROPN
ejpam-3484	181	5	or	or	CCONJ
ejpam-3484	181	6	h	h	NOUN
ejpam-3484	181	7	has	have	VERB
ejpam-3484	181	8	a	a	DET
ejpam-3484	181	9	unique	unique	ADJ
ejpam-3484	181	10	γi	γi	NOUN
ejpam-3484	181	11	-	-	PUNCT
ejpam-3484	181	12	set	set	NOUN
ejpam-3484	181	13	.	.	PUNCT
ejpam-3484	182	1	w.l.o.g	w.l.o.g	PROPN
ejpam-3484	182	2	.	.	PROPN
ejpam-3484	182	3	,	,	PUNCT
ejpam-3484	182	4	suppose	suppose	VERB
ejpam-3484	182	5	that	that	SCONJ
ejpam-3484	182	6	g	g	PROPN
ejpam-3484	182	7	has	have	VERB
ejpam-3484	182	8	a	a	DET
ejpam-3484	182	9	unique	unique	ADJ
ejpam-3484	182	10	γi	γi	NOUN
ejpam-3484	182	11	-	-	PUNCT
ejpam-3484	182	12	set	set	NOUN
ejpam-3484	182	13	,	,	PUNCT
ejpam-3484	182	14	say	say	VERB
ejpam-3484	182	15	s.	s.	PROPN
ejpam-3484	182	16	then	then	ADV
ejpam-3484	182	17	by	by	ADP
ejpam-3484	182	18	corollary	corollary	ADJ
ejpam-3484	182	19	3.7	3.7	NUM
ejpam-3484	182	20	,	,	PUNCT
ejpam-3484	182	21	s	s	X
ejpam-3484	182	22	and	and	CCONJ
ejpam-3484	182	23	the	the	DET
ejpam-3484	182	24	γi	γi	NOUN
ejpam-3484	182	25	-	-	PUNCT
ejpam-3484	182	26	sets	set	NOUN
ejpam-3484	182	27	of	of	ADP
ejpam-3484	182	28	h	h	NOUN
ejpam-3484	182	29	are	be	AUX
ejpam-3484	182	30	γi	γi	NOUN
ejpam-3484	182	31	-	-	PUNCT
ejpam-3484	182	32	sets	set	NOUN
ejpam-3484	182	33	of	of	ADP
ejpam-3484	182	34	g+h	g+h	PROPN
ejpam-3484	182	35	.	.	PUNCT
ejpam-3484	183	1	clearly	clearly	ADV
ejpam-3484	183	2	,	,	PUNCT
ejpam-3484	183	3	for	for	ADP
ejpam-3484	183	4	any	any	DET
ejpam-3484	183	5	x	x	SYM
ejpam-3484	183	6	∈	∈	PROPN
ejpam-3484	183	7	s	s	NOUN
ejpam-3484	183	8	,	,	PUNCT
ejpam-3484	183	9	{	{	PUNCT
ejpam-3484	183	10	x	x	X
ejpam-3484	183	11	}	}	PUNCT
ejpam-3484	183	12	is	be	AUX
ejpam-3484	183	13	uniquely	uniquely	ADV
ejpam-3484	183	14	contained	contain	VERB
ejpam-3484	183	15	in	in	ADP
ejpam-3484	183	16	s	s	PRON
ejpam-3484	183	17	and	and	CCONJ
ejpam-3484	183	18	not	not	PART
ejpam-3484	183	19	in	in	ADP
ejpam-3484	183	20	any	any	DET
ejpam-3484	183	21	γi	γi	NOUN
ejpam-3484	183	22	-	-	PUNCT
ejpam-3484	183	23	set	set	NOUN
ejpam-3484	183	24	of	of	ADP
ejpam-3484	183	25	g+h	g+h	PROPN
ejpam-3484	183	26	.	.	PUNCT
ejpam-3484	184	1	by	by	ADP
ejpam-3484	184	2	remark	remark	NOUN
ejpam-3484	184	3	3.1(ii	3.1(ii	NUM
ejpam-3484	184	4	)	)	PUNCT
ejpam-3484	184	5	,	,	PUNCT
ejpam-3484	184	6	fγi(s	fγi(s	NOUN
ejpam-3484	184	7	)	)	PUNCT
ejpam-3484	184	8	=	=	SYM
ejpam-3484	184	9	1	1	NUM
ejpam-3484	184	10	=	=	SYM
ejpam-3484	184	11	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	184	12	)	)	PUNCT
ejpam-3484	184	13	.	.	PUNCT
ejpam-3484	185	1	c.	c.	PROPN
ejpam-3484	185	2	armada	armada	PROPN
ejpam-3484	185	3	,	,	PUNCT
ejpam-3484	185	4	s.	s.	PROPN
ejpam-3484	185	5	canoy	canoy	PROPN
ejpam-3484	185	6	jr	jr	PROPN
ejpam-3484	185	7	.	.	PROPN
ejpam-3484	185	8	/	/	SYM
ejpam-3484	185	9	eur	eur	PROPN
ejpam-3484	185	10	.	.	PUNCT
ejpam-3484	186	1	j.	j.	PROPN
ejpam-3484	186	2	pure	pure	PROPN
ejpam-3484	186	3	appl	appl	PROPN
ejpam-3484	186	4	.	.	PROPN
ejpam-3484	186	5	math	math	PROPN
ejpam-3484	186	6	,	,	PUNCT
ejpam-3484	186	7	12	12	NUM
ejpam-3484	186	8	(	(	PUNCT
ejpam-3484	186	9	4	4	NUM
ejpam-3484	186	10	)	)	PUNCT
ejpam-3484	186	11	(	(	PUNCT
ejpam-3484	186	12	2019	2019	NUM
ejpam-3484	186	13	)	)	PUNCT
ejpam-3484	186	14	,	,	PUNCT
ejpam-3484	186	15	1371	1371	NUM
ejpam-3484	186	16	-	-	SYM
ejpam-3484	186	17	1381	1381	NUM
ejpam-3484	186	18	1376	1376	NUM
ejpam-3484	186	19	suppose	suppose	VERB
ejpam-3484	186	20	that	that	SCONJ
ejpam-3484	186	21	both	both	PRON
ejpam-3484	186	22	g	g	PROPN
ejpam-3484	186	23	and	and	CCONJ
ejpam-3484	186	24	h	h	NOUN
ejpam-3484	186	25	have	have	VERB
ejpam-3484	186	26	no	no	DET
ejpam-3484	186	27	unique	unique	ADJ
ejpam-3484	186	28	γi	γi	NOUN
ejpam-3484	186	29	-	-	PUNCT
ejpam-3484	186	30	sets	set	NOUN
ejpam-3484	186	31	.	.	PUNCT
ejpam-3484	187	1	we	we	PRON
ejpam-3484	187	2	may	may	AUX
ejpam-3484	187	3	assume	assume	VERB
ejpam-3484	187	4	that	that	SCONJ
ejpam-3484	187	5	fγi(g	fγi(g	PROPN
ejpam-3484	187	6	)	)	PUNCT
ejpam-3484	187	7	≤	≤	NUM
ejpam-3484	187	8	fγi(h	fγi(h	PROPN
ejpam-3484	187	9	)	)	PUNCT
ejpam-3484	187	10	.	.	PUNCT
ejpam-3484	188	1	since	since	SCONJ
ejpam-3484	188	2	every	every	DET
ejpam-3484	188	3	γi	γi	NOUN
ejpam-3484	188	4	-	-	PUNCT
ejpam-3484	188	5	set	set	NOUN
ejpam-3484	188	6	of	of	ADP
ejpam-3484	188	7	g	g	PROPN
ejpam-3484	188	8	and	and	CCONJ
ejpam-3484	188	9	h	h	NOUN
ejpam-3484	188	10	is	be	AUX
ejpam-3484	188	11	a	a	DET
ejpam-3484	188	12	γi	γi	NOUN
ejpam-3484	188	13	-	-	PUNCT
ejpam-3484	188	14	set	set	NOUN
ejpam-3484	188	15	of	of	ADP
ejpam-3484	188	16	g	g	PROPN
ejpam-3484	188	17	+	+	CCONJ
ejpam-3484	188	18	h	h	NOUN
ejpam-3484	188	19	,	,	PUNCT
ejpam-3484	188	20	fγi(g	fγi(g	PROPN
ejpam-3484	188	21	)	)	PUNCT
ejpam-3484	188	22	≥	≥	NOUN
ejpam-3484	189	1	fγi(g	fγi(g	PROPN
ejpam-3484	190	1	+	+	NUM
ejpam-3484	190	2	h	h	NOUN
ejpam-3484	190	3	)	)	PUNCT
ejpam-3484	190	4	.	.	PUNCT
ejpam-3484	191	1	now	now	ADV
ejpam-3484	191	2	,	,	PUNCT
ejpam-3484	191	3	let	let	VERB
ejpam-3484	191	4	s0	s0	PROPN
ejpam-3484	191	5	be	be	AUX
ejpam-3484	191	6	a	a	DET
ejpam-3484	191	7	γi	γi	NOUN
ejpam-3484	191	8	-	-	PUNCT
ejpam-3484	191	9	set	set	NOUN
ejpam-3484	191	10	of	of	ADP
ejpam-3484	191	11	g	g	PROPN
ejpam-3484	192	1	+	+	CCONJ
ejpam-3484	192	2	h	h	NOUN
ejpam-3484	193	1	such	such	ADJ
ejpam-3484	193	2	that	that	SCONJ
ejpam-3484	193	3	fγi(g	fγi(g	PROPN
ejpam-3484	193	4	+	+	NUM
ejpam-3484	193	5	h	h	NOUN
ejpam-3484	193	6	)	)	PUNCT
ejpam-3484	193	7	=	=	PUNCT
ejpam-3484	193	8	fγi(s0	fγi(s0	ADJ
ejpam-3484	193	9	)	)	PUNCT
ejpam-3484	193	10	.	.	PUNCT
ejpam-3484	194	1	if	if	SCONJ
ejpam-3484	194	2	s0	s0	PROPN
ejpam-3484	194	3	⊆	⊆	NUM
ejpam-3484	194	4	v	v	NOUN
ejpam-3484	194	5	(	(	PUNCT
ejpam-3484	194	6	g	g	NOUN
ejpam-3484	194	7	)	)	PUNCT
ejpam-3484	194	8	,	,	PUNCT
ejpam-3484	194	9	then	then	ADV
ejpam-3484	194	10	s0	s0	PROPN
ejpam-3484	194	11	is	be	AUX
ejpam-3484	194	12	a	a	DET
ejpam-3484	194	13	γi	γi	NOUN
ejpam-3484	194	14	-	-	PUNCT
ejpam-3484	194	15	set	set	NOUN
ejpam-3484	194	16	of	of	ADP
ejpam-3484	194	17	g.	g.	PROPN
ejpam-3484	194	18	hence	hence	ADV
ejpam-3484	194	19	,	,	PUNCT
ejpam-3484	194	20	fγi(g	fγi(g	PROPN
ejpam-3484	195	1	+	+	NUM
ejpam-3484	195	2	h	h	NOUN
ejpam-3484	195	3	)	)	PUNCT
ejpam-3484	195	4	=	=	SYM
ejpam-3484	195	5	fγi(s0	fγi(s0	PROPN
ejpam-3484	195	6	)	)	PUNCT
ejpam-3484	195	7	≥	≥	NOUN
ejpam-3484	195	8	fγi(g	fγi(g	PROPN
ejpam-3484	195	9	)	)	PUNCT
ejpam-3484	195	10	.	.	PUNCT
ejpam-3484	196	1	if	if	SCONJ
ejpam-3484	196	2	s0	s0	PROPN
ejpam-3484	196	3	⊆	⊆	NUM
ejpam-3484	196	4	v	v	NOUN
ejpam-3484	196	5	(	(	PUNCT
ejpam-3484	196	6	h	h	NOUN
ejpam-3484	196	7	)	)	PUNCT
ejpam-3484	196	8	,	,	PUNCT
ejpam-3484	196	9	then	then	ADV
ejpam-3484	196	10	s0	s0	PROPN
ejpam-3484	196	11	is	be	AUX
ejpam-3484	196	12	a	a	DET
ejpam-3484	196	13	γi	γi	NOUN
ejpam-3484	196	14	-	-	PUNCT
ejpam-3484	196	15	set	set	NOUN
ejpam-3484	196	16	of	of	ADP
ejpam-3484	196	17	h.	h.	PROPN
ejpam-3484	196	18	hence	hence	ADV
ejpam-3484	196	19	,	,	PUNCT
ejpam-3484	196	20	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	196	21	)	)	PUNCT
ejpam-3484	196	22	=	=	SYM
ejpam-3484	196	23	fγi(s0	fγi(s0	PROPN
ejpam-3484	196	24	)	)	PUNCT
ejpam-3484	196	25	≥	≥	NOUN
ejpam-3484	196	26	fγi(h	fγi(h	PROPN
ejpam-3484	196	27	)	)	PUNCT
ejpam-3484	196	28	≥	≥	NOUN
ejpam-3484	196	29	fγi(g	fγi(g	PROPN
ejpam-3484	196	30	)	)	PUNCT
ejpam-3484	196	31	.	.	PUNCT
ejpam-3484	197	1	hence	hence	ADV
ejpam-3484	197	2	,	,	PUNCT
ejpam-3484	197	3	in	in	ADP
ejpam-3484	197	4	any	any	DET
ejpam-3484	197	5	case	case	NOUN
ejpam-3484	197	6	,	,	PUNCT
ejpam-3484	197	7	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	197	8	)	)	PUNCT
ejpam-3484	197	9	=	=	SYM
ejpam-3484	197	10	fγi(g	fγi(g	PROPN
ejpam-3484	197	11	)	)	PUNCT
ejpam-3484	197	12	.	.	PUNCT
ejpam-3484	198	1	theorem	theorem	VERB
ejpam-3484	198	2	3.9	3.9	NUM
ejpam-3484	198	3	.	.	PUNCT
ejpam-3484	199	1	for	for	ADP
ejpam-3484	199	2	any	any	DET
ejpam-3484	199	3	graphs	graph	NOUN
ejpam-3484	199	4	g	g	NOUN
ejpam-3484	199	5	and	and	CCONJ
ejpam-3484	199	6	h	h	NOUN
ejpam-3484	199	7	with	with	ADP
ejpam-3484	199	8	γi(g	γi(g	NOUN
ejpam-3484	199	9	)	)	PUNCT
ejpam-3484	199	10	6=	6=	ADP
ejpam-3484	199	11	γi(h	γi(h	NOUN
ejpam-3484	199	12	)	)	PUNCT
ejpam-3484	199	13	,	,	PUNCT
ejpam-3484	199	14	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	199	15	)	)	PUNCT
ejpam-3484	199	16	=	=	SYM
ejpam-3484	200	1			NUM
ejpam-3484	200	2	0	0	NUM
ejpam-3484	200	3	,	,	PUNCT
ejpam-3484	200	4	if	if	SCONJ
ejpam-3484	200	5	γi(g	γi(g	NOUN
ejpam-3484	200	6	)	)	PUNCT
ejpam-3484	200	7	<	<	X
ejpam-3484	200	8	γi(h	γi(h	NOUN
ejpam-3484	200	9	)	)	PUNCT
ejpam-3484	200	10	and	and	CCONJ
ejpam-3484	200	11	g	g	PROPN
ejpam-3484	200	12	has	have	VERB
ejpam-3484	200	13	a	a	DET
ejpam-3484	200	14	unique	unique	ADJ
ejpam-3484	200	15	γi	γi	NOUN
ejpam-3484	200	16	-	-	PUNCT
ejpam-3484	200	17	set	set	VERB
ejpam-3484	200	18	or	or	CCONJ
ejpam-3484	200	19	if	if	SCONJ
ejpam-3484	200	20	γi(h	γi(h	NOUN
ejpam-3484	200	21	)	)	PUNCT
ejpam-3484	200	22	<	<	X
ejpam-3484	200	23	γi(g	γi(g	NOUN
ejpam-3484	200	24	)	)	PUNCT
ejpam-3484	200	25	and	and	CCONJ
ejpam-3484	200	26	h	h	NOUN
ejpam-3484	200	27	has	have	VERB
ejpam-3484	200	28	a	a	DET
ejpam-3484	200	29	unique	unique	ADJ
ejpam-3484	200	30	γi	γi	NOUN
ejpam-3484	200	31	-	-	PUNCT
ejpam-3484	200	32	set	set	VERB
ejpam-3484	200	33	,	,	PUNCT
ejpam-3484	200	34	fγi(g	fγi(g	PROPN
ejpam-3484	200	35	)	)	PUNCT
ejpam-3484	200	36	,	,	PUNCT
ejpam-3484	200	37	if	if	SCONJ
ejpam-3484	200	38	γi(g	γi(g	NOUN
ejpam-3484	200	39	)	)	PUNCT
ejpam-3484	200	40	<	<	X
ejpam-3484	200	41	γi(h	γi(h	NOUN
ejpam-3484	200	42	)	)	PUNCT
ejpam-3484	200	43	and	and	CCONJ
ejpam-3484	200	44	g	g	NOUN
ejpam-3484	200	45	has	have	VERB
ejpam-3484	200	46	no	no	DET
ejpam-3484	200	47	unique	unique	ADJ
ejpam-3484	200	48	γi	γi	NOUN
ejpam-3484	200	49	-	-	PUNCT
ejpam-3484	200	50	sets	set	NOUN
ejpam-3484	200	51	,	,	PUNCT
ejpam-3484	200	52	fγi(h	fγi(h	PROPN
ejpam-3484	200	53	)	)	PUNCT
ejpam-3484	200	54	,	,	PUNCT
ejpam-3484	200	55	if	if	SCONJ
ejpam-3484	200	56	γi(h	γi(h	NOUN
ejpam-3484	200	57	)	)	PUNCT
ejpam-3484	200	58	<	<	X
ejpam-3484	200	59	γi(g	γi(g	NOUN
ejpam-3484	200	60	)	)	PUNCT
ejpam-3484	200	61	and	and	CCONJ
ejpam-3484	200	62	h	h	NOUN
ejpam-3484	200	63	has	have	VERB
ejpam-3484	200	64	no	no	DET
ejpam-3484	200	65	unique	unique	ADJ
ejpam-3484	200	66	γi	γi	NOUN
ejpam-3484	200	67	-	-	PUNCT
ejpam-3484	200	68	sets	set	NOUN
ejpam-3484	200	69	.	.	PUNCT
ejpam-3484	201	1	proof	proof	NOUN
ejpam-3484	201	2	.	.	PUNCT
ejpam-3484	202	1	suppose	suppose	VERB
ejpam-3484	202	2	that	that	SCONJ
ejpam-3484	202	3	γi(g	γi(g	NOUN
ejpam-3484	202	4	)	)	PUNCT
ejpam-3484	202	5	<	<	X
ejpam-3484	202	6	γi(h	γi(h	NOUN
ejpam-3484	202	7	)	)	PUNCT
ejpam-3484	202	8	.	.	PUNCT
ejpam-3484	203	1	by	by	ADP
ejpam-3484	203	2	theorem	theorem	NOUN
ejpam-3484	203	3	3.7	3.7	NUM
ejpam-3484	203	4	,	,	PUNCT
ejpam-3484	203	5	γi(g	γi(g	PUNCT
ejpam-3484	203	6	+	+	CCONJ
ejpam-3484	203	7	h	h	X
ejpam-3484	203	8	)	)	PUNCT
ejpam-3484	203	9	=	=	NOUN
ejpam-3484	203	10	γi(g	γi(g	NOUN
ejpam-3484	203	11	)	)	PUNCT
ejpam-3484	203	12	.	.	PUNCT
ejpam-3484	204	1	suppose	suppose	VERB
ejpam-3484	204	2	that	that	SCONJ
ejpam-3484	204	3	g	g	PROPN
ejpam-3484	204	4	has	have	VERB
ejpam-3484	204	5	a	a	DET
ejpam-3484	204	6	unique	unique	ADJ
ejpam-3484	204	7	γi	γi	NOUN
ejpam-3484	204	8	-	-	PUNCT
ejpam-3484	204	9	set	set	NOUN
ejpam-3484	204	10	,	,	PUNCT
ejpam-3484	204	11	say	say	VERB
ejpam-3484	204	12	s.	s.	PROPN
ejpam-3484	204	13	then	then	ADV
ejpam-3484	204	14	by	by	ADP
ejpam-3484	204	15	corollary	corollary	ADJ
ejpam-3484	204	16	3.7	3.7	NUM
ejpam-3484	204	17	,	,	PUNCT
ejpam-3484	204	18	s	s	PART
ejpam-3484	204	19	is	be	AUX
ejpam-3484	204	20	the	the	DET
ejpam-3484	204	21	only	only	ADJ
ejpam-3484	204	22	γi	γi	NOUN
ejpam-3484	204	23	-	-	PUNCT
ejpam-3484	204	24	set	set	NOUN
ejpam-3484	204	25	of	of	ADP
ejpam-3484	204	26	g+h	g+h	PROPN
ejpam-3484	204	27	.	.	PUNCT
ejpam-3484	205	1	by	by	ADP
ejpam-3484	205	2	remark	remark	NOUN
ejpam-3484	205	3	3.1(i	3.1(i	NUM
ejpam-3484	205	4	)	)	PUNCT
ejpam-3484	205	5	,	,	PUNCT
ejpam-3484	205	6	fγi(g	fγi(g	PROPN
ejpam-3484	206	1	+	+	NUM
ejpam-3484	206	2	h	h	NOUN
ejpam-3484	206	3	)	)	PUNCT
ejpam-3484	206	4	=	=	NOUN
ejpam-3484	207	1	0	0	X
ejpam-3484	207	2	.	.	PUNCT
ejpam-3484	208	1	now	now	ADV
ejpam-3484	208	2	,	,	PUNCT
ejpam-3484	208	3	suppose	suppose	VERB
ejpam-3484	208	4	that	that	SCONJ
ejpam-3484	208	5	g	g	PROPN
ejpam-3484	208	6	has	have	VERB
ejpam-3484	208	7	no	no	DET
ejpam-3484	208	8	unique	unique	ADJ
ejpam-3484	208	9	γi	γi	NOUN
ejpam-3484	208	10	-	-	PUNCT
ejpam-3484	208	11	sets	set	NOUN
ejpam-3484	208	12	.	.	PUNCT
ejpam-3484	209	1	by	by	ADP
ejpam-3484	209	2	corollary	corollary	ADJ
ejpam-3484	209	3	3.7	3.7	NUM
ejpam-3484	209	4	,	,	PUNCT
ejpam-3484	209	5	the	the	DET
ejpam-3484	209	6	γi	γi	NOUN
ejpam-3484	209	7	-	-	PUNCT
ejpam-3484	209	8	sets	set	NOUN
ejpam-3484	209	9	of	of	ADP
ejpam-3484	209	10	g	g	NOUN
ejpam-3484	209	11	are	be	AUX
ejpam-3484	209	12	also	also	ADV
ejpam-3484	209	13	the	the	DET
ejpam-3484	209	14	γi	γi	NOUN
ejpam-3484	209	15	-	-	PUNCT
ejpam-3484	209	16	sets	set	NOUN
ejpam-3484	209	17	of	of	ADP
ejpam-3484	209	18	g+h	g+h	PROPN
ejpam-3484	209	19	.	.	PUNCT
ejpam-3484	210	1	thus	thus	ADV
ejpam-3484	210	2	,	,	PUNCT
ejpam-3484	210	3	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	210	4	)	)	PUNCT
ejpam-3484	210	5	=	=	SYM
ejpam-3484	210	6	fγi(g	fγi(g	PROPN
ejpam-3484	210	7	)	)	PUNCT
ejpam-3484	210	8	.	.	PUNCT
ejpam-3484	211	1	similarly	similarly	ADV
ejpam-3484	211	2	,	,	PUNCT
ejpam-3484	211	3	if	if	SCONJ
ejpam-3484	211	4	γi(h	γi(h	NOUN
ejpam-3484	211	5	)	)	PUNCT
ejpam-3484	211	6	<	<	X
ejpam-3484	211	7	γi(g	γi(g	NOUN
ejpam-3484	211	8	)	)	PUNCT
ejpam-3484	211	9	,	,	PUNCT
ejpam-3484	211	10	then	then	ADV
ejpam-3484	211	11	fγi(g	fγi(g	PROPN
ejpam-3484	211	12	+	+	NUM
ejpam-3484	211	13	h	h	NOUN
ejpam-3484	211	14	)	)	PUNCT
ejpam-3484	211	15	=	=	SYM
ejpam-3484	212	1	0	0	PUNCT
ejpam-3484	212	2	whenever	whenever	SCONJ
ejpam-3484	212	3	h	h	NOUN
ejpam-3484	212	4	has	have	VERB
ejpam-3484	212	5	a	a	DET
ejpam-3484	212	6	unique	unique	ADJ
ejpam-3484	212	7	γi	γi	NOUN
ejpam-3484	212	8	-	-	PUNCT
ejpam-3484	212	9	set	set	NOUN
ejpam-3484	212	10	,	,	PUNCT
ejpam-3484	212	11	and	and	CCONJ
ejpam-3484	212	12	fγi(g+h	fγi(g+h	ADJ
ejpam-3484	212	13	)	)	PUNCT
ejpam-3484	212	14	=	=	SYM
ejpam-3484	212	15	fγi(h	fγi(h	PROPN
ejpam-3484	212	16	)	)	PUNCT
ejpam-3484	212	17	whenever	whenever	SCONJ
ejpam-3484	212	18	h	h	NOUN
ejpam-3484	212	19	has	have	VERB
ejpam-3484	212	20	no	no	DET
ejpam-3484	212	21	unique	unique	ADJ
ejpam-3484	212	22	γi	γi	NOUN
ejpam-3484	212	23	-	-	PUNCT
ejpam-3484	212	24	sets	set	NOUN
ejpam-3484	212	25	.	.	PUNCT
ejpam-3484	213	1	the	the	DET
ejpam-3484	213	2	next	next	ADJ
ejpam-3484	213	3	results	result	NOUN
ejpam-3484	213	4	are	be	AUX
ejpam-3484	213	5	direct	direct	ADJ
ejpam-3484	213	6	consequences	consequence	NOUN
ejpam-3484	213	7	of	of	ADP
ejpam-3484	213	8	theorem	theorem	ADJ
ejpam-3484	213	9	3.8	3.8	NUM
ejpam-3484	213	10	and	and	CCONJ
ejpam-3484	213	11	theorem	theorem	VERB
ejpam-3484	213	12	3.9	3.9	NUM
ejpam-3484	213	13	corollary	corollary	NOUN
ejpam-3484	213	14	3.10	3.10	NUM
ejpam-3484	213	15	.	.	PUNCT
ejpam-3484	214	1	for	for	ADP
ejpam-3484	214	2	any	any	DET
ejpam-3484	214	3	graph	graph	NOUN
ejpam-3484	214	4	h	h	NOUN
ejpam-3484	214	5	,	,	PUNCT
ejpam-3484	214	6	fγ(k1	fγ(k1	VERB
ejpam-3484	214	7	+	+	NOUN
ejpam-3484	214	8	h	h	NOUN
ejpam-3484	214	9	)	)	PUNCT
ejpam-3484	214	10	=	=	NOUN
ejpam-3484	214	11	{	{	PUNCT
ejpam-3484	214	12	1	1	NUM
ejpam-3484	214	13	,	,	PUNCT
ejpam-3484	214	14	γi(h	γi(h	NOUN
ejpam-3484	214	15	)	)	PUNCT
ejpam-3484	214	16	=	=	SYM
ejpam-3484	215	1	1	1	NUM
ejpam-3484	215	2	,	,	PUNCT
ejpam-3484	215	3	0	0	NUM
ejpam-3484	215	4	,	,	PUNCT
ejpam-3484	215	5	γi(h	γi(h	NOUN
ejpam-3484	215	6	)	)	PUNCT
ejpam-3484	215	7	>	>	X
ejpam-3484	216	1	1	1	X
ejpam-3484	216	2	.	.	PUNCT
ejpam-3484	216	3	corollary	corollary	ADJ
ejpam-3484	216	4	3.11	3.11	NUM
ejpam-3484	216	5	.	.	PUNCT
ejpam-3484	217	1	for	for	SCONJ
ejpam-3484	217	2	the	the	DET
ejpam-3484	217	3	complete	complete	ADJ
ejpam-3484	217	4	bipartite	bipartite	PROPN
ejpam-3484	217	5	graph	graph	NOUN
ejpam-3484	217	6	kn	kn	PROPN
ejpam-3484	217	7	,	,	PUNCT
ejpam-3484	217	8	m	m	VERB
ejpam-3484	217	9	such	such	ADJ
ejpam-3484	217	10	that	that	SCONJ
ejpam-3484	217	11	n	n	CCONJ
ejpam-3484	217	12	,	,	PUNCT
ejpam-3484	217	13	m	m	VERB
ejpam-3484	217	14	≥	≥	NOUN
ejpam-3484	217	15	1	1	NUM
ejpam-3484	217	16	,	,	PUNCT
ejpam-3484	217	17	fγi(kn	fγi(kn	PROPN
ejpam-3484	217	18	,	,	PUNCT
ejpam-3484	217	19	m	m	PROPN
ejpam-3484	217	20	)	)	PUNCT
ejpam-3484	217	21	=	=	PRON
ejpam-3484	217	22	{	{	PUNCT
ejpam-3484	217	23	0	0	NUM
ejpam-3484	217	24	,	,	PUNCT
ejpam-3484	217	25	n	n	PROPN
ejpam-3484	217	26	6=	6=	NOUN
ejpam-3484	217	27	m	m	PROPN
ejpam-3484	217	28	,	,	PUNCT
ejpam-3484	217	29	1	1	NUM
ejpam-3484	217	30	,	,	PUNCT
ejpam-3484	217	31	n	n	NOUN
ejpam-3484	217	32	=	=	PUNCT
ejpam-3484	217	33	m.	m.	NOUN
ejpam-3484	217	34	corollary	corollary	NOUN
ejpam-3484	217	35	3.12	3.12	NUM
ejpam-3484	217	36	.	.	PUNCT
ejpam-3484	218	1	for	for	ADP
ejpam-3484	218	2	the	the	DET
ejpam-3484	218	3	generalized	generalized	ADJ
ejpam-3484	218	4	fan	fan	NOUN
ejpam-3484	218	5	fn	fn	PROPN
ejpam-3484	218	6	,	,	PUNCT
ejpam-3484	218	7	m	m	VERB
ejpam-3484	218	8	=	=	ADJ
ejpam-3484	218	9	kn	kn	PROPN
ejpam-3484	218	10	+	+	CCONJ
ejpam-3484	218	11	pm	pm	PROPN
ejpam-3484	218	12	,	,	PUNCT
ejpam-3484	218	13	where	where	SCONJ
ejpam-3484	218	14	n	n	PRON
ejpam-3484	218	15	≥	≥	NOUN
ejpam-3484	218	16	1	1	NUM
ejpam-3484	218	17	and	and	CCONJ
ejpam-3484	218	18	m	m	PROPN
ejpam-3484	218	19	≥	≥	NOUN
ejpam-3484	218	20	2	2	NUM
ejpam-3484	218	21	,	,	PUNCT
ejpam-3484	218	22	fγi(fn	fγi(fn	X
ejpam-3484	218	23	,	,	PUNCT
ejpam-3484	218	24	m	m	NOUN
ejpam-3484	218	25	)	)	PUNCT
ejpam-3484	218	26	=	=	PRON
ejpam-3484	218	27	{	{	PUNCT
ejpam-3484	218	28	0	0	NUM
ejpam-3484	218	29	,	,	PUNCT
ejpam-3484	218	30	if	if	SCONJ
ejpam-3484	218	31	either	either	CCONJ
ejpam-3484	218	32	n	n	ADV
ejpam-3484	218	33	<	<	X
ejpam-3484	218	34	dm	dm	PROPN
ejpam-3484	218	35	3	3	NUM
ejpam-3484	218	36	e	e	NOUN
ejpam-3484	218	37	or	or	CCONJ
ejpam-3484	218	38	n	n	NOUN
ejpam-3484	218	39	>	>	X
ejpam-3484	218	40	dm	dm	PROPN
ejpam-3484	218	41	3	3	NUM
ejpam-3484	218	42	e	e	NOUN
ejpam-3484	218	43	with	with	ADP
ejpam-3484	218	44	m	m	PROPN
ejpam-3484	218	45	≡	≡	ADJ
ejpam-3484	218	46	0(mod	0(mod	NOUN
ejpam-3484	218	47	3	3	NUM
ejpam-3484	218	48	)	)	PUNCT
ejpam-3484	218	49	,	,	PUNCT
ejpam-3484	218	50	1	1	NUM
ejpam-3484	218	51	,	,	PUNCT
ejpam-3484	218	52	if	if	SCONJ
ejpam-3484	218	53	either	either	PRON
ejpam-3484	218	54	n	n	ADV
ejpam-3484	218	55	=	=	SYM
ejpam-3484	218	56	dm	dm	NUM
ejpam-3484	218	57	3	3	NUM
ejpam-3484	218	58	e	e	NOUN
ejpam-3484	218	59	or	or	CCONJ
ejpam-3484	218	60	n	n	NOUN
ejpam-3484	218	61	>	>	X
ejpam-3484	218	62	dm	dm	PROPN
ejpam-3484	218	63	3	3	NUM
ejpam-3484	218	64	e	e	NOUN
ejpam-3484	218	65	with	with	ADP
ejpam-3484	218	66	m	m	PROPN
ejpam-3484	218	67	6≡	6≡	NUM
ejpam-3484	218	68	0(mod	0(mod	NOUN
ejpam-3484	218	69	3	3	NUM
ejpam-3484	218	70	)	)	PUNCT
ejpam-3484	218	71	.	.	PUNCT
ejpam-3484	219	1	corollary	corollary	ADJ
ejpam-3484	219	2	3.13	3.13	NUM
ejpam-3484	219	3	.	.	PUNCT
ejpam-3484	220	1	for	for	ADP
ejpam-3484	220	2	the	the	DET
ejpam-3484	220	3	fan	fan	NOUN
ejpam-3484	220	4	fn	fn	PROPN
ejpam-3484	220	5	=	=	PROPN
ejpam-3484	220	6	k1	k1	PROPN
ejpam-3484	220	7	+	+	CCONJ
ejpam-3484	220	8	pn	pn	NOUN
ejpam-3484	220	9	,	,	PUNCT
ejpam-3484	220	10	where	where	SCONJ
ejpam-3484	220	11	n	n	PRON
ejpam-3484	220	12	≥	≥	NOUN
ejpam-3484	220	13	2	2	NUM
ejpam-3484	220	14	,	,	PUNCT
ejpam-3484	220	15	fγi(fn	fγi(fn	X
ejpam-3484	220	16	)	)	PUNCT
ejpam-3484	220	17	=	=	SYM
ejpam-3484	220	18	{	{	PUNCT
ejpam-3484	220	19	0	0	NUM
ejpam-3484	220	20	,	,	PUNCT
ejpam-3484	220	21	n	n	PROPN
ejpam-3484	220	22	>	>	X
ejpam-3484	220	23	3	3	NUM
ejpam-3484	220	24	,	,	PUNCT
ejpam-3484	220	25	1	1	NUM
ejpam-3484	220	26	,	,	PUNCT
ejpam-3484	220	27	n	n	PRON
ejpam-3484	220	28	≤	≤	NOUN
ejpam-3484	220	29	3	3	NUM
ejpam-3484	220	30	.	.	PUNCT
ejpam-3484	220	31	c.	c.	PROPN
ejpam-3484	220	32	armada	armada	PROPN
ejpam-3484	220	33	,	,	PUNCT
ejpam-3484	220	34	s.	s.	PROPN
ejpam-3484	220	35	canoy	canoy	PROPN
ejpam-3484	220	36	jr	jr	PROPN
ejpam-3484	220	37	.	.	PROPN
ejpam-3484	220	38	/	/	SYM
ejpam-3484	220	39	eur	eur	PROPN
ejpam-3484	220	40	.	.	PUNCT
ejpam-3484	221	1	j.	j.	PROPN
ejpam-3484	221	2	pure	pure	PROPN
ejpam-3484	221	3	appl	appl	PROPN
ejpam-3484	221	4	.	.	PROPN
ejpam-3484	221	5	math	math	PROPN
ejpam-3484	221	6	,	,	PUNCT
ejpam-3484	221	7	12	12	NUM
ejpam-3484	221	8	(	(	PUNCT
ejpam-3484	221	9	4	4	NUM
ejpam-3484	221	10	)	)	PUNCT
ejpam-3484	221	11	(	(	PUNCT
ejpam-3484	221	12	2019	2019	NUM
ejpam-3484	221	13	)	)	PUNCT
ejpam-3484	221	14	,	,	PUNCT
ejpam-3484	221	15	1371	1371	NUM
ejpam-3484	221	16	-	-	SYM
ejpam-3484	221	17	1381	1381	NUM
ejpam-3484	221	18	1377	1377	NUM
ejpam-3484	221	19	corollary	corollary	NOUN
ejpam-3484	221	20	3.14	3.14	NUM
ejpam-3484	221	21	.	.	PUNCT
ejpam-3484	222	1	for	for	ADP
ejpam-3484	222	2	the	the	DET
ejpam-3484	222	3	generalized	generalize	VERB
ejpam-3484	222	4	wheel	wheel	NOUN
ejpam-3484	222	5	wn	wn	PROPN
ejpam-3484	222	6	,	,	PUNCT
ejpam-3484	222	7	m	m	VERB
ejpam-3484	222	8	=	=	ADJ
ejpam-3484	222	9	kn	kn	PROPN
ejpam-3484	222	10	+	+	CCONJ
ejpam-3484	222	11	cm	cm	NOUN
ejpam-3484	222	12	,	,	PUNCT
ejpam-3484	223	1	where	where	SCONJ
ejpam-3484	223	2	n	n	PRON
ejpam-3484	223	3	≥	≥	NOUN
ejpam-3484	223	4	1	1	NUM
ejpam-3484	223	5	and	and	CCONJ
ejpam-3484	223	6	m	m	PROPN
ejpam-3484	223	7	≥	≥	NOUN
ejpam-3484	223	8	3	3	NUM
ejpam-3484	223	9	,	,	PUNCT
ejpam-3484	223	10	fγi(wn	fγi(wn	NUM
ejpam-3484	223	11	,	,	PUNCT
ejpam-3484	223	12	m	m	NOUN
ejpam-3484	223	13	)	)	PUNCT
ejpam-3484	223	14	=	=	SYM
ejpam-3484	223	15			X
ejpam-3484	223	16	0	0	NUM
ejpam-3484	223	17	,	,	PUNCT
ejpam-3484	223	18	if	if	SCONJ
ejpam-3484	223	19	n	n	ADV
ejpam-3484	223	20	<	<	X
ejpam-3484	223	21	dm	dm	PROPN
ejpam-3484	223	22	3	3	NUM
ejpam-3484	223	23	e	e	NOUN
ejpam-3484	223	24	1	1	NUM
ejpam-3484	223	25	,	,	PUNCT
ejpam-3484	223	26	if	if	SCONJ
ejpam-3484	223	27	either	either	DET
ejpam-3484	223	28	n	n	ADV
ejpam-3484	223	29	=	=	SYM
ejpam-3484	223	30	dm	dm	NUM
ejpam-3484	223	31	3	3	NUM
ejpam-3484	223	32	e	e	NOUN
ejpam-3484	223	33	or	or	CCONJ
ejpam-3484	223	34	n	n	NOUN
ejpam-3484	223	35	>	>	X
ejpam-3484	223	36	dm	dm	PROPN
ejpam-3484	223	37	3	3	NUM
ejpam-3484	223	38	e	e	NOUN
ejpam-3484	223	39	with	with	ADP
ejpam-3484	223	40	m	m	PROPN
ejpam-3484	223	41	=	=	SYM
ejpam-3484	223	42	4	4	NUM
ejpam-3484	223	43	or	or	CCONJ
ejpam-3484	223	44	m	m	PROPN
ejpam-3484	223	45	≡	≡	ADJ
ejpam-3484	223	46	0(mod	0(mod	NOUN
ejpam-3484	223	47	3	3	NUM
ejpam-3484	223	48	)	)	PUNCT
ejpam-3484	223	49	,	,	PUNCT
ejpam-3484	223	50	2	2	NUM
ejpam-3484	223	51	,	,	PUNCT
ejpam-3484	223	52	if	if	SCONJ
ejpam-3484	223	53	n	n	PROPN
ejpam-3484	223	54	>	>	X
ejpam-3484	223	55	dm	dm	PROPN
ejpam-3484	223	56	3	3	NUM
ejpam-3484	223	57	e	e	NOUN
ejpam-3484	223	58	with	with	ADP
ejpam-3484	223	59	m	m	PROPN
ejpam-3484	223	60	6=	6=	ADP
ejpam-3484	223	61	4	4	NUM
ejpam-3484	223	62	or	or	CCONJ
ejpam-3484	223	63	m	m	PRON
ejpam-3484	223	64	6≡	6≡	NUM
ejpam-3484	223	65	0(mod	0(mod	NOUN
ejpam-3484	223	66	3	3	NUM
ejpam-3484	223	67	)	)	PUNCT
ejpam-3484	223	68	.	.	PUNCT
ejpam-3484	224	1	corollary	corollary	ADJ
ejpam-3484	224	2	3.15	3.15	NUM
ejpam-3484	224	3	.	.	PUNCT
ejpam-3484	225	1	for	for	ADP
ejpam-3484	225	2	the	the	DET
ejpam-3484	225	3	wheel	wheel	NOUN
ejpam-3484	225	4	wn	wn	PROPN
ejpam-3484	225	5	=	=	PROPN
ejpam-3484	225	6	k1	k1	PROPN
ejpam-3484	225	7	+	+	CCONJ
ejpam-3484	225	8	cn	cn	PROPN
ejpam-3484	225	9	,	,	PUNCT
ejpam-3484	225	10	where	where	SCONJ
ejpam-3484	225	11	n	n	PRON
ejpam-3484	225	12	≥	≥	NOUN
ejpam-3484	225	13	3	3	NUM
ejpam-3484	225	14	,	,	PUNCT
ejpam-3484	225	15	fγi(wn	fγi(wn	NUM
ejpam-3484	225	16	)	)	PUNCT
ejpam-3484	225	17	=	=	NOUN
ejpam-3484	225	18	{	{	PUNCT
ejpam-3484	225	19	0	0	NUM
ejpam-3484	225	20	,	,	PUNCT
ejpam-3484	225	21	n	n	PROPN
ejpam-3484	225	22	>	>	X
ejpam-3484	225	23	3	3	NUM
ejpam-3484	225	24	,	,	PUNCT
ejpam-3484	225	25	1	1	NUM
ejpam-3484	225	26	,	,	PUNCT
ejpam-3484	225	27	n	n	NOUN
ejpam-3484	225	28	=	=	SYM
ejpam-3484	225	29	3	3	X
ejpam-3484	225	30	.	.	PUNCT
ejpam-3484	226	1	the	the	DET
ejpam-3484	226	2	following	follow	VERB
ejpam-3484	226	3	results	result	NOUN
ejpam-3484	226	4	are	be	AUX
ejpam-3484	226	5	restatements	restatement	NOUN
ejpam-3484	226	6	of	of	ADP
ejpam-3484	226	7	theorems	theorem	NOUN
ejpam-3484	226	8	2.3	2.3	NUM
ejpam-3484	226	9	and	and	CCONJ
ejpam-3484	226	10	2.4	2.4	NUM
ejpam-3484	226	11	.	.	PUNCT
ejpam-3484	227	1	theorem	theorem	VERB
ejpam-3484	227	2	3.16	3.16	NUM
ejpam-3484	227	3	.	.	PUNCT
ejpam-3484	228	1	let	let	VERB
ejpam-3484	228	2	g	g	PRON
ejpam-3484	228	3	be	be	AUX
ejpam-3484	228	4	a	a	DET
ejpam-3484	228	5	connected	connected	ADJ
ejpam-3484	228	6	graph	graph	NOUN
ejpam-3484	228	7	of	of	ADP
ejpam-3484	228	8	order	order	NOUN
ejpam-3484	228	9	n	n	NOUN
ejpam-3484	228	10	and	and	CCONJ
ejpam-3484	228	11	let	let	VERB
ejpam-3484	228	12	h	h	NOUN
ejpam-3484	228	13	be	be	AUX
ejpam-3484	228	14	any	any	DET
ejpam-3484	228	15	graph	graph	NOUN
ejpam-3484	228	16	.	.	PUNCT
ejpam-3484	229	1	then	then	ADV
ejpam-3484	229	2	c	c	PROPN
ejpam-3484	229	3	⊆	⊆	NUM
ejpam-3484	229	4	v	v	NOUN
ejpam-3484	229	5	(	(	PUNCT
ejpam-3484	229	6	g	g	PROPN
ejpam-3484	229	7	◦	◦	NOUN
ejpam-3484	229	8	h	h	NOUN
ejpam-3484	229	9	)	)	PUNCT
ejpam-3484	229	10	is	be	AUX
ejpam-3484	229	11	an	an	DET
ejpam-3484	229	12	independent	independent	ADJ
ejpam-3484	229	13	dominating	dominating	NOUN
ejpam-3484	229	14	set	set	VERB
ejpam-3484	229	15	in	in	ADP
ejpam-3484	229	16	g	g	PROPN
ejpam-3484	229	17	◦	◦	NOUN
ejpam-3484	229	18	h	h	NOUN
ejpam-3484	229	19	if	if	SCONJ
ejpam-3484	230	1	and	and	CCONJ
ejpam-3484	230	2	only	only	ADV
ejpam-3484	230	3	if	if	SCONJ
ejpam-3484	230	4	c	c	PROPN
ejpam-3484	230	5	=	=	SYM
ejpam-3484	230	6	a∪	a∪	PROPN
ejpam-3484	230	7	(	(	PUNCT
ejpam-3484	230	8	⋃	⋃	NOUN
ejpam-3484	230	9	v∈v	v∈v	NOUN
ejpam-3484	230	10	(	(	PUNCT
ejpam-3484	230	11	g)\a	g)\a	NOUN
ejpam-3484	230	12	sv	sv	PROPN
ejpam-3484	230	13	)	)	PUNCT
ejpam-3484	230	14	,	,	PUNCT
ejpam-3484	230	15	where	where	SCONJ
ejpam-3484	230	16	a	a	PRON
ejpam-3484	230	17	is	be	AUX
ejpam-3484	230	18	an	an	DET
ejpam-3484	230	19	independent	independent	ADJ
ejpam-3484	230	20	set	set	NOUN
ejpam-3484	230	21	(	(	PUNCT
ejpam-3484	230	22	may	may	AUX
ejpam-3484	230	23	be	be	AUX
ejpam-3484	230	24	empty	empty	ADJ
ejpam-3484	230	25	)	)	PUNCT
ejpam-3484	230	26	of	of	ADP
ejpam-3484	230	27	g	g	PROPN
ejpam-3484	230	28	and	and	CCONJ
ejpam-3484	230	29	sv	sv	PROPN
ejpam-3484	230	30	is	be	AUX
ejpam-3484	230	31	an	an	DET
ejpam-3484	230	32	independent	independent	ADJ
ejpam-3484	230	33	dominating	dominating	NOUN
ejpam-3484	230	34	set	set	NOUN
ejpam-3484	230	35	of	of	ADP
ejpam-3484	230	36	hv	hv	PROPN
ejpam-3484	230	37	for	for	ADP
ejpam-3484	230	38	all	all	DET
ejpam-3484	230	39	v	v	ADP
ejpam-3484	230	40	∈	∈	NOUN
ejpam-3484	230	41	v	v	NOUN
ejpam-3484	230	42	(	(	PUNCT
ejpam-3484	230	43	g)\a	g)\a	NOUN
ejpam-3484	230	44	.	.	PUNCT
ejpam-3484	231	1	theorem	theorem	VERB
ejpam-3484	231	2	3.17	3.17	NUM
ejpam-3484	231	3	.	.	PUNCT
ejpam-3484	232	1	let	let	VERB
ejpam-3484	232	2	g	g	PRON
ejpam-3484	232	3	be	be	AUX
ejpam-3484	232	4	a	a	DET
ejpam-3484	232	5	connected	connected	ADJ
ejpam-3484	232	6	graph	graph	NOUN
ejpam-3484	232	7	of	of	ADP
ejpam-3484	232	8	order	order	NOUN
ejpam-3484	232	9	n	n	NOUN
ejpam-3484	232	10	and	and	CCONJ
ejpam-3484	232	11	let	let	VERB
ejpam-3484	232	12	h	h	NOUN
ejpam-3484	232	13	be	be	AUX
ejpam-3484	232	14	any	any	DET
ejpam-3484	232	15	graph	graph	NOUN
ejpam-3484	232	16	with	with	ADP
ejpam-3484	232	17	γi(h	γi(h	NOUN
ejpam-3484	232	18	)	)	PUNCT
ejpam-3484	232	19	=	=	SYM
ejpam-3484	233	1	1	1	X
ejpam-3484	233	2	.	.	PUNCT
ejpam-3484	233	3	then	then	ADV
ejpam-3484	233	4	c	c	PROPN
ejpam-3484	233	5	is	be	AUX
ejpam-3484	233	6	a	a	DET
ejpam-3484	233	7	γi	γi	NOUN
ejpam-3484	233	8	-	-	PUNCT
ejpam-3484	233	9	set	set	NOUN
ejpam-3484	233	10	of	of	ADP
ejpam-3484	233	11	g	g	PROPN
ejpam-3484	233	12	◦	◦	NOUN
ejpam-3484	233	13	h	h	NOUN
ejpam-3484	233	14	if	if	SCONJ
ejpam-3484	234	1	and	and	CCONJ
ejpam-3484	234	2	only	only	ADV
ejpam-3484	234	3	if	if	SCONJ
ejpam-3484	234	4	c	c	X
ejpam-3484	234	5	=	=	PUNCT
ejpam-3484	234	6	a	a	DET
ejpam-3484	234	7	∪	∪	X
ejpam-3484	234	8	(	(	PUNCT
ejpam-3484	234	9	⋃	⋃	NOUN
ejpam-3484	234	10	v∈v	v∈v	NOUN
ejpam-3484	234	11	(	(	PUNCT
ejpam-3484	234	12	g)\a	g)\a	NOUN
ejpam-3484	234	13	sv	sv	PROPN
ejpam-3484	234	14	)	)	PUNCT
ejpam-3484	234	15	where	where	SCONJ
ejpam-3484	234	16	a	a	PRON
ejpam-3484	234	17	is	be	AUX
ejpam-3484	234	18	an	an	DET
ejpam-3484	234	19	independent	independent	ADJ
ejpam-3484	234	20	set	set	NOUN
ejpam-3484	234	21	of	of	ADP
ejpam-3484	234	22	g	g	PROPN
ejpam-3484	234	23	and	and	CCONJ
ejpam-3484	234	24	sv	sv	PROPN
ejpam-3484	234	25	is	be	AUX
ejpam-3484	234	26	a	a	DET
ejpam-3484	234	27	γi	γi	NOUN
ejpam-3484	234	28	-	-	PUNCT
ejpam-3484	234	29	set	set	NOUN
ejpam-3484	234	30	of	of	ADP
ejpam-3484	234	31	hv	hv	NOUN
ejpam-3484	234	32	for	for	ADP
ejpam-3484	234	33	each	each	DET
ejpam-3484	234	34	v	v	NUM
ejpam-3484	234	35	∈	∈	PROPN
ejpam-3484	234	36	v	v	NOUN
ejpam-3484	234	37	(	(	PUNCT
ejpam-3484	234	38	g)\a	g)\a	NOUN
ejpam-3484	234	39	.	.	PUNCT
ejpam-3484	235	1	in	in	ADP
ejpam-3484	235	2	particular	particular	ADJ
ejpam-3484	235	3	,	,	PUNCT
ejpam-3484	235	4	γi(g	γi(g	PUNCT
ejpam-3484	235	5	◦	◦	NOUN
ejpam-3484	235	6	h	h	NOUN
ejpam-3484	235	7	)	)	PUNCT
ejpam-3484	235	8	=	=	SYM
ejpam-3484	235	9	n.	n.	NOUN
ejpam-3484	235	10	theorem	theorem	VERB
ejpam-3484	235	11	3.18	3.18	NUM
ejpam-3484	235	12	.	.	PUNCT
ejpam-3484	236	1	let	let	VERB
ejpam-3484	236	2	g	g	PRON
ejpam-3484	236	3	be	be	AUX
ejpam-3484	236	4	a	a	DET
ejpam-3484	236	5	connected	connected	ADJ
ejpam-3484	236	6	graph	graph	NOUN
ejpam-3484	236	7	of	of	ADP
ejpam-3484	236	8	order	order	NOUN
ejpam-3484	236	9	n	n	NOUN
ejpam-3484	236	10	and	and	CCONJ
ejpam-3484	236	11	let	let	VERB
ejpam-3484	236	12	h	h	NOUN
ejpam-3484	236	13	be	be	AUX
ejpam-3484	236	14	any	any	DET
ejpam-3484	236	15	graph	graph	NOUN
ejpam-3484	236	16	with	with	ADP
ejpam-3484	236	17	γi(h	γi(h	NOUN
ejpam-3484	236	18	)	)	PUNCT
ejpam-3484	236	19	≥	≥	NOUN
ejpam-3484	237	1	2	2	NUM
ejpam-3484	237	2	.	.	PUNCT
ejpam-3484	237	3	then	then	ADV
ejpam-3484	237	4	c	c	PROPN
ejpam-3484	237	5	is	be	AUX
ejpam-3484	237	6	a	a	DET
ejpam-3484	237	7	γi	γi	NOUN
ejpam-3484	237	8	-	-	PUNCT
ejpam-3484	237	9	set	set	NOUN
ejpam-3484	237	10	of	of	ADP
ejpam-3484	237	11	g	g	PROPN
ejpam-3484	237	12	◦	◦	NOUN
ejpam-3484	237	13	h	h	NOUN
ejpam-3484	237	14	if	if	SCONJ
ejpam-3484	238	1	and	and	CCONJ
ejpam-3484	238	2	only	only	ADV
ejpam-3484	238	3	if	if	SCONJ
ejpam-3484	238	4	c	c	X
ejpam-3484	238	5	=	=	PUNCT
ejpam-3484	238	6	a	a	DET
ejpam-3484	238	7	∪	∪	X
ejpam-3484	238	8	(	(	PUNCT
ejpam-3484	238	9	⋃	⋃	NOUN
ejpam-3484	238	10	v∈v	v∈v	NOUN
ejpam-3484	238	11	(	(	PUNCT
ejpam-3484	238	12	g)\a	g)\a	NOUN
ejpam-3484	238	13	sv	sv	PROPN
ejpam-3484	238	14	)	)	PUNCT
ejpam-3484	238	15	where	where	SCONJ
ejpam-3484	238	16	a	a	PRON
ejpam-3484	238	17	is	be	AUX
ejpam-3484	238	18	a	a	DET
ejpam-3484	238	19	maximum	maximum	ADJ
ejpam-3484	238	20	independent	independent	ADJ
ejpam-3484	238	21	set	set	NOUN
ejpam-3484	238	22	of	of	ADP
ejpam-3484	238	23	g	g	PROPN
ejpam-3484	238	24	and	and	CCONJ
ejpam-3484	238	25	sv	sv	PROPN
ejpam-3484	238	26	is	be	AUX
ejpam-3484	238	27	a	a	DET
ejpam-3484	238	28	γi	γi	NOUN
ejpam-3484	238	29	-	-	PUNCT
ejpam-3484	238	30	set	set	NOUN
ejpam-3484	238	31	of	of	ADP
ejpam-3484	238	32	hv	hv	NOUN
ejpam-3484	238	33	for	for	ADP
ejpam-3484	238	34	each	each	DET
ejpam-3484	238	35	v	v	NUM
ejpam-3484	238	36	∈	∈	PROPN
ejpam-3484	238	37	v	v	NOUN
ejpam-3484	238	38	(	(	PUNCT
ejpam-3484	238	39	g)\a	g)\a	NOUN
ejpam-3484	238	40	.	.	PUNCT
ejpam-3484	239	1	in	in	ADP
ejpam-3484	239	2	particular	particular	ADJ
ejpam-3484	239	3	,	,	PUNCT
ejpam-3484	239	4	γi(g	γi(g	PUNCT
ejpam-3484	239	5	◦	◦	NOUN
ejpam-3484	239	6	h	h	NOUN
ejpam-3484	239	7	)	)	PUNCT
ejpam-3484	239	8	=	=	SYM
ejpam-3484	239	9	α(g	α(g	NUM
ejpam-3484	239	10	)	)	PUNCT
ejpam-3484	239	11	+	+	CCONJ
ejpam-3484	240	1	[	[	X
ejpam-3484	240	2	n−	n−	NOUN
ejpam-3484	240	3	α(g)]γi(h	α(g)]γi(h	NOUN
ejpam-3484	240	4	)	)	PUNCT
ejpam-3484	240	5	.	.	PUNCT
ejpam-3484	241	1	theorem	theorem	VERB
ejpam-3484	241	2	3.19	3.19	NUM
ejpam-3484	241	3	.	.	PUNCT
ejpam-3484	242	1	let	let	VERB
ejpam-3484	242	2	g	g	PRON
ejpam-3484	242	3	be	be	AUX
ejpam-3484	242	4	a	a	DET
ejpam-3484	242	5	connected	connected	ADJ
ejpam-3484	242	6	graph	graph	NOUN
ejpam-3484	242	7	of	of	ADP
ejpam-3484	242	8	order	order	NOUN
ejpam-3484	242	9	n	n	NOUN
ejpam-3484	242	10	and	and	CCONJ
ejpam-3484	242	11	let	let	VERB
ejpam-3484	242	12	h	h	NOUN
ejpam-3484	242	13	be	be	AUX
ejpam-3484	242	14	any	any	DET
ejpam-3484	242	15	graph	graph	NOUN
ejpam-3484	242	16	with	with	ADP
ejpam-3484	242	17	γi(h	γi(h	NOUN
ejpam-3484	242	18	)	)	PUNCT
ejpam-3484	242	19	=	=	SYM
ejpam-3484	243	1	1	1	X
ejpam-3484	243	2	.	.	PUNCT
ejpam-3484	244	1	then	then	ADV
ejpam-3484	244	2	fγi(g	fγi(g	PROPN
ejpam-3484	244	3	◦	◦	NOUN
ejpam-3484	244	4	h	h	NOUN
ejpam-3484	244	5	)	)	PUNCT
ejpam-3484	244	6	=	=	PRON
ejpam-3484	244	7	{	{	PUNCT
ejpam-3484	244	8	γi(g	γi(g	NOUN
ejpam-3484	244	9	)	)	PUNCT
ejpam-3484	244	10	,	,	PUNCT
ejpam-3484	244	11	if	if	SCONJ
ejpam-3484	244	12	h	h	NOUN
ejpam-3484	244	13	has	have	VERB
ejpam-3484	244	14	a	a	DET
ejpam-3484	244	15	unique	unique	ADJ
ejpam-3484	244	16	γi	γi	NOUN
ejpam-3484	244	17	-	-	PUNCT
ejpam-3484	244	18	set	set	VERB
ejpam-3484	244	19	,	,	PUNCT
ejpam-3484	244	20	n	n	CCONJ
ejpam-3484	244	21	,	,	PUNCT
ejpam-3484	244	22	otherwise	otherwise	ADV
ejpam-3484	244	23	.	.	PUNCT
ejpam-3484	245	1	proof	proof	NOUN
ejpam-3484	245	2	.	.	PUNCT
ejpam-3484	246	1	since	since	SCONJ
ejpam-3484	246	2	γi(h	γi(h	NOUN
ejpam-3484	246	3	)	)	PUNCT
ejpam-3484	246	4	=	=	SYM
ejpam-3484	246	5	1	1	X
ejpam-3484	246	6	,	,	PUNCT
ejpam-3484	246	7	by	by	ADP
ejpam-3484	246	8	theorem	theorem	NOUN
ejpam-3484	246	9	3.17	3.17	NUM
ejpam-3484	246	10	,	,	PUNCT
ejpam-3484	246	11	γi(g	γi(g	PUNCT
ejpam-3484	246	12	◦	◦	NOUN
ejpam-3484	246	13	h	h	NOUN
ejpam-3484	246	14	)	)	PUNCT
ejpam-3484	246	15	=	=	SYM
ejpam-3484	246	16	n.	n.	NOUN
ejpam-3484	246	17	suppose	suppose	VERB
ejpam-3484	246	18	that	that	SCONJ
ejpam-3484	246	19	h	h	NOUN
ejpam-3484	246	20	has	have	VERB
ejpam-3484	246	21	a	a	DET
ejpam-3484	246	22	unique	unique	ADJ
ejpam-3484	246	23	γi	γi	NOUN
ejpam-3484	246	24	-	-	PUNCT
ejpam-3484	246	25	set	set	NOUN
ejpam-3484	246	26	,	,	PUNCT
ejpam-3484	246	27	say	say	VERB
ejpam-3484	246	28	p	p	X
ejpam-3484	246	29	=	=	X
ejpam-3484	246	30	{	{	PUNCT
ejpam-3484	246	31	x	x	NOUN
ejpam-3484	246	32	}	}	PUNCT
ejpam-3484	246	33	.	.	PUNCT
ejpam-3484	247	1	for	for	ADP
ejpam-3484	247	2	each	each	DET
ejpam-3484	247	3	v	v	NUM
ejpam-3484	247	4	∈	∈	PROPN
ejpam-3484	247	5	v	v	NOUN
ejpam-3484	247	6	(	(	PUNCT
ejpam-3484	247	7	g	g	NOUN
ejpam-3484	247	8	)	)	PUNCT
ejpam-3484	247	9	,	,	PUNCT
ejpam-3484	247	10	let	let	VERB
ejpam-3484	247	11	pv	pv	VERB
ejpam-3484	247	12	=	=	PUNCT
ejpam-3484	247	13	{	{	PUNCT
ejpam-3484	247	14	xv	xv	PROPN
ejpam-3484	247	15	}	}	PUNCT
ejpam-3484	247	16	⊆	⊆	NUM
ejpam-3484	247	17	v	v	ADP
ejpam-3484	247	18	(	(	PUNCT
ejpam-3484	247	19	hv	hv	NOUN
ejpam-3484	247	20	)	)	PUNCT
ejpam-3484	247	21	be	be	VERB
ejpam-3484	247	22	such	such	ADJ
ejpam-3484	247	23	that	that	SCONJ
ejpam-3484	247	24	〈	〈	PROPN
ejpam-3484	247	25	p	p	PROPN
ejpam-3484	247	26	〉	〉	PROPN
ejpam-3484	247	27	∼=	∼=	PROPN
ejpam-3484	247	28	〈	〈	PROPN
ejpam-3484	247	29	pv	pv	PROPN
ejpam-3484	247	30	〉	〉	PROPN
ejpam-3484	247	31	,	,	PUNCT
ejpam-3484	247	32	where	where	SCONJ
ejpam-3484	247	33	〈	〈	PROPN
ejpam-3484	247	34	p	p	PROPN
ejpam-3484	247	35	〉	〉	PROPN
ejpam-3484	247	36	is	be	AUX
ejpam-3484	247	37	the	the	DET
ejpam-3484	247	38	subgraph	subgraph	NOUN
ejpam-3484	247	39	induced	induce	VERB
ejpam-3484	247	40	by	by	ADP
ejpam-3484	247	41	p	p	PROPN
ejpam-3484	247	42	.	.	PUNCT
ejpam-3484	248	1	let	let	VERB
ejpam-3484	248	2	s	s	PRON
ejpam-3484	248	3	=	=	VERB
ejpam-3484	248	4	t	t	PROPN
ejpam-3484	248	5	∪	∪	X
ejpam-3484	248	6	u	u	PROPN
ejpam-3484	248	7	where	where	SCONJ
ejpam-3484	248	8	t	t	PROPN
ejpam-3484	248	9	is	be	AUX
ejpam-3484	248	10	a	a	DET
ejpam-3484	248	11	γi	γi	NOUN
ejpam-3484	248	12	-	-	PUNCT
ejpam-3484	248	13	set	set	NOUN
ejpam-3484	248	14	of	of	ADP
ejpam-3484	248	15	g	g	NOUN
ejpam-3484	248	16	and	and	CCONJ
ejpam-3484	248	17	u	u	NOUN
ejpam-3484	248	18	=	=	PUNCT
ejpam-3484	248	19	{	{	PUNCT
ejpam-3484	248	20	xv	xv	PROPN
ejpam-3484	248	21	∈	∈	PROPN
ejpam-3484	248	22	v	v	PROPN
ejpam-3484	248	23	(	(	PUNCT
ejpam-3484	248	24	hv	hv	PROPN
ejpam-3484	248	25	)	)	PUNCT
ejpam-3484	248	26	:	:	PUNCT
ejpam-3484	248	27	xv	xv	PROPN
ejpam-3484	248	28	∈	∈	PROPN
ejpam-3484	248	29	pv	pv	PROPN
ejpam-3484	248	30	∀v	∀v	PROPN
ejpam-3484	248	31	∈	∈	PROPN
ejpam-3484	248	32	v	v	NOUN
ejpam-3484	248	33	(	(	PUNCT
ejpam-3484	248	34	g)\t	g)\t	PROPN
ejpam-3484	248	35	}	}	PUNCT
ejpam-3484	248	36	.	.	PUNCT
ejpam-3484	249	1	clearly	clearly	ADV
ejpam-3484	249	2	,	,	PUNCT
ejpam-3484	249	3	s	s	VERB
ejpam-3484	249	4	is	be	AUX
ejpam-3484	249	5	a	a	DET
ejpam-3484	249	6	γi	γi	NOUN
ejpam-3484	249	7	-	-	PUNCT
ejpam-3484	249	8	set	set	NOUN
ejpam-3484	249	9	of	of	ADP
ejpam-3484	249	10	g	g	PROPN
ejpam-3484	249	11	◦	◦	PROPN
ejpam-3484	249	12	h.	h.	NOUN
ejpam-3484	249	13	since	since	SCONJ
ejpam-3484	249	14	h	h	NOUN
ejpam-3484	249	15	has	have	VERB
ejpam-3484	249	16	a	a	DET
ejpam-3484	249	17	unique	unique	ADJ
ejpam-3484	249	18	γi	γi	NOUN
ejpam-3484	249	19	-	-	PUNCT
ejpam-3484	249	20	set	set	VERB
ejpam-3484	249	21	and	and	CCONJ
ejpam-3484	249	22	any	any	DET
ejpam-3484	249	23	vertex	vertex	NOUN
ejpam-3484	249	24	v	v	ADP
ejpam-3484	249	25	∈	∈	NOUN
ejpam-3484	249	26	v	v	NOUN
ejpam-3484	249	27	(	(	PUNCT
ejpam-3484	249	28	g)\t	g)\t	NOUN
ejpam-3484	249	29	is	be	AUX
ejpam-3484	249	30	adjacent	adjacent	ADJ
ejpam-3484	249	31	to	to	ADP
ejpam-3484	249	32	a	a	DET
ejpam-3484	249	33	vertex	vertex	NOUN
ejpam-3484	249	34	in	in	ADP
ejpam-3484	249	35	t	t	PROPN
ejpam-3484	249	36	,	,	PUNCT
ejpam-3484	249	37	no	no	DET
ejpam-3484	249	38	element	element	NOUN
ejpam-3484	249	39	in	in	ADP
ejpam-3484	249	40	u	u	NOUN
ejpam-3484	249	41	can	can	AUX
ejpam-3484	249	42	be	be	AUX
ejpam-3484	249	43	replaced	replace	VERB
ejpam-3484	249	44	by	by	ADP
ejpam-3484	249	45	any	any	DET
ejpam-3484	249	46	vertex	vertex	NOUN
ejpam-3484	249	47	in	in	ADP
ejpam-3484	249	48	v	v	NUM
ejpam-3484	249	49	+	+	CCONJ
ejpam-3484	249	50	v	v	PROPN
ejpam-3484	249	51	(	(	PUNCT
ejpam-3484	249	52	hv	hv	NOUN
ejpam-3484	249	53	)	)	PUNCT
ejpam-3484	249	54	for	for	ADP
ejpam-3484	249	55	all	all	PRON
ejpam-3484	249	56	v	v	ADP
ejpam-3484	249	57	∈	∈	NOUN
ejpam-3484	249	58	v	v	NOUN
ejpam-3484	249	59	(	(	PUNCT
ejpam-3484	249	60	g)\t	g)\t	NOUN
ejpam-3484	249	61	to	to	PART
ejpam-3484	249	62	form	form	VERB
ejpam-3484	249	63	another	another	DET
ejpam-3484	249	64	γi	γi	NOUN
ejpam-3484	249	65	-	-	PUNCT
ejpam-3484	249	66	set	set	NOUN
ejpam-3484	249	67	of	of	ADP
ejpam-3484	249	68	g	g	PROPN
ejpam-3484	249	69	◦	◦	NOUN
ejpam-3484	249	70	h.	h.	PROPN
ejpam-3484	249	71	hence	hence	ADV
ejpam-3484	249	72	,	,	PUNCT
ejpam-3484	249	73	t	t	PROPN
ejpam-3484	249	74	is	be	AUX
ejpam-3484	249	75	uniquely	uniquely	ADV
ejpam-3484	249	76	contained	contain	VERB
ejpam-3484	249	77	in	in	ADP
ejpam-3484	249	78	s	s	PROPN
ejpam-3484	249	79	,	,	PUNCT
ejpam-3484	249	80	that	that	ADV
ejpam-3484	249	81	is	is	ADV
ejpam-3484	249	82	,	,	PUNCT
ejpam-3484	249	83	t	t	PROPN
ejpam-3484	249	84	is	be	AUX
ejpam-3484	249	85	a	a	DET
ejpam-3484	249	86	forcing	forcing	NOUN
ejpam-3484	249	87	subset	subset	NOUN
ejpam-3484	249	88	for	for	ADP
ejpam-3484	249	89	s.	s.	PROPN
ejpam-3484	249	90	c.	c.	PROPN
ejpam-3484	249	91	armada	armada	PROPN
ejpam-3484	249	92	,	,	PUNCT
ejpam-3484	249	93	s.	s.	PROPN
ejpam-3484	249	94	canoy	canoy	PROPN
ejpam-3484	249	95	jr	jr	PROPN
ejpam-3484	249	96	.	.	PROPN
ejpam-3484	249	97	/	/	SYM
ejpam-3484	249	98	eur	eur	PROPN
ejpam-3484	249	99	.	.	PUNCT
ejpam-3484	250	1	j.	j.	PROPN
ejpam-3484	250	2	pure	pure	PROPN
ejpam-3484	250	3	appl	appl	PROPN
ejpam-3484	250	4	.	.	PROPN
ejpam-3484	250	5	math	math	PROPN
ejpam-3484	250	6	,	,	PUNCT
ejpam-3484	250	7	12	12	NUM
ejpam-3484	250	8	(	(	PUNCT
ejpam-3484	250	9	4	4	NUM
ejpam-3484	250	10	)	)	PUNCT
ejpam-3484	250	11	(	(	PUNCT
ejpam-3484	250	12	2019	2019	NUM
ejpam-3484	250	13	)	)	PUNCT
ejpam-3484	250	14	,	,	PUNCT
ejpam-3484	250	15	1371	1371	NUM
ejpam-3484	250	16	-	-	SYM
ejpam-3484	250	17	1381	1381	NUM
ejpam-3484	250	18	1378	1378	NUM
ejpam-3484	250	19	therefore	therefore	ADV
ejpam-3484	250	20	,	,	PUNCT
ejpam-3484	250	21	fγi(s	fγi(s	NOUN
ejpam-3484	250	22	)	)	PUNCT
ejpam-3484	250	23	≤	≤	NOUN
ejpam-3484	250	24	|t	|t	VERB
ejpam-3484	250	25	|	|	ADV
ejpam-3484	250	26	.	.	PUNCT
ejpam-3484	251	1	suppose	suppose	VERB
ejpam-3484	251	2	that	that	SCONJ
ejpam-3484	251	3	there	there	PRON
ejpam-3484	251	4	exists	exist	VERB
ejpam-3484	251	5	b	b	NOUN
ejpam-3484	251	6	s	s	VERB
ejpam-3484	251	7	such	such	ADJ
ejpam-3484	251	8	that	that	DET
ejpam-3484	251	9	fγi(s	fγi(s	NOUN
ejpam-3484	251	10	)	)	PUNCT
ejpam-3484	251	11	=	=	PRON
ejpam-3484	251	12	|b|	|b|	PROPN
ejpam-3484	251	13	<	<	X
ejpam-3484	251	14	|t	|t	VERB
ejpam-3484	251	15	|	|	ADV
ejpam-3484	251	16	.	.	PUNCT
ejpam-3484	252	1	suppose	suppose	VERB
ejpam-3484	252	2	that	that	SCONJ
ejpam-3484	252	3	b	b	PROPN
ejpam-3484	252	4	∩	∩	ADJ
ejpam-3484	252	5	u	u	NOUN
ejpam-3484	252	6	6=	6=	PROPN
ejpam-3484	252	7	∅	∅	NOUN
ejpam-3484	252	8	,	,	PUNCT
ejpam-3484	252	9	say	say	VERB
ejpam-3484	252	10	w	w	PROPN
ejpam-3484	252	11	∈	∈	PROPN
ejpam-3484	252	12	b	b	PROPN
ejpam-3484	252	13	∩	∩	ADJ
ejpam-3484	252	14	u	u	NOUN
ejpam-3484	252	15	.	.	PUNCT
ejpam-3484	253	1	let	let	VERB
ejpam-3484	253	2	v	v	NUM
ejpam-3484	253	3	∈	∈	PROPN
ejpam-3484	253	4	v	v	NOUN
ejpam-3484	253	5	(	(	PUNCT
ejpam-3484	253	6	g)\t	g)\t	NOUN
ejpam-3484	253	7	such	such	ADJ
ejpam-3484	253	8	that	that	PRON
ejpam-3484	253	9	w	w	PROPN
ejpam-3484	253	10	=	=	PUNCT
ejpam-3484	253	11	xv	xv	PROPN
ejpam-3484	253	12	∈	∈	PROPN
ejpam-3484	253	13	v	v	PROPN
ejpam-3484	253	14	(	(	PUNCT
ejpam-3484	253	15	hv	hv	PROPN
ejpam-3484	253	16	)	)	PUNCT
ejpam-3484	253	17	.	.	PUNCT
ejpam-3484	254	1	pick	pick	VERB
ejpam-3484	254	2	y	y	PROPN
ejpam-3484	254	3	∈	∈	PROPN
ejpam-3484	254	4	t	t	PROPN
ejpam-3484	254	5	∩ng(v	∩ng(v	PROPN
ejpam-3484	254	6	)	)	PUNCT
ejpam-3484	254	7	and	and	CCONJ
ejpam-3484	254	8	let	let	VERB
ejpam-3484	254	9	t	t	NOUN
ejpam-3484	254	10	′	′	NUM
ejpam-3484	254	11	=	=	PUNCT
ejpam-3484	254	12	t\{y	t\{y	VERB
ejpam-3484	254	13	}	}	PUNCT
ejpam-3484	254	14	and	and	CCONJ
ejpam-3484	254	15	u	u	NOUN
ejpam-3484	254	16	′	′	NOUN
ejpam-3484	254	17	=	=	PUNCT
ejpam-3484	254	18	u	u	NOUN
ejpam-3484	254	19	∪	∪	X
ejpam-3484	254	20	{	{	PUNCT
ejpam-3484	254	21	xy	xy	NOUN
ejpam-3484	254	22	}	}	PUNCT
ejpam-3484	254	23	.	.	PUNCT
ejpam-3484	255	1	then	then	ADV
ejpam-3484	255	2	s′	s′	ADJ
ejpam-3484	255	3	=	=	SYM
ejpam-3484	255	4	t	t	NOUN
ejpam-3484	255	5	′	′	NOUN
ejpam-3484	255	6	∪	∪	ADP
ejpam-3484	255	7	u	u	NOUN
ejpam-3484	255	8	′	′	NOUN
ejpam-3484	255	9	is	be	AUX
ejpam-3484	255	10	a	a	DET
ejpam-3484	255	11	γi	γi	NOUN
ejpam-3484	255	12	-	-	PUNCT
ejpam-3484	255	13	set	set	NOUN
ejpam-3484	255	14	of	of	ADP
ejpam-3484	255	15	g	g	PROPN
ejpam-3484	255	16	◦	◦	NOUN
ejpam-3484	255	17	h	h	NOUN
ejpam-3484	255	18	with	with	ADP
ejpam-3484	255	19	s′	s′	NUM
ejpam-3484	255	20	6=	6=	NUM
ejpam-3484	255	21	s	s	NOUN
ejpam-3484	255	22	and	and	CCONJ
ejpam-3484	255	23	b	b	NOUN
ejpam-3484	255	24	⊆	⊆	NUM
ejpam-3484	255	25	s′	s′	NOUN
ejpam-3484	255	26	,	,	PUNCT
ejpam-3484	255	27	a	a	DET
ejpam-3484	255	28	contradiction	contradiction	NOUN
ejpam-3484	255	29	.	.	PUNCT
ejpam-3484	256	1	hence	hence	ADV
ejpam-3484	256	2	,	,	PUNCT
ejpam-3484	256	3	b	b	PROPN
ejpam-3484	256	4	t	t	PROPN
ejpam-3484	256	5	.	.	PUNCT
ejpam-3484	257	1	let	let	VERB
ejpam-3484	257	2	z	z	NOUN
ejpam-3484	257	3	∈	∈	PROPN
ejpam-3484	257	4	t\b	t\b	NOUN
ejpam-3484	257	5	and	and	CCONJ
ejpam-3484	257	6	let	let	VERB
ejpam-3484	257	7	sz	sz	NOUN
ejpam-3484	257	8	=	=	VERB
ejpam-3484	257	9	(	(	PUNCT
ejpam-3484	257	10	t\{z	t\{z	NOUN
ejpam-3484	257	11	}	}	PUNCT
ejpam-3484	257	12	)	)	PUNCT
ejpam-3484	257	13	∪	∪	NOUN
ejpam-3484	257	14	(	(	PUNCT
ejpam-3484	257	15	u	u	NOUN
ejpam-3484	257	16	∪	∪	X
ejpam-3484	257	17	{	{	PUNCT
ejpam-3484	257	18	xz	xz	NOUN
ejpam-3484	257	19	}	}	PUNCT
ejpam-3484	257	20	)	)	PUNCT
ejpam-3484	257	21	where	where	SCONJ
ejpam-3484	257	22	〈	〈	PROPN
ejpam-3484	257	23	{	{	PUNCT
ejpam-3484	257	24	xz	xz	PROPN
ejpam-3484	257	25	}	}	PUNCT
ejpam-3484	257	26	〉	〉	PROPN
ejpam-3484	257	27	∼=	∼=	PROPN
ejpam-3484	257	28	〈	〈	PROPN
ejpam-3484	257	29	x	x	SYM
ejpam-3484	257	30	〉	〉	PROPN
ejpam-3484	257	31	and	and	CCONJ
ejpam-3484	257	32	xz	xz	PROPN
ejpam-3484	257	33	∈	∈	PROPN
ejpam-3484	257	34	v	v	PROPN
ejpam-3484	257	35	(	(	PUNCT
ejpam-3484	257	36	hz	hz	PROPN
ejpam-3484	257	37	)	)	PUNCT
ejpam-3484	257	38	.	.	PUNCT
ejpam-3484	258	1	then	then	ADV
ejpam-3484	258	2	sz	sz	PROPN
ejpam-3484	258	3	is	be	AUX
ejpam-3484	258	4	a	a	DET
ejpam-3484	258	5	γi	γi	NOUN
ejpam-3484	258	6	-	-	PUNCT
ejpam-3484	258	7	set	set	NOUN
ejpam-3484	258	8	of	of	ADP
ejpam-3484	258	9	g	g	PROPN
ejpam-3484	258	10	◦	◦	NOUN
ejpam-3484	258	11	h	h	NOUN
ejpam-3484	258	12	,	,	PUNCT
ejpam-3484	258	13	sz	sz	PROPN
ejpam-3484	258	14	6=	6=	ADP
ejpam-3484	258	15	s	s	NOUN
ejpam-3484	258	16	and	and	CCONJ
ejpam-3484	258	17	b	b	NOUN
ejpam-3484	258	18	⊆	⊆	NUM
ejpam-3484	258	19	sz	sz	NOUN
ejpam-3484	258	20	.	.	PUNCT
ejpam-3484	259	1	this	this	PRON
ejpam-3484	259	2	is	be	AUX
ejpam-3484	259	3	a	a	DET
ejpam-3484	259	4	contradiction	contradiction	NOUN
ejpam-3484	259	5	since	since	SCONJ
ejpam-3484	259	6	b	b	NOUN
ejpam-3484	259	7	is	be	AUX
ejpam-3484	259	8	a	a	DET
ejpam-3484	259	9	forcing	forcing	NOUN
ejpam-3484	259	10	subset	subset	NOUN
ejpam-3484	259	11	for	for	ADP
ejpam-3484	259	12	s.	s.	PROPN
ejpam-3484	259	13	therefore	therefore	ADV
ejpam-3484	259	14	,	,	PUNCT
ejpam-3484	259	15	fγi(s	fγi(s	NOUN
ejpam-3484	259	16	)	)	PUNCT
ejpam-3484	259	17	=	=	PRON
ejpam-3484	260	1	|b|	|b|	PROPN
ejpam-3484	260	2	=	=	PUNCT
ejpam-3484	260	3	|t	|t	PROPN
ejpam-3484	260	4	|	|	ADV
ejpam-3484	260	5	=	=	SYM
ejpam-3484	260	6	γi(g	γi(g	NOUN
ejpam-3484	260	7	)	)	PUNCT
ejpam-3484	260	8	.	.	PUNCT
ejpam-3484	261	1	now	now	ADV
ejpam-3484	261	2	,	,	PUNCT
ejpam-3484	261	3	suppose	suppose	VERB
ejpam-3484	261	4	that	that	SCONJ
ejpam-3484	261	5	h	h	NOUN
ejpam-3484	261	6	does	do	AUX
ejpam-3484	261	7	not	not	PART
ejpam-3484	261	8	have	have	VERB
ejpam-3484	261	9	a	a	DET
ejpam-3484	261	10	unique	unique	ADJ
ejpam-3484	261	11	γi	γi	NOUN
ejpam-3484	261	12	-	-	PUNCT
ejpam-3484	261	13	set	set	NOUN
ejpam-3484	261	14	.	.	PUNCT
ejpam-3484	262	1	let	let	VERB
ejpam-3484	262	2	c	c	PRON
ejpam-3484	262	3	be	be	AUX
ejpam-3484	262	4	a	a	DET
ejpam-3484	262	5	γi	γi	NOUN
ejpam-3484	262	6	-	-	PUNCT
ejpam-3484	262	7	set	set	NOUN
ejpam-3484	262	8	of	of	ADP
ejpam-3484	262	9	g	g	NOUN
ejpam-3484	262	10	◦	◦	NOUN
ejpam-3484	262	11	h	h	NOUN
ejpam-3484	262	12	and	and	CCONJ
ejpam-3484	262	13	let	let	VERB
ejpam-3484	262	14	s	s	PRON
ejpam-3484	262	15	be	be	AUX
ejpam-3484	262	16	a	a	DET
ejpam-3484	262	17	forcing	forcing	NOUN
ejpam-3484	262	18	subset	subset	NOUN
ejpam-3484	262	19	for	for	ADP
ejpam-3484	262	20	c.	c.	NOUN
ejpam-3484	262	21	by	by	ADP
ejpam-3484	262	22	theorem	theorem	NOUN
ejpam-3484	262	23	3.17	3.17	NUM
ejpam-3484	262	24	,	,	PUNCT
ejpam-3484	262	25	c	c	PROPN
ejpam-3484	262	26	=	=	SYM
ejpam-3484	262	27	a∪	a∪	PROPN
ejpam-3484	262	28	(	(	PUNCT
ejpam-3484	262	29	⋃	⋃	VERB
ejpam-3484	262	30	v∈v	v∈v	NOUN
ejpam-3484	262	31	\a	\a	ADJ
ejpam-3484	262	32	sv	sv	PROPN
ejpam-3484	262	33	)	)	PUNCT
ejpam-3484	262	34	where	where	SCONJ
ejpam-3484	262	35	a	a	PRON
ejpam-3484	262	36	is	be	AUX
ejpam-3484	262	37	an	an	DET
ejpam-3484	262	38	independent	independent	ADJ
ejpam-3484	262	39	set	set	NOUN
ejpam-3484	262	40	of	of	ADP
ejpam-3484	262	41	g	g	PROPN
ejpam-3484	262	42	and	and	CCONJ
ejpam-3484	262	43	sv	sv	PROPN
ejpam-3484	262	44	is	be	AUX
ejpam-3484	262	45	a	a	DET
ejpam-3484	262	46	γi	γi	NOUN
ejpam-3484	262	47	-	-	PUNCT
ejpam-3484	262	48	set	set	NOUN
ejpam-3484	262	49	of	of	ADP
ejpam-3484	262	50	hv	hv	NOUN
ejpam-3484	262	51	for	for	ADP
ejpam-3484	262	52	each	each	DET
ejpam-3484	262	53	v	v	NUM
ejpam-3484	262	54	∈	∈	PROPN
ejpam-3484	262	55	v	v	NOUN
ejpam-3484	262	56	(	(	PUNCT
ejpam-3484	262	57	g)\a	g)\a	NOUN
ejpam-3484	262	58	.	.	PUNCT
ejpam-3484	262	59	suppose	suppose	VERB
ejpam-3484	262	60	that	that	SCONJ
ejpam-3484	262	61	s	s	VERB
ejpam-3484	262	62	6=	6=	ADP
ejpam-3484	262	63	c	c	X
ejpam-3484	262	64	,	,	PUNCT
ejpam-3484	262	65	say	say	VERB
ejpam-3484	262	66	w	w	PROPN
ejpam-3484	262	67	∈	∈	PROPN
ejpam-3484	262	68	c\s	c\s	NOUN
ejpam-3484	262	69	.	.	PUNCT
ejpam-3484	263	1	let	let	VERB
ejpam-3484	263	2	z	z	NOUN
ejpam-3484	263	3	∈	∈	PROPN
ejpam-3484	263	4	v	v	ADP
ejpam-3484	263	5	(	(	PUNCT
ejpam-3484	263	6	g	g	NOUN
ejpam-3484	263	7	)	)	PUNCT
ejpam-3484	263	8	such	such	ADJ
ejpam-3484	263	9	that	that	SCONJ
ejpam-3484	263	10	w	w	PROPN
ejpam-3484	263	11	∈	∈	PROPN
ejpam-3484	263	12	v	v	ADP
ejpam-3484	263	13	(	(	PUNCT
ejpam-3484	263	14	z	z	NOUN
ejpam-3484	263	15	+	+	NOUN
ejpam-3484	263	16	hz	hz	NOUN
ejpam-3484	263	17	)	)	PUNCT
ejpam-3484	263	18	.	.	PUNCT
ejpam-3484	264	1	if	if	SCONJ
ejpam-3484	264	2	w	w	PROPN
ejpam-3484	264	3	=	=	SYM
ejpam-3484	264	4	z	z	PROPN
ejpam-3484	264	5	,	,	PUNCT
ejpam-3484	264	6	then	then	ADV
ejpam-3484	264	7	w	w	PROPN
ejpam-3484	264	8	∈	∈	PROPN
ejpam-3484	264	9	a.	a.	NOUN
ejpam-3484	264	10	let	let	VERB
ejpam-3484	264	11	a′	a′	NOUN
ejpam-3484	264	12	=	=	SYM
ejpam-3484	264	13	a\{w	a\{w	NOUN
ejpam-3484	264	14	}	}	PUNCT
ejpam-3484	264	15	and	and	CCONJ
ejpam-3484	264	16	let	let	VERB
ejpam-3484	264	17	sw	sw	PROPN
ejpam-3484	264	18	=	=	PRON
ejpam-3484	264	19	{	{	PUNCT
ejpam-3484	264	20	xw	xw	PROPN
ejpam-3484	264	21	}	}	PUNCT
ejpam-3484	264	22	be	be	AUX
ejpam-3484	264	23	a	a	DET
ejpam-3484	264	24	γi	γi	NOUN
ejpam-3484	264	25	-	-	PUNCT
ejpam-3484	264	26	set	set	NOUN
ejpam-3484	264	27	of	of	ADP
ejpam-3484	264	28	hw	hw	PRON
ejpam-3484	264	29	.	.	PUNCT
ejpam-3484	265	1	then	then	ADV
ejpam-3484	265	2	by	by	ADP
ejpam-3484	265	3	theorem	theorem	NOUN
ejpam-3484	265	4	3.17	3.17	NUM
ejpam-3484	265	5	,	,	PUNCT
ejpam-3484	265	6	c	c	NOUN
ejpam-3484	265	7	′	′	NOUN
ejpam-3484	266	1	=	=	PUNCT
ejpam-3484	266	2	a′	a′	NOUN
ejpam-3484	266	3	∪	∪	X
ejpam-3484	266	4	(	(	PUNCT
ejpam-3484	266	5	⋃	⋃	NOUN
ejpam-3484	266	6	v∈v	v∈v	NOUN
ejpam-3484	266	7	\a′	\a′	ADP
ejpam-3484	266	8	sv	sv	PROPN
ejpam-3484	266	9	)	)	PUNCT
ejpam-3484	266	10	is	be	AUX
ejpam-3484	266	11	a	a	DET
ejpam-3484	266	12	γi	γi	NOUN
ejpam-3484	266	13	-	-	PUNCT
ejpam-3484	266	14	set	set	NOUN
ejpam-3484	266	15	of	of	ADP
ejpam-3484	266	16	g	g	PROPN
ejpam-3484	266	17	◦	◦	NOUN
ejpam-3484	266	18	h	h	NOUN
ejpam-3484	266	19	with	with	ADP
ejpam-3484	266	20	c	c	NOUN
ejpam-3484	266	21	′	′	NUM
ejpam-3484	266	22	6=	6=	NUM
ejpam-3484	266	23	c	c	NOUN
ejpam-3484	266	24	and	and	CCONJ
ejpam-3484	266	25	s	s	VERB
ejpam-3484	266	26	⊆	⊆	NUM
ejpam-3484	266	27	c	c	NOUN
ejpam-3484	266	28	′.	′.	NOUN
ejpam-3484	266	29	if	if	SCONJ
ejpam-3484	266	30	w	w	PROPN
ejpam-3484	266	31	6=	6=	PROPN
ejpam-3484	266	32	z	z	PROPN
ejpam-3484	266	33	,	,	PUNCT
ejpam-3484	266	34	then	then	ADV
ejpam-3484	266	35	sz	sz	NOUN
ejpam-3484	266	36	=	=	SYM
ejpam-3484	266	37	{	{	PUNCT
ejpam-3484	266	38	w	w	NOUN
ejpam-3484	266	39	}	}	PUNCT
ejpam-3484	266	40	is	be	AUX
ejpam-3484	266	41	a	a	DET
ejpam-3484	266	42	γi	γi	NOUN
ejpam-3484	266	43	-	-	PUNCT
ejpam-3484	266	44	set	set	NOUN
ejpam-3484	266	45	of	of	ADP
ejpam-3484	266	46	hz	hz	PROPN
ejpam-3484	266	47	.	.	PROPN
ejpam-3484	267	1	let	let	VERB
ejpam-3484	267	2	s∗z	s∗z	ADJ
ejpam-3484	267	3	=	=	SYM
ejpam-3484	267	4	{	{	PUNCT
ejpam-3484	267	5	w′	w′	NOUN
ejpam-3484	267	6	}	}	PUNCT
ejpam-3484	267	7	be	be	VERB
ejpam-3484	267	8	a	a	DET
ejpam-3484	267	9	γi	γi	NOUN
ejpam-3484	267	10	-	-	PUNCT
ejpam-3484	267	11	set	set	NOUN
ejpam-3484	267	12	of	of	ADP
ejpam-3484	267	13	hz	hz	VERB
ejpam-3484	267	14	with	with	ADP
ejpam-3484	267	15	w	w	PROPN
ejpam-3484	267	16	6=	6=	PROPN
ejpam-3484	267	17	w′.	w′.	X
ejpam-3484	267	18	then	then	ADV
ejpam-3484	267	19	c∗	c∗	PROPN
ejpam-3484	267	20	=	=	PUNCT
ejpam-3484	267	21	a	a	DET
ejpam-3484	267	22	∪	∪	X
ejpam-3484	267	23	(	(	PUNCT
ejpam-3484	267	24	⋃	⋃	VERB
ejpam-3484	267	25	v∈v	v∈v	NOUN
ejpam-3484	267	26	\(a∪{z	\(a∪{z	NOUN
ejpam-3484	267	27	}	}	PUNCT
ejpam-3484	267	28	)	)	PUNCT
ejpam-3484	267	29	sv	sv	NOUN
ejpam-3484	267	30	)	)	PUNCT
ejpam-3484	267	31	∪	∪	ADP
ejpam-3484	267	32	s∗z	s∗z	NUM
ejpam-3484	267	33	is	be	AUX
ejpam-3484	267	34	a	a	DET
ejpam-3484	267	35	γi	γi	NOUN
ejpam-3484	267	36	-	-	PUNCT
ejpam-3484	267	37	set	set	NOUN
ejpam-3484	267	38	of	of	ADP
ejpam-3484	267	39	g	g	PROPN
ejpam-3484	267	40	◦	◦	NOUN
ejpam-3484	267	41	h	h	NOUN
ejpam-3484	267	42	with	with	ADP
ejpam-3484	267	43	c∗	c∗	PROPN
ejpam-3484	267	44	6=	6=	PROPN
ejpam-3484	267	45	c	c	PROPN
ejpam-3484	267	46	and	and	CCONJ
ejpam-3484	267	47	s	s	NOUN
ejpam-3484	267	48	⊆	⊆	NUM
ejpam-3484	267	49	c∗.	c∗.	NOUN
ejpam-3484	267	50	in	in	ADP
ejpam-3484	267	51	either	either	DET
ejpam-3484	267	52	case	case	NOUN
ejpam-3484	267	53	,	,	PUNCT
ejpam-3484	267	54	we	we	PRON
ejpam-3484	267	55	get	get	VERB
ejpam-3484	267	56	a	a	DET
ejpam-3484	267	57	contradiction	contradiction	NOUN
ejpam-3484	267	58	.	.	PUNCT
ejpam-3484	268	1	thus	thus	ADV
ejpam-3484	268	2	,	,	PUNCT
ejpam-3484	268	3	s	s	VERB
ejpam-3484	268	4	=	=	SYM
ejpam-3484	268	5	c	c	PROPN
ejpam-3484	268	6	and	and	CCONJ
ejpam-3484	268	7	fγi(c	fγi(c	PROPN
ejpam-3484	268	8	)	)	PUNCT
ejpam-3484	268	9	=	=	SYM
ejpam-3484	268	10	|c|	|c|	PROPN
ejpam-3484	268	11	=	=	PUNCT
ejpam-3484	268	12	n.	n.	NOUN
ejpam-3484	268	13	consequently	consequently	ADV
ejpam-3484	268	14	,	,	PUNCT
ejpam-3484	268	15	fγi(g	fγi(g	PROPN
ejpam-3484	268	16	◦	◦	NOUN
ejpam-3484	268	17	h	h	NOUN
ejpam-3484	268	18	)	)	PUNCT
ejpam-3484	268	19	=	=	SYM
ejpam-3484	268	20	n.	n.	NOUN
ejpam-3484	268	21	theorem	theorem	VERB
ejpam-3484	268	22	3.20	3.20	NUM
ejpam-3484	268	23	.	.	PUNCT
ejpam-3484	269	1	let	let	VERB
ejpam-3484	269	2	g	g	PRON
ejpam-3484	269	3	be	be	AUX
ejpam-3484	269	4	a	a	DET
ejpam-3484	269	5	connected	connected	ADJ
ejpam-3484	269	6	graph	graph	NOUN
ejpam-3484	269	7	of	of	ADP
ejpam-3484	269	8	order	order	NOUN
ejpam-3484	269	9	n	n	NOUN
ejpam-3484	269	10	and	and	CCONJ
ejpam-3484	269	11	let	let	VERB
ejpam-3484	269	12	h	h	NOUN
ejpam-3484	269	13	be	be	AUX
ejpam-3484	269	14	any	any	DET
ejpam-3484	269	15	graph	graph	NOUN
ejpam-3484	269	16	with	with	ADP
ejpam-3484	269	17	γi(h	γi(h	NOUN
ejpam-3484	269	18	)	)	PUNCT
ejpam-3484	269	19	6=	6=	ADP
ejpam-3484	270	1	1	1	X
ejpam-3484	270	2	.	.	PUNCT
ejpam-3484	271	1	then	then	ADV
ejpam-3484	271	2	fγi(g	fγi(g	PROPN
ejpam-3484	271	3	◦	◦	NOUN
ejpam-3484	271	4	h	h	NOUN
ejpam-3484	271	5	)	)	PUNCT
ejpam-3484	271	6	=	=	PRON
ejpam-3484	271	7	{	{	PUNCT
ejpam-3484	271	8	fα(g	fα(g	PUNCT
ejpam-3484	271	9	)	)	PUNCT
ejpam-3484	271	10	,	,	PUNCT
ejpam-3484	271	11	if	if	SCONJ
ejpam-3484	271	12	h	h	NOUN
ejpam-3484	271	13	has	have	VERB
ejpam-3484	271	14	a	a	DET
ejpam-3484	271	15	unique	unique	ADJ
ejpam-3484	271	16	γi	γi	NOUN
ejpam-3484	271	17	-	-	PUNCT
ejpam-3484	271	18	set	set	VERB
ejpam-3484	271	19	[	[	X
ejpam-3484	271	20	n−	n−	NOUN
ejpam-3484	271	21	α(g)][fγi(h	α(g)][fγi(h	NOUN
ejpam-3484	271	22	)	)	PUNCT
ejpam-3484	271	23	]	]	PUNCT
ejpam-3484	271	24	,	,	PUNCT
ejpam-3484	271	25	if	if	SCONJ
ejpam-3484	271	26	h	h	NOUN
ejpam-3484	271	27	has	have	VERB
ejpam-3484	271	28	no	no	DET
ejpam-3484	271	29	unique	unique	ADJ
ejpam-3484	271	30	γi	γi	NOUN
ejpam-3484	271	31	-	-	PUNCT
ejpam-3484	271	32	sets	set	NOUN
ejpam-3484	271	33	.	.	PUNCT
ejpam-3484	272	1	in	in	ADP
ejpam-3484	272	2	particular	particular	ADJ
ejpam-3484	272	3	,	,	PUNCT
ejpam-3484	272	4	fγi(g	fγi(g	PROPN
ejpam-3484	272	5	◦	◦	NOUN
ejpam-3484	272	6	h	h	NOUN
ejpam-3484	272	7	)	)	PUNCT
ejpam-3484	272	8	=	=	SYM
ejpam-3484	272	9	0	0	PUNCT
ejpam-3484	272	10	if	if	SCONJ
ejpam-3484	272	11	g	g	PROPN
ejpam-3484	272	12	has	have	VERB
ejpam-3484	272	13	a	a	DET
ejpam-3484	272	14	unique	unique	ADJ
ejpam-3484	272	15	α	α	NOUN
ejpam-3484	272	16	-	-	PUNCT
ejpam-3484	272	17	set	set	VERB
ejpam-3484	272	18	and	and	CCONJ
ejpam-3484	272	19	h	h	NOUN
ejpam-3484	272	20	has	have	VERB
ejpam-3484	272	21	a	a	DET
ejpam-3484	272	22	unique	unique	ADJ
ejpam-3484	272	23	γi	γi	NOUN
ejpam-3484	272	24	-	-	PUNCT
ejpam-3484	272	25	set	set	NOUN
ejpam-3484	272	26	.	.	PUNCT
ejpam-3484	273	1	proof	proof	NOUN
ejpam-3484	273	2	.	.	PUNCT
ejpam-3484	274	1	since	since	SCONJ
ejpam-3484	274	2	γi(h	γi(h	NOUN
ejpam-3484	274	3	)	)	PUNCT
ejpam-3484	274	4	≥	≥	NOUN
ejpam-3484	274	5	2	2	NUM
ejpam-3484	274	6	,	,	PUNCT
ejpam-3484	274	7	by	by	ADP
ejpam-3484	274	8	theorem	theorem	NOUN
ejpam-3484	274	9	3.18	3.18	NUM
ejpam-3484	274	10	,	,	PUNCT
ejpam-3484	274	11	γi(g	γi(g	PUNCT
ejpam-3484	274	12	◦	◦	NOUN
ejpam-3484	274	13	h	h	NOUN
ejpam-3484	274	14	)	)	PUNCT
ejpam-3484	274	15	=	=	SYM
ejpam-3484	274	16	α(g	α(g	NUM
ejpam-3484	274	17	)	)	PUNCT
ejpam-3484	274	18	+	+	CCONJ
ejpam-3484	275	1	[	[	X
ejpam-3484	275	2	n−	n−	NOUN
ejpam-3484	275	3	α(g)]γi(h	α(g)]γi(h	NOUN
ejpam-3484	275	4	)	)	PUNCT
ejpam-3484	275	5	.	.	PUNCT
ejpam-3484	276	1	let	let	VERB
ejpam-3484	276	2	t	t	NOUN
ejpam-3484	276	3	be	be	AUX
ejpam-3484	276	4	a	a	DET
ejpam-3484	276	5	maximum	maximum	ADJ
ejpam-3484	276	6	independent	independent	ADJ
ejpam-3484	276	7	set	set	NOUN
ejpam-3484	276	8	of	of	ADP
ejpam-3484	276	9	g.	g.	PROPN
ejpam-3484	276	10	then	then	ADV
ejpam-3484	276	11	|t	|t	VERB
ejpam-3484	277	1	|	|	ADV
ejpam-3484	277	2	=	=	SYM
ejpam-3484	277	3	α(g	α(g	NUM
ejpam-3484	277	4	)	)	PUNCT
ejpam-3484	277	5	and	and	CCONJ
ejpam-3484	277	6	|v	|v	PROPN
ejpam-3484	277	7	(	(	PUNCT
ejpam-3484	277	8	g)\t	g)\t	NOUN
ejpam-3484	277	9	|	|	NOUN
ejpam-3484	277	10	=	=	SYM
ejpam-3484	277	11	n	n	CCONJ
ejpam-3484	277	12	−	−	PROPN
ejpam-3484	277	13	α(g	α(g	NUM
ejpam-3484	277	14	)	)	PUNCT
ejpam-3484	277	15	.	.	PUNCT
ejpam-3484	278	1	consider	consider	VERB
ejpam-3484	278	2	the	the	DET
ejpam-3484	278	3	following	follow	VERB
ejpam-3484	278	4	cases	case	NOUN
ejpam-3484	278	5	:	:	PUNCT
ejpam-3484	278	6	case	case	NOUN
ejpam-3484	278	7	1	1	NUM
ejpam-3484	278	8	:	:	PUNCT
ejpam-3484	278	9	suppose	suppose	VERB
ejpam-3484	278	10	that	that	SCONJ
ejpam-3484	278	11	h	h	NOUN
ejpam-3484	278	12	has	have	VERB
ejpam-3484	278	13	a	a	DET
ejpam-3484	278	14	unique	unique	ADJ
ejpam-3484	278	15	γi	γi	NOUN
ejpam-3484	278	16	-	-	PUNCT
ejpam-3484	278	17	set	set	NOUN
ejpam-3484	278	18	,	,	PUNCT
ejpam-3484	278	19	say	say	VERB
ejpam-3484	278	20	r.	r.	PROPN
ejpam-3484	278	21	for	for	ADP
ejpam-3484	278	22	each	each	DET
ejpam-3484	278	23	v	v	NUM
ejpam-3484	278	24	∈	∈	PROPN
ejpam-3484	278	25	v	v	NOUN
ejpam-3484	278	26	(	(	PUNCT
ejpam-3484	278	27	g	g	NOUN
ejpam-3484	278	28	)	)	PUNCT
ejpam-3484	278	29	,	,	PUNCT
ejpam-3484	278	30	let	let	VERB
ejpam-3484	278	31	rv	rv	PRON
ejpam-3484	278	32	⊆	⊆	NUM
ejpam-3484	278	33	v	v	X
ejpam-3484	278	34	(	(	PUNCT
ejpam-3484	278	35	hv	hv	NOUN
ejpam-3484	278	36	)	)	PUNCT
ejpam-3484	278	37	such	such	ADJ
ejpam-3484	278	38	that	that	SCONJ
ejpam-3484	278	39	〈	〈	PROPN
ejpam-3484	278	40	rv	rv	PROPN
ejpam-3484	278	41	〉	〉	NOUN
ejpam-3484	278	42	∼=	∼=	PROPN
ejpam-3484	278	43	〈	〈	PROPN
ejpam-3484	278	44	r	r	PROPN
ejpam-3484	278	45	〉	〉	PROPN
ejpam-3484	278	46	.	.	PUNCT
ejpam-3484	278	47	suppose	suppose	VERB
ejpam-3484	278	48	that	that	SCONJ
ejpam-3484	278	49	g	g	PROPN
ejpam-3484	278	50	has	have	VERB
ejpam-3484	278	51	a	a	DET
ejpam-3484	278	52	unique	unique	ADJ
ejpam-3484	278	53	α	α	NOUN
ejpam-3484	278	54	-	-	NOUN
ejpam-3484	278	55	set	set	NOUN
ejpam-3484	278	56	,	,	PUNCT
ejpam-3484	278	57	say	say	VERB
ejpam-3484	278	58	d.	d.	PROPN
ejpam-3484	278	59	then	then	ADV
ejpam-3484	278	60	by	by	ADP
ejpam-3484	278	61	theorem	theorem	NOUN
ejpam-3484	278	62	3.18	3.18	NUM
ejpam-3484	278	63	,	,	PUNCT
ejpam-3484	278	64	c	c	PROPN
ejpam-3484	278	65	=	=	SYM
ejpam-3484	278	66	d∪	d∪	PROPN
ejpam-3484	278	67	(	(	PUNCT
ejpam-3484	278	68	⋃	⋃	NOUN
ejpam-3484	278	69	v∈v	v∈v	NOUN
ejpam-3484	278	70	(	(	PUNCT
ejpam-3484	278	71	g)\d	g)\d	NOUN
ejpam-3484	278	72	rv	rv	PROPN
ejpam-3484	278	73	)	)	PUNCT
ejpam-3484	278	74	is	be	AUX
ejpam-3484	278	75	the	the	DET
ejpam-3484	278	76	unique	unique	ADJ
ejpam-3484	278	77	γi	γi	NOUN
ejpam-3484	278	78	-	-	PUNCT
ejpam-3484	278	79	set	set	NOUN
ejpam-3484	278	80	of	of	ADP
ejpam-3484	278	81	g	g	PROPN
ejpam-3484	278	82	◦	◦	NOUN
ejpam-3484	278	83	h.	h.	NOUN
ejpam-3484	278	84	thus	thus	ADV
ejpam-3484	278	85	,	,	PUNCT
ejpam-3484	278	86	by	by	ADP
ejpam-3484	278	87	remark	remark	NOUN
ejpam-3484	278	88	3.1(i	3.1(i	NUM
ejpam-3484	278	89	)	)	PUNCT
ejpam-3484	278	90	,	,	PUNCT
ejpam-3484	278	91	fγi(g	fγi(g	PROPN
ejpam-3484	278	92	◦	◦	NOUN
ejpam-3484	278	93	h	h	NOUN
ejpam-3484	278	94	)	)	PUNCT
ejpam-3484	278	95	=	=	SYM
ejpam-3484	278	96	0	0	X
ejpam-3484	278	97	.	.	PUNCT
ejpam-3484	278	98	suppose	suppose	VERB
ejpam-3484	278	99	that	that	SCONJ
ejpam-3484	278	100	g	g	PROPN
ejpam-3484	278	101	does	do	AUX
ejpam-3484	278	102	not	not	PART
ejpam-3484	278	103	have	have	VERB
ejpam-3484	278	104	a	a	DET
ejpam-3484	278	105	unique	unique	ADJ
ejpam-3484	278	106	α	α	NOUN
ejpam-3484	278	107	-	-	NOUN
ejpam-3484	278	108	set	set	NOUN
ejpam-3484	278	109	.	.	PUNCT
ejpam-3484	279	1	let	let	VERB
ejpam-3484	279	2	a	a	DET
ejpam-3484	279	3	be	be	AUX
ejpam-3484	279	4	an	an	DET
ejpam-3484	279	5	α	α	NOUN
ejpam-3484	279	6	-	-	PUNCT
ejpam-3484	279	7	set	set	NOUN
ejpam-3484	279	8	of	of	ADP
ejpam-3484	279	9	g	g	NOUN
ejpam-3484	279	10	and	and	CCONJ
ejpam-3484	279	11	let	let	VERB
ejpam-3484	279	12	da	da	NOUN
ejpam-3484	279	13	be	be	AUX
ejpam-3484	279	14	a	a	DET
ejpam-3484	279	15	forcing	forcing	NOUN
ejpam-3484	279	16	subset	subset	NOUN
ejpam-3484	279	17	for	for	ADP
ejpam-3484	279	18	a	a	DET
ejpam-3484	279	19	such	such	ADJ
ejpam-3484	279	20	that	that	PRON
ejpam-3484	279	21	fα(g	fα(g	PUNCT
ejpam-3484	279	22	)	)	PUNCT
ejpam-3484	279	23	=	=	SYM
ejpam-3484	279	24	fα(a	fα(a	NOUN
ejpam-3484	279	25	)	)	PUNCT
ejpam-3484	279	26	=	=	SYM
ejpam-3484	280	1	|da|	|da|	PROPN
ejpam-3484	280	2	.	.	PUNCT
ejpam-3484	281	1	let	let	VERB
ejpam-3484	281	2	c	c	VERB
ejpam-3484	281	3	=	=	PUNCT
ejpam-3484	281	4	a	a	DET
ejpam-3484	281	5	∪	∪	X
ejpam-3484	281	6	(	(	PUNCT
ejpam-3484	281	7	⋃	⋃	NOUN
ejpam-3484	281	8	v∈v	v∈v	NOUN
ejpam-3484	281	9	(	(	PUNCT
ejpam-3484	281	10	g)\a	g)\a	NOUN
ejpam-3484	281	11	rv	rv	PROPN
ejpam-3484	281	12	)	)	PUNCT
ejpam-3484	281	13	.	.	PUNCT
ejpam-3484	282	1	then	then	ADV
ejpam-3484	282	2	,	,	PUNCT
ejpam-3484	282	3	by	by	ADP
ejpam-3484	282	4	theorem	theorem	NOUN
ejpam-3484	282	5	3.18	3.18	NUM
ejpam-3484	282	6	,	,	PUNCT
ejpam-3484	282	7	c	c	PROPN
ejpam-3484	282	8	is	be	AUX
ejpam-3484	282	9	a	a	DET
ejpam-3484	282	10	γi	γi	NOUN
ejpam-3484	282	11	-	-	PUNCT
ejpam-3484	282	12	set	set	NOUN
ejpam-3484	282	13	of	of	ADP
ejpam-3484	282	14	g	g	PROPN
ejpam-3484	282	15	◦	◦	NOUN
ejpam-3484	282	16	h.	h.	PROPN
ejpam-3484	282	17	since	since	SCONJ
ejpam-3484	282	18	each	each	DET
ejpam-3484	282	19	hv	hv	PROPN
ejpam-3484	282	20	has	have	VERB
ejpam-3484	282	21	a	a	DET
ejpam-3484	282	22	unique	unique	ADJ
ejpam-3484	282	23	γi	γi	NOUN
ejpam-3484	282	24	-	-	PUNCT
ejpam-3484	282	25	set	set	VERB
ejpam-3484	282	26	rv	rv	NOUN
ejpam-3484	282	27	,	,	PUNCT
ejpam-3484	282	28	it	it	PRON
ejpam-3484	282	29	follows	follow	VERB
ejpam-3484	282	30	that	that	SCONJ
ejpam-3484	282	31	da	da	PROPN
ejpam-3484	282	32	is	be	AUX
ejpam-3484	282	33	a	a	DET
ejpam-3484	282	34	forcing	forcing	NOUN
ejpam-3484	282	35	subset	subset	NOUN
ejpam-3484	282	36	for	for	ADP
ejpam-3484	282	37	c.	c.	PROPN
ejpam-3484	282	38	thus	thus	ADV
ejpam-3484	282	39	,	,	PUNCT
ejpam-3484	282	40	fγi(g	fγi(g	PROPN
ejpam-3484	282	41	◦	◦	NOUN
ejpam-3484	282	42	h	h	NOUN
ejpam-3484	282	43	)	)	PUNCT
ejpam-3484	282	44	≤	≤	NOUN
ejpam-3484	283	1	fγi(c	fγi(c	PROPN
ejpam-3484	283	2	)	)	PUNCT
ejpam-3484	283	3	≤	≤	NOUN
ejpam-3484	283	4	|da|	|da|	PROPN
ejpam-3484	283	5	=	=	NUM
ejpam-3484	283	6	fα(g	fα(g	PUNCT
ejpam-3484	283	7	)	)	PUNCT
ejpam-3484	283	8	.	.	PUNCT
ejpam-3484	284	1	c.	c.	PROPN
ejpam-3484	284	2	armada	armada	PROPN
ejpam-3484	284	3	,	,	PUNCT
ejpam-3484	284	4	s.	s.	PROPN
ejpam-3484	284	5	canoy	canoy	PROPN
ejpam-3484	284	6	jr	jr	PROPN
ejpam-3484	284	7	.	.	PROPN
ejpam-3484	284	8	/	/	SYM
ejpam-3484	284	9	eur	eur	PROPN
ejpam-3484	284	10	.	.	PUNCT
ejpam-3484	285	1	j.	j.	PROPN
ejpam-3484	285	2	pure	pure	PROPN
ejpam-3484	285	3	appl	appl	PROPN
ejpam-3484	285	4	.	.	PROPN
ejpam-3484	285	5	math	math	PROPN
ejpam-3484	285	6	,	,	PUNCT
ejpam-3484	285	7	12	12	NUM
ejpam-3484	285	8	(	(	PUNCT
ejpam-3484	285	9	4	4	NUM
ejpam-3484	285	10	)	)	PUNCT
ejpam-3484	285	11	(	(	PUNCT
ejpam-3484	285	12	2019	2019	NUM
ejpam-3484	285	13	)	)	PUNCT
ejpam-3484	285	14	,	,	PUNCT
ejpam-3484	285	15	1371	1371	NUM
ejpam-3484	285	16	-	-	SYM
ejpam-3484	285	17	1381	1381	NUM
ejpam-3484	285	18	1379	1379	NUM
ejpam-3484	285	19	next	next	ADV
ejpam-3484	285	20	,	,	PUNCT
ejpam-3484	285	21	let	let	VERB
ejpam-3484	285	22	c0	c0	PROPN
ejpam-3484	285	23	be	be	AUX
ejpam-3484	285	24	a	a	DET
ejpam-3484	285	25	γi	γi	NOUN
ejpam-3484	285	26	-	-	PUNCT
ejpam-3484	285	27	set	set	NOUN
ejpam-3484	285	28	of	of	ADP
ejpam-3484	285	29	g	g	PROPN
ejpam-3484	285	30	◦	◦	NOUN
ejpam-3484	285	31	h	h	NOUN
ejpam-3484	285	32	such	such	ADJ
ejpam-3484	285	33	that	that	SCONJ
ejpam-3484	285	34	fγi(g	fγi(g	PROPN
ejpam-3484	285	35	◦	◦	NOUN
ejpam-3484	285	36	h	h	NOUN
ejpam-3484	285	37	)	)	PUNCT
ejpam-3484	286	1	=	=	SYM
ejpam-3484	286	2	fγi(c0	fγi(c0	NOUN
ejpam-3484	286	3	)	)	PUNCT
ejpam-3484	286	4	.	.	PUNCT
ejpam-3484	287	1	then	then	ADV
ejpam-3484	287	2	c0	c0	PROPN
ejpam-3484	287	3	=	=	SYM
ejpam-3484	287	4	a0	a0	PROPN
ejpam-3484	287	5	∪	∪	X
ejpam-3484	287	6	(	(	PUNCT
ejpam-3484	287	7	⋃	⋃	NOUN
ejpam-3484	287	8	v∈v	v∈v	NOUN
ejpam-3484	287	9	(	(	PUNCT
ejpam-3484	287	10	g)\a0	g)\a0	PROPN
ejpam-3484	287	11	rv	rv	PROPN
ejpam-3484	287	12	)	)	PUNCT
ejpam-3484	287	13	,	,	PUNCT
ejpam-3484	287	14	where	where	SCONJ
ejpam-3484	287	15	a0	a0	PROPN
ejpam-3484	287	16	is	be	AUX
ejpam-3484	287	17	an	an	DET
ejpam-3484	287	18	α	α	NOUN
ejpam-3484	287	19	-	-	PUNCT
ejpam-3484	287	20	set	set	NOUN
ejpam-3484	287	21	of	of	ADP
ejpam-3484	287	22	g.	g.	PROPN
ejpam-3484	287	23	let	let	VERB
ejpam-3484	287	24	s	s	PRON
ejpam-3484	287	25	be	be	AUX
ejpam-3484	287	26	a	a	DET
ejpam-3484	287	27	forcing	forcing	NOUN
ejpam-3484	287	28	subset	subset	NOUN
ejpam-3484	287	29	for	for	ADP
ejpam-3484	287	30	c0	c0	NOUN
ejpam-3484	287	31	such	such	ADJ
ejpam-3484	287	32	that	that	DET
ejpam-3484	287	33	fγi(c0	fγi(c0	NOUN
ejpam-3484	287	34	)	)	PUNCT
ejpam-3484	287	35	=	=	PUNCT
ejpam-3484	287	36	|s|	|s|	PROPN
ejpam-3484	287	37	.	.	PUNCT
ejpam-3484	288	1	since	since	SCONJ
ejpam-3484	288	2	each	each	DET
ejpam-3484	288	3	hv	hv	PROPN
ejpam-3484	288	4	has	have	VERB
ejpam-3484	288	5	a	a	DET
ejpam-3484	288	6	unique	unique	ADJ
ejpam-3484	288	7	γi	γi	NOUN
ejpam-3484	288	8	-	-	PUNCT
ejpam-3484	288	9	set	set	VERB
ejpam-3484	288	10	rv	rv	PROPN
ejpam-3484	288	11	,	,	PUNCT
ejpam-3484	288	12	s	s	PROPN
ejpam-3484	288	13	⊆	⊆	NUM
ejpam-3484	288	14	a0	a0	NOUN
ejpam-3484	288	15	.	.	PUNCT
ejpam-3484	289	1	since	since	SCONJ
ejpam-3484	289	2	s	s	PROPN
ejpam-3484	289	3	is	be	AUX
ejpam-3484	289	4	a	a	DET
ejpam-3484	289	5	forcing	forcing	NOUN
ejpam-3484	289	6	subset	subset	NOUN
ejpam-3484	289	7	for	for	ADP
ejpam-3484	289	8	c0	c0	NOUN
ejpam-3484	289	9	,	,	PUNCT
ejpam-3484	289	10	s	s	VERB
ejpam-3484	289	11	must	must	AUX
ejpam-3484	289	12	be	be	AUX
ejpam-3484	289	13	a	a	DET
ejpam-3484	289	14	forcing	forcing	NOUN
ejpam-3484	289	15	subset	subset	NOUN
ejpam-3484	289	16	for	for	ADP
ejpam-3484	289	17	the	the	DET
ejpam-3484	289	18	α	α	NOUN
ejpam-3484	289	19	-	-	PUNCT
ejpam-3484	289	20	set	set	VERB
ejpam-3484	289	21	a0	a0	NOUN
ejpam-3484	289	22	.	.	PUNCT
ejpam-3484	290	1	thus	thus	ADV
ejpam-3484	290	2	,	,	PUNCT
ejpam-3484	290	3	fγi(g	fγi(g	PROPN
ejpam-3484	290	4	◦	◦	NOUN
ejpam-3484	290	5	h	h	NOUN
ejpam-3484	290	6	)	)	PUNCT
ejpam-3484	291	1	=	=	SYM
ejpam-3484	291	2	fγi(c0	fγi(c0	NOUN
ejpam-3484	291	3	)	)	PUNCT
ejpam-3484	291	4	=	=	PUNCT
ejpam-3484	291	5	|s|	|s|	NOUN
ejpam-3484	291	6	≥	≥	NOUN
ejpam-3484	291	7	fα(a0	fα(a0	NOUN
ejpam-3484	291	8	)	)	PUNCT
ejpam-3484	291	9	≥	≥	NOUN
ejpam-3484	291	10	fα(g	fα(g	PUNCT
ejpam-3484	291	11	)	)	PUNCT
ejpam-3484	291	12	.	.	PUNCT
ejpam-3484	292	1	therefore	therefore	ADV
ejpam-3484	292	2	,	,	PUNCT
ejpam-3484	292	3	fγi(g	fγi(g	PROPN
ejpam-3484	292	4	◦	◦	NOUN
ejpam-3484	292	5	h	h	NOUN
ejpam-3484	292	6	)	)	PUNCT
ejpam-3484	292	7	=	=	PUNCT
ejpam-3484	292	8	fα(g	fα(g	PUNCT
ejpam-3484	292	9	)	)	PUNCT
ejpam-3484	292	10	.	.	PUNCT
ejpam-3484	293	1	case	case	NOUN
ejpam-3484	293	2	2	2	NUM
ejpam-3484	293	3	:	:	PUNCT
ejpam-3484	293	4	suppose	suppose	VERB
ejpam-3484	293	5	that	that	SCONJ
ejpam-3484	293	6	h	h	NOUN
ejpam-3484	293	7	does	do	AUX
ejpam-3484	293	8	not	not	PART
ejpam-3484	293	9	have	have	VERB
ejpam-3484	293	10	a	a	DET
ejpam-3484	293	11	unique	unique	ADJ
ejpam-3484	293	12	γi	γi	NOUN
ejpam-3484	293	13	-	-	PUNCT
ejpam-3484	293	14	set	set	NOUN
ejpam-3484	293	15	.	.	PUNCT
ejpam-3484	294	1	let	let	VERB
ejpam-3484	294	2	q	q	PRON
ejpam-3484	294	3	be	be	AUX
ejpam-3484	294	4	a	a	DET
ejpam-3484	294	5	γi	γi	NOUN
ejpam-3484	294	6	-	-	PUNCT
ejpam-3484	294	7	set	set	NOUN
ejpam-3484	294	8	of	of	ADP
ejpam-3484	294	9	h	h	NOUN
ejpam-3484	294	10	with	with	ADP
ejpam-3484	294	11	fγi(h	fγi(h	PROPN
ejpam-3484	294	12	)	)	PUNCT
ejpam-3484	294	13	=	=	SYM
ejpam-3484	294	14	fγi(q	fγi(q	PROPN
ejpam-3484	294	15	)	)	PUNCT
ejpam-3484	294	16	and	and	CCONJ
ejpam-3484	294	17	let	let	VERB
ejpam-3484	294	18	pq	pq	INTJ
ejpam-3484	294	19	be	be	AUX
ejpam-3484	294	20	a	a	DET
ejpam-3484	294	21	forcing	forcing	NOUN
ejpam-3484	294	22	subset	subset	NOUN
ejpam-3484	294	23	for	for	ADP
ejpam-3484	294	24	q	q	NOUN
ejpam-3484	294	25	with	with	ADP
ejpam-3484	294	26	fγi(q	fγi(q	NOUN
ejpam-3484	294	27	)	)	PUNCT
ejpam-3484	294	28	=	=	SYM
ejpam-3484	295	1	|pq|	|pq|	NOUN
ejpam-3484	295	2	.	.	PUNCT
ejpam-3484	296	1	for	for	ADP
ejpam-3484	296	2	each	each	DET
ejpam-3484	296	3	v	v	NUM
ejpam-3484	296	4	∈	∈	PROPN
ejpam-3484	296	5	v	v	NOUN
ejpam-3484	296	6	(	(	PUNCT
ejpam-3484	296	7	g	g	NOUN
ejpam-3484	296	8	)	)	PUNCT
ejpam-3484	296	9	,	,	PUNCT
ejpam-3484	296	10	let	let	VERB
ejpam-3484	296	11	qv	qv	PRON
ejpam-3484	296	12	⊆	⊆	NUM
ejpam-3484	296	13	v	v	X
ejpam-3484	296	14	(	(	PUNCT
ejpam-3484	296	15	hv	hv	NOUN
ejpam-3484	296	16	)	)	PUNCT
ejpam-3484	296	17	and	and	CCONJ
ejpam-3484	296	18	pqv	pqv	PROPN
ejpam-3484	296	19	⊆	⊆	NUM
ejpam-3484	296	20	qv	qv	ADP
ejpam-3484	296	21	such	such	ADJ
ejpam-3484	296	22	that	that	SCONJ
ejpam-3484	296	23	〈	〈	PROPN
ejpam-3484	296	24	qv	qv	PROPN
ejpam-3484	296	25	〉	〉	NOUN
ejpam-3484	296	26	∼=	∼=	PROPN
ejpam-3484	296	27	〈	〈	PROPN
ejpam-3484	296	28	q	q	PROPN
ejpam-3484	296	29	〉	〉	NOUN
ejpam-3484	296	30	and	and	CCONJ
ejpam-3484	296	31	〈	〈	PROPN
ejpam-3484	296	32	pqv	pqv	NOUN
ejpam-3484	296	33	〉	〉	PROPN
ejpam-3484	296	34	∼=	∼=	PROPN
ejpam-3484	296	35	〈	〈	PROPN
ejpam-3484	296	36	pq	pq	NOUN
ejpam-3484	296	37	〉	〉	PROPN
ejpam-3484	296	38	.	.	PUNCT
ejpam-3484	297	1	let	let	VERB
ejpam-3484	297	2	aq	aq	PRON
ejpam-3484	297	3	be	be	AUX
ejpam-3484	297	4	an	an	DET
ejpam-3484	297	5	α	α	NOUN
ejpam-3484	297	6	-	-	PUNCT
ejpam-3484	297	7	set	set	NOUN
ejpam-3484	297	8	of	of	ADP
ejpam-3484	297	9	g.	g.	PROPN
ejpam-3484	297	10	then	then	ADV
ejpam-3484	297	11	by	by	ADP
ejpam-3484	297	12	theorem	theorem	NOUN
ejpam-3484	297	13	3.18	3.18	NUM
ejpam-3484	297	14	,	,	PUNCT
ejpam-3484	297	15	cq	cq	X
ejpam-3484	298	1	=	=	NOUN
ejpam-3484	298	2	aq	aq	X
ejpam-3484	298	3	∪	∪	X
ejpam-3484	298	4	(	(	PUNCT
ejpam-3484	298	5	⋃	⋃	NOUN
ejpam-3484	298	6	v∈v	v∈v	NOUN
ejpam-3484	298	7	(	(	PUNCT
ejpam-3484	298	8	g)\aq	g)\aq	PROPN
ejpam-3484	298	9	qv	qv	NOUN
ejpam-3484	298	10	)	)	PUNCT
ejpam-3484	298	11	is	be	AUX
ejpam-3484	298	12	a	a	DET
ejpam-3484	298	13	γi	γi	NOUN
ejpam-3484	298	14	-	-	PUNCT
ejpam-3484	298	15	set	set	NOUN
ejpam-3484	298	16	of	of	ADP
ejpam-3484	298	17	g	g	PROPN
ejpam-3484	298	18	◦	◦	PROPN
ejpam-3484	298	19	h.	h.	PROPN
ejpam-3484	298	20	let	let	VERB
ejpam-3484	298	21	s	s	NOUN
ejpam-3484	298	22	=	=	PUNCT
ejpam-3484	298	23	⋃	⋃	NOUN
ejpam-3484	298	24	v∈v	v∈v	NOUN
ejpam-3484	298	25	(	(	PUNCT
ejpam-3484	298	26	g)\aq	g)\aq	PROPN
ejpam-3484	298	27	pqv	pqv	NOUN
ejpam-3484	298	28	.	.	PUNCT
ejpam-3484	299	1	then	then	ADV
ejpam-3484	299	2	s	s	VERB
ejpam-3484	299	3	is	be	AUX
ejpam-3484	299	4	a	a	DET
ejpam-3484	299	5	forcing	forcing	NOUN
ejpam-3484	299	6	subset	subset	NOUN
ejpam-3484	299	7	for	for	ADP
ejpam-3484	299	8	cq	cq	PROPN
ejpam-3484	299	9	.	.	PUNCT
ejpam-3484	300	1	thus	thus	ADV
ejpam-3484	300	2	,	,	PUNCT
ejpam-3484	300	3	fγi(g	fγi(g	PROPN
ejpam-3484	300	4	◦	◦	NOUN
ejpam-3484	300	5	h	h	NOUN
ejpam-3484	300	6	)	)	PUNCT
ejpam-3484	300	7	≤	≤	NOUN
ejpam-3484	300	8	fγi(cq	fγi(cq	NOUN
ejpam-3484	300	9	)	)	PUNCT
ejpam-3484	300	10	≤	≤	NUM
ejpam-3484	300	11	|s|	|s|	NOUN
ejpam-3484	300	12	=	=	PUNCT
ejpam-3484	301	1	[	[	X
ejpam-3484	301	2	n−	n−	NOUN
ejpam-3484	301	3	α(g)]fγi(h	α(g)]fγi(h	PROPN
ejpam-3484	301	4	)	)	PUNCT
ejpam-3484	301	5	.	.	PUNCT
ejpam-3484	302	1	next	next	ADV
ejpam-3484	302	2	,	,	PUNCT
ejpam-3484	302	3	let	let	VERB
ejpam-3484	302	4	c	c	NOUN
ejpam-3484	302	5	′	′	VERB
ejpam-3484	302	6	be	be	AUX
ejpam-3484	302	7	a	a	DET
ejpam-3484	302	8	γi	γi	NOUN
ejpam-3484	302	9	-	-	PUNCT
ejpam-3484	302	10	set	set	NOUN
ejpam-3484	302	11	of	of	ADP
ejpam-3484	302	12	g	g	PROPN
ejpam-3484	302	13	◦	◦	NOUN
ejpam-3484	302	14	h	h	NOUN
ejpam-3484	302	15	such	such	ADJ
ejpam-3484	302	16	that	that	SCONJ
ejpam-3484	302	17	fγi(g	fγi(g	PROPN
ejpam-3484	302	18	◦	◦	NOUN
ejpam-3484	302	19	h	h	NOUN
ejpam-3484	302	20	)	)	PUNCT
ejpam-3484	302	21	=	=	SYM
ejpam-3484	303	1	fγi(c	fγi(c	PROPN
ejpam-3484	303	2	′	′	NUM
ejpam-3484	303	3	)	)	PUNCT
ejpam-3484	303	4	.	.	PUNCT
ejpam-3484	304	1	then	then	ADV
ejpam-3484	304	2	by	by	ADP
ejpam-3484	304	3	theorem	theorem	NOUN
ejpam-3484	304	4	3.18	3.18	NUM
ejpam-3484	304	5	,	,	PUNCT
ejpam-3484	304	6	let	let	VERB
ejpam-3484	304	7	c	c	NOUN
ejpam-3484	304	8	′	′	VERB
ejpam-3484	305	1	=	=	PUNCT
ejpam-3484	305	2	a′	a′	NOUN
ejpam-3484	305	3	∪	∪	X
ejpam-3484	305	4	(	(	PUNCT
ejpam-3484	305	5	⋃	⋃	NOUN
ejpam-3484	305	6	v∈v	v∈v	NOUN
ejpam-3484	305	7	(	(	PUNCT
ejpam-3484	305	8	g)\a′	g)\a′	NOUN
ejpam-3484	305	9	rv	rv	PROPN
ejpam-3484	305	10	)	)	PUNCT
ejpam-3484	305	11	,	,	PUNCT
ejpam-3484	305	12	where	where	SCONJ
ejpam-3484	305	13	a′	a′	PROPN
ejpam-3484	305	14	is	be	AUX
ejpam-3484	305	15	an	an	DET
ejpam-3484	305	16	α	α	NOUN
ejpam-3484	305	17	-	-	PUNCT
ejpam-3484	305	18	set	set	NOUN
ejpam-3484	305	19	of	of	ADP
ejpam-3484	305	20	g	g	PROPN
ejpam-3484	305	21	and	and	CCONJ
ejpam-3484	305	22	rv	rv	PROPN
ejpam-3484	305	23	is	be	AUX
ejpam-3484	305	24	a	a	DET
ejpam-3484	305	25	γi	γi	NOUN
ejpam-3484	305	26	-	-	PUNCT
ejpam-3484	305	27	set	set	NOUN
ejpam-3484	305	28	of	of	ADP
ejpam-3484	305	29	hv	hv	NOUN
ejpam-3484	305	30	for	for	ADP
ejpam-3484	305	31	each	each	DET
ejpam-3484	305	32	v	v	NUM
ejpam-3484	305	33	∈	∈	NOUN
ejpam-3484	305	34	v	v	NOUN
ejpam-3484	305	35	(	(	PUNCT
ejpam-3484	305	36	g)\a′.	g)\a′.	NOUN
ejpam-3484	305	37	let	let	VERB
ejpam-3484	305	38	s′	s′	NOUN
ejpam-3484	305	39	be	be	AUX
ejpam-3484	305	40	a	a	DET
ejpam-3484	305	41	forcing	forcing	NOUN
ejpam-3484	305	42	subset	subset	NOUN
ejpam-3484	305	43	for	for	ADP
ejpam-3484	305	44	c	c	NOUN
ejpam-3484	305	45	′	′	NOUN
ejpam-3484	305	46	such	such	ADJ
ejpam-3484	305	47	that	that	SCONJ
ejpam-3484	305	48	fγi(c	fγi(c	PROPN
ejpam-3484	305	49	′	′	NOUN
ejpam-3484	305	50	)	)	PUNCT
ejpam-3484	305	51	=	=	PUNCT
ejpam-3484	305	52	|s′|	|s′|	NOUN
ejpam-3484	305	53	.	.	PUNCT
ejpam-3484	306	1	suppose	suppose	VERB
ejpam-3484	306	2	that	that	SCONJ
ejpam-3484	306	3	there	there	PRON
ejpam-3484	306	4	exists	exist	VERB
ejpam-3484	306	5	w	w	PROPN
ejpam-3484	306	6	∈	∈	PROPN
ejpam-3484	306	7	v	v	NOUN
ejpam-3484	306	8	(	(	PUNCT
ejpam-3484	306	9	g)\a′	g)\a′	NOUN
ejpam-3484	306	10	such	such	ADJ
ejpam-3484	306	11	that	that	SCONJ
ejpam-3484	306	12	s′	s′	ADJ
ejpam-3484	306	13	∩	∩	ADJ
ejpam-3484	306	14	rw	rw	NOUN
ejpam-3484	306	15	=	=	PROPN
ejpam-3484	306	16	sw	sw	PROPN
ejpam-3484	306	17	is	be	AUX
ejpam-3484	306	18	not	not	PART
ejpam-3484	306	19	a	a	DET
ejpam-3484	306	20	forcing	forcing	NOUN
ejpam-3484	306	21	subset	subset	NOUN
ejpam-3484	306	22	for	for	ADP
ejpam-3484	306	23	rw	rw	NOUN
ejpam-3484	306	24	.	.	PUNCT
ejpam-3484	307	1	let	let	AUX
ejpam-3484	307	2	r′w	r′w	AUX
ejpam-3484	307	3	be	be	AUX
ejpam-3484	307	4	a	a	DET
ejpam-3484	307	5	γi	γi	NOUN
ejpam-3484	307	6	-	-	PUNCT
ejpam-3484	307	7	set	set	NOUN
ejpam-3484	307	8	of	of	ADP
ejpam-3484	307	9	hw	hw	PRON
ejpam-3484	307	10	with	with	ADP
ejpam-3484	307	11	r′w	r′w	PROPN
ejpam-3484	307	12	6=	6=	ADP
ejpam-3484	307	13	rw	rw	NOUN
ejpam-3484	307	14	.	.	PUNCT
ejpam-3484	308	1	then	then	ADV
ejpam-3484	308	2	c	c	X
ejpam-3484	308	3	”	"	PUNCT
ejpam-3484	308	4	=	=	SYM
ejpam-3484	308	5	a′	a′	NOUN
ejpam-3484	308	6	∪	∪	X
ejpam-3484	308	7	(	(	PUNCT
ejpam-3484	308	8	⋃	⋃	NOUN
ejpam-3484	308	9	v∈v	v∈v	NOUN
ejpam-3484	308	10	(	(	PUNCT
ejpam-3484	308	11	g)\(a′∪{w	g)\(a′∪{w	NOUN
ejpam-3484	308	12	}	}	PUNCT
ejpam-3484	308	13	)	)	PUNCT
ejpam-3484	308	14	rv	rv	X
ejpam-3484	308	15	)	)	PUNCT
ejpam-3484	308	16	∪	∪	NOUN
ejpam-3484	308	17	r′w	r′w	NOUN
ejpam-3484	308	18	is	be	AUX
ejpam-3484	308	19	a	a	DET
ejpam-3484	308	20	γi	γi	NOUN
ejpam-3484	308	21	-	-	PUNCT
ejpam-3484	308	22	set	set	NOUN
ejpam-3484	308	23	of	of	ADP
ejpam-3484	308	24	g	g	PROPN
ejpam-3484	308	25	◦	◦	NOUN
ejpam-3484	308	26	h	h	NOUN
ejpam-3484	308	27	with	with	ADP
ejpam-3484	308	28	c	c	NOUN
ejpam-3484	308	29	”	"	PUNCT
ejpam-3484	308	30	6=	6=	ADP
ejpam-3484	308	31	c	c	NOUN
ejpam-3484	308	32	′	′	NOUN
ejpam-3484	308	33	and	and	CCONJ
ejpam-3484	308	34	s′	s′	ADJ
ejpam-3484	308	35	⊆	⊆	NUM
ejpam-3484	308	36	c	c	NOUN
ejpam-3484	308	37	”	"	PUNCT
ejpam-3484	308	38	,	,	PUNCT
ejpam-3484	308	39	a	a	DET
ejpam-3484	308	40	contradiction	contradiction	NOUN
ejpam-3484	308	41	.	.	PUNCT
ejpam-3484	309	1	thus	thus	ADV
ejpam-3484	309	2	,	,	PUNCT
ejpam-3484	309	3	sv	sv	PROPN
ejpam-3484	309	4	=	=	SYM
ejpam-3484	309	5	s′	s′	NOUN
ejpam-3484	309	6	∩	∩	NOUN
ejpam-3484	309	7	rv	rv	PROPN
ejpam-3484	309	8	is	be	AUX
ejpam-3484	309	9	a	a	DET
ejpam-3484	309	10	forcing	forcing	NOUN
ejpam-3484	309	11	subset	subset	NOUN
ejpam-3484	309	12	for	for	ADP
ejpam-3484	309	13	rv	rv	PROPN
ejpam-3484	309	14	for	for	ADP
ejpam-3484	309	15	each	each	DET
ejpam-3484	309	16	v	v	NUM
ejpam-3484	309	17	∈	∈	NOUN
ejpam-3484	309	18	v	v	NOUN
ejpam-3484	309	19	(	(	PUNCT
ejpam-3484	309	20	g)\a′.	g)\a′.	NOUN
ejpam-3484	309	21	note	note	VERB
ejpam-3484	309	22	that	that	SCONJ
ejpam-3484	309	23	sv	sv	PROPN
ejpam-3484	309	24	6=	6=	NOUN
ejpam-3484	309	25	∅	∅	NOUN
ejpam-3484	309	26	for	for	ADP
ejpam-3484	309	27	each	each	DET
ejpam-3484	309	28	v	v	NUM
ejpam-3484	309	29	∈	∈	NOUN
ejpam-3484	309	30	v	v	NOUN
ejpam-3484	309	31	(	(	PUNCT
ejpam-3484	309	32	g)\a′.	g)\a′.	NOUN
ejpam-3484	309	33	let	let	VERB
ejpam-3484	309	34	s0	s0	PROPN
ejpam-3484	309	35	=	=	PUNCT
ejpam-3484	309	36	⋃	⋃	PROPN
ejpam-3484	309	37	v∈v	v∈v	NOUN
ejpam-3484	309	38	(	(	PUNCT
ejpam-3484	309	39	g)\a′	g)\a′	NOUN
ejpam-3484	309	40	sv	sv	PROPN
ejpam-3484	309	41	.	.	PUNCT
ejpam-3484	310	1	then	then	ADV
ejpam-3484	310	2	fγi(g	fγi(g	PROPN
ejpam-3484	310	3	◦	◦	NOUN
ejpam-3484	310	4	h	h	NOUN
ejpam-3484	310	5	)	)	PUNCT
ejpam-3484	310	6	=	=	PUNCT
ejpam-3484	310	7	|s′|	|s′|	NOUN
ejpam-3484	310	8	≥	≥	NOUN
ejpam-3484	310	9	|s0|	|s0|	NOUN
ejpam-3484	310	10	=	=	SYM
ejpam-3484	310	11	∑	∑	PUNCT
ejpam-3484	310	12	v∈v	v∈v	PROPN
ejpam-3484	310	13	(	(	PUNCT
ejpam-3484	310	14	g)\a′	g)\a′	PROPN
ejpam-3484	310	15	|sv|	|sv|	PROPN
ejpam-3484	310	16	≥	≥	PROPN
ejpam-3484	310	17	∑	∑	PUNCT
ejpam-3484	310	18	v∈v	v∈v	PROPN
ejpam-3484	310	19	(	(	PUNCT
ejpam-3484	310	20	g)\a′	g)\a′	PROPN
ejpam-3484	310	21	fγi(h	fγi(h	PROPN
ejpam-3484	310	22	)	)	PUNCT
ejpam-3484	310	23	=	=	PUNCT
ejpam-3484	311	1	[	[	PUNCT
ejpam-3484	311	2	n−	n−	NOUN
ejpam-3484	311	3	α(g)]fγi(h	α(g)]fγi(h	PROPN
ejpam-3484	311	4	)	)	PUNCT
ejpam-3484	311	5	.	.	PUNCT
ejpam-3484	312	1	therefore	therefore	ADV
ejpam-3484	312	2	,	,	PUNCT
ejpam-3484	312	3	fγi(g	fγi(g	PROPN
ejpam-3484	312	4	◦	◦	NOUN
ejpam-3484	312	5	h	h	NOUN
ejpam-3484	312	6	)	)	PUNCT
ejpam-3484	312	7	=	=	PUNCT
ejpam-3484	313	1	[	[	PUNCT
ejpam-3484	313	2	n−	n−	NOUN
ejpam-3484	313	3	α(g)]fγi(h	α(g)]fγi(h	PROPN
ejpam-3484	313	4	)	)	PUNCT
ejpam-3484	313	5	.	.	PUNCT
ejpam-3484	314	1	theorem	theorem	VERB
ejpam-3484	314	2	3.21	3.21	NUM
ejpam-3484	314	3	.	.	PUNCT
ejpam-3484	315	1	let	let	VERB
ejpam-3484	315	2	g	g	NOUN
ejpam-3484	315	3	and	and	CCONJ
ejpam-3484	315	4	h	h	NOUN
ejpam-3484	315	5	be	be	AUX
ejpam-3484	315	6	connected	connect	VERB
ejpam-3484	315	7	graphs	graph	NOUN
ejpam-3484	315	8	.	.	PUNCT
ejpam-3484	316	1	then	then	ADV
ejpam-3484	316	2	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	316	3	]	]	PUNCT
ejpam-3484	316	4	)	)	PUNCT
ejpam-3484	316	5	=	=	SYM
ejpam-3484	316	6	{	{	PUNCT
ejpam-3484	316	7	fγi(g	fγi(g	PROPN
ejpam-3484	316	8	)	)	PUNCT
ejpam-3484	316	9	,	,	PUNCT
ejpam-3484	316	10	if	if	SCONJ
ejpam-3484	316	11	h	h	NOUN
ejpam-3484	316	12	has	have	VERB
ejpam-3484	316	13	a	a	DET
ejpam-3484	316	14	unique	unique	ADJ
ejpam-3484	316	15	γi	γi	NOUN
ejpam-3484	316	16	-	-	PUNCT
ejpam-3484	316	17	set	set	NOUN
ejpam-3484	316	18	,	,	PUNCT
ejpam-3484	316	19	[	[	X
ejpam-3484	316	20	γi(g)][fγi(h	γi(g)][fγi(h	NOUN
ejpam-3484	316	21	)	)	PUNCT
ejpam-3484	316	22	]	]	PUNCT
ejpam-3484	316	23	,	,	PUNCT
ejpam-3484	316	24	if	if	SCONJ
ejpam-3484	316	25	h	h	NOUN
ejpam-3484	316	26	has	have	VERB
ejpam-3484	316	27	no	no	DET
ejpam-3484	316	28	unique	unique	ADJ
ejpam-3484	316	29	γi	γi	NOUN
ejpam-3484	316	30	-	-	PUNCT
ejpam-3484	316	31	sets	set	NOUN
ejpam-3484	316	32	.	.	PUNCT
ejpam-3484	317	1	in	in	ADP
ejpam-3484	317	2	particular	particular	ADJ
ejpam-3484	317	3	,	,	PUNCT
ejpam-3484	317	4	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	317	5	]	]	PUNCT
ejpam-3484	317	6	)	)	PUNCT
ejpam-3484	318	1	=	=	SYM
ejpam-3484	318	2	0	0	PUNCT
ejpam-3484	319	1	if	if	SCONJ
ejpam-3484	319	2	g	g	PROPN
ejpam-3484	319	3	and	and	CCONJ
ejpam-3484	319	4	h	h	NOUN
ejpam-3484	319	5	have	have	AUX
ejpam-3484	319	6	unique	unique	ADJ
ejpam-3484	319	7	γi	γi	NOUN
ejpam-3484	319	8	-	-	PUNCT
ejpam-3484	319	9	sets	set	NOUN
ejpam-3484	319	10	.	.	PUNCT
ejpam-3484	320	1	also	also	ADV
ejpam-3484	320	2	,	,	PUNCT
ejpam-3484	320	3	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	320	4	]	]	PUNCT
ejpam-3484	320	5	)	)	PUNCT
ejpam-3484	320	6	=	=	SYM
ejpam-3484	320	7	γi(g[h	γi(g[h	NOUN
ejpam-3484	320	8	]	]	X
ejpam-3484	320	9	)	)	PUNCT
ejpam-3484	320	10	if	if	SCONJ
ejpam-3484	320	11	fγi(h	fγi(h	PROPN
ejpam-3484	320	12	)	)	PUNCT
ejpam-3484	320	13	=	=	SYM
ejpam-3484	320	14	γi(h	γi(h	NOUN
ejpam-3484	320	15	)	)	PUNCT
ejpam-3484	320	16	.	.	PUNCT
ejpam-3484	321	1	c.	c.	PROPN
ejpam-3484	321	2	armada	armada	PROPN
ejpam-3484	321	3	,	,	PUNCT
ejpam-3484	321	4	s.	s.	PROPN
ejpam-3484	321	5	canoy	canoy	PROPN
ejpam-3484	321	6	jr	jr	PROPN
ejpam-3484	321	7	.	.	PROPN
ejpam-3484	321	8	/	/	SYM
ejpam-3484	321	9	eur	eur	PROPN
ejpam-3484	321	10	.	.	PUNCT
ejpam-3484	322	1	j.	j.	PROPN
ejpam-3484	322	2	pure	pure	PROPN
ejpam-3484	322	3	appl	appl	PROPN
ejpam-3484	322	4	.	.	PROPN
ejpam-3484	322	5	math	math	PROPN
ejpam-3484	322	6	,	,	PUNCT
ejpam-3484	322	7	12	12	NUM
ejpam-3484	322	8	(	(	PUNCT
ejpam-3484	322	9	4	4	NUM
ejpam-3484	322	10	)	)	PUNCT
ejpam-3484	322	11	(	(	PUNCT
ejpam-3484	322	12	2019	2019	NUM
ejpam-3484	322	13	)	)	PUNCT
ejpam-3484	322	14	,	,	PUNCT
ejpam-3484	322	15	1371	1371	NUM
ejpam-3484	322	16	-	-	SYM
ejpam-3484	322	17	1381	1381	NUM
ejpam-3484	322	18	1380	1380	NUM
ejpam-3484	322	19	proof	proof	NOUN
ejpam-3484	322	20	.	.	PUNCT
ejpam-3484	323	1	by	by	ADP
ejpam-3484	323	2	corollary	corollary	ADJ
ejpam-3484	323	3	2.6	2.6	NUM
ejpam-3484	323	4	,	,	PUNCT
ejpam-3484	323	5	γi(g[h	γi(g[h	NOUN
ejpam-3484	323	6	]	]	X
ejpam-3484	323	7	)	)	PUNCT
ejpam-3484	323	8	=	=	SYM
ejpam-3484	323	9	γi(g)γi(h	γi(g)γi(h	NOUN
ejpam-3484	323	10	)	)	PUNCT
ejpam-3484	323	11	.	.	PUNCT
ejpam-3484	324	1	consider	consider	VERB
ejpam-3484	324	2	the	the	DET
ejpam-3484	324	3	following	follow	VERB
ejpam-3484	324	4	cases	case	NOUN
ejpam-3484	324	5	:	:	PUNCT
ejpam-3484	324	6	case	case	NOUN
ejpam-3484	324	7	1	1	NUM
ejpam-3484	324	8	:	:	PUNCT
ejpam-3484	324	9	suppose	suppose	VERB
ejpam-3484	324	10	that	that	SCONJ
ejpam-3484	324	11	h	h	NOUN
ejpam-3484	324	12	has	have	VERB
ejpam-3484	324	13	a	a	DET
ejpam-3484	324	14	unique	unique	ADJ
ejpam-3484	324	15	γi	γi	NOUN
ejpam-3484	324	16	-	-	PUNCT
ejpam-3484	324	17	set	set	NOUN
ejpam-3484	324	18	,	,	PUNCT
ejpam-3484	324	19	say	say	VERB
ejpam-3484	324	20	r.	r.	PROPN
ejpam-3484	324	21	let	let	VERB
ejpam-3484	324	22	s	s	PRON
ejpam-3484	324	23	be	be	AUX
ejpam-3484	324	24	a	a	DET
ejpam-3484	324	25	γi	γi	NOUN
ejpam-3484	324	26	-	-	PUNCT
ejpam-3484	324	27	set	set	NOUN
ejpam-3484	324	28	of	of	ADP
ejpam-3484	324	29	g	g	NOUN
ejpam-3484	324	30	and	and	CCONJ
ejpam-3484	324	31	let	let	VERB
ejpam-3484	324	32	u	u	PRON
ejpam-3484	324	33	be	be	AUX
ejpam-3484	324	34	a	a	DET
ejpam-3484	324	35	forcing	forcing	NOUN
ejpam-3484	324	36	subset	subset	NOUN
ejpam-3484	324	37	for	for	ADP
ejpam-3484	324	38	s	s	PRON
ejpam-3484	324	39	such	such	ADJ
ejpam-3484	324	40	that	that	PRON
ejpam-3484	324	41	fγi(g	fγi(g	PROPN
ejpam-3484	324	42	)	)	PUNCT
ejpam-3484	324	43	=	=	SYM
ejpam-3484	324	44	fγi(s	fγi(s	NOUN
ejpam-3484	324	45	)	)	PUNCT
ejpam-3484	324	46	=	=	SYM
ejpam-3484	325	1	|u	|u	ADJ
ejpam-3484	325	2	|	|	NOUN
ejpam-3484	325	3	.	.	PUNCT
ejpam-3484	326	1	by	by	ADP
ejpam-3484	326	2	theorem	theorem	NOUN
ejpam-3484	326	3	2.5	2.5	NUM
ejpam-3484	326	4	,	,	PUNCT
ejpam-3484	326	5	c	c	X
ejpam-3484	326	6	=	=	SYM
ejpam-3484	326	7	s	s	PART
ejpam-3484	326	8	×	×	NOUN
ejpam-3484	326	9	r	r	NOUN
ejpam-3484	326	10	is	be	AUX
ejpam-3484	326	11	a	a	DET
ejpam-3484	326	12	γi	γi	NOUN
ejpam-3484	326	13	-	-	PUNCT
ejpam-3484	326	14	set	set	NOUN
ejpam-3484	326	15	of	of	ADP
ejpam-3484	326	16	g[h	g[h	NOUN
ejpam-3484	326	17	]	]	PUNCT
ejpam-3484	326	18	.	.	PUNCT
ejpam-3484	327	1	now	now	ADV
ejpam-3484	327	2	,	,	PUNCT
ejpam-3484	327	3	since	since	SCONJ
ejpam-3484	327	4	u	u	NOUN
ejpam-3484	327	5	is	be	AUX
ejpam-3484	327	6	a	a	DET
ejpam-3484	327	7	forcing	forcing	NOUN
ejpam-3484	327	8	subset	subset	NOUN
ejpam-3484	327	9	for	for	ADP
ejpam-3484	327	10	s	s	PROPN
ejpam-3484	327	11	,	,	PUNCT
ejpam-3484	327	12	uc	uc	PROPN
ejpam-3484	327	13	=	=	PUNCT
ejpam-3484	327	14	u	u	ADJ
ejpam-3484	327	15	×	×	NOUN
ejpam-3484	327	16	{	{	PUNCT
ejpam-3484	327	17	c	c	NOUN
ejpam-3484	327	18	}	}	PUNCT
ejpam-3484	327	19	is	be	AUX
ejpam-3484	327	20	a	a	DET
ejpam-3484	327	21	forcing	forcing	NOUN
ejpam-3484	327	22	subset	subset	NOUN
ejpam-3484	327	23	for	for	ADP
ejpam-3484	327	24	c	c	PROPN
ejpam-3484	327	25	for	for	ADP
ejpam-3484	327	26	each	each	DET
ejpam-3484	327	27	c	c	PROPN
ejpam-3484	327	28	∈	∈	PROPN
ejpam-3484	327	29	r.	r.	PROPN
ejpam-3484	327	30	hence	hence	ADV
ejpam-3484	327	31	,	,	PUNCT
ejpam-3484	327	32	for	for	ADP
ejpam-3484	327	33	each	each	DET
ejpam-3484	327	34	c	c	NOUN
ejpam-3484	327	35	∈	∈	PROPN
ejpam-3484	327	36	r	r	NOUN
ejpam-3484	327	37	,	,	PUNCT
ejpam-3484	327	38	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	327	39	]	]	PUNCT
ejpam-3484	327	40	)	)	PUNCT
ejpam-3484	327	41	≤	≤	PUNCT
ejpam-3484	328	1	fγi(c	fγi(c	PROPN
ejpam-3484	328	2	)	)	PUNCT
ejpam-3484	328	3	≤	≤	NOUN
ejpam-3484	328	4	|uc|	|uc|	VERB
ejpam-3484	328	5	=	=	PUNCT
ejpam-3484	328	6	|u	|u	ADJ
ejpam-3484	328	7	|	|	NOUN
ejpam-3484	328	8	=	=	SYM
ejpam-3484	328	9	fγi(g	fγi(g	PROPN
ejpam-3484	328	10	)	)	PUNCT
ejpam-3484	328	11	.	.	PUNCT
ejpam-3484	329	1	let	let	VERB
ejpam-3484	329	2	c0	c0	PROPN
ejpam-3484	329	3	=	=	PROPN
ejpam-3484	329	4	s0	s0	PROPN
ejpam-3484	329	5	×	×	PROPN
ejpam-3484	329	6	r	r	NOUN
ejpam-3484	329	7	be	be	VERB
ejpam-3484	329	8	a	a	DET
ejpam-3484	329	9	γi	γi	NOUN
ejpam-3484	329	10	-	-	PUNCT
ejpam-3484	329	11	set	set	NOUN
ejpam-3484	329	12	of	of	ADP
ejpam-3484	329	13	g[h	g[h	NOUN
ejpam-3484	329	14	]	]	PUNCT
ejpam-3484	329	15	such	such	ADJ
ejpam-3484	330	1	that	that	SCONJ
ejpam-3484	330	2	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	330	3	]	]	PUNCT
ejpam-3484	330	4	)	)	PUNCT
ejpam-3484	330	5	=	=	SYM
ejpam-3484	330	6	fγi(c0	fγi(c0	NOUN
ejpam-3484	330	7	)	)	PUNCT
ejpam-3484	330	8	.	.	PUNCT
ejpam-3484	331	1	by	by	ADP
ejpam-3484	331	2	theorem	theorem	NOUN
ejpam-3484	331	3	2.5	2.5	NUM
ejpam-3484	331	4	,	,	PUNCT
ejpam-3484	331	5	s0	s0	PROPN
ejpam-3484	331	6	is	be	AUX
ejpam-3484	331	7	a	a	DET
ejpam-3484	331	8	γi	γi	NOUN
ejpam-3484	331	9	-	-	PUNCT
ejpam-3484	331	10	set	set	NOUN
ejpam-3484	331	11	of	of	ADP
ejpam-3484	331	12	g.	g.	PROPN
ejpam-3484	331	13	let	let	VERB
ejpam-3484	331	14	q0	q0	PROPN
ejpam-3484	331	15	be	be	AUX
ejpam-3484	331	16	a	a	DET
ejpam-3484	331	17	forcing	forcing	NOUN
ejpam-3484	331	18	subset	subset	NOUN
ejpam-3484	331	19	for	for	ADP
ejpam-3484	331	20	c0	c0	PROPN
ejpam-3484	331	21	with	with	ADP
ejpam-3484	331	22	fγi(c0	fγi(c0	PROPN
ejpam-3484	331	23	)	)	PUNCT
ejpam-3484	331	24	=	=	SYM
ejpam-3484	332	1	|q0|	|q0|	NOUN
ejpam-3484	332	2	.	.	PUNCT
ejpam-3484	333	1	let	let	VERB
ejpam-3484	333	2	q0	q0	PROPN
ejpam-3484	334	1	=	=	SYM
ejpam-3484	334	2	∪x∈k	∪x∈k	PROPN
ejpam-3484	335	1	[	[	X
ejpam-3484	335	2	{	{	PUNCT
ejpam-3484	335	3	x	x	NOUN
ejpam-3484	335	4	}	}	PUNCT
ejpam-3484	335	5	×	×	PROPN
ejpam-3484	335	6	tx	tx	PROPN
ejpam-3484	335	7	]	]	X
ejpam-3484	335	8	,	,	PUNCT
ejpam-3484	335	9	where	where	SCONJ
ejpam-3484	335	10	k	k	PROPN
ejpam-3484	335	11	⊆	⊆	NUM
ejpam-3484	335	12	s0	s0	NOUN
ejpam-3484	335	13	and	and	CCONJ
ejpam-3484	335	14	tx	tx	VERB
ejpam-3484	335	15	⊆	⊆	NUM
ejpam-3484	335	16	r	r	NOUN
ejpam-3484	335	17	for	for	ADP
ejpam-3484	335	18	all	all	DET
ejpam-3484	335	19	x	x	SYM
ejpam-3484	335	20	∈	∈	PROPN
ejpam-3484	335	21	k.	k.	NOUN
ejpam-3484	335	22	since	since	SCONJ
ejpam-3484	335	23	q0	q0	PROPN
ejpam-3484	335	24	is	be	AUX
ejpam-3484	335	25	a	a	DET
ejpam-3484	335	26	forcing	forcing	NOUN
ejpam-3484	335	27	subset	subset	NOUN
ejpam-3484	335	28	for	for	ADP
ejpam-3484	335	29	c0	c0	NOUN
ejpam-3484	335	30	,	,	PUNCT
ejpam-3484	335	31	it	it	PRON
ejpam-3484	335	32	follows	follow	VERB
ejpam-3484	335	33	that	that	SCONJ
ejpam-3484	335	34	k	k	PROPN
ejpam-3484	335	35	is	be	AUX
ejpam-3484	335	36	a	a	DET
ejpam-3484	335	37	forcing	forcing	NOUN
ejpam-3484	335	38	subset	subset	NOUN
ejpam-3484	335	39	for	for	ADP
ejpam-3484	335	40	s0	s0	PROPN
ejpam-3484	335	41	.	.	PUNCT
ejpam-3484	336	1	choose	choose	VERB
ejpam-3484	336	2	any	any	DET
ejpam-3484	336	3	x	x	SYM
ejpam-3484	336	4	∈	∈	PROPN
ejpam-3484	336	5	k	k	PROPN
ejpam-3484	336	6	and	and	CCONJ
ejpam-3484	336	7	a	a	DET
ejpam-3484	336	8	∈	∈	PROPN
ejpam-3484	336	9	tx	tx	PROPN
ejpam-3484	336	10	.	.	PUNCT
ejpam-3484	337	1	then	then	ADV
ejpam-3484	337	2	qa	qa	PROPN
ejpam-3484	338	1	=	=	PUNCT
ejpam-3484	339	1	k	k	PROPN
ejpam-3484	339	2	×	×	PROPN
ejpam-3484	339	3	{	{	PUNCT
ejpam-3484	339	4	a	a	NOUN
ejpam-3484	339	5	}	}	PUNCT
ejpam-3484	339	6	⊆	⊆	NUM
ejpam-3484	339	7	q0	q0	NOUN
ejpam-3484	339	8	.	.	PUNCT
ejpam-3484	340	1	thus	thus	ADV
ejpam-3484	340	2	,	,	PUNCT
ejpam-3484	340	3	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	340	4	]	]	PUNCT
ejpam-3484	340	5	)	)	PUNCT
ejpam-3484	341	1	=	=	SYM
ejpam-3484	341	2	fγi(c0	fγi(c0	NOUN
ejpam-3484	341	3	)	)	PUNCT
ejpam-3484	341	4	=	=	PUNCT
ejpam-3484	341	5	|q0|	|q0|	NOUN
ejpam-3484	341	6	≥	≥	NOUN
ejpam-3484	341	7	|qa|	|qa|	VERB
ejpam-3484	341	8	=	=	PUNCT
ejpam-3484	341	9	|k|	|k|	PROPN
ejpam-3484	341	10	≥	≥	NOUN
ejpam-3484	341	11	fγi(s0	fγi(s0	PROPN
ejpam-3484	341	12	)	)	PUNCT
ejpam-3484	341	13	≥	≥	NOUN
ejpam-3484	341	14	fγi(g	fγi(g	PROPN
ejpam-3484	341	15	)	)	PUNCT
ejpam-3484	341	16	.	.	PUNCT
ejpam-3484	342	1	therefore	therefore	ADV
ejpam-3484	342	2	,	,	PUNCT
ejpam-3484	342	3	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	342	4	]	]	PUNCT
ejpam-3484	342	5	)	)	PUNCT
ejpam-3484	342	6	=	=	SYM
ejpam-3484	342	7	fγi(g	fγi(g	PROPN
ejpam-3484	342	8	)	)	PUNCT
ejpam-3484	342	9	.	.	PUNCT
ejpam-3484	343	1	in	in	ADP
ejpam-3484	343	2	particular	particular	ADJ
ejpam-3484	343	3	,	,	PUNCT
ejpam-3484	343	4	if	if	SCONJ
ejpam-3484	343	5	g	g	PROPN
ejpam-3484	343	6	has	have	VERB
ejpam-3484	343	7	a	a	DET
ejpam-3484	343	8	unique	unique	ADJ
ejpam-3484	343	9	γi	γi	NOUN
ejpam-3484	343	10	-	-	PUNCT
ejpam-3484	343	11	set	set	ADJ
ejpam-3484	343	12	,	,	PUNCT
ejpam-3484	343	13	then	then	ADV
ejpam-3484	343	14	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	343	15	]	]	PUNCT
ejpam-3484	343	16	)	)	PUNCT
ejpam-3484	343	17	=	=	SYM
ejpam-3484	343	18	0	0	X
ejpam-3484	343	19	.	.	PUNCT
ejpam-3484	343	20	case	case	NOUN
ejpam-3484	343	21	2	2	NUM
ejpam-3484	343	22	:	:	PUNCT
ejpam-3484	343	23	suppose	suppose	VERB
ejpam-3484	343	24	that	that	SCONJ
ejpam-3484	343	25	h	h	NOUN
ejpam-3484	343	26	does	do	AUX
ejpam-3484	343	27	not	not	PART
ejpam-3484	343	28	have	have	VERB
ejpam-3484	343	29	a	a	DET
ejpam-3484	343	30	unique	unique	ADJ
ejpam-3484	343	31	γi	γi	NOUN
ejpam-3484	343	32	-	-	PUNCT
ejpam-3484	343	33	set	set	NOUN
ejpam-3484	343	34	.	.	PUNCT
ejpam-3484	344	1	let	let	VERB
ejpam-3484	344	2	r0	r0	NOUN
ejpam-3484	344	3	be	be	AUX
ejpam-3484	344	4	a	a	DET
ejpam-3484	344	5	γi	γi	NOUN
ejpam-3484	344	6	-	-	PUNCT
ejpam-3484	344	7	set	set	NOUN
ejpam-3484	344	8	of	of	ADP
ejpam-3484	344	9	h	h	NOUN
ejpam-3484	344	10	and	and	CCONJ
ejpam-3484	344	11	t0	t0	PROPN
ejpam-3484	344	12	be	be	AUX
ejpam-3484	344	13	a	a	DET
ejpam-3484	344	14	forcing	forcing	NOUN
ejpam-3484	344	15	subset	subset	NOUN
ejpam-3484	344	16	for	for	ADP
ejpam-3484	344	17	r0	r0	NOUN
ejpam-3484	344	18	such	such	ADJ
ejpam-3484	344	19	that	that	SCONJ
ejpam-3484	344	20	fγi(h	fγi(h	PROPN
ejpam-3484	344	21	)	)	PUNCT
ejpam-3484	344	22	=	=	SYM
ejpam-3484	344	23	fγi(r0	fγi(r0	PROPN
ejpam-3484	344	24	)	)	PUNCT
ejpam-3484	344	25	=	=	SYM
ejpam-3484	344	26	|t0|	|t0|	NOUN
ejpam-3484	344	27	.	.	PUNCT
ejpam-3484	345	1	let	let	VERB
ejpam-3484	345	2	s0	s0	PROPN
ejpam-3484	345	3	be	be	AUX
ejpam-3484	345	4	a	a	DET
ejpam-3484	345	5	γi	γi	NOUN
ejpam-3484	345	6	-	-	PUNCT
ejpam-3484	345	7	set	set	NOUN
ejpam-3484	345	8	of	of	ADP
ejpam-3484	345	9	g.	g.	PROPN
ejpam-3484	345	10	for	for	ADP
ejpam-3484	345	11	each	each	DET
ejpam-3484	345	12	x	x	SYM
ejpam-3484	345	13	∈	∈	PROPN
ejpam-3484	345	14	s0	s0	NOUN
ejpam-3484	345	15	,	,	PUNCT
ejpam-3484	345	16	let	let	VERB
ejpam-3484	345	17	tx	tx	VERB
ejpam-3484	345	18	=	=	PUNCT
ejpam-3484	345	19	t0	t0	PROPN
ejpam-3484	345	20	and	and	CCONJ
ejpam-3484	345	21	rx	rx	VERB
ejpam-3484	345	22	=	=	NOUN
ejpam-3484	345	23	r0	r0	NOUN
ejpam-3484	345	24	.	.	PUNCT
ejpam-3484	346	1	by	by	ADP
ejpam-3484	346	2	theorem	theorem	NOUN
ejpam-3484	346	3	2.5	2.5	NUM
ejpam-3484	346	4	,	,	PUNCT
ejpam-3484	346	5	c	c	NOUN
ejpam-3484	346	6	=	=	SYM
ejpam-3484	346	7	∪x∈s0	∪x∈s0	PROPN
ejpam-3484	347	1	[	[	X
ejpam-3484	347	2	{	{	PUNCT
ejpam-3484	347	3	x	x	NOUN
ejpam-3484	347	4	}	}	PUNCT
ejpam-3484	347	5	×	×	NOUN
ejpam-3484	347	6	rx	rx	NOUN
ejpam-3484	347	7	]	]	X
ejpam-3484	347	8	is	be	AUX
ejpam-3484	347	9	a	a	DET
ejpam-3484	347	10	γi	γi	NOUN
ejpam-3484	347	11	-	-	PUNCT
ejpam-3484	347	12	set	set	NOUN
ejpam-3484	347	13	of	of	ADP
ejpam-3484	347	14	g[h	g[h	NOUN
ejpam-3484	347	15	]	]	PUNCT
ejpam-3484	347	16	.	.	PUNCT
ejpam-3484	348	1	then	then	ADV
ejpam-3484	348	2	c0	c0	PROPN
ejpam-3484	348	3	=	=	SYM
ejpam-3484	348	4	∪x∈s0	∪x∈s0	PROPN
ejpam-3484	349	1	[	[	X
ejpam-3484	349	2	{	{	PUNCT
ejpam-3484	349	3	x	x	NOUN
ejpam-3484	349	4	}	}	PUNCT
ejpam-3484	349	5	×	×	NOUN
ejpam-3484	349	6	tx	tx	NOUN
ejpam-3484	349	7	]	]	X
ejpam-3484	349	8	=	=	SYM
ejpam-3484	349	9	s0	s0	PROPN
ejpam-3484	349	10	×	×	PROPN
ejpam-3484	349	11	t0	t0	PROPN
ejpam-3484	349	12	is	be	AUX
ejpam-3484	349	13	a	a	DET
ejpam-3484	349	14	forcing	forcing	NOUN
ejpam-3484	349	15	subset	subset	NOUN
ejpam-3484	349	16	for	for	ADP
ejpam-3484	349	17	c.	c.	NOUN
ejpam-3484	349	18	hence	hence	ADV
ejpam-3484	349	19	,	,	PUNCT
ejpam-3484	349	20	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	349	21	]	]	PUNCT
ejpam-3484	349	22	)	)	PUNCT
ejpam-3484	349	23	≤	≤	NUM
ejpam-3484	349	24	fγi(c0	fγi(c0	NOUN
ejpam-3484	349	25	)	)	PUNCT
ejpam-3484	349	26	≤	≤	NOUN
ejpam-3484	349	27	|c0|	|c0|	NOUN
ejpam-3484	349	28	=	=	SYM
ejpam-3484	349	29	|s0	|s0	ADJ
ejpam-3484	349	30	×	×	NOUN
ejpam-3484	349	31	t0|	t0|	PUNCT
ejpam-3484	349	32	=	=	SYM
ejpam-3484	349	33	γi(g)fγi(h	γi(g)fγi(h	NOUN
ejpam-3484	349	34	)	)	PUNCT
ejpam-3484	349	35	.	.	PUNCT
ejpam-3484	350	1	next	next	ADV
ejpam-3484	350	2	,	,	PUNCT
ejpam-3484	350	3	let	let	VERB
ejpam-3484	350	4	c	c	NOUN
ejpam-3484	350	5	=	=	PUNCT
ejpam-3484	350	6	∪x∈s	∪x∈s	PROPN
ejpam-3484	350	7	[	[	X
ejpam-3484	350	8	{	{	PUNCT
ejpam-3484	350	9	x	x	NOUN
ejpam-3484	350	10	}	}	PUNCT
ejpam-3484	350	11	×	×	PROPN
ejpam-3484	350	12	tx	tx	PROPN
ejpam-3484	350	13	]	]	PUNCT
ejpam-3484	350	14	be	be	AUX
ejpam-3484	350	15	a	a	DET
ejpam-3484	350	16	γi	γi	NOUN
ejpam-3484	350	17	-	-	PUNCT
ejpam-3484	350	18	set	set	NOUN
ejpam-3484	350	19	of	of	ADP
ejpam-3484	350	20	g[h	g[h	NOUN
ejpam-3484	350	21	]	]	PUNCT
ejpam-3484	350	22	and	and	CCONJ
ejpam-3484	350	23	let	let	VERB
ejpam-3484	350	24	d	d	PRON
ejpam-3484	350	25	be	be	AUX
ejpam-3484	350	26	a	a	DET
ejpam-3484	350	27	forcing	forcing	NOUN
ejpam-3484	350	28	subset	subset	NOUN
ejpam-3484	350	29	for	for	ADP
ejpam-3484	350	30	c	c	PROPN
ejpam-3484	350	31	such	such	ADJ
ejpam-3484	350	32	that	that	SCONJ
ejpam-3484	350	33	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	350	34	]	]	PUNCT
ejpam-3484	350	35	)	)	PUNCT
ejpam-3484	351	1	=	=	SYM
ejpam-3484	351	2	fγi(c	fγi(c	X
ejpam-3484	351	3	)	)	PUNCT
ejpam-3484	351	4	=	=	SYM
ejpam-3484	351	5	|d|	|d|	PROPN
ejpam-3484	351	6	.	.	PUNCT
ejpam-3484	352	1	then	then	ADV
ejpam-3484	352	2	by	by	ADP
ejpam-3484	352	3	theorem	theorem	NOUN
ejpam-3484	352	4	2.5	2.5	NUM
ejpam-3484	352	5	,	,	PUNCT
ejpam-3484	352	6	s	s	VERB
ejpam-3484	352	7	is	be	AUX
ejpam-3484	352	8	a	a	DET
ejpam-3484	352	9	γi	γi	NOUN
ejpam-3484	352	10	-	-	PUNCT
ejpam-3484	352	11	set	set	NOUN
ejpam-3484	352	12	of	of	ADP
ejpam-3484	352	13	g	g	PROPN
ejpam-3484	352	14	and	and	CCONJ
ejpam-3484	352	15	tx	tx	PROPN
ejpam-3484	352	16	is	be	AUX
ejpam-3484	352	17	a	a	DET
ejpam-3484	352	18	γi	γi	NOUN
ejpam-3484	352	19	-	-	PUNCT
ejpam-3484	352	20	set	set	NOUN
ejpam-3484	352	21	of	of	ADP
ejpam-3484	352	22	h	h	NOUN
ejpam-3484	352	23	for	for	ADP
ejpam-3484	352	24	each	each	DET
ejpam-3484	352	25	x	x	SYM
ejpam-3484	352	26	∈	∈	PROPN
ejpam-3484	352	27	s.	s.	PROPN
ejpam-3484	352	28	let	let	VERB
ejpam-3484	352	29	d	d	PROPN
ejpam-3484	352	30	=	=	SYM
ejpam-3484	352	31	∪x∈k	∪x∈k	PROPN
ejpam-3484	353	1	[	[	X
ejpam-3484	353	2	{	{	PUNCT
ejpam-3484	353	3	x	x	NOUN
ejpam-3484	353	4	}	}	PUNCT
ejpam-3484	353	5	×	×	NOUN
ejpam-3484	353	6	ex	ex	NOUN
ejpam-3484	353	7	]	]	X
ejpam-3484	353	8	where	where	SCONJ
ejpam-3484	353	9	k	k	PROPN
ejpam-3484	353	10	⊆	⊆	NUM
ejpam-3484	353	11	s	s	NOUN
ejpam-3484	353	12	and	and	CCONJ
ejpam-3484	353	13	ex	ex	ADJ
ejpam-3484	353	14	⊆	⊆	NUM
ejpam-3484	353	15	tx	tx	NOUN
ejpam-3484	353	16	for	for	ADP
ejpam-3484	353	17	each	each	PRON
ejpam-3484	353	18	x	x	SYM
ejpam-3484	353	19	∈	∈	PROPN
ejpam-3484	353	20	s.	s.	PROPN
ejpam-3484	353	21	suppose	suppose	VERB
ejpam-3484	353	22	that	that	SCONJ
ejpam-3484	353	23	k	k	PROPN
ejpam-3484	353	24	6=	6=	PROPN
ejpam-3484	353	25	s	s	PROPN
ejpam-3484	353	26	,	,	PUNCT
ejpam-3484	353	27	say	say	VERB
ejpam-3484	353	28	v	v	NUM
ejpam-3484	353	29	∈	∈	PROPN
ejpam-3484	353	30	s\k	s\k	PROPN
ejpam-3484	353	31	.	.	PUNCT
ejpam-3484	354	1	let	let	VERB
ejpam-3484	354	2	t	t	PROPN
ejpam-3484	354	3	′v	′v	PROPN
ejpam-3484	354	4	be	be	AUX
ejpam-3484	354	5	a	a	DET
ejpam-3484	354	6	γi	γi	NOUN
ejpam-3484	354	7	-	-	PUNCT
ejpam-3484	354	8	set	set	NOUN
ejpam-3484	354	9	of	of	ADP
ejpam-3484	354	10	h	h	NOUN
ejpam-3484	354	11	with	with	ADP
ejpam-3484	354	12	t	t	PROPN
ejpam-3484	354	13	′v	′v	PROPN
ejpam-3484	354	14	6=	6=	PROPN
ejpam-3484	354	15	tv	tv	NOUN
ejpam-3484	354	16	.	.	PUNCT
ejpam-3484	355	1	then	then	ADV
ejpam-3484	355	2	c	c	ADP
ejpam-3484	355	3	′	′	NOUN
ejpam-3484	356	1	=	=	SYM
ejpam-3484	356	2	∪x∈s\{v}[{x	∪x∈s\{v}[{x	NOUN
ejpam-3484	356	3	}	}	PUNCT
ejpam-3484	356	4	×	×	NOUN
ejpam-3484	356	5	tx	tx	PROPN
ejpam-3484	356	6	]	]	PUNCT
ejpam-3484	356	7	∪	∪	X
ejpam-3484	356	8	{	{	PUNCT
ejpam-3484	356	9	v	v	NOUN
ejpam-3484	356	10	}	}	PUNCT
ejpam-3484	356	11	×	×	PROPN
ejpam-3484	356	12	t	t	PROPN
ejpam-3484	356	13	′v	′v	PROPN
ejpam-3484	356	14	is	be	AUX
ejpam-3484	356	15	a	a	DET
ejpam-3484	356	16	a	a	DET
ejpam-3484	356	17	γi	γi	NOUN
ejpam-3484	356	18	-	-	PUNCT
ejpam-3484	356	19	set	set	NOUN
ejpam-3484	356	20	of	of	ADP
ejpam-3484	356	21	g[h	g[h	NOUN
ejpam-3484	356	22	]	]	PUNCT
ejpam-3484	356	23	and	and	CCONJ
ejpam-3484	356	24	d	d	X
ejpam-3484	356	25	⊆	⊆	NUM
ejpam-3484	356	26	c	c	NOUN
ejpam-3484	356	27	′	′	NUM
ejpam-3484	356	28	6=	6=	PROPN
ejpam-3484	357	1	c	c	X
ejpam-3484	357	2	,	,	PUNCT
ejpam-3484	357	3	a	a	DET
ejpam-3484	357	4	contradiction	contradiction	NOUN
ejpam-3484	357	5	.	.	PUNCT
ejpam-3484	358	1	thus	thus	ADV
ejpam-3484	358	2	,	,	PUNCT
ejpam-3484	358	3	k	k	PROPN
ejpam-3484	358	4	=	=	SYM
ejpam-3484	358	5	s	s	X
ejpam-3484	358	6	and	and	CCONJ
ejpam-3484	358	7	since	since	SCONJ
ejpam-3484	358	8	d	d	PRON
ejpam-3484	358	9	be	be	AUX
ejpam-3484	358	10	a	a	DET
ejpam-3484	358	11	forcing	forcing	NOUN
ejpam-3484	358	12	subset	subset	NOUN
ejpam-3484	358	13	for	for	ADP
ejpam-3484	358	14	c	c	PROPN
ejpam-3484	358	15	,	,	PUNCT
ejpam-3484	358	16	ex	ex	PRON
ejpam-3484	358	17	must	must	AUX
ejpam-3484	358	18	be	be	AUX
ejpam-3484	358	19	a	a	DET
ejpam-3484	358	20	forcing	forcing	NOUN
ejpam-3484	358	21	subset	subset	NOUN
ejpam-3484	358	22	for	for	ADP
ejpam-3484	358	23	tx	tx	PROPN
ejpam-3484	358	24	for	for	ADP
ejpam-3484	358	25	each	each	DET
ejpam-3484	358	26	x	x	PROPN
ejpam-3484	358	27	∈	∈	PROPN
ejpam-3484	358	28	s.	s.	PROPN
ejpam-3484	358	29	hence	hence	ADV
ejpam-3484	358	30	,	,	PUNCT
ejpam-3484	358	31	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	358	32	]	]	PUNCT
ejpam-3484	358	33	)	)	PUNCT
ejpam-3484	358	34	=	=	SYM
ejpam-3484	358	35	|d|	|d|	PROPN
ejpam-3484	358	36	=	=	PUNCT
ejpam-3484	358	37	∑	∑	PROPN
ejpam-3484	358	38	x∈s	x∈s	PROPN
ejpam-3484	358	39	|ex|	|ex|	PROPN
ejpam-3484	358	40	≥	≥	NUM
ejpam-3484	358	41	γi(g)fγi(h	γi(g)fγi(h	NOUN
ejpam-3484	358	42	)	)	PUNCT
ejpam-3484	358	43	.	.	PUNCT
ejpam-3484	359	1	therefore	therefore	ADV
ejpam-3484	359	2	,	,	PUNCT
ejpam-3484	359	3	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	359	4	]	]	PUNCT
ejpam-3484	359	5	)	)	PUNCT
ejpam-3484	359	6	=	=	SYM
ejpam-3484	359	7	γi(g)fγi(h	γi(g)fγi(h	NOUN
ejpam-3484	359	8	)	)	PUNCT
ejpam-3484	359	9	.	.	PUNCT
ejpam-3484	360	1	in	in	ADP
ejpam-3484	360	2	particular	particular	ADJ
ejpam-3484	360	3	,	,	PUNCT
ejpam-3484	360	4	if	if	SCONJ
ejpam-3484	360	5	fγi(h	fγi(h	PROPN
ejpam-3484	360	6	)	)	PUNCT
ejpam-3484	360	7	=	=	SYM
ejpam-3484	361	1	γi(h	γi(h	NOUN
ejpam-3484	361	2	)	)	PUNCT
ejpam-3484	361	3	,	,	PUNCT
ejpam-3484	361	4	then	then	ADV
ejpam-3484	361	5	fγi(g[h	fγi(g[h	NOUN
ejpam-3484	361	6	]	]	PUNCT
ejpam-3484	361	7	)	)	PUNCT
ejpam-3484	361	8	=	=	SYM
ejpam-3484	361	9	γi(g)γi(h	γi(g)γi(h	X
ejpam-3484	361	10	)	)	PUNCT
ejpam-3484	361	11	=	=	PUNCT
ejpam-3484	362	1	γi(g[h	γi(g[h	NOUN
ejpam-3484	362	2	]	]	PUNCT
ejpam-3484	362	3	)	)	PUNCT
ejpam-3484	362	4	.	.	PUNCT
ejpam-3484	363	1	since	since	SCONJ
ejpam-3484	363	2	the	the	DET
ejpam-3484	363	3	complete	complete	ADJ
ejpam-3484	363	4	graph	graph	NOUN
ejpam-3484	363	5	kn	kn	PROPN
ejpam-3484	363	6	has	have	VERB
ejpam-3484	363	7	no	no	DET
ejpam-3484	363	8	unique	unique	ADJ
ejpam-3484	363	9	γi	γi	NOUN
ejpam-3484	363	10	-	-	PUNCT
ejpam-3484	363	11	sets	set	NOUN
ejpam-3484	363	12	and	and	CCONJ
ejpam-3484	363	13	fγi(kn	fγi(kn	NOUN
ejpam-3484	363	14	)	)	PUNCT
ejpam-3484	363	15	=	=	SYM
ejpam-3484	363	16	1	1	NUM
ejpam-3484	363	17	except	except	SCONJ
ejpam-3484	363	18	when	when	SCONJ
ejpam-3484	363	19	n	n	X
ejpam-3484	363	20	=	=	SYM
ejpam-3484	363	21	1	1	NUM
ejpam-3484	363	22	,	,	PUNCT
ejpam-3484	363	23	the	the	DET
ejpam-3484	363	24	following	following	ADJ
ejpam-3484	363	25	result	result	NOUN
ejpam-3484	363	26	is	be	AUX
ejpam-3484	363	27	immediate	immediate	ADJ
ejpam-3484	363	28	from	from	ADP
ejpam-3484	363	29	theorem	theorem	ADJ
ejpam-3484	363	30	3.21	3.21	NUM
ejpam-3484	363	31	.	.	PUNCT
ejpam-3484	364	1	corollary	corollary	ADJ
ejpam-3484	364	2	3.22	3.22	NUM
ejpam-3484	364	3	.	.	PUNCT
ejpam-3484	365	1	let	let	VERB
ejpam-3484	365	2	g	g	PRON
ejpam-3484	365	3	be	be	AUX
ejpam-3484	365	4	a	a	DET
ejpam-3484	365	5	connected	connected	ADJ
ejpam-3484	365	6	graph	graph	NOUN
ejpam-3484	365	7	and	and	CCONJ
ejpam-3484	365	8	kn	kn	PROPN
ejpam-3484	365	9	the	the	DET
ejpam-3484	365	10	complete	complete	ADJ
ejpam-3484	365	11	graph	graph	NOUN
ejpam-3484	365	12	of	of	ADP
ejpam-3484	365	13	order	order	NOUN
ejpam-3484	365	14	n	n	PRON
ejpam-3484	365	15	≥	≥	NOUN
ejpam-3484	365	16	1	1	NUM
ejpam-3484	365	17	.	.	PUNCT
ejpam-3484	366	1	then	then	ADV
ejpam-3484	366	2	fγi(g[kn	fγi(g[kn	PROPN
ejpam-3484	366	3	]	]	X
ejpam-3484	366	4	)	)	PUNCT
ejpam-3484	366	5	=	=	SYM
ejpam-3484	366	6	{	{	PUNCT
ejpam-3484	366	7	fγi(g	fγi(g	PROPN
ejpam-3484	366	8	)	)	PUNCT
ejpam-3484	366	9	,	,	PUNCT
ejpam-3484	366	10	n	n	NOUN
ejpam-3484	366	11	=	=	SYM
ejpam-3484	366	12	1	1	NUM
ejpam-3484	366	13	γi(g	γi(g	NOUN
ejpam-3484	366	14	)	)	PUNCT
ejpam-3484	366	15	,	,	PUNCT
ejpam-3484	366	16	n	n	CCONJ
ejpam-3484	366	17	>	>	SYM
ejpam-3484	366	18	1	1	NUM
ejpam-3484	366	19	references	reference	NOUN
ejpam-3484	366	20	1381	1381	NUM
ejpam-3484	366	21	acknowledgements	acknowledgement	NOUN
ejpam-3484	366	22	the	the	DET
ejpam-3484	366	23	authors	author	NOUN
ejpam-3484	366	24	would	would	AUX
ejpam-3484	366	25	like	like	VERB
ejpam-3484	366	26	to	to	PART
ejpam-3484	366	27	thank	thank	VERB
ejpam-3484	366	28	the	the	DET
ejpam-3484	366	29	referees	referee	NOUN
ejpam-3484	366	30	for	for	ADP
ejpam-3484	366	31	their	their	PRON
ejpam-3484	366	32	invaluable	invaluable	ADJ
ejpam-3484	366	33	suggestions	suggestion	NOUN
ejpam-3484	366	34	and	and	CCONJ
ejpam-3484	366	35	comments	comment	NOUN
ejpam-3484	366	36	which	which	PRON
ejpam-3484	366	37	greatly	greatly	ADV
ejpam-3484	366	38	contributed	contribute	VERB
ejpam-3484	366	39	in	in	ADP
ejpam-3484	366	40	the	the	DET
ejpam-3484	366	41	improvement	improvement	NOUN
ejpam-3484	366	42	of	of	ADP
ejpam-3484	366	43	the	the	DET
ejpam-3484	366	44	paper	paper	NOUN
ejpam-3484	366	45	.	.	PUNCT
ejpam-3484	367	1	the	the	DET
ejpam-3484	367	2	authors	author	NOUN
ejpam-3484	367	3	would	would	AUX
ejpam-3484	367	4	like	like	VERB
ejpam-3484	367	5	to	to	PART
ejpam-3484	367	6	thank	thank	VERB
ejpam-3484	367	7	also	also	ADV
ejpam-3484	367	8	the	the	DET
ejpam-3484	367	9	following	follow	VERB
ejpam-3484	367	10	funding	funding	NOUN
ejpam-3484	367	11	agencies	agency	NOUN
ejpam-3484	367	12	:	:	PUNCT
ejpam-3484	367	13	department	department	NOUN
ejpam-3484	367	14	of	of	ADP
ejpam-3484	367	15	science	science	NOUN
ejpam-3484	367	16	and	and	CCONJ
ejpam-3484	367	17	technology	technology	NOUN
ejpam-3484	367	18	-	-	PUNCT
ejpam-3484	367	19	science	science	NOUN
ejpam-3484	367	20	education	education	PROPN
ejpam-3484	367	21	institute	institute	NOUN
ejpam-3484	367	22	-	-	PUNCT
ejpam-3484	367	23	accelerated	accelerate	VERB
ejpam-3484	367	24	science	science	NOUN
ejpam-3484	367	25	and	and	CCONJ
ejpam-3484	367	26	technology	technology	NOUN
ejpam-3484	367	27	human	human	ADJ
ejpam-3484	367	28	resource	resource	NOUN
ejpam-3484	367	29	development	development	NOUN
ejpam-3484	367	30	program	program	NOUN
ejpam-3484	367	31	(	(	PUNCT
ejpam-3484	367	32	dost	dost	NOUN
ejpam-3484	367	33	-	-	PUNCT
ejpam-3484	367	34	sei	sei	ADJ
ejpam-3484	367	35	-	-	PUNCT
ejpam-3484	367	36	asthrdp	asthrdp	NOUN
ejpam-3484	367	37	)	)	PUNCT
ejpam-3484	367	38	,	,	PUNCT
ejpam-3484	367	39	mindanao	mindanao	PROPN
ejpam-3484	367	40	state	state	PROPN
ejpam-3484	367	41	university	university	PROPN
ejpam-3484	367	42	-	-	PUNCT
ejpam-3484	367	43	iligan	iligan	PROPN
ejpam-3484	367	44	institute	institute	PROPN
ejpam-3484	367	45	of	of	ADP
ejpam-3484	367	46	technology	technology	PROPN
ejpam-3484	367	47	and	and	CCONJ
ejpam-3484	367	48	cebu	cebu	NOUN
ejpam-3484	367	49	normal	normal	ADJ
ejpam-3484	367	50	university	university	NOUN
ejpam-3484	367	51	.	.	PUNCT
ejpam-3484	368	1	references	reference	NOUN
ejpam-3484	368	2	[	[	X
ejpam-3484	368	3	1	1	NUM
ejpam-3484	368	4	]	]	X
ejpam-3484	368	5	c.	c.	PROPN
ejpam-3484	368	6	armada	armada	PROPN
ejpam-3484	368	7	,	,	PUNCT
ejpam-3484	368	8	s.	s.	PROPN
ejpam-3484	368	9	canoy	canoy	PROPN
ejpam-3484	368	10	jr	jr	PROPN
ejpam-3484	368	11	.	.	PROPN
ejpam-3484	368	12	,	,	PUNCT
ejpam-3484	368	13	and	and	CCONJ
ejpam-3484	368	14	c.	c.	PROPN
ejpam-3484	368	15	go	go	VERB
ejpam-3484	368	16	,	,	PUNCT
ejpam-3484	368	17	forcing	force	VERB
ejpam-3484	368	18	domination	domination	NOUN
ejpam-3484	368	19	numbers	number	NOUN
ejpam-3484	368	20	of	of	ADP
ejpam-3484	368	21	graphs	graph	NOUN
ejpam-3484	368	22	under	under	ADP
ejpam-3484	368	23	some	some	DET
ejpam-3484	368	24	binary	binary	ADJ
ejpam-3484	368	25	operations	operation	NOUN
ejpam-3484	368	26	,	,	PUNCT
ejpam-3484	368	27	advances	advance	NOUN
ejpam-3484	368	28	and	and	CCONJ
ejpam-3484	368	29	applications	application	NOUN
ejpam-3484	368	30	in	in	ADP
ejpam-3484	368	31	discrete	discrete	ADJ
ejpam-3484	368	32	mathematics	mathematic	NOUN
ejpam-3484	368	33	,	,	PUNCT
ejpam-3484	368	34	19	19	NUM
ejpam-3484	368	35	:	:	SYM
ejpam-3484	368	36	213	213	NUM
ejpam-3484	368	37	-	-	SYM
ejpam-3484	368	38	228	228	NUM
ejpam-3484	368	39	,	,	PUNCT
ejpam-3484	368	40	2018	2018	NUM
ejpam-3484	368	41	[	[	X
ejpam-3484	368	42	2	2	X
ejpam-3484	368	43	]	]	PUNCT
ejpam-3484	368	44	s.	s.	PROPN
ejpam-3484	368	45	canoy	canoy	PROPN
ejpam-3484	368	46	jr	jr	PROPN
ejpam-3484	368	47	.	.	PROPN
ejpam-3484	368	48	,	,	PUNCT
ejpam-3484	368	49	another	another	DET
ejpam-3484	368	50	look	look	NOUN
ejpam-3484	368	51	at	at	ADP
ejpam-3484	368	52	independent	independent	ADJ
ejpam-3484	368	53	domination	domination	NOUN
ejpam-3484	368	54	in	in	ADP
ejpam-3484	368	55	graphs	graph	NOUN
ejpam-3484	368	56	,	,	PUNCT
ejpam-3484	368	57	international	international	ADJ
ejpam-3484	368	58	journal	journal	NOUN
ejpam-3484	368	59	of	of	ADP
ejpam-3484	368	60	mathematical	mathematical	ADJ
ejpam-3484	368	61	analysis	analysis	NOUN
ejpam-3484	368	62	,	,	PUNCT
ejpam-3484	368	63	8:2075	8:2075	NUM
ejpam-3484	368	64	2082	2082	NUM
ejpam-3484	368	65	,	,	PUNCT
ejpam-3484	368	66	2014	2014	NUM
ejpam-3484	369	1	[	[	X
ejpam-3484	369	2	3	3	NUM
ejpam-3484	369	3	]	]	X
ejpam-3484	369	4	g.	g.	PROPN
ejpam-3484	369	5	chartrand	chartrand	PROPN
ejpam-3484	369	6	,	,	PUNCT
ejpam-3484	369	7	h.	h.	PROPN
ejpam-3484	369	8	gavlas	gavlas	PROPN
ejpam-3484	369	9	,	,	PUNCT
ejpam-3484	369	10	k.c	k.c	PROPN
ejpam-3484	369	11	.	.	PROPN
ejpam-3484	369	12	vandell	vandell	PROPN
ejpam-3484	369	13	,	,	PUNCT
ejpam-3484	369	14	and	and	CCONJ
ejpam-3484	369	15	f.	f.	PROPN
ejpam-3484	369	16	harary	harary	PROPN
ejpam-3484	369	17	,	,	PUNCT
ejpam-3484	369	18	the	the	DET
ejpam-3484	369	19	forcing	force	VERB
ejpam-3484	369	20	domination	domination	NOUN
ejpam-3484	369	21	number	number	NOUN
ejpam-3484	369	22	of	of	ADP
ejpam-3484	369	23	a	a	DET
ejpam-3484	369	24	graph	graph	NOUN
ejpam-3484	369	25	,	,	PUNCT
ejpam-3484	369	26	j.combin	j.combin	NOUN
ejpam-3484	369	27	.	.	PUNCT
ejpam-3484	369	28	math	math	NOUN
ejpam-3484	369	29	.	.	PUNCT
ejpam-3484	370	1	combin	combin	NOUN
ejpam-3484	370	2	.	.	PUNCT
ejpam-3484	371	1	comput	comput	NOUN
ejpam-3484	371	2	.	.	PUNCT
ejpam-3484	371	3	,	,	PUNCT
ejpam-3484	371	4	25:161	25:161	NUM
ejpam-3484	371	5	-	-	SYM
ejpam-3484	371	6	174	174	NUM
ejpam-3484	371	7	,	,	PUNCT
ejpam-3484	371	8	1997	1997	NUM
ejpam-3484	371	9	[	[	X
ejpam-3484	371	10	4	4	X
ejpam-3484	371	11	]	]	PUNCT
ejpam-3484	371	12	w.	w.	PROPN
ejpam-3484	371	13	goddard	goddard	PROPN
ejpam-3484	371	14	,	,	PUNCT
ejpam-3484	371	15	and	and	CCONJ
ejpam-3484	371	16	m.	m.	PROPN
ejpam-3484	371	17	henning	henning	PROPN
ejpam-3484	371	18	,	,	PUNCT
ejpam-3484	371	19	independent	independent	ADJ
ejpam-3484	371	20	domination	domination	NOUN
ejpam-3484	371	21	in	in	ADP
ejpam-3484	371	22	graphs	graph	NOUN
ejpam-3484	371	23	:	:	PUNCT
ejpam-3484	371	24	a	a	DET
ejpam-3484	371	25	survey	survey	NOUN
ejpam-3484	371	26	and	and	CCONJ
ejpam-3484	371	27	recent	recent	ADJ
ejpam-3484	371	28	results	result	NOUN
ejpam-3484	371	29	.	.	PUNCT
ejpam-3484	372	1	,	,	PUNCT
ejpam-3484	372	2	discrete	discrete	ADJ
ejpam-3484	372	3	mathematics	mathematic	NOUN
ejpam-3484	372	4	,	,	PUNCT
ejpam-3484	372	5	313:839	313:839	PROPN
ejpam-3484	372	6	-	-	PUNCT
ejpam-3484	372	7	854	854	NUM
ejpam-3484	372	8	,	,	PUNCT
ejpam-3484	372	9	2013	2013	NUM
ejpam-3484	372	10	[	[	X
ejpam-3484	372	11	5	5	NUM
ejpam-3484	372	12	]	]	PUNCT
ejpam-3484	372	13	c.	c.	PROPN
ejpam-3484	372	14	larson	larson	PROPN
ejpam-3484	372	15	,	,	PUNCT
ejpam-3484	372	16	and	and	CCONJ
ejpam-3484	372	17	n.	n.	PROPN
ejpam-3484	372	18	van	van	PROPN
ejpam-3484	372	19	cleemput	cleemput	NOUN
ejpam-3484	372	20	,	,	PUNCT
ejpam-3484	372	21	forcing	force	VERB
ejpam-3484	372	22	independence	independence	NOUN
ejpam-3484	372	23	,	,	PUNCT
ejpam-3484	372	24	croatica	croatica	PROPN
ejpam-3484	372	25	chemica	chemica	PROPN
ejpam-3484	372	26	acta	acta	PROPN
ejpam-3484	372	27	,	,	PUNCT
ejpam-3484	372	28	86:469	86:469	NUM
ejpam-3484	372	29	-	-	SYM
ejpam-3484	372	30	475	475	NUM
ejpam-3484	372	31	,	,	PUNCT
ejpam-3484	372	32	2013	2013	NUM