id	sid	tid	token	lemma	pos
ejpam-6040	1	1	european	european	PROPN
ejpam-6040	1	2	journal	journal	PROPN
ejpam-6040	1	3	of	of	ADP
ejpam-6040	1	4	pure	pure	ADJ
ejpam-6040	1	5	and	and	CCONJ
ejpam-6040	1	6	applied	applied	ADJ
ejpam-6040	1	7	mathematics	mathematic	NOUN
ejpam-6040	1	8	2025	2025	NUM
ejpam-6040	1	9	,	,	PUNCT
ejpam-6040	1	10	vol	vol	NOUN
ejpam-6040	1	11	.	.	PROPN
ejpam-6040	1	12	18	18	NUM
ejpam-6040	1	13	,	,	PUNCT
ejpam-6040	1	14	issue	issue	NOUN
ejpam-6040	1	15	2	2	NUM
ejpam-6040	1	16	,	,	PUNCT
ejpam-6040	1	17	article	article	NOUN
ejpam-6040	1	18	number	number	NOUN
ejpam-6040	1	19	6040	6040	NUM
ejpam-6040	1	20	issn	issn	VERB
ejpam-6040	1	21	1307	1307	NUM
ejpam-6040	1	22	-	-	SYM
ejpam-6040	1	23	5543	5543	NUM
ejpam-6040	1	24	–	–	PUNCT
ejpam-6040	1	25	ejpam.com	ejpam.com	X
ejpam-6040	1	26	published	publish	VERB
ejpam-6040	1	27	by	by	ADP
ejpam-6040	1	28	new	new	PROPN
ejpam-6040	1	29	york	york	PROPN
ejpam-6040	1	30	business	business	PROPN
ejpam-6040	1	31	global	global	PROPN
ejpam-6040	1	32	geodetically	geodetically	ADV
ejpam-6040	1	33	undominated	undominate	VERB
ejpam-6040	1	34	vertices	vertex	NOUN
ejpam-6040	1	35	in	in	ADP
ejpam-6040	1	36	a	a	DET
ejpam-6040	1	37	graph	graph	NOUN
ejpam-6040	1	38	sergio	sergio	PROPN
ejpam-6040	1	39	r.	r.	PROPN
ejpam-6040	1	40	canoy	canoy	PROPN
ejpam-6040	1	41	,	,	PUNCT
ejpam-6040	1	42	jr.1,2	jr.1,2	PROPN
ejpam-6040	1	43	,	,	PUNCT
ejpam-6040	1	44	jesica	jesica	PROPN
ejpam-6040	1	45	m.	m.	NOUN
ejpam-6040	1	46	anoche1,2,∗	anoche1,2,∗	PROPN
ejpam-6040	1	47	1	1	NUM
ejpam-6040	1	48	department	department	NOUN
ejpam-6040	1	49	of	of	ADP
ejpam-6040	1	50	mathematics	mathematic	NOUN
ejpam-6040	1	51	and	and	CCONJ
ejpam-6040	1	52	statistics	statistic	NOUN
ejpam-6040	1	53	,	,	PUNCT
ejpam-6040	1	54	college	college	NOUN
ejpam-6040	1	55	of	of	ADP
ejpam-6040	1	56	science	science	NOUN
ejpam-6040	1	57	and	and	CCONJ
ejpam-6040	1	58	mathematics	mathematic	NOUN
ejpam-6040	1	59	,	,	PUNCT
ejpam-6040	1	60	msu	msu	PROPN
ejpam-6040	1	61	-	-	PUNCT
ejpam-6040	1	62	iligan	iligan	PROPN
ejpam-6040	1	63	institute	institute	PROPN
ejpam-6040	1	64	of	of	ADP
ejpam-6040	1	65	technology	technology	PROPN
ejpam-6040	1	66	,	,	PUNCT
ejpam-6040	1	67	9200	9200	NUM
ejpam-6040	1	68	iligan	iligan	ADJ
ejpam-6040	1	69	city	city	NOUN
ejpam-6040	1	70	,	,	PUNCT
ejpam-6040	1	71	philippines	philippine	NOUN
ejpam-6040	1	72	2	2	NUM
ejpam-6040	1	73	center	center	NOUN
ejpam-6040	1	74	of	of	ADP
ejpam-6040	1	75	mathematical	mathematical	ADJ
ejpam-6040	1	76	and	and	CCONJ
ejpam-6040	1	77	theoretical	theoretical	ADJ
ejpam-6040	1	78	physical	physical	ADJ
ejpam-6040	1	79	sciences	science	NOUN
ejpam-6040	1	80	-	-	PUNCT
ejpam-6040	1	81	prism	prism	NOUN
ejpam-6040	1	82	,	,	PUNCT
ejpam-6040	1	83	msu	msu	PROPN
ejpam-6040	1	84	-	-	PUNCT
ejpam-6040	1	85	iligan	iligan	PROPN
ejpam-6040	1	86	institute	institute	PROPN
ejpam-6040	1	87	of	of	ADP
ejpam-6040	1	88	technology	technology	PROPN
ejpam-6040	1	89	,	,	PUNCT
ejpam-6040	1	90	9200	9200	NUM
ejpam-6040	1	91	iligan	iligan	ADJ
ejpam-6040	1	92	city	city	NOUN
ejpam-6040	1	93	,	,	PUNCT
ejpam-6040	1	94	philippines	philippine	NOUN
ejpam-6040	1	95	abstract	abstract	ADJ
ejpam-6040	1	96	.	.	PUNCT
ejpam-6040	2	1	let	let	VERB
ejpam-6040	2	2	g	g	PROPN
ejpam-6040	2	3	=	=	SYM
ejpam-6040	2	4	(	(	PUNCT
ejpam-6040	2	5	v	v	NOUN
ejpam-6040	2	6	(	(	PUNCT
ejpam-6040	2	7	g	g	NOUN
ejpam-6040	2	8	)	)	PUNCT
ejpam-6040	2	9	,	,	PUNCT
ejpam-6040	2	10	e(g	e(g	PROPN
ejpam-6040	2	11	)	)	PUNCT
ejpam-6040	2	12	)	)	PUNCT
ejpam-6040	3	1	be	be	AUX
ejpam-6040	3	2	a	a	DET
ejpam-6040	3	3	simple	simple	ADJ
ejpam-6040	3	4	undirected	undirected	ADJ
ejpam-6040	3	5	graph	graph	NOUN
ejpam-6040	3	6	.	.	PUNCT
ejpam-6040	4	1	if	if	SCONJ
ejpam-6040	4	2	γg(g	γg(g	NUM
ejpam-6040	4	3	)	)	PUNCT
ejpam-6040	5	1	is	be	AUX
ejpam-6040	5	2	the	the	DET
ejpam-6040	5	3	geodetic	geodetic	ADJ
ejpam-6040	5	4	domination	domination	NOUN
ejpam-6040	5	5	number	number	NOUN
ejpam-6040	5	6	of	of	ADP
ejpam-6040	5	7	g	g	PROPN
ejpam-6040	5	8	and	and	CCONJ
ejpam-6040	5	9	s	s	VERB
ejpam-6040	5	10	⊆	⊆	NUM
ejpam-6040	5	11	v	v	NOUN
ejpam-6040	5	12	(	(	PUNCT
ejpam-6040	5	13	g	g	NOUN
ejpam-6040	5	14	)	)	PUNCT
ejpam-6040	5	15	such	such	ADJ
ejpam-6040	5	16	that	that	PRON
ejpam-6040	5	17	|s|	|s|	VERB
ejpam-6040	5	18	<	<	X
ejpam-6040	5	19	γg(g	γg(g	NOUN
ejpam-6040	5	20	)	)	PUNCT
ejpam-6040	5	21	,	,	PUNCT
ejpam-6040	5	22	then	then	ADV
ejpam-6040	5	23	definitely	definitely	ADV
ejpam-6040	5	24	,	,	PUNCT
ejpam-6040	5	25	there	there	PRON
ejpam-6040	5	26	is	be	VERB
ejpam-6040	5	27	at	at	ADV
ejpam-6040	5	28	least	least	ADJ
ejpam-6040	5	29	one	one	NUM
ejpam-6040	5	30	vertex	vertex	NOUN
ejpam-6040	5	31	of	of	ADP
ejpam-6040	5	32	g	g	NOUN
ejpam-6040	5	33	that	that	PRON
ejpam-6040	5	34	is	be	AUX
ejpam-6040	5	35	not	not	PART
ejpam-6040	5	36	geodetically	geodetically	ADV
ejpam-6040	5	37	dominated	dominate	VERB
ejpam-6040	5	38	by	by	ADP
ejpam-6040	5	39	s	s	PROPN
ejpam-6040	5	40	,	,	PUNCT
ejpam-6040	5	41	that	that	ADV
ejpam-6040	5	42	is	is	AUX
ejpam-6040	5	43	,	,	PUNCT
ejpam-6040	5	44	not	not	PART
ejpam-6040	5	45	dominated	dominate	VERB
ejpam-6040	5	46	by	by	ADP
ejpam-6040	5	47	any	any	DET
ejpam-6040	5	48	vertex	vertex	NOUN
ejpam-6040	5	49	in	in	ADP
ejpam-6040	5	50	s	s	PRON
ejpam-6040	5	51	or	or	CCONJ
ejpam-6040	5	52	not	not	PART
ejpam-6040	5	53	in	in	ADP
ejpam-6040	5	54	any	any	DET
ejpam-6040	5	55	geodesic	geodesic	NOUN
ejpam-6040	5	56	of	of	ADP
ejpam-6040	5	57	any	any	DET
ejpam-6040	5	58	two	two	NUM
ejpam-6040	5	59	vertices	vertex	NOUN
ejpam-6040	5	60	in	in	ADP
ejpam-6040	5	61	s.	s.	PROPN
ejpam-6040	5	62	if	if	SCONJ
ejpam-6040	5	63	k	k	PROPN
ejpam-6040	5	64	is	be	AUX
ejpam-6040	5	65	a	a	DET
ejpam-6040	5	66	positive	positive	ADJ
ejpam-6040	5	67	integer	integer	NOUN
ejpam-6040	5	68	with	with	ADP
ejpam-6040	5	69	k	k	PROPN
ejpam-6040	5	70	≤	≤	PROPN
ejpam-6040	6	1	γg(g	γg(g	ADP
ejpam-6040	6	2	)	)	PUNCT
ejpam-6040	7	1	−	−	PROPN
ejpam-6040	7	2	1	1	NUM
ejpam-6040	7	3	and	and	CCONJ
ejpam-6040	7	4	s	s	VERB
ejpam-6040	7	5	⊆	⊆	NUM
ejpam-6040	7	6	v	v	NOUN
ejpam-6040	7	7	(	(	PUNCT
ejpam-6040	7	8	g	g	NOUN
ejpam-6040	7	9	)	)	PUNCT
ejpam-6040	7	10	with	with	ADP
ejpam-6040	7	11	|s|	|s|	NOUN
ejpam-6040	7	12	=	=	PUNCT
ejpam-6040	7	13	γg(g)−	γg(g)−	NOUN
ejpam-6040	7	14	k	k	PROPN
ejpam-6040	7	15	,	,	PUNCT
ejpam-6040	7	16	then	then	ADV
ejpam-6040	7	17	the	the	DET
ejpam-6040	7	18	number	number	NOUN
ejpam-6040	7	19	ζgk(s	ζgk(s	PROPN
ejpam-6040	7	20	)	)	PUNCT
ejpam-6040	7	21	given	give	VERB
ejpam-6040	7	22	by	by	ADP
ejpam-6040	7	23	ζgk(s	ζgk(s	PROPN
ejpam-6040	7	24	)	)	PUNCT
ejpam-6040	8	1	=	=	SYM
ejpam-6040	8	2	|v	|v	X
ejpam-6040	8	3	(	(	PUNCT
ejpam-6040	8	4	g	g	NOUN
ejpam-6040	8	5	)	)	PUNCT
ejpam-6040	8	6	\ng	\ng	PROPN
ejpam-6040	8	7	g[s]|	g[s]|	PROPN
ejpam-6040	8	8	,	,	PUNCT
ejpam-6040	8	9	where	where	SCONJ
ejpam-6040	8	10	ng	ng	PROPN
ejpam-6040	8	11	g[s	g[s	X
ejpam-6040	8	12	]	]	X
ejpam-6040	8	13	=	=	SYM
ejpam-6040	8	14	ng[s]∩	ng[s]∩	SYM
ejpam-6040	8	15	ig[s	ig[	NOUN
ejpam-6040	8	16	]	]	PUNCT
ejpam-6040	8	17	,	,	PUNCT
ejpam-6040	8	18	is	be	AUX
ejpam-6040	8	19	called	call	VERB
ejpam-6040	8	20	the	the	DET
ejpam-6040	8	21	k	k	ADJ
ejpam-6040	8	22	-	-	ADJ
ejpam-6040	8	23	geodetic	geodetic	ADJ
ejpam-6040	8	24	domination	domination	NOUN
ejpam-6040	8	25	defect	defect	NOUN
ejpam-6040	8	26	of	of	ADP
ejpam-6040	8	27	s	s	PRON
ejpam-6040	8	28	in	in	ADP
ejpam-6040	8	29	g.	g.	PROPN
ejpam-6040	8	30	the	the	DET
ejpam-6040	8	31	k	k	ADJ
ejpam-6040	8	32	-	-	ADJ
ejpam-6040	8	33	geodetic	geodetic	ADJ
ejpam-6040	8	34	domination	domination	NOUN
ejpam-6040	8	35	defect	defect	NOUN
ejpam-6040	8	36	of	of	ADP
ejpam-6040	8	37	g	g	PROPN
ejpam-6040	8	38	is	be	AUX
ejpam-6040	8	39	denoted	denote	VERB
ejpam-6040	8	40	and	and	CCONJ
ejpam-6040	8	41	given	give	VERB
ejpam-6040	8	42	by	by	ADP
ejpam-6040	8	43	ζgk(g	ζgk(g	PROPN
ejpam-6040	8	44	)	)	PUNCT
ejpam-6040	8	45	=	=	SYM
ejpam-6040	8	46	min{ζgk(s	min{ζgk(s	PROPN
ejpam-6040	8	47	)	)	PUNCT
ejpam-6040	8	48	:	:	PUNCT
ejpam-6040	8	49	s	s	VERB
ejpam-6040	8	50	⊆	⊆	NUM
ejpam-6040	8	51	v	v	NOUN
ejpam-6040	8	52	(	(	PUNCT
ejpam-6040	8	53	g	g	NOUN
ejpam-6040	8	54	)	)	PUNCT
ejpam-6040	8	55	and	and	CCONJ
ejpam-6040	8	56	|s|	|s|	PROPN
ejpam-6040	8	57	=	=	NOUN
ejpam-6040	8	58	γg(g)−	γg(g)−	NOUN
ejpam-6040	8	59	k	k	NOUN
ejpam-6040	8	60	}	}	PUNCT
ejpam-6040	8	61	.	.	PUNCT
ejpam-6040	9	1	in	in	ADP
ejpam-6040	9	2	this	this	DET
ejpam-6040	9	3	paper	paper	NOUN
ejpam-6040	9	4	,	,	PUNCT
ejpam-6040	9	5	we	we	PRON
ejpam-6040	9	6	study	study	VERB
ejpam-6040	9	7	this	this	DET
ejpam-6040	9	8	newly	newly	ADV
ejpam-6040	9	9	defined	define	VERB
ejpam-6040	9	10	parameter	parameter	NOUN
ejpam-6040	9	11	for	for	ADP
ejpam-6040	9	12	some	some	DET
ejpam-6040	9	13	known	know	VERB
ejpam-6040	9	14	classes	class	NOUN
ejpam-6040	9	15	of	of	ADP
ejpam-6040	9	16	graphs	graph	NOUN
ejpam-6040	9	17	.	.	PUNCT
ejpam-6040	10	1	moreover	moreover	ADV
ejpam-6040	10	2	,	,	PUNCT
ejpam-6040	10	3	we	we	PRON
ejpam-6040	10	4	determine	determine	VERB
ejpam-6040	10	5	some	some	DET
ejpam-6040	10	6	sharp	sharp	ADJ
ejpam-6040	10	7	bounds	bound	NOUN
ejpam-6040	10	8	of	of	ADP
ejpam-6040	10	9	the	the	DET
ejpam-6040	10	10	parameter	parameter	NOUN
ejpam-6040	10	11	.	.	PUNCT
ejpam-6040	11	1	2020	2020	NUM
ejpam-6040	11	2	mathematics	mathematic	NOUN
ejpam-6040	11	3	subject	subject	NOUN
ejpam-6040	11	4	classifications	classification	NOUN
ejpam-6040	11	5	:	:	PUNCT
ejpam-6040	11	6	05c69	05c69	X
ejpam-6040	11	7	key	key	ADJ
ejpam-6040	11	8	words	word	NOUN
ejpam-6040	11	9	and	and	CCONJ
ejpam-6040	11	10	phrases	phrase	NOUN
ejpam-6040	11	11	:	:	PUNCT
ejpam-6040	11	12	geodetic	geodetic	ADJ
ejpam-6040	11	13	set	set	NOUN
ejpam-6040	11	14	,	,	PUNCT
ejpam-6040	11	15	domination	domination	NOUN
ejpam-6040	11	16	,	,	PUNCT
ejpam-6040	11	17	geodetic	geodetic	ADJ
ejpam-6040	11	18	domination	domination	NOUN
ejpam-6040	11	19	,	,	PUNCT
ejpam-6040	11	20	k	k	ADJ
ejpam-6040	11	21	-	-	ADJ
ejpam-6040	11	22	geodetic	geodetic	ADJ
ejpam-6040	11	23	domination	domination	NOUN
ejpam-6040	11	24	defect	defect	VERB
ejpam-6040	11	25	1	1	NUM
ejpam-6040	11	26	.	.	PUNCT
ejpam-6040	12	1	introduction	introduction	NOUN
ejpam-6040	12	2	domination	domination	NOUN
ejpam-6040	12	3	is	be	AUX
ejpam-6040	12	4	a	a	DET
ejpam-6040	12	5	fundamental	fundamental	ADJ
ejpam-6040	12	6	concept	concept	NOUN
ejpam-6040	12	7	in	in	ADP
ejpam-6040	12	8	graph	graph	NOUN
ejpam-6040	12	9	theory	theory	NOUN
ejpam-6040	12	10	with	with	ADP
ejpam-6040	12	11	numerous	numerous	ADJ
ejpam-6040	12	12	applications	application	NOUN
ejpam-6040	12	13	across	across	ADP
ejpam-6040	12	14	various	various	ADJ
ejpam-6040	12	15	fields	field	NOUN
ejpam-6040	12	16	,	,	PUNCT
ejpam-6040	12	17	including	include	VERB
ejpam-6040	12	18	network	network	NOUN
ejpam-6040	12	19	design	design	NOUN
ejpam-6040	12	20	,	,	PUNCT
ejpam-6040	12	21	resource	resource	NOUN
ejpam-6040	12	22	allocation	allocation	NOUN
ejpam-6040	12	23	,	,	PUNCT
ejpam-6040	12	24	and	and	CCONJ
ejpam-6040	12	25	social	social	ADJ
ejpam-6040	12	26	network	network	NOUN
ejpam-6040	12	27	analysis	analysis	NOUN
ejpam-6040	12	28	(	(	PUNCT
ejpam-6040	12	29	see	see	VERB
ejpam-6040	12	30	[	[	X
ejpam-6040	12	31	1	1	X
ejpam-6040	12	32	]	]	PUNCT
ejpam-6040	12	33	and	and	CCONJ
ejpam-6040	12	34	[	[	X
ejpam-6040	12	35	2	2	NUM
ejpam-6040	12	36	]	]	NUM
ejpam-6040	12	37	)	)	PUNCT
ejpam-6040	12	38	.	.	PUNCT
ejpam-6040	13	1	the	the	DET
ejpam-6040	13	2	domination	domination	NOUN
ejpam-6040	13	3	number	number	PROPN
ejpam-6040	13	4	γ(g	γ(g	PROPN
ejpam-6040	13	5	)	)	PUNCT
ejpam-6040	13	6	of	of	ADP
ejpam-6040	13	7	a	a	DET
ejpam-6040	13	8	graph	graph	NOUN
ejpam-6040	13	9	g	g	NOUN
ejpam-6040	13	10	refers	refer	VERB
ejpam-6040	13	11	to	to	ADP
ejpam-6040	13	12	the	the	DET
ejpam-6040	13	13	smallest	small	ADJ
ejpam-6040	13	14	number	number	NOUN
ejpam-6040	13	15	of	of	ADP
ejpam-6040	13	16	vertices	vertex	NOUN
ejpam-6040	13	17	required	require	VERB
ejpam-6040	13	18	to	to	PART
ejpam-6040	13	19	dominate	dominate	VERB
ejpam-6040	13	20	all	all	DET
ejpam-6040	13	21	the	the	DET
ejpam-6040	13	22	vertices	vertex	NOUN
ejpam-6040	13	23	of	of	ADP
ejpam-6040	13	24	g.	g.	PROPN
ejpam-6040	13	25	in	in	ADP
ejpam-6040	13	26	other	other	ADJ
ejpam-6040	13	27	words	word	NOUN
ejpam-6040	13	28	,	,	PUNCT
ejpam-6040	13	29	it	it	PRON
ejpam-6040	13	30	is	be	AUX
ejpam-6040	13	31	the	the	DET
ejpam-6040	13	32	minimum	minimum	ADJ
ejpam-6040	13	33	cardinality	cardinality	NOUN
ejpam-6040	13	34	of	of	ADP
ejpam-6040	13	35	a	a	DET
ejpam-6040	13	36	set	set	NOUN
ejpam-6040	13	37	s	s	NOUN
ejpam-6040	13	38	of	of	ADP
ejpam-6040	13	39	vertices	vertex	NOUN
ejpam-6040	13	40	such	such	ADJ
ejpam-6040	13	41	that	that	SCONJ
ejpam-6040	13	42	every	every	DET
ejpam-6040	13	43	vertex	vertex	NOUN
ejpam-6040	13	44	in	in	ADP
ejpam-6040	13	45	the	the	DET
ejpam-6040	13	46	graph	graph	NOUN
ejpam-6040	13	47	is	be	AUX
ejpam-6040	13	48	either	either	CCONJ
ejpam-6040	13	49	in	in	ADP
ejpam-6040	13	50	the	the	DET
ejpam-6040	13	51	set	set	NOUN
ejpam-6040	13	52	s	s	X
ejpam-6040	13	53	or	or	CCONJ
ejpam-6040	13	54	is	be	AUX
ejpam-6040	13	55	adjacent	adjacent	ADJ
ejpam-6040	13	56	to	to	ADP
ejpam-6040	13	57	at	at	ADV
ejpam-6040	13	58	least	least	ADV
ejpam-6040	13	59	one	one	NUM
ejpam-6040	13	60	vertex	vertex	NOUN
ejpam-6040	13	61	in	in	ADP
ejpam-6040	13	62	s.	s.	PROPN
ejpam-6040	13	63	if	if	SCONJ
ejpam-6040	13	64	a	a	DET
ejpam-6040	13	65	set	set	NOUN
ejpam-6040	13	66	s	s	NOUN
ejpam-6040	13	67	of	of	ADP
ejpam-6040	13	68	vertices	vertex	NOUN
ejpam-6040	13	69	has	have	VERB
ejpam-6040	13	70	cardinality	cardinality	NOUN
ejpam-6040	13	71	strictly	strictly	ADV
ejpam-6040	13	72	less	less	ADJ
ejpam-6040	13	73	than	than	ADP
ejpam-6040	13	74	γ(g	γ(g	PROPN
ejpam-6040	13	75	)	)	PUNCT
ejpam-6040	13	76	,	,	PUNCT
ejpam-6040	13	77	then	then	ADV
ejpam-6040	13	78	there	there	PRON
ejpam-6040	13	79	will	will	AUX
ejpam-6040	13	80	exist	exist	VERB
ejpam-6040	13	81	vertices	vertex	NOUN
ejpam-6040	13	82	in	in	ADP
ejpam-6040	13	83	the	the	DET
ejpam-6040	13	84	graph	graph	NOUN
ejpam-6040	13	85	that	that	PRON
ejpam-6040	13	86	are	be	AUX
ejpam-6040	13	87	not	not	PART
ejpam-6040	13	88	dominated	dominate	VERB
ejpam-6040	13	89	by	by	ADP
ejpam-6040	13	90	any	any	DET
ejpam-6040	13	91	vertex	vertex	NOUN
ejpam-6040	13	92	in	in	ADP
ejpam-6040	13	93	the	the	DET
ejpam-6040	13	94	set	set	NOUN
ejpam-6040	13	95	s.	s.	PROPN
ejpam-6040	13	96	recently	recently	ADV
ejpam-6040	13	97	,	,	PUNCT
ejpam-6040	13	98	das	das	PROPN
ejpam-6040	13	99	et	et	PROPN
ejpam-6040	13	100	al	al	PROPN
ejpam-6040	13	101	.	.	PUNCT
ejpam-6040	14	1	[	[	X
ejpam-6040	14	2	3	3	NUM
ejpam-6040	14	3	]	]	PUNCT
ejpam-6040	14	4	introduced	introduce	VERB
ejpam-6040	14	5	and	and	CCONJ
ejpam-6040	14	6	studied	study	VERB
ejpam-6040	14	7	the	the	DET
ejpam-6040	14	8	notion	notion	NOUN
ejpam-6040	14	9	of	of	ADP
ejpam-6040	14	10	kdomination	kdomination	NOUN
ejpam-6040	14	11	defect	defect	NOUN
ejpam-6040	14	12	of	of	ADP
ejpam-6040	14	13	a	a	DET
ejpam-6040	14	14	graph	graph	NOUN
ejpam-6040	14	15	,	,	PUNCT
ejpam-6040	14	16	where	where	SCONJ
ejpam-6040	14	17	k	k	PROPN
ejpam-6040	14	18	is	be	AUX
ejpam-6040	14	19	a	a	DET
ejpam-6040	14	20	positive	positive	ADJ
ejpam-6040	14	21	integer	integer	NOUN
ejpam-6040	14	22	strictly	strictly	ADV
ejpam-6040	14	23	less	less	ADJ
ejpam-6040	14	24	than	than	ADP
ejpam-6040	14	25	the	the	DET
ejpam-6040	14	26	domination	domination	NOUN
ejpam-6040	14	27	∗corresponding	∗corresponde	VERB
ejpam-6040	14	28	author	author	NOUN
ejpam-6040	14	29	.	.	PUNCT
ejpam-6040	15	1	doi	doi	NOUN
ejpam-6040	15	2	:	:	PUNCT
ejpam-6040	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6040	https://doi.org/10.29020/nybg.ejpam.v18i2.6040	ADJ
ejpam-6040	15	4	email	email	NOUN
ejpam-6040	15	5	addresses	address	VERB
ejpam-6040	15	6	:	:	PUNCT
ejpam-6040	15	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6040	15	8	(	(	PUNCT
ejpam-6040	15	9	s.	s.	PROPN
ejpam-6040	15	10	canoy	canoy	PROPN
ejpam-6040	15	11	,	,	PUNCT
ejpam-6040	15	12	jr	jr	PROPN
ejpam-6040	15	13	.	.	PUNCT
ejpam-6040	15	14	)	)	PUNCT
ejpam-6040	16	1	jesica.anoche@g.msuiit.edu.ph	jesica.anoche@g.msuiit.edu.ph	PROPN
ejpam-6040	16	2	(	(	PUNCT
ejpam-6040	16	3	j.	j.	PROPN
ejpam-6040	16	4	anoche	anoche	PROPN
ejpam-6040	16	5	)	)	PUNCT
ejpam-6040	16	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6040	17	1	1	1	NUM
ejpam-6040	17	2	copyright	copyright	NOUN
ejpam-6040	17	3	:	:	PUNCT
ejpam-6040	17	4	©	©	PROPN
ejpam-6040	17	5	2025	2025	NUM
ejpam-6040	17	6	the	the	DET
ejpam-6040	17	7	author(s	author(s	NOUN
ejpam-6040	17	8	)	)	PUNCT
ejpam-6040	17	9	.	.	PUNCT
ejpam-6040	18	1	(	(	PUNCT
ejpam-6040	18	2	cc	cc	NOUN
ejpam-6040	18	3	by	by	ADP
ejpam-6040	18	4	-	-	PUNCT
ejpam-6040	18	5	nc	nc	PROPN
ejpam-6040	18	6	4.0	4.0	NUM
ejpam-6040	18	7	)	)	PUNCT
ejpam-6040	18	8	s.	s.	PROPN
ejpam-6040	18	9	canoy	canoy	PROPN
ejpam-6040	18	10	,	,	PUNCT
ejpam-6040	18	11	jr	jr	PROPN
ejpam-6040	18	12	.	.	PROPN
ejpam-6040	18	13	,	,	PUNCT
ejpam-6040	18	14	j.	j.	PROPN
ejpam-6040	18	15	anoche	anoche	PROPN
ejpam-6040	18	16	/	/	SYM
ejpam-6040	18	17	eur	eur	PROPN
ejpam-6040	18	18	.	.	PUNCT
ejpam-6040	19	1	j.	j.	PROPN
ejpam-6040	19	2	pure	pure	PROPN
ejpam-6040	19	3	appl	appl	PROPN
ejpam-6040	19	4	.	.	PROPN
ejpam-6040	19	5	math	math	PROPN
ejpam-6040	19	6	,	,	PUNCT
ejpam-6040	19	7	18	18	NUM
ejpam-6040	19	8	(	(	PUNCT
ejpam-6040	19	9	2	2	NUM
ejpam-6040	19	10	)	)	PUNCT
ejpam-6040	19	11	(	(	PUNCT
ejpam-6040	19	12	2025	2025	NUM
ejpam-6040	19	13	)	)	PUNCT
ejpam-6040	19	14	,	,	PUNCT
ejpam-6040	19	15	6040	6040	NUM
ejpam-6040	19	16	2	2	NUM
ejpam-6040	19	17	of	of	ADP
ejpam-6040	19	18	16	16	NUM
ejpam-6040	19	19	number	number	NOUN
ejpam-6040	19	20	of	of	ADP
ejpam-6040	19	21	the	the	DET
ejpam-6040	19	22	graph	graph	NOUN
ejpam-6040	19	23	.	.	PUNCT
ejpam-6040	20	1	in	in	ADP
ejpam-6040	20	2	their	their	PRON
ejpam-6040	20	3	study	study	NOUN
ejpam-6040	20	4	,	,	PUNCT
ejpam-6040	20	5	the	the	DET
ejpam-6040	20	6	authors	author	NOUN
ejpam-6040	20	7	established	establish	VERB
ejpam-6040	20	8	various	various	ADJ
ejpam-6040	20	9	bounds	bound	NOUN
ejpam-6040	20	10	on	on	ADP
ejpam-6040	20	11	the	the	DET
ejpam-6040	20	12	kdomination	kdomination	NOUN
ejpam-6040	20	13	defect	defect	NOUN
ejpam-6040	20	14	of	of	ADP
ejpam-6040	20	15	a	a	DET
ejpam-6040	20	16	graph	graph	NOUN
ejpam-6040	20	17	,	,	PUNCT
ejpam-6040	20	18	based	base	VERB
ejpam-6040	20	19	on	on	ADP
ejpam-6040	20	20	its	its	PRON
ejpam-6040	20	21	maximum	maximum	ADJ
ejpam-6040	20	22	degree	degree	NOUN
ejpam-6040	20	23	,	,	PUNCT
ejpam-6040	20	24	domination	domination	NOUN
ejpam-6040	20	25	number	number	NOUN
ejpam-6040	20	26	,	,	PUNCT
ejpam-6040	20	27	and	and	CCONJ
ejpam-6040	20	28	other	other	ADJ
ejpam-6040	20	29	parameters	parameter	NOUN
ejpam-6040	20	30	.	.	PUNCT
ejpam-6040	21	1	subsequent	subsequent	ADJ
ejpam-6040	21	2	studies	study	NOUN
ejpam-6040	21	3	on	on	ADP
ejpam-6040	21	4	this	this	DET
ejpam-6040	21	5	topic	topic	NOUN
ejpam-6040	21	6	(	(	PUNCT
ejpam-6040	21	7	see	see	VERB
ejpam-6040	21	8	[	[	X
ejpam-6040	21	9	4–6	4–6	X
ejpam-6040	21	10	]	]	X
ejpam-6040	21	11	)	)	PUNCT
ejpam-6040	21	12	focused	focus	VERB
ejpam-6040	21	13	on	on	ADP
ejpam-6040	21	14	characterizing	characterize	VERB
ejpam-6040	21	15	k	k	ADJ
ejpam-6040	21	16	-	-	PUNCT
ejpam-6040	21	17	domination	domination	NOUN
ejpam-6040	21	18	defect	defect	NOUN
ejpam-6040	21	19	sets	set	NOUN
ejpam-6040	21	20	and	and	CCONJ
ejpam-6040	21	21	determining	determine	VERB
ejpam-6040	21	22	the	the	DET
ejpam-6040	21	23	k	k	ADJ
ejpam-6040	21	24	-	-	PUNCT
ejpam-6040	21	25	domination	domination	NOUN
ejpam-6040	21	26	defect	defect	NOUN
ejpam-6040	21	27	in	in	ADP
ejpam-6040	21	28	the	the	DET
ejpam-6040	21	29	join	join	NOUN
ejpam-6040	21	30	,	,	PUNCT
ejpam-6040	21	31	corona	corona	PROPN
ejpam-6040	21	32	,	,	PUNCT
ejpam-6040	21	33	edge	edge	NOUN
ejpam-6040	21	34	corona	corona	NOUN
ejpam-6040	21	35	,	,	PUNCT
ejpam-6040	21	36	and	and	CCONJ
ejpam-6040	21	37	composition	composition	NOUN
ejpam-6040	21	38	of	of	ADP
ejpam-6040	21	39	two	two	NUM
ejpam-6040	21	40	graphs	graph	NOUN
ejpam-6040	21	41	.	.	PUNCT
ejpam-6040	22	1	recently	recently	ADV
ejpam-6040	22	2	,	,	PUNCT
ejpam-6040	22	3	a	a	DET
ejpam-6040	22	4	new	new	ADJ
ejpam-6040	22	5	variant	variant	NOUN
ejpam-6040	22	6	of	of	ADP
ejpam-6040	22	7	the	the	DET
ejpam-6040	22	8	domination	domination	NOUN
ejpam-6040	22	9	defect	defect	NOUN
ejpam-6040	22	10	was	be	AUX
ejpam-6040	22	11	introduced	introduce	VERB
ejpam-6040	22	12	and	and	CCONJ
ejpam-6040	22	13	explored	explore	VERB
ejpam-6040	22	14	in	in	ADP
ejpam-6040	22	15	[	[	X
ejpam-6040	22	16	7	7	NUM
ejpam-6040	22	17	]	]	PUNCT
ejpam-6040	22	18	.	.	PUNCT
ejpam-6040	23	1	some	some	DET
ejpam-6040	23	2	variations	variation	NOUN
ejpam-6040	23	3	of	of	ADP
ejpam-6040	23	4	the	the	DET
ejpam-6040	23	5	standard	standard	ADJ
ejpam-6040	23	6	domination	domination	NOUN
ejpam-6040	23	7	utilize	utilize	VERB
ejpam-6040	23	8	the	the	DET
ejpam-6040	23	9	concept	concept	NOUN
ejpam-6040	23	10	of	of	ADP
ejpam-6040	23	11	geodetic	geodetic	ADJ
ejpam-6040	23	12	set	set	NOUN
ejpam-6040	23	13	(	(	PUNCT
ejpam-6040	23	14	see	see	VERB
ejpam-6040	23	15	[	[	X
ejpam-6040	23	16	8–12	8–12	NOUN
ejpam-6040	23	17	]	]	PUNCT
ejpam-6040	23	18	)	)	PUNCT
ejpam-6040	23	19	.	.	PUNCT
ejpam-6040	24	1	the	the	DET
ejpam-6040	24	2	associated	associated	ADJ
ejpam-6040	24	3	parameter	parameter	NOUN
ejpam-6040	24	4	,	,	PUNCT
ejpam-6040	24	5	called	call	VERB
ejpam-6040	24	6	geodetic	geodetic	ADJ
ejpam-6040	24	7	number	number	NOUN
ejpam-6040	24	8	of	of	ADP
ejpam-6040	24	9	a	a	DET
ejpam-6040	24	10	graph	graph	NOUN
ejpam-6040	24	11	,	,	PUNCT
ejpam-6040	24	12	was	be	AUX
ejpam-6040	24	13	introduced	introduce	VERB
ejpam-6040	24	14	by	by	ADP
ejpam-6040	24	15	harary	harary	PROPN
ejpam-6040	24	16	et	et	PROPN
ejpam-6040	24	17	al	al	PROPN
ejpam-6040	24	18	.	.	PUNCT
ejpam-6040	25	1	[	[	X
ejpam-6040	25	2	13	13	NUM
ejpam-6040	25	3	]	]	PUNCT
ejpam-6040	25	4	.	.	PUNCT
ejpam-6040	26	1	geodetic	geodetic	ADJ
ejpam-6040	26	2	number	number	NOUN
ejpam-6040	26	3	and	and	CCONJ
ejpam-6040	26	4	geodetic	geodetic	ADJ
ejpam-6040	26	5	domination	domination	NOUN
ejpam-6040	26	6	were	be	AUX
ejpam-6040	26	7	considered	consider	VERB
ejpam-6040	26	8	in	in	ADP
ejpam-6040	26	9	[	[	X
ejpam-6040	26	10	14	14	NUM
ejpam-6040	26	11	]	]	PUNCT
ejpam-6040	26	12	,	,	PUNCT
ejpam-6040	26	13	[	[	X
ejpam-6040	26	14	15	15	NUM
ejpam-6040	26	15	]	]	PUNCT
ejpam-6040	26	16	,	,	PUNCT
ejpam-6040	26	17	[	[	X
ejpam-6040	26	18	16	16	NUM
ejpam-6040	26	19	]	]	PUNCT
ejpam-6040	26	20	,	,	PUNCT
ejpam-6040	26	21	[	[	X
ejpam-6040	26	22	17	17	NUM
ejpam-6040	26	23	]	]	PUNCT
ejpam-6040	26	24	,	,	PUNCT
ejpam-6040	26	25	[	[	X
ejpam-6040	26	26	18	18	NUM
ejpam-6040	26	27	]	]	PUNCT
ejpam-6040	26	28	,	,	PUNCT
ejpam-6040	26	29	and	and	CCONJ
ejpam-6040	26	30	[	[	X
ejpam-6040	26	31	19	19	NUM
ejpam-6040	26	32	]	]	PUNCT
ejpam-6040	26	33	.	.	PUNCT
ejpam-6040	27	1	note	note	VERB
ejpam-6040	27	2	that	that	SCONJ
ejpam-6040	27	3	if	if	SCONJ
ejpam-6040	27	4	g	g	PROPN
ejpam-6040	27	5	is	be	AUX
ejpam-6040	27	6	a	a	DET
ejpam-6040	27	7	graph	graph	NOUN
ejpam-6040	27	8	and	and	CCONJ
ejpam-6040	27	9	s	s	NOUN
ejpam-6040	27	10	is	be	AUX
ejpam-6040	27	11	a	a	DET
ejpam-6040	27	12	set	set	NOUN
ejpam-6040	27	13	of	of	ADP
ejpam-6040	27	14	vertices	vertex	NOUN
ejpam-6040	27	15	of	of	ADP
ejpam-6040	27	16	g	g	NOUN
ejpam-6040	27	17	with	with	ADP
ejpam-6040	27	18	cardinality	cardinality	NOUN
ejpam-6040	27	19	strictly	strictly	ADV
ejpam-6040	27	20	less	less	ADJ
ejpam-6040	27	21	than	than	ADP
ejpam-6040	27	22	the	the	DET
ejpam-6040	27	23	geodetic	geodetic	ADJ
ejpam-6040	27	24	domination	domination	NOUN
ejpam-6040	27	25	number	number	NOUN
ejpam-6040	27	26	γg(g	γg(g	NOUN
ejpam-6040	27	27	)	)	PUNCT
ejpam-6040	27	28	of	of	ADP
ejpam-6040	27	29	g	g	PROPN
ejpam-6040	27	30	,	,	PUNCT
ejpam-6040	27	31	then	then	ADV
ejpam-6040	27	32	there	there	PRON
ejpam-6040	27	33	is	be	VERB
ejpam-6040	27	34	at	at	ADV
ejpam-6040	27	35	least	least	ADJ
ejpam-6040	27	36	one	one	NUM
ejpam-6040	27	37	vertex	vertex	NOUN
ejpam-6040	27	38	outside	outside	ADP
ejpam-6040	27	39	s	s	PRON
ejpam-6040	27	40	that	that	PRON
ejpam-6040	27	41	is	be	AUX
ejpam-6040	27	42	not	not	PART
ejpam-6040	27	43	geodetically	geodetically	ADV
ejpam-6040	27	44	dominated	dominate	VERB
ejpam-6040	27	45	,	,	PUNCT
ejpam-6040	27	46	that	that	ADV
ejpam-6040	27	47	is	is	ADV
ejpam-6040	27	48	,	,	PUNCT
ejpam-6040	27	49	has	have	VERB
ejpam-6040	27	50	no	no	DET
ejpam-6040	27	51	neighbor	neighbor	NOUN
ejpam-6040	27	52	in	in	ADP
ejpam-6040	27	53	s	s	PRON
ejpam-6040	27	54	or	or	CCONJ
ejpam-6040	27	55	is	be	AUX
ejpam-6040	27	56	not	not	PART
ejpam-6040	27	57	in	in	ADP
ejpam-6040	27	58	any	any	DET
ejpam-6040	27	59	shortest	short	ADJ
ejpam-6040	27	60	path	path	NOUN
ejpam-6040	27	61	joining	join	VERB
ejpam-6040	27	62	any	any	DET
ejpam-6040	27	63	two	two	NUM
ejpam-6040	27	64	vertices	vertex	NOUN
ejpam-6040	27	65	in	in	ADP
ejpam-6040	27	66	s.	s.	PROPN
ejpam-6040	27	67	in	in	ADP
ejpam-6040	27	68	this	this	DET
ejpam-6040	27	69	paper	paper	NOUN
ejpam-6040	27	70	,	,	PUNCT
ejpam-6040	27	71	we	we	PRON
ejpam-6040	27	72	introduce	introduce	VERB
ejpam-6040	27	73	the	the	DET
ejpam-6040	27	74	notion	notion	NOUN
ejpam-6040	27	75	k	k	ADJ
ejpam-6040	27	76	-	-	ADJ
ejpam-6040	27	77	geodetic	geodetic	ADJ
ejpam-6040	27	78	domination	domination	NOUN
ejpam-6040	27	79	defect	defect	NOUN
ejpam-6040	27	80	and	and	CCONJ
ejpam-6040	27	81	study	study	VERB
ejpam-6040	27	82	it	it	PRON
ejpam-6040	27	83	for	for	ADP
ejpam-6040	27	84	some	some	DET
ejpam-6040	27	85	classes	class	NOUN
ejpam-6040	27	86	of	of	ADP
ejpam-6040	27	87	graphs	graph	NOUN
ejpam-6040	27	88	.	.	PUNCT
ejpam-6040	28	1	for	for	ADP
ejpam-6040	28	2	the	the	DET
ejpam-6040	28	3	motivation	motivation	NOUN
ejpam-6040	28	4	of	of	ADP
ejpam-6040	28	5	the	the	DET
ejpam-6040	28	6	study	study	NOUN
ejpam-6040	28	7	,	,	PUNCT
ejpam-6040	28	8	consider	consider	VERB
ejpam-6040	28	9	a	a	DET
ejpam-6040	28	10	prison	prison	NOUN
ejpam-6040	28	11	facility	facility	NOUN
ejpam-6040	28	12	with	with	ADP
ejpam-6040	28	13	numerous	numerous	ADJ
ejpam-6040	28	14	prisoners	prisoner	NOUN
ejpam-6040	28	15	who	who	PRON
ejpam-6040	28	16	need	need	VERB
ejpam-6040	28	17	to	to	PART
ejpam-6040	28	18	undergo	undergo	VERB
ejpam-6040	28	19	routine	routine	ADJ
ejpam-6040	28	20	assessments	assessment	NOUN
ejpam-6040	28	21	such	such	ADJ
ejpam-6040	28	22	as	as	ADP
ejpam-6040	28	23	behavior	behavior	NOUN
ejpam-6040	28	24	evaluations	evaluation	NOUN
ejpam-6040	28	25	or	or	CCONJ
ejpam-6040	28	26	security	security	NOUN
ejpam-6040	28	27	checks	check	NOUN
ejpam-6040	28	28	.	.	PUNCT
ejpam-6040	29	1	the	the	DET
ejpam-6040	29	2	warden	warden	NOUN
ejpam-6040	29	3	needs	need	VERB
ejpam-6040	29	4	to	to	PART
ejpam-6040	29	5	ensure	ensure	VERB
ejpam-6040	29	6	that	that	SCONJ
ejpam-6040	29	7	every	every	DET
ejpam-6040	29	8	prisoner	prisoner	NOUN
ejpam-6040	29	9	is	be	AUX
ejpam-6040	29	10	evaluated	evaluate	VERB
ejpam-6040	29	11	by	by	ADP
ejpam-6040	29	12	a	a	DET
ejpam-6040	29	13	jail	jail	NOUN
ejpam-6040	29	14	guard	guard	NOUN
ejpam-6040	29	15	.	.	PUNCT
ejpam-6040	30	1	this	this	DET
ejpam-6040	30	2	situation	situation	NOUN
ejpam-6040	30	3	can	can	AUX
ejpam-6040	30	4	be	be	AUX
ejpam-6040	30	5	modeled	model	VERB
ejpam-6040	30	6	by	by	ADP
ejpam-6040	30	7	constructing	construct	VERB
ejpam-6040	30	8	a	a	DET
ejpam-6040	30	9	graph	graph	NOUN
ejpam-6040	30	10	,	,	PUNCT
ejpam-6040	30	11	where	where	SCONJ
ejpam-6040	30	12	each	each	DET
ejpam-6040	30	13	vertex	vertex	NOUN
ejpam-6040	30	14	represents	represent	VERB
ejpam-6040	30	15	a	a	DET
ejpam-6040	30	16	prisoner	prisoner	NOUN
ejpam-6040	30	17	or	or	CCONJ
ejpam-6040	30	18	a	a	DET
ejpam-6040	30	19	jail	jail	NOUN
ejpam-6040	30	20	guard	guard	NOUN
ejpam-6040	30	21	,	,	PUNCT
ejpam-6040	30	22	and	and	CCONJ
ejpam-6040	30	23	an	an	DET
ejpam-6040	30	24	edge	edge	NOUN
ejpam-6040	30	25	between	between	ADP
ejpam-6040	30	26	a	a	DET
ejpam-6040	30	27	prisoner	prisoner	NOUN
ejpam-6040	30	28	and	and	CCONJ
ejpam-6040	30	29	a	a	DET
ejpam-6040	30	30	jail	jail	NOUN
ejpam-6040	30	31	guard	guard	NOUN
ejpam-6040	30	32	indicates	indicate	VERB
ejpam-6040	30	33	that	that	SCONJ
ejpam-6040	30	34	the	the	DET
ejpam-6040	30	35	jail	jail	NOUN
ejpam-6040	30	36	guard	guard	NOUN
ejpam-6040	30	37	is	be	AUX
ejpam-6040	30	38	responsible	responsible	ADJ
ejpam-6040	30	39	for	for	ADP
ejpam-6040	30	40	evaluating	evaluate	VERB
ejpam-6040	30	41	the	the	DET
ejpam-6040	30	42	prisoner	prisoner	NOUN
ejpam-6040	30	43	.	.	PUNCT
ejpam-6040	31	1	moreover	moreover	ADV
ejpam-6040	31	2	,	,	PUNCT
ejpam-6040	31	3	to	to	PART
ejpam-6040	31	4	ensure	ensure	VERB
ejpam-6040	31	5	visibility	visibility	NOUN
ejpam-6040	31	6	and	and	CCONJ
ejpam-6040	31	7	security	security	NOUN
ejpam-6040	31	8	,	,	PUNCT
ejpam-6040	31	9	it	it	PRON
ejpam-6040	31	10	is	be	AUX
ejpam-6040	31	11	required	require	VERB
ejpam-6040	31	12	that	that	SCONJ
ejpam-6040	31	13	every	every	DET
ejpam-6040	31	14	prisoner	prisoner	NOUN
ejpam-6040	31	15	must	must	AUX
ejpam-6040	31	16	be	be	AUX
ejpam-6040	31	17	on	on	ADP
ejpam-6040	31	18	a	a	DET
ejpam-6040	31	19	shortest	short	ADJ
ejpam-6040	31	20	path	path	NOUN
ejpam-6040	31	21	connecting	connect	VERB
ejpam-6040	31	22	two	two	NUM
ejpam-6040	31	23	jail	jail	NOUN
ejpam-6040	31	24	guards	guard	NOUN
ejpam-6040	31	25	.	.	PUNCT
ejpam-6040	32	1	however	however	ADV
ejpam-6040	32	2	,	,	PUNCT
ejpam-6040	32	3	due	due	ADP
ejpam-6040	32	4	to	to	ADP
ejpam-6040	32	5	a	a	DET
ejpam-6040	32	6	lack	lack	NOUN
ejpam-6040	32	7	of	of	ADP
ejpam-6040	32	8	personnel	personnel	NOUN
ejpam-6040	32	9	and	and	CCONJ
ejpam-6040	32	10	financial	financial	ADJ
ejpam-6040	32	11	support	support	NOUN
ejpam-6040	32	12	,	,	PUNCT
ejpam-6040	32	13	the	the	DET
ejpam-6040	32	14	required	require	VERB
ejpam-6040	32	15	minimum	minimum	ADJ
ejpam-6040	32	16	number	number	NOUN
ejpam-6040	32	17	of	of	ADP
ejpam-6040	32	18	jail	jail	NOUN
ejpam-6040	32	19	guards	guard	NOUN
ejpam-6040	32	20	to	to	PART
ejpam-6040	32	21	do	do	VERB
ejpam-6040	32	22	the	the	DET
ejpam-6040	32	23	task	task	NOUN
ejpam-6040	32	24	may	may	AUX
ejpam-6040	32	25	not	not	PART
ejpam-6040	32	26	always	always	ADV
ejpam-6040	32	27	be	be	AUX
ejpam-6040	32	28	met	meet	VERB
ejpam-6040	32	29	.	.	PUNCT
ejpam-6040	33	1	furthermore	furthermore	ADV
ejpam-6040	33	2	,	,	PUNCT
ejpam-6040	33	3	it	it	PRON
ejpam-6040	33	4	may	may	AUX
ejpam-6040	33	5	happen	happen	VERB
ejpam-6040	33	6	that	that	SCONJ
ejpam-6040	33	7	during	during	ADP
ejpam-6040	33	8	the	the	DET
ejpam-6040	33	9	assessment	assessment	NOUN
ejpam-6040	33	10	,	,	PUNCT
ejpam-6040	33	11	a	a	DET
ejpam-6040	33	12	designated	designate	VERB
ejpam-6040	33	13	jail	jail	NOUN
ejpam-6040	33	14	guard	guard	NOUN
ejpam-6040	33	15	may	may	AUX
ejpam-6040	33	16	be	be	AUX
ejpam-6040	33	17	absent	absent	ADJ
ejpam-6040	33	18	and	and	CCONJ
ejpam-6040	33	19	,	,	PUNCT
ejpam-6040	33	20	subsequently	subsequently	ADV
ejpam-6040	33	21	,	,	PUNCT
ejpam-6040	33	22	unable	unable	ADJ
ejpam-6040	33	23	to	to	PART
ejpam-6040	33	24	perform	perform	VERB
ejpam-6040	33	25	his	his	PRON
ejpam-6040	33	26	or	or	CCONJ
ejpam-6040	33	27	her	her	PRON
ejpam-6040	33	28	task	task	NOUN
ejpam-6040	33	29	.	.	PUNCT
ejpam-6040	34	1	as	as	ADP
ejpam-6040	34	2	a	a	DET
ejpam-6040	34	3	result	result	NOUN
ejpam-6040	34	4	,	,	PUNCT
ejpam-6040	34	5	some	some	DET
ejpam-6040	34	6	prisoners	prisoner	NOUN
ejpam-6040	34	7	may	may	AUX
ejpam-6040	34	8	not	not	PART
ejpam-6040	34	9	be	be	AUX
ejpam-6040	34	10	evaluated	evaluate	VERB
ejpam-6040	34	11	in	in	ADP
ejpam-6040	34	12	the	the	DET
ejpam-6040	34	13	manner	manner	NOUN
ejpam-6040	34	14	expected	expect	VERB
ejpam-6040	34	15	.	.	PUNCT
ejpam-6040	35	1	determining	determine	VERB
ejpam-6040	35	2	the	the	DET
ejpam-6040	35	3	number	number	NOUN
ejpam-6040	35	4	of	of	ADP
ejpam-6040	35	5	unevaluated	unevaluated	ADJ
ejpam-6040	35	6	prisoners	prisoner	NOUN
ejpam-6040	35	7	when	when	SCONJ
ejpam-6040	35	8	a	a	DET
ejpam-6040	35	9	designated	designate	VERB
ejpam-6040	35	10	team	team	NOUN
ejpam-6040	35	11	of	of	ADP
ejpam-6040	35	12	jail	jail	NOUN
ejpam-6040	35	13	guards	guard	NOUN
ejpam-6040	35	14	does	do	AUX
ejpam-6040	35	15	not	not	PART
ejpam-6040	35	16	meet	meet	VERB
ejpam-6040	35	17	the	the	DET
ejpam-6040	35	18	required	require	VERB
ejpam-6040	35	19	minimum	minimum	ADJ
ejpam-6040	35	20	number	number	NOUN
ejpam-6040	35	21	of	of	ADP
ejpam-6040	35	22	members	member	NOUN
ejpam-6040	35	23	could	could	AUX
ejpam-6040	35	24	assist	assist	VERB
ejpam-6040	35	25	the	the	DET
ejpam-6040	35	26	management	management	NOUN
ejpam-6040	35	27	to	to	PART
ejpam-6040	35	28	act	act	VERB
ejpam-6040	35	29	accordingly	accordingly	ADV
ejpam-6040	35	30	.	.	PUNCT
ejpam-6040	36	1	this	this	DET
ejpam-6040	36	2	situation	situation	NOUN
ejpam-6040	36	3	led	lead	VERB
ejpam-6040	36	4	us	we	PRON
ejpam-6040	36	5	to	to	PART
ejpam-6040	36	6	introduce	introduce	VERB
ejpam-6040	36	7	the	the	DET
ejpam-6040	36	8	concept	concept	NOUN
ejpam-6040	36	9	of	of	ADP
ejpam-6040	36	10	geodetic	geodetic	ADJ
ejpam-6040	36	11	domination	domination	NOUN
ejpam-6040	36	12	defect	defect	NOUN
ejpam-6040	36	13	in	in	ADP
ejpam-6040	36	14	a	a	DET
ejpam-6040	36	15	graph	graph	NOUN
ejpam-6040	36	16	.	.	PUNCT
ejpam-6040	37	1	2	2	X
ejpam-6040	37	2	.	.	X
ejpam-6040	37	3	terminology	terminology	NOUN
ejpam-6040	37	4	and	and	CCONJ
ejpam-6040	37	5	notation	notation	NOUN
ejpam-6040	37	6	for	for	ADP
ejpam-6040	37	7	any	any	DET
ejpam-6040	37	8	two	two	NUM
ejpam-6040	37	9	vertices	vertex	NOUN
ejpam-6040	37	10	u	u	NOUN
ejpam-6040	37	11	and	and	CCONJ
ejpam-6040	37	12	v	v	NOUN
ejpam-6040	37	13	in	in	ADP
ejpam-6040	37	14	an	an	DET
ejpam-6040	37	15	undirected	undirected	ADJ
ejpam-6040	37	16	connected	connected	ADJ
ejpam-6040	37	17	graph	graph	NOUN
ejpam-6040	37	18	g	g	PROPN
ejpam-6040	37	19	,	,	PUNCT
ejpam-6040	37	20	the	the	DET
ejpam-6040	37	21	distance	distance	NOUN
ejpam-6040	37	22	dg(u	dg(u	X
ejpam-6040	37	23	,	,	PUNCT
ejpam-6040	37	24	v	v	NOUN
ejpam-6040	37	25	)	)	PUNCT
ejpam-6040	37	26	is	be	AUX
ejpam-6040	37	27	the	the	DET
ejpam-6040	37	28	length	length	NOUN
ejpam-6040	37	29	of	of	ADP
ejpam-6040	37	30	a	a	DET
ejpam-6040	37	31	shortest	short	ADJ
ejpam-6040	37	32	path	path	NOUN
ejpam-6040	37	33	joining	join	VERB
ejpam-6040	37	34	u	u	NOUN
ejpam-6040	37	35	and	and	CCONJ
ejpam-6040	37	36	v.	v.	ADP
ejpam-6040	37	37	any	any	DET
ejpam-6040	37	38	u	u	NOUN
ejpam-6040	37	39	-	-	NOUN
ejpam-6040	37	40	v	v	ADJ
ejpam-6040	37	41	path	path	NOUN
ejpam-6040	37	42	of	of	ADP
ejpam-6040	37	43	length	length	NOUN
ejpam-6040	37	44	dg(u	dg(u	PROPN
ejpam-6040	37	45	,	,	PUNCT
ejpam-6040	37	46	v	v	NOUN
ejpam-6040	37	47	)	)	PUNCT
ejpam-6040	37	48	is	be	AUX
ejpam-6040	37	49	called	call	VERB
ejpam-6040	37	50	a	a	DET
ejpam-6040	37	51	u	u	NOUN
ejpam-6040	37	52	-	-	NOUN
ejpam-6040	37	53	v	v	ADJ
ejpam-6040	37	54	geodesic	geodesic	NOUN
ejpam-6040	37	55	.	.	PUNCT
ejpam-6040	38	1	the	the	DET
ejpam-6040	38	2	diameter	diameter	NOUN
ejpam-6040	38	3	of	of	ADP
ejpam-6040	38	4	g	g	PROPN
ejpam-6040	38	5	,	,	PUNCT
ejpam-6040	38	6	denoted	denote	VERB
ejpam-6040	38	7	by	by	ADP
ejpam-6040	38	8	diam(g	diam(g	PROPN
ejpam-6040	38	9	)	)	PUNCT
ejpam-6040	38	10	,	,	PUNCT
ejpam-6040	38	11	is	be	AUX
ejpam-6040	38	12	the	the	DET
ejpam-6040	38	13	maximum	maximum	ADJ
ejpam-6040	38	14	distance	distance	NOUN
ejpam-6040	38	15	between	between	ADP
ejpam-6040	38	16	any	any	DET
ejpam-6040	38	17	two	two	NUM
ejpam-6040	38	18	vertices	vertex	NOUN
ejpam-6040	38	19	in	in	ADP
ejpam-6040	38	20	g.	g.	PROPN
ejpam-6040	38	21	the	the	DET
ejpam-6040	38	22	distance	distance	NOUN
ejpam-6040	38	23	between	between	ADP
ejpam-6040	38	24	two	two	NUM
ejpam-6040	38	25	subsets	subset	NOUN
ejpam-6040	38	26	a	a	PRON
ejpam-6040	38	27	and	and	CCONJ
ejpam-6040	38	28	b	b	NOUN
ejpam-6040	38	29	of	of	ADP
ejpam-6040	38	30	v	v	NOUN
ejpam-6040	38	31	(	(	PUNCT
ejpam-6040	38	32	g	g	NOUN
ejpam-6040	38	33	)	)	PUNCT
ejpam-6040	38	34	is	be	AUX
ejpam-6040	38	35	given	give	VERB
ejpam-6040	38	36	by	by	ADP
ejpam-6040	38	37	dg(a	dg(a	PROPN
ejpam-6040	38	38	,	,	PUNCT
ejpam-6040	38	39	b	b	NOUN
ejpam-6040	38	40	)	)	PUNCT
ejpam-6040	38	41	=	=	SYM
ejpam-6040	38	42	min{dg(a	min{dg(a	PROPN
ejpam-6040	38	43	,	,	PUNCT
ejpam-6040	38	44	b	b	NOUN
ejpam-6040	38	45	)	)	PUNCT
ejpam-6040	38	46	:	:	PUNCT
ejpam-6040	38	47	a	a	DET
ejpam-6040	38	48	∈	∈	PROPN
ejpam-6040	38	49	a	a	PRON
ejpam-6040	38	50	and	and	CCONJ
ejpam-6040	38	51	b	b	NOUN
ejpam-6040	38	52	∈	∈	PROPN
ejpam-6040	38	53	b	b	NOUN
ejpam-6040	38	54	}	}	PUNCT
ejpam-6040	38	55	.	.	PUNCT
ejpam-6040	39	1	the	the	DET
ejpam-6040	39	2	open	open	ADJ
ejpam-6040	39	3	neighborhood	neighborhood	NOUN
ejpam-6040	39	4	of	of	ADP
ejpam-6040	39	5	a	a	DET
ejpam-6040	39	6	vertex	vertex	NOUN
ejpam-6040	39	7	u	u	NOUN
ejpam-6040	39	8	is	be	AUX
ejpam-6040	39	9	the	the	DET
ejpam-6040	39	10	set	set	NOUN
ejpam-6040	39	11	ng(u	ng(u	NOUN
ejpam-6040	39	12	)	)	PUNCT
ejpam-6040	39	13	consisting	consist	VERB
ejpam-6040	39	14	of	of	ADP
ejpam-6040	39	15	all	all	DET
ejpam-6040	39	16	vertices	vertex	NOUN
ejpam-6040	39	17	v	v	NUM
ejpam-6040	39	18	which	which	PRON
ejpam-6040	39	19	are	be	AUX
ejpam-6040	39	20	adjacent	adjacent	ADJ
ejpam-6040	39	21	to	to	PART
ejpam-6040	39	22	u.	u.	VERB
ejpam-6040	39	23	the	the	DET
ejpam-6040	39	24	closed	closed	ADJ
ejpam-6040	39	25	neighborhood	neighborhood	NOUN
ejpam-6040	39	26	of	of	ADP
ejpam-6040	39	27	u	u	NOUN
ejpam-6040	39	28	is	be	AUX
ejpam-6040	39	29	ng[u	ng[u	PROPN
ejpam-6040	39	30	]	]	X
ejpam-6040	39	31	=	=	SYM
ejpam-6040	39	32	ng(u	ng(u	PROPN
ejpam-6040	39	33	)	)	PUNCT
ejpam-6040	39	34	∪	∪	NOUN
ejpam-6040	39	35	{	{	PUNCT
ejpam-6040	39	36	u	u	NOUN
ejpam-6040	39	37	}	}	PUNCT
ejpam-6040	39	38	.	.	PUNCT
ejpam-6040	40	1	for	for	ADP
ejpam-6040	40	2	any	any	DET
ejpam-6040	40	3	a	a	DET
ejpam-6040	40	4	⊆	⊆	NUM
ejpam-6040	40	5	v	v	NOUN
ejpam-6040	40	6	(	(	PUNCT
ejpam-6040	40	7	g	g	NOUN
ejpam-6040	40	8	)	)	PUNCT
ejpam-6040	40	9	,	,	PUNCT
ejpam-6040	40	10	ng(a	ng(a	X
ejpam-6040	40	11	)	)	PUNCT
ejpam-6040	40	12	=	=	PUNCT
ejpam-6040	40	13	⋃	⋃	NOUN
ejpam-6040	40	14	v∈a	v∈a	NOUN
ejpam-6040	40	15	ng(v	ng(v	PUNCT
ejpam-6040	40	16	)	)	PUNCT
ejpam-6040	40	17	is	be	AUX
ejpam-6040	40	18	called	call	VERB
ejpam-6040	40	19	the	the	DET
ejpam-6040	40	20	open	open	ADJ
ejpam-6040	40	21	neighborhood	neighborhood	NOUN
ejpam-6040	40	22	of	of	ADP
ejpam-6040	40	23	a	a	PRON
ejpam-6040	40	24	and	and	CCONJ
ejpam-6040	40	25	ng[a	ng[a	NOUN
ejpam-6040	40	26	]	]	X
ejpam-6040	40	27	=	=	PUNCT
ejpam-6040	40	28	ng(a	ng(a	X
ejpam-6040	40	29	)	)	PUNCT
ejpam-6040	40	30	∪	∪	ADP
ejpam-6040	40	31	a	a	PRON
ejpam-6040	40	32	is	be	AUX
ejpam-6040	40	33	called	call	VERB
ejpam-6040	40	34	the	the	DET
ejpam-6040	40	35	closed	closed	ADJ
ejpam-6040	40	36	neighborhood	neighborhood	NOUN
ejpam-6040	40	37	of	of	ADP
ejpam-6040	40	38	a.	a.	NOUN
ejpam-6040	40	39	a	a	DET
ejpam-6040	40	40	vertex	vertex	NOUN
ejpam-6040	40	41	v	v	NOUN
ejpam-6040	40	42	of	of	ADP
ejpam-6040	40	43	g	g	PROPN
ejpam-6040	40	44	is	be	AUX
ejpam-6040	40	45	isolated	isolate	VERB
ejpam-6040	40	46	if	if	SCONJ
ejpam-6040	40	47	|ng(v)|	|ng(v)|	NOUN
ejpam-6040	40	48	=	=	SYM
ejpam-6040	40	49	0	0	NUM
ejpam-6040	40	50	.	.	PUNCT
ejpam-6040	41	1	the	the	DET
ejpam-6040	41	2	set	set	NOUN
ejpam-6040	41	3	containing	contain	VERB
ejpam-6040	41	4	all	all	DET
ejpam-6040	41	5	the	the	DET
ejpam-6040	41	6	isolated	isolated	ADJ
ejpam-6040	41	7	vertices	vertex	NOUN
ejpam-6040	41	8	of	of	ADP
ejpam-6040	41	9	g	g	PROPN
ejpam-6040	41	10	is	be	AUX
ejpam-6040	41	11	denoted	denote	VERB
ejpam-6040	41	12	by	by	ADP
ejpam-6040	41	13	i(g	i(g	NOUN
ejpam-6040	41	14	)	)	PUNCT
ejpam-6040	41	15	.	.	PUNCT
ejpam-6040	42	1	if	if	SCONJ
ejpam-6040	42	2	c	c	PROPN
ejpam-6040	42	3	⊆	⊆	NUM
ejpam-6040	42	4	v	v	NOUN
ejpam-6040	42	5	(	(	PUNCT
ejpam-6040	42	6	g	g	NOUN
ejpam-6040	42	7	)	)	PUNCT
ejpam-6040	42	8	,	,	PUNCT
ejpam-6040	42	9	then	then	ADV
ejpam-6040	42	10	the	the	DET
ejpam-6040	42	11	induced	induced	ADJ
ejpam-6040	42	12	subgraph	subgraph	NOUN
ejpam-6040	42	13	⟨c⟩	⟨c⟩	PROPN
ejpam-6040	42	14	is	be	AUX
ejpam-6040	42	15	the	the	DET
ejpam-6040	42	16	graph	graph	NOUN
ejpam-6040	42	17	with	with	ADP
ejpam-6040	42	18	vertex	vertex	NOUN
ejpam-6040	42	19	-	-	PUNCT
ejpam-6040	42	20	set	set	VERB
ejpam-6040	42	21	s.	s.	PROPN
ejpam-6040	42	22	canoy	canoy	PROPN
ejpam-6040	42	23	,	,	PUNCT
ejpam-6040	42	24	jr	jr	PROPN
ejpam-6040	42	25	.	.	PROPN
ejpam-6040	42	26	,	,	PUNCT
ejpam-6040	42	27	j.	j.	PROPN
ejpam-6040	42	28	anoche	anoche	PROPN
ejpam-6040	42	29	/	/	SYM
ejpam-6040	42	30	eur	eur	PROPN
ejpam-6040	42	31	.	.	PUNCT
ejpam-6040	43	1	j.	j.	PROPN
ejpam-6040	43	2	pure	pure	PROPN
ejpam-6040	43	3	appl	appl	PROPN
ejpam-6040	43	4	.	.	PROPN
ejpam-6040	43	5	math	math	PROPN
ejpam-6040	43	6	,	,	PUNCT
ejpam-6040	43	7	18	18	NUM
ejpam-6040	43	8	(	(	PUNCT
ejpam-6040	43	9	2	2	NUM
ejpam-6040	43	10	)	)	PUNCT
ejpam-6040	43	11	(	(	PUNCT
ejpam-6040	43	12	2025	2025	NUM
ejpam-6040	43	13	)	)	PUNCT
ejpam-6040	43	14	,	,	PUNCT
ejpam-6040	43	15	6040	6040	NUM
ejpam-6040	43	16	3	3	NUM
ejpam-6040	43	17	of	of	ADP
ejpam-6040	43	18	16	16	NUM
ejpam-6040	43	19	c	c	NOUN
ejpam-6040	43	20	and	and	CCONJ
ejpam-6040	43	21	uv	uv	PROPN
ejpam-6040	43	22	∈	∈	PROPN
ejpam-6040	43	23	e(⟨c⟩	e(⟨c⟩	NOUN
ejpam-6040	43	24	)	)	PUNCT
ejpam-6040	43	25	whenever	whenever	SCONJ
ejpam-6040	43	26	u	u	NOUN
ejpam-6040	43	27	,	,	PUNCT
ejpam-6040	43	28	v	v	ADP
ejpam-6040	43	29	∈	∈	NOUN
ejpam-6040	43	30	c	c	NOUN
ejpam-6040	43	31	and	and	CCONJ
ejpam-6040	43	32	uv	uv	PROPN
ejpam-6040	43	33	∈	∈	PROPN
ejpam-6040	43	34	e(g	e(g	PROPN
ejpam-6040	43	35	)	)	PUNCT
ejpam-6040	43	36	.	.	PUNCT
ejpam-6040	44	1	a	a	DET
ejpam-6040	44	2	set	set	NOUN
ejpam-6040	44	3	s	s	NOUN
ejpam-6040	44	4	⊆	⊆	NUM
ejpam-6040	44	5	v	v	NOUN
ejpam-6040	44	6	(	(	PUNCT
ejpam-6040	44	7	g	g	NOUN
ejpam-6040	44	8	)	)	PUNCT
ejpam-6040	44	9	is	be	AUX
ejpam-6040	44	10	a	a	DET
ejpam-6040	44	11	dominating	dominating	NOUN
ejpam-6040	44	12	set	set	NOUN
ejpam-6040	44	13	of	of	ADP
ejpam-6040	44	14	g	g	PROPN
ejpam-6040	44	15	if	if	SCONJ
ejpam-6040	44	16	ng[s	ng[	NOUN
ejpam-6040	44	17	]	]	PUNCT
ejpam-6040	44	18	=	=	SYM
ejpam-6040	44	19	v	v	NOUN
ejpam-6040	44	20	(	(	PUNCT
ejpam-6040	44	21	g	g	NOUN
ejpam-6040	44	22	)	)	PUNCT
ejpam-6040	44	23	.	.	PUNCT
ejpam-6040	45	1	the	the	DET
ejpam-6040	45	2	smallest	small	ADJ
ejpam-6040	45	3	cardinality	cardinality	NOUN
ejpam-6040	45	4	of	of	ADP
ejpam-6040	45	5	a	a	DET
ejpam-6040	45	6	dominating	dominating	NOUN
ejpam-6040	45	7	set	set	NOUN
ejpam-6040	45	8	of	of	ADP
ejpam-6040	45	9	g	g	NOUN
ejpam-6040	45	10	,	,	PUNCT
ejpam-6040	45	11	denoted	denote	VERB
ejpam-6040	45	12	by	by	ADP
ejpam-6040	45	13	γ(g	γ(g	PROPN
ejpam-6040	45	14	)	)	PUNCT
ejpam-6040	45	15	,	,	PUNCT
ejpam-6040	45	16	is	be	AUX
ejpam-6040	45	17	called	call	VERB
ejpam-6040	45	18	the	the	DET
ejpam-6040	45	19	domination	domination	NOUN
ejpam-6040	45	20	number	number	NOUN
ejpam-6040	45	21	of	of	ADP
ejpam-6040	45	22	g.	g.	PROPN
ejpam-6040	45	23	a	a	DET
ejpam-6040	45	24	dominating	dominating	NOUN
ejpam-6040	45	25	set	set	NOUN
ejpam-6040	45	26	s	s	NOUN
ejpam-6040	45	27	of	of	ADP
ejpam-6040	45	28	g	g	NOUN
ejpam-6040	45	29	with	with	ADP
ejpam-6040	45	30	|s|	|s|	PROPN
ejpam-6040	45	31	=	=	SYM
ejpam-6040	45	32	γ(g	γ(g	PROPN
ejpam-6040	45	33	)	)	PUNCT
ejpam-6040	45	34	,	,	PUNCT
ejpam-6040	45	35	is	be	AUX
ejpam-6040	45	36	called	call	VERB
ejpam-6040	45	37	a	a	DET
ejpam-6040	45	38	γ	γ	NOUN
ejpam-6040	45	39	-	-	PUNCT
ejpam-6040	45	40	set	set	NOUN
ejpam-6040	45	41	of	of	ADP
ejpam-6040	45	42	g.	g.	PROPN
ejpam-6040	45	43	for	for	ADP
ejpam-6040	45	44	every	every	DET
ejpam-6040	45	45	two	two	NUM
ejpam-6040	45	46	vertices	vertex	NOUN
ejpam-6040	45	47	u	u	NOUN
ejpam-6040	45	48	and	and	CCONJ
ejpam-6040	45	49	v	v	NOUN
ejpam-6040	45	50	in	in	ADP
ejpam-6040	45	51	g	g	PROPN
ejpam-6040	45	52	,	,	PUNCT
ejpam-6040	45	53	the	the	DET
ejpam-6040	45	54	symbol	symbol	NOUN
ejpam-6040	45	55	ig	ig	PROPN
ejpam-6040	46	1	[	[	X
ejpam-6040	46	2	u	u	NOUN
ejpam-6040	46	3	,	,	PUNCT
ejpam-6040	46	4	v	v	ADP
ejpam-6040	46	5	]	]	PUNCT
ejpam-6040	46	6	,	,	PUNCT
ejpam-6040	46	7	is	be	AUX
ejpam-6040	46	8	the	the	DET
ejpam-6040	46	9	set	set	ADJ
ejpam-6040	46	10	interval	interval	NOUN
ejpam-6040	46	11	containing	contain	VERB
ejpam-6040	46	12	u	u	NOUN
ejpam-6040	46	13	,	,	PUNCT
ejpam-6040	46	14	v	v	NOUN
ejpam-6040	46	15	and	and	CCONJ
ejpam-6040	46	16	all	all	DET
ejpam-6040	46	17	vertices	vertex	NOUN
ejpam-6040	46	18	lying	lie	VERB
ejpam-6040	46	19	in	in	ADP
ejpam-6040	46	20	some	some	DET
ejpam-6040	46	21	u	u	NOUN
ejpam-6040	46	22	-	-	NOUN
ejpam-6040	46	23	v	v	ADJ
ejpam-6040	46	24	geodesic	geodesic	NOUN
ejpam-6040	46	25	.	.	PUNCT
ejpam-6040	47	1	the	the	DET
ejpam-6040	47	2	geodetic	geodetic	ADJ
ejpam-6040	47	3	closure	closure	NOUN
ejpam-6040	47	4	of	of	ADP
ejpam-6040	47	5	a	a	DET
ejpam-6040	47	6	set	set	NOUN
ejpam-6040	47	7	s	s	NOUN
ejpam-6040	47	8	⊆	⊆	NUM
ejpam-6040	47	9	v	v	NOUN
ejpam-6040	47	10	(	(	PUNCT
ejpam-6040	47	11	g	g	NOUN
ejpam-6040	47	12	)	)	PUNCT
ejpam-6040	47	13	,	,	PUNCT
ejpam-6040	47	14	denoted	denote	VERB
ejpam-6040	47	15	by	by	ADP
ejpam-6040	47	16	ig[s	ig[	NOUN
ejpam-6040	47	17	]	]	PUNCT
ejpam-6040	47	18	,	,	PUNCT
ejpam-6040	47	19	is	be	AUX
ejpam-6040	47	20	the	the	DET
ejpam-6040	47	21	union	union	NOUN
ejpam-6040	47	22	of	of	ADP
ejpam-6040	47	23	the	the	DET
ejpam-6040	47	24	intervals	interval	NOUN
ejpam-6040	47	25	ig[u	ig[u	VERB
ejpam-6040	47	26	,	,	PUNCT
ejpam-6040	47	27	v	v	NOUN
ejpam-6040	47	28	]	]	X
ejpam-6040	47	29	,	,	PUNCT
ejpam-6040	47	30	where	where	SCONJ
ejpam-6040	47	31	u	u	NOUN
ejpam-6040	47	32	,	,	PUNCT
ejpam-6040	47	33	v	v	ADP
ejpam-6040	47	34	∈	∈	PROPN
ejpam-6040	47	35	s.	s.	PROPN
ejpam-6040	48	1	the	the	DET
ejpam-6040	48	2	set	set	PROPN
ejpam-6040	48	3	s	s	VERB
ejpam-6040	48	4	is	be	AUX
ejpam-6040	48	5	a	a	DET
ejpam-6040	48	6	geodetic	geodetic	ADJ
ejpam-6040	48	7	set	set	NOUN
ejpam-6040	48	8	in	in	ADP
ejpam-6040	48	9	g	g	PROPN
ejpam-6040	48	10	if	if	SCONJ
ejpam-6040	48	11	ig[s	ig[	NOUN
ejpam-6040	48	12	]	]	X
ejpam-6040	48	13	=	=	SYM
ejpam-6040	48	14	v	v	X
ejpam-6040	48	15	(	(	PUNCT
ejpam-6040	48	16	g	g	NOUN
ejpam-6040	48	17	)	)	PUNCT
ejpam-6040	48	18	.	.	PUNCT
ejpam-6040	49	1	the	the	DET
ejpam-6040	49	2	smallest	small	ADJ
ejpam-6040	49	3	cardinality	cardinality	NOUN
ejpam-6040	49	4	among	among	ADP
ejpam-6040	49	5	all	all	DET
ejpam-6040	49	6	geodetic	geodetic	ADJ
ejpam-6040	49	7	sets	set	NOUN
ejpam-6040	49	8	in	in	ADP
ejpam-6040	49	9	g	g	NOUN
ejpam-6040	49	10	,	,	PUNCT
ejpam-6040	49	11	denoted	denote	VERB
ejpam-6040	49	12	by	by	ADP
ejpam-6040	49	13	g(g	g(g	PROPN
ejpam-6040	49	14	)	)	PUNCT
ejpam-6040	49	15	,	,	PUNCT
ejpam-6040	49	16	is	be	AUX
ejpam-6040	49	17	called	call	VERB
ejpam-6040	49	18	the	the	DET
ejpam-6040	49	19	geodetic	geodetic	ADJ
ejpam-6040	49	20	number	number	NOUN
ejpam-6040	49	21	of	of	ADP
ejpam-6040	49	22	g.	g.	PROPN
ejpam-6040	49	23	a	a	DET
ejpam-6040	49	24	geodetic	geodetic	ADJ
ejpam-6040	49	25	set	set	NOUN
ejpam-6040	49	26	of	of	ADP
ejpam-6040	49	27	cardinality	cardinality	PROPN
ejpam-6040	49	28	g(g	g(g	PROPN
ejpam-6040	49	29	)	)	PUNCT
ejpam-6040	49	30	is	be	AUX
ejpam-6040	49	31	called	call	VERB
ejpam-6040	49	32	a	a	DET
ejpam-6040	49	33	g	g	NOUN
ejpam-6040	49	34	-	-	PUNCT
ejpam-6040	49	35	set	set	NOUN
ejpam-6040	49	36	of	of	ADP
ejpam-6040	49	37	g.	g.	PROPN
ejpam-6040	49	38	a	a	DET
ejpam-6040	49	39	set	set	NOUN
ejpam-6040	49	40	s	s	PROPN
ejpam-6040	49	41	⊆	⊆	NUM
ejpam-6040	49	42	v	v	NOUN
ejpam-6040	49	43	(	(	PUNCT
ejpam-6040	49	44	g	g	NOUN
ejpam-6040	49	45	)	)	PUNCT
ejpam-6040	49	46	is	be	AUX
ejpam-6040	49	47	a	a	DET
ejpam-6040	49	48	geodetic	geodetic	ADJ
ejpam-6040	49	49	dominating	dominating	NOUN
ejpam-6040	49	50	set	set	VERB
ejpam-6040	49	51	in	in	ADP
ejpam-6040	49	52	g	g	PROPN
ejpam-6040	49	53	if	if	SCONJ
ejpam-6040	49	54	it	it	PRON
ejpam-6040	49	55	is	be	AUX
ejpam-6040	49	56	both	both	CCONJ
ejpam-6040	49	57	a	a	DET
ejpam-6040	49	58	dominating	dominating	NOUN
ejpam-6040	49	59	and	and	CCONJ
ejpam-6040	49	60	a	a	DET
ejpam-6040	49	61	geodetic	geodetic	ADJ
ejpam-6040	49	62	set	set	NOUN
ejpam-6040	49	63	.	.	PUNCT
ejpam-6040	50	1	the	the	DET
ejpam-6040	50	2	geodetic	geodetic	ADJ
ejpam-6040	50	3	domination	domination	NOUN
ejpam-6040	50	4	number	number	NOUN
ejpam-6040	50	5	γg(g	γg(g	NOUN
ejpam-6040	50	6	)	)	PUNCT
ejpam-6040	50	7	of	of	ADP
ejpam-6040	50	8	g	g	PROPN
ejpam-6040	50	9	is	be	AUX
ejpam-6040	50	10	the	the	DET
ejpam-6040	50	11	minimum	minimum	ADJ
ejpam-6040	50	12	cardinality	cardinality	NOUN
ejpam-6040	50	13	among	among	ADP
ejpam-6040	50	14	all	all	DET
ejpam-6040	50	15	geodetic	geodetic	ADJ
ejpam-6040	50	16	dominating	dominating	NOUN
ejpam-6040	50	17	sets	set	NOUN
ejpam-6040	50	18	in	in	ADP
ejpam-6040	50	19	g.	g.	PROPN
ejpam-6040	50	20	any	any	DET
ejpam-6040	50	21	geodetic	geodetic	ADJ
ejpam-6040	50	22	dominating	dominating	NOUN
ejpam-6040	50	23	set	set	NOUN
ejpam-6040	50	24	of	of	ADP
ejpam-6040	50	25	g	g	PROPN
ejpam-6040	50	26	with	with	ADP
ejpam-6040	50	27	cardinality	cardinality	NOUN
ejpam-6040	50	28	γg(g	γg(g	CCONJ
ejpam-6040	50	29	)	)	PUNCT
ejpam-6040	50	30	is	be	AUX
ejpam-6040	50	31	called	call	VERB
ejpam-6040	50	32	a	a	DET
ejpam-6040	50	33	γg	γg	ADV
ejpam-6040	50	34	-	-	PUNCT
ejpam-6040	50	35	set	set	NOUN
ejpam-6040	50	36	.	.	PUNCT
ejpam-6040	51	1	let	let	VERB
ejpam-6040	51	2	g	g	PRON
ejpam-6040	51	3	be	be	AUX
ejpam-6040	51	4	a	a	DET
ejpam-6040	51	5	non	non	ADJ
ejpam-6040	51	6	-	-	ADJ
ejpam-6040	51	7	trivial	trivial	ADJ
ejpam-6040	51	8	graph	graph	NOUN
ejpam-6040	51	9	of	of	ADP
ejpam-6040	51	10	order	order	NOUN
ejpam-6040	51	11	n	n	NOUN
ejpam-6040	51	12	and	and	CCONJ
ejpam-6040	51	13	let	let	VERB
ejpam-6040	51	14	1	1	NUM
ejpam-6040	51	15	≤	≤	NOUN
ejpam-6040	52	1	k	k	X
ejpam-6040	52	2	<	<	X
ejpam-6040	52	3	γg(g	γg(g	NOUN
ejpam-6040	52	4	)	)	PUNCT
ejpam-6040	52	5	.	.	PUNCT
ejpam-6040	53	1	let	let	VERB
ejpam-6040	53	2	s	s	PRON
ejpam-6040	53	3	⊆	⊆	NUM
ejpam-6040	53	4	v	v	NOUN
ejpam-6040	53	5	(	(	PUNCT
ejpam-6040	53	6	g	g	NOUN
ejpam-6040	53	7	)	)	PUNCT
ejpam-6040	53	8	with	with	ADP
ejpam-6040	53	9	cardinality	cardinality	PROPN
ejpam-6040	53	10	|s|	|s|	PROPN
ejpam-6040	53	11	=	=	PROPN
ejpam-6040	53	12	γg(g	γg(g	PROPN
ejpam-6040	53	13	)	)	PUNCT
ejpam-6040	53	14	−	−	PROPN
ejpam-6040	54	1	k	k	PROPN
ejpam-6040	54	2	and	and	CCONJ
ejpam-6040	54	3	let	let	VERB
ejpam-6040	54	4	ng	ng	PROPN
ejpam-6040	54	5	g[s	g[s	PROPN
ejpam-6040	54	6	]	]	X
ejpam-6040	54	7	=	=	SYM
ejpam-6040	54	8	ng[s	ng[s	PROPN
ejpam-6040	54	9	]	]	PUNCT
ejpam-6040	54	10	∩	∩	X
ejpam-6040	54	11	ig[s	ig[s	PROPN
ejpam-6040	54	12	]	]	PUNCT
ejpam-6040	54	13	,	,	PUNCT
ejpam-6040	54	14	the	the	DET
ejpam-6040	54	15	set	set	NOUN
ejpam-6040	54	16	of	of	ADP
ejpam-6040	54	17	geodetically	geodetically	ADV
ejpam-6040	54	18	dominated	dominate	VERB
ejpam-6040	54	19	set	set	NOUN
ejpam-6040	54	20	of	of	ADP
ejpam-6040	54	21	vertices	vertex	NOUN
ejpam-6040	54	22	of	of	ADP
ejpam-6040	54	23	g.	g.	PROPN
ejpam-6040	54	24	the	the	DET
ejpam-6040	54	25	set	set	NOUN
ejpam-6040	54	26	v	v	NOUN
ejpam-6040	54	27	(	(	PUNCT
ejpam-6040	54	28	g	g	NOUN
ejpam-6040	54	29	)	)	PUNCT
ejpam-6040	54	30	\ng	\ng	PROPN
ejpam-6040	54	31	g[s	g[	NOUN
ejpam-6040	54	32	]	]	PUNCT
ejpam-6040	54	33	is	be	AUX
ejpam-6040	54	34	called	call	VERB
ejpam-6040	54	35	the	the	DET
ejpam-6040	54	36	k	k	ADJ
ejpam-6040	54	37	-	-	ADJ
ejpam-6040	54	38	geodetic	geodetic	ADJ
ejpam-6040	54	39	domination	domination	NOUN
ejpam-6040	54	40	defect	defect	NOUN
ejpam-6040	54	41	set	set	NOUN
ejpam-6040	54	42	of	of	ADP
ejpam-6040	54	43	s	s	PRON
ejpam-6040	54	44	and	and	CCONJ
ejpam-6040	54	45	the	the	DET
ejpam-6040	54	46	k	k	ADJ
ejpam-6040	54	47	-	-	ADJ
ejpam-6040	54	48	geodetic	geodetic	ADJ
ejpam-6040	54	49	domination	domination	NOUN
ejpam-6040	54	50	defect	defect	NOUN
ejpam-6040	54	51	of	of	ADP
ejpam-6040	54	52	s	s	PRON
ejpam-6040	54	53	in	in	ADP
ejpam-6040	54	54	g	g	PROPN
ejpam-6040	54	55	is	be	AUX
ejpam-6040	54	56	ζgk(s	ζgk(s	PROPN
ejpam-6040	54	57	)	)	PUNCT
ejpam-6040	54	58	=	=	SYM
ejpam-6040	54	59	|v	|v	PROPN
ejpam-6040	54	60	(	(	PUNCT
ejpam-6040	54	61	g)\ng	g)\ng	X
ejpam-6040	54	62	g[s]|	g[s]|	X
ejpam-6040	54	63	=	=	SYM
ejpam-6040	54	64	n−|ng	n−|ng	NOUN
ejpam-6040	54	65	g[s]|	g[s]|	PROPN
ejpam-6040	54	66	.	.	PUNCT
ejpam-6040	55	1	the	the	DET
ejpam-6040	55	2	minimum	minimum	ADJ
ejpam-6040	55	3	cardinality	cardinality	NOUN
ejpam-6040	55	4	of	of	ADP
ejpam-6040	55	5	a	a	DET
ejpam-6040	55	6	k	k	ADJ
ejpam-6040	55	7	-	-	ADJ
ejpam-6040	55	8	geodetic	geodetic	ADJ
ejpam-6040	55	9	domination	domination	NOUN
ejpam-6040	55	10	defect	defect	NOUN
ejpam-6040	55	11	set	set	VERB
ejpam-6040	55	12	in	in	ADP
ejpam-6040	55	13	g	g	NOUN
ejpam-6040	55	14	,	,	PUNCT
ejpam-6040	55	15	denoted	denote	VERB
ejpam-6040	55	16	by	by	ADP
ejpam-6040	55	17	ζgk(g	ζgk(g	PROPN
ejpam-6040	55	18	)	)	PUNCT
ejpam-6040	55	19	,	,	PUNCT
ejpam-6040	55	20	is	be	AUX
ejpam-6040	55	21	called	call	VERB
ejpam-6040	55	22	the	the	DET
ejpam-6040	55	23	k	k	ADJ
ejpam-6040	55	24	-	-	ADJ
ejpam-6040	55	25	geodetic	geodetic	ADJ
ejpam-6040	55	26	domination	domination	NOUN
ejpam-6040	55	27	defect	defect	NOUN
ejpam-6040	55	28	of	of	ADP
ejpam-6040	55	29	g	g	NOUN
ejpam-6040	55	30	,	,	PUNCT
ejpam-6040	55	31	i.e.	i.e.	X
ejpam-6040	55	32	,	,	PUNCT
ejpam-6040	55	33	ζgk(g	ζgk(g	PROPN
ejpam-6040	55	34	)	)	PUNCT
ejpam-6040	55	35	=	=	SYM
ejpam-6040	55	36	min{ζgk(s	min{ζgk(s	PROPN
ejpam-6040	55	37	)	)	PUNCT
ejpam-6040	55	38	:	:	PUNCT
ejpam-6040	55	39	s	s	VERB
ejpam-6040	55	40	⊆	⊆	NUM
ejpam-6040	55	41	v	v	NOUN
ejpam-6040	55	42	(	(	PUNCT
ejpam-6040	55	43	g	g	NOUN
ejpam-6040	55	44	)	)	PUNCT
ejpam-6040	55	45	with	with	ADP
ejpam-6040	55	46	|s|	|s|	NOUN
ejpam-6040	55	47	=	=	PUNCT
ejpam-6040	55	48	γg(g)−	γg(g)−	NOUN
ejpam-6040	55	49	k	k	NOUN
ejpam-6040	55	50	}	}	PUNCT
ejpam-6040	55	51	.	.	PUNCT
ejpam-6040	56	1	a	a	DET
ejpam-6040	56	2	set	set	NOUN
ejpam-6040	56	3	s	s	NOUN
ejpam-6040	56	4	⊆	⊆	NUM
ejpam-6040	56	5	v	v	NOUN
ejpam-6040	56	6	(	(	PUNCT
ejpam-6040	56	7	g	g	NOUN
ejpam-6040	56	8	)	)	PUNCT
ejpam-6040	56	9	of	of	ADP
ejpam-6040	56	10	cardinality	cardinality	PROPN
ejpam-6040	56	11	γg(g	γg(g	ADP
ejpam-6040	56	12	)	)	PUNCT
ejpam-6040	56	13	−	−	PROPN
ejpam-6040	56	14	k	k	NOUN
ejpam-6040	56	15	for	for	ADP
ejpam-6040	56	16	which	which	PRON
ejpam-6040	56	17	|v	|v	PROPN
ejpam-6040	56	18	(	(	PUNCT
ejpam-6040	56	19	g	g	NOUN
ejpam-6040	56	20	)	)	PUNCT
ejpam-6040	56	21	\	\	PUNCT
ejpam-6040	57	1	ng	ng	PROPN
ejpam-6040	57	2	g[s]|	g[s]|	PROPN
ejpam-6040	57	3	=	=	SYM
ejpam-6040	57	4	ζgk(g	ζgk(g	PROPN
ejpam-6040	57	5	)	)	PUNCT
ejpam-6040	57	6	is	be	AUX
ejpam-6040	57	7	called	call	VERB
ejpam-6040	57	8	a	a	DET
ejpam-6040	57	9	ζgk	ζgk	NOUN
ejpam-6040	57	10	-set	-set	ADJ
ejpam-6040	57	11	of	of	ADP
ejpam-6040	57	12	g.	g.	PROPN
ejpam-6040	57	13	thus	thus	ADV
ejpam-6040	57	14	,	,	PUNCT
ejpam-6040	57	15	〈	〈	PROPN
ejpam-6040	57	16	ng	ng	PROPN
ejpam-6040	57	17	g[s	g[s	PROPN
ejpam-6040	57	18	]	]	PUNCT
ejpam-6040	57	19	〉	〉	NOUN
ejpam-6040	57	20	,	,	PUNCT
ejpam-6040	57	21	the	the	DET
ejpam-6040	57	22	subgraph	subgraph	NOUN
ejpam-6040	57	23	induced	induce	VERB
ejpam-6040	57	24	by	by	ADP
ejpam-6040	57	25	ng	ng	PROPN
ejpam-6040	57	26	g[s	g[s	PROPN
ejpam-6040	57	27	]	]	PUNCT
ejpam-6040	57	28	,	,	PUNCT
ejpam-6040	57	29	is	be	AUX
ejpam-6040	57	30	a	a	DET
ejpam-6040	57	31	subgraph	subgraph	NOUN
ejpam-6040	57	32	of	of	ADP
ejpam-6040	57	33	g	g	NOUN
ejpam-6040	57	34	with	with	ADP
ejpam-6040	57	35	n−	n−	PROPN
ejpam-6040	57	36	ζgk(g	ζgk(g	PROPN
ejpam-6040	57	37	)	)	PUNCT
ejpam-6040	57	38	vertices	vertex	NOUN
ejpam-6040	57	39	and	and	CCONJ
ejpam-6040	57	40	geodetic	geodetic	ADJ
ejpam-6040	57	41	domination	domination	NOUN
ejpam-6040	57	42	number	number	NOUN
ejpam-6040	57	43	γg	γg	PROPN
ejpam-6040	57	44	−	−	PROPN
ejpam-6040	57	45	k.	k.	PROPN
ejpam-6040	57	46	consider	consider	VERB
ejpam-6040	57	47	the	the	DET
ejpam-6040	57	48	graph	graph	NOUN
ejpam-6040	57	49	g	g	NOUN
ejpam-6040	57	50	in	in	ADP
ejpam-6040	57	51	figure	figure	NOUN
ejpam-6040	57	52	1	1	NUM
ejpam-6040	57	53	.	.	PUNCT
ejpam-6040	58	1	then	then	ADV
ejpam-6040	58	2	r	r	NOUN
ejpam-6040	58	3	=	=	PUNCT
ejpam-6040	58	4	{	{	PUNCT
ejpam-6040	58	5	a	a	PRON
ejpam-6040	58	6	,	,	PUNCT
ejpam-6040	58	7	b	b	NOUN
ejpam-6040	58	8	,	,	PUNCT
ejpam-6040	58	9	x	x	NOUN
ejpam-6040	58	10	,	,	PUNCT
ejpam-6040	58	11	y	y	PRON
ejpam-6040	58	12	}	}	PUNCT
ejpam-6040	58	13	is	be	AUX
ejpam-6040	58	14	a	a	DET
ejpam-6040	58	15	γg	γg	ADV
ejpam-6040	58	16	-	-	PUNCT
ejpam-6040	58	17	set	set	NOUN
ejpam-6040	58	18	of	of	ADP
ejpam-6040	58	19	g	g	NOUN
ejpam-6040	58	20	,	,	PUNCT
ejpam-6040	58	21	i.e.	i.e.	X
ejpam-6040	58	22	,	,	PUNCT
ejpam-6040	58	23	γg(g	γg(g	NOUN
ejpam-6040	58	24	)	)	PUNCT
ejpam-6040	58	25	=	=	SYM
ejpam-6040	59	1	4	4	X
ejpam-6040	59	2	.	.	PUNCT
ejpam-6040	60	1	if	if	SCONJ
ejpam-6040	60	2	k	k	PROPN
ejpam-6040	60	3	=	=	SYM
ejpam-6040	60	4	1	1	NUM
ejpam-6040	60	5	,	,	PUNCT
ejpam-6040	60	6	then	then	ADV
ejpam-6040	60	7	d1	d1	PROPN
ejpam-6040	60	8	=	=	PUNCT
ejpam-6040	60	9	{	{	PUNCT
ejpam-6040	60	10	a	a	PRON
ejpam-6040	60	11	,	,	PUNCT
ejpam-6040	60	12	b	b	NOUN
ejpam-6040	60	13	,	,	PUNCT
ejpam-6040	60	14	x	x	PRON
ejpam-6040	60	15	}	}	PUNCT
ejpam-6040	60	16	is	be	AUX
ejpam-6040	60	17	a	a	DET
ejpam-6040	60	18	ζg1	ζg1	PROPN
ejpam-6040	60	19	-set	-set	ADJ
ejpam-6040	60	20	of	of	ADP
ejpam-6040	60	21	g.	g.	PROPN
ejpam-6040	60	22	since	since	SCONJ
ejpam-6040	60	23	ng	ng	PROPN
ejpam-6040	60	24	g[d1	g[d1	PROPN
ejpam-6040	60	25	]	]	X
ejpam-6040	60	26	=	=	X
ejpam-6040	60	27	{	{	PUNCT
ejpam-6040	60	28	a	a	PRON
ejpam-6040	60	29	,	,	PUNCT
ejpam-6040	60	30	b	b	NOUN
ejpam-6040	60	31	,	,	PUNCT
ejpam-6040	60	32	c	c	NOUN
ejpam-6040	60	33	,	,	PUNCT
ejpam-6040	60	34	d	d	NOUN
ejpam-6040	60	35	,	,	PUNCT
ejpam-6040	60	36	u	u	NOUN
ejpam-6040	60	37	,	,	PUNCT
ejpam-6040	60	38	v	v	NOUN
ejpam-6040	60	39	,	,	PUNCT
ejpam-6040	60	40	x	x	NOUN
ejpam-6040	60	41	}	}	PUNCT
ejpam-6040	60	42	,	,	PUNCT
ejpam-6040	60	43	it	it	PRON
ejpam-6040	60	44	follows	follow	VERB
ejpam-6040	60	45	that	that	SCONJ
ejpam-6040	60	46	ζg1	ζg1	PROPN
ejpam-6040	60	47	(	(	PUNCT
ejpam-6040	60	48	g	g	NOUN
ejpam-6040	60	49	)	)	PUNCT
ejpam-6040	60	50	=	=	PUNCT
ejpam-6040	60	51	ζg1	ζg1	X
ejpam-6040	60	52	(	(	PUNCT
ejpam-6040	60	53	d1	d1	PROPN
ejpam-6040	60	54	)	)	PUNCT
ejpam-6040	60	55	=	=	SYM
ejpam-6040	60	56	|v	|v	PROPN
ejpam-6040	60	57	(	(	PUNCT
ejpam-6040	60	58	g)|	g)|	PROPN
ejpam-6040	60	59	−	−	PROPN
ejpam-6040	60	60	|ng	|ng	PUNCT
ejpam-6040	60	61	g[d1]|	g[d1]|	PROPN
ejpam-6040	60	62	=	=	PUNCT
ejpam-6040	60	63	8−	8−	NUM
ejpam-6040	60	64	7	7	NUM
ejpam-6040	60	65	=	=	SYM
ejpam-6040	60	66	1	1	NUM
ejpam-6040	60	67	.	.	PUNCT
ejpam-6040	61	1	the	the	DET
ejpam-6040	61	2	set	set	NOUN
ejpam-6040	61	3	{	{	PUNCT
ejpam-6040	61	4	x	x	NOUN
ejpam-6040	61	5	,	,	PUNCT
ejpam-6040	61	6	y	y	PROPN
ejpam-6040	61	7	,	,	PUNCT
ejpam-6040	61	8	c	c	NOUN
ejpam-6040	61	9	}	}	PUNCT
ejpam-6040	61	10	is	be	AUX
ejpam-6040	61	11	not	not	PART
ejpam-6040	61	12	a	a	DET
ejpam-6040	61	13	ζg1	ζg1	PROPN
ejpam-6040	61	14	-set	-set	PUNCT
ejpam-6040	61	15	of	of	ADP
ejpam-6040	61	16	g	g	PROPN
ejpam-6040	61	17	because	because	SCONJ
ejpam-6040	61	18	ng	ng	PROPN
ejpam-6040	61	19	g[{x	g[{x	PROPN
ejpam-6040	61	20	,	,	PUNCT
ejpam-6040	61	21	y	y	PROPN
ejpam-6040	61	22	,	,	PUNCT
ejpam-6040	61	23	c	c	NOUN
ejpam-6040	61	24	}	}	PUNCT
ejpam-6040	61	25	]	]	PUNCT
ejpam-6040	62	1	=	=	PUNCT
ejpam-6040	62	2	{	{	PUNCT
ejpam-6040	62	3	x	x	PROPN
ejpam-6040	62	4	,	,	PUNCT
ejpam-6040	62	5	y	y	PROPN
ejpam-6040	62	6	,	,	PUNCT
ejpam-6040	62	7	c	c	X
ejpam-6040	62	8	,	,	PUNCT
ejpam-6040	62	9	d	d	NOUN
ejpam-6040	62	10	,	,	PUNCT
ejpam-6040	62	11	u	u	NOUN
ejpam-6040	62	12	,	,	PUNCT
ejpam-6040	62	13	v	v	NOUN
ejpam-6040	62	14	}	}	PUNCT
ejpam-6040	62	15	,	,	PUNCT
ejpam-6040	62	16	i.e.	i.e.	X
ejpam-6040	62	17	,	,	PUNCT
ejpam-6040	62	18	ζg1	ζg1	X
ejpam-6040	62	19	(	(	PUNCT
ejpam-6040	62	20	{	{	PUNCT
ejpam-6040	62	21	x	x	NOUN
ejpam-6040	62	22	,	,	PUNCT
ejpam-6040	62	23	y	y	PROPN
ejpam-6040	62	24	,	,	PUNCT
ejpam-6040	62	25	c	c	NOUN
ejpam-6040	62	26	}	}	PUNCT
ejpam-6040	62	27	)	)	PUNCT
ejpam-6040	62	28	=	=	SYM
ejpam-6040	63	1	8	8	NUM
ejpam-6040	63	2	−	−	NUM
ejpam-6040	63	3	6	6	NUM
ejpam-6040	63	4	=	=	SYM
ejpam-6040	63	5	2	2	NUM
ejpam-6040	63	6	.	.	PUNCT
ejpam-6040	64	1	if	if	SCONJ
ejpam-6040	64	2	k	k	PROPN
ejpam-6040	64	3	=	=	SYM
ejpam-6040	64	4	2	2	NUM
ejpam-6040	64	5	,	,	PUNCT
ejpam-6040	64	6	then	then	ADV
ejpam-6040	64	7	d2	d2	PROPN
ejpam-6040	64	8	=	=	SYM
ejpam-6040	64	9	{	{	PUNCT
ejpam-6040	64	10	a	a	X
ejpam-6040	64	11	,	,	PUNCT
ejpam-6040	64	12	x	x	PRON
ejpam-6040	64	13	}	}	PUNCT
ejpam-6040	64	14	is	be	AUX
ejpam-6040	64	15	a	a	DET
ejpam-6040	64	16	ζg2	ζg2	NOUN
ejpam-6040	64	17	-set	-set	NOUN
ejpam-6040	64	18	of	of	ADP
ejpam-6040	64	19	g	g	PROPN
ejpam-6040	64	20	and	and	CCONJ
ejpam-6040	64	21	ng	ng	PROPN
ejpam-6040	64	22	g[d2	g[d2	NOUN
ejpam-6040	64	23	]	]	X
ejpam-6040	65	1	=	=	PUNCT
ejpam-6040	65	2	{	{	PUNCT
ejpam-6040	65	3	a	a	X
ejpam-6040	65	4	,	,	PUNCT
ejpam-6040	65	5	x	x	NOUN
ejpam-6040	65	6	,	,	PUNCT
ejpam-6040	65	7	c	c	X
ejpam-6040	65	8	,	,	PUNCT
ejpam-6040	65	9	d	d	NOUN
ejpam-6040	65	10	,	,	PUNCT
ejpam-6040	65	11	u	u	NOUN
ejpam-6040	65	12	,	,	PUNCT
ejpam-6040	65	13	v	v	NOUN
ejpam-6040	65	14	}	}	PUNCT
ejpam-6040	65	15	.	.	PUNCT
ejpam-6040	66	1	hence	hence	ADV
ejpam-6040	66	2	,	,	PUNCT
ejpam-6040	66	3	ζg2	ζg2	PROPN
ejpam-6040	66	4	(	(	PUNCT
ejpam-6040	66	5	g	g	NOUN
ejpam-6040	66	6	)	)	PUNCT
ejpam-6040	66	7	=	=	SYM
ejpam-6040	67	1	8	8	NUM
ejpam-6040	67	2	−	−	NUM
ejpam-6040	67	3	6	6	NUM
ejpam-6040	67	4	=	=	SYM
ejpam-6040	67	5	2	2	NUM
ejpam-6040	67	6	.	.	PUNCT
ejpam-6040	68	1	it	it	PRON
ejpam-6040	68	2	is	be	AUX
ejpam-6040	68	3	easy	easy	ADJ
ejpam-6040	68	4	to	to	PART
ejpam-6040	68	5	verify	verify	VERB
ejpam-6040	68	6	that	that	SCONJ
ejpam-6040	68	7	the	the	DET
ejpam-6040	68	8	sets	set	NOUN
ejpam-6040	68	9	{	{	PUNCT
ejpam-6040	68	10	a	a	DET
ejpam-6040	68	11	,	,	PUNCT
ejpam-6040	68	12	y	y	NOUN
ejpam-6040	68	13	}	}	PUNCT
ejpam-6040	68	14	and	and	CCONJ
ejpam-6040	68	15	{	{	PUNCT
ejpam-6040	68	16	c	c	X
ejpam-6040	68	17	,	,	PUNCT
ejpam-6040	68	18	v	v	NOUN
ejpam-6040	68	19	}	}	PUNCT
ejpam-6040	68	20	are	be	AUX
ejpam-6040	68	21	not	not	PART
ejpam-6040	68	22	ζg2	ζg2	VERB
ejpam-6040	68	23	-sets	-set	NOUN
ejpam-6040	68	24	of	of	ADP
ejpam-6040	68	25	g.	g.	NOUN
ejpam-6040	68	26	finally	finally	ADV
ejpam-6040	68	27	,	,	PUNCT
ejpam-6040	68	28	if	if	SCONJ
ejpam-6040	68	29	k	k	PROPN
ejpam-6040	68	30	=	=	SYM
ejpam-6040	68	31	3	3	NUM
ejpam-6040	68	32	,	,	PUNCT
ejpam-6040	68	33	then	then	ADV
ejpam-6040	68	34	any	any	DET
ejpam-6040	68	35	1	1	NUM
ejpam-6040	68	36	-	-	PUNCT
ejpam-6040	68	37	element	element	NOUN
ejpam-6040	68	38	subset	subset	NOUN
ejpam-6040	68	39	d3	d3	PROPN
ejpam-6040	68	40	of	of	ADP
ejpam-6040	68	41	v	v	NOUN
ejpam-6040	68	42	(	(	PUNCT
ejpam-6040	68	43	g	g	NOUN
ejpam-6040	68	44	)	)	PUNCT
ejpam-6040	68	45	is	be	AUX
ejpam-6040	68	46	a	a	DET
ejpam-6040	68	47	ζg3	ζg3	NOUN
ejpam-6040	68	48	-set	-set	ADJ
ejpam-6040	68	49	of	of	ADP
ejpam-6040	68	50	g.	g.	PROPN
ejpam-6040	68	51	since	since	SCONJ
ejpam-6040	68	52	ng	ng	PROPN
ejpam-6040	68	53	g[d3	g[d3	PROPN
ejpam-6040	68	54	]	]	PUNCT
ejpam-6040	68	55	=	=	SYM
ejpam-6040	68	56	d3	d3	PROPN
ejpam-6040	68	57	,	,	PUNCT
ejpam-6040	68	58	it	it	PRON
ejpam-6040	68	59	follows	follow	VERB
ejpam-6040	68	60	that	that	SCONJ
ejpam-6040	68	61	ζ	ζ	NOUN
ejpam-6040	68	62	g	g	NOUN
ejpam-6040	68	63	3	3	NUM
ejpam-6040	68	64	(	(	PUNCT
ejpam-6040	68	65	g	g	NOUN
ejpam-6040	68	66	)	)	PUNCT
ejpam-6040	68	67	=	=	SYM
ejpam-6040	68	68	|v	|v	PROPN
ejpam-6040	68	69	(	(	PUNCT
ejpam-6040	68	70	g)|	g)|	NOUN
ejpam-6040	68	71	−	−	NOUN
ejpam-6040	68	72	|ng	|ng	NOUN
ejpam-6040	68	73	g[d3]|	g[d3]|	NOUN
ejpam-6040	68	74	=	=	PUNCT
ejpam-6040	68	75	8−	8−	NUM
ejpam-6040	68	76	1	1	NUM
ejpam-6040	68	77	=	=	SYM
ejpam-6040	68	78	7	7	NUM
ejpam-6040	68	79	.	.	PUNCT
ejpam-6040	68	80	................................................................................................................	................................................................................................................	PROPN
ejpam-6040	68	81	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	68	82	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	68	83	....................................	....................................	PUNCT
ejpam-6040	68	84	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	68	85	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	68	86	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	69	1	....................................	....................................	PUNCT
ejpam-6040	69	2	.........	.........	PUNCT
ejpam-6040	69	3	........	........	PUNCT
ejpam-6040	69	4	........	........	PUNCT
ejpam-6040	69	5	........	........	PUNCT
ejpam-6040	69	6	........	........	PUNCT
ejpam-6040	69	7	........	........	PUNCT
ejpam-6040	69	8	........	........	PUNCT
ejpam-6040	69	9	........	........	PUNCT
ejpam-6040	69	10	........	........	PUNCT
ejpam-6040	69	11	...	...	PUNCT
ejpam-6040	70	1	....................................	....................................	PUNCT
ejpam-6040	70	2	....................................	....................................	PUNCT
ejpam-6040	70	3	.........	.........	PUNCT
ejpam-6040	70	4	........	........	PUNCT
ejpam-6040	70	5	........	........	PUNCT
ejpam-6040	70	6	........	........	PUNCT
ejpam-6040	70	7	........	........	PUNCT
ejpam-6040	70	8	........	........	PUNCT
ejpam-6040	70	9	........	........	PUNCT
ejpam-6040	70	10	........	........	PUNCT
ejpam-6040	70	11	........	........	PUNCT
ejpam-6040	70	12	...	...	PUNCT
ejpam-6040	71	1	....................................	....................................	PUNCT
ejpam-6040	71	2	...................................................................................................................................................	...................................................................................................................................................	PUNCT
ejpam-6040	72	1	....................................	....................................	PUNCT
ejpam-6040	72	2	....................................	....................................	PUNCT
ejpam-6040	72	3	............	............	PUNCT
ejpam-6040	72	4	...........	...........	PUNCT
ejpam-6040	73	1	...........	...........	PUNCT
ejpam-6040	73	2	...........	...........	PUNCT
ejpam-6040	73	3	...........	...........	PUNCT
ejpam-6040	73	4	...........	...........	PUNCT
ejpam-6040	73	5	...........	...........	PUNCT
ejpam-6040	73	6	...........	...........	PUNCT
ejpam-6040	73	7	...........	...........	PUNCT
ejpam-6040	73	8	...........	...........	PUNCT
ejpam-6040	73	9	....................................	....................................	PUNCT
ejpam-6040	73	10	....................................	....................................	PUNCT
ejpam-6040	74	1	a	a	DET
ejpam-6040	74	2	b	b	X
ejpam-6040	74	3	x	x	SYM
ejpam-6040	74	4	y	y	NOUN
ejpam-6040	74	5	c	c	NOUN
ejpam-6040	74	6	u	u	PROPN
ejpam-6040	74	7	d	d	X
ejpam-6040	74	8	v	v	NUM
ejpam-6040	74	9	figure	figure	NOUN
ejpam-6040	74	10	1	1	NUM
ejpam-6040	74	11	:	:	PUNCT
ejpam-6040	74	12	graph	graph	VERB
ejpam-6040	74	13	g	g	NOUN
ejpam-6040	74	14	with	with	ADP
ejpam-6040	74	15	γg(g	γg(g	NOUN
ejpam-6040	74	16	)	)	PUNCT
ejpam-6040	74	17	=	=	SYM
ejpam-6040	74	18	4	4	NUM
ejpam-6040	74	19	,	,	PUNCT
ejpam-6040	74	20	ζg1	ζg1	X
ejpam-6040	74	21	(	(	PUNCT
ejpam-6040	74	22	g	g	NOUN
ejpam-6040	74	23	)	)	PUNCT
ejpam-6040	74	24	=	=	SYM
ejpam-6040	74	25	1	1	NUM
ejpam-6040	74	26	,	,	PUNCT
ejpam-6040	74	27	ζg2	ζg2	NOUN
ejpam-6040	74	28	(	(	PUNCT
ejpam-6040	74	29	g	g	NOUN
ejpam-6040	74	30	)	)	PUNCT
ejpam-6040	74	31	=	=	SYM
ejpam-6040	74	32	2	2	NUM
ejpam-6040	74	33	,	,	PUNCT
ejpam-6040	74	34	and	and	CCONJ
ejpam-6040	74	35	ζg3	ζg3	PROPN
ejpam-6040	74	36	(	(	PUNCT
ejpam-6040	74	37	g	g	NOUN
ejpam-6040	74	38	)	)	PUNCT
ejpam-6040	74	39	=	=	SYM
ejpam-6040	74	40	7	7	NUM
ejpam-6040	74	41	s.	s.	PROPN
ejpam-6040	74	42	canoy	canoy	PROPN
ejpam-6040	74	43	,	,	PUNCT
ejpam-6040	74	44	jr	jr	PROPN
ejpam-6040	74	45	.	.	PROPN
ejpam-6040	74	46	,	,	PUNCT
ejpam-6040	74	47	j.	j.	PROPN
ejpam-6040	74	48	anoche	anoche	PROPN
ejpam-6040	74	49	/	/	SYM
ejpam-6040	74	50	eur	eur	PROPN
ejpam-6040	74	51	.	.	PUNCT
ejpam-6040	75	1	j.	j.	PROPN
ejpam-6040	75	2	pure	pure	PROPN
ejpam-6040	75	3	appl	appl	PROPN
ejpam-6040	75	4	.	.	PROPN
ejpam-6040	75	5	math	math	PROPN
ejpam-6040	75	6	,	,	PUNCT
ejpam-6040	75	7	18	18	NUM
ejpam-6040	75	8	(	(	PUNCT
ejpam-6040	75	9	2	2	NUM
ejpam-6040	75	10	)	)	PUNCT
ejpam-6040	75	11	(	(	PUNCT
ejpam-6040	75	12	2025	2025	NUM
ejpam-6040	75	13	)	)	PUNCT
ejpam-6040	75	14	,	,	PUNCT
ejpam-6040	75	15	6040	6040	NUM
ejpam-6040	75	16	4	4	NUM
ejpam-6040	75	17	of	of	ADP
ejpam-6040	75	18	16	16	NUM
ejpam-6040	75	19	3	3	NUM
ejpam-6040	75	20	.	.	PUNCT
ejpam-6040	76	1	results	result	NOUN
ejpam-6040	76	2	theorem	theorem	VERB
ejpam-6040	76	3	1	1	NUM
ejpam-6040	76	4	(	(	PUNCT
ejpam-6040	76	5	[	[	X
ejpam-6040	76	6	20	20	NUM
ejpam-6040	76	7	]	]	NUM
ejpam-6040	76	8	)	)	PUNCT
ejpam-6040	76	9	.	.	PUNCT
ejpam-6040	77	1	let	let	VERB
ejpam-6040	77	2	n	n	PRON
ejpam-6040	77	3	be	be	AUX
ejpam-6040	77	4	positive	positive	ADJ
ejpam-6040	77	5	integer	integer	NOUN
ejpam-6040	77	6	.	.	PUNCT
ejpam-6040	78	1	then	then	ADV
ejpam-6040	78	2	each	each	PRON
ejpam-6040	78	3	of	of	ADP
ejpam-6040	78	4	the	the	DET
ejpam-6040	78	5	following	follow	VERB
ejpam-6040	78	6	holds	hold	NOUN
ejpam-6040	78	7	.	.	PUNCT
ejpam-6040	79	1	(	(	PUNCT
ejpam-6040	79	2	i	i	NOUN
ejpam-6040	79	3	)	)	PUNCT
ejpam-6040	79	4	for	for	ADP
ejpam-6040	79	5	a	a	DET
ejpam-6040	79	6	complete	complete	ADJ
ejpam-6040	79	7	graph	graph	NOUN
ejpam-6040	79	8	kn	kn	PROPN
ejpam-6040	79	9	,	,	PUNCT
ejpam-6040	79	10	γg(kn	γg(kn	NOUN
ejpam-6040	79	11	)	)	PUNCT
ejpam-6040	80	1	=	=	PUNCT
ejpam-6040	80	2	n.	n.	NOUN
ejpam-6040	80	3	(	(	PUNCT
ejpam-6040	80	4	ii	ii	PROPN
ejpam-6040	80	5	)	)	PUNCT
ejpam-6040	80	6	for	for	ADP
ejpam-6040	80	7	a	a	DET
ejpam-6040	80	8	star	star	NOUN
ejpam-6040	80	9	graph	graph	NOUN
ejpam-6040	80	10	k1,n−1	k1,n−1	ADJ
ejpam-6040	80	11	,	,	PUNCT
ejpam-6040	80	12	γg(k1,n−1	γg(k1,n−1	PROPN
ejpam-6040	80	13	)	)	PUNCT
ejpam-6040	80	14	=	=	PUNCT
ejpam-6040	80	15	n−	n−	NOUN
ejpam-6040	80	16	1	1	NUM
ejpam-6040	80	17	.	.	PUNCT
ejpam-6040	80	18	(	(	PUNCT
ejpam-6040	80	19	iii	iii	NOUN
ejpam-6040	80	20	)	)	PUNCT
ejpam-6040	80	21	for	for	ADP
ejpam-6040	80	22	a	a	DET
ejpam-6040	80	23	complete	complete	ADJ
ejpam-6040	80	24	bipartite	bipartite	NOUN
ejpam-6040	80	25	graph	graph	NOUN
ejpam-6040	80	26	km	km	PROPN
ejpam-6040	80	27	,	,	PUNCT
ejpam-6040	80	28	n	n	CCONJ
ejpam-6040	80	29	with	with	ADP
ejpam-6040	80	30	m	m	PROPN
ejpam-6040	80	31	,	,	PUNCT
ejpam-6040	80	32	n	n	PRON
ejpam-6040	80	33	≥	≥	NOUN
ejpam-6040	80	34	2	2	NUM
ejpam-6040	80	35	,	,	PUNCT
ejpam-6040	80	36	γg(km	γg(km	PROPN
ejpam-6040	80	37	,	,	PUNCT
ejpam-6040	80	38	n	n	CCONJ
ejpam-6040	80	39	)	)	PUNCT
ejpam-6040	80	40	=	=	SYM
ejpam-6040	80	41	min{m	min{m	PROPN
ejpam-6040	80	42	,	,	PUNCT
ejpam-6040	80	43	n	n	CCONJ
ejpam-6040	80	44	,	,	PUNCT
ejpam-6040	80	45	4	4	NUM
ejpam-6040	80	46	}	}	PUNCT
ejpam-6040	80	47	.	.	PUNCT
ejpam-6040	81	1	(	(	PUNCT
ejpam-6040	81	2	iv	iv	X
ejpam-6040	81	3	)	)	PUNCT
ejpam-6040	81	4	for	for	ADP
ejpam-6040	81	5	a	a	DET
ejpam-6040	81	6	wheel	wheel	NOUN
ejpam-6040	81	7	graph	graph	NOUN
ejpam-6040	81	8	wn	wn	PROPN
ejpam-6040	81	9	,	,	PUNCT
ejpam-6040	81	10	γg(wn	γg(wn	PROPN
ejpam-6040	81	11	)	)	PUNCT
ejpam-6040	82	1	=	=	SYM
ejpam-6040	82	2	⌈n−1	⌈n−1	NOUN
ejpam-6040	82	3	2	2	NUM
ejpam-6040	82	4	⌉	⌉	NOUN
ejpam-6040	82	5	,	,	PUNCT
ejpam-6040	82	6	n	n	PRON
ejpam-6040	82	7	≥	≥	NOUN
ejpam-6040	82	8	5	5	NUM
ejpam-6040	82	9	.	.	PUNCT
ejpam-6040	83	1	(	(	PUNCT
ejpam-6040	83	2	v	v	NOUN
ejpam-6040	83	3	)	)	PUNCT
ejpam-6040	83	4	for	for	ADP
ejpam-6040	83	5	a	a	DET
ejpam-6040	83	6	cycle	cycle	NOUN
ejpam-6040	83	7	cn	cn	NOUN
ejpam-6040	83	8	on	on	ADP
ejpam-6040	83	9	n	n	PRON
ejpam-6040	83	10	vertices	vertex	NOUN
ejpam-6040	83	11	,	,	PUNCT
ejpam-6040	83	12	we	we	PRON
ejpam-6040	83	13	have	have	VERB
ejpam-6040	83	14	γg(cn	γg(cn	NOUN
ejpam-6040	83	15	)	)	PUNCT
ejpam-6040	84	1	=	=	X
ejpam-6040	84	2	⌈n3	⌈n3	X
ejpam-6040	84	3	⌉	⌉	X
ejpam-6040	84	4	,	,	PUNCT
ejpam-6040	84	5	n	n	PRON
ejpam-6040	84	6	≥	≥	NOUN
ejpam-6040	84	7	6	6	NUM
ejpam-6040	84	8	.	.	PUNCT
ejpam-6040	85	1	(	(	PUNCT
ejpam-6040	85	2	vi	vi	NOUN
ejpam-6040	85	3	)	)	PUNCT
ejpam-6040	85	4	for	for	ADP
ejpam-6040	85	5	a	a	DET
ejpam-6040	85	6	path	path	NOUN
ejpam-6040	85	7	pn	pn	NOUN
ejpam-6040	85	8	on	on	ADP
ejpam-6040	85	9	n	n	PRON
ejpam-6040	85	10	vertices	vertex	NOUN
ejpam-6040	85	11	,	,	PUNCT
ejpam-6040	85	12	γg(pn	γg(pn	NOUN
ejpam-6040	85	13	)	)	PUNCT
ejpam-6040	86	1	=	=	SYM
ejpam-6040	87	1	⌈n+2	⌈n+2	NUM
ejpam-6040	87	2	3	3	NUM
ejpam-6040	87	3	⌉.	⌉.	ADV
ejpam-6040	87	4	(	(	PUNCT
ejpam-6040	87	5	vii	vii	PROPN
ejpam-6040	87	6	)	)	PUNCT
ejpam-6040	87	7	for	for	ADP
ejpam-6040	87	8	the	the	DET
ejpam-6040	87	9	petersen	petersen	PROPN
ejpam-6040	87	10	graph	graph	NOUN
ejpam-6040	87	11	p	p	NOUN
ejpam-6040	87	12	,	,	PUNCT
ejpam-6040	87	13	γg(p	γg(p	NUM
ejpam-6040	87	14	)	)	PUNCT
ejpam-6040	87	15	=	=	SYM
ejpam-6040	88	1	4	4	X
ejpam-6040	88	2	.	.	NOUN
ejpam-6040	88	3	remark	remark	NOUN
ejpam-6040	88	4	1	1	NUM
ejpam-6040	88	5	.	.	PUNCT
ejpam-6040	89	1	let	let	VERB
ejpam-6040	89	2	g1	g1	PROPN
ejpam-6040	89	3	,	,	PUNCT
ejpam-6040	89	4	g2	g2	PROPN
ejpam-6040	89	5	,	,	PUNCT
ejpam-6040	89	6	·	·	PUNCT
ejpam-6040	89	7	·	·	PUNCT
ejpam-6040	89	8	·	·	PUNCT
ejpam-6040	89	9	,	,	PUNCT
ejpam-6040	89	10	gr	gr	INTJ
ejpam-6040	89	11	be	be	AUX
ejpam-6040	89	12	the	the	DET
ejpam-6040	89	13	components	component	NOUN
ejpam-6040	89	14	of	of	ADP
ejpam-6040	89	15	a	a	DET
ejpam-6040	89	16	graph	graph	NOUN
ejpam-6040	89	17	g.	g.	NOUN
ejpam-6040	90	1	then	then	ADV
ejpam-6040	90	2	each	each	PRON
ejpam-6040	90	3	of	of	ADP
ejpam-6040	90	4	the	the	DET
ejpam-6040	90	5	following	follow	VERB
ejpam-6040	90	6	holds	hold	VERB
ejpam-6040	90	7	:	:	PUNCT
ejpam-6040	90	8	(	(	PUNCT
ejpam-6040	90	9	i	i	NOUN
ejpam-6040	90	10	)	)	PUNCT
ejpam-6040	90	11	γg(g	γg(g	PUNCT
ejpam-6040	90	12	)	)	PUNCT
ejpam-6040	91	1	=	=	PUNCT
ejpam-6040	92	1	∑r	∑r	PROPN
ejpam-6040	92	2	j=1	j=1	PROPN
ejpam-6040	92	3	γg(gj	γg(gj	PROPN
ejpam-6040	92	4	)	)	PUNCT
ejpam-6040	92	5	.	.	PUNCT
ejpam-6040	93	1	(	(	PUNCT
ejpam-6040	93	2	ii	ii	NOUN
ejpam-6040	93	3	)	)	PUNCT
ejpam-6040	93	4	if	if	SCONJ
ejpam-6040	93	5	aj	aj	PROPN
ejpam-6040	93	6	⊆	⊆	NUM
ejpam-6040	93	7	v	v	NOUN
ejpam-6040	93	8	(	(	PUNCT
ejpam-6040	93	9	gj	gj	NOUN
ejpam-6040	93	10	)	)	PUNCT
ejpam-6040	93	11	for	for	ADP
ejpam-6040	93	12	each	each	DET
ejpam-6040	93	13	j	j	PROPN
ejpam-6040	93	14	∈	∈	PROPN
ejpam-6040	94	1	[	[	X
ejpam-6040	94	2	r	r	X
ejpam-6040	94	3	]	]	X
ejpam-6040	94	4	=	=	PUNCT
ejpam-6040	94	5	{	{	PUNCT
ejpam-6040	94	6	1	1	NUM
ejpam-6040	94	7	,	,	PUNCT
ejpam-6040	94	8	2	2	NUM
ejpam-6040	94	9	,	,	PUNCT
ejpam-6040	94	10	·	·	PUNCT
ejpam-6040	94	11	·	·	PUNCT
ejpam-6040	94	12	·	·	PUNCT
ejpam-6040	94	13	,	,	PUNCT
ejpam-6040	94	14	r	r	X
ejpam-6040	94	15	}	}	PUNCT
ejpam-6040	94	16	and	and	CCONJ
ejpam-6040	94	17	a	a	DET
ejpam-6040	94	18	=	=	X
ejpam-6040	94	19	∪r	∪r	NUM
ejpam-6040	94	20	j=1aj	j=1aj	PROPN
ejpam-6040	94	21	,	,	PUNCT
ejpam-6040	94	22	then	then	ADV
ejpam-6040	94	23	ng	ng	PROPN
ejpam-6040	94	24	g[a	g[a	PROPN
ejpam-6040	94	25	]	]	X
ejpam-6040	94	26	=	=	SYM
ejpam-6040	94	27	∪r	∪r	PUNCT
ejpam-6040	94	28	j=1n	j=1n	VERB
ejpam-6040	94	29	g	g	PROPN
ejpam-6040	94	30	g[aj	g[aj	PROPN
ejpam-6040	94	31	]	]	X
ejpam-6040	94	32	(	(	PUNCT
ejpam-6040	94	33	a	a	DET
ejpam-6040	94	34	disjoint	disjoint	NOUN
ejpam-6040	94	35	union	union	NOUN
ejpam-6040	94	36	)	)	PUNCT
ejpam-6040	94	37	.	.	PUNCT
ejpam-6040	95	1	theorem	theorem	NOUN
ejpam-6040	95	2	2	2	NUM
ejpam-6040	95	3	.	.	PUNCT
ejpam-6040	95	4	let	let	VERB
ejpam-6040	95	5	g1	g1	PROPN
ejpam-6040	95	6	,	,	PUNCT
ejpam-6040	95	7	g2	g2	PROPN
ejpam-6040	95	8	,	,	PUNCT
ejpam-6040	95	9	·	·	PUNCT
ejpam-6040	95	10	·	·	PUNCT
ejpam-6040	95	11	·	·	PUNCT
ejpam-6040	95	12	,	,	PUNCT
ejpam-6040	95	13	gr	gr	INTJ
ejpam-6040	95	14	be	be	AUX
ejpam-6040	95	15	the	the	DET
ejpam-6040	95	16	components	component	NOUN
ejpam-6040	95	17	of	of	ADP
ejpam-6040	95	18	graph	graph	NOUN
ejpam-6040	95	19	g	g	PROPN
ejpam-6040	95	20	and	and	CCONJ
ejpam-6040	95	21	let	let	VERB
ejpam-6040	95	22	ζg1	ζg1	PROPN
ejpam-6040	95	23	(	(	PUNCT
ejpam-6040	95	24	gi	gi	INTJ
ejpam-6040	95	25	)	)	PUNCT
ejpam-6040	95	26	be	be	AUX
ejpam-6040	95	27	the	the	DET
ejpam-6040	95	28	1	1	NUM
ejpam-6040	95	29	-	-	PUNCT
ejpam-6040	95	30	geodetic	geodetic	ADJ
ejpam-6040	95	31	domination	domination	NOUN
ejpam-6040	95	32	defect	defect	NOUN
ejpam-6040	95	33	of	of	ADP
ejpam-6040	95	34	gi	gi	NOUN
ejpam-6040	95	35	for	for	ADP
ejpam-6040	95	36	each	each	DET
ejpam-6040	95	37	i	i	PRON
ejpam-6040	95	38	∈	∈	PROPN
ejpam-6040	96	1	[	[	X
ejpam-6040	96	2	r	r	X
ejpam-6040	96	3	]	]	X
ejpam-6040	96	4	=	=	PUNCT
ejpam-6040	96	5	{	{	PUNCT
ejpam-6040	96	6	1	1	NUM
ejpam-6040	96	7	,	,	PUNCT
ejpam-6040	96	8	2	2	NUM
ejpam-6040	96	9	,	,	PUNCT
ejpam-6040	96	10	·	·	PUNCT
ejpam-6040	96	11	·	·	PUNCT
ejpam-6040	96	12	·	·	PUNCT
ejpam-6040	96	13	,	,	PUNCT
ejpam-6040	96	14	r	r	NOUN
ejpam-6040	96	15	}	}	PUNCT
ejpam-6040	96	16	.	.	PUNCT
ejpam-6040	97	1	then	then	ADV
ejpam-6040	97	2	ζg1	ζg1	PROPN
ejpam-6040	97	3	(	(	PUNCT
ejpam-6040	97	4	g	g	NOUN
ejpam-6040	97	5	)	)	PUNCT
ejpam-6040	97	6	=	=	NOUN
ejpam-6040	97	7	min{ζg1	min{ζg1	NOUN
ejpam-6040	97	8	(	(	PUNCT
ejpam-6040	97	9	gi	gi	NOUN
ejpam-6040	97	10	)	)	PUNCT
ejpam-6040	97	11	:	:	PUNCT
ejpam-6040	98	1	i	i	PRON
ejpam-6040	98	2	∈	∈	VERB
ejpam-6040	99	1	[	[	X
ejpam-6040	99	2	r	r	X
ejpam-6040	99	3	]	]	PUNCT
ejpam-6040	99	4	}	}	PUNCT
ejpam-6040	99	5	.	.	PUNCT
ejpam-6040	100	1	proof	proof	NOUN
ejpam-6040	100	2	.	.	PUNCT
ejpam-6040	101	1	let	let	VERB
ejpam-6040	101	2	γg(gi	γg(gi	PROPN
ejpam-6040	101	3	)	)	PUNCT
ejpam-6040	101	4	and	and	CCONJ
ejpam-6040	101	5	γg(g	γg(g	PRON
ejpam-6040	101	6	)	)	PUNCT
ejpam-6040	101	7	be	be	VERB
ejpam-6040	101	8	the	the	DET
ejpam-6040	101	9	geodetic	geodetic	ADJ
ejpam-6040	101	10	domination	domination	NOUN
ejpam-6040	101	11	numbers	number	NOUN
ejpam-6040	101	12	of	of	ADP
ejpam-6040	101	13	gi	gi	NOUN
ejpam-6040	101	14	and	and	CCONJ
ejpam-6040	101	15	g	g	NOUN
ejpam-6040	101	16	,	,	PUNCT
ejpam-6040	101	17	respectively	respectively	ADV
ejpam-6040	101	18	.	.	PUNCT
ejpam-6040	102	1	by	by	ADP
ejpam-6040	102	2	remark	remark	NOUN
ejpam-6040	102	3	1(i	1(i	NUM
ejpam-6040	102	4	)	)	PUNCT
ejpam-6040	102	5	,	,	PUNCT
ejpam-6040	102	6	γg(g	γg(g	PUNCT
ejpam-6040	102	7	)	)	PUNCT
ejpam-6040	102	8	=	=	PUNCT
ejpam-6040	103	1	∑r	∑r	PROPN
ejpam-6040	103	2	j=1	j=1	PROPN
ejpam-6040	103	3	γg(gi	γg(gi	PROPN
ejpam-6040	103	4	)	)	PUNCT
ejpam-6040	103	5	.	.	PUNCT
ejpam-6040	104	1	for	for	ADP
ejpam-6040	104	2	each	each	DET
ejpam-6040	104	3	i	i	PRON
ejpam-6040	104	4	∈	∈	PROPN
ejpam-6040	105	1	[	[	X
ejpam-6040	105	2	r	r	X
ejpam-6040	105	3	]	]	PUNCT
ejpam-6040	105	4	,	,	PUNCT
ejpam-6040	105	5	let	let	VERB
ejpam-6040	105	6	di	di	PART
ejpam-6040	105	7	be	be	AUX
ejpam-6040	105	8	a	a	DET
ejpam-6040	105	9	ζg1	ζg1	PROPN
ejpam-6040	105	10	-set	-set	ADJ
ejpam-6040	105	11	of	of	ADP
ejpam-6040	105	12	gi	gi	PROPN
ejpam-6040	105	13	.	.	PUNCT
ejpam-6040	106	1	then	then	ADV
ejpam-6040	106	2	|di|	|di|	PROPN
ejpam-6040	106	3	=	=	SYM
ejpam-6040	106	4	γg(gi	γg(gi	PROPN
ejpam-6040	106	5	)	)	PUNCT
ejpam-6040	107	1	−	−	PROPN
ejpam-6040	107	2	1	1	NUM
ejpam-6040	107	3	and	and	CCONJ
ejpam-6040	107	4	ζg1	ζg1	PROPN
ejpam-6040	107	5	(	(	PUNCT
ejpam-6040	107	6	gi	gi	NOUN
ejpam-6040	107	7	)	)	PUNCT
ejpam-6040	107	8	=	=	SYM
ejpam-6040	108	1	|v	|v	PROPN
ejpam-6040	108	2	(	(	PUNCT
ejpam-6040	108	3	gi	gi	INTJ
ejpam-6040	108	4	)	)	PUNCT
ejpam-6040	108	5	−	−	PROPN
ejpam-6040	109	1	ng	ng	PROPN
ejpam-6040	109	2	g[di]|	g[di]|	PROPN
ejpam-6040	109	3	.	.	PUNCT
ejpam-6040	110	1	let	let	VERB
ejpam-6040	110	2	j	j	PROPN
ejpam-6040	110	3	∈	∈	PROPN
ejpam-6040	111	1	[	[	X
ejpam-6040	111	2	r	r	X
ejpam-6040	111	3	]	]	PUNCT
ejpam-6040	111	4	be	be	AUX
ejpam-6040	111	5	such	such	ADJ
ejpam-6040	111	6	that	that	SCONJ
ejpam-6040	111	7	ζg1	ζg1	PROPN
ejpam-6040	111	8	(	(	PUNCT
ejpam-6040	111	9	gj	gj	NOUN
ejpam-6040	111	10	)	)	PUNCT
ejpam-6040	111	11	=	=	NOUN
ejpam-6040	112	1	min{ζg1	min{ζg1	NOUN
ejpam-6040	112	2	(	(	PUNCT
ejpam-6040	112	3	gi	gi	NOUN
ejpam-6040	112	4	)	)	PUNCT
ejpam-6040	112	5	:	:	PUNCT
ejpam-6040	113	1	i	i	PRON
ejpam-6040	113	2	∈	∈	VERB
ejpam-6040	114	1	[	[	X
ejpam-6040	114	2	r	r	X
ejpam-6040	114	3	]	]	PUNCT
ejpam-6040	114	4	}	}	PUNCT
ejpam-6040	114	5	.	.	PUNCT
ejpam-6040	115	1	let	let	VERB
ejpam-6040	115	2	si	si	X
ejpam-6040	115	3	be	be	AUX
ejpam-6040	115	4	a	a	DET
ejpam-6040	115	5	γg	γg	ADV
ejpam-6040	115	6	-	-	PUNCT
ejpam-6040	115	7	set	set	VERB
ejpam-6040	115	8	in	in	ADP
ejpam-6040	115	9	gi	gi	NOUN
ejpam-6040	115	10	for	for	ADP
ejpam-6040	115	11	each	each	DET
ejpam-6040	115	12	i	i	PRON
ejpam-6040	115	13	∈	∈	PROPN
ejpam-6040	116	1	[	[	X
ejpam-6040	116	2	r	r	X
ejpam-6040	116	3	]	]	PUNCT
ejpam-6040	116	4	and	and	CCONJ
ejpam-6040	116	5	let	let	VERB
ejpam-6040	116	6	s	s	PRON
ejpam-6040	116	7	=	=	PUNCT
ejpam-6040	116	8	(	(	PUNCT
ejpam-6040	116	9	∪i∈[r]\{j}si	∪i∈[r]\{j}si	NOUN
ejpam-6040	116	10	)	)	PUNCT
ejpam-6040	116	11	∪dj	∪dj	NOUN
ejpam-6040	116	12	.	.	PUNCT
ejpam-6040	117	1	then	then	ADV
ejpam-6040	117	2	|s|	|s|	PROPN
ejpam-6040	117	3	=	=	SYM
ejpam-6040	117	4	∑	∑	SYM
ejpam-6040	117	5	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-6040	117	6	}	}	PUNCT
ejpam-6040	117	7	|si|+	|si|+	NOUN
ejpam-6040	117	8	|dj	|dj	PUNCT
ejpam-6040	117	9	|	|	NOUN
ejpam-6040	117	10	=	=	SYM
ejpam-6040	117	11	γg(g)−	γg(g)−	NOUN
ejpam-6040	117	12	1	1	NUM
ejpam-6040	117	13	and	and	CCONJ
ejpam-6040	117	14	,	,	PUNCT
ejpam-6040	117	15	by	by	ADP
ejpam-6040	117	16	remark	remark	NOUN
ejpam-6040	117	17	1(ii	1(ii	NUM
ejpam-6040	117	18	)	)	PUNCT
ejpam-6040	117	19	,	,	PUNCT
ejpam-6040	117	20	|ng	|ng	X
ejpam-6040	117	21	g[s]|	g[s]|	X
ejpam-6040	117	22	=	=	PUNCT
ejpam-6040	117	23	|ng	|ng	X
ejpam-6040	117	24	gj	gj	NOUN
ejpam-6040	118	1	[	[	X
ejpam-6040	118	2	dj	dj	X
ejpam-6040	118	3	]	]	X
ejpam-6040	118	4	|+	|+	NOUN
ejpam-6040	118	5	∑	∑	ADV
ejpam-6040	118	6	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-6040	118	7	}	}	PUNCT
ejpam-6040	118	8	|ng	|ng	AUX
ejpam-6040	118	9	gi	gi	NOUN
ejpam-6040	119	1	[	[	X
ejpam-6040	119	2	si]|	si]|	ADP
ejpam-6040	119	3	=	=	SYM
ejpam-6040	119	4	|v	|v	X
ejpam-6040	119	5	(	(	PUNCT
ejpam-6040	119	6	gj)|	gj)|	NOUN
ejpam-6040	119	7	−	−	PROPN
ejpam-6040	119	8	ζg1	ζg1	X
ejpam-6040	119	9	(	(	PUNCT
ejpam-6040	119	10	gj	gj	NOUN
ejpam-6040	119	11	)	)	PUNCT
ejpam-6040	119	12	+	+	CCONJ
ejpam-6040	119	13	∑	∑	PUNCT
ejpam-6040	119	14	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-6040	119	15	}	}	PUNCT
ejpam-6040	119	16	|v	|v	NOUN
ejpam-6040	119	17	(	(	PUNCT
ejpam-6040	119	18	gi)|	gi)|	X
ejpam-6040	119	19	=	=	PUNCT
ejpam-6040	119	20	r∑	r∑	NOUN
ejpam-6040	119	21	i=1	i=1	PROPN
ejpam-6040	119	22	|v	|v	X
ejpam-6040	119	23	(	(	PUNCT
ejpam-6040	119	24	gi)|	gi)|	INTJ
ejpam-6040	119	25	−	−	PROPN
ejpam-6040	119	26	ζg1	ζg1	X
ejpam-6040	119	27	(	(	PUNCT
ejpam-6040	119	28	gj	gj	PROPN
ejpam-6040	119	29	)	)	PUNCT
ejpam-6040	119	30	.	.	PUNCT
ejpam-6040	120	1	s.	s.	PROPN
ejpam-6040	120	2	canoy	canoy	PROPN
ejpam-6040	120	3	,	,	PUNCT
ejpam-6040	120	4	jr	jr	PROPN
ejpam-6040	120	5	.	.	PROPN
ejpam-6040	120	6	,	,	PUNCT
ejpam-6040	120	7	j.	j.	PROPN
ejpam-6040	120	8	anoche	anoche	PROPN
ejpam-6040	120	9	/	/	SYM
ejpam-6040	120	10	eur	eur	PROPN
ejpam-6040	120	11	.	.	PUNCT
ejpam-6040	121	1	j.	j.	PROPN
ejpam-6040	121	2	pure	pure	PROPN
ejpam-6040	121	3	appl	appl	PROPN
ejpam-6040	121	4	.	.	PROPN
ejpam-6040	121	5	math	math	PROPN
ejpam-6040	121	6	,	,	PUNCT
ejpam-6040	121	7	18	18	NUM
ejpam-6040	121	8	(	(	PUNCT
ejpam-6040	121	9	2	2	NUM
ejpam-6040	121	10	)	)	PUNCT
ejpam-6040	121	11	(	(	PUNCT
ejpam-6040	121	12	2025	2025	NUM
ejpam-6040	121	13	)	)	PUNCT
ejpam-6040	121	14	,	,	PUNCT
ejpam-6040	121	15	6040	6040	NUM
ejpam-6040	121	16	5	5	NUM
ejpam-6040	121	17	of	of	ADP
ejpam-6040	121	18	16	16	NUM
ejpam-6040	121	19	thus	thus	ADV
ejpam-6040	121	20	,	,	PUNCT
ejpam-6040	121	21	in	in	ADP
ejpam-6040	121	22	g	g	NOUN
ejpam-6040	121	23	,	,	PUNCT
ejpam-6040	121	24	ζg1	ζg1	X
ejpam-6040	121	25	(	(	PUNCT
ejpam-6040	121	26	s	s	NOUN
ejpam-6040	121	27	)	)	PUNCT
ejpam-6040	121	28	=	=	SYM
ejpam-6040	121	29	|v	|v	PROPN
ejpam-6040	121	30	(	(	PUNCT
ejpam-6040	121	31	g)|	g)|	NOUN
ejpam-6040	121	32	−	−	NOUN
ejpam-6040	121	33	|ng	|ng	PUNCT
ejpam-6040	121	34	g[s]|	g[s]|	NOUN
ejpam-6040	121	35	=	=	PUNCT
ejpam-6040	121	36	ζg1	ζg1	X
ejpam-6040	121	37	(	(	PUNCT
ejpam-6040	121	38	gj	gj	NOUN
ejpam-6040	121	39	)	)	PUNCT
ejpam-6040	121	40	.	.	PUNCT
ejpam-6040	122	1	we	we	PRON
ejpam-6040	122	2	claim	claim	VERB
ejpam-6040	122	3	that	that	SCONJ
ejpam-6040	122	4	ζg1	ζg1	PROPN
ejpam-6040	122	5	(	(	PUNCT
ejpam-6040	122	6	s	s	X
ejpam-6040	122	7	)	)	PUNCT
ejpam-6040	122	8	is	be	AUX
ejpam-6040	122	9	the	the	DET
ejpam-6040	122	10	minimum	minimum	NOUN
ejpam-6040	122	11	among	among	ADP
ejpam-6040	122	12	all	all	DET
ejpam-6040	122	13	subsets	subset	NOUN
ejpam-6040	122	14	of	of	ADP
ejpam-6040	122	15	v	v	NOUN
ejpam-6040	122	16	(	(	PUNCT
ejpam-6040	122	17	g	g	NOUN
ejpam-6040	122	18	)	)	PUNCT
ejpam-6040	122	19	with	with	ADP
ejpam-6040	122	20	cardinality	cardinality	NOUN
ejpam-6040	122	21	γg(g	γg(g	PRON
ejpam-6040	122	22	)	)	PUNCT
ejpam-6040	122	23	−	−	PROPN
ejpam-6040	123	1	1	1	X
ejpam-6040	123	2	.	.	PUNCT
ejpam-6040	123	3	to	to	ADP
ejpam-6040	123	4	this	this	DET
ejpam-6040	123	5	end	end	NOUN
ejpam-6040	123	6	,	,	PUNCT
ejpam-6040	123	7	suppose	suppose	VERB
ejpam-6040	123	8	there	there	PRON
ejpam-6040	123	9	exists	exist	VERB
ejpam-6040	123	10	q	q	PROPN
ejpam-6040	123	11	⊆	⊆	NUM
ejpam-6040	123	12	v	v	NOUN
ejpam-6040	123	13	(	(	PUNCT
ejpam-6040	123	14	g	g	NOUN
ejpam-6040	123	15	)	)	PUNCT
ejpam-6040	123	16	such	such	ADJ
ejpam-6040	123	17	that	that	DET
ejpam-6040	123	18	|q|	|q|	X
ejpam-6040	123	19	=	=	SYM
ejpam-6040	123	20	γg(g	γg(g	NOUN
ejpam-6040	123	21	)	)	PUNCT
ejpam-6040	123	22	−	−	PROPN
ejpam-6040	123	23	1	1	NUM
ejpam-6040	123	24	and	and	CCONJ
ejpam-6040	123	25	ζg1	ζg1	X
ejpam-6040	123	26	(	(	PUNCT
ejpam-6040	123	27	q	q	X
ejpam-6040	123	28	)	)	PUNCT
ejpam-6040	123	29	<	<	X
ejpam-6040	123	30	ζg1	ζg1	X
ejpam-6040	123	31	(	(	PUNCT
ejpam-6040	123	32	s	s	NOUN
ejpam-6040	123	33	)	)	PUNCT
ejpam-6040	123	34	.	.	PUNCT
ejpam-6040	124	1	let	let	VERB
ejpam-6040	124	2	q	q	NOUN
ejpam-6040	124	3	=	=	PROPN
ejpam-6040	124	4	q1	q1	PROPN
ejpam-6040	124	5	∪	∪	PROPN
ejpam-6040	124	6	q2	q2	PROPN
ejpam-6040	124	7	∪	∪	X
ejpam-6040	124	8	·	·	PUNCT
ejpam-6040	124	9	·	·	PUNCT
ejpam-6040	124	10	·	·	PUNCT
ejpam-6040	124	11	∪	∪	ADP
ejpam-6040	124	12	qr	qr	NOUN
ejpam-6040	124	13	where	where	SCONJ
ejpam-6040	124	14	qi	qi	PROPN
ejpam-6040	124	15	⊆	⊆	NUM
ejpam-6040	124	16	v	v	NOUN
ejpam-6040	124	17	(	(	PUNCT
ejpam-6040	124	18	gi	gi	INTJ
ejpam-6040	124	19	)	)	PUNCT
ejpam-6040	124	20	for	for	ADP
ejpam-6040	124	21	each	each	DET
ejpam-6040	124	22	i	i	PRON
ejpam-6040	124	23	∈	∈	PROPN
ejpam-6040	125	1	[	[	X
ejpam-6040	125	2	r	r	X
ejpam-6040	125	3	]	]	X
ejpam-6040	125	4	.	.	PUNCT
ejpam-6040	126	1	since	since	SCONJ
ejpam-6040	126	2	|q|	|q|	PROPN
ejpam-6040	126	3	=	=	SYM
ejpam-6040	126	4	γg(g)−1	γg(g)−1	X
ejpam-6040	126	5	,	,	PUNCT
ejpam-6040	126	6	at	at	ADP
ejpam-6040	126	7	least	least	ADV
ejpam-6040	126	8	one	one	NUM
ejpam-6040	126	9	qt	qt	NOUN
ejpam-6040	126	10	is	be	AUX
ejpam-6040	126	11	not	not	PART
ejpam-6040	126	12	a	a	DET
ejpam-6040	126	13	geodetic	geodetic	ADJ
ejpam-6040	126	14	dominating	dominating	NOUN
ejpam-6040	126	15	set	set	NOUN
ejpam-6040	126	16	of	of	ADP
ejpam-6040	126	17	gt	gt	PROPN
ejpam-6040	126	18	by	by	ADP
ejpam-6040	126	19	remark	remark	NOUN
ejpam-6040	126	20	1(i	1(i	NUM
ejpam-6040	126	21	)	)	PUNCT
ejpam-6040	126	22	.	.	PUNCT
ejpam-6040	127	1	thus	thus	ADV
ejpam-6040	127	2	,	,	PUNCT
ejpam-6040	127	3	|qt|	|qt|	PROPN
ejpam-6040	127	4	=	=	SYM
ejpam-6040	127	5	γg(gt	γg(gt	PROPN
ejpam-6040	127	6	)	)	PUNCT
ejpam-6040	128	1	−	−	PROPN
ejpam-6040	128	2	1	1	NUM
ejpam-6040	128	3	and	and	CCONJ
ejpam-6040	128	4	ζg1	ζg1	X
ejpam-6040	128	5	(	(	PUNCT
ejpam-6040	128	6	qt	qt	PROPN
ejpam-6040	128	7	)	)	PUNCT
ejpam-6040	128	8	≥	≥	NOUN
ejpam-6040	128	9	ζg1	ζg1	X
ejpam-6040	128	10	(	(	PUNCT
ejpam-6040	128	11	gt	gt	PROPN
ejpam-6040	128	12	)	)	PUNCT
ejpam-6040	128	13	≥	≥	NOUN
ejpam-6040	128	14	ζg1	ζg1	X
ejpam-6040	128	15	(	(	PUNCT
ejpam-6040	128	16	gj	gj	PROPN
ejpam-6040	128	17	)	)	PUNCT
ejpam-6040	128	18	.	.	PUNCT
ejpam-6040	129	1	hence	hence	ADV
ejpam-6040	129	2	,	,	PUNCT
ejpam-6040	129	3	ζg1	ζg1	X
ejpam-6040	129	4	(	(	PUNCT
ejpam-6040	129	5	q	q	X
ejpam-6040	129	6	)	)	PUNCT
ejpam-6040	129	7	=	=	SYM
ejpam-6040	129	8	|v	|v	PROPN
ejpam-6040	129	9	(	(	PUNCT
ejpam-6040	129	10	g)|	g)|	NOUN
ejpam-6040	129	11	−	−	PROPN
ejpam-6040	129	12	|ng	|ng	PUNCT
ejpam-6040	129	13	g[q]|	g[q]|	NOUN
ejpam-6040	129	14	=	=	SYM
ejpam-6040	130	1	r∑	r∑	X
ejpam-6040	130	2	i=1	i=1	PROPN
ejpam-6040	130	3	(	(	PUNCT
ejpam-6040	130	4	|v	|v	X
ejpam-6040	130	5	(	(	PUNCT
ejpam-6040	130	6	gi)|	gi)|	INTJ
ejpam-6040	130	7	−	−	PROPN
ejpam-6040	130	8	|ng	|ng	AUX
ejpam-6040	130	9	gi	gi	PROPN
ejpam-6040	130	10	[	[	X
ejpam-6040	130	11	qi]|	qi]|	PROPN
ejpam-6040	130	12	)	)	PUNCT
ejpam-6040	130	13	≥	≥	NOUN
ejpam-6040	130	14	|v	|v	NOUN
ejpam-6040	130	15	(	(	PUNCT
ejpam-6040	130	16	gt)|	gt)|	PROPN
ejpam-6040	130	17	−	−	PROPN
ejpam-6040	130	18	|ng	|ng	AUX
ejpam-6040	130	19	gt	gt	PROPN
ejpam-6040	131	1	[	[	X
ejpam-6040	131	2	qt]|	qt]|	NOUN
ejpam-6040	131	3	=	=	VERB
ejpam-6040	131	4	ζg1	ζg1	X
ejpam-6040	131	5	(	(	PUNCT
ejpam-6040	131	6	qt	qt	PROPN
ejpam-6040	131	7	)	)	PUNCT
ejpam-6040	131	8	≥	≥	NOUN
ejpam-6040	131	9	ζg1	ζg1	X
ejpam-6040	131	10	(	(	PUNCT
ejpam-6040	131	11	gj	gj	NOUN
ejpam-6040	131	12	)	)	PUNCT
ejpam-6040	131	13	=	=	VERB
ejpam-6040	132	1	ζg1	ζg1	X
ejpam-6040	132	2	(	(	PUNCT
ejpam-6040	132	3	s	s	NOUN
ejpam-6040	132	4	)	)	PUNCT
ejpam-6040	132	5	,	,	PUNCT
ejpam-6040	132	6	contrary	contrary	ADV
ejpam-6040	132	7	to	to	ADP
ejpam-6040	132	8	the	the	DET
ejpam-6040	132	9	assumption	assumption	NOUN
ejpam-6040	132	10	that	that	SCONJ
ejpam-6040	132	11	ζg1	ζg1	PROPN
ejpam-6040	132	12	(	(	PUNCT
ejpam-6040	132	13	q	q	X
ejpam-6040	132	14	)	)	PUNCT
ejpam-6040	132	15	<	<	X
ejpam-6040	132	16	ζg1	ζg1	X
ejpam-6040	132	17	(	(	PUNCT
ejpam-6040	132	18	s	s	NOUN
ejpam-6040	132	19	)	)	PUNCT
ejpam-6040	132	20	.	.	PUNCT
ejpam-6040	133	1	therefore	therefore	ADV
ejpam-6040	133	2	,	,	PUNCT
ejpam-6040	133	3	ζ	ζ	NOUN
ejpam-6040	133	4	g	g	NOUN
ejpam-6040	133	5	1	1	NUM
ejpam-6040	133	6	(	(	PUNCT
ejpam-6040	133	7	g	g	NOUN
ejpam-6040	133	8	)	)	PUNCT
ejpam-6040	133	9	=	=	PUNCT
ejpam-6040	133	10	ζg1	ζg1	X
ejpam-6040	133	11	(	(	PUNCT
ejpam-6040	133	12	s	s	X
ejpam-6040	133	13	)	)	PUNCT
ejpam-6040	133	14	=	=	SYM
ejpam-6040	133	15	ζg1	ζg1	X
ejpam-6040	133	16	(	(	PUNCT
ejpam-6040	133	17	gj	gj	NOUN
ejpam-6040	133	18	)	)	PUNCT
ejpam-6040	133	19	.	.	PUNCT
ejpam-6040	134	1	theorem	theorem	NOUN
ejpam-6040	134	2	3	3	X
ejpam-6040	134	3	.	.	PUNCT
ejpam-6040	135	1	let	let	VERB
ejpam-6040	135	2	g	g	PRON
ejpam-6040	135	3	be	be	AUX
ejpam-6040	135	4	a	a	DET
ejpam-6040	135	5	graph	graph	NOUN
ejpam-6040	135	6	with	with	ADP
ejpam-6040	135	7	i(g	i(g	NOUN
ejpam-6040	135	8	)	)	PUNCT
ejpam-6040	136	1	̸=	̸=	NOUN
ejpam-6040	136	2	∅	∅	NOUN
ejpam-6040	136	3	and	and	CCONJ
ejpam-6040	136	4	suppose	suppose	VERB
ejpam-6040	136	5	|i(g)|	|i(g)|	NOUN
ejpam-6040	136	6	=	=	PROPN
ejpam-6040	136	7	r.	r.	PROPN
ejpam-6040	136	8	then	then	ADV
ejpam-6040	136	9	ζgj	ζgj	PROPN
ejpam-6040	136	10	(	(	PUNCT
ejpam-6040	136	11	g	g	NOUN
ejpam-6040	136	12	)	)	PUNCT
ejpam-6040	136	13	=	=	SYM
ejpam-6040	136	14	j	j	PROPN
ejpam-6040	136	15	for	for	ADP
ejpam-6040	136	16	every	every	DET
ejpam-6040	136	17	j	j	PROPN
ejpam-6040	136	18	∈	∈	PROPN
ejpam-6040	137	1	[	[	X
ejpam-6040	137	2	r	r	X
ejpam-6040	137	3	]	]	X
ejpam-6040	137	4	=	=	PUNCT
ejpam-6040	137	5	{	{	PUNCT
ejpam-6040	137	6	1	1	NUM
ejpam-6040	137	7	,	,	PUNCT
ejpam-6040	137	8	2	2	NUM
ejpam-6040	137	9	,	,	PUNCT
ejpam-6040	137	10	·	·	PUNCT
ejpam-6040	137	11	·	·	PUNCT
ejpam-6040	137	12	·	·	PUNCT
ejpam-6040	137	13	,	,	PUNCT
ejpam-6040	137	14	r	r	NOUN
ejpam-6040	137	15	}	}	PUNCT
ejpam-6040	137	16	and	and	CCONJ
ejpam-6040	137	17	ζgk(g	ζgk(g	PROPN
ejpam-6040	137	18	)	)	PUNCT
ejpam-6040	137	19	=	=	SYM
ejpam-6040	137	20	r+ζgk−r(g	r+ζgk−r(g	PROPN
ejpam-6040	137	21	′	′	NOUN
ejpam-6040	137	22	)	)	PUNCT
ejpam-6040	137	23	for	for	ADP
ejpam-6040	137	24	every	every	DET
ejpam-6040	137	25	k	k	PROPN
ejpam-6040	137	26	∈	∈	PROPN
ejpam-6040	137	27	{	{	PUNCT
ejpam-6040	137	28	r+1	r+1	PROPN
ejpam-6040	137	29	,	,	PUNCT
ejpam-6040	137	30	·	·	PUNCT
ejpam-6040	137	31	·	·	PUNCT
ejpam-6040	137	32	·	·	PUNCT
ejpam-6040	137	33	,	,	PUNCT
ejpam-6040	137	34	γg(g)−1	γg(g)−1	ADP
ejpam-6040	137	35	}	}	PUNCT
ejpam-6040	137	36	,	,	PUNCT
ejpam-6040	137	37	where	where	SCONJ
ejpam-6040	137	38	g′	g′	NOUN
ejpam-6040	137	39	=	=	SYM
ejpam-6040	137	40	⟨v	⟨v	PUNCT
ejpam-6040	137	41	(	(	PUNCT
ejpam-6040	137	42	g	g	NOUN
ejpam-6040	137	43	)	)	PUNCT
ejpam-6040	137	44	\	\	NOUN
ejpam-6040	137	45	i(g)⟩.	i(g)⟩.	VERB
ejpam-6040	137	46	proof	proof	NOUN
ejpam-6040	137	47	.	.	PUNCT
ejpam-6040	138	1	let	let	VERB
ejpam-6040	138	2	i(g	i(g	NOUN
ejpam-6040	138	3	)	)	PUNCT
ejpam-6040	139	1	=	=	PRON
ejpam-6040	139	2	{	{	PUNCT
ejpam-6040	139	3	v1	v1	PROPN
ejpam-6040	139	4	,	,	PUNCT
ejpam-6040	139	5	v2	v2	PROPN
ejpam-6040	139	6	,	,	PUNCT
ejpam-6040	139	7	·	·	PUNCT
ejpam-6040	139	8	·	·	PUNCT
ejpam-6040	139	9	·	·	PUNCT
ejpam-6040	139	10	,	,	PUNCT
ejpam-6040	139	11	vr	vr	NOUN
ejpam-6040	139	12	}	}	PUNCT
ejpam-6040	139	13	and	and	CCONJ
ejpam-6040	139	14	let	let	VERB
ejpam-6040	139	15	s	s	PRON
ejpam-6040	139	16	be	be	AUX
ejpam-6040	139	17	a	a	DET
ejpam-6040	139	18	γg	γg	ADV
ejpam-6040	139	19	-	-	PUNCT
ejpam-6040	139	20	set	set	NOUN
ejpam-6040	139	21	in	in	ADP
ejpam-6040	139	22	g.	g.	PROPN
ejpam-6040	139	23	then	then	ADV
ejpam-6040	139	24	i(g	i(g	ADV
ejpam-6040	139	25	)	)	PUNCT
ejpam-6040	140	1	⊆	⊆	NUM
ejpam-6040	140	2	s.	s.	PROPN
ejpam-6040	140	3	let	let	VERB
ejpam-6040	140	4	j	j	PROPN
ejpam-6040	140	5	∈	∈	PROPN
ejpam-6040	141	1	[	[	X
ejpam-6040	141	2	r	r	X
ejpam-6040	141	3	]	]	PUNCT
ejpam-6040	141	4	.	.	PUNCT
ejpam-6040	142	1	then	then	ADV
ejpam-6040	142	2	d	d	X
ejpam-6040	142	3	=	=	SYM
ejpam-6040	142	4	s	s	PART
ejpam-6040	142	5	\	\	X
ejpam-6040	142	6	{	{	PUNCT
ejpam-6040	142	7	v1	v1	NOUN
ejpam-6040	142	8	,	,	PUNCT
ejpam-6040	142	9	v2	v2	PROPN
ejpam-6040	142	10	,	,	PUNCT
ejpam-6040	142	11	·	·	PUNCT
ejpam-6040	142	12	·	·	PUNCT
ejpam-6040	142	13	·	·	PUNCT
ejpam-6040	142	14	,	,	PUNCT
ejpam-6040	142	15	vj	vj	INTJ
ejpam-6040	142	16	}	}	PUNCT
ejpam-6040	142	17	is	be	AUX
ejpam-6040	142	18	a	a	DET
ejpam-6040	142	19	ζgj	ζgj	NOUN
ejpam-6040	142	20	-set	-set	PUNCT
ejpam-6040	142	21	in	in	ADP
ejpam-6040	142	22	g	g	PROPN
ejpam-6040	142	23	and	and	CCONJ
ejpam-6040	142	24	|ng	|ng	VERB
ejpam-6040	142	25	g[d]|	g[d]|	PROPN
ejpam-6040	142	26	=	=	SYM
ejpam-6040	142	27	|ng	|ng	X
ejpam-6040	142	28	g[s]|	g[s]|	X
ejpam-6040	142	29	−	−	PROPN
ejpam-6040	142	30	|ng	|ng	PUNCT
ejpam-6040	142	31	g[{v1	g[{v1	PROPN
ejpam-6040	142	32	,	,	PUNCT
ejpam-6040	142	33	v2	v2	PROPN
ejpam-6040	142	34	,	,	PUNCT
ejpam-6040	142	35	·	·	PUNCT
ejpam-6040	142	36	·	·	PUNCT
ejpam-6040	142	37	·	·	PUNCT
ejpam-6040	142	38	,	,	PUNCT
ejpam-6040	142	39	vj}]|	vj}]|	NOUN
ejpam-6040	142	40	=	=	SYM
ejpam-6040	142	41	|v	|v	PROPN
ejpam-6040	142	42	(	(	PUNCT
ejpam-6040	142	43	g)|	g)|	PROPN
ejpam-6040	142	44	−	−	PROPN
ejpam-6040	142	45	j.	j.	PROPN
ejpam-6040	142	46	hence	hence	PROPN
ejpam-6040	142	47	,	,	PUNCT
ejpam-6040	142	48	ζgj	ζgj	PROPN
ejpam-6040	142	49	(	(	PUNCT
ejpam-6040	142	50	g	g	NOUN
ejpam-6040	142	51	)	)	PUNCT
ejpam-6040	143	1	=	=	SYM
ejpam-6040	143	2	|v	|v	PROPN
ejpam-6040	143	3	(	(	PUNCT
ejpam-6040	143	4	g)|	g)|	INTJ
ejpam-6040	143	5	−	−	PROPN
ejpam-6040	143	6	(	(	PUNCT
ejpam-6040	143	7	|v	|v	PROPN
ejpam-6040	143	8	(	(	PUNCT
ejpam-6040	143	9	g)|	g)|	PROPN
ejpam-6040	143	10	−	−	PROPN
ejpam-6040	143	11	j	j	PROPN
ejpam-6040	143	12	)	)	PUNCT
ejpam-6040	143	13	=	=	PUNCT
ejpam-6040	144	1	j.	j.	PROPN
ejpam-6040	144	2	next	next	ADV
ejpam-6040	144	3	,	,	PUNCT
ejpam-6040	144	4	let	let	VERB
ejpam-6040	144	5	k	k	PROPN
ejpam-6040	144	6	∈	∈	PROPN
ejpam-6040	144	7	{	{	PUNCT
ejpam-6040	144	8	r+1	r+1	PROPN
ejpam-6040	144	9	,	,	PUNCT
ejpam-6040	144	10	·	·	PUNCT
ejpam-6040	144	11	·	·	PUNCT
ejpam-6040	144	12	·	·	PUNCT
ejpam-6040	144	13	,	,	PUNCT
ejpam-6040	144	14	γg(g)−1	γg(g)−1	ADP
ejpam-6040	144	15	}	}	PUNCT
ejpam-6040	144	16	.	.	PUNCT
ejpam-6040	145	1	then	then	ADV
ejpam-6040	145	2	s0	s0	PROPN
ejpam-6040	145	3	=	=	PUNCT
ejpam-6040	145	4	s\i(g	s\i(g	PROPN
ejpam-6040	145	5	)	)	PUNCT
ejpam-6040	145	6	is	be	AUX
ejpam-6040	145	7	γg	γg	ADV
ejpam-6040	145	8	-	-	PUNCT
ejpam-6040	145	9	set	set	VERB
ejpam-6040	145	10	ing′	ing′	VERB
ejpam-6040	145	11	=	=	SYM
ejpam-6040	145	12	⟨v	⟨v	PUNCT
ejpam-6040	145	13	(	(	PUNCT
ejpam-6040	145	14	g	g	NOUN
ejpam-6040	145	15	)	)	PUNCT
ejpam-6040	145	16	\	\	PUNCT
ejpam-6040	145	17	i(g)⟩.	i(g)⟩.	VERB
ejpam-6040	145	18	hence	hence	ADV
ejpam-6040	145	19	,	,	PUNCT
ejpam-6040	145	20	γg(g	γg(g	CCONJ
ejpam-6040	145	21	′	′	NUM
ejpam-6040	145	22	)	)	PUNCT
ejpam-6040	146	1	=	=	PUNCT
ejpam-6040	146	2	γg(g)−r	γg(g)−r	PROPN
ejpam-6040	146	3	.	.	PUNCT
ejpam-6040	147	1	since	since	SCONJ
ejpam-6040	147	2	k	k	PROPN
ejpam-6040	147	3	≤	≤	PROPN
ejpam-6040	147	4	γg(g)−1	γg(g)−1	ADP
ejpam-6040	147	5	,	,	PUNCT
ejpam-6040	147	6	k−r	k−r	PROPN
ejpam-6040	147	7	≤	≤	PUNCT
ejpam-6040	147	8	γg(g)−(r+1	γg(g)−(r+1	PROPN
ejpam-6040	147	9	)	)	PUNCT
ejpam-6040	147	10	<	<	X
ejpam-6040	148	1	γg(g)−r	γg(g)−r	PROPN
ejpam-6040	148	2	.	.	PUNCT
ejpam-6040	149	1	let	let	VERB
ejpam-6040	149	2	s′	s′	PROPN
ejpam-6040	149	3	be	be	AUX
ejpam-6040	149	4	a	a	DET
ejpam-6040	149	5	ζgk−r	ζgk−r	NOUN
ejpam-6040	149	6	-	-	PUNCT
ejpam-6040	149	7	set	set	NOUN
ejpam-6040	149	8	in	in	ADP
ejpam-6040	149	9	g′.	g′.	PROPN
ejpam-6040	149	10	then	then	ADV
ejpam-6040	149	11	|s′|	|s′|	NOUN
ejpam-6040	149	12	=	=	SYM
ejpam-6040	149	13	(	(	PUNCT
ejpam-6040	149	14	γg(g)−r)−(k−r	γg(g)−r)−(k−r	NOUN
ejpam-6040	149	15	)	)	PUNCT
ejpam-6040	149	16	=	=	SYM
ejpam-6040	150	1	γg(g)−k	γg(g)−k	PROPN
ejpam-6040	150	2	and	and	CCONJ
ejpam-6040	150	3	ζgk−r(g	ζgk−r(g	PROPN
ejpam-6040	150	4	′	′	NUM
ejpam-6040	150	5	)	)	PUNCT
ejpam-6040	151	1	=	=	SYM
ejpam-6040	151	2	|v	|v	PROPN
ejpam-6040	151	3	(	(	PUNCT
ejpam-6040	151	4	g′)|−	g′)|−	PROPN
ejpam-6040	151	5	|ng	|ng	PUNCT
ejpam-6040	151	6	g′	g′	NOUN
ejpam-6040	152	1	[	[	X
ejpam-6040	152	2	s′]|	s′]|	NOUN
ejpam-6040	152	3	=	=	SYM
ejpam-6040	152	4	(	(	PUNCT
ejpam-6040	152	5	|v	|v	X
ejpam-6040	152	6	(	(	PUNCT
ejpam-6040	152	7	g)|	g)|	INTJ
ejpam-6040	152	8	−	−	NOUN
ejpam-6040	152	9	r	r	NOUN
ejpam-6040	152	10	)	)	PUNCT
ejpam-6040	152	11	−	−	NOUN
ejpam-6040	152	12	|ng	|ng	PUNCT
ejpam-6040	152	13	g[s	g[s	PROPN
ejpam-6040	152	14	′]|	′]|	NOUN
ejpam-6040	152	15	.	.	PUNCT
ejpam-6040	153	1	this	this	PRON
ejpam-6040	153	2	implies	imply	VERB
ejpam-6040	153	3	that	that	SCONJ
ejpam-6040	153	4	|v	|v	PROPN
ejpam-6040	153	5	(	(	PUNCT
ejpam-6040	153	6	g)|	g)|	NOUN
ejpam-6040	153	7	−	−	NOUN
ejpam-6040	153	8	|ng	|ng	NOUN
ejpam-6040	153	9	g[s	g[s	PROPN
ejpam-6040	153	10	′]|	′]|	NOUN
ejpam-6040	153	11	=	=	SYM
ejpam-6040	153	12	r	r	NOUN
ejpam-6040	153	13	+	+	NUM
ejpam-6040	153	14	ζgk−r(g	ζgk−r(g	PROPN
ejpam-6040	153	15	′	′	NUM
ejpam-6040	153	16	)	)	PUNCT
ejpam-6040	153	17	.	.	PUNCT
ejpam-6040	154	1	therefore	therefore	ADV
ejpam-6040	154	2	,	,	PUNCT
ejpam-6040	154	3	since	since	SCONJ
ejpam-6040	154	4	s′	s′	ADJ
ejpam-6040	154	5	is	be	AUX
ejpam-6040	154	6	also	also	ADV
ejpam-6040	154	7	a	a	DET
ejpam-6040	154	8	ζgk	ζgk	ADJ
ejpam-6040	154	9	-set	-set	ADJ
ejpam-6040	154	10	in	in	ADP
ejpam-6040	154	11	g	g	PROPN
ejpam-6040	154	12	,	,	PUNCT
ejpam-6040	154	13	ζgk(g	ζgk(g	PROPN
ejpam-6040	154	14	)	)	PUNCT
ejpam-6040	154	15	=	=	SYM
ejpam-6040	154	16	r	r	NOUN
ejpam-6040	154	17	+	+	NUM
ejpam-6040	154	18	ζgk−r(g	ζgk−r(g	PROPN
ejpam-6040	154	19	′	′	NUM
ejpam-6040	154	20	)	)	PUNCT
ejpam-6040	154	21	.	.	PUNCT
ejpam-6040	155	1	theorem	theorem	VERB
ejpam-6040	155	2	4	4	NUM
ejpam-6040	155	3	.	.	PUNCT
ejpam-6040	156	1	if	if	SCONJ
ejpam-6040	156	2	g	g	PROPN
ejpam-6040	156	3	is	be	AUX
ejpam-6040	156	4	a	a	DET
ejpam-6040	156	5	graph	graph	NOUN
ejpam-6040	156	6	of	of	ADP
ejpam-6040	156	7	order	order	NOUN
ejpam-6040	156	8	n	n	PRON
ejpam-6040	156	9	≥	≥	NOUN
ejpam-6040	156	10	2	2	NUM
ejpam-6040	156	11	and	and	CCONJ
ejpam-6040	156	12	k	k	PROPN
ejpam-6040	156	13	≤	≤	NOUN
ejpam-6040	156	14	γg(g)−	γg(g)−	NOUN
ejpam-6040	156	15	1	1	NUM
ejpam-6040	156	16	,	,	PUNCT
ejpam-6040	156	17	then	then	ADV
ejpam-6040	156	18	1	1	NUM
ejpam-6040	156	19	≤	≤	NUM
ejpam-6040	156	20	ζgk(g	ζgk(g	NOUN
ejpam-6040	156	21	)	)	PUNCT
ejpam-6040	156	22	≤	≤	NUM
ejpam-6040	156	23	n−	n−	NOUN
ejpam-6040	156	24	1	1	NUM
ejpam-6040	156	25	.	.	PUNCT
ejpam-6040	157	1	proof	proof	NOUN
ejpam-6040	157	2	.	.	PUNCT
ejpam-6040	158	1	let	let	VERB
ejpam-6040	158	2	s	s	PRON
ejpam-6040	158	3	be	be	AUX
ejpam-6040	158	4	a	a	DET
ejpam-6040	158	5	ζgk	ζgk	ADJ
ejpam-6040	158	6	-set	-set	ADJ
ejpam-6040	158	7	in	in	ADP
ejpam-6040	158	8	g.	g.	PROPN
ejpam-6040	158	9	then	then	ADV
ejpam-6040	158	10	|s|	|s|	PROPN
ejpam-6040	158	11	=	=	SYM
ejpam-6040	158	12	γg(g	γg(g	PROPN
ejpam-6040	158	13	)	)	PUNCT
ejpam-6040	159	1	−	−	PROPN
ejpam-6040	159	2	k.	k.	PROPN
ejpam-6040	159	3	hence	hence	ADV
ejpam-6040	159	4	,	,	PUNCT
ejpam-6040	159	5	v	v	X
ejpam-6040	159	6	(	(	PUNCT
ejpam-6040	159	7	g	g	NOUN
ejpam-6040	159	8	)	)	PUNCT
ejpam-6040	159	9	\ng	\ng	PROPN
ejpam-6040	159	10	g[s	g[	NOUN
ejpam-6040	159	11	]	]	X
ejpam-6040	159	12	̸=	̸=	PROPN
ejpam-6040	159	13	∅.	∅.	NOUN
ejpam-6040	159	14	it	it	PRON
ejpam-6040	159	15	follows	follow	VERB
ejpam-6040	159	16	that	that	SCONJ
ejpam-6040	159	17	ζgk(g	ζgk(g	PROPN
ejpam-6040	159	18	)	)	PUNCT
ejpam-6040	159	19	=	=	SYM
ejpam-6040	159	20	|v	|v	PROPN
ejpam-6040	159	21	(	(	PUNCT
ejpam-6040	159	22	g)|	g)|	NOUN
ejpam-6040	159	23	−	−	PROPN
ejpam-6040	159	24	|ng	|ng	PUNCT
ejpam-6040	159	25	g[s]|	g[s]|	X
ejpam-6040	159	26	≥	≥	NOUN
ejpam-6040	159	27	1	1	NUM
ejpam-6040	159	28	.	.	PUNCT
ejpam-6040	160	1	also	also	ADV
ejpam-6040	160	2	,	,	PUNCT
ejpam-6040	160	3	since	since	SCONJ
ejpam-6040	160	4	|ng	|ng	X
ejpam-6040	160	5	g[s]|	g[s]|	PROPN
ejpam-6040	160	6	≥	≥	NUM
ejpam-6040	160	7	1	1	NUM
ejpam-6040	160	8	,	,	PUNCT
ejpam-6040	160	9	ζgk(g	ζgk(g	PROPN
ejpam-6040	160	10	)	)	PUNCT
ejpam-6040	160	11	=	=	SYM
ejpam-6040	160	12	|v	|v	PROPN
ejpam-6040	160	13	(	(	PUNCT
ejpam-6040	160	14	g)|	g)|	NOUN
ejpam-6040	160	15	−	−	NOUN
ejpam-6040	160	16	|ng	|ng	PUNCT
ejpam-6040	160	17	g[s]|	g[s]|	PROPN
ejpam-6040	160	18	≤	≤	PUNCT
ejpam-6040	160	19	n−	n−	PROPN
ejpam-6040	160	20	1	1	NUM
ejpam-6040	160	21	.	.	PUNCT
ejpam-6040	161	1	this	this	PRON
ejpam-6040	161	2	proves	prove	VERB
ejpam-6040	161	3	the	the	DET
ejpam-6040	161	4	assertion	assertion	NOUN
ejpam-6040	161	5	.	.	PUNCT
ejpam-6040	162	1	theorem	theorem	ADJ
ejpam-6040	162	2	5	5	NUM
ejpam-6040	162	3	.	.	PUNCT
ejpam-6040	163	1	let	let	VERB
ejpam-6040	163	2	g	g	PRON
ejpam-6040	163	3	be	be	AUX
ejpam-6040	163	4	a	a	DET
ejpam-6040	163	5	non	non	ADJ
ejpam-6040	163	6	-	-	ADJ
ejpam-6040	163	7	trivial	trivial	ADJ
ejpam-6040	163	8	graph	graph	NOUN
ejpam-6040	163	9	of	of	ADP
ejpam-6040	163	10	order	order	NOUN
ejpam-6040	164	1	n.	n.	NOUN
ejpam-6040	164	2	then	then	ADV
ejpam-6040	164	3	ζg1	ζg1	PROPN
ejpam-6040	164	4	(	(	PUNCT
ejpam-6040	164	5	g	g	NOUN
ejpam-6040	164	6	)	)	PUNCT
ejpam-6040	164	7	=	=	SYM
ejpam-6040	164	8	1	1	NUM
ejpam-6040	164	9	if	if	SCONJ
ejpam-6040	164	10	and	and	CCONJ
ejpam-6040	164	11	only	only	ADV
ejpam-6040	164	12	if	if	SCONJ
ejpam-6040	164	13	there	there	PRON
ejpam-6040	164	14	exists	exist	VERB
ejpam-6040	164	15	v	v	ADP
ejpam-6040	164	16	∈	∈	PROPN
ejpam-6040	164	17	v	v	NOUN
ejpam-6040	164	18	(	(	PUNCT
ejpam-6040	164	19	g	g	NOUN
ejpam-6040	164	20	)	)	PUNCT
ejpam-6040	164	21	such	such	ADJ
ejpam-6040	164	22	that	that	SCONJ
ejpam-6040	164	23	γg(g−	γg(g−	PROPN
ejpam-6040	164	24	v	v	NOUN
ejpam-6040	164	25	)	)	PUNCT
ejpam-6040	164	26	=	=	NOUN
ejpam-6040	164	27	γg(g)−	γg(g)−	NOUN
ejpam-6040	164	28	1	1	NUM
ejpam-6040	164	29	.	.	PUNCT
ejpam-6040	165	1	proof	proof	NOUN
ejpam-6040	165	2	.	.	PUNCT
ejpam-6040	166	1	suppose	suppose	VERB
ejpam-6040	166	2	ζg1	ζg1	PROPN
ejpam-6040	166	3	(	(	PUNCT
ejpam-6040	166	4	g	g	NOUN
ejpam-6040	166	5	)	)	PUNCT
ejpam-6040	166	6	=	=	SYM
ejpam-6040	166	7	1	1	NUM
ejpam-6040	166	8	and	and	CCONJ
ejpam-6040	166	9	let	let	VERB
ejpam-6040	166	10	s	s	PRON
ejpam-6040	166	11	be	be	AUX
ejpam-6040	166	12	a	a	DET
ejpam-6040	166	13	ζg1	ζg1	PROPN
ejpam-6040	166	14	-set	-set	PUNCT
ejpam-6040	166	15	in	in	ADP
ejpam-6040	166	16	g.	g.	PROPN
ejpam-6040	166	17	then	then	ADV
ejpam-6040	166	18	|s|	|s|	PROPN
ejpam-6040	166	19	=	=	SYM
ejpam-6040	166	20	γg(g	γg(g	PROPN
ejpam-6040	166	21	)	)	PUNCT
ejpam-6040	166	22	−	−	PROPN
ejpam-6040	166	23	1	1	NUM
ejpam-6040	166	24	and	and	CCONJ
ejpam-6040	166	25	ζgk(g	ζgk(g	NUM
ejpam-6040	166	26	)	)	PUNCT
ejpam-6040	166	27	=	=	SYM
ejpam-6040	166	28	|v	|v	PROPN
ejpam-6040	166	29	(	(	PUNCT
ejpam-6040	166	30	g)\ng	g)\ng	X
ejpam-6040	166	31	g[s]|	g[s]|	X
ejpam-6040	166	32	=	=	PUNCT
ejpam-6040	167	1	1	1	X
ejpam-6040	167	2	.	.	PUNCT
ejpam-6040	167	3	let	let	VERB
ejpam-6040	167	4	v	v	NUM
ejpam-6040	167	5	∈	∈	PROPN
ejpam-6040	167	6	v	v	NOUN
ejpam-6040	167	7	(	(	PUNCT
ejpam-6040	167	8	g)\ng	g)\ng	PRON
ejpam-6040	167	9	g[s	g[s	PROPN
ejpam-6040	167	10	]	]	PUNCT
ejpam-6040	167	11	.	.	PUNCT
ejpam-6040	168	1	then	then	ADV
ejpam-6040	168	2	ng	ng	PROPN
ejpam-6040	168	3	g[s	g[s	PROPN
ejpam-6040	168	4	]	]	X
ejpam-6040	168	5	=	=	SYM
ejpam-6040	168	6	v	v	X
ejpam-6040	168	7	(	(	PUNCT
ejpam-6040	168	8	g)\{v	g)\{v	PROPN
ejpam-6040	168	9	}	}	PUNCT
ejpam-6040	168	10	.	.	PUNCT
ejpam-6040	169	1	therefore	therefore	ADV
ejpam-6040	169	2	,	,	PUNCT
ejpam-6040	169	3	γg(g−	γg(g−	NOUN
ejpam-6040	169	4	v	v	NOUN
ejpam-6040	169	5	)	)	PUNCT
ejpam-6040	169	6	=	=	SYM
ejpam-6040	170	1	γg	γg	ADV
ejpam-6040	170	2	(	(	PUNCT
ejpam-6040	170	3	〈	〈	PROPN
ejpam-6040	170	4	ng	ng	PROPN
ejpam-6040	170	5	g[s	g[s	PROPN
ejpam-6040	170	6	]	]	PUNCT
ejpam-6040	170	7	〉	〉	NOUN
ejpam-6040	170	8	)	)	PUNCT
ejpam-6040	170	9	=	=	NOUN
ejpam-6040	170	10	γg(g)−	γg(g)−	NOUN
ejpam-6040	170	11	1	1	NUM
ejpam-6040	170	12	.	.	PUNCT
ejpam-6040	170	13	conversely	conversely	ADV
ejpam-6040	170	14	,	,	PUNCT
ejpam-6040	170	15	let	let	VERB
ejpam-6040	170	16	v	v	NUM
ejpam-6040	170	17	∈	∈	PROPN
ejpam-6040	170	18	v	v	NOUN
ejpam-6040	170	19	(	(	PUNCT
ejpam-6040	170	20	g	g	NOUN
ejpam-6040	170	21	)	)	PUNCT
ejpam-6040	170	22	such	such	ADJ
ejpam-6040	170	23	that	that	SCONJ
ejpam-6040	170	24	γg(g−v	γg(g−v	NOUN
ejpam-6040	170	25	)	)	PUNCT
ejpam-6040	170	26	=	=	SYM
ejpam-6040	170	27	γg(g)−1	γg(g)−1	X
ejpam-6040	170	28	.	.	PUNCT
ejpam-6040	171	1	then	then	ADV
ejpam-6040	171	2	there	there	PRON
ejpam-6040	171	3	exists	exist	VERB
ejpam-6040	171	4	d	d	PROPN
ejpam-6040	171	5	⊆	⊆	NUM
ejpam-6040	171	6	v	v	ADP
ejpam-6040	171	7	(	(	PUNCT
ejpam-6040	171	8	g	g	NOUN
ejpam-6040	171	9	)	)	PUNCT
ejpam-6040	171	10	with	with	ADP
ejpam-6040	171	11	|d|	|d|	PROPN
ejpam-6040	171	12	=	=	SYM
ejpam-6040	171	13	γg(g)−1	γg(g)−1	PUNCT
ejpam-6040	171	14	andng	andng	PROPN
ejpam-6040	171	15	g[d	g[d	PROPN
ejpam-6040	171	16	]	]	X
ejpam-6040	171	17	=	=	SYM
ejpam-6040	171	18	v	v	X
ejpam-6040	171	19	(	(	PUNCT
ejpam-6040	171	20	g)\{v	g)\{v	PROPN
ejpam-6040	171	21	}	}	PUNCT
ejpam-6040	171	22	.	.	PUNCT
ejpam-6040	172	1	this	this	PRON
ejpam-6040	172	2	implies	imply	VERB
ejpam-6040	172	3	that	that	SCONJ
ejpam-6040	172	4	ζg1	ζg1	PROPN
ejpam-6040	172	5	(	(	PUNCT
ejpam-6040	172	6	g	g	NOUN
ejpam-6040	172	7	)	)	PUNCT
ejpam-6040	172	8	=	=	SYM
ejpam-6040	173	1	|v	|v	PROPN
ejpam-6040	173	2	(	(	PUNCT
ejpam-6040	173	3	g)\ng	g)\ng	NOUN
ejpam-6040	173	4	g[d]|	g[d]|	VERB
ejpam-6040	173	5	=	=	SYM
ejpam-6040	173	6	|{v}|	|{v}|	PUNCT
ejpam-6040	173	7	=	=	SYM
ejpam-6040	173	8	1	1	X
ejpam-6040	173	9	.	.	PUNCT
ejpam-6040	174	1	therefore	therefore	ADV
ejpam-6040	174	2	,	,	PUNCT
ejpam-6040	174	3	ζg1	ζg1	X
ejpam-6040	174	4	(	(	PUNCT
ejpam-6040	174	5	g	g	NOUN
ejpam-6040	174	6	)	)	PUNCT
ejpam-6040	174	7	=	=	SYM
ejpam-6040	174	8	1	1	X
ejpam-6040	174	9	.	.	PUNCT
ejpam-6040	174	10	s.	s.	PROPN
ejpam-6040	174	11	canoy	canoy	PROPN
ejpam-6040	174	12	,	,	PUNCT
ejpam-6040	174	13	jr	jr	PROPN
ejpam-6040	174	14	.	.	PROPN
ejpam-6040	174	15	,	,	PUNCT
ejpam-6040	174	16	j.	j.	PROPN
ejpam-6040	174	17	anoche	anoche	PROPN
ejpam-6040	174	18	/	/	SYM
ejpam-6040	174	19	eur	eur	PROPN
ejpam-6040	174	20	.	.	PUNCT
ejpam-6040	175	1	j.	j.	PROPN
ejpam-6040	175	2	pure	pure	PROPN
ejpam-6040	175	3	appl	appl	PROPN
ejpam-6040	175	4	.	.	PROPN
ejpam-6040	175	5	math	math	PROPN
ejpam-6040	175	6	,	,	PUNCT
ejpam-6040	175	7	18	18	NUM
ejpam-6040	175	8	(	(	PUNCT
ejpam-6040	175	9	2	2	NUM
ejpam-6040	175	10	)	)	PUNCT
ejpam-6040	175	11	(	(	PUNCT
ejpam-6040	175	12	2025	2025	NUM
ejpam-6040	175	13	)	)	PUNCT
ejpam-6040	175	14	,	,	PUNCT
ejpam-6040	175	15	6040	6040	NUM
ejpam-6040	175	16	6	6	NUM
ejpam-6040	175	17	of	of	ADP
ejpam-6040	175	18	16	16	NUM
ejpam-6040	175	19	lemma	lemma	PROPN
ejpam-6040	175	20	1	1	NUM
ejpam-6040	175	21	.	.	PUNCT
ejpam-6040	176	1	let	let	VERB
ejpam-6040	176	2	g	g	PRON
ejpam-6040	176	3	be	be	AUX
ejpam-6040	176	4	a	a	DET
ejpam-6040	176	5	non	non	ADJ
ejpam-6040	176	6	-	-	ADJ
ejpam-6040	176	7	trivial	trivial	ADJ
ejpam-6040	176	8	graph	graph	NOUN
ejpam-6040	176	9	of	of	ADP
ejpam-6040	176	10	order	order	NOUN
ejpam-6040	176	11	n.	n.	VERB
ejpam-6040	176	12	if	if	SCONJ
ejpam-6040	176	13	k	k	PROPN
ejpam-6040	176	14	=	=	PUNCT
ejpam-6040	176	15	γg(g)−1	γg(g)−1	PROPN
ejpam-6040	176	16	,	,	PUNCT
ejpam-6040	176	17	then	then	ADV
ejpam-6040	176	18	ζgk(g	ζgk(g	PROPN
ejpam-6040	176	19	)	)	PUNCT
ejpam-6040	177	1	=	=	SYM
ejpam-6040	177	2	n−1	n−1	PROPN
ejpam-6040	177	3	.	.	PUNCT
ejpam-6040	177	4	proof	proof	NOUN
ejpam-6040	177	5	.	.	PUNCT
ejpam-6040	178	1	let	let	VERB
ejpam-6040	178	2	k	k	NOUN
ejpam-6040	178	3	=	=	PUNCT
ejpam-6040	178	4	γg(g)−	γg(g)−	NOUN
ejpam-6040	178	5	1	1	NUM
ejpam-6040	178	6	and	and	CCONJ
ejpam-6040	178	7	let	let	VERB
ejpam-6040	178	8	s	s	PRON
ejpam-6040	178	9	be	be	AUX
ejpam-6040	178	10	a	a	DET
ejpam-6040	178	11	ζgk	ζgk	ADJ
ejpam-6040	178	12	-set	-set	ADJ
ejpam-6040	178	13	of	of	ADP
ejpam-6040	178	14	g.	g.	PROPN
ejpam-6040	178	15	then	then	ADV
ejpam-6040	178	16	|s|	|s|	PROPN
ejpam-6040	178	17	=	=	SYM
ejpam-6040	178	18	1	1	NUM
ejpam-6040	178	19	,	,	PUNCT
ejpam-6040	178	20	say	say	VERB
ejpam-6040	178	21	,	,	PUNCT
ejpam-6040	178	22	s	s	PART
ejpam-6040	178	23	=	=	PUNCT
ejpam-6040	178	24	{	{	PUNCT
ejpam-6040	178	25	x	x	NOUN
ejpam-6040	178	26	}	}	PUNCT
ejpam-6040	178	27	and	and	CCONJ
ejpam-6040	178	28	ζgk(g	ζgk(g	PROPN
ejpam-6040	178	29	)	)	PUNCT
ejpam-6040	178	30	=	=	SYM
ejpam-6040	178	31	ζgk(s	ζgk(s	PROPN
ejpam-6040	178	32	)	)	PUNCT
ejpam-6040	179	1	=	=	PUNCT
ejpam-6040	179	2	n−	n−	NOUN
ejpam-6040	179	3	|ng	|ng	X
ejpam-6040	179	4	g[s]|	g[s]|	PROPN
ejpam-6040	179	5	.	.	PUNCT
ejpam-6040	180	1	since	since	SCONJ
ejpam-6040	180	2	x	x	PROPN
ejpam-6040	180	3	∈	∈	PROPN
ejpam-6040	180	4	ng[s	ng[s	PROPN
ejpam-6040	180	5	]	]	PUNCT
ejpam-6040	180	6	and	and	CCONJ
ejpam-6040	180	7	ig[s	ig[s	PROPN
ejpam-6040	180	8	]	]	PUNCT
ejpam-6040	180	9	=	=	SYM
ejpam-6040	180	10	s	s	X
ejpam-6040	180	11	,	,	PUNCT
ejpam-6040	180	12	it	it	PRON
ejpam-6040	180	13	follows	follow	VERB
ejpam-6040	180	14	that	that	SCONJ
ejpam-6040	180	15	ng	ng	PROPN
ejpam-6040	180	16	g[s	g[s	PROPN
ejpam-6040	180	17	]	]	PUNCT
ejpam-6040	180	18	=	=	PUNCT
ejpam-6040	180	19	s.	s.	PROPN
ejpam-6040	180	20	it	it	PRON
ejpam-6040	180	21	follows	follow	VERB
ejpam-6040	180	22	that	that	SCONJ
ejpam-6040	180	23	ζgk(g	ζgk(g	PROPN
ejpam-6040	180	24	)	)	PUNCT
ejpam-6040	180	25	=	=	SYM
ejpam-6040	180	26	n−	n−	NOUN
ejpam-6040	180	27	|ng	|ng	X
ejpam-6040	180	28	g[s]|	g[s]|	X
ejpam-6040	180	29	=	=	PUNCT
ejpam-6040	180	30	n−	n−	NOUN
ejpam-6040	180	31	1	1	NUM
ejpam-6040	180	32	.	.	PUNCT
ejpam-6040	181	1	lemma	lemma	PROPN
ejpam-6040	181	2	2	2	X
ejpam-6040	181	3	.	.	PUNCT
ejpam-6040	182	1	let	let	VERB
ejpam-6040	182	2	g	g	PRON
ejpam-6040	182	3	be	be	AUX
ejpam-6040	182	4	a	a	DET
ejpam-6040	182	5	graph	graph	NOUN
ejpam-6040	182	6	and	and	CCONJ
ejpam-6040	182	7	s	s	VERB
ejpam-6040	182	8	⊆	⊆	NUM
ejpam-6040	182	9	v	v	NOUN
ejpam-6040	182	10	(	(	PUNCT
ejpam-6040	182	11	g	g	NOUN
ejpam-6040	182	12	)	)	PUNCT
ejpam-6040	182	13	.	.	PUNCT
ejpam-6040	183	1	if	if	SCONJ
ejpam-6040	183	2	every	every	DET
ejpam-6040	183	3	component	component	NOUN
ejpam-6040	183	4	of	of	ADP
ejpam-6040	183	5	⟨s⟩	⟨s⟩	PROPN
ejpam-6040	183	6	is	be	AUX
ejpam-6040	183	7	complete	complete	ADJ
ejpam-6040	183	8	,	,	PUNCT
ejpam-6040	183	9	then	then	ADV
ejpam-6040	183	10	ng	ng	PROPN
ejpam-6040	183	11	g[s	g[s	PROPN
ejpam-6040	183	12	]	]	PUNCT
ejpam-6040	183	13	=	=	PUNCT
ejpam-6040	183	14	s.	s.	PROPN
ejpam-6040	183	15	proof	proof	PROPN
ejpam-6040	183	16	.	.	PUNCT
ejpam-6040	184	1	let	let	VERB
ejpam-6040	184	2	h1	h1	PROPN
ejpam-6040	184	3	,	,	PUNCT
ejpam-6040	184	4	h2	h2	PROPN
ejpam-6040	184	5	,	,	PUNCT
ejpam-6040	184	6	·	·	PUNCT
ejpam-6040	184	7	·	·	PUNCT
ejpam-6040	184	8	·	·	PUNCT
ejpam-6040	184	9	,	,	PUNCT
ejpam-6040	184	10	ht	ht	INTJ
ejpam-6040	184	11	be	be	AUX
ejpam-6040	184	12	the	the	DET
ejpam-6040	184	13	components	component	NOUN
ejpam-6040	184	14	of	of	ADP
ejpam-6040	184	15	⟨s⟩.	⟨s⟩.	PROPN
ejpam-6040	184	16	then	then	ADV
ejpam-6040	184	17	s	s	VERB
ejpam-6040	184	18	=	=	SYM
ejpam-6040	184	19	∪t	∪t	NUM
ejpam-6040	184	20	i=1v	i=1v	PROPN
ejpam-6040	184	21	(	(	PUNCT
ejpam-6040	184	22	hi	hi	INTJ
ejpam-6040	184	23	)	)	PUNCT
ejpam-6040	184	24	.	.	PUNCT
ejpam-6040	185	1	by	by	ADP
ejpam-6040	185	2	remark	remark	NOUN
ejpam-6040	185	3	1(ii	1(ii	NUM
ejpam-6040	185	4	)	)	PUNCT
ejpam-6040	185	5	,	,	PUNCT
ejpam-6040	185	6	ng	ng	PROPN
ejpam-6040	185	7	g[s	g[s	PROPN
ejpam-6040	185	8	]	]	X
ejpam-6040	185	9	=	=	SYM
ejpam-6040	185	10	∪t	∪t	NUM
ejpam-6040	185	11	i=1n	i=1n	VERB
ejpam-6040	185	12	g	g	PROPN
ejpam-6040	185	13	gi	gi	PROPN
ejpam-6040	186	1	[	[	X
ejpam-6040	186	2	v	v	X
ejpam-6040	186	3	(	(	PUNCT
ejpam-6040	186	4	hi	hi	INTJ
ejpam-6040	186	5	)	)	PUNCT
ejpam-6040	186	6	]	]	PUNCT
ejpam-6040	186	7	=	=	PUNCT
ejpam-6040	186	8	∪t	∪t	NUM
ejpam-6040	186	9	i=1v	i=1v	PROPN
ejpam-6040	186	10	(	(	PUNCT
ejpam-6040	186	11	hi	hi	INTJ
ejpam-6040	186	12	)	)	PUNCT
ejpam-6040	186	13	=	=	VERB
ejpam-6040	186	14	s.	s.	PROPN
ejpam-6040	186	15	this	this	PRON
ejpam-6040	186	16	proves	prove	VERB
ejpam-6040	186	17	the	the	DET
ejpam-6040	186	18	assertion	assertion	NOUN
ejpam-6040	186	19	.	.	PUNCT
ejpam-6040	187	1	theorem	theorem	ADJ
ejpam-6040	187	2	6	6	NUM
ejpam-6040	187	3	.	.	PUNCT
ejpam-6040	188	1	if	if	SCONJ
ejpam-6040	188	2	kn	kn	PROPN
ejpam-6040	188	3	is	be	AUX
ejpam-6040	188	4	a	a	DET
ejpam-6040	188	5	complete	complete	ADJ
ejpam-6040	188	6	graph	graph	NOUN
ejpam-6040	188	7	on	on	ADP
ejpam-6040	188	8	n	n	DET
ejpam-6040	188	9	vertices	vertex	NOUN
ejpam-6040	188	10	,	,	PUNCT
ejpam-6040	188	11	where	where	SCONJ
ejpam-6040	188	12	n	n	PRON
ejpam-6040	188	13	≥	≥	NOUN
ejpam-6040	188	14	2	2	NUM
ejpam-6040	188	15	,	,	PUNCT
ejpam-6040	188	16	and	and	CCONJ
ejpam-6040	188	17	1	1	NUM
ejpam-6040	188	18	≤	≤	NUM
ejpam-6040	188	19	k	k	NOUN
ejpam-6040	188	20	≤	≤	NUM
ejpam-6040	188	21	n	n	CCONJ
ejpam-6040	188	22	−	−	PROPN
ejpam-6040	188	23	1	1	NUM
ejpam-6040	188	24	,	,	PUNCT
ejpam-6040	188	25	then	then	ADV
ejpam-6040	188	26	ζgk(kn	ζgk(kn	NOUN
ejpam-6040	188	27	)	)	PUNCT
ejpam-6040	189	1	=	=	PUNCT
ejpam-6040	189	2	k.	k.	NOUN
ejpam-6040	189	3	proof	proof	NOUN
ejpam-6040	189	4	.	.	PUNCT
ejpam-6040	190	1	let	let	VERB
ejpam-6040	190	2	k	k	PRON
ejpam-6040	190	3	be	be	AUX
ejpam-6040	190	4	a	a	DET
ejpam-6040	190	5	positive	positive	ADJ
ejpam-6040	190	6	integer	integer	NOUN
ejpam-6040	190	7	with	with	ADP
ejpam-6040	190	8	k	k	PROPN
ejpam-6040	190	9	≤	≤	PROPN
ejpam-6040	190	10	γg(kn)−	γg(kn)−	NUM
ejpam-6040	191	1	1	1	X
ejpam-6040	191	2	.	.	PUNCT
ejpam-6040	191	3	since	since	SCONJ
ejpam-6040	191	4	γg(kn	γg(kn	NOUN
ejpam-6040	191	5	)	)	PUNCT
ejpam-6040	191	6	=	=	SYM
ejpam-6040	191	7	n	n	CCONJ
ejpam-6040	191	8	,	,	PUNCT
ejpam-6040	191	9	k	k	PROPN
ejpam-6040	191	10	≤	≤	PROPN
ejpam-6040	191	11	n−	n−	PROPN
ejpam-6040	191	12	1	1	NUM
ejpam-6040	191	13	.	.	PUNCT
ejpam-6040	192	1	let	let	VERB
ejpam-6040	192	2	s	s	PRON
ejpam-6040	192	3	be	be	AUX
ejpam-6040	192	4	a	a	DET
ejpam-6040	192	5	ζgk	ζgk	ADJ
ejpam-6040	192	6	-set	-set	ADJ
ejpam-6040	192	7	of	of	ADP
ejpam-6040	192	8	kn	kn	PROPN
ejpam-6040	192	9	.	.	PUNCT
ejpam-6040	193	1	then	then	ADV
ejpam-6040	193	2	s	s	VERB
ejpam-6040	193	3	is	be	AUX
ejpam-6040	193	4	a	a	DET
ejpam-6040	193	5	clique	clique	NOUN
ejpam-6040	193	6	,	,	PUNCT
ejpam-6040	193	7	|s|	|s|	NOUN
ejpam-6040	193	8	=	=	SYM
ejpam-6040	193	9	n	n	CCONJ
ejpam-6040	193	10	−	−	PROPN
ejpam-6040	193	11	k	k	PROPN
ejpam-6040	193	12	and	and	CCONJ
ejpam-6040	193	13	ζgk(g	ζgk(g	PROPN
ejpam-6040	193	14	)	)	PUNCT
ejpam-6040	193	15	=	=	SYM
ejpam-6040	193	16	n	n	PRON
ejpam-6040	193	17	−	−	PROPN
ejpam-6040	193	18	|ng	|ng	PUNCT
ejpam-6040	193	19	g[s]|	g[s]|	PROPN
ejpam-6040	193	20	.	.	PUNCT
ejpam-6040	194	1	therefore	therefore	ADV
ejpam-6040	194	2	,	,	PUNCT
ejpam-6040	194	3	by	by	ADP
ejpam-6040	194	4	lemma	lemma	PROPN
ejpam-6040	194	5	2	2	NUM
ejpam-6040	194	6	,	,	PUNCT
ejpam-6040	194	7	ζgk(g	ζgk(g	NOUN
ejpam-6040	194	8	)	)	PUNCT
ejpam-6040	194	9	=	=	SYM
ejpam-6040	194	10	n−	n−	NOUN
ejpam-6040	194	11	(	(	PUNCT
ejpam-6040	194	12	n−	n−	NOUN
ejpam-6040	194	13	k	k	NOUN
ejpam-6040	194	14	)	)	PUNCT
ejpam-6040	195	1	=	=	VERB
ejpam-6040	195	2	k.	k.	PROPN
ejpam-6040	195	3	let	let	VERB
ejpam-6040	195	4	g	g	NOUN
ejpam-6040	195	5	be	be	AUX
ejpam-6040	195	6	a	a	DET
ejpam-6040	195	7	graph	graph	NOUN
ejpam-6040	195	8	and	and	CCONJ
ejpam-6040	195	9	let	let	VERB
ejpam-6040	195	10	s	s	PRON
ejpam-6040	195	11	be	be	AUX
ejpam-6040	195	12	a	a	DET
ejpam-6040	195	13	subset	subset	NOUN
ejpam-6040	195	14	of	of	ADP
ejpam-6040	195	15	v	v	NOUN
ejpam-6040	195	16	(	(	PUNCT
ejpam-6040	195	17	g	g	NOUN
ejpam-6040	195	18	)	)	PUNCT
ejpam-6040	195	19	.	.	PUNCT
ejpam-6040	196	1	then	then	ADV
ejpam-6040	196	2	the	the	DET
ejpam-6040	196	3	set	set	NOUN
ejpam-6040	196	4	i2g(s	i2g(s	PROPN
ejpam-6040	196	5	)	)	PUNCT
ejpam-6040	196	6	is	be	AUX
ejpam-6040	196	7	given	give	VERB
ejpam-6040	196	8	by	by	ADP
ejpam-6040	196	9	i2g(s	i2g(s	PROPN
ejpam-6040	196	10	)	)	PUNCT
ejpam-6040	196	11	=	=	PRON
ejpam-6040	197	1	{	{	PUNCT
ejpam-6040	197	2	x	x	PUNCT
ejpam-6040	197	3	∈	∈	PROPN
ejpam-6040	197	4	v	v	ADP
ejpam-6040	197	5	(	(	PUNCT
ejpam-6040	197	6	g	g	NOUN
ejpam-6040	197	7	)	)	PUNCT
ejpam-6040	197	8	\	\	PUNCT
ejpam-6040	198	1	s	s	PART
ejpam-6040	198	2	:	:	PUNCT
ejpam-6040	198	3	x	x	SYM
ejpam-6040	198	4	∈	∈	PROPN
ejpam-6040	198	5	ig(y	ig(y	NOUN
ejpam-6040	198	6	,	,	PUNCT
ejpam-6040	198	7	z	z	NOUN
ejpam-6040	198	8	)	)	PUNCT
ejpam-6040	198	9	for	for	ADP
ejpam-6040	198	10	some	some	DET
ejpam-6040	198	11	y	y	PROPN
ejpam-6040	198	12	,	,	PUNCT
ejpam-6040	198	13	z	z	PROPN
ejpam-6040	198	14	∈	∈	PROPN
ejpam-6040	198	15	s	s	PART
ejpam-6040	198	16	with	with	ADP
ejpam-6040	198	17	dg(y	dg(y	ADJ
ejpam-6040	198	18	,	,	PUNCT
ejpam-6040	198	19	z	z	NOUN
ejpam-6040	198	20	)	)	PUNCT
ejpam-6040	198	21	=	=	SYM
ejpam-6040	198	22	2	2	NUM
ejpam-6040	198	23	}	}	PUNCT
ejpam-6040	198	24	.	.	PUNCT
ejpam-6040	199	1	if	if	SCONJ
ejpam-6040	199	2	g	g	PROPN
ejpam-6040	199	3	is	be	AUX
ejpam-6040	199	4	non	non	ADJ
ejpam-6040	199	5	-	-	ADJ
ejpam-6040	199	6	trivial	trivial	ADJ
ejpam-6040	199	7	and	and	CCONJ
ejpam-6040	199	8	k	k	PROPN
ejpam-6040	199	9	is	be	AUX
ejpam-6040	199	10	a	a	DET
ejpam-6040	199	11	positive	positive	ADJ
ejpam-6040	199	12	integer	integer	NOUN
ejpam-6040	199	13	with	with	ADP
ejpam-6040	199	14	k	k	PROPN
ejpam-6040	199	15	≤	≤	X
ejpam-6040	199	16	γg(g)−	γg(g)−	NOUN
ejpam-6040	199	17	1	1	NUM
ejpam-6040	199	18	,	,	PUNCT
ejpam-6040	199	19	then	then	ADV
ejpam-6040	199	20	the	the	DET
ejpam-6040	199	21	number	number	NOUN
ejpam-6040	199	22	λk	λk	ADP
ejpam-6040	199	23	2(g	2(g	NUM
ejpam-6040	199	24	)	)	PUNCT
ejpam-6040	199	25	is	be	AUX
ejpam-6040	199	26	given	give	VERB
ejpam-6040	199	27	by	by	ADP
ejpam-6040	199	28	λk	λk	ADP
ejpam-6040	199	29	2(g	2(g	NUM
ejpam-6040	199	30	)	)	PUNCT
ejpam-6040	200	1	=	=	PRON
ejpam-6040	200	2	max{|i2g(s)|	max{|i2g(s)|	NOUN
ejpam-6040	200	3	:	:	PUNCT
ejpam-6040	200	4	s	s	VERB
ejpam-6040	200	5	⊆	⊆	NUM
ejpam-6040	200	6	v	v	NOUN
ejpam-6040	200	7	(	(	PUNCT
ejpam-6040	200	8	g	g	NOUN
ejpam-6040	200	9	)	)	PUNCT
ejpam-6040	200	10	and	and	CCONJ
ejpam-6040	200	11	|s|	|s|	PROPN
ejpam-6040	200	12	=	=	NOUN
ejpam-6040	200	13	γg(g)−	γg(g)−	NOUN
ejpam-6040	200	14	k	k	NOUN
ejpam-6040	200	15	}	}	PUNCT
ejpam-6040	200	16	.	.	PUNCT
ejpam-6040	201	1	remark	remark	NOUN
ejpam-6040	201	2	2	2	NUM
ejpam-6040	201	3	.	.	PUNCT
ejpam-6040	202	1	let	let	VERB
ejpam-6040	202	2	g	g	PRON
ejpam-6040	202	3	be	be	AUX
ejpam-6040	202	4	a	a	DET
ejpam-6040	202	5	graph	graph	NOUN
ejpam-6040	202	6	and	and	CCONJ
ejpam-6040	202	7	let	let	VERB
ejpam-6040	202	8	k	k	PRON
ejpam-6040	202	9	be	be	AUX
ejpam-6040	202	10	a	a	DET
ejpam-6040	202	11	postive	postive	ADJ
ejpam-6040	202	12	integer	integer	NOUN
ejpam-6040	202	13	with	with	ADP
ejpam-6040	202	14	k	k	PROPN
ejpam-6040	202	15	≤	≤	X
ejpam-6040	202	16	γg(g)−	γg(g)−	NOUN
ejpam-6040	202	17	1	1	NUM
ejpam-6040	202	18	.	.	PUNCT
ejpam-6040	203	1	if	if	SCONJ
ejpam-6040	203	2	s	s	PROPN
ejpam-6040	203	3	is	be	AUX
ejpam-6040	203	4	a	a	DET
ejpam-6040	203	5	(	(	PUNCT
ejpam-6040	203	6	γg(g)−	γg(g)−	NOUN
ejpam-6040	203	7	k)-element	k)-element	PUNCT
ejpam-6040	203	8	subset	subset	NOUN
ejpam-6040	203	9	of	of	ADP
ejpam-6040	203	10	v	v	NOUN
ejpam-6040	203	11	(	(	PUNCT
ejpam-6040	203	12	g	g	NOUN
ejpam-6040	203	13	)	)	PUNCT
ejpam-6040	203	14	and	and	CCONJ
ejpam-6040	203	15	λk	λk	ADP
ejpam-6040	203	16	2(g	2(g	NUM
ejpam-6040	203	17	)	)	PUNCT
ejpam-6040	203	18	=	=	SYM
ejpam-6040	203	19	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	203	20	,	,	PUNCT
ejpam-6040	203	21	then	then	ADV
ejpam-6040	203	22	s	s	AUX
ejpam-6040	203	23	need	need	AUX
ejpam-6040	203	24	not	not	PART
ejpam-6040	203	25	be	be	AUX
ejpam-6040	203	26	a	a	DET
ejpam-6040	203	27	ζgk	ζgk	ADJ
ejpam-6040	203	28	-set	-set	ADJ
ejpam-6040	203	29	in	in	ADP
ejpam-6040	203	30	g.	g.	PROPN
ejpam-6040	203	31	to	to	PART
ejpam-6040	203	32	see	see	VERB
ejpam-6040	203	33	this	this	PRON
ejpam-6040	203	34	,	,	PUNCT
ejpam-6040	203	35	consider	consider	VERB
ejpam-6040	203	36	graph	graph	NOUN
ejpam-6040	203	37	g	g	NOUN
ejpam-6040	203	38	in	in	ADP
ejpam-6040	203	39	figure	figure	NOUN
ejpam-6040	203	40	2	2	NUM
ejpam-6040	203	41	.	.	PUNCT
ejpam-6040	204	1	the	the	DET
ejpam-6040	204	2	set	set	NOUN
ejpam-6040	204	3	d	d	PROPN
ejpam-6040	204	4	=	=	PUNCT
ejpam-6040	204	5	{	{	PUNCT
ejpam-6040	204	6	a	a	PRON
ejpam-6040	204	7	,	,	PUNCT
ejpam-6040	204	8	b	b	NOUN
ejpam-6040	204	9	,	,	PUNCT
ejpam-6040	204	10	f	f	X
ejpam-6040	204	11	}	}	PUNCT
ejpam-6040	204	12	is	be	AUX
ejpam-6040	204	13	a	a	DET
ejpam-6040	204	14	γg	γg	ADV
ejpam-6040	204	15	-	-	PUNCT
ejpam-6040	204	16	set	set	NOUN
ejpam-6040	204	17	in	in	ADP
ejpam-6040	204	18	g.	g.	PROPN
ejpam-6040	204	19	hence	hence	ADV
ejpam-6040	204	20	,	,	PUNCT
ejpam-6040	204	21	γg(g	γg(g	NOUN
ejpam-6040	204	22	)	)	PUNCT
ejpam-6040	204	23	=	=	SYM
ejpam-6040	205	1	3	3	X
ejpam-6040	205	2	.	.	PUNCT
ejpam-6040	205	3	let	let	VERB
ejpam-6040	205	4	k	k	NOUN
ejpam-6040	205	5	=	=	SYM
ejpam-6040	205	6	1	1	X
ejpam-6040	205	7	.	.	X
ejpam-6040	205	8	consider	consider	VERB
ejpam-6040	205	9	s	s	PRON
ejpam-6040	205	10	=	=	X
ejpam-6040	205	11	{	{	PUNCT
ejpam-6040	205	12	b	b	PROPN
ejpam-6040	205	13	,	,	PUNCT
ejpam-6040	205	14	d	d	NOUN
ejpam-6040	205	15	}	}	PUNCT
ejpam-6040	205	16	and	and	CCONJ
ejpam-6040	205	17	s′	s′	ADJ
ejpam-6040	205	18	=	=	PUNCT
ejpam-6040	205	19	{	{	PUNCT
ejpam-6040	205	20	b	b	NOUN
ejpam-6040	205	21	,	,	PUNCT
ejpam-6040	205	22	f	f	PROPN
ejpam-6040	205	23	}	}	PUNCT
ejpam-6040	205	24	.	.	PUNCT
ejpam-6040	206	1	then	then	ADV
ejpam-6040	206	2	ng	ng	PROPN
ejpam-6040	206	3	g[s	g[s	PROPN
ejpam-6040	206	4	]	]	X
ejpam-6040	206	5	=	=	SYM
ejpam-6040	206	6	{	{	PUNCT
ejpam-6040	206	7	b	b	PROPN
ejpam-6040	206	8	,	,	PUNCT
ejpam-6040	206	9	c	c	NOUN
ejpam-6040	206	10	,	,	PUNCT
ejpam-6040	206	11	d	d	NOUN
ejpam-6040	206	12	,	,	PUNCT
ejpam-6040	206	13	e	e	NOUN
ejpam-6040	206	14	}	}	PUNCT
ejpam-6040	206	15	and	and	CCONJ
ejpam-6040	206	16	ng	ng	PROPN
ejpam-6040	206	17	g[s	g[s	PROPN
ejpam-6040	206	18	′	′	NUM
ejpam-6040	206	19	]	]	X
ejpam-6040	206	20	=	=	PUNCT
ejpam-6040	206	21	{	{	PUNCT
ejpam-6040	206	22	b	b	PROPN
ejpam-6040	206	23	,	,	PUNCT
ejpam-6040	206	24	c	c	NOUN
ejpam-6040	206	25	,	,	PUNCT
ejpam-6040	206	26	d	d	NOUN
ejpam-6040	206	27	,	,	PUNCT
ejpam-6040	206	28	e	e	NOUN
ejpam-6040	206	29	,	,	PUNCT
ejpam-6040	206	30	f	f	NOUN
ejpam-6040	206	31	}	}	PUNCT
ejpam-6040	206	32	.	.	PUNCT
ejpam-6040	207	1	thus	thus	ADV
ejpam-6040	207	2	,	,	PUNCT
ejpam-6040	207	3	ζg1	ζg1	X
ejpam-6040	207	4	(	(	PUNCT
ejpam-6040	207	5	s	s	NOUN
ejpam-6040	207	6	)	)	PUNCT
ejpam-6040	207	7	=	=	SYM
ejpam-6040	207	8	6	6	NUM
ejpam-6040	207	9	−	−	NUM
ejpam-6040	207	10	4	4	NUM
ejpam-6040	207	11	=	=	SYM
ejpam-6040	207	12	2	2	NUM
ejpam-6040	207	13	>	>	SYM
ejpam-6040	207	14	1	1	NUM
ejpam-6040	207	15	=	=	X
ejpam-6040	207	16	ζg1	ζg1	X
ejpam-6040	207	17	(	(	PUNCT
ejpam-6040	207	18	s	s	NOUN
ejpam-6040	207	19	′	′	NUM
ejpam-6040	207	20	)	)	PUNCT
ejpam-6040	207	21	.	.	PUNCT
ejpam-6040	208	1	this	this	PRON
ejpam-6040	208	2	implies	imply	VERB
ejpam-6040	208	3	that	that	SCONJ
ejpam-6040	208	4	s′	s′	ADJ
ejpam-6040	208	5	is	be	AUX
ejpam-6040	208	6	a	a	DET
ejpam-6040	208	7	ζ1	ζ1	NOUN
ejpam-6040	208	8	-	-	PUNCT
ejpam-6040	208	9	set	set	NOUN
ejpam-6040	208	10	in	in	ADP
ejpam-6040	208	11	g.	g.	PROPN
ejpam-6040	208	12	since	since	SCONJ
ejpam-6040	208	13	dg(b	dg(b	NOUN
ejpam-6040	208	14	,	,	PUNCT
ejpam-6040	208	15	f	f	X
ejpam-6040	208	16	)	)	PUNCT
ejpam-6040	208	17	=	=	SYM
ejpam-6040	208	18	3	3	X
ejpam-6040	208	19	,	,	PUNCT
ejpam-6040	208	20	it	it	PRON
ejpam-6040	208	21	follows	follow	VERB
ejpam-6040	208	22	that	that	SCONJ
ejpam-6040	208	23	|i2g(s′)|	|i2g(s′)|	NOUN
ejpam-6040	208	24	=	=	SYM
ejpam-6040	208	25	0	0	NUM
ejpam-6040	208	26	.	.	PUNCT
ejpam-6040	209	1	it	it	PRON
ejpam-6040	209	2	is	be	AUX
ejpam-6040	209	3	easy	easy	ADJ
ejpam-6040	209	4	to	to	PART
ejpam-6040	209	5	see	see	VERB
ejpam-6040	209	6	that	that	PRON
ejpam-6040	209	7	λk	λk	ADP
ejpam-6040	209	8	2(g	2(g	NUM
ejpam-6040	209	9	)	)	PUNCT
ejpam-6040	209	10	=	=	SYM
ejpam-6040	210	1	|i2g(s)|	|i2g(s)|	NOUN
ejpam-6040	210	2	=	=	SYM
ejpam-6040	210	3	2	2	NUM
ejpam-6040	210	4	where	where	SCONJ
ejpam-6040	210	5	s	s	VERB
ejpam-6040	210	6	is	be	AUX
ejpam-6040	210	7	not	not	PART
ejpam-6040	210	8	a	a	DET
ejpam-6040	210	9	ζ1	ζ1	NOUN
ejpam-6040	210	10	-	-	PUNCT
ejpam-6040	210	11	set	set	NOUN
ejpam-6040	210	12	in	in	ADP
ejpam-6040	210	13	g.	g.	PROPN
ejpam-6040	210	14	s.	s.	PROPN
ejpam-6040	210	15	canoy	canoy	PROPN
ejpam-6040	210	16	,	,	PUNCT
ejpam-6040	210	17	jr	jr	PROPN
ejpam-6040	210	18	.	.	PROPN
ejpam-6040	210	19	,	,	PUNCT
ejpam-6040	210	20	j.	j.	PROPN
ejpam-6040	210	21	anoche	anoche	PROPN
ejpam-6040	210	22	/	/	SYM
ejpam-6040	210	23	eur	eur	PROPN
ejpam-6040	210	24	.	.	PUNCT
ejpam-6040	211	1	j.	j.	PROPN
ejpam-6040	211	2	pure	pure	PROPN
ejpam-6040	211	3	appl	appl	PROPN
ejpam-6040	211	4	.	.	PROPN
ejpam-6040	211	5	math	math	PROPN
ejpam-6040	211	6	,	,	PUNCT
ejpam-6040	211	7	18	18	NUM
ejpam-6040	211	8	(	(	PUNCT
ejpam-6040	211	9	2	2	NUM
ejpam-6040	211	10	)	)	PUNCT
ejpam-6040	211	11	(	(	PUNCT
ejpam-6040	211	12	2025	2025	NUM
ejpam-6040	211	13	)	)	PUNCT
ejpam-6040	211	14	,	,	PUNCT
ejpam-6040	211	15	6040	6040	NUM
ejpam-6040	211	16	7	7	NUM
ejpam-6040	211	17	of	of	ADP
ejpam-6040	211	18	16	16	NUM
ejpam-6040	211	19	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	211	20	.........	.........	PUNCT
ejpam-6040	211	21	........	........	PUNCT
ejpam-6040	211	22	........	........	PUNCT
ejpam-6040	211	23	........	........	PUNCT
ejpam-6040	211	24	........	........	PUNCT
ejpam-6040	211	25	........	........	PUNCT
ejpam-6040	211	26	........	........	PUNCT
ejpam-6040	211	27	........	........	PUNCT
ejpam-6040	211	28	........	........	PUNCT
ejpam-6040	211	29	...	...	PUNCT
ejpam-6040	212	1	....................................	....................................	PUNCT
ejpam-6040	212	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	213	1	.........	.........	PUNCT
ejpam-6040	213	2	........	........	PUNCT
ejpam-6040	213	3	........	........	PUNCT
ejpam-6040	213	4	........	........	PUNCT
ejpam-6040	213	5	........	........	PUNCT
ejpam-6040	213	6	........	........	PUNCT
ejpam-6040	213	7	........	........	PUNCT
ejpam-6040	213	8	........	........	PUNCT
ejpam-6040	213	9	........	........	PUNCT
ejpam-6040	213	10	...	...	PUNCT
ejpam-6040	214	1	....................................	....................................	PUNCT
ejpam-6040	214	2	............................................................................	............................................................................	PUNCT
ejpam-6040	214	3	........................................................................	........................................................................	PUNCT
ejpam-6040	215	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	215	2	....................................	....................................	PUNCT
ejpam-6040	216	1	a	a	DET
ejpam-6040	216	2	b	b	X
ejpam-6040	216	3	c	c	NOUN
ejpam-6040	216	4	d	d	X
ejpam-6040	216	5	e	e	X
ejpam-6040	216	6	f	f	PROPN
ejpam-6040	216	7	figure	figure	NOUN
ejpam-6040	216	8	2	2	NUM
ejpam-6040	216	9	:	:	PUNCT
ejpam-6040	216	10	graph	graph	VERB
ejpam-6040	216	11	g	g	NOUN
ejpam-6040	216	12	with	with	ADP
ejpam-6040	216	13	γg(g	γg(g	NOUN
ejpam-6040	216	14	)	)	PUNCT
ejpam-6040	216	15	=	=	SYM
ejpam-6040	216	16	3	3	NUM
ejpam-6040	216	17	,	,	PUNCT
ejpam-6040	216	18	ζg1	ζg1	X
ejpam-6040	216	19	(	(	PUNCT
ejpam-6040	216	20	g	g	NOUN
ejpam-6040	216	21	)	)	PUNCT
ejpam-6040	216	22	=	=	SYM
ejpam-6040	216	23	1	1	NUM
ejpam-6040	216	24	,	,	PUNCT
ejpam-6040	216	25	and	and	CCONJ
ejpam-6040	216	26	ζg2	ζg2	NOUN
ejpam-6040	216	27	(	(	PUNCT
ejpam-6040	216	28	g	g	NOUN
ejpam-6040	216	29	)	)	PUNCT
ejpam-6040	216	30	=	=	SYM
ejpam-6040	216	31	5	5	NUM
ejpam-6040	216	32	theorem	theorem	VERB
ejpam-6040	216	33	7	7	NUM
ejpam-6040	216	34	.	.	PUNCT
ejpam-6040	217	1	let	let	VERB
ejpam-6040	217	2	g	g	PRON
ejpam-6040	217	3	be	be	AUX
ejpam-6040	217	4	a	a	DET
ejpam-6040	217	5	non	non	ADJ
ejpam-6040	217	6	-	-	ADJ
ejpam-6040	217	7	trivial	trivial	ADJ
ejpam-6040	217	8	graph	graph	NOUN
ejpam-6040	217	9	and	and	CCONJ
ejpam-6040	217	10	let	let	VERB
ejpam-6040	217	11	s	s	PRON
ejpam-6040	217	12	⊆	⊆	NUM
ejpam-6040	217	13	v	v	NOUN
ejpam-6040	217	14	(	(	PUNCT
ejpam-6040	217	15	g	g	NOUN
ejpam-6040	217	16	)	)	PUNCT
ejpam-6040	217	17	.	.	PUNCT
ejpam-6040	218	1	then	then	ADV
ejpam-6040	218	2	the	the	DET
ejpam-6040	218	3	following	following	ADJ
ejpam-6040	218	4	statements	statement	NOUN
ejpam-6040	218	5	hold	hold	VERB
ejpam-6040	218	6	:	:	PUNCT
ejpam-6040	218	7	(	(	PUNCT
ejpam-6040	218	8	i	i	NOUN
ejpam-6040	218	9	)	)	PUNCT
ejpam-6040	218	10	s	s	VERB
ejpam-6040	218	11	∪	∪	PROPN
ejpam-6040	218	12	i2g(s	i2g(s	PROPN
ejpam-6040	218	13	)	)	PUNCT
ejpam-6040	218	14	⊆	⊆	NUM
ejpam-6040	218	15	ng	ng	PROPN
ejpam-6040	218	16	g[s	g[s	PROPN
ejpam-6040	218	17	]	]	PUNCT
ejpam-6040	218	18	.	.	PUNCT
ejpam-6040	219	1	(	(	PUNCT
ejpam-6040	219	2	ii	ii	NOUN
ejpam-6040	219	3	)	)	PUNCT
ejpam-6040	219	4	if	if	SCONJ
ejpam-6040	219	5	diam(g	diam(g	NOUN
ejpam-6040	219	6	)	)	PUNCT
ejpam-6040	219	7	=	=	SYM
ejpam-6040	219	8	2	2	NUM
ejpam-6040	219	9	,	,	PUNCT
ejpam-6040	219	10	then	then	ADV
ejpam-6040	219	11	ng	ng	PROPN
ejpam-6040	219	12	g[s	g[s	PROPN
ejpam-6040	219	13	]	]	X
ejpam-6040	219	14	=	=	SYM
ejpam-6040	219	15	s	s	X
ejpam-6040	219	16	∪	∪	ADJ
ejpam-6040	219	17	i2g(s	i2g(s	PROPN
ejpam-6040	219	18	)	)	PUNCT
ejpam-6040	219	19	.	.	PUNCT
ejpam-6040	220	1	(	(	PUNCT
ejpam-6040	220	2	iii	iii	X
ejpam-6040	220	3	)	)	PUNCT
ejpam-6040	220	4	if	if	SCONJ
ejpam-6040	220	5	diam(g	diam(g	NOUN
ejpam-6040	220	6	)	)	PUNCT
ejpam-6040	220	7	=	=	SYM
ejpam-6040	220	8	2	2	NUM
ejpam-6040	220	9	,	,	PUNCT
ejpam-6040	220	10	k	k	X
ejpam-6040	220	11	is	be	AUX
ejpam-6040	220	12	a	a	DET
ejpam-6040	220	13	positive	positive	ADJ
ejpam-6040	220	14	integer	integer	NOUN
ejpam-6040	220	15	with	with	ADP
ejpam-6040	220	16	k	k	PROPN
ejpam-6040	220	17	≤	≤	X
ejpam-6040	220	18	γg(g)−	γg(g)−	NOUN
ejpam-6040	220	19	1	1	NUM
ejpam-6040	220	20	,	,	PUNCT
ejpam-6040	220	21	and	and	CCONJ
ejpam-6040	220	22	s	s	VERB
ejpam-6040	220	23	is	be	AUX
ejpam-6040	220	24	a	a	DET
ejpam-6040	220	25	ζgk	ζgk	NOUN
ejpam-6040	220	26	-set	-set	ADJ
ejpam-6040	220	27	in	in	ADP
ejpam-6040	220	28	g	g	PROPN
ejpam-6040	220	29	,	,	PUNCT
ejpam-6040	220	30	then	then	ADV
ejpam-6040	220	31	λk	λk	ADP
ejpam-6040	220	32	2(g	2(g	NUM
ejpam-6040	220	33	)	)	PUNCT
ejpam-6040	221	1	=	=	SYM
ejpam-6040	221	2	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	221	3	.	.	PUNCT
ejpam-6040	222	1	proof	proof	NOUN
ejpam-6040	222	2	.	.	PUNCT
ejpam-6040	223	1	(	(	PUNCT
ejpam-6040	223	2	i	i	NOUN
ejpam-6040	223	3	)	)	PUNCT
ejpam-6040	223	4	note	note	VERB
ejpam-6040	223	5	that	that	SCONJ
ejpam-6040	223	6	if	if	SCONJ
ejpam-6040	223	7	x	x	PROPN
ejpam-6040	223	8	∈	∈	PROPN
ejpam-6040	223	9	i2g(s	i2g(s	PROPN
ejpam-6040	223	10	)	)	PUNCT
ejpam-6040	223	11	,	,	PUNCT
ejpam-6040	223	12	then	then	ADV
ejpam-6040	223	13	x	x	X
ejpam-6040	223	14	∈	∈	PROPN
ejpam-6040	223	15	ng	ng	PROPN
ejpam-6040	223	16	g[s	g[s	PROPN
ejpam-6040	223	17	]	]	PUNCT
ejpam-6040	223	18	.	.	PUNCT
ejpam-6040	224	1	hence	hence	ADV
ejpam-6040	224	2	,	,	PUNCT
ejpam-6040	224	3	i2g(s	i2g(s	PROPN
ejpam-6040	224	4	)	)	PUNCT
ejpam-6040	224	5	⊆	⊆	NUM
ejpam-6040	224	6	ng	ng	PROPN
ejpam-6040	224	7	g[s	g[s	PROPN
ejpam-6040	224	8	]	]	PUNCT
ejpam-6040	224	9	.	.	PUNCT
ejpam-6040	225	1	since	since	SCONJ
ejpam-6040	225	2	s	s	PRON
ejpam-6040	225	3	⊆	⊆	NUM
ejpam-6040	225	4	ng	ng	PROPN
ejpam-6040	225	5	g[s	g[s	PROPN
ejpam-6040	225	6	]	]	PUNCT
ejpam-6040	225	7	,	,	PUNCT
ejpam-6040	225	8	it	it	PRON
ejpam-6040	225	9	follows	follow	VERB
ejpam-6040	225	10	that	that	SCONJ
ejpam-6040	225	11	s	s	VERB
ejpam-6040	225	12	∪	∪	ADJ
ejpam-6040	225	13	i2g(s	i2g(s	PROPN
ejpam-6040	225	14	)	)	PUNCT
ejpam-6040	225	15	⊆	⊆	NUM
ejpam-6040	225	16	ng	ng	PROPN
ejpam-6040	225	17	g[s	g[s	PROPN
ejpam-6040	225	18	]	]	PUNCT
ejpam-6040	225	19	.	.	PUNCT
ejpam-6040	226	1	(	(	PUNCT
ejpam-6040	226	2	ii	ii	NOUN
ejpam-6040	226	3	)	)	PUNCT
ejpam-6040	226	4	suppose	suppose	VERB
ejpam-6040	226	5	diam(g	diam(g	NOUN
ejpam-6040	226	6	)	)	PUNCT
ejpam-6040	226	7	=	=	SYM
ejpam-6040	226	8	2	2	X
ejpam-6040	226	9	.	.	X
ejpam-6040	226	10	let	let	VERB
ejpam-6040	226	11	x	x	SYM
ejpam-6040	226	12	∈	∈	PROPN
ejpam-6040	226	13	ng	ng	PROPN
ejpam-6040	226	14	g[s	g[s	PROPN
ejpam-6040	226	15	]	]	PUNCT
ejpam-6040	226	16	.	.	PUNCT
ejpam-6040	227	1	then	then	ADV
ejpam-6040	227	2	x	x	SYM
ejpam-6040	227	3	∈	∈	PROPN
ejpam-6040	227	4	ng[s	ng[s	PROPN
ejpam-6040	227	5	]	]	PUNCT
ejpam-6040	227	6	∩	∩	X
ejpam-6040	227	7	ig[s	ig[s	PROPN
ejpam-6040	227	8	]	]	PUNCT
ejpam-6040	227	9	.	.	PUNCT
ejpam-6040	228	1	if	if	SCONJ
ejpam-6040	228	2	x	x	SYM
ejpam-6040	228	3	∈	∈	PROPN
ejpam-6040	228	4	s	s	NOUN
ejpam-6040	228	5	,	,	PUNCT
ejpam-6040	228	6	then	then	ADV
ejpam-6040	228	7	x	x	PART
ejpam-6040	228	8	∈	∈	NOUN
ejpam-6040	228	9	s	s	VERB
ejpam-6040	228	10	∪	∪	ADJ
ejpam-6040	228	11	i2g(s	i2g(s	PROPN
ejpam-6040	228	12	)	)	PUNCT
ejpam-6040	228	13	.	.	PUNCT
ejpam-6040	229	1	if	if	SCONJ
ejpam-6040	229	2	x	x	X
ejpam-6040	229	3	/∈	/∈	PROPN
ejpam-6040	229	4	s	s	X
ejpam-6040	229	5	,	,	PUNCT
ejpam-6040	229	6	then	then	ADV
ejpam-6040	229	7	there	there	PRON
ejpam-6040	229	8	exist	exist	VERB
ejpam-6040	229	9	y	y	PROPN
ejpam-6040	229	10	,	,	PUNCT
ejpam-6040	229	11	z	z	PROPN
ejpam-6040	229	12	∈	∈	PROPN
ejpam-6040	229	13	s	s	VERB
ejpam-6040	229	14	such	such	ADJ
ejpam-6040	229	15	that	that	SCONJ
ejpam-6040	229	16	x	x	SYM
ejpam-6040	229	17	∈	∈	PROPN
ejpam-6040	229	18	ig(y	ig(y	NOUN
ejpam-6040	229	19	,	,	PUNCT
ejpam-6040	229	20	z	z	NOUN
ejpam-6040	229	21	)	)	PUNCT
ejpam-6040	229	22	.	.	PUNCT
ejpam-6040	230	1	since	since	SCONJ
ejpam-6040	230	2	diam(g	diam(g	NOUN
ejpam-6040	230	3	)	)	PUNCT
ejpam-6040	230	4	=	=	SYM
ejpam-6040	230	5	2	2	NUM
ejpam-6040	230	6	,	,	PUNCT
ejpam-6040	230	7	it	it	PRON
ejpam-6040	230	8	follows	follow	VERB
ejpam-6040	230	9	that	that	SCONJ
ejpam-6040	230	10	dg(y	dg(y	ADJ
ejpam-6040	230	11	,	,	PUNCT
ejpam-6040	230	12	z	z	NOUN
ejpam-6040	230	13	)	)	PUNCT
ejpam-6040	230	14	=	=	SYM
ejpam-6040	230	15	2	2	X
ejpam-6040	230	16	.	.	PUNCT
ejpam-6040	230	17	thus	thus	ADV
ejpam-6040	230	18	,	,	PUNCT
ejpam-6040	230	19	x	x	PROPN
ejpam-6040	230	20	∈	∈	PROPN
ejpam-6040	230	21	i2g(s	i2g(s	PROPN
ejpam-6040	230	22	)	)	PUNCT
ejpam-6040	230	23	.	.	PUNCT
ejpam-6040	231	1	therefore	therefore	ADV
ejpam-6040	231	2	,	,	PUNCT
ejpam-6040	231	3	n	n	PRON
ejpam-6040	231	4	g	g	PROPN
ejpam-6040	231	5	g[s	g[s	PROPN
ejpam-6040	231	6	]	]	PUNCT
ejpam-6040	231	7	⊆	⊆	NUM
ejpam-6040	231	8	s∪i2g(s	s∪i2g(s	NOUN
ejpam-6040	231	9	)	)	PUNCT
ejpam-6040	231	10	.	.	PUNCT
ejpam-6040	232	1	with	with	ADP
ejpam-6040	232	2	(	(	PUNCT
ejpam-6040	232	3	i	i	NOUN
ejpam-6040	232	4	)	)	PUNCT
ejpam-6040	232	5	,	,	PUNCT
ejpam-6040	232	6	we	we	PRON
ejpam-6040	232	7	get	get	VERB
ejpam-6040	232	8	the	the	DET
ejpam-6040	232	9	desired	desire	VERB
ejpam-6040	232	10	equality	equality	NOUN
ejpam-6040	232	11	ng	ng	PROPN
ejpam-6040	232	12	g[s	g[s	PROPN
ejpam-6040	232	13	]	]	X
ejpam-6040	233	1	=	=	SYM
ejpam-6040	233	2	s	s	X
ejpam-6040	233	3	∪	∪	ADJ
ejpam-6040	233	4	i2g(s	i2g(s	PROPN
ejpam-6040	233	5	)	)	PUNCT
ejpam-6040	233	6	.	.	PUNCT
ejpam-6040	234	1	(	(	PUNCT
ejpam-6040	234	2	iii	iii	X
ejpam-6040	234	3	)	)	PUNCT
ejpam-6040	234	4	let	let	VERB
ejpam-6040	234	5	s′	s′	NOUN
ejpam-6040	234	6	be	be	AUX
ejpam-6040	234	7	a	a	DET
ejpam-6040	234	8	(	(	PUNCT
ejpam-6040	234	9	γg(g)−k)-element	γg(g)−k)-element	ADJ
ejpam-6040	234	10	subset	subset	NOUN
ejpam-6040	234	11	of	of	ADP
ejpam-6040	234	12	v	v	NOUN
ejpam-6040	234	13	(	(	PUNCT
ejpam-6040	234	14	g	g	NOUN
ejpam-6040	234	15	)	)	PUNCT
ejpam-6040	234	16	.	.	PUNCT
ejpam-6040	235	1	by	by	ADP
ejpam-6040	235	2	part	part	NOUN
ejpam-6040	235	3	(	(	PUNCT
ejpam-6040	235	4	ii	ii	NOUN
ejpam-6040	235	5	)	)	PUNCT
ejpam-6040	235	6	,	,	PUNCT
ejpam-6040	235	7	ng	ng	PROPN
ejpam-6040	235	8	g[s	g[s	PROPN
ejpam-6040	235	9	′	′	NUM
ejpam-6040	235	10	]	]	X
ejpam-6040	235	11	=	=	SYM
ejpam-6040	235	12	s∪i2g(s	s∪i2g(s	NOUN
ejpam-6040	235	13	)	)	PUNCT
ejpam-6040	235	14	.	.	PUNCT
ejpam-6040	236	1	it	it	PRON
ejpam-6040	236	2	follows	follow	VERB
ejpam-6040	236	3	that	that	SCONJ
ejpam-6040	236	4	ζgk(s	ζgk(s	PROPN
ejpam-6040	236	5	′	′	NOUN
ejpam-6040	236	6	)	)	PUNCT
ejpam-6040	236	7	=	=	SYM
ejpam-6040	236	8	n	n	NUM
ejpam-6040	236	9	−	−	NOUN
ejpam-6040	236	10	γg(g	γg(g	NUM
ejpam-6040	236	11	)	)	PUNCT
ejpam-6040	237	1	+	+	CCONJ
ejpam-6040	238	1	k	k	X
ejpam-6040	238	2	−	−	NOUN
ejpam-6040	238	3	|i2g(s′)|	|i2g(s′)|	NOUN
ejpam-6040	238	4	.	.	PUNCT
ejpam-6040	239	1	since	since	SCONJ
ejpam-6040	239	2	s	s	PROPN
ejpam-6040	239	3	is	be	AUX
ejpam-6040	239	4	a	a	DET
ejpam-6040	239	5	ζgk	ζgk	ADJ
ejpam-6040	239	6	-set	-set	ADJ
ejpam-6040	239	7	in	in	ADP
ejpam-6040	239	8	g	g	PROPN
ejpam-6040	239	9	,	,	PUNCT
ejpam-6040	239	10	ζgk(s	ζgk(s	PROPN
ejpam-6040	239	11	)	)	PUNCT
ejpam-6040	239	12	=	=	SYM
ejpam-6040	240	1	n	n	NUM
ejpam-6040	240	2	−	−	NOUN
ejpam-6040	240	3	γg(g	γg(g	NUM
ejpam-6040	240	4	)	)	PUNCT
ejpam-6040	241	1	+	+	CCONJ
ejpam-6040	242	1	k	k	X
ejpam-6040	242	2	−	−	NOUN
ejpam-6040	243	1	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	243	2	≤	≤	PROPN
ejpam-6040	243	3	ζgk(s	ζgk(s	PROPN
ejpam-6040	243	4	′	′	NUM
ejpam-6040	243	5	)	)	PUNCT
ejpam-6040	243	6	.	.	PUNCT
ejpam-6040	244	1	this	this	PRON
ejpam-6040	244	2	implies	imply	VERB
ejpam-6040	244	3	that	that	SCONJ
ejpam-6040	244	4	|i2g(s′)|	|i2g(s′)|	ADJ
ejpam-6040	244	5	≤	≤	NUM
ejpam-6040	244	6	|i2g(s)|	|i2g(s)|	NOUN
ejpam-6040	244	7	.	.	PUNCT
ejpam-6040	245	1	since	since	SCONJ
ejpam-6040	245	2	s′	s′	NUM
ejpam-6040	245	3	was	be	AUX
ejpam-6040	245	4	arbitrarily	arbitrarily	ADV
ejpam-6040	245	5	chosen	choose	VERB
ejpam-6040	245	6	,	,	PUNCT
ejpam-6040	245	7	we	we	PRON
ejpam-6040	245	8	have	have	VERB
ejpam-6040	245	9	λk	λk	ADP
ejpam-6040	245	10	2(g	2(g	NUM
ejpam-6040	245	11	)	)	PUNCT
ejpam-6040	245	12	=	=	SYM
ejpam-6040	245	13	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	245	14	.	.	PUNCT
ejpam-6040	245	15	theorem	theorem	VERB
ejpam-6040	245	16	8	8	NUM
ejpam-6040	245	17	.	.	PUNCT
ejpam-6040	246	1	let	let	VERB
ejpam-6040	246	2	g	g	PRON
ejpam-6040	246	3	be	be	AUX
ejpam-6040	246	4	a	a	DET
ejpam-6040	246	5	non	non	ADJ
ejpam-6040	246	6	-	-	ADJ
ejpam-6040	246	7	trivial	trivial	ADJ
ejpam-6040	246	8	graph	graph	NOUN
ejpam-6040	246	9	of	of	ADP
ejpam-6040	246	10	order	order	NOUN
ejpam-6040	246	11	n	n	NOUN
ejpam-6040	246	12	and	and	CCONJ
ejpam-6040	246	13	let	let	VERB
ejpam-6040	246	14	k	k	PRON
ejpam-6040	246	15	be	be	AUX
ejpam-6040	246	16	a	a	DET
ejpam-6040	246	17	positive	positive	ADJ
ejpam-6040	246	18	integer	integer	NOUN
ejpam-6040	246	19	with	with	ADP
ejpam-6040	246	20	k	k	PROPN
ejpam-6040	246	21	≤	≤	X
ejpam-6040	246	22	γg(g)−	γg(g)−	NOUN
ejpam-6040	246	23	1	1	NUM
ejpam-6040	246	24	.	.	PUNCT
ejpam-6040	247	1	then	then	ADV
ejpam-6040	247	2	ζgk(g	ζgk(g	NUM
ejpam-6040	247	3	)	)	PUNCT
ejpam-6040	247	4	≤	≤	NUM
ejpam-6040	247	5	n−	n−	NOUN
ejpam-6040	247	6	γg(g	γg(g	PUNCT
ejpam-6040	247	7	)	)	PUNCT
ejpam-6040	248	1	+	+	CCONJ
ejpam-6040	249	1	k	k	PROPN
ejpam-6040	249	2	−	−	X
ejpam-6040	249	3	λk	λk	ADP
ejpam-6040	249	4	2(g	2(g	NUM
ejpam-6040	249	5	)	)	PUNCT
ejpam-6040	249	6	and	and	CCONJ
ejpam-6040	249	7	equality	equality	NOUN
ejpam-6040	249	8	holds	hold	VERB
ejpam-6040	249	9	if	if	SCONJ
ejpam-6040	249	10	k	k	PROPN
ejpam-6040	249	11	=	=	PUNCT
ejpam-6040	249	12	γg(g)−	γg(g)−	NOUN
ejpam-6040	249	13	1	1	NUM
ejpam-6040	249	14	or	or	CCONJ
ejpam-6040	249	15	1	1	NUM
ejpam-6040	249	16	≤	≤	NUM
ejpam-6040	249	17	diam(g	diam(g	NOUN
ejpam-6040	249	18	)	)	PUNCT
ejpam-6040	249	19	≤	≤	NOUN
ejpam-6040	249	20	2	2	NUM
ejpam-6040	249	21	.	.	PUNCT
ejpam-6040	250	1	proof	proof	NOUN
ejpam-6040	250	2	.	.	PUNCT
ejpam-6040	251	1	let	let	VERB
ejpam-6040	251	2	k	k	PRON
ejpam-6040	251	3	be	be	AUX
ejpam-6040	251	4	a	a	DET
ejpam-6040	251	5	positive	positive	ADJ
ejpam-6040	251	6	integer	integer	NOUN
ejpam-6040	251	7	with	with	ADP
ejpam-6040	251	8	k	k	PROPN
ejpam-6040	251	9	≤	≤	PROPN
ejpam-6040	251	10	γg(g)−1	γg(g)−1	PUNCT
ejpam-6040	251	11	and	and	CCONJ
ejpam-6040	251	12	let	let	VERB
ejpam-6040	251	13	s	s	PRON
ejpam-6040	251	14	be	be	AUX
ejpam-6040	251	15	a	a	DET
ejpam-6040	251	16	(	(	PUNCT
ejpam-6040	251	17	γg(g)−k)-element	γg(g)−k)-element	ADJ
ejpam-6040	251	18	subset	subset	NOUN
ejpam-6040	251	19	of	of	ADP
ejpam-6040	251	20	v	v	NOUN
ejpam-6040	251	21	(	(	PUNCT
ejpam-6040	251	22	g	g	NOUN
ejpam-6040	251	23	)	)	PUNCT
ejpam-6040	251	24	such	such	ADJ
ejpam-6040	251	25	that	that	PRON
ejpam-6040	251	26	λk	λk	ADP
ejpam-6040	251	27	2(g	2(g	NUM
ejpam-6040	251	28	)	)	PUNCT
ejpam-6040	252	1	=	=	SYM
ejpam-6040	252	2	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	252	3	.	.	PUNCT
ejpam-6040	253	1	by	by	ADP
ejpam-6040	253	2	theorem	theorem	NOUN
ejpam-6040	253	3	7(i	7(i	NUM
ejpam-6040	253	4	)	)	PUNCT
ejpam-6040	253	5	,	,	PUNCT
ejpam-6040	253	6	s	s	VERB
ejpam-6040	253	7	∪	∪	PROPN
ejpam-6040	253	8	i2g(s	i2g(s	PROPN
ejpam-6040	253	9	)	)	PUNCT
ejpam-6040	253	10	⊆	⊆	NUM
ejpam-6040	253	11	ng	ng	PROPN
ejpam-6040	253	12	g[s	g[s	PROPN
ejpam-6040	253	13	]	]	PUNCT
ejpam-6040	253	14	.	.	PUNCT
ejpam-6040	254	1	hence	hence	ADV
ejpam-6040	254	2	,	,	PUNCT
ejpam-6040	254	3	ζgk(g	ζgk(g	PROPN
ejpam-6040	254	4	)	)	PUNCT
ejpam-6040	254	5	≤	≤	NOUN
ejpam-6040	254	6	ζgk(s	ζgk(s	PROPN
ejpam-6040	254	7	)	)	PUNCT
ejpam-6040	255	1	=	=	PUNCT
ejpam-6040	255	2	n−	n−	NOUN
ejpam-6040	255	3	|ng	|ng	X
ejpam-6040	255	4	g[s]|	g[s]|	PROPN
ejpam-6040	255	5	≤	≤	PROPN
ejpam-6040	255	6	n−	n−	PROPN
ejpam-6040	255	7	(	(	PUNCT
ejpam-6040	255	8	|s|+	|s|+	PROPN
ejpam-6040	255	9	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	255	10	)	)	PUNCT
ejpam-6040	255	11	=	=	NUM
ejpam-6040	255	12	n−	n−	NOUN
ejpam-6040	255	13	γg(g	γg(g	PRON
ejpam-6040	255	14	)	)	PUNCT
ejpam-6040	256	1	+	+	CCONJ
ejpam-6040	257	1	k	k	PROPN
ejpam-6040	257	2	−	−	X
ejpam-6040	257	3	λk	λk	ADP
ejpam-6040	257	4	2(g	2(g	NUM
ejpam-6040	257	5	)	)	PUNCT
ejpam-6040	257	6	.	.	PUNCT
ejpam-6040	258	1	suppose	suppose	VERB
ejpam-6040	258	2	k	k	PROPN
ejpam-6040	258	3	=	=	PUNCT
ejpam-6040	258	4	γg(g)−1	γg(g)−1	PROPN
ejpam-6040	258	5	.	.	PUNCT
ejpam-6040	259	1	then	then	ADV
ejpam-6040	259	2	ζgk(g	ζgk(g	NUM
ejpam-6040	259	3	)	)	PUNCT
ejpam-6040	259	4	=	=	SYM
ejpam-6040	259	5	n−1	n−1	PROPN
ejpam-6040	259	6	by	by	ADP
ejpam-6040	259	7	lemma	lemma	PROPN
ejpam-6040	259	8	1	1	NUM
ejpam-6040	259	9	.	.	PUNCT
ejpam-6040	260	1	in	in	ADP
ejpam-6040	260	2	this	this	DET
ejpam-6040	260	3	case	case	NOUN
ejpam-6040	260	4	,	,	PUNCT
ejpam-6040	260	5	λk	λk	ADP
ejpam-6040	260	6	2	2	NUM
ejpam-6040	260	7	=	=	SYM
ejpam-6040	260	8	0	0	NUM
ejpam-6040	260	9	.	.	PUNCT
ejpam-6040	261	1	hence	hence	ADV
ejpam-6040	261	2	,	,	PUNCT
ejpam-6040	261	3	ζgk(g	ζgk(g	PROPN
ejpam-6040	261	4	)	)	PUNCT
ejpam-6040	261	5	=	=	SYM
ejpam-6040	261	6	n−	n−	NOUN
ejpam-6040	261	7	1	1	NUM
ejpam-6040	261	8	=	=	SYM
ejpam-6040	261	9	n−	n−	NOUN
ejpam-6040	261	10	γg(g	γg(g	PRON
ejpam-6040	261	11	)	)	PUNCT
ejpam-6040	262	1	+	+	CCONJ
ejpam-6040	263	1	k	k	PROPN
ejpam-6040	263	2	−	−	X
ejpam-6040	263	3	λk	λk	ADP
ejpam-6040	263	4	2(g	2(g	NUM
ejpam-6040	263	5	)	)	PUNCT
ejpam-6040	263	6	.	.	PUNCT
ejpam-6040	264	1	suppose	suppose	VERB
ejpam-6040	264	2	1	1	NUM
ejpam-6040	264	3	≤	≤	NUM
ejpam-6040	264	4	diam(g	diam(g	NOUN
ejpam-6040	264	5	)	)	PUNCT
ejpam-6040	264	6	≤	≤	NOUN
ejpam-6040	264	7	2	2	NUM
ejpam-6040	264	8	and	and	CCONJ
ejpam-6040	264	9	let	let	VERB
ejpam-6040	264	10	s	s	PRON
ejpam-6040	264	11	be	be	AUX
ejpam-6040	264	12	a	a	DET
ejpam-6040	264	13	ζgk	ζgk	ADJ
ejpam-6040	264	14	-set	-set	ADJ
ejpam-6040	264	15	of	of	ADP
ejpam-6040	264	16	g.	g.	PROPN
ejpam-6040	264	17	if	if	SCONJ
ejpam-6040	264	18	diam(g	diam(g	PROPN
ejpam-6040	264	19	)	)	PUNCT
ejpam-6040	264	20	=	=	SYM
ejpam-6040	264	21	1	1	NUM
ejpam-6040	264	22	,	,	PUNCT
ejpam-6040	264	23	then	then	ADV
ejpam-6040	264	24	every	every	DET
ejpam-6040	264	25	component	component	NOUN
ejpam-6040	264	26	of	of	ADP
ejpam-6040	264	27	g	g	PROPN
ejpam-6040	264	28	is	be	AUX
ejpam-6040	264	29	complete	complete	ADJ
ejpam-6040	264	30	and	and	CCONJ
ejpam-6040	264	31	γg(g	γg(g	NOUN
ejpam-6040	264	32	)	)	PUNCT
ejpam-6040	264	33	=	=	VERB
ejpam-6040	265	1	n.	n.	NOUN
ejpam-6040	265	2	hence	hence	ADV
ejpam-6040	265	3	,	,	PUNCT
ejpam-6040	265	4	if	if	SCONJ
ejpam-6040	265	5	s′	s′	ADJ
ejpam-6040	265	6	is	be	AUX
ejpam-6040	265	7	any	any	DET
ejpam-6040	265	8	(	(	PUNCT
ejpam-6040	265	9	γg(g)−	γg(g)−	NOUN
ejpam-6040	265	10	k)-element	k)-element	PUNCT
ejpam-6040	265	11	set	set	VERB
ejpam-6040	265	12	in	in	ADP
ejpam-6040	265	13	s.	s.	PROPN
ejpam-6040	265	14	canoy	canoy	PROPN
ejpam-6040	265	15	,	,	PUNCT
ejpam-6040	265	16	jr	jr	PROPN
ejpam-6040	265	17	.	.	PROPN
ejpam-6040	265	18	,	,	PUNCT
ejpam-6040	265	19	j.	j.	PROPN
ejpam-6040	265	20	anoche	anoche	PROPN
ejpam-6040	265	21	/	/	SYM
ejpam-6040	265	22	eur	eur	PROPN
ejpam-6040	265	23	.	.	PUNCT
ejpam-6040	266	1	j.	j.	PROPN
ejpam-6040	266	2	pure	pure	PROPN
ejpam-6040	266	3	appl	appl	PROPN
ejpam-6040	266	4	.	.	PROPN
ejpam-6040	266	5	math	math	PROPN
ejpam-6040	266	6	,	,	PUNCT
ejpam-6040	266	7	18	18	NUM
ejpam-6040	266	8	(	(	PUNCT
ejpam-6040	266	9	2	2	NUM
ejpam-6040	266	10	)	)	PUNCT
ejpam-6040	266	11	(	(	PUNCT
ejpam-6040	266	12	2025	2025	NUM
ejpam-6040	266	13	)	)	PUNCT
ejpam-6040	266	14	,	,	PUNCT
ejpam-6040	266	15	6040	6040	NUM
ejpam-6040	266	16	8	8	NUM
ejpam-6040	266	17	of	of	ADP
ejpam-6040	266	18	16	16	NUM
ejpam-6040	266	19	g	g	NOUN
ejpam-6040	266	20	,	,	PUNCT
ejpam-6040	266	21	then	then	ADV
ejpam-6040	266	22	|i2g(s′)|	|i2g(s′)|	NOUN
ejpam-6040	266	23	=	=	SYM
ejpam-6040	266	24	0	0	NUM
ejpam-6040	266	25	.	.	PUNCT
ejpam-6040	267	1	it	it	PRON
ejpam-6040	267	2	follows	follow	VERB
ejpam-6040	267	3	that	that	PRON
ejpam-6040	267	4	λk	λk	ADP
ejpam-6040	267	5	2(g	2(g	NUM
ejpam-6040	267	6	)	)	PUNCT
ejpam-6040	267	7	=	=	SYM
ejpam-6040	268	1	0	0	X
ejpam-6040	268	2	.	.	PUNCT
ejpam-6040	269	1	since	since	SCONJ
ejpam-6040	269	2	ng	ng	PROPN
ejpam-6040	269	3	g[s	g[s	PROPN
ejpam-6040	269	4	]	]	X
ejpam-6040	269	5	=	=	SYM
ejpam-6040	269	6	s	s	NOUN
ejpam-6040	269	7	by	by	ADP
ejpam-6040	269	8	lemma	lemma	PROPN
ejpam-6040	269	9	2	2	NUM
ejpam-6040	269	10	,	,	PUNCT
ejpam-6040	269	11	we	we	PRON
ejpam-6040	269	12	have	have	VERB
ejpam-6040	269	13	ζgk(g	ζgk(g	NOUN
ejpam-6040	269	14	)	)	PUNCT
ejpam-6040	269	15	=	=	SYM
ejpam-6040	269	16	ζgk(s	ζgk(s	PROPN
ejpam-6040	269	17	)	)	PUNCT
ejpam-6040	270	1	=	=	SYM
ejpam-6040	270	2	n−	n−	NOUN
ejpam-6040	270	3	(	(	PUNCT
ejpam-6040	270	4	γg(g)−	γg(g)−	NOUN
ejpam-6040	270	5	k	k	NOUN
ejpam-6040	270	6	)	)	PUNCT
ejpam-6040	270	7	=	=	VERB
ejpam-6040	270	8	n−	n−	NOUN
ejpam-6040	270	9	γg(g	γg(g	PRON
ejpam-6040	270	10	)	)	PUNCT
ejpam-6040	271	1	+	+	CCONJ
ejpam-6040	272	1	k	k	PROPN
ejpam-6040	272	2	−	−	X
ejpam-6040	272	3	λk	λk	ADP
ejpam-6040	272	4	2(g	2(g	NUM
ejpam-6040	272	5	)	)	PUNCT
ejpam-6040	272	6	=	=	VERB
ejpam-6040	273	1	k.	k.	PROPN
ejpam-6040	273	2	next	next	ADV
ejpam-6040	273	3	,	,	PUNCT
ejpam-6040	273	4	suppose	suppose	VERB
ejpam-6040	273	5	that	that	SCONJ
ejpam-6040	273	6	diam(g	diam(g	NOUN
ejpam-6040	273	7	)	)	PUNCT
ejpam-6040	273	8	=	=	SYM
ejpam-6040	274	1	2	2	X
ejpam-6040	274	2	.	.	X
ejpam-6040	274	3	then	then	ADV
ejpam-6040	274	4	ng	ng	PROPN
ejpam-6040	274	5	g[s	g[s	PROPN
ejpam-6040	274	6	]	]	X
ejpam-6040	274	7	=	=	SYM
ejpam-6040	274	8	s	s	X
ejpam-6040	274	9	∪	∪	X
ejpam-6040	274	10	i2g(s	i2g(s	PROPN
ejpam-6040	274	11	)	)	PUNCT
ejpam-6040	274	12	by	by	ADP
ejpam-6040	274	13	theorem	theorem	ADJ
ejpam-6040	274	14	7(ii	7(ii	PROPN
ejpam-6040	274	15	)	)	PUNCT
ejpam-6040	274	16	and	and	CCONJ
ejpam-6040	274	17	λk	λk	ADP
ejpam-6040	274	18	2(g	2(g	NUM
ejpam-6040	274	19	)	)	PUNCT
ejpam-6040	275	1	=	=	SYM
ejpam-6040	275	2	|i2g(s)|	|i2g(s)|	PROPN
ejpam-6040	275	3	by	by	ADP
ejpam-6040	275	4	theorem	theorem	NOUN
ejpam-6040	275	5	7(iii	7(iii	NUM
ejpam-6040	275	6	)	)	PUNCT
ejpam-6040	275	7	.	.	PUNCT
ejpam-6040	276	1	thus	thus	ADV
ejpam-6040	276	2	,	,	PUNCT
ejpam-6040	276	3	ζgk(g	ζgk(g	PROPN
ejpam-6040	276	4	)	)	PUNCT
ejpam-6040	276	5	=	=	SYM
ejpam-6040	276	6	ζgk(s	ζgk(s	PROPN
ejpam-6040	276	7	)	)	PUNCT
ejpam-6040	277	1	=	=	PUNCT
ejpam-6040	277	2	n−	n−	NOUN
ejpam-6040	277	3	γg(g	γg(g	PRON
ejpam-6040	277	4	)	)	PUNCT
ejpam-6040	278	1	+	+	CCONJ
ejpam-6040	279	1	k	k	X
ejpam-6040	279	2	−	−	NOUN
ejpam-6040	280	1	|i2g(s)|	|i2g(s)|	NOUN
ejpam-6040	280	2	=	=	SYM
ejpam-6040	280	3	n−	n−	PROPN
ejpam-6040	280	4	γg(g	γg(g	PRON
ejpam-6040	280	5	)	)	PUNCT
ejpam-6040	281	1	+	+	CCONJ
ejpam-6040	282	1	k	k	PROPN
ejpam-6040	282	2	−	−	X
ejpam-6040	282	3	λk	λk	ADP
ejpam-6040	282	4	2(g	2(g	NUM
ejpam-6040	282	5	)	)	PUNCT
ejpam-6040	282	6	.	.	PUNCT
ejpam-6040	283	1	this	this	PRON
ejpam-6040	283	2	proves	prove	VERB
ejpam-6040	283	3	the	the	DET
ejpam-6040	283	4	assertion	assertion	NOUN
ejpam-6040	283	5	.	.	PUNCT
ejpam-6040	284	1	remark	remark	NOUN
ejpam-6040	284	2	3	3	NUM
ejpam-6040	284	3	.	.	PUNCT
ejpam-6040	284	4	strict	strict	ADJ
ejpam-6040	284	5	inequality	inequality	NOUN
ejpam-6040	284	6	in	in	ADP
ejpam-6040	284	7	theorem	theorem	ADJ
ejpam-6040	284	8	8	8	NUM
ejpam-6040	284	9	is	be	AUX
ejpam-6040	284	10	possible	possible	ADJ
ejpam-6040	284	11	.	.	PUNCT
ejpam-6040	285	1	to	to	PART
ejpam-6040	285	2	see	see	VERB
ejpam-6040	285	3	this	this	PRON
ejpam-6040	285	4	,	,	PUNCT
ejpam-6040	285	5	consider	consider	VERB
ejpam-6040	285	6	graph	graph	NOUN
ejpam-6040	285	7	h	h	NOUN
ejpam-6040	285	8	=	=	NOUN
ejpam-6040	285	9	p8	p8	PROPN
ejpam-6040	285	10	in	in	ADP
ejpam-6040	285	11	figure	figure	NOUN
ejpam-6040	285	12	3	3	NUM
ejpam-6040	285	13	.	.	PUNCT
ejpam-6040	285	14	by	by	ADP
ejpam-6040	285	15	theorem	theorem	ADJ
ejpam-6040	285	16	1(vi	1(vi	NUM
ejpam-6040	285	17	)	)	PUNCT
ejpam-6040	285	18	,	,	PUNCT
ejpam-6040	285	19	γg(h	γg(h	PUNCT
ejpam-6040	285	20	)	)	PUNCT
ejpam-6040	285	21	=	=	SYM
ejpam-6040	286	1	4	4	X
ejpam-6040	286	2	.	.	PUNCT
ejpam-6040	286	3	let	let	VERB
ejpam-6040	286	4	p8	p8	VERB
ejpam-6040	286	5	=	=	PUNCT
ejpam-6040	287	1	[	[	X
ejpam-6040	287	2	v1	v1	NOUN
ejpam-6040	287	3	,	,	PUNCT
ejpam-6040	287	4	v2	v2	PROPN
ejpam-6040	287	5	,	,	PUNCT
ejpam-6040	287	6	·	·	PUNCT
ejpam-6040	287	7	·	·	PUNCT
ejpam-6040	287	8	·	·	PUNCT
ejpam-6040	287	9	,	,	PUNCT
ejpam-6040	287	10	v8	v8	PROPN
ejpam-6040	287	11	]	]	PUNCT
ejpam-6040	287	12	and	and	CCONJ
ejpam-6040	287	13	let	let	VERB
ejpam-6040	287	14	k	k	NOUN
ejpam-6040	287	15	=	=	NOUN
ejpam-6040	287	16	1	1	X
ejpam-6040	287	17	.	.	PUNCT
ejpam-6040	287	18	let	let	VERB
ejpam-6040	287	19	s1	s1	PROPN
ejpam-6040	287	20	=	=	SYM
ejpam-6040	287	21	{	{	PUNCT
ejpam-6040	287	22	v1	v1	PROPN
ejpam-6040	287	23	,	,	PUNCT
ejpam-6040	287	24	v4	v4	NOUN
ejpam-6040	287	25	,	,	PUNCT
ejpam-6040	287	26	v7	v7	NOUN
ejpam-6040	287	27	}	}	PUNCT
ejpam-6040	287	28	.	.	PUNCT
ejpam-6040	288	1	then	then	ADV
ejpam-6040	288	2	|s|	|s|	PROPN
ejpam-6040	288	3	=	=	SYM
ejpam-6040	288	4	3	3	NUM
ejpam-6040	288	5	and	and	CCONJ
ejpam-6040	288	6	ng	ng	PROPN
ejpam-6040	288	7	h	h	PROPN
ejpam-6040	289	1	[	[	X
ejpam-6040	289	2	s1	s1	X
ejpam-6040	289	3	]	]	X
ejpam-6040	289	4	=	=	SYM
ejpam-6040	289	5	{	{	PUNCT
ejpam-6040	289	6	v1	v1	PROPN
ejpam-6040	289	7	,	,	PUNCT
ejpam-6040	289	8	v2	v2	PROPN
ejpam-6040	289	9	,	,	PUNCT
ejpam-6040	289	10	·	·	PUNCT
ejpam-6040	289	11	·	·	PUNCT
ejpam-6040	289	12	·	·	PUNCT
ejpam-6040	289	13	,	,	PUNCT
ejpam-6040	289	14	v7	v7	VERB
ejpam-6040	289	15	}	}	PUNCT
ejpam-6040	289	16	.	.	PUNCT
ejpam-6040	290	1	hence	hence	ADV
ejpam-6040	290	2	,	,	PUNCT
ejpam-6040	290	3	ζg1	ζg1	X
ejpam-6040	290	4	(	(	PUNCT
ejpam-6040	290	5	s1	s1	PROPN
ejpam-6040	290	6	)	)	PUNCT
ejpam-6040	290	7	=	=	SYM
ejpam-6040	290	8	1	1	X
ejpam-6040	290	9	.	.	PUNCT
ejpam-6040	291	1	it	it	PRON
ejpam-6040	291	2	follows	follow	VERB
ejpam-6040	291	3	that	that	SCONJ
ejpam-6040	291	4	s1	s1	NOUN
ejpam-6040	291	5	is	be	AUX
ejpam-6040	291	6	a	a	DET
ejpam-6040	291	7	ζg1	ζg1	PROPN
ejpam-6040	291	8	-set	-set	PUNCT
ejpam-6040	291	9	of	of	ADP
ejpam-6040	291	10	h.	h.	PROPN
ejpam-6040	291	11	it	it	PRON
ejpam-6040	291	12	can	can	AUX
ejpam-6040	291	13	be	be	AUX
ejpam-6040	291	14	verified	verify	VERB
ejpam-6040	291	15	that	that	SCONJ
ejpam-6040	291	16	λ1	λ1	PROPN
ejpam-6040	291	17	2(g	2(g	NUM
ejpam-6040	291	18	)	)	PUNCT
ejpam-6040	291	19	=	=	SYM
ejpam-6040	291	20	2	2	X
ejpam-6040	291	21	.	.	X
ejpam-6040	291	22	hence	hence	ADV
ejpam-6040	291	23	,	,	PUNCT
ejpam-6040	291	24	ζg1	ζg1	X
ejpam-6040	291	25	(	(	PUNCT
ejpam-6040	291	26	h	h	NOUN
ejpam-6040	291	27	)	)	PUNCT
ejpam-6040	291	28	=	=	PUNCT
ejpam-6040	291	29	ζg1	ζg1	X
ejpam-6040	291	30	(	(	PUNCT
ejpam-6040	291	31	s1	s1	PROPN
ejpam-6040	291	32	)	)	PUNCT
ejpam-6040	291	33	=	=	SYM
ejpam-6040	291	34	1	1	NUM
ejpam-6040	291	35	<	<	SYM
ejpam-6040	291	36	3	3	NUM
ejpam-6040	291	37	=	=	SYM
ejpam-6040	291	38	8−	8−	NUM
ejpam-6040	291	39	γg(h	γg(h	PUNCT
ejpam-6040	291	40	)	)	PUNCT
ejpam-6040	292	1	+	+	CCONJ
ejpam-6040	292	2	1−	1−	NUM
ejpam-6040	292	3	λ1	λ1	NUM
ejpam-6040	292	4	2(g	2(g	NUM
ejpam-6040	292	5	)	)	PUNCT
ejpam-6040	292	6	.	.	PUNCT
ejpam-6040	293	1	if	if	SCONJ
ejpam-6040	293	2	k	k	PROPN
ejpam-6040	293	3	=	=	SYM
ejpam-6040	293	4	2	2	NUM
ejpam-6040	293	5	,	,	PUNCT
ejpam-6040	293	6	then	then	ADV
ejpam-6040	293	7	s2	s2	VERB
ejpam-6040	293	8	=	=	SYM
ejpam-6040	293	9	{	{	PUNCT
ejpam-6040	293	10	v1	v1	PROPN
ejpam-6040	293	11	,	,	PUNCT
ejpam-6040	293	12	v4	v4	PROPN
ejpam-6040	293	13	}	}	PUNCT
ejpam-6040	293	14	is	be	AUX
ejpam-6040	293	15	a	a	DET
ejpam-6040	293	16	ζg2	ζg2	NOUN
ejpam-6040	293	17	-set	-set	NOUN
ejpam-6040	293	18	of	of	ADP
ejpam-6040	293	19	h	h	PROPN
ejpam-6040	293	20	and	and	CCONJ
ejpam-6040	293	21	ng	ng	PROPN
ejpam-6040	293	22	h	h	PROPN
ejpam-6040	294	1	[	[	X
ejpam-6040	294	2	s2	s2	X
ejpam-6040	294	3	]	]	X
ejpam-6040	294	4	=	=	SYM
ejpam-6040	294	5	{	{	PUNCT
ejpam-6040	294	6	v1	v1	PROPN
ejpam-6040	294	7	,	,	PUNCT
ejpam-6040	294	8	v2	v2	PROPN
ejpam-6040	294	9	,	,	PUNCT
ejpam-6040	294	10	v3	v3	PROPN
ejpam-6040	294	11	,	,	PUNCT
ejpam-6040	294	12	v4	v4	PROPN
ejpam-6040	294	13	}	}	PUNCT
ejpam-6040	294	14	.	.	PUNCT
ejpam-6040	295	1	also	also	ADV
ejpam-6040	295	2	,	,	PUNCT
ejpam-6040	295	3	λ2	λ2	NOUN
ejpam-6040	295	4	2(h	2(h	NUM
ejpam-6040	295	5	)	)	PUNCT
ejpam-6040	295	6	=	=	SYM
ejpam-6040	295	7	1	1	X
ejpam-6040	295	8	.	.	PUNCT
ejpam-6040	296	1	thus	thus	ADV
ejpam-6040	296	2	,	,	PUNCT
ejpam-6040	296	3	ζg2	ζg2	NOUN
ejpam-6040	296	4	(	(	PUNCT
ejpam-6040	296	5	h	h	NOUN
ejpam-6040	296	6	)	)	PUNCT
ejpam-6040	296	7	=	=	SYM
ejpam-6040	296	8	4	4	NUM
ejpam-6040	296	9	<	<	SYM
ejpam-6040	296	10	5	5	NUM
ejpam-6040	296	11	=	=	SYM
ejpam-6040	296	12	8−	8−	NUM
ejpam-6040	296	13	γg(h	γg(h	PUNCT
ejpam-6040	296	14	)	)	PUNCT
ejpam-6040	297	1	+	+	CCONJ
ejpam-6040	297	2	2−	2−	NUM
ejpam-6040	297	3	λ2	λ2	NOUN
ejpam-6040	297	4	2(g	2(g	NUM
ejpam-6040	297	5	)	)	PUNCT
ejpam-6040	297	6	.	.	PUNCT
ejpam-6040	298	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	298	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	299	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	299	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	300	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	300	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	301	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-6040	302	1	....................................	....................................	PUNCT
ejpam-6040	303	1	v1	v1	VERB
ejpam-6040	303	2	v2	v2	PROPN
ejpam-6040	303	3	v3	v3	PROPN
ejpam-6040	303	4	v4	v4	PROPN
ejpam-6040	303	5	v5	v5	PROPN
ejpam-6040	303	6	v6	v6	NOUN
ejpam-6040	303	7	v7	v7	PROPN
ejpam-6040	303	8	v8	v8	PROPN
ejpam-6040	303	9	figure	figure	NOUN
ejpam-6040	303	10	3	3	NUM
ejpam-6040	303	11	:	:	PUNCT
ejpam-6040	303	12	h	h	NOUN
ejpam-6040	303	13	=	=	PROPN
ejpam-6040	303	14	p8	p8	PROPN
ejpam-6040	303	15	and	and	CCONJ
ejpam-6040	303	16	γg(h	γg(h	NUM
ejpam-6040	303	17	)	)	PUNCT
ejpam-6040	303	18	=	=	SYM
ejpam-6040	304	1	4	4	NUM
ejpam-6040	304	2	corollary	corollary	NOUN
ejpam-6040	304	3	1	1	NUM
ejpam-6040	304	4	.	.	PUNCT
ejpam-6040	304	5	for	for	ADP
ejpam-6040	304	6	a	a	DET
ejpam-6040	304	7	star	star	NOUN
ejpam-6040	304	8	graph	graph	NOUN
ejpam-6040	304	9	k1,n	k1,n	PROPN
ejpam-6040	304	10	,	,	PUNCT
ejpam-6040	304	11	ζgk(k1,n	ζgk(k1,n	PROPN
ejpam-6040	304	12	)	)	PUNCT
ejpam-6040	304	13	=	=	PRON
ejpam-6040	304	14	{	{	PUNCT
ejpam-6040	304	15	n	n	NOUN
ejpam-6040	304	16	if	if	SCONJ
ejpam-6040	304	17	k	k	PROPN
ejpam-6040	304	18	=	=	PUNCT
ejpam-6040	304	19	n−	n−	NOUN
ejpam-6040	304	20	1	1	NUM
ejpam-6040	304	21	k	k	NOUN
ejpam-6040	304	22	if	if	SCONJ
ejpam-6040	304	23	k	k	PROPN
ejpam-6040	304	24	<	<	X
ejpam-6040	304	25	n−	n−	NOUN
ejpam-6040	304	26	1	1	NUM
ejpam-6040	304	27	.	.	PUNCT
ejpam-6040	305	1	proof	proof	NOUN
ejpam-6040	305	2	.	.	PUNCT
ejpam-6040	306	1	let	let	VERB
ejpam-6040	306	2	v	v	X
ejpam-6040	306	3	(	(	PUNCT
ejpam-6040	306	4	k1,n	k1,n	PROPN
ejpam-6040	306	5	)	)	PUNCT
ejpam-6040	306	6	=	=	PROPN
ejpam-6040	306	7	{	{	PUNCT
ejpam-6040	306	8	v0	v0	PROPN
ejpam-6040	306	9	,	,	PUNCT
ejpam-6040	306	10	w1	w1	NOUN
ejpam-6040	306	11	,	,	PUNCT
ejpam-6040	306	12	w2	w2	NOUN
ejpam-6040	306	13	,	,	PUNCT
ejpam-6040	306	14	·	·	PUNCT
ejpam-6040	306	15	·	·	PUNCT
ejpam-6040	306	16	·	·	PUNCT
ejpam-6040	306	17	,	,	PUNCT
ejpam-6040	306	18	wn	wn	PROPN
ejpam-6040	306	19	}	}	PUNCT
ejpam-6040	306	20	where	where	SCONJ
ejpam-6040	306	21	v0	v0	NOUN
ejpam-6040	306	22	has	have	VERB
ejpam-6040	306	23	degree	degree	NOUN
ejpam-6040	306	24	n.	n.	NOUN
ejpam-6040	306	25	by	by	ADP
ejpam-6040	306	26	theorem	theorem	NOUN
ejpam-6040	306	27	1(ii	1(ii	NUM
ejpam-6040	306	28	)	)	PUNCT
ejpam-6040	306	29	,	,	PUNCT
ejpam-6040	306	30	γg(k1,n	γg(k1,n	PROPN
ejpam-6040	306	31	)	)	PUNCT
ejpam-6040	307	1	=	=	PUNCT
ejpam-6040	307	2	n.	n.	PROPN
ejpam-6040	307	3	thus	thus	ADV
ejpam-6040	307	4	,	,	PUNCT
ejpam-6040	307	5	k	k	PROPN
ejpam-6040	307	6	≤	≤	PROPN
ejpam-6040	307	7	n−	n−	PROPN
ejpam-6040	307	8	1	1	NUM
ejpam-6040	307	9	.	.	PUNCT
ejpam-6040	308	1	if	if	SCONJ
ejpam-6040	308	2	k	k	PROPN
ejpam-6040	308	3	=	=	PUNCT
ejpam-6040	308	4	n−	n−	NOUN
ejpam-6040	308	5	1	1	NUM
ejpam-6040	308	6	,	,	PUNCT
ejpam-6040	308	7	then	then	ADV
ejpam-6040	308	8	by	by	ADP
ejpam-6040	308	9	lemma	lemma	PROPN
ejpam-6040	308	10	1	1	NUM
ejpam-6040	308	11	,	,	PUNCT
ejpam-6040	308	12	ζgk(k1,n	ζgk(k1,n	PROPN
ejpam-6040	308	13	)	)	PUNCT
ejpam-6040	309	1	=	=	PUNCT
ejpam-6040	309	2	n+1−	n+1−	PROPN
ejpam-6040	309	3	1	1	NUM
ejpam-6040	309	4	=	=	SYM
ejpam-6040	309	5	n.	n.	NOUN
ejpam-6040	309	6	suppose	suppose	VERB
ejpam-6040	309	7	k	k	X
ejpam-6040	309	8	<	<	X
ejpam-6040	309	9	n−	n−	PROPN
ejpam-6040	309	10	1	1	NUM
ejpam-6040	309	11	.	.	PUNCT
ejpam-6040	310	1	choose	choose	VERB
ejpam-6040	310	2	an	an	DET
ejpam-6040	310	3	(	(	PUNCT
ejpam-6040	310	4	n−	n−	NOUN
ejpam-6040	310	5	k)-element	k)-element	PUNCT
ejpam-6040	310	6	set	set	VERB
ejpam-6040	310	7	s	s	PART
ejpam-6040	310	8	=	=	SYM
ejpam-6040	310	9	{	{	PUNCT
ejpam-6040	310	10	w1	w1	NOUN
ejpam-6040	310	11	,	,	PUNCT
ejpam-6040	310	12	w2	w2	NOUN
ejpam-6040	310	13	,	,	PUNCT
ejpam-6040	310	14	·	·	PUNCT
ejpam-6040	310	15	·	·	PUNCT
ejpam-6040	310	16	·	·	PUNCT
ejpam-6040	310	17	,	,	PUNCT
ejpam-6040	310	18	wn−k	wn−k	PROPN
ejpam-6040	310	19	}	}	PUNCT
ejpam-6040	310	20	.	.	PUNCT
ejpam-6040	311	1	then	then	ADV
ejpam-6040	311	2	s	s	VERB
ejpam-6040	311	3	is	be	AUX
ejpam-6040	311	4	a	a	DET
ejpam-6040	311	5	ζgk	ζgk	ADJ
ejpam-6040	311	6	-set	-set	ADJ
ejpam-6040	311	7	of	of	ADP
ejpam-6040	311	8	k1,n	k1,n	PROPN
ejpam-6040	311	9	and	and	CCONJ
ejpam-6040	311	10	,	,	PUNCT
ejpam-6040	311	11	theorem	theorem	VERB
ejpam-6040	311	12	7(iii	7(iii	NOUN
ejpam-6040	311	13	)	)	PUNCT
ejpam-6040	311	14	,	,	PUNCT
ejpam-6040	311	15	λk	λk	ADP
ejpam-6040	311	16	2(k1,n	2(k1,n	NUM
ejpam-6040	311	17	)	)	PUNCT
ejpam-6040	311	18	=	=	SYM
ejpam-6040	311	19	|i2k1,n	|i2k1,n	NOUN
ejpam-6040	311	20	(	(	PUNCT
ejpam-6040	311	21	s)|	s)|	NOUN
ejpam-6040	311	22	=	=	NOUN
ejpam-6040	311	23	1	1	NUM
ejpam-6040	311	24	.	.	PUNCT
ejpam-6040	311	25	hence	hence	ADV
ejpam-6040	311	26	,	,	PUNCT
ejpam-6040	311	27	ζgk(k1,n	ζgk(k1,n	PROPN
ejpam-6040	311	28	)	)	PUNCT
ejpam-6040	311	29	=	=	SYM
ejpam-6040	311	30	ζgk(s	ζgk(s	PROPN
ejpam-6040	311	31	)	)	PUNCT
ejpam-6040	311	32	=	=	SYM
ejpam-6040	311	33	n+	n+	NUM
ejpam-6040	311	34	1−	1−	NUM
ejpam-6040	311	35	n+	n+	NUM
ejpam-6040	312	1	k	k	NOUN
ejpam-6040	312	2	−	−	NOUN
ejpam-6040	313	1	1	1	NUM
ejpam-6040	313	2	=	=	SYM
ejpam-6040	313	3	k	k	X
ejpam-6040	313	4	by	by	ADP
ejpam-6040	313	5	theorem	theorem	ADJ
ejpam-6040	313	6	8	8	NUM
ejpam-6040	313	7	.	.	PUNCT
ejpam-6040	313	8	corollary	corollary	ADJ
ejpam-6040	313	9	2	2	NUM
ejpam-6040	313	10	.	.	PUNCT
ejpam-6040	314	1	for	for	ADP
ejpam-6040	314	2	a	a	DET
ejpam-6040	314	3	wheel	wheel	NOUN
ejpam-6040	314	4	graph	graph	NOUN
ejpam-6040	314	5	wn	wn	NOUN
ejpam-6040	314	6	of	of	ADP
ejpam-6040	314	7	order	order	NOUN
ejpam-6040	314	8	n	n	CCONJ
ejpam-6040	314	9	,	,	PUNCT
ejpam-6040	314	10	where	where	SCONJ
ejpam-6040	314	11	n	n	PRON
ejpam-6040	314	12	≥	≥	NOUN
ejpam-6040	314	13	5	5	NUM
ejpam-6040	314	14	,	,	PUNCT
ejpam-6040	314	15	ζgk(wn	ζgk(wn	NUM
ejpam-6040	314	16	)	)	PUNCT
ejpam-6040	315	1	=	=	PUNCT
ejpam-6040	316	1			PRON
ejpam-6040	316	2	n−	n−	NOUN
ejpam-6040	316	3	1	1	NUM
ejpam-6040	316	4	if	if	SCONJ
ejpam-6040	316	5	k	k	PROPN
ejpam-6040	316	6	=	=	PUNCT
ejpam-6040	316	7	γg(wn)−	γg(wn)−	NOUN
ejpam-6040	316	8	1	1	NUM
ejpam-6040	316	9	2k	2k	NUM
ejpam-6040	316	10	+	+	CCONJ
ejpam-6040	316	11	1	1	NUM
ejpam-6040	316	12	if	if	SCONJ
ejpam-6040	316	13	n	n	NOUN
ejpam-6040	316	14	is	be	AUX
ejpam-6040	316	15	odd	odd	ADJ
ejpam-6040	316	16	2k	2k	NOUN
ejpam-6040	316	17	if	if	SCONJ
ejpam-6040	316	18	n	n	PRON
ejpam-6040	316	19	is	be	AUX
ejpam-6040	316	20	even	even	ADV
ejpam-6040	316	21	.	.	PUNCT
ejpam-6040	317	1	s.	s.	PROPN
ejpam-6040	317	2	canoy	canoy	PROPN
ejpam-6040	317	3	,	,	PUNCT
ejpam-6040	317	4	jr	jr	PROPN
ejpam-6040	317	5	.	.	PROPN
ejpam-6040	317	6	,	,	PUNCT
ejpam-6040	317	7	j.	j.	PROPN
ejpam-6040	317	8	anoche	anoche	PROPN
ejpam-6040	317	9	/	/	SYM
ejpam-6040	317	10	eur	eur	PROPN
ejpam-6040	317	11	.	.	PUNCT
ejpam-6040	318	1	j.	j.	PROPN
ejpam-6040	318	2	pure	pure	PROPN
ejpam-6040	318	3	appl	appl	PROPN
ejpam-6040	318	4	.	.	PROPN
ejpam-6040	318	5	math	math	PROPN
ejpam-6040	318	6	,	,	PUNCT
ejpam-6040	318	7	18	18	NUM
ejpam-6040	318	8	(	(	PUNCT
ejpam-6040	318	9	2	2	NUM
ejpam-6040	318	10	)	)	PUNCT
ejpam-6040	318	11	(	(	PUNCT
ejpam-6040	318	12	2025	2025	NUM
ejpam-6040	318	13	)	)	PUNCT
ejpam-6040	318	14	,	,	PUNCT
ejpam-6040	318	15	6040	6040	NUM
ejpam-6040	318	16	9	9	NUM
ejpam-6040	318	17	of	of	ADP
ejpam-6040	318	18	16	16	NUM
ejpam-6040	318	19	proof	proof	NOUN
ejpam-6040	318	20	.	.	PUNCT
ejpam-6040	319	1	let	let	VERB
ejpam-6040	319	2	v	v	X
ejpam-6040	319	3	(	(	PUNCT
ejpam-6040	319	4	wn	wn	PROPN
ejpam-6040	319	5	)	)	PUNCT
ejpam-6040	319	6	=	=	SYM
ejpam-6040	319	7	{	{	PUNCT
ejpam-6040	319	8	w1	w1	NOUN
ejpam-6040	319	9	,	,	PUNCT
ejpam-6040	319	10	w2	w2	NOUN
ejpam-6040	319	11	,	,	PUNCT
ejpam-6040	319	12	·	·	PUNCT
ejpam-6040	319	13	·	·	PUNCT
ejpam-6040	319	14	·	·	PUNCT
ejpam-6040	319	15	wn	wn	NOUN
ejpam-6040	319	16	}	}	PUNCT
ejpam-6040	319	17	where	where	SCONJ
ejpam-6040	319	18	w1	w1	NOUN
ejpam-6040	319	19	has	have	VERB
ejpam-6040	319	20	degree	degree	NOUN
ejpam-6040	319	21	n	n	CCONJ
ejpam-6040	319	22	−	−	PROPN
ejpam-6040	319	23	1	1	NUM
ejpam-6040	319	24	.	.	PUNCT
ejpam-6040	319	25	by	by	ADP
ejpam-6040	319	26	theorem	theorem	NOUN
ejpam-6040	319	27	1(iv	1(iv	NUM
ejpam-6040	319	28	)	)	PUNCT
ejpam-6040	319	29	,	,	PUNCT
ejpam-6040	319	30	γg(wn	γg(wn	PROPN
ejpam-6040	319	31	)	)	PUNCT
ejpam-6040	320	1	=	=	SYM
ejpam-6040	320	2	⌈n−1	⌈n−1	NOUN
ejpam-6040	320	3	2	2	NUM
ejpam-6040	320	4	⌉.	⌉.	ADV
ejpam-6040	320	5	if	if	SCONJ
ejpam-6040	320	6	k	k	NOUN
ejpam-6040	320	7	=	=	PUNCT
ejpam-6040	320	8	⌈n−1	⌈n−1	PROPN
ejpam-6040	320	9	2	2	NUM
ejpam-6040	320	10	⌉	⌉	X
ejpam-6040	320	11	−	−	PROPN
ejpam-6040	320	12	1	1	NUM
ejpam-6040	320	13	,	,	PUNCT
ejpam-6040	320	14	then	then	ADV
ejpam-6040	320	15	ζgk(wn	ζgk(wn	X
ejpam-6040	320	16	)	)	PUNCT
ejpam-6040	320	17	=	=	SYM
ejpam-6040	320	18	n	n	CCONJ
ejpam-6040	320	19	−	−	PROPN
ejpam-6040	320	20	1	1	NUM
ejpam-6040	320	21	by	by	ADP
ejpam-6040	320	22	lemma	lemma	PROPN
ejpam-6040	320	23	1	1	NUM
ejpam-6040	320	24	.	.	PUNCT
ejpam-6040	321	1	let	let	VERB
ejpam-6040	321	2	1	1	NUM
ejpam-6040	321	3	≤	≤	NOUN
ejpam-6040	322	1	k	k	X
ejpam-6040	322	2	<	<	X
ejpam-6040	322	3	⌈n−1	⌈n−1	PROPN
ejpam-6040	322	4	2	2	NUM
ejpam-6040	322	5	⌉	⌉	SCONJ
ejpam-6040	322	6	−	−	PROPN
ejpam-6040	322	7	1	1	NUM
ejpam-6040	322	8	.	.	PUNCT
ejpam-6040	323	1	if	if	SCONJ
ejpam-6040	323	2	n	n	NOUN
ejpam-6040	323	3	is	be	AUX
ejpam-6040	323	4	odd	odd	ADJ
ejpam-6040	323	5	,	,	PUNCT
ejpam-6040	323	6	then	then	ADV
ejpam-6040	323	7	γg(wn	γg(wn	PROPN
ejpam-6040	323	8	)	)	PUNCT
ejpam-6040	324	1	=	=	SYM
ejpam-6040	324	2	n−1	n−1	PROPN
ejpam-6040	324	3	2	2	NUM
ejpam-6040	324	4	.	.	PUNCT
ejpam-6040	325	1	choose	choose	VERB
ejpam-6040	325	2	the	the	DET
ejpam-6040	325	3	(	(	PUNCT
ejpam-6040	325	4	n−1	n−1	PROPN
ejpam-6040	325	5	2	2	NUM
ejpam-6040	325	6	−	−	NOUN
ejpam-6040	325	7	k)-element	k)-element	PUNCT
ejpam-6040	325	8	set	set	NOUN
ejpam-6040	325	9	s	s	PART
ejpam-6040	325	10	=	=	PUNCT
ejpam-6040	325	11	{	{	PUNCT
ejpam-6040	325	12	w2	w2	NOUN
ejpam-6040	325	13	,	,	PUNCT
ejpam-6040	325	14	w4	w4	NOUN
ejpam-6040	325	15	,	,	PUNCT
ejpam-6040	325	16	·	·	PUNCT
ejpam-6040	325	17	·	·	PUNCT
ejpam-6040	325	18	·	·	PUNCT
ejpam-6040	325	19	,	,	PUNCT
ejpam-6040	325	20	wn−2k−1	wn−2k−1	NOUN
ejpam-6040	325	21	}	}	PUNCT
ejpam-6040	325	22	.	.	PUNCT
ejpam-6040	326	1	then	then	ADV
ejpam-6040	326	2	s	s	VERB
ejpam-6040	326	3	is	be	AUX
ejpam-6040	326	4	a	a	DET
ejpam-6040	326	5	ζgk	ζgk	ADJ
ejpam-6040	326	6	-set	-set	ADJ
ejpam-6040	326	7	of	of	ADP
ejpam-6040	326	8	wn	wn	PROPN
ejpam-6040	326	9	and	and	CCONJ
ejpam-6040	326	10	λk	λk	ADP
ejpam-6040	326	11	2(wn	2(wn	NUM
ejpam-6040	326	12	)	)	PUNCT
ejpam-6040	326	13	=	=	PUNCT
ejpam-6040	327	1	n−2k−1	n−2k−1	ADV
ejpam-6040	327	2	2	2	NUM
ejpam-6040	327	3	.	.	PUNCT
ejpam-6040	328	1	by	by	ADP
ejpam-6040	328	2	theorem	theorem	ADJ
ejpam-6040	328	3	8	8	NUM
ejpam-6040	328	4	,	,	PUNCT
ejpam-6040	328	5	ζgk(wn	ζgk(wn	NUM
ejpam-6040	328	6	)	)	PUNCT
ejpam-6040	328	7	=	=	SYM
ejpam-6040	328	8	ζgk(s	ζgk(s	PROPN
ejpam-6040	328	9	)	)	PUNCT
ejpam-6040	328	10	=	=	SYM
ejpam-6040	329	1	n	n	PRON
ejpam-6040	329	2	−	−	PROPN
ejpam-6040	330	1	n−1	n−1	PROPN
ejpam-6040	330	2	2	2	NUM
ejpam-6040	330	3	+	+	CCONJ
ejpam-6040	330	4	k	k	PROPN
ejpam-6040	330	5	−	−	NOUN
ejpam-6040	331	1	n−2k−1	n−2k−1	ADV
ejpam-6040	331	2	2	2	NUM
ejpam-6040	331	3	=	=	SYM
ejpam-6040	331	4	2k	2k	NOUN
ejpam-6040	331	5	+	+	CCONJ
ejpam-6040	331	6	1	1	X
ejpam-6040	331	7	.	.	X
ejpam-6040	331	8	hence	hence	ADV
ejpam-6040	331	9	,	,	PUNCT
ejpam-6040	331	10	ζgk(wn	ζgk(wn	X
ejpam-6040	331	11	)	)	PUNCT
ejpam-6040	332	1	=	=	SYM
ejpam-6040	332	2	2k	2k	NUM
ejpam-6040	332	3	+	+	CCONJ
ejpam-6040	332	4	1	1	X
ejpam-6040	332	5	.	.	X
ejpam-6040	333	1	if	if	SCONJ
ejpam-6040	333	2	n	n	PRON
ejpam-6040	333	3	is	be	AUX
ejpam-6040	333	4	even	even	ADV
ejpam-6040	333	5	,	,	PUNCT
ejpam-6040	333	6	then	then	ADV
ejpam-6040	333	7	choose	choose	VERB
ejpam-6040	333	8	the	the	DET
ejpam-6040	333	9	(	(	PUNCT
ejpam-6040	333	10	n2	n2	PROPN
ejpam-6040	333	11	−	−	PROPN
ejpam-6040	333	12	k)-element	k)-element	PUNCT
ejpam-6040	333	13	set	set	VERB
ejpam-6040	333	14	s	s	PART
ejpam-6040	333	15	=	=	PUNCT
ejpam-6040	333	16	{	{	PUNCT
ejpam-6040	333	17	w2	w2	NOUN
ejpam-6040	333	18	,	,	PUNCT
ejpam-6040	333	19	w4	w4	NOUN
ejpam-6040	333	20	,	,	PUNCT
ejpam-6040	333	21	·	·	PUNCT
ejpam-6040	333	22	·	·	PUNCT
ejpam-6040	333	23	·	·	PUNCT
ejpam-6040	333	24	,	,	PUNCT
ejpam-6040	333	25	wn−2k	wn−2k	PROPN
ejpam-6040	333	26	}	}	PUNCT
ejpam-6040	333	27	.	.	PUNCT
ejpam-6040	334	1	then	then	ADV
ejpam-6040	334	2	s	s	VERB
ejpam-6040	334	3	is	be	AUX
ejpam-6040	334	4	a	a	DET
ejpam-6040	334	5	ζgk	ζgk	ADJ
ejpam-6040	334	6	-set	-set	ADJ
ejpam-6040	334	7	of	of	ADP
ejpam-6040	334	8	wn	wn	PROPN
ejpam-6040	334	9	and	and	CCONJ
ejpam-6040	334	10	λk	λk	ADP
ejpam-6040	334	11	2(wn	2(wn	NUM
ejpam-6040	334	12	)	)	PUNCT
ejpam-6040	334	13	=	=	SYM
ejpam-6040	335	1	n−2k	n−2k	ADV
ejpam-6040	335	2	2	2	NUM
ejpam-6040	335	3	.	.	PUNCT
ejpam-6040	336	1	by	by	ADP
ejpam-6040	336	2	theorem	theorem	NOUN
ejpam-6040	336	3	8	8	NUM
ejpam-6040	336	4	,	,	PUNCT
ejpam-6040	336	5	ζgk(wn	ζgk(wn	NUM
ejpam-6040	336	6	)	)	PUNCT
ejpam-6040	336	7	=	=	SYM
ejpam-6040	336	8	ζgk(s	ζgk(s	PROPN
ejpam-6040	336	9	)	)	PUNCT
ejpam-6040	336	10	=	=	PUNCT
ejpam-6040	336	11	n−	n−	NOUN
ejpam-6040	336	12	n	n	NOUN
ejpam-6040	336	13	2	2	NUM
ejpam-6040	336	14	+	+	CCONJ
ejpam-6040	336	15	k	k	NOUN
ejpam-6040	336	16	−	−	NOUN
ejpam-6040	336	17	n−2k	n−2k	NOUN
ejpam-6040	336	18	2	2	NUM
ejpam-6040	336	19	=	=	SYM
ejpam-6040	336	20	2k	2k	NUM
ejpam-6040	336	21	.	.	PUNCT
ejpam-6040	337	1	corollary	corollary	ADJ
ejpam-6040	337	2	3	3	NUM
ejpam-6040	337	3	.	.	PUNCT
ejpam-6040	338	1	for	for	ADP
ejpam-6040	338	2	the	the	DET
ejpam-6040	338	3	petersen	petersen	PROPN
ejpam-6040	338	4	graph	graph	NOUN
ejpam-6040	338	5	p	p	PROPN
ejpam-6040	338	6	,	,	PUNCT
ejpam-6040	338	7	ζgk(p	ζgk(p	PROPN
ejpam-6040	338	8	)	)	PUNCT
ejpam-6040	339	1	=	=	PUNCT
ejpam-6040	339	2			NOUN
ejpam-6040	339	3	4	4	NUM
ejpam-6040	339	4	if	if	SCONJ
ejpam-6040	339	5	k	k	NOUN
ejpam-6040	339	6	=	=	NOUN
ejpam-6040	339	7	1	1	NUM
ejpam-6040	339	8	7	7	NUM
ejpam-6040	339	9	if	if	SCONJ
ejpam-6040	339	10	k	k	NOUN
ejpam-6040	339	11	=	=	NOUN
ejpam-6040	339	12	2	2	NUM
ejpam-6040	339	13	9	9	NUM
ejpam-6040	339	14	if	if	SCONJ
ejpam-6040	339	15	k	k	PROPN
ejpam-6040	339	16	=	=	NOUN
ejpam-6040	339	17	3	3	X
ejpam-6040	339	18	.	.	PUNCT
ejpam-6040	340	1	proof	proof	NOUN
ejpam-6040	340	2	.	.	PUNCT
ejpam-6040	341	1	let	let	VERB
ejpam-6040	341	2	v	v	X
ejpam-6040	341	3	(	(	PUNCT
ejpam-6040	341	4	p	p	NOUN
ejpam-6040	341	5	)	)	PUNCT
ejpam-6040	341	6	=	=	SYM
ejpam-6040	341	7	{	{	PUNCT
ejpam-6040	341	8	w1	w1	NOUN
ejpam-6040	341	9	,	,	PUNCT
ejpam-6040	341	10	w2	w2	NOUN
ejpam-6040	341	11	,	,	PUNCT
ejpam-6040	341	12	·	·	PUNCT
ejpam-6040	341	13	·	·	PUNCT
ejpam-6040	341	14	·	·	PUNCT
ejpam-6040	341	15	,	,	PUNCT
ejpam-6040	341	16	w10	w10	PROPN
ejpam-6040	341	17	}	}	PUNCT
ejpam-6040	341	18	.	.	PUNCT
ejpam-6040	342	1	by	by	ADP
ejpam-6040	342	2	theorem	theorem	NOUN
ejpam-6040	342	3	1(vii	1(vii	NUM
ejpam-6040	342	4	)	)	PUNCT
ejpam-6040	342	5	,	,	PUNCT
ejpam-6040	342	6	γg(p	γg(p	ADP
ejpam-6040	342	7	)	)	PUNCT
ejpam-6040	342	8	=	=	SYM
ejpam-6040	343	1	4	4	X
ejpam-6040	343	2	.	.	PUNCT
ejpam-6040	344	1	if	if	SCONJ
ejpam-6040	344	2	k	k	PROPN
ejpam-6040	344	3	=	=	SYM
ejpam-6040	344	4	3	3	NUM
ejpam-6040	344	5	,	,	PUNCT
ejpam-6040	344	6	then	then	ADV
ejpam-6040	344	7	ζg3	ζg3	PROPN
ejpam-6040	344	8	(	(	PUNCT
ejpam-6040	344	9	p	p	NOUN
ejpam-6040	344	10	)	)	PUNCT
ejpam-6040	344	11	=	=	SYM
ejpam-6040	344	12	9	9	NUM
ejpam-6040	344	13	by	by	ADP
ejpam-6040	344	14	lemma	lemma	PROPN
ejpam-6040	344	15	1	1	NUM
ejpam-6040	344	16	.	.	PUNCT
ejpam-6040	345	1	let	let	VERB
ejpam-6040	345	2	1	1	NUM
ejpam-6040	345	3	≤	≤	NOUN
ejpam-6040	345	4	k	k	X
ejpam-6040	345	5	≤	≤	NUM
ejpam-6040	345	6	2	2	NUM
ejpam-6040	345	7	.	.	PUNCT
ejpam-6040	346	1	choose	choose	VERB
ejpam-6040	346	2	the	the	DET
ejpam-6040	346	3	(	(	PUNCT
ejpam-6040	346	4	4−k)-element	4−k)-element	NUM
ejpam-6040	346	5	set	set	VERB
ejpam-6040	346	6	sk	sk	X
ejpam-6040	346	7	=	=	PUNCT
ejpam-6040	346	8	{	{	PUNCT
ejpam-6040	346	9	w1	w1	NOUN
ejpam-6040	346	10	,	,	PUNCT
ejpam-6040	346	11	w2	w2	NOUN
ejpam-6040	346	12	,	,	PUNCT
ejpam-6040	346	13	w4−k	w4−k	PROPN
ejpam-6040	346	14	}	}	PUNCT
ejpam-6040	346	15	as	as	SCONJ
ejpam-6040	346	16	shown	show	VERB
ejpam-6040	346	17	in	in	ADP
ejpam-6040	346	18	figure	figure	NOUN
ejpam-6040	346	19	4	4	NUM
ejpam-6040	346	20	.	.	PUNCT
ejpam-6040	347	1	then	then	ADV
ejpam-6040	347	2	sk	sk	INTJ
ejpam-6040	347	3	is	be	AUX
ejpam-6040	347	4	a	a	DET
ejpam-6040	347	5	ζgk	ζgk	ADJ
ejpam-6040	347	6	-set	-set	ADJ
ejpam-6040	347	7	of	of	ADP
ejpam-6040	347	8	p	p	PROPN
ejpam-6040	347	9	.	.	PUNCT
ejpam-6040	348	1	thus	thus	ADV
ejpam-6040	348	2	,	,	PUNCT
ejpam-6040	348	3	λ1	λ1	PROPN
ejpam-6040	348	4	2(p	2(p	NUM
ejpam-6040	348	5	)	)	PUNCT
ejpam-6040	349	1	=	=	SYM
ejpam-6040	349	2	|i2p	|i2p	PROPN
ejpam-6040	349	3	(	(	PUNCT
ejpam-6040	349	4	s1)|	s1)|	NOUN
ejpam-6040	349	5	=	=	SYM
ejpam-6040	349	6	3	3	NUM
ejpam-6040	349	7	and	and	CCONJ
ejpam-6040	349	8	λ2	λ2	NOUN
ejpam-6040	349	9	2(p	2(p	NUM
ejpam-6040	349	10	)	)	PUNCT
ejpam-6040	350	1	=	=	SYM
ejpam-6040	350	2	|i2p	|i2p	PROPN
ejpam-6040	350	3	(	(	PUNCT
ejpam-6040	350	4	s2)|	s2)|	NOUN
ejpam-6040	350	5	=	=	SYM
ejpam-6040	350	6	1	1	NUM
ejpam-6040	350	7	by	by	ADP
ejpam-6040	350	8	theorem	theorem	NOUN
ejpam-6040	350	9	7(iii	7(iii	NUM
ejpam-6040	350	10	)	)	PUNCT
ejpam-6040	350	11	.	.	PUNCT
ejpam-6040	351	1	therefore	therefore	ADV
ejpam-6040	351	2	,	,	PUNCT
ejpam-6040	351	3	by	by	ADP
ejpam-6040	351	4	theorem	theorem	NOUN
ejpam-6040	351	5	8	8	NUM
ejpam-6040	351	6	,	,	PUNCT
ejpam-6040	351	7	ζg1	ζg1	X
ejpam-6040	351	8	(	(	PUNCT
ejpam-6040	351	9	p	p	NOUN
ejpam-6040	351	10	)	)	PUNCT
ejpam-6040	351	11	=	=	SYM
ejpam-6040	351	12	10−	10−	NOUN
ejpam-6040	351	13	4	4	NUM
ejpam-6040	351	14	+	+	NUM
ejpam-6040	351	15	k	k	NOUN
ejpam-6040	351	16	−	−	PROPN
ejpam-6040	351	17	3	3	NUM
ejpam-6040	351	18	=	=	SYM
ejpam-6040	351	19	4	4	NUM
ejpam-6040	351	20	.............	.............	PUNCT
ejpam-6040	351	21	............	............	PUNCT
ejpam-6040	351	22	............	............	PUNCT
ejpam-6040	351	23	............	............	PUNCT
ejpam-6040	351	24	............	............	PUNCT
ejpam-6040	351	25	............	............	PUNCT
ejpam-6040	351	26	............	............	PUNCT
ejpam-6040	351	27	............	............	PUNCT
ejpam-6040	351	28	............	............	PUNCT
ejpam-6040	351	29	............	............	PUNCT
ejpam-6040	351	30	............	............	PUNCT
ejpam-6040	351	31	............	............	PUNCT
ejpam-6040	351	32	............	............	PUNCT
ejpam-6040	351	33	............	............	PUNCT
ejpam-6040	351	34	............	............	PUNCT
ejpam-6040	351	35	..	..	PUNCT
ejpam-6040	351	36	....................................	....................................	PUNCT
ejpam-6040	351	37	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-6040	351	38	....................................	....................................	PUNCT
ejpam-6040	351	39	..........	..........	PUNCT
ejpam-6040	351	40	.........	.........	PUNCT
ejpam-6040	351	41	.........	.........	PUNCT
ejpam-6040	351	42	.........	.........	PUNCT
ejpam-6040	351	43	.........	.........	PUNCT
ejpam-6040	351	44	.........	.........	PUNCT
ejpam-6040	351	45	.........	.........	PUNCT
ejpam-6040	351	46	.........	.........	PUNCT
ejpam-6040	351	47	.........	.........	PUNCT
ejpam-6040	351	48	.........	.........	PUNCT
ejpam-6040	351	49	.........	.........	PUNCT
ejpam-6040	351	50	.........	.........	PUNCT
ejpam-6040	351	51	.........	.........	PUNCT
ejpam-6040	351	52	.........	.........	PUNCT
ejpam-6040	351	53	.........	.........	PUNCT
ejpam-6040	351	54	.........	.........	PUNCT
ejpam-6040	351	55	.....	.....	PUNCT
ejpam-6040	351	56	....................................	....................................	PUNCT
ejpam-6040	351	57	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-6040	351	58	....................................	....................................	PUNCT
ejpam-6040	352	1	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-6040	352	2	....................................	....................................	PUNCT
ejpam-6040	353	1	....................................	....................................	PUNCT
ejpam-6040	353	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6040	353	3	..............	..............	PUNCT
ejpam-6040	353	4	.............	.............	PUNCT
ejpam-6040	353	5	.............	.............	PUNCT
ejpam-6040	353	6	.............	.............	PUNCT
ejpam-6040	353	7	.............	.............	PUNCT
ejpam-6040	353	8	.............	.............	PUNCT
ejpam-6040	353	9	.............	.............	PUNCT
ejpam-6040	353	10	.............	.............	PUNCT
ejpam-6040	353	11	.............	.............	PUNCT
ejpam-6040	353	12	.............	.............	PUNCT
ejpam-6040	353	13	..	..	PUNCT
ejpam-6040	353	14	....	....	PUNCT
ejpam-6040	353	15	................................	................................	PUNCT
ejpam-6040	354	1	..........	..........	PUNCT
ejpam-6040	354	2	.........	.........	PUNCT
ejpam-6040	355	1	.........	.........	PUNCT
ejpam-6040	355	2	.........	.........	PUNCT
ejpam-6040	356	1	.........	.........	PUNCT
ejpam-6040	356	2	.........	.........	PUNCT
ejpam-6040	357	1	.........	.........	PUNCT
ejpam-6040	357	2	.........	.........	PUNCT
ejpam-6040	358	1	.........	.........	PUNCT
ejpam-6040	358	2	.........	.........	PUNCT
ejpam-6040	359	1	.........	.........	PUNCT
ejpam-6040	359	2	.........	.........	PUNCT
ejpam-6040	360	1	.........	.........	PUNCT
ejpam-6040	360	2	.........	.........	PUNCT
ejpam-6040	361	1	.........	.........	PUNCT
ejpam-6040	361	2	...	...	PUNCT
ejpam-6040	362	1	....................................	....................................	PUNCT
ejpam-6040	362	2	...........................................................................................................................................	...........................................................................................................................................	PUNCT
ejpam-6040	363	1	....................................	....................................	PUNCT
ejpam-6040	363	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-6040	364	1	....................................	....................................	PUNCT
ejpam-6040	364	2	......................................................................................................................................	......................................................................................................................................	PUNCT
ejpam-6040	365	1	....................................	....................................	PUNCT
ejpam-6040	365	2	.........	.........	PUNCT
ejpam-6040	365	3	........	........	PUNCT
ejpam-6040	365	4	........	........	PUNCT
ejpam-6040	365	5	........	........	PUNCT
ejpam-6040	365	6	........	........	PUNCT
ejpam-6040	365	7	........	........	PUNCT
ejpam-6040	366	1	........	........	PUNCT
ejpam-6040	366	2	.....	.....	PUNCT
ejpam-6040	367	1	....................................	....................................	PUNCT
ejpam-6040	367	2	....................................	....................................	PUNCT
ejpam-6040	368	1	..............................................................	..............................................................	PUNCT
ejpam-6040	368	2	........................................................................	........................................................................	PUNCT
ejpam-6040	368	3	......................................................	......................................................	PUNCT
ejpam-6040	368	4	....................................	....................................	PUNCT
ejpam-6040	369	1	....................................	....................................	PUNCT
ejpam-6040	369	2	..........	..........	PUNCT
ejpam-6040	370	1	.........	.........	PUNCT
ejpam-6040	370	2	.........	.........	PUNCT
ejpam-6040	371	1	.........	.........	PUNCT
ejpam-6040	371	2	.........	.........	PUNCT
ejpam-6040	371	3	........	........	PUNCT
ejpam-6040	372	1	....................................	....................................	PUNCT
ejpam-6040	373	1	....................................	....................................	PUNCT
ejpam-6040	374	1	w8	w8	PROPN
ejpam-6040	374	2	w6	w6	PROPN
ejpam-6040	374	3	w7	w7	PROPN
ejpam-6040	374	4	w3w2	w3w2	PROPN
ejpam-6040	374	5	w1	w1	NOUN
ejpam-6040	374	6	w5	w5	PROPN
ejpam-6040	374	7	w4	w4	PROPN
ejpam-6040	374	8	w10w9	w10w9	PROPN
ejpam-6040	374	9	p	p	X
ejpam-6040	374	10	:	:	PUNCT
ejpam-6040	374	11	•	•	NUM
ejpam-6040	374	12	•	•	NOUN
ejpam-6040	374	13	•	•	NOUN
ejpam-6040	374	14	.............	.............	PUNCT
ejpam-6040	374	15	............	............	PUNCT
ejpam-6040	374	16	............	............	PUNCT
ejpam-6040	374	17	............	............	PUNCT
ejpam-6040	374	18	............	............	PUNCT
ejpam-6040	374	19	............	............	PUNCT
ejpam-6040	374	20	............	............	PUNCT
ejpam-6040	374	21	............	............	PUNCT
ejpam-6040	374	22	............	............	PUNCT
ejpam-6040	374	23	............	............	PUNCT
ejpam-6040	374	24	............	............	PUNCT
ejpam-6040	374	25	............	............	PUNCT
ejpam-6040	374	26	............	............	PUNCT
ejpam-6040	374	27	............	............	PUNCT
ejpam-6040	374	28	............	............	PUNCT
ejpam-6040	374	29	..	..	PUNCT
ejpam-6040	374	30	....................................	....................................	PUNCT
ejpam-6040	375	1	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-6040	375	2	....................................	....................................	PUNCT
ejpam-6040	376	1	..........	..........	PUNCT
ejpam-6040	376	2	.........	.........	PUNCT
ejpam-6040	377	1	.........	.........	PUNCT
ejpam-6040	377	2	.........	.........	PUNCT
ejpam-6040	378	1	.........	.........	PUNCT
ejpam-6040	378	2	.........	.........	PUNCT
ejpam-6040	379	1	.........	.........	PUNCT
ejpam-6040	379	2	.........	.........	PUNCT
ejpam-6040	380	1	.........	.........	PUNCT
ejpam-6040	380	2	.........	.........	PUNCT
ejpam-6040	381	1	.........	.........	PUNCT
ejpam-6040	381	2	.........	.........	PUNCT
ejpam-6040	382	1	.........	.........	PUNCT
ejpam-6040	382	2	.........	.........	PUNCT
ejpam-6040	383	1	.........	.........	PUNCT
ejpam-6040	383	2	.........	.........	PUNCT
ejpam-6040	384	1	.....	.....	PUNCT
ejpam-6040	384	2	....................................	....................................	PUNCT
ejpam-6040	385	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-6040	385	2	....................................	....................................	PUNCT
ejpam-6040	386	1	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-6040	386	2	....................................	....................................	PUNCT
ejpam-6040	387	1	....................................	....................................	PUNCT
ejpam-6040	387	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-6040	387	3	..............	..............	PUNCT
ejpam-6040	387	4	.............	.............	PUNCT
ejpam-6040	387	5	.............	.............	PUNCT
ejpam-6040	387	6	.............	.............	PUNCT
ejpam-6040	387	7	.............	.............	PUNCT
ejpam-6040	387	8	.............	.............	PUNCT
ejpam-6040	387	9	.............	.............	PUNCT
ejpam-6040	387	10	.............	.............	PUNCT
ejpam-6040	387	11	.............	.............	PUNCT
ejpam-6040	387	12	.............	.............	PUNCT
ejpam-6040	387	13	..	..	PUNCT
ejpam-6040	387	14	....	....	PUNCT
ejpam-6040	387	15	................................	................................	PUNCT
ejpam-6040	388	1	..........	..........	PUNCT
ejpam-6040	388	2	.........	.........	PUNCT
ejpam-6040	389	1	.........	.........	PUNCT
ejpam-6040	389	2	.........	.........	PUNCT
ejpam-6040	390	1	.........	.........	PUNCT
ejpam-6040	390	2	.........	.........	PUNCT
ejpam-6040	391	1	.........	.........	PUNCT
ejpam-6040	391	2	.........	.........	PUNCT
ejpam-6040	392	1	.........	.........	PUNCT
ejpam-6040	392	2	.........	.........	PUNCT
ejpam-6040	393	1	.........	.........	PUNCT
ejpam-6040	393	2	.........	.........	PUNCT
ejpam-6040	394	1	.........	.........	PUNCT
ejpam-6040	394	2	.........	.........	PUNCT
ejpam-6040	395	1	.........	.........	PUNCT
ejpam-6040	395	2	...	...	PUNCT
ejpam-6040	396	1	....................................	....................................	PUNCT
ejpam-6040	396	2	...........................................................................................................................................	...........................................................................................................................................	PUNCT
ejpam-6040	397	1	....................................	....................................	PUNCT
ejpam-6040	397	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-6040	398	1	....................................	....................................	PUNCT
ejpam-6040	398	2	......................................................................................................................................	......................................................................................................................................	PUNCT
ejpam-6040	399	1	....................................	....................................	PUNCT
ejpam-6040	399	2	.........	.........	PUNCT
ejpam-6040	399	3	........	........	PUNCT
ejpam-6040	399	4	........	........	PUNCT
ejpam-6040	399	5	........	........	PUNCT
ejpam-6040	399	6	........	........	PUNCT
ejpam-6040	399	7	........	........	PUNCT
ejpam-6040	400	1	........	........	PUNCT
ejpam-6040	400	2	.....	.....	PUNCT
ejpam-6040	401	1	....................................	....................................	PUNCT
ejpam-6040	401	2	....................................	....................................	PUNCT
ejpam-6040	402	1	..............................................................	..............................................................	PUNCT
ejpam-6040	402	2	........................................................................	........................................................................	PUNCT
ejpam-6040	402	3	......................................................	......................................................	PUNCT
ejpam-6040	402	4	....................................	....................................	PUNCT
ejpam-6040	403	1	....................................	....................................	PUNCT
ejpam-6040	403	2	..........	..........	PUNCT
ejpam-6040	404	1	.........	.........	PUNCT
ejpam-6040	404	2	.........	.........	PUNCT
ejpam-6040	405	1	.........	.........	PUNCT
ejpam-6040	405	2	.........	.........	PUNCT
ejpam-6040	405	3	........	........	PUNCT
ejpam-6040	406	1	....................................	....................................	PUNCT
ejpam-6040	407	1	....................................	....................................	PUNCT
ejpam-6040	408	1	w8	w8	PROPN
ejpam-6040	408	2	w6	w6	PROPN
ejpam-6040	408	3	w7	w7	PROPN
ejpam-6040	408	4	w3w2	w3w2	PROPN
ejpam-6040	408	5	w1	w1	NOUN
ejpam-6040	408	6	w5	w5	PROPN
ejpam-6040	408	7	w4	w4	PROPN
ejpam-6040	408	8	w10w9	w10w9	PROPN
ejpam-6040	408	9	p	p	X
ejpam-6040	408	10	:	:	PUNCT
ejpam-6040	408	11	•	•	NUM
ejpam-6040	408	12	•	•	NUM
ejpam-6040	408	13	figure	figure	NOUN
ejpam-6040	408	14	4	4	NUM
ejpam-6040	408	15	:	:	PUNCT
ejpam-6040	408	16	s1	s1	NOUN
ejpam-6040	408	17	=	=	PUNCT
ejpam-6040	408	18	{	{	PUNCT
ejpam-6040	408	19	w1	w1	NOUN
ejpam-6040	408	20	,	,	PUNCT
ejpam-6040	408	21	w2	w2	NOUN
ejpam-6040	408	22	,	,	PUNCT
ejpam-6040	408	23	w3	w3	PROPN
ejpam-6040	408	24	}	}	PUNCT
ejpam-6040	408	25	and	and	CCONJ
ejpam-6040	408	26	s2	s2	VERB
ejpam-6040	408	27	=	=	SYM
ejpam-6040	408	28	{	{	PUNCT
ejpam-6040	408	29	w1	w1	NOUN
ejpam-6040	408	30	,	,	PUNCT
ejpam-6040	408	31	w2	w2	NOUN
ejpam-6040	408	32	}	}	PUNCT
ejpam-6040	408	33	and	and	CCONJ
ejpam-6040	408	34	ζg2	ζg2	NOUN
ejpam-6040	408	35	(	(	PUNCT
ejpam-6040	408	36	p	p	NOUN
ejpam-6040	408	37	)	)	PUNCT
ejpam-6040	408	38	=	=	SYM
ejpam-6040	409	1	10−	10−	NOUN
ejpam-6040	409	2	4	4	NUM
ejpam-6040	409	3	+	+	NUM
ejpam-6040	409	4	2−	2−	NUM
ejpam-6040	409	5	1	1	NUM
ejpam-6040	409	6	=	=	SYM
ejpam-6040	409	7	7	7	NUM
ejpam-6040	409	8	.	.	PUNCT
ejpam-6040	410	1	this	this	PRON
ejpam-6040	410	2	proves	prove	VERB
ejpam-6040	410	3	the	the	DET
ejpam-6040	410	4	assertion	assertion	NOUN
ejpam-6040	410	5	.	.	PUNCT
ejpam-6040	411	1	theorem	theorem	ADJ
ejpam-6040	411	2	9	9	NUM
ejpam-6040	411	3	(	(	PUNCT
ejpam-6040	411	4	[	[	X
ejpam-6040	411	5	9	9	NUM
ejpam-6040	411	6	]	]	PUNCT
ejpam-6040	411	7	)	)	PUNCT
ejpam-6040	411	8	.	.	PUNCT
ejpam-6040	412	1	if	if	SCONJ
ejpam-6040	412	2	g	g	PROPN
ejpam-6040	412	3	=	=	SYM
ejpam-6040	412	4	km1,m2	km1,m2	PROPN
ejpam-6040	412	5	,	,	PUNCT
ejpam-6040	412	6	·	·	PUNCT
ejpam-6040	412	7	·	·	PUNCT
ejpam-6040	412	8	·	·	PUNCT
ejpam-6040	412	9	,	,	PUNCT
ejpam-6040	412	10	mr	mr	PROPN
ejpam-6040	412	11	is	be	AUX
ejpam-6040	412	12	a	a	DET
ejpam-6040	412	13	complete	complete	ADJ
ejpam-6040	412	14	multipartite	multipartite	ADJ
ejpam-6040	412	15	graph	graph	NOUN
ejpam-6040	412	16	with	with	ADP
ejpam-6040	412	17	2	2	NUM
ejpam-6040	412	18	≤	≤	NOUN
ejpam-6040	412	19	m1	m1	NOUN
ejpam-6040	412	20	≤	≤	NUM
ejpam-6040	412	21	m2	m2	PROPN
ejpam-6040	412	22	≤	≤	NOUN
ejpam-6040	412	23	·	·	PUNCT
ejpam-6040	412	24	·	·	PUNCT
ejpam-6040	412	25	·	·	PUNCT
ejpam-6040	413	1	≤	≤	NUM
ejpam-6040	414	1	mr	mr	PROPN
ejpam-6040	414	2	,	,	PUNCT
ejpam-6040	414	3	where	where	SCONJ
ejpam-6040	414	4	r	r	NOUN
ejpam-6040	414	5	≥	≥	NOUN
ejpam-6040	414	6	2	2	NUM
ejpam-6040	414	7	,	,	PUNCT
ejpam-6040	414	8	then	then	ADV
ejpam-6040	414	9	γg(g	γg(g	PUNCT
ejpam-6040	414	10	)	)	PUNCT
ejpam-6040	415	1	=	=	SYM
ejpam-6040	415	2			NOUN
ejpam-6040	415	3	2	2	NUM
ejpam-6040	415	4	if	if	SCONJ
ejpam-6040	415	5	m1	m1	NOUN
ejpam-6040	415	6	=	=	NOUN
ejpam-6040	415	7	2	2	NUM
ejpam-6040	415	8	3	3	NUM
ejpam-6040	415	9	if	if	SCONJ
ejpam-6040	415	10	m1	m1	PROPN
ejpam-6040	415	11	=	=	NOUN
ejpam-6040	415	12	3	3	NUM
ejpam-6040	415	13	4	4	NUM
ejpam-6040	415	14	if	if	SCONJ
ejpam-6040	415	15	m1	m1	PROPN
ejpam-6040	415	16	≥	≥	NUM
ejpam-6040	415	17	4	4	NUM
ejpam-6040	415	18	.	.	PUNCT
ejpam-6040	415	19	theorem	theorem	VERB
ejpam-6040	415	20	10	10	NUM
ejpam-6040	415	21	.	.	PUNCT
ejpam-6040	416	1	for	for	ADP
ejpam-6040	416	2	a	a	DET
ejpam-6040	416	3	complete	complete	ADJ
ejpam-6040	416	4	multipartite	multipartite	ADJ
ejpam-6040	416	5	graph	graph	NOUN
ejpam-6040	416	6	g	g	PROPN
ejpam-6040	416	7	=	=	PUNCT
ejpam-6040	416	8	km1,m2	km1,m2	PROPN
ejpam-6040	416	9	,	,	PUNCT
ejpam-6040	416	10	·	·	PUNCT
ejpam-6040	416	11	·	·	PUNCT
ejpam-6040	416	12	·	·	PUNCT
ejpam-6040	416	13	,	,	PUNCT
ejpam-6040	416	14	mr	mr	PROPN
ejpam-6040	416	15	where	where	SCONJ
ejpam-6040	416	16	r	r	NOUN
ejpam-6040	416	17	≥	≥	NUM
ejpam-6040	416	18	2	2	NUM
ejpam-6040	416	19	and	and	CCONJ
ejpam-6040	416	20	2	2	NUM
ejpam-6040	416	21	≤	≤	NOUN
ejpam-6040	416	22	m1	m1	NOUN
ejpam-6040	416	23	≤	≤	NUM
ejpam-6040	416	24	m2	m2	PROPN
ejpam-6040	416	25	≤	≤	NOUN
ejpam-6040	416	26	·	·	PUNCT
ejpam-6040	416	27	·	·	PUNCT
ejpam-6040	416	28	·	·	PUNCT
ejpam-6040	416	29	≤	≤	NUM
ejpam-6040	417	1	mr	mr	PROPN
ejpam-6040	417	2	,	,	PUNCT
ejpam-6040	417	3	we	we	PRON
ejpam-6040	417	4	have	have	VERB
ejpam-6040	417	5	s.	s.	PROPN
ejpam-6040	417	6	canoy	canoy	PROPN
ejpam-6040	417	7	,	,	PUNCT
ejpam-6040	417	8	jr	jr	PROPN
ejpam-6040	417	9	.	.	PROPN
ejpam-6040	417	10	,	,	PUNCT
ejpam-6040	417	11	j.	j.	PROPN
ejpam-6040	417	12	anoche	anoche	PROPN
ejpam-6040	417	13	/	/	SYM
ejpam-6040	417	14	eur	eur	PROPN
ejpam-6040	417	15	.	.	PUNCT
ejpam-6040	418	1	j.	j.	PROPN
ejpam-6040	418	2	pure	pure	PROPN
ejpam-6040	418	3	appl	appl	PROPN
ejpam-6040	418	4	.	.	PROPN
ejpam-6040	418	5	math	math	PROPN
ejpam-6040	418	6	,	,	PUNCT
ejpam-6040	418	7	18	18	NUM
ejpam-6040	418	8	(	(	PUNCT
ejpam-6040	418	9	2	2	NUM
ejpam-6040	418	10	)	)	PUNCT
ejpam-6040	418	11	(	(	PUNCT
ejpam-6040	418	12	2025	2025	NUM
ejpam-6040	418	13	)	)	PUNCT
ejpam-6040	418	14	,	,	PUNCT
ejpam-6040	418	15	6040	6040	NUM
ejpam-6040	418	16	10	10	NUM
ejpam-6040	418	17	of	of	ADP
ejpam-6040	418	18	16	16	NUM
ejpam-6040	418	19	ζgk(g	ζgk(g	NOUN
ejpam-6040	418	20	)	)	PUNCT
ejpam-6040	418	21	=	=	PUNCT
ejpam-6040	419	1			PRON
ejpam-6040	419	2	n−	n−	NOUN
ejpam-6040	419	3	1	1	NUM
ejpam-6040	419	4	if	if	SCONJ
ejpam-6040	419	5	k	k	NOUN
ejpam-6040	419	6	=	=	PUNCT
ejpam-6040	419	7	γg(g)−	γg(g)−	NOUN
ejpam-6040	419	8	1	1	NUM
ejpam-6040	419	9	1	1	NUM
ejpam-6040	419	10	if	if	SCONJ
ejpam-6040	419	11	m1	m1	PROPN
ejpam-6040	419	12	=	=	PUNCT
ejpam-6040	419	13	3	3	NUM
ejpam-6040	419	14	and	and	CCONJ
ejpam-6040	419	15	k	k	NOUN
ejpam-6040	419	16	=	=	SYM
ejpam-6040	419	17	1	1	NUM
ejpam-6040	419	18	m1	m1	PROPN
ejpam-6040	420	1	+	+	CCONJ
ejpam-6040	420	2	k	k	PROPN
ejpam-6040	421	1	−	−	PROPN
ejpam-6040	421	2	4	4	NUM
ejpam-6040	421	3	if	if	SCONJ
ejpam-6040	421	4	m1	m1	PROPN
ejpam-6040	421	5	≥	≥	NUM
ejpam-6040	421	6	4	4	NUM
ejpam-6040	421	7	and	and	CCONJ
ejpam-6040	421	8	1	1	NUM
ejpam-6040	421	9	≤	≤	NUM
ejpam-6040	421	10	k	k	X
ejpam-6040	421	11	≤	≤	NUM
ejpam-6040	421	12	2	2	NUM
ejpam-6040	421	13	.	.	PUNCT
ejpam-6040	421	14	where	where	SCONJ
ejpam-6040	421	15	n	n	NOUN
ejpam-6040	421	16	=	=	SYM
ejpam-6040	421	17	∑r	∑r	PROPN
ejpam-6040	421	18	j=1mj	j=1mj	PROPN
ejpam-6040	421	19	.	.	PUNCT
ejpam-6040	422	1	proof	proof	NOUN
ejpam-6040	422	2	.	.	PUNCT
ejpam-6040	423	1	let	let	VERB
ejpam-6040	423	2	q1	q1	PROPN
ejpam-6040	423	3	,	,	PUNCT
ejpam-6040	423	4	q2	q2	NOUN
ejpam-6040	423	5	,	,	PUNCT
ejpam-6040	423	6	·	·	PUNCT
ejpam-6040	423	7	·	·	PUNCT
ejpam-6040	423	8	·	·	PUNCT
ejpam-6040	423	9	,	,	PUNCT
ejpam-6040	423	10	qr	qr	INTJ
ejpam-6040	423	11	be	be	AUX
ejpam-6040	423	12	the	the	DET
ejpam-6040	423	13	partite	partite	ADJ
ejpam-6040	423	14	sets	set	NOUN
ejpam-6040	423	15	of	of	ADP
ejpam-6040	423	16	g	g	NOUN
ejpam-6040	423	17	with	with	ADP
ejpam-6040	423	18	|qj	|qj	NUM
ejpam-6040	423	19	|	|	ADV
ejpam-6040	423	20	=	=	SYM
ejpam-6040	423	21	mj	mj	PROPN
ejpam-6040	423	22	for	for	ADP
ejpam-6040	423	23	each	each	DET
ejpam-6040	423	24	j	j	PROPN
ejpam-6040	423	25	∈	∈	PROPN
ejpam-6040	424	1	[	[	X
ejpam-6040	424	2	r	r	X
ejpam-6040	424	3	]	]	PUNCT
ejpam-6040	424	4	.	.	PUNCT
ejpam-6040	425	1	consider	consider	VERB
ejpam-6040	425	2	the	the	DET
ejpam-6040	425	3	following	follow	VERB
ejpam-6040	425	4	cases	case	NOUN
ejpam-6040	425	5	:	:	PUNCT
ejpam-6040	425	6	case	case	NOUN
ejpam-6040	425	7	1	1	NUM
ejpam-6040	425	8	:	:	PUNCT
ejpam-6040	425	9	k	k	X
ejpam-6040	425	10	=	=	NOUN
ejpam-6040	425	11	γg(g)−	γg(g)−	NOUN
ejpam-6040	425	12	1	1	NUM
ejpam-6040	425	13	.	.	PUNCT
ejpam-6040	425	14	by	by	ADP
ejpam-6040	425	15	lemma	lemma	PROPN
ejpam-6040	425	16	1	1	NUM
ejpam-6040	425	17	,	,	PUNCT
ejpam-6040	425	18	ζgk(g	ζgk(g	PROPN
ejpam-6040	425	19	)	)	PUNCT
ejpam-6040	425	20	=	=	SYM
ejpam-6040	425	21	n−	n−	NOUN
ejpam-6040	425	22	1	1	NUM
ejpam-6040	425	23	.	.	PUNCT
ejpam-6040	425	24	case	case	NOUN
ejpam-6040	425	25	2	2	NUM
ejpam-6040	425	26	:	:	PUNCT
ejpam-6040	425	27	m1	m1	PROPN
ejpam-6040	425	28	=	=	SYM
ejpam-6040	425	29	3	3	NUM
ejpam-6040	425	30	and	and	CCONJ
ejpam-6040	425	31	k	k	NOUN
ejpam-6040	425	32	=	=	NOUN
ejpam-6040	425	33	1	1	X
ejpam-6040	425	34	.	.	PUNCT
ejpam-6040	425	35	by	by	ADP
ejpam-6040	425	36	theorem	theorem	NOUN
ejpam-6040	425	37	9	9	NUM
ejpam-6040	425	38	,	,	PUNCT
ejpam-6040	425	39	γg(g	γg(g	NOUN
ejpam-6040	425	40	)	)	PUNCT
ejpam-6040	425	41	=	=	SYM
ejpam-6040	426	1	3	3	X
ejpam-6040	426	2	.	.	PUNCT
ejpam-6040	426	3	then	then	ADV
ejpam-6040	426	4	any	any	DET
ejpam-6040	426	5	2	2	NUM
ejpam-6040	426	6	-	-	PUNCT
ejpam-6040	426	7	element	element	NOUN
ejpam-6040	426	8	subset	subset	NOUN
ejpam-6040	426	9	s	s	PROPN
ejpam-6040	426	10	of	of	ADP
ejpam-6040	426	11	v	v	PROPN
ejpam-6040	426	12	(	(	PUNCT
ejpam-6040	426	13	q1	q1	PROPN
ejpam-6040	426	14	)	)	PUNCT
ejpam-6040	426	15	is	be	AUX
ejpam-6040	426	16	a	a	DET
ejpam-6040	426	17	ζgk	ζgk	ADJ
ejpam-6040	426	18	-set	-set	ADJ
ejpam-6040	426	19	of	of	ADP
ejpam-6040	426	20	g	g	PROPN
ejpam-6040	426	21	and	and	CCONJ
ejpam-6040	426	22	λk	λk	ADP
ejpam-6040	426	23	2(g	2(g	NUM
ejpam-6040	426	24	)	)	PUNCT
ejpam-6040	426	25	=	=	SYM
ejpam-6040	427	1	∑r	∑r	PROPN
ejpam-6040	427	2	j=2mj	j=2mj	ADP
ejpam-6040	427	3	.	.	PUNCT
ejpam-6040	428	1	by	by	ADP
ejpam-6040	428	2	theorem	theorem	ADJ
ejpam-6040	428	3	8	8	NUM
ejpam-6040	428	4	,	,	PUNCT
ejpam-6040	428	5	ζgk(g	ζgk(g	PROPN
ejpam-6040	428	6	)	)	PUNCT
ejpam-6040	428	7	=	=	SYM
ejpam-6040	428	8	ζgk(s	ζgk(s	PROPN
ejpam-6040	428	9	)	)	PUNCT
ejpam-6040	429	1	=	=	PUNCT
ejpam-6040	429	2	∑r	∑r	PROPN
ejpam-6040	429	3	j=1mj	j=1mj	PROPN
ejpam-6040	430	1	−	−	NOUN
ejpam-6040	430	2	3	3	NUM
ejpam-6040	431	1	+	+	SYM
ejpam-6040	431	2	1−	1−	NUM
ejpam-6040	431	3	∑r	∑r	PROPN
ejpam-6040	431	4	j=2mj	j=2mj	PUNCT
ejpam-6040	431	5	=	=	SYM
ejpam-6040	431	6	1	1	X
ejpam-6040	431	7	.	.	X
ejpam-6040	431	8	case	case	NOUN
ejpam-6040	431	9	3	3	NUM
ejpam-6040	431	10	:	:	PUNCT
ejpam-6040	431	11	m1	m1	NOUN
ejpam-6040	431	12	≥	≥	NUM
ejpam-6040	431	13	4	4	NUM
ejpam-6040	431	14	and	and	CCONJ
ejpam-6040	431	15	1	1	NUM
ejpam-6040	431	16	≤	≤	NUM
ejpam-6040	431	17	k	k	X
ejpam-6040	431	18	≤	≤	ADJ
ejpam-6040	431	19	2	2	NUM
ejpam-6040	431	20	.	.	PUNCT
ejpam-6040	431	21	by	by	ADP
ejpam-6040	431	22	theorem	theorem	NOUN
ejpam-6040	431	23	9	9	NUM
ejpam-6040	431	24	,	,	PUNCT
ejpam-6040	431	25	γg(g	γg(g	NOUN
ejpam-6040	431	26	)	)	PUNCT
ejpam-6040	431	27	=	=	SYM
ejpam-6040	431	28	4	4	X
ejpam-6040	431	29	.	.	X
ejpam-6040	431	30	choose	choose	VERB
ejpam-6040	431	31	an	an	DET
ejpam-6040	431	32	(	(	PUNCT
ejpam-6040	431	33	4	4	NUM
ejpam-6040	431	34	−	−	NOUN
ejpam-6040	431	35	k)-element	k)-element	PUNCT
ejpam-6040	431	36	set	set	VERB
ejpam-6040	431	37	s′	s′	ADJ
ejpam-6040	431	38	=	=	PUNCT
ejpam-6040	431	39	{	{	PUNCT
ejpam-6040	431	40	{	{	PUNCT
ejpam-6040	431	41	q11	q11	NOUN
ejpam-6040	431	42	,	,	PUNCT
ejpam-6040	431	43	q21	q21	NOUN
ejpam-6040	431	44	,	,	PUNCT
ejpam-6040	431	45	q	q	NOUN
ejpam-6040	431	46	4−k	4−k	NUM
ejpam-6040	431	47	1	1	NUM
ejpam-6040	431	48	}	}	PUNCT
ejpam-6040	431	49	where	where	SCONJ
ejpam-6040	431	50	qt1	qt1	PROPN
ejpam-6040	431	51	∈	∈	PROPN
ejpam-6040	431	52	q1	q1	PROPN
ejpam-6040	431	53	and	and	CCONJ
ejpam-6040	431	54	t	t	NOUN
ejpam-6040	431	55	∈	∈	PROPN
ejpam-6040	431	56	{	{	PUNCT
ejpam-6040	431	57	1	1	NUM
ejpam-6040	431	58	,	,	PUNCT
ejpam-6040	431	59	2	2	NUM
ejpam-6040	431	60	,	,	PUNCT
ejpam-6040	431	61	4−k	4−k	NUM
ejpam-6040	431	62	}	}	PUNCT
ejpam-6040	431	63	.	.	PUNCT
ejpam-6040	432	1	then	then	ADV
ejpam-6040	432	2	s′	s′	PROPN
ejpam-6040	432	3	is	be	AUX
ejpam-6040	432	4	a	a	DET
ejpam-6040	432	5	ζgk	ζgk	ADJ
ejpam-6040	432	6	-set	-set	ADJ
ejpam-6040	432	7	of	of	ADP
ejpam-6040	432	8	g	g	PROPN
ejpam-6040	432	9	and	and	CCONJ
ejpam-6040	432	10	λk	λk	ADP
ejpam-6040	432	11	2(g	2(g	NUM
ejpam-6040	432	12	)	)	PUNCT
ejpam-6040	433	1	=	=	SYM
ejpam-6040	434	1	∑r	∑r	PROPN
ejpam-6040	434	2	j=2mj	j=2mj	ADP
ejpam-6040	434	3	.	.	PUNCT
ejpam-6040	435	1	by	by	ADP
ejpam-6040	435	2	theorem	theorem	ADJ
ejpam-6040	435	3	8	8	NUM
ejpam-6040	435	4	,	,	PUNCT
ejpam-6040	435	5	ζgk(g	ζgk(g	PROPN
ejpam-6040	435	6	)	)	PUNCT
ejpam-6040	435	7	=	=	SYM
ejpam-6040	435	8	ζgk(s	ζgk(s	PROPN
ejpam-6040	435	9	)	)	PUNCT
ejpam-6040	435	10	=	=	PUNCT
ejpam-6040	436	1	r∑	r∑	NOUN
ejpam-6040	436	2	j=1	j=1	NOUN
ejpam-6040	436	3	mj	mj	PROPN
ejpam-6040	436	4	−	−	NOUN
ejpam-6040	437	1	4	4	NUM
ejpam-6040	437	2	+	+	CCONJ
ejpam-6040	437	3	k	k	NOUN
ejpam-6040	437	4	−	−	X
ejpam-6040	437	5	r∑	r∑	NOUN
ejpam-6040	437	6	j=2	j=2	PROPN
ejpam-6040	437	7	mj	mj	NOUN
ejpam-6040	437	8	=	=	SYM
ejpam-6040	437	9	m1	m1	PROPN
ejpam-6040	438	1	+	+	CCONJ
ejpam-6040	438	2	k	k	PROPN
ejpam-6040	438	3	−	−	NOUN
ejpam-6040	439	1	4	4	X
ejpam-6040	439	2	.	.	PUNCT
ejpam-6040	440	1	this	this	PRON
ejpam-6040	440	2	proves	prove	VERB
ejpam-6040	440	3	the	the	DET
ejpam-6040	440	4	assertion	assertion	NOUN
ejpam-6040	440	5	.	.	PUNCT
ejpam-6040	441	1	the	the	DET
ejpam-6040	441	2	next	next	ADJ
ejpam-6040	441	3	result	result	NOUN
ejpam-6040	441	4	is	be	AUX
ejpam-6040	441	5	a	a	DET
ejpam-6040	441	6	consequence	consequence	NOUN
ejpam-6040	441	7	of	of	ADP
ejpam-6040	441	8	theorem	theorem	ADJ
ejpam-6040	441	9	10	10	NUM
ejpam-6040	441	10	.	.	PUNCT
ejpam-6040	441	11	corollary	corollary	ADJ
ejpam-6040	441	12	4	4	NUM
ejpam-6040	441	13	.	.	PUNCT
ejpam-6040	441	14	for	for	ADP
ejpam-6040	441	15	a	a	DET
ejpam-6040	441	16	complete	complete	ADJ
ejpam-6040	441	17	bipartite	bipartite	NOUN
ejpam-6040	441	18	graph	graph	NOUN
ejpam-6040	441	19	km	km	PROPN
ejpam-6040	441	20	,	,	PUNCT
ejpam-6040	441	21	n	n	CCONJ
ejpam-6040	441	22	where	where	SCONJ
ejpam-6040	441	23	2	2	NUM
ejpam-6040	441	24	≤	≤	NUM
ejpam-6040	441	25	m	m	VERB
ejpam-6040	441	26	≤	≤	NOUN
ejpam-6040	441	27	n	n	CCONJ
ejpam-6040	441	28	,	,	PUNCT
ejpam-6040	441	29	ζgk(km	ζgk(km	NOUN
ejpam-6040	441	30	,	,	PUNCT
ejpam-6040	441	31	n	n	CCONJ
ejpam-6040	441	32	)	)	PUNCT
ejpam-6040	441	33	=	=	SYM
ejpam-6040	442	1			PRON
ejpam-6040	442	2	m+	m+	VERB
ejpam-6040	442	3	n−	n−	NOUN
ejpam-6040	442	4	1	1	NUM
ejpam-6040	442	5	if	if	SCONJ
ejpam-6040	442	6	k	k	NOUN
ejpam-6040	442	7	=	=	PUNCT
ejpam-6040	442	8	γg(g)−	γg(g)−	NOUN
ejpam-6040	442	9	1	1	NUM
ejpam-6040	442	10	1	1	NUM
ejpam-6040	442	11	if	if	SCONJ
ejpam-6040	442	12	m	m	VERB
ejpam-6040	442	13	=	=	NOUN
ejpam-6040	442	14	3	3	NUM
ejpam-6040	442	15	and	and	CCONJ
ejpam-6040	442	16	k	k	NOUN
ejpam-6040	442	17	=	=	SYM
ejpam-6040	442	18	1	1	NUM
ejpam-6040	442	19	m+	m+	NUM
ejpam-6040	442	20	k	k	NOUN
ejpam-6040	442	21	−	−	PROPN
ejpam-6040	442	22	4	4	NUM
ejpam-6040	442	23	if	if	SCONJ
ejpam-6040	442	24	m	m	PROPN
ejpam-6040	442	25	≥	≥	VERB
ejpam-6040	442	26	4	4	NUM
ejpam-6040	442	27	and	and	CCONJ
ejpam-6040	442	28	1	1	NUM
ejpam-6040	442	29	≤	≤	NUM
ejpam-6040	442	30	k	k	X
ejpam-6040	442	31	≤	≤	NUM
ejpam-6040	442	32	2	2	NUM
ejpam-6040	442	33	.	.	PUNCT
ejpam-6040	443	1	s.	s.	PROPN
ejpam-6040	443	2	canoy	canoy	PROPN
ejpam-6040	443	3	,	,	PUNCT
ejpam-6040	443	4	jr	jr	PROPN
ejpam-6040	443	5	.	.	PROPN
ejpam-6040	443	6	,	,	PUNCT
ejpam-6040	443	7	j.	j.	PROPN
ejpam-6040	443	8	anoche	anoche	PROPN
ejpam-6040	443	9	/	/	SYM
ejpam-6040	443	10	eur	eur	PROPN
ejpam-6040	443	11	.	.	PUNCT
ejpam-6040	444	1	j.	j.	PROPN
ejpam-6040	444	2	pure	pure	PROPN
ejpam-6040	444	3	appl	appl	PROPN
ejpam-6040	444	4	.	.	PROPN
ejpam-6040	444	5	math	math	PROPN
ejpam-6040	444	6	,	,	PUNCT
ejpam-6040	444	7	18	18	NUM
ejpam-6040	444	8	(	(	PUNCT
ejpam-6040	444	9	2	2	NUM
ejpam-6040	444	10	)	)	PUNCT
ejpam-6040	444	11	(	(	PUNCT
ejpam-6040	444	12	2025	2025	NUM
ejpam-6040	444	13	)	)	PUNCT
ejpam-6040	444	14	,	,	PUNCT
ejpam-6040	444	15	6040	6040	NUM
ejpam-6040	444	16	11	11	NUM
ejpam-6040	444	17	of	of	ADP
ejpam-6040	444	18	16	16	NUM
ejpam-6040	444	19	theorem	theorem	VERB
ejpam-6040	444	20	11	11	NUM
ejpam-6040	444	21	.	.	PUNCT
ejpam-6040	445	1	for	for	ADP
ejpam-6040	445	2	a	a	DET
ejpam-6040	445	3	path	path	NOUN
ejpam-6040	445	4	pn	pn	NOUN
ejpam-6040	445	5	with	with	ADP
ejpam-6040	445	6	n	n	PRON
ejpam-6040	445	7	≥	≥	NUM
ejpam-6040	445	8	2	2	NUM
ejpam-6040	445	9	vertices	vertex	NOUN
ejpam-6040	445	10	,	,	PUNCT
ejpam-6040	445	11	ζgk(pn	ζgk(pn	NOUN
ejpam-6040	445	12	)	)	PUNCT
ejpam-6040	445	13	=	=	PUNCT
ejpam-6040	445	14			NOUN
ejpam-6040	445	15	3k	3k	NOUN
ejpam-6040	446	1	−	−	NOUN
ejpam-6040	446	2	2	2	NUM
ejpam-6040	446	3	if	if	SCONJ
ejpam-6040	446	4	n	n	NOUN
ejpam-6040	446	5	=	=	SYM
ejpam-6040	446	6	2	2	NUM
ejpam-6040	446	7	and	and	CCONJ
ejpam-6040	446	8	k	k	NOUN
ejpam-6040	446	9	=	=	SYM
ejpam-6040	446	10	2	2	NUM
ejpam-6040	446	11	or	or	CCONJ
ejpam-6040	446	12	n	n	NOUN
ejpam-6040	446	13	=	=	NOUN
ejpam-6040	446	14	3r	3r	NUM
ejpam-6040	446	15	+	+	CCONJ
ejpam-6040	446	16	2	2	NUM
ejpam-6040	446	17	and	and	CCONJ
ejpam-6040	446	18	k	k	PROPN
ejpam-6040	446	19	≤	≤	PROPN
ejpam-6040	446	20	r	r	NOUN
ejpam-6040	447	1	+	+	CCONJ
ejpam-6040	447	2	1	1	NUM
ejpam-6040	447	3	3k	3k	NOUN
ejpam-6040	447	4	−	−	NOUN
ejpam-6040	447	5	1	1	NUM
ejpam-6040	447	6	if	if	SCONJ
ejpam-6040	447	7	n	n	NOUN
ejpam-6040	447	8	=	=	NOUN
ejpam-6040	447	9	3r	3r	NUM
ejpam-6040	447	10	and	and	CCONJ
ejpam-6040	447	11	k	k	PROPN
ejpam-6040	447	12	≤	≤	NUM
ejpam-6040	447	13	r	r	NOUN
ejpam-6040	447	14	3k	3k	NUM
ejpam-6040	448	1	if	if	SCONJ
ejpam-6040	448	2	n	n	NOUN
ejpam-6040	448	3	=	=	NOUN
ejpam-6040	448	4	3r	3r	NUM
ejpam-6040	448	5	+	+	CCONJ
ejpam-6040	448	6	1	1	NUM
ejpam-6040	448	7	and	and	CCONJ
ejpam-6040	448	8	k	k	PROPN
ejpam-6040	448	9	≤	≤	PROPN
ejpam-6040	448	10	r.	r.	PROPN
ejpam-6040	448	11	proof	proof	NOUN
ejpam-6040	448	12	.	.	PUNCT
ejpam-6040	449	1	let	let	VERB
ejpam-6040	449	2	pn	pn	VERB
ejpam-6040	449	3	=	=	PUNCT
ejpam-6040	450	1	[	[	X
ejpam-6040	450	2	v1	v1	NOUN
ejpam-6040	450	3	,	,	PUNCT
ejpam-6040	450	4	v2	v2	PROPN
ejpam-6040	450	5	,	,	PUNCT
ejpam-6040	450	6	·	·	PUNCT
ejpam-6040	450	7	·	·	PUNCT
ejpam-6040	450	8	·	·	PUNCT
ejpam-6040	450	9	,	,	PUNCT
ejpam-6040	450	10	vn	vn	X
ejpam-6040	450	11	]	]	PUNCT
ejpam-6040	450	12	and	and	CCONJ
ejpam-6040	450	13	let	let	VERB
ejpam-6040	450	14	r	r	PRON
ejpam-6040	450	15	≥	≥	NOUN
ejpam-6040	450	16	1	1	NUM
ejpam-6040	450	17	.	.	PUNCT
ejpam-6040	450	18	by	by	ADP
ejpam-6040	450	19	theorem	theorem	ADJ
ejpam-6040	450	20	1(vi	1(vi	NUM
ejpam-6040	450	21	)	)	PUNCT
ejpam-6040	450	22	,	,	PUNCT
ejpam-6040	450	23	γg(pn	γg(pn	NOUN
ejpam-6040	450	24	)	)	PUNCT
ejpam-6040	450	25	=	=	SYM
ejpam-6040	451	1	⌈n+2	⌈n+2	NUM
ejpam-6040	451	2	3	3	NUM
ejpam-6040	452	1	⌉.	⌉.	ADV
ejpam-6040	452	2	if	if	SCONJ
ejpam-6040	452	3	n	n	NOUN
ejpam-6040	452	4	=	=	SYM
ejpam-6040	452	5	2	2	NUM
ejpam-6040	452	6	,	,	PUNCT
ejpam-6040	452	7	then	then	ADV
ejpam-6040	452	8	γg(p2	γg(p2	NUM
ejpam-6040	452	9	)	)	PUNCT
ejpam-6040	452	10	=	=	SYM
ejpam-6040	453	1	2	2	X
ejpam-6040	453	2	.	.	PUNCT
ejpam-6040	453	3	thus	thus	ADV
ejpam-6040	453	4	,	,	PUNCT
ejpam-6040	453	5	ζg1	ζg1	X
ejpam-6040	453	6	(	(	PUNCT
ejpam-6040	453	7	p2	p2	PROPN
ejpam-6040	453	8	)	)	PUNCT
ejpam-6040	453	9	=	=	SYM
ejpam-6040	453	10	1	1	X
ejpam-6040	453	11	.	.	PUNCT
ejpam-6040	453	12	let	let	VERB
ejpam-6040	453	13	n	n	PRON
ejpam-6040	453	14	≥	≥	NOUN
ejpam-6040	453	15	3	3	X
ejpam-6040	453	16	.	.	PUNCT
ejpam-6040	453	17	consider	consider	VERB
ejpam-6040	453	18	the	the	DET
ejpam-6040	453	19	following	follow	VERB
ejpam-6040	453	20	cases	case	NOUN
ejpam-6040	453	21	:	:	PUNCT
ejpam-6040	453	22	case	case	NOUN
ejpam-6040	453	23	1	1	NUM
ejpam-6040	453	24	:	:	PUNCT
ejpam-6040	453	25	n	n	NOUN
ejpam-6040	453	26	=	=	NOUN
ejpam-6040	453	27	3r	3r	NUM
ejpam-6040	453	28	.	.	PUNCT
ejpam-6040	454	1	by	by	ADP
ejpam-6040	454	2	theorem	theorem	ADJ
ejpam-6040	454	3	1(vi	1(vi	NUM
ejpam-6040	454	4	)	)	PUNCT
ejpam-6040	454	5	,	,	PUNCT
ejpam-6040	454	6	γg(pn	γg(pn	NOUN
ejpam-6040	454	7	)	)	PUNCT
ejpam-6040	454	8	=	=	SYM
ejpam-6040	455	1	⌈n+2	⌈n+2	NUM
ejpam-6040	455	2	3	3	NUM
ejpam-6040	456	1	⌉	⌉	ADP
ejpam-6040	456	2	=	=	PUNCT
ejpam-6040	456	3	r	r	NOUN
ejpam-6040	456	4	+	+	NOUN
ejpam-6040	456	5	1	1	NUM
ejpam-6040	456	6	.	.	PUNCT
ejpam-6040	457	1	here	here	ADV
ejpam-6040	457	2	,	,	PUNCT
ejpam-6040	457	3	k	k	PROPN
ejpam-6040	457	4	≤	≤	NUM
ejpam-6040	457	5	r	r	NOUN
ejpam-6040	457	6	and	and	CCONJ
ejpam-6040	457	7	γg(pn	γg(pn	NOUN
ejpam-6040	457	8	)	)	PUNCT
ejpam-6040	458	1	−	−	PROPN
ejpam-6040	459	1	k	k	NOUN
ejpam-6040	459	2	=	=	PUNCT
ejpam-6040	459	3	r	r	NOUN
ejpam-6040	459	4	−	−	PROPN
ejpam-6040	460	1	k	k	NOUN
ejpam-6040	460	2	+	+	NOUN
ejpam-6040	460	3	1	1	X
ejpam-6040	460	4	.	.	X
ejpam-6040	460	5	consider	consider	VERB
ejpam-6040	460	6	an	an	DET
ejpam-6040	460	7	(	(	PUNCT
ejpam-6040	460	8	r	r	NOUN
ejpam-6040	460	9	−	−	PROPN
ejpam-6040	460	10	k	k	PROPN
ejpam-6040	461	1	+	+	PROPN
ejpam-6040	461	2	1)-element	1)-element	NUM
ejpam-6040	461	3	set	set	NOUN
ejpam-6040	461	4	s1	s1	NOUN
ejpam-6040	461	5	=	=	SYM
ejpam-6040	461	6	{	{	PUNCT
ejpam-6040	461	7	v1	v1	PROPN
ejpam-6040	461	8	,	,	PUNCT
ejpam-6040	461	9	v4	v4	NOUN
ejpam-6040	461	10	,	,	PUNCT
ejpam-6040	461	11	·	·	PUNCT
ejpam-6040	461	12	·	·	PUNCT
ejpam-6040	461	13	·	·	PUNCT
ejpam-6040	461	14	,	,	PUNCT
ejpam-6040	461	15	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	461	16	}	}	PUNCT
ejpam-6040	461	17	.	.	PUNCT
ejpam-6040	462	1	the	the	DET
ejpam-6040	462	2	set	set	NOUN
ejpam-6040	462	3	s1	s1	NOUN
ejpam-6040	462	4	is	be	AUX
ejpam-6040	462	5	a	a	DET
ejpam-6040	462	6	ζgk	ζgk	ADJ
ejpam-6040	462	7	-set	-set	ADJ
ejpam-6040	462	8	of	of	ADP
ejpam-6040	462	9	pn	pn	PROPN
ejpam-6040	462	10	and	and	CCONJ
ejpam-6040	462	11	ng	ng	PROPN
ejpam-6040	462	12	g[s1	g[s1	PROPN
ejpam-6040	462	13	]	]	X
ejpam-6040	462	14	=	=	SYM
ejpam-6040	462	15	{	{	PUNCT
ejpam-6040	462	16	v1	v1	PROPN
ejpam-6040	462	17	,	,	PUNCT
ejpam-6040	462	18	v2	v2	PROPN
ejpam-6040	462	19	,	,	PUNCT
ejpam-6040	462	20	v3	v3	PROPN
ejpam-6040	462	21	,	,	PUNCT
ejpam-6040	462	22	v4	v4	PROPN
ejpam-6040	462	23	,	,	PUNCT
ejpam-6040	462	24	·	·	PUNCT
ejpam-6040	462	25	·	·	PUNCT
ejpam-6040	462	26	·	·	PUNCT
ejpam-6040	462	27	,	,	PUNCT
ejpam-6040	462	28	v3r−3k+1	v3r−3k+1	PROPN
ejpam-6040	462	29	}	}	PUNCT
ejpam-6040	462	30	.	.	PUNCT
ejpam-6040	463	1	therefore	therefore	ADV
ejpam-6040	463	2	,	,	PUNCT
ejpam-6040	463	3	ζgk(pn	ζgk(pn	NOUN
ejpam-6040	463	4	)	)	PUNCT
ejpam-6040	463	5	=	=	SYM
ejpam-6040	463	6	ζgk(s1	ζgk(s1	NOUN
ejpam-6040	463	7	)	)	PUNCT
ejpam-6040	463	8	=	=	SYM
ejpam-6040	463	9	n−	n−	NOUN
ejpam-6040	463	10	|ng	|ng	PUNCT
ejpam-6040	463	11	g[s1]|	g[s1]|	PROPN
ejpam-6040	463	12	=	=	PROPN
ejpam-6040	463	13	3r	3r	NUM
ejpam-6040	463	14	−	−	NOUN
ejpam-6040	463	15	(	(	PUNCT
ejpam-6040	463	16	3r	3r	NUM
ejpam-6040	463	17	−	−	NOUN
ejpam-6040	463	18	3k	3k	NOUN
ejpam-6040	463	19	+	+	CCONJ
ejpam-6040	463	20	1	1	X
ejpam-6040	463	21	)	)	PUNCT
ejpam-6040	463	22	=	=	PUNCT
ejpam-6040	463	23	3k	3k	X
ejpam-6040	464	1	−	−	NOUN
ejpam-6040	464	2	1	1	X
ejpam-6040	464	3	.	.	PUNCT
ejpam-6040	464	4	case	case	NOUN
ejpam-6040	464	5	2	2	NUM
ejpam-6040	464	6	:	:	SYM
ejpam-6040	464	7	n	n	NOUN
ejpam-6040	464	8	=	=	SYM
ejpam-6040	464	9	3r	3r	NUM
ejpam-6040	464	10	+	+	CCONJ
ejpam-6040	464	11	1	1	X
ejpam-6040	464	12	.	.	PUNCT
ejpam-6040	464	13	by	by	ADP
ejpam-6040	464	14	theorem	theorem	ADJ
ejpam-6040	464	15	1(vi	1(vi	NUM
ejpam-6040	464	16	)	)	PUNCT
ejpam-6040	464	17	,	,	PUNCT
ejpam-6040	464	18	γg(pn	γg(pn	NOUN
ejpam-6040	464	19	)	)	PUNCT
ejpam-6040	464	20	=	=	SYM
ejpam-6040	465	1	⌈n+2	⌈n+2	NUM
ejpam-6040	465	2	3	3	NUM
ejpam-6040	466	1	⌉	⌉	ADP
ejpam-6040	466	2	=	=	PUNCT
ejpam-6040	466	3	r	r	NOUN
ejpam-6040	466	4	+	+	NOUN
ejpam-6040	466	5	1	1	NUM
ejpam-6040	466	6	.	.	PUNCT
ejpam-6040	466	7	then	then	ADV
ejpam-6040	466	8	k	k	PROPN
ejpam-6040	466	9	≤	≤	PROPN
ejpam-6040	466	10	r.	r.	PROPN
ejpam-6040	466	11	choose	choose	VERB
ejpam-6040	466	12	an	an	DET
ejpam-6040	466	13	(	(	PUNCT
ejpam-6040	466	14	r	r	NOUN
ejpam-6040	466	15	−	−	PROPN
ejpam-6040	466	16	k	k	PROPN
ejpam-6040	467	1	+	+	PROPN
ejpam-6040	467	2	1)-element	1)-element	NUM
ejpam-6040	467	3	set	set	NOUN
ejpam-6040	467	4	s2	s2	NOUN
ejpam-6040	467	5	=	=	SYM
ejpam-6040	467	6	{	{	PUNCT
ejpam-6040	467	7	v1	v1	PROPN
ejpam-6040	467	8	,	,	PUNCT
ejpam-6040	467	9	v4	v4	NOUN
ejpam-6040	467	10	,	,	PUNCT
ejpam-6040	467	11	·	·	PUNCT
ejpam-6040	467	12	·	·	PUNCT
ejpam-6040	467	13	·	·	PUNCT
ejpam-6040	467	14	,	,	PUNCT
ejpam-6040	467	15	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	467	16	}	}	PUNCT
ejpam-6040	467	17	.	.	PUNCT
ejpam-6040	468	1	then	then	ADV
ejpam-6040	468	2	s2	s2	PROPN
ejpam-6040	468	3	is	be	AUX
ejpam-6040	468	4	a	a	DET
ejpam-6040	468	5	ζgk	ζgk	ADJ
ejpam-6040	468	6	-set	-set	ADJ
ejpam-6040	468	7	of	of	ADP
ejpam-6040	468	8	pn	pn	PROPN
ejpam-6040	468	9	and	and	CCONJ
ejpam-6040	468	10	ng	ng	PROPN
ejpam-6040	468	11	g[s2	g[s2	NOUN
ejpam-6040	468	12	]	]	X
ejpam-6040	468	13	=	=	SYM
ejpam-6040	468	14	{	{	PUNCT
ejpam-6040	468	15	v1	v1	PROPN
ejpam-6040	468	16	,	,	PUNCT
ejpam-6040	468	17	v2	v2	PROPN
ejpam-6040	468	18	,	,	PUNCT
ejpam-6040	468	19	v3	v3	PROPN
ejpam-6040	468	20	,	,	PUNCT
ejpam-6040	468	21	v4	v4	PROPN
ejpam-6040	468	22	,	,	PUNCT
ejpam-6040	468	23	·	·	PUNCT
ejpam-6040	468	24	·	·	PUNCT
ejpam-6040	468	25	·	·	PUNCT
ejpam-6040	468	26	,	,	PUNCT
ejpam-6040	468	27	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	468	28	}	}	PUNCT
ejpam-6040	468	29	.	.	PUNCT
ejpam-6040	469	1	thus	thus	ADV
ejpam-6040	469	2	,	,	PUNCT
ejpam-6040	469	3	ζgk(pn	ζgk(pn	NOUN
ejpam-6040	469	4	)	)	PUNCT
ejpam-6040	469	5	=	=	SYM
ejpam-6040	469	6	ζgk(s2	ζgk(s2	NOUN
ejpam-6040	469	7	)	)	PUNCT
ejpam-6040	469	8	=	=	SYM
ejpam-6040	469	9	n−	n−	NOUN
ejpam-6040	469	10	|ng	|ng	NOUN
ejpam-6040	469	11	g[s2]|	g[s2]|	NOUN
ejpam-6040	469	12	=	=	SYM
ejpam-6040	469	13	(	(	PUNCT
ejpam-6040	469	14	3r	3r	NUM
ejpam-6040	469	15	+	+	SYM
ejpam-6040	469	16	1)−	1)−	NUM
ejpam-6040	469	17	(	(	PUNCT
ejpam-6040	469	18	3r	3r	NUM
ejpam-6040	469	19	−	−	NOUN
ejpam-6040	469	20	3k	3k	NOUN
ejpam-6040	470	1	+	+	CCONJ
ejpam-6040	470	2	1	1	X
ejpam-6040	470	3	)	)	PUNCT
ejpam-6040	470	4	=	=	SYM
ejpam-6040	470	5	3k	3k	X
ejpam-6040	470	6	.	.	PUNCT
ejpam-6040	471	1	case	case	NOUN
ejpam-6040	471	2	3	3	NUM
ejpam-6040	471	3	:	:	PUNCT
ejpam-6040	471	4	n	n	NOUN
ejpam-6040	471	5	=	=	SYM
ejpam-6040	471	6	3r	3r	NUM
ejpam-6040	471	7	+	+	CCONJ
ejpam-6040	471	8	2	2	X
ejpam-6040	471	9	.	.	PUNCT
ejpam-6040	471	10	by	by	ADP
ejpam-6040	471	11	theorem	theorem	ADJ
ejpam-6040	471	12	1(vi	1(vi	NUM
ejpam-6040	471	13	)	)	PUNCT
ejpam-6040	471	14	,	,	PUNCT
ejpam-6040	471	15	γg(pn	γg(pn	NOUN
ejpam-6040	471	16	)	)	PUNCT
ejpam-6040	471	17	=	=	SYM
ejpam-6040	472	1	⌈n+2	⌈n+2	NUM
ejpam-6040	472	2	3	3	NUM
ejpam-6040	473	1	⌉	⌉	ADP
ejpam-6040	473	2	=	=	PUNCT
ejpam-6040	473	3	r	r	NOUN
ejpam-6040	473	4	+	+	NOUN
ejpam-6040	473	5	2	2	NUM
ejpam-6040	473	6	.	.	X
ejpam-6040	473	7	then	then	ADV
ejpam-6040	473	8	k	k	PROPN
ejpam-6040	473	9	≤	≤	PROPN
ejpam-6040	473	10	r	r	NOUN
ejpam-6040	473	11	+	+	CCONJ
ejpam-6040	473	12	1	1	NUM
ejpam-6040	473	13	and	and	CCONJ
ejpam-6040	473	14	γg(pn)−	γg(pn)−	NOUN
ejpam-6040	473	15	k	k	X
ejpam-6040	474	1	=	=	PUNCT
ejpam-6040	474	2	r	r	NOUN
ejpam-6040	474	3	−	−	PROPN
ejpam-6040	475	1	k	k	NOUN
ejpam-6040	475	2	+	+	NOUN
ejpam-6040	475	3	2	2	X
ejpam-6040	475	4	.	.	X
ejpam-6040	475	5	consider	consider	VERB
ejpam-6040	475	6	an	an	DET
ejpam-6040	475	7	(	(	PUNCT
ejpam-6040	475	8	r	r	NOUN
ejpam-6040	475	9	−	−	PROPN
ejpam-6040	475	10	k	k	PROPN
ejpam-6040	476	1	+	+	PROPN
ejpam-6040	476	2	2)-element	2)-element	NUM
ejpam-6040	476	3	set	set	NOUN
ejpam-6040	476	4	s3	s3	PROPN
ejpam-6040	476	5	=	=	SYM
ejpam-6040	476	6	{	{	PUNCT
ejpam-6040	476	7	v1	v1	PROPN
ejpam-6040	476	8	,	,	PUNCT
ejpam-6040	476	9	v4	v4	NOUN
ejpam-6040	476	10	,	,	PUNCT
ejpam-6040	476	11	·	·	PUNCT
ejpam-6040	476	12	·	·	PUNCT
ejpam-6040	476	13	·	·	PUNCT
ejpam-6040	476	14	,	,	PUNCT
ejpam-6040	476	15	v3r−3k+4	v3r−3k+4	VERB
ejpam-6040	476	16	}	}	PUNCT
ejpam-6040	476	17	.	.	PUNCT
ejpam-6040	477	1	the	the	DET
ejpam-6040	477	2	set	set	NOUN
ejpam-6040	477	3	s3	s3	PROPN
ejpam-6040	477	4	is	be	AUX
ejpam-6040	477	5	a	a	DET
ejpam-6040	477	6	ζgk	ζgk	ADJ
ejpam-6040	477	7	-set	-set	ADJ
ejpam-6040	477	8	of	of	ADP
ejpam-6040	477	9	pn	pn	PROPN
ejpam-6040	477	10	and	and	CCONJ
ejpam-6040	477	11	ng	ng	PROPN
ejpam-6040	477	12	g[s3	g[s3	NOUN
ejpam-6040	477	13	]	]	X
ejpam-6040	477	14	=	=	SYM
ejpam-6040	477	15	{	{	PUNCT
ejpam-6040	477	16	v1	v1	PROPN
ejpam-6040	477	17	,	,	PUNCT
ejpam-6040	477	18	v2	v2	PROPN
ejpam-6040	477	19	,	,	PUNCT
ejpam-6040	477	20	v3	v3	PROPN
ejpam-6040	477	21	,	,	PUNCT
ejpam-6040	477	22	v4	v4	PROPN
ejpam-6040	477	23	,	,	PUNCT
ejpam-6040	477	24	·	·	PUNCT
ejpam-6040	477	25	·	·	PUNCT
ejpam-6040	477	26	·	·	PUNCT
ejpam-6040	477	27	,	,	PUNCT
ejpam-6040	477	28	v3r−3k+4	v3r−3k+4	VERB
ejpam-6040	477	29	}	}	PUNCT
ejpam-6040	477	30	.	.	PUNCT
ejpam-6040	478	1	therefore	therefore	ADV
ejpam-6040	478	2	,	,	PUNCT
ejpam-6040	478	3	ζgk(pn	ζgk(pn	NOUN
ejpam-6040	478	4	)	)	PUNCT
ejpam-6040	478	5	=	=	SYM
ejpam-6040	478	6	ζgk(s3	ζgk(s3	PROPN
ejpam-6040	478	7	)	)	PUNCT
ejpam-6040	479	1	=	=	SYM
ejpam-6040	479	2	n−	n−	NOUN
ejpam-6040	479	3	|ng	|ng	NOUN
ejpam-6040	479	4	g[s3]|	g[s3]|	NOUN
ejpam-6040	479	5	=	=	NOUN
ejpam-6040	479	6	3r	3r	NUM
ejpam-6040	479	7	+	+	CCONJ
ejpam-6040	479	8	2−	2−	NUM
ejpam-6040	479	9	(	(	PUNCT
ejpam-6040	479	10	3r	3r	NUM
ejpam-6040	479	11	−	−	NOUN
ejpam-6040	479	12	3k	3k	NOUN
ejpam-6040	479	13	+	+	CCONJ
ejpam-6040	479	14	4	4	X
ejpam-6040	479	15	)	)	PUNCT
ejpam-6040	479	16	=	=	PUNCT
ejpam-6040	480	1	3k	3k	X
ejpam-6040	480	2	−	−	NOUN
ejpam-6040	480	3	2	2	X
ejpam-6040	480	4	.	.	PUNCT
ejpam-6040	480	5	s.	s.	PROPN
ejpam-6040	480	6	canoy	canoy	PROPN
ejpam-6040	480	7	,	,	PUNCT
ejpam-6040	480	8	jr	jr	PROPN
ejpam-6040	480	9	.	.	PROPN
ejpam-6040	480	10	,	,	PUNCT
ejpam-6040	480	11	j.	j.	PROPN
ejpam-6040	480	12	anoche	anoche	PROPN
ejpam-6040	480	13	/	/	SYM
ejpam-6040	480	14	eur	eur	PROPN
ejpam-6040	480	15	.	.	PUNCT
ejpam-6040	481	1	j.	j.	PROPN
ejpam-6040	481	2	pure	pure	PROPN
ejpam-6040	481	3	appl	appl	PROPN
ejpam-6040	481	4	.	.	PROPN
ejpam-6040	481	5	math	math	PROPN
ejpam-6040	481	6	,	,	PUNCT
ejpam-6040	481	7	18	18	NUM
ejpam-6040	481	8	(	(	PUNCT
ejpam-6040	481	9	2	2	NUM
ejpam-6040	481	10	)	)	PUNCT
ejpam-6040	481	11	(	(	PUNCT
ejpam-6040	481	12	2025	2025	NUM
ejpam-6040	481	13	)	)	PUNCT
ejpam-6040	481	14	,	,	PUNCT
ejpam-6040	481	15	6040	6040	NUM
ejpam-6040	481	16	12	12	NUM
ejpam-6040	481	17	of	of	ADP
ejpam-6040	481	18	16	16	NUM
ejpam-6040	481	19	theorem	theorem	NOUN
ejpam-6040	481	20	12	12	NUM
ejpam-6040	481	21	.	.	PUNCT
ejpam-6040	482	1	if	if	SCONJ
ejpam-6040	482	2	cn	cn	PROPN
ejpam-6040	482	3	is	be	AUX
ejpam-6040	482	4	the	the	DET
ejpam-6040	482	5	cycle	cycle	NOUN
ejpam-6040	482	6	with	with	ADP
ejpam-6040	482	7	n	n	ADP
ejpam-6040	482	8	vertices	vertex	NOUN
ejpam-6040	482	9	and	and	CCONJ
ejpam-6040	482	10	k	k	PROPN
ejpam-6040	482	11	≤	≤	ADJ
ejpam-6040	482	12	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	482	13	1	1	NUM
ejpam-6040	482	14	,	,	PUNCT
ejpam-6040	482	15	then	then	ADV
ejpam-6040	482	16	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	482	17	)	)	PUNCT
ejpam-6040	482	18	=	=	SYM
ejpam-6040	483	1			NUM
ejpam-6040	483	2	3k	3k	NOUN
ejpam-6040	484	1	+	+	CCONJ
ejpam-6040	484	2	2	2	NUM
ejpam-6040	484	3	if	if	SCONJ
ejpam-6040	484	4	n	n	NOUN
ejpam-6040	484	5	=	=	NOUN
ejpam-6040	484	6	3r	3r	NUM
ejpam-6040	484	7	,	,	PUNCT
ejpam-6040	484	8	r	r	NOUN
ejpam-6040	484	9	≥	≥	NUM
ejpam-6040	484	10	2	2	NUM
ejpam-6040	484	11	and	and	CCONJ
ejpam-6040	484	12	k	k	NOUN
ejpam-6040	485	1	=	=	SYM
ejpam-6040	485	2	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	485	3	1	1	NUM
ejpam-6040	485	4	or	or	CCONJ
ejpam-6040	485	5	r	r	NOUN
ejpam-6040	485	6	is	be	AUX
ejpam-6040	485	7	odd	odd	ADJ
ejpam-6040	485	8	,	,	PUNCT
ejpam-6040	485	9	r	r	NOUN
ejpam-6040	485	10	≥	≥	NOUN
ejpam-6040	485	11	3	3	NUM
ejpam-6040	485	12	,	,	PUNCT
ejpam-6040	485	13	and	and	CCONJ
ejpam-6040	485	14	k	k	X
ejpam-6040	486	1	=	=	SYM
ejpam-6040	486	2	γg(cn)−	γg(cn)−	NOUN
ejpam-6040	486	3	2	2	NUM
ejpam-6040	486	4	3k	3k	NUM
ejpam-6040	486	5	+	+	CCONJ
ejpam-6040	486	6	1	1	NUM
ejpam-6040	486	7	if	if	SCONJ
ejpam-6040	486	8	n	n	NOUN
ejpam-6040	486	9	=	=	NOUN
ejpam-6040	486	10	3r	3r	NUM
ejpam-6040	486	11	+	+	CCONJ
ejpam-6040	486	12	2	2	NUM
ejpam-6040	486	13	,	,	PUNCT
ejpam-6040	486	14	r	r	NOUN
ejpam-6040	486	15	≥	≥	NUM
ejpam-6040	486	16	2	2	NUM
ejpam-6040	486	17	and	and	CCONJ
ejpam-6040	486	18	k	k	NOUN
ejpam-6040	486	19	=	=	SYM
ejpam-6040	486	20	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	486	21	1	1	NUM
ejpam-6040	486	22	or	or	CCONJ
ejpam-6040	486	23	r	r	NOUN
ejpam-6040	486	24	is	be	AUX
ejpam-6040	486	25	odd	odd	ADJ
ejpam-6040	486	26	,	,	PUNCT
ejpam-6040	486	27	r	r	NOUN
ejpam-6040	486	28	≥	≥	NOUN
ejpam-6040	486	29	3	3	NUM
ejpam-6040	486	30	,	,	PUNCT
ejpam-6040	486	31	and	and	CCONJ
ejpam-6040	486	32	k	k	X
ejpam-6040	487	1	=	=	SYM
ejpam-6040	487	2	γg(cn)−	γg(cn)−	NOUN
ejpam-6040	487	3	2	2	NUM
ejpam-6040	487	4	3k	3k	NOUN
ejpam-6040	487	5	if	if	SCONJ
ejpam-6040	487	6	n	n	NOUN
ejpam-6040	487	7	=	=	NOUN
ejpam-6040	487	8	3r	3r	NUM
ejpam-6040	487	9	,	,	PUNCT
ejpam-6040	487	10	r	r	NOUN
ejpam-6040	487	11	≥	≥	NOUN
ejpam-6040	487	12	4	4	NUM
ejpam-6040	487	13	and	and	CCONJ
ejpam-6040	487	14	,	,	PUNCT
ejpam-6040	487	15	1	1	NUM
ejpam-6040	487	16	≤	≤	NUM
ejpam-6040	487	17	k	k	NOUN
ejpam-6040	487	18	≤	≤	NUM
ejpam-6040	487	19	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	487	20	3	3	NUM
ejpam-6040	487	21	or	or	CCONJ
ejpam-6040	487	22	n	n	NOUN
ejpam-6040	487	23	=	=	NOUN
ejpam-6040	487	24	3r	3r	NUM
ejpam-6040	487	25	,	,	PUNCT
ejpam-6040	487	26	r	r	NOUN
ejpam-6040	487	27	is	be	AUX
ejpam-6040	487	28	even	even	ADV
ejpam-6040	487	29	,	,	PUNCT
ejpam-6040	487	30	r	r	NOUN
ejpam-6040	487	31	≥	≥	NOUN
ejpam-6040	487	32	4	4	NUM
ejpam-6040	487	33	,	,	PUNCT
ejpam-6040	487	34	and	and	CCONJ
ejpam-6040	487	35	k	k	X
ejpam-6040	488	1	=	=	SYM
ejpam-6040	488	2	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	488	3	2	2	NUM
ejpam-6040	488	4	or	or	CCONJ
ejpam-6040	488	5	n	n	NOUN
ejpam-6040	488	6	=	=	NOUN
ejpam-6040	488	7	3r	3r	NUM
ejpam-6040	488	8	+	+	CCONJ
ejpam-6040	488	9	1	1	NUM
ejpam-6040	488	10	and	and	CCONJ
ejpam-6040	488	11	k	k	NOUN
ejpam-6040	488	12	=	=	SYM
ejpam-6040	489	1	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	489	2	1	1	NUM
ejpam-6040	489	3	or	or	CCONJ
ejpam-6040	489	4	n	n	NOUN
ejpam-6040	489	5	=	=	NOUN
ejpam-6040	489	6	3r	3r	NUM
ejpam-6040	489	7	+	+	CCONJ
ejpam-6040	489	8	1	1	NUM
ejpam-6040	489	9	,	,	PUNCT
ejpam-6040	489	10	r	r	NOUN
ejpam-6040	489	11	is	be	AUX
ejpam-6040	489	12	even	even	ADV
ejpam-6040	489	13	,	,	PUNCT
ejpam-6040	489	14	and	and	CCONJ
ejpam-6040	489	15	k	k	X
ejpam-6040	490	1	=	=	SYM
ejpam-6040	490	2	γg(cn)−	γg(cn)−	X
ejpam-6040	490	3	2	2	NUM
ejpam-6040	490	4	3k	3k	NOUN
ejpam-6040	490	5	−	−	NOUN
ejpam-6040	490	6	2	2	NUM
ejpam-6040	490	7	if	if	SCONJ
ejpam-6040	490	8	n	n	NOUN
ejpam-6040	490	9	=	=	NOUN
ejpam-6040	490	10	3r	3r	NUM
ejpam-6040	490	11	+	+	CCONJ
ejpam-6040	490	12	1	1	NUM
ejpam-6040	490	13	,	,	PUNCT
ejpam-6040	490	14	r	r	NOUN
ejpam-6040	490	15	≥	≥	NOUN
ejpam-6040	490	16	3	3	NUM
ejpam-6040	490	17	,	,	PUNCT
ejpam-6040	490	18	and	and	CCONJ
ejpam-6040	490	19	1	1	NUM
ejpam-6040	490	20	≤	≤	NUM
ejpam-6040	490	21	k	k	NOUN
ejpam-6040	490	22	≤	≤	NUM
ejpam-6040	491	1	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	491	2	3	3	NUM
ejpam-6040	491	3	or	or	CCONJ
ejpam-6040	491	4	n	n	NOUN
ejpam-6040	491	5	=	=	NOUN
ejpam-6040	491	6	3r	3r	NUM
ejpam-6040	491	7	+	+	CCONJ
ejpam-6040	491	8	1	1	NUM
ejpam-6040	491	9	,	,	PUNCT
ejpam-6040	491	10	r	r	NOUN
ejpam-6040	491	11	is	be	AUX
ejpam-6040	491	12	odd	odd	ADJ
ejpam-6040	491	13	,	,	PUNCT
ejpam-6040	491	14	r	r	NOUN
ejpam-6040	491	15	≥	≥	NOUN
ejpam-6040	491	16	3	3	NUM
ejpam-6040	491	17	,	,	PUNCT
ejpam-6040	491	18	and	and	CCONJ
ejpam-6040	491	19	k	k	X
ejpam-6040	492	1	=	=	SYM
ejpam-6040	492	2	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	492	3	2	2	NUM
ejpam-6040	492	4	or	or	CCONJ
ejpam-6040	492	5	n	n	NOUN
ejpam-6040	492	6	=	=	SYM
ejpam-6040	492	7	5	5	NUM
ejpam-6040	492	8	and	and	CCONJ
ejpam-6040	492	9	k	k	NOUN
ejpam-6040	492	10	=	=	SYM
ejpam-6040	492	11	2	2	NUM
ejpam-6040	492	12	3k	3k	NOUN
ejpam-6040	492	13	−	−	NOUN
ejpam-6040	492	14	1	1	NUM
ejpam-6040	492	15	if	if	SCONJ
ejpam-6040	492	16	n	n	NOUN
ejpam-6040	492	17	=	=	NOUN
ejpam-6040	492	18	3r	3r	NUM
ejpam-6040	492	19	+	+	CCONJ
ejpam-6040	492	20	2	2	NUM
ejpam-6040	492	21	,	,	PUNCT
ejpam-6040	492	22	r	r	NOUN
ejpam-6040	492	23	≥	≥	NUM
ejpam-6040	492	24	3	3	NUM
ejpam-6040	492	25	and	and	CCONJ
ejpam-6040	492	26	k	k	NOUN
ejpam-6040	492	27	=	=	SYM
ejpam-6040	492	28	1	1	NUM
ejpam-6040	492	29	or	or	CCONJ
ejpam-6040	492	30	n	n	NOUN
ejpam-6040	492	31	=	=	NOUN
ejpam-6040	492	32	3r	3r	NUM
ejpam-6040	492	33	+	+	CCONJ
ejpam-6040	492	34	2	2	NUM
ejpam-6040	492	35	,	,	PUNCT
ejpam-6040	492	36	r	r	NOUN
ejpam-6040	492	37	is	be	AUX
ejpam-6040	492	38	even	even	ADV
ejpam-6040	492	39	and	and	CCONJ
ejpam-6040	492	40	k	k	PROPN
ejpam-6040	492	41	=	=	SYM
ejpam-6040	493	1	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	493	2	2	2	NUM
ejpam-6040	493	3	or	or	CCONJ
ejpam-6040	493	4	n	n	NOUN
ejpam-6040	493	5	=	=	NOUN
ejpam-6040	493	6	3r	3r	NUM
ejpam-6040	493	7	+	+	CCONJ
ejpam-6040	493	8	2	2	NUM
ejpam-6040	493	9	,	,	PUNCT
ejpam-6040	493	10	r	r	NOUN
ejpam-6040	493	11	≥	≥	NUM
ejpam-6040	493	12	4	4	NUM
ejpam-6040	493	13	and	and	CCONJ
ejpam-6040	493	14	2	2	NUM
ejpam-6040	493	15	≤	≤	NOUN
ejpam-6040	493	16	k	k	NOUN
ejpam-6040	493	17	≤	≤	NUM
ejpam-6040	493	18	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	493	19	3	3	NUM
ejpam-6040	493	20	or	or	CCONJ
ejpam-6040	493	21	n	n	NOUN
ejpam-6040	493	22	=	=	SYM
ejpam-6040	493	23	5	5	NUM
ejpam-6040	493	24	and	and	CCONJ
ejpam-6040	493	25	k	k	NOUN
ejpam-6040	494	1	=	=	SYM
ejpam-6040	494	2	1	1	NUM
ejpam-6040	494	3	k	k	NOUN
ejpam-6040	494	4	if	if	SCONJ
ejpam-6040	494	5	n	n	X
ejpam-6040	494	6	=	=	SYM
ejpam-6040	494	7	3	3	X
ejpam-6040	494	8	.	.	PUNCT
ejpam-6040	494	9	proof	proof	NOUN
ejpam-6040	494	10	.	.	PUNCT
ejpam-6040	495	1	let	let	VERB
ejpam-6040	495	2	cn	cn	PROPN
ejpam-6040	495	3	=	=	PUNCT
ejpam-6040	496	1	[	[	X
ejpam-6040	496	2	v1	v1	NOUN
ejpam-6040	496	3	,	,	PUNCT
ejpam-6040	496	4	v2	v2	PROPN
ejpam-6040	496	5	,	,	PUNCT
ejpam-6040	496	6	·	·	PUNCT
ejpam-6040	496	7	·	·	PUNCT
ejpam-6040	496	8	·	·	PUNCT
ejpam-6040	496	9	,	,	PUNCT
ejpam-6040	496	10	vn	vn	X
ejpam-6040	496	11	,	,	PUNCT
ejpam-6040	496	12	v1	v1	PROPN
ejpam-6040	496	13	]	]	PUNCT
ejpam-6040	496	14	and	and	CCONJ
ejpam-6040	496	15	let	let	VERB
ejpam-6040	496	16	k	k	PROPN
ejpam-6040	496	17	≤	≤	NUM
ejpam-6040	496	18	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	497	1	1	1	X
ejpam-6040	497	2	.	.	PUNCT
ejpam-6040	498	1	if	if	SCONJ
ejpam-6040	498	2	n	n	NUM
ejpam-6040	498	3	=	=	SYM
ejpam-6040	498	4	3	3	NUM
ejpam-6040	498	5	,	,	PUNCT
ejpam-6040	498	6	then	then	ADV
ejpam-6040	498	7	ζgk(c3	ζgk(c3	VERB
ejpam-6040	498	8	)	)	PUNCT
ejpam-6040	498	9	=	=	SYM
ejpam-6040	499	1	k	k	X
ejpam-6040	499	2	by	by	ADP
ejpam-6040	499	3	theorem	theorem	NOUN
ejpam-6040	499	4	6	6	NUM
ejpam-6040	499	5	.	.	PUNCT
ejpam-6040	500	1	if	if	SCONJ
ejpam-6040	500	2	n	n	NOUN
ejpam-6040	500	3	=	=	SYM
ejpam-6040	500	4	5	5	NUM
ejpam-6040	500	5	,	,	PUNCT
ejpam-6040	500	6	then	then	ADV
ejpam-6040	500	7	ζg1	ζg1	PROPN
ejpam-6040	500	8	(	(	PUNCT
ejpam-6040	500	9	c5	c5	PROPN
ejpam-6040	500	10	)	)	PUNCT
ejpam-6040	500	11	=	=	SYM
ejpam-6040	500	12	2	2	NUM
ejpam-6040	500	13	=	=	SYM
ejpam-6040	500	14	3k−	3k−	PROPN
ejpam-6040	500	15	1	1	NUM
ejpam-6040	500	16	and	and	CCONJ
ejpam-6040	500	17	ζg2	ζg2	PROPN
ejpam-6040	500	18	(	(	PUNCT
ejpam-6040	500	19	c5	c5	PROPN
ejpam-6040	500	20	)	)	PUNCT
ejpam-6040	500	21	=	=	SYM
ejpam-6040	501	1	4	4	NUM
ejpam-6040	501	2	=	=	SYM
ejpam-6040	501	3	3k−	3k−	PROPN
ejpam-6040	501	4	2	2	NUM
ejpam-6040	501	5	.	.	PUNCT
ejpam-6040	502	1	let	let	VERB
ejpam-6040	502	2	n	n	NOUN
ejpam-6040	502	3	=	=	SYM
ejpam-6040	502	4	4	4	NUM
ejpam-6040	502	5	or	or	CCONJ
ejpam-6040	502	6	n	n	PRON
ejpam-6040	502	7	≥	≥	NOUN
ejpam-6040	502	8	6	6	NUM
ejpam-6040	502	9	.	.	PUNCT
ejpam-6040	503	1	consider	consider	VERB
ejpam-6040	503	2	the	the	DET
ejpam-6040	503	3	following	follow	VERB
ejpam-6040	503	4	cases	case	NOUN
ejpam-6040	503	5	:	:	PUNCT
ejpam-6040	503	6	case	case	NOUN
ejpam-6040	503	7	1	1	NUM
ejpam-6040	503	8	:	:	PUNCT
ejpam-6040	503	9	n	n	PROPN
ejpam-6040	503	10	=	=	NOUN
ejpam-6040	503	11	3r	3r	NUM
ejpam-6040	503	12	where	where	SCONJ
ejpam-6040	503	13	r	r	NOUN
ejpam-6040	503	14	≥	≥	NOUN
ejpam-6040	503	15	2	2	NUM
ejpam-6040	503	16	.	.	PUNCT
ejpam-6040	503	17	by	by	ADP
ejpam-6040	503	18	theorem	theorem	NOUN
ejpam-6040	503	19	1(v	1(v	NUM
ejpam-6040	503	20	)	)	PUNCT
ejpam-6040	503	21	,	,	PUNCT
ejpam-6040	503	22	γg(cn	γg(cn	NOUN
ejpam-6040	503	23	)	)	PUNCT
ejpam-6040	503	24	=	=	PUNCT
ejpam-6040	504	1	⌈n3	⌈n3	X
ejpam-6040	504	2	⌉	⌉	X
ejpam-6040	504	3	=	=	SYM
ejpam-6040	504	4	r.	r.	PROPN
ejpam-6040	504	5	thus	thus	ADV
ejpam-6040	504	6	,	,	PUNCT
ejpam-6040	504	7	k	k	PROPN
ejpam-6040	504	8	≤	≤	PROPN
ejpam-6040	504	9	r−1	r−1	PROPN
ejpam-6040	504	10	.	.	PUNCT
ejpam-6040	505	1	consider	consider	VERB
ejpam-6040	505	2	the	the	DET
ejpam-6040	505	3	following	follow	VERB
ejpam-6040	505	4	subcases	subcase	NOUN
ejpam-6040	505	5	:	:	PUNCT
ejpam-6040	505	6	subcase	subcase	NOUN
ejpam-6040	505	7	1	1	NUM
ejpam-6040	505	8	:	:	PUNCT
ejpam-6040	505	9	k	k	X
ejpam-6040	505	10	=	=	PUNCT
ejpam-6040	506	1	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	506	2	1	1	NUM
ejpam-6040	506	3	=	=	SYM
ejpam-6040	506	4	r	r	NOUN
ejpam-6040	506	5	−	−	NOUN
ejpam-6040	506	6	1	1	NUM
ejpam-6040	506	7	.	.	PUNCT
ejpam-6040	506	8	by	by	ADP
ejpam-6040	506	9	lemma	lemma	PROPN
ejpam-6040	506	10	1	1	NUM
ejpam-6040	506	11	,	,	PUNCT
ejpam-6040	506	12	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	506	13	)	)	PUNCT
ejpam-6040	507	1	=	=	PUNCT
ejpam-6040	507	2	n−	n−	NOUN
ejpam-6040	507	3	1	1	NUM
ejpam-6040	507	4	=	=	SYM
ejpam-6040	507	5	3r	3r	NUM
ejpam-6040	507	6	−	−	NOUN
ejpam-6040	507	7	1	1	NUM
ejpam-6040	507	8	=	=	SYM
ejpam-6040	507	9	3k	3k	NOUN
ejpam-6040	507	10	+	+	CCONJ
ejpam-6040	507	11	2	2	X
ejpam-6040	507	12	.	.	X
ejpam-6040	507	13	subcase	subcase	NOUN
ejpam-6040	507	14	2	2	NUM
ejpam-6040	507	15	:	:	PUNCT
ejpam-6040	507	16	r	r	NOUN
ejpam-6040	507	17	is	be	AUX
ejpam-6040	507	18	odd	odd	ADJ
ejpam-6040	507	19	and	and	CCONJ
ejpam-6040	507	20	k	k	NOUN
ejpam-6040	507	21	=	=	SYM
ejpam-6040	508	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	508	2	2	2	NUM
ejpam-6040	508	3	=	=	SYM
ejpam-6040	508	4	r	r	NOUN
ejpam-6040	508	5	−	−	NOUN
ejpam-6040	508	6	2	2	NUM
ejpam-6040	508	7	.	.	PUNCT
ejpam-6040	509	1	let	let	VERB
ejpam-6040	509	2	d2	d2	PROPN
ejpam-6040	509	3	=	=	SYM
ejpam-6040	509	4	{	{	PUNCT
ejpam-6040	509	5	v1	v1	PROPN
ejpam-6040	509	6	,	,	PUNCT
ejpam-6040	509	7	v4	v4	NOUN
ejpam-6040	509	8	}	}	PUNCT
ejpam-6040	509	9	.	.	PUNCT
ejpam-6040	510	1	then	then	ADV
ejpam-6040	510	2	d2	d2	PROPN
ejpam-6040	510	3	is	be	AUX
ejpam-6040	510	4	a	a	DET
ejpam-6040	510	5	ζgk	ζgk	ADJ
ejpam-6040	510	6	-set	-set	ADJ
ejpam-6040	510	7	of	of	ADP
ejpam-6040	510	8	cn	cn	PROPN
ejpam-6040	510	9	and	and	CCONJ
ejpam-6040	510	10	ng	ng	PROPN
ejpam-6040	510	11	g[d2	g[d2	NOUN
ejpam-6040	510	12	]	]	PUNCT
ejpam-6040	511	1	=	=	SYM
ejpam-6040	511	2	{	{	PUNCT
ejpam-6040	511	3	v1	v1	PROPN
ejpam-6040	511	4	,	,	PUNCT
ejpam-6040	511	5	v2	v2	PROPN
ejpam-6040	511	6	,	,	PUNCT
ejpam-6040	511	7	v3	v3	PROPN
ejpam-6040	511	8	,	,	PUNCT
ejpam-6040	511	9	v4	v4	PROPN
ejpam-6040	511	10	}	}	PUNCT
ejpam-6040	511	11	.	.	PUNCT
ejpam-6040	512	1	thus	thus	ADV
ejpam-6040	512	2	,	,	PUNCT
ejpam-6040	512	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	512	4	)	)	PUNCT
ejpam-6040	513	1	=	=	SYM
ejpam-6040	513	2	ζgk(d2	ζgk(d2	ADJ
ejpam-6040	513	3	)	)	PUNCT
ejpam-6040	513	4	=	=	NOUN
ejpam-6040	513	5	3r	3r	NUM
ejpam-6040	513	6	−	−	NOUN
ejpam-6040	513	7	|ng	|ng	PUNCT
ejpam-6040	513	8	g[d2]|	g[d2]|	NOUN
ejpam-6040	513	9	=	=	NOUN
ejpam-6040	513	10	3r	3r	NUM
ejpam-6040	513	11	−	−	NOUN
ejpam-6040	513	12	4	4	NUM
ejpam-6040	513	13	=	=	SYM
ejpam-6040	513	14	3k	3k	NOUN
ejpam-6040	513	15	+	+	CCONJ
ejpam-6040	513	16	2	2	X
ejpam-6040	513	17	.	.	X
ejpam-6040	513	18	subcase	subcase	NOUN
ejpam-6040	513	19	3	3	NUM
ejpam-6040	513	20	:	:	PUNCT
ejpam-6040	513	21	r	r	NOUN
ejpam-6040	513	22	≥	≥	NUM
ejpam-6040	513	23	4	4	NUM
ejpam-6040	513	24	and	and	CCONJ
ejpam-6040	513	25	1	1	NUM
ejpam-6040	513	26	≤	≤	NUM
ejpam-6040	513	27	k	k	NOUN
ejpam-6040	513	28	≤	≤	NUM
ejpam-6040	513	29	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	514	1	3	3	X
ejpam-6040	514	2	.	.	PUNCT
ejpam-6040	514	3	let	let	VERB
ejpam-6040	514	4	k	k	PROPN
ejpam-6040	514	5	≤	≤	X
ejpam-6040	514	6	⌊γg(cn)−2	⌊γg(cn)−2	PUNCT
ejpam-6040	514	7	2	2	NUM
ejpam-6040	514	8	⌋	⌋	NOUN
ejpam-6040	514	9	and	and	CCONJ
ejpam-6040	514	10	let	let	VERB
ejpam-6040	514	11	d3	d3	PROPN
ejpam-6040	514	12	=	=	SYM
ejpam-6040	514	13	{	{	PUNCT
ejpam-6040	514	14	v1	v1	PROPN
ejpam-6040	514	15	,	,	PUNCT
ejpam-6040	514	16	v4	v4	NOUN
ejpam-6040	514	17	,	,	PUNCT
ejpam-6040	514	18	·	·	PUNCT
ejpam-6040	514	19	·	·	PUNCT
ejpam-6040	514	20	·	·	PUNCT
ejpam-6040	514	21	,	,	PUNCT
ejpam-6040	514	22	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	514	23	}	}	PUNCT
ejpam-6040	514	24	.	.	PUNCT
ejpam-6040	515	1	then	then	ADV
ejpam-6040	515	2	d3	d3	PROPN
ejpam-6040	515	3	is	be	AUX
ejpam-6040	515	4	a	a	DET
ejpam-6040	515	5	ζgk	ζgk	ADJ
ejpam-6040	515	6	-set	-set	ADJ
ejpam-6040	515	7	of	of	ADP
ejpam-6040	515	8	s.	s.	PROPN
ejpam-6040	515	9	canoy	canoy	PROPN
ejpam-6040	515	10	,	,	PUNCT
ejpam-6040	515	11	jr	jr	PROPN
ejpam-6040	515	12	.	.	PROPN
ejpam-6040	515	13	,	,	PUNCT
ejpam-6040	515	14	j.	j.	PROPN
ejpam-6040	515	15	anoche	anoche	PROPN
ejpam-6040	515	16	/	/	SYM
ejpam-6040	515	17	eur	eur	PROPN
ejpam-6040	515	18	.	.	PUNCT
ejpam-6040	516	1	j.	j.	PROPN
ejpam-6040	516	2	pure	pure	PROPN
ejpam-6040	516	3	appl	appl	PROPN
ejpam-6040	516	4	.	.	PROPN
ejpam-6040	516	5	math	math	PROPN
ejpam-6040	516	6	,	,	PUNCT
ejpam-6040	516	7	18	18	NUM
ejpam-6040	516	8	(	(	PUNCT
ejpam-6040	516	9	2	2	NUM
ejpam-6040	516	10	)	)	PUNCT
ejpam-6040	516	11	(	(	PUNCT
ejpam-6040	516	12	2025	2025	NUM
ejpam-6040	516	13	)	)	PUNCT
ejpam-6040	516	14	,	,	PUNCT
ejpam-6040	516	15	6040	6040	NUM
ejpam-6040	516	16	13	13	NUM
ejpam-6040	516	17	of	of	ADP
ejpam-6040	516	18	16	16	NUM
ejpam-6040	516	19	cn	cn	PROPN
ejpam-6040	516	20	and	and	CCONJ
ejpam-6040	516	21	ng	ng	PROPN
ejpam-6040	516	22	g[d3	g[d3	NOUN
ejpam-6040	516	23	]	]	PUNCT
ejpam-6040	516	24	=	=	SYM
ejpam-6040	516	25	{	{	PUNCT
ejpam-6040	516	26	v1	v1	PROPN
ejpam-6040	516	27	,	,	PUNCT
ejpam-6040	516	28	v2	v2	PROPN
ejpam-6040	516	29	,	,	PUNCT
ejpam-6040	516	30	v3	v3	PROPN
ejpam-6040	516	31	,	,	PUNCT
ejpam-6040	516	32	v4	v4	PROPN
ejpam-6040	516	33	,	,	PUNCT
ejpam-6040	516	34	·	·	PUNCT
ejpam-6040	516	35	·	·	PUNCT
ejpam-6040	516	36	·	·	PUNCT
ejpam-6040	516	37	,	,	PUNCT
ejpam-6040	516	38	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	516	39	,	,	PUNCT
ejpam-6040	516	40	v3r−3k−1	v3r−3k−1	NOUN
ejpam-6040	516	41	,	,	PUNCT
ejpam-6040	516	42	v3r	v3r	NOUN
ejpam-6040	516	43	}	}	PUNCT
ejpam-6040	516	44	.	.	PUNCT
ejpam-6040	517	1	thus	thus	ADV
ejpam-6040	517	2	,	,	PUNCT
ejpam-6040	517	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	517	4	)	)	PUNCT
ejpam-6040	517	5	=	=	SYM
ejpam-6040	517	6	ζgk(d3	ζgk(d3	NOUN
ejpam-6040	517	7	)	)	PUNCT
ejpam-6040	517	8	=	=	SYM
ejpam-6040	518	1	n	n	CCONJ
ejpam-6040	519	1	−	−	NOUN
ejpam-6040	519	2	|ng	|ng	NOUN
ejpam-6040	519	3	g[d3]|	g[d3]|	NOUN
ejpam-6040	519	4	=	=	NOUN
ejpam-6040	519	5	3r	3r	NUM
ejpam-6040	519	6	−	−	PROPN
ejpam-6040	520	1	[	[	X
ejpam-6040	520	2	(	(	PUNCT
ejpam-6040	520	3	3r	3r	NUM
ejpam-6040	520	4	−	−	NOUN
ejpam-6040	520	5	3k	3k	NOUN
ejpam-6040	520	6	−	−	PROPN
ejpam-6040	520	7	2	2	NUM
ejpam-6040	520	8	)	)	PUNCT
ejpam-6040	520	9	+	+	CCONJ
ejpam-6040	520	10	2	2	X
ejpam-6040	520	11	]	]	PUNCT
ejpam-6040	520	12	=	=	SYM
ejpam-6040	520	13	3k	3k	X
ejpam-6040	520	14	.	.	PUNCT
ejpam-6040	521	1	next	next	ADV
ejpam-6040	521	2	,	,	PUNCT
ejpam-6040	521	3	let	let	VERB
ejpam-6040	521	4	⌊γg(cn)−2	⌊γg(cn)−2	ADP
ejpam-6040	521	5	2	2	NUM
ejpam-6040	521	6	⌋	⌋	NOUN
ejpam-6040	521	7	<	<	X
ejpam-6040	521	8	k	k	PROPN
ejpam-6040	521	9	≤	≤	PROPN
ejpam-6040	521	10	γg(cn	γg(cn	NOUN
ejpam-6040	521	11	)	)	PUNCT
ejpam-6040	522	1	−	−	PROPN
ejpam-6040	522	2	3	3	X
ejpam-6040	522	3	.	.	PUNCT
ejpam-6040	522	4	choose	choose	VERB
ejpam-6040	522	5	an	an	DET
ejpam-6040	522	6	(	(	PUNCT
ejpam-6040	522	7	r−	r−	PROPN
ejpam-6040	522	8	k)-element	k)-element	PUNCT
ejpam-6040	522	9	set	set	VERB
ejpam-6040	522	10	d4	d4	PROPN
ejpam-6040	522	11	=	=	PUNCT
ejpam-6040	522	12	{	{	PUNCT
ejpam-6040	522	13	v⌈	v⌈	NOUN
ejpam-6040	522	14	3r+2	3r+2	PROPN
ejpam-6040	522	15	2	2	NUM
ejpam-6040	522	16	⌉	⌉	NOUN
ejpam-6040	522	17	,	,	PUNCT
ejpam-6040	522	18	v1	v1	NOUN
ejpam-6040	522	19	,	,	PUNCT
ejpam-6040	522	20	v4	v4	NOUN
ejpam-6040	522	21	,	,	PUNCT
ejpam-6040	522	22	·	·	PUNCT
ejpam-6040	522	23	·	·	PUNCT
ejpam-6040	522	24	·	·	PUNCT
ejpam-6040	522	25	,	,	PUNCT
ejpam-6040	522	26	v3r−3k−5	v3r−3k−5	VERB
ejpam-6040	522	27	}	}	PUNCT
ejpam-6040	522	28	.	.	PUNCT
ejpam-6040	523	1	then	then	ADV
ejpam-6040	523	2	d4	d4	PROPN
ejpam-6040	523	3	is	be	AUX
ejpam-6040	523	4	a	a	DET
ejpam-6040	523	5	ζgk	ζgk	ADJ
ejpam-6040	523	6	-set	-set	ADJ
ejpam-6040	523	7	of	of	ADP
ejpam-6040	523	8	cn	cn	PROPN
ejpam-6040	523	9	and	and	CCONJ
ejpam-6040	523	10	ng	ng	PROPN
ejpam-6040	523	11	g[d4	g[d4	NOUN
ejpam-6040	523	12	]	]	X
ejpam-6040	523	13	=	=	SYM
ejpam-6040	523	14	{	{	PUNCT
ejpam-6040	523	15	v1	v1	PROPN
ejpam-6040	523	16	,	,	PUNCT
ejpam-6040	523	17	v2	v2	PROPN
ejpam-6040	523	18	,	,	PUNCT
ejpam-6040	523	19	v3	v3	PROPN
ejpam-6040	523	20	,	,	PUNCT
ejpam-6040	523	21	v4	v4	PROPN
ejpam-6040	523	22	,	,	PUNCT
ejpam-6040	523	23	·	·	PUNCT
ejpam-6040	523	24	·	·	PUNCT
ejpam-6040	523	25	·	·	PUNCT
ejpam-6040	523	26	,	,	PUNCT
ejpam-6040	523	27	v3r−3k−5	v3r−3k−5	NUM
ejpam-6040	523	28	,	,	PUNCT
ejpam-6040	523	29	v3r−3k−4	v3r−3k−4	PROPN
ejpam-6040	523	30	,	,	PUNCT
ejpam-6040	523	31	v⌈	v⌈	NOUN
ejpam-6040	523	32	3r+2	3r+2	PROPN
ejpam-6040	523	33	2	2	NUM
ejpam-6040	523	34	⌉−1	⌉−1	PROPN
ejpam-6040	523	35	,	,	PUNCT
ejpam-6040	523	36	v⌈	v⌈	NOUN
ejpam-6040	523	37	3r+2	3r+2	PROPN
ejpam-6040	523	38	2	2	NUM
ejpam-6040	523	39	⌉	⌉	NOUN
ejpam-6040	523	40	,	,	PUNCT
ejpam-6040	523	41	v⌈	v⌈	NOUN
ejpam-6040	523	42	3r+2	3r+2	PROPN
ejpam-6040	523	43	2	2	NUM
ejpam-6040	523	44	⌉+1	⌉+1	PROPN
ejpam-6040	523	45	,	,	PUNCT
ejpam-6040	523	46	v3r	v3r	NOUN
ejpam-6040	523	47	}	}	PUNCT
ejpam-6040	523	48	.	.	PUNCT
ejpam-6040	524	1	this	this	PRON
ejpam-6040	524	2	implies	imply	VERB
ejpam-6040	524	3	that	that	DET
ejpam-6040	524	4	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	524	5	)	)	PUNCT
ejpam-6040	524	6	=	=	PUNCT
ejpam-6040	525	1	ζgk(d4	ζgk(d4	ADJ
ejpam-6040	525	2	)	)	PUNCT
ejpam-6040	525	3	=	=	SYM
ejpam-6040	525	4	n−	n−	NOUN
ejpam-6040	525	5	|ng	|ng	NOUN
ejpam-6040	525	6	g[d4]|	g[d4]|	NOUN
ejpam-6040	525	7	=	=	NOUN
ejpam-6040	525	8	3r	3r	NUM
ejpam-6040	525	9	−	−	PROPN
ejpam-6040	526	1	[	[	X
ejpam-6040	526	2	(	(	PUNCT
ejpam-6040	526	3	3r	3r	NUM
ejpam-6040	526	4	−	−	NOUN
ejpam-6040	526	5	3k	3k	NOUN
ejpam-6040	526	6	−	−	PROPN
ejpam-6040	526	7	4	4	NUM
ejpam-6040	526	8	)	)	PUNCT
ejpam-6040	526	9	+	+	CCONJ
ejpam-6040	526	10	4	4	X
ejpam-6040	526	11	]	]	PUNCT
ejpam-6040	526	12	=	=	SYM
ejpam-6040	526	13	3k	3k	X
ejpam-6040	526	14	.	.	PUNCT
ejpam-6040	527	1	subcase	subcase	PROPN
ejpam-6040	527	2	4	4	NUM
ejpam-6040	527	3	:	:	PUNCT
ejpam-6040	527	4	r	r	NOUN
ejpam-6040	527	5	≥	≥	NOUN
ejpam-6040	527	6	4	4	NUM
ejpam-6040	527	7	is	be	AUX
ejpam-6040	527	8	even	even	ADV
ejpam-6040	527	9	and	and	CCONJ
ejpam-6040	527	10	k	k	PROPN
ejpam-6040	527	11	=	=	SYM
ejpam-6040	528	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	528	2	2	2	NUM
ejpam-6040	528	3	=	=	SYM
ejpam-6040	528	4	r	r	NOUN
ejpam-6040	528	5	−	−	NOUN
ejpam-6040	528	6	2	2	NUM
ejpam-6040	528	7	.	.	PUNCT
ejpam-6040	529	1	let	let	VERB
ejpam-6040	529	2	d5	d5	NOUN
ejpam-6040	529	3	=	=	SYM
ejpam-6040	529	4	{	{	PUNCT
ejpam-6040	529	5	v1	v1	PROPN
ejpam-6040	529	6	,	,	PUNCT
ejpam-6040	529	7	v	v	ADP
ejpam-6040	529	8	3r+2	3r+2	NUM
ejpam-6040	529	9	2	2	NUM
ejpam-6040	529	10	}	}	PUNCT
ejpam-6040	529	11	.	.	PUNCT
ejpam-6040	530	1	then	then	ADV
ejpam-6040	530	2	d5	d5	NOUN
ejpam-6040	530	3	is	be	AUX
ejpam-6040	530	4	a	a	DET
ejpam-6040	530	5	ζgk	ζgk	ADJ
ejpam-6040	530	6	-set	-set	ADJ
ejpam-6040	530	7	of	of	ADP
ejpam-6040	530	8	cn	cn	PROPN
ejpam-6040	530	9	and	and	CCONJ
ejpam-6040	530	10	ng	ng	PROPN
ejpam-6040	530	11	g[d5	g[d5	NOUN
ejpam-6040	530	12	]	]	PUNCT
ejpam-6040	531	1	=	=	SYM
ejpam-6040	531	2	{	{	PUNCT
ejpam-6040	531	3	v1	v1	PROPN
ejpam-6040	531	4	,	,	PUNCT
ejpam-6040	531	5	v2	v2	PROPN
ejpam-6040	531	6	,	,	PUNCT
ejpam-6040	531	7	v	v	ADJ
ejpam-6040	531	8	3r	3r	NUM
ejpam-6040	531	9	2	2	NUM
ejpam-6040	531	10	,	,	PUNCT
ejpam-6040	531	11	v	v	ADP
ejpam-6040	531	12	3r+2	3r+2	NUM
ejpam-6040	531	13	2	2	NUM
ejpam-6040	531	14	,	,	PUNCT
ejpam-6040	531	15	v	v	ADP
ejpam-6040	531	16	3r+4	3r+4	PROPN
ejpam-6040	531	17	2	2	NUM
ejpam-6040	531	18	,	,	PUNCT
ejpam-6040	531	19	v3r	v3r	NOUN
ejpam-6040	531	20	}	}	PUNCT
ejpam-6040	531	21	.	.	PUNCT
ejpam-6040	532	1	hence	hence	ADV
ejpam-6040	532	2	,	,	PUNCT
ejpam-6040	532	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	532	4	)	)	PUNCT
ejpam-6040	532	5	=	=	SYM
ejpam-6040	532	6	ζgk(d5	ζgk(d5	X
ejpam-6040	532	7	)	)	PUNCT
ejpam-6040	532	8	=	=	NOUN
ejpam-6040	532	9	3r	3r	NUM
ejpam-6040	532	10	−	−	NOUN
ejpam-6040	532	11	|ng	|ng	PUNCT
ejpam-6040	532	12	g[d5]|	g[d5]|	NOUN
ejpam-6040	532	13	=	=	PUNCT
ejpam-6040	532	14	3r	3r	NUM
ejpam-6040	532	15	−	−	PROPN
ejpam-6040	532	16	6	6	NUM
ejpam-6040	532	17	=	=	SYM
ejpam-6040	532	18	3k	3k	NUM
ejpam-6040	532	19	.	.	PUNCT
ejpam-6040	533	1	case	case	NOUN
ejpam-6040	533	2	2	2	NUM
ejpam-6040	533	3	:	:	SYM
ejpam-6040	533	4	n	n	NOUN
ejpam-6040	533	5	=	=	SYM
ejpam-6040	533	6	3r	3r	NUM
ejpam-6040	533	7	+	+	CCONJ
ejpam-6040	533	8	1	1	X
ejpam-6040	533	9	.	.	PUNCT
ejpam-6040	533	10	by	by	ADP
ejpam-6040	533	11	theorem	theorem	NOUN
ejpam-6040	533	12	1(v	1(v	NUM
ejpam-6040	533	13	)	)	PUNCT
ejpam-6040	533	14	,	,	PUNCT
ejpam-6040	533	15	γg(cn	γg(cn	NOUN
ejpam-6040	533	16	)	)	PUNCT
ejpam-6040	533	17	=	=	PUNCT
ejpam-6040	534	1	⌈n3	⌈n3	X
ejpam-6040	534	2	⌉	⌉	PRON
ejpam-6040	534	3	=	=	SYM
ejpam-6040	534	4	r+1	r+1	PROPN
ejpam-6040	534	5	.	.	PUNCT
ejpam-6040	535	1	thus	thus	ADV
ejpam-6040	535	2	,	,	PUNCT
ejpam-6040	535	3	k	k	PROPN
ejpam-6040	535	4	≤	≤	PROPN
ejpam-6040	535	5	r.	r.	PROPN
ejpam-6040	535	6	consider	consider	VERB
ejpam-6040	535	7	the	the	DET
ejpam-6040	535	8	following	follow	VERB
ejpam-6040	535	9	subcases	subcase	NOUN
ejpam-6040	535	10	:	:	PUNCT
ejpam-6040	535	11	subcase	subcase	NOUN
ejpam-6040	535	12	1	1	NUM
ejpam-6040	535	13	:	:	PUNCT
ejpam-6040	536	1	k	k	X
ejpam-6040	536	2	=	=	PUNCT
ejpam-6040	536	3	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	536	4	1	1	NUM
ejpam-6040	536	5	=	=	SYM
ejpam-6040	536	6	r.	r.	X
ejpam-6040	536	7	by	by	ADP
ejpam-6040	536	8	lemma	lemma	PROPN
ejpam-6040	536	9	1	1	NUM
ejpam-6040	536	10	,	,	PUNCT
ejpam-6040	536	11	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	536	12	)	)	PUNCT
ejpam-6040	536	13	=	=	PUNCT
ejpam-6040	537	1	n−	n−	NOUN
ejpam-6040	537	2	1	1	NUM
ejpam-6040	537	3	=	=	SYM
ejpam-6040	537	4	3r	3r	NUM
ejpam-6040	537	5	+	+	CCONJ
ejpam-6040	537	6	1−	1−	NUM
ejpam-6040	537	7	1	1	NUM
ejpam-6040	537	8	=	=	SYM
ejpam-6040	537	9	3r	3r	NUM
ejpam-6040	537	10	=	=	SYM
ejpam-6040	537	11	3k	3k	X
ejpam-6040	537	12	.	.	PUNCT
ejpam-6040	538	1	subcase	subcase	PROPN
ejpam-6040	538	2	2	2	NUM
ejpam-6040	538	3	:	:	PUNCT
ejpam-6040	538	4	r	r	NOUN
ejpam-6040	538	5	is	be	AUX
ejpam-6040	538	6	even	even	ADV
ejpam-6040	538	7	and	and	CCONJ
ejpam-6040	538	8	k	k	PROPN
ejpam-6040	538	9	=	=	SYM
ejpam-6040	539	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	539	2	2	2	NUM
ejpam-6040	539	3	=	=	SYM
ejpam-6040	539	4	r	r	NOUN
ejpam-6040	539	5	−	−	NOUN
ejpam-6040	539	6	1	1	NUM
ejpam-6040	539	7	.	.	PUNCT
ejpam-6040	540	1	let	let	VERB
ejpam-6040	540	2	d6	d6	NOUN
ejpam-6040	540	3	=	=	SYM
ejpam-6040	540	4	{	{	PUNCT
ejpam-6040	540	5	v1	v1	NOUN
ejpam-6040	540	6	,	,	PUNCT
ejpam-6040	540	7	v4	v4	NOUN
ejpam-6040	540	8	}	}	PUNCT
ejpam-6040	540	9	.	.	PUNCT
ejpam-6040	541	1	then	then	ADV
ejpam-6040	541	2	d6	d6	NOUN
ejpam-6040	541	3	is	be	AUX
ejpam-6040	541	4	a	a	DET
ejpam-6040	541	5	ζgk	ζgk	ADJ
ejpam-6040	541	6	-set	-set	ADJ
ejpam-6040	541	7	of	of	ADP
ejpam-6040	541	8	cn	cn	PROPN
ejpam-6040	541	9	and	and	CCONJ
ejpam-6040	541	10	ng	ng	PROPN
ejpam-6040	541	11	g[d6	g[d6	PROPN
ejpam-6040	541	12	]	]	X
ejpam-6040	541	13	=	=	SYM
ejpam-6040	541	14	{	{	PUNCT
ejpam-6040	541	15	v1	v1	PROPN
ejpam-6040	541	16	,	,	PUNCT
ejpam-6040	541	17	v2	v2	PROPN
ejpam-6040	541	18	,	,	PUNCT
ejpam-6040	541	19	v3	v3	PROPN
ejpam-6040	541	20	,	,	PUNCT
ejpam-6040	541	21	v4	v4	PROPN
ejpam-6040	541	22	}	}	PUNCT
ejpam-6040	541	23	.	.	PUNCT
ejpam-6040	542	1	hence	hence	ADV
ejpam-6040	542	2	,	,	PUNCT
ejpam-6040	542	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	542	4	)	)	PUNCT
ejpam-6040	542	5	=	=	SYM
ejpam-6040	543	1	ζgk(d6	ζgk(d6	PROPN
ejpam-6040	543	2	)	)	PUNCT
ejpam-6040	543	3	=	=	SYM
ejpam-6040	543	4	3r	3r	NUM
ejpam-6040	543	5	+	+	CCONJ
ejpam-6040	543	6	1−	1−	NUM
ejpam-6040	543	7	|ng	|ng	PUNCT
ejpam-6040	543	8	g[d6]|	g[d6]|	NOUN
ejpam-6040	543	9	=	=	SYM
ejpam-6040	543	10	3r	3r	NUM
ejpam-6040	543	11	+	+	CCONJ
ejpam-6040	543	12	1−	1−	NUM
ejpam-6040	543	13	4	4	NUM
ejpam-6040	543	14	=	=	SYM
ejpam-6040	543	15	3k	3k	NUM
ejpam-6040	543	16	.	.	PUNCT
ejpam-6040	543	17	subcase	subcase	PROPN
ejpam-6040	543	18	3	3	NUM
ejpam-6040	543	19	:	:	PUNCT
ejpam-6040	544	1	r	r	NOUN
ejpam-6040	544	2	≥	≥	NUM
ejpam-6040	544	3	3	3	NUM
ejpam-6040	544	4	and	and	CCONJ
ejpam-6040	544	5	1	1	NUM
ejpam-6040	544	6	≤	≤	NUM
ejpam-6040	544	7	k	k	NOUN
ejpam-6040	544	8	≤	≤	NUM
ejpam-6040	544	9	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	544	10	3	3	X
ejpam-6040	544	11	.	.	PUNCT
ejpam-6040	545	1	let	let	VERB
ejpam-6040	545	2	k	k	PROPN
ejpam-6040	545	3	≤	≤	X
ejpam-6040	545	4	⌊γg(cn)−2	⌊γg(cn)−2	PUNCT
ejpam-6040	545	5	2	2	NUM
ejpam-6040	545	6	⌋	⌋	NOUN
ejpam-6040	545	7	and	and	CCONJ
ejpam-6040	545	8	d8	d8	PROPN
ejpam-6040	545	9	=	=	SYM
ejpam-6040	545	10	{	{	PUNCT
ejpam-6040	545	11	v1	v1	PROPN
ejpam-6040	545	12	,	,	PUNCT
ejpam-6040	545	13	v4	v4	NOUN
ejpam-6040	545	14	,	,	PUNCT
ejpam-6040	545	15	·	·	PUNCT
ejpam-6040	545	16	·	·	PUNCT
ejpam-6040	545	17	·	·	PUNCT
ejpam-6040	545	18	,	,	PUNCT
ejpam-6040	545	19	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	545	20	}	}	PUNCT
ejpam-6040	545	21	.	.	PUNCT
ejpam-6040	546	1	then	then	ADV
ejpam-6040	546	2	d8	d8	PROPN
ejpam-6040	546	3	is	be	AUX
ejpam-6040	546	4	a	a	DET
ejpam-6040	546	5	ζgk	ζgk	ADJ
ejpam-6040	546	6	-set	-set	ADJ
ejpam-6040	546	7	of	of	ADP
ejpam-6040	546	8	cn	cn	PROPN
ejpam-6040	546	9	and	and	CCONJ
ejpam-6040	546	10	ng	ng	PROPN
ejpam-6040	546	11	g[d8	g[d8	NOUN
ejpam-6040	546	12	]	]	PUNCT
ejpam-6040	546	13	=	=	SYM
ejpam-6040	546	14	{	{	PUNCT
ejpam-6040	546	15	v1	v1	PROPN
ejpam-6040	546	16	,	,	PUNCT
ejpam-6040	546	17	v2	v2	PROPN
ejpam-6040	546	18	,	,	PUNCT
ejpam-6040	546	19	v3	v3	PROPN
ejpam-6040	546	20	,	,	PUNCT
ejpam-6040	546	21	v4	v4	PROPN
ejpam-6040	546	22	,	,	PUNCT
ejpam-6040	546	23	·	·	PUNCT
ejpam-6040	546	24	·	·	PUNCT
ejpam-6040	546	25	·	·	PUNCT
ejpam-6040	546	26	,	,	PUNCT
ejpam-6040	546	27	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	546	28	,	,	PUNCT
ejpam-6040	546	29	v3r−3k+2	v3r−3k+2	PROPN
ejpam-6040	546	30	,	,	PUNCT
ejpam-6040	546	31	v3r+1	v3r+1	ADJ
ejpam-6040	546	32	}	}	PUNCT
ejpam-6040	546	33	.	.	PUNCT
ejpam-6040	547	1	this	this	PRON
ejpam-6040	547	2	implies	imply	VERB
ejpam-6040	547	3	that	that	PRON
ejpam-6040	547	4	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	547	5	)	)	PUNCT
ejpam-6040	547	6	=	=	SYM
ejpam-6040	547	7	ζgk(d8	ζgk(d8	NOUN
ejpam-6040	547	8	)	)	PUNCT
ejpam-6040	548	1	=	=	PUNCT
ejpam-6040	548	2	n−	n−	NOUN
ejpam-6040	548	3	|ng	|ng	X
ejpam-6040	548	4	g[d8]|	g[d8]|	X
ejpam-6040	548	5	=	=	PUNCT
ejpam-6040	549	1	3r+1−	3r+1−	NUM
ejpam-6040	550	1	[	[	X
ejpam-6040	550	2	(	(	PUNCT
ejpam-6040	550	3	3r−	3r−	PROPN
ejpam-6040	550	4	3k+2)+1	3k+2)+1	NUM
ejpam-6040	550	5	]	]	X
ejpam-6040	550	6	=	=	PUNCT
ejpam-6040	550	7	3k−	3k−	NUM
ejpam-6040	550	8	2	2	NUM
ejpam-6040	550	9	.	.	PUNCT
ejpam-6040	551	1	hence	hence	ADV
ejpam-6040	551	2	,	,	PUNCT
ejpam-6040	551	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	551	4	)	)	PUNCT
ejpam-6040	551	5	=	=	PUNCT
ejpam-6040	552	1	3k	3k	X
ejpam-6040	553	1	−	−	NOUN
ejpam-6040	554	1	2	2	X
ejpam-6040	554	2	.	.	PUNCT
ejpam-6040	555	1	next	next	ADV
ejpam-6040	555	2	,	,	PUNCT
ejpam-6040	555	3	let	let	VERB
ejpam-6040	555	4	⌊γg(cn)−2	⌊γg(cn)−2	ADP
ejpam-6040	555	5	2	2	NUM
ejpam-6040	555	6	⌋	⌋	NOUN
ejpam-6040	555	7	<	<	X
ejpam-6040	555	8	k	k	PROPN
ejpam-6040	555	9	≤	≤	PROPN
ejpam-6040	555	10	γg(cn	γg(cn	NOUN
ejpam-6040	555	11	)	)	PUNCT
ejpam-6040	556	1	−	−	PROPN
ejpam-6040	556	2	3	3	X
ejpam-6040	556	3	.	.	PUNCT
ejpam-6040	556	4	choose	choose	VERB
ejpam-6040	556	5	an	an	DET
ejpam-6040	556	6	(	(	PUNCT
ejpam-6040	556	7	r	r	NOUN
ejpam-6040	556	8	−	−	PROPN
ejpam-6040	556	9	k	k	PROPN
ejpam-6040	556	10	+	+	PROPN
ejpam-6040	556	11	1)element	1)element	NUM
ejpam-6040	556	12	set	set	VERB
ejpam-6040	556	13	d9	d9	PROPN
ejpam-6040	556	14	=	=	PUNCT
ejpam-6040	556	15	{	{	PUNCT
ejpam-6040	556	16	v⌈	v⌈	NOUN
ejpam-6040	556	17	3r+3	3r+3	PROPN
ejpam-6040	556	18	2	2	NUM
ejpam-6040	556	19	⌉	⌉	NOUN
ejpam-6040	556	20	,	,	PUNCT
ejpam-6040	556	21	v1	v1	NOUN
ejpam-6040	556	22	,	,	PUNCT
ejpam-6040	556	23	v4	v4	NOUN
ejpam-6040	556	24	,	,	PUNCT
ejpam-6040	556	25	·	·	PUNCT
ejpam-6040	556	26	·	·	PUNCT
ejpam-6040	556	27	·	·	PUNCT
ejpam-6040	556	28	,	,	PUNCT
ejpam-6040	556	29	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	556	30	}	}	PUNCT
ejpam-6040	556	31	.	.	PUNCT
ejpam-6040	557	1	then	then	ADV
ejpam-6040	557	2	d9	d9	PROPN
ejpam-6040	557	3	is	be	AUX
ejpam-6040	557	4	a	a	DET
ejpam-6040	557	5	ζgk	ζgk	ADJ
ejpam-6040	557	6	-set	-set	ADJ
ejpam-6040	557	7	of	of	ADP
ejpam-6040	557	8	cn	cn	PROPN
ejpam-6040	557	9	and	and	CCONJ
ejpam-6040	557	10	ng	ng	PROPN
ejpam-6040	557	11	g[d9	g[d9	NOUN
ejpam-6040	557	12	]	]	X
ejpam-6040	557	13	=	=	SYM
ejpam-6040	557	14	{	{	PUNCT
ejpam-6040	557	15	v1	v1	PROPN
ejpam-6040	557	16	,	,	PUNCT
ejpam-6040	557	17	v2	v2	PROPN
ejpam-6040	557	18	,	,	PUNCT
ejpam-6040	557	19	v3	v3	PROPN
ejpam-6040	557	20	,	,	PUNCT
ejpam-6040	557	21	v4	v4	PROPN
ejpam-6040	557	22	,	,	PUNCT
ejpam-6040	557	23	·	·	PUNCT
ejpam-6040	557	24	·	·	PUNCT
ejpam-6040	557	25	·	·	PUNCT
ejpam-6040	557	26	,	,	PUNCT
ejpam-6040	557	27	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	557	28	,	,	PUNCT
ejpam-6040	557	29	v3r−3k−1	v3r−3k−1	NOUN
ejpam-6040	557	30	,	,	PUNCT
ejpam-6040	557	31	v⌈	v⌈	NOUN
ejpam-6040	557	32	3r+3	3r+3	PROPN
ejpam-6040	557	33	2	2	NUM
ejpam-6040	557	34	⌉−1	⌉−1	PROPN
ejpam-6040	557	35	,	,	PUNCT
ejpam-6040	557	36	v⌈	v⌈	NOUN
ejpam-6040	557	37	3r+3	3r+3	PROPN
ejpam-6040	557	38	2	2	NUM
ejpam-6040	557	39	⌉	⌉	NOUN
ejpam-6040	557	40	,	,	PUNCT
ejpam-6040	557	41	v⌈	v⌈	NOUN
ejpam-6040	557	42	3r+3	3r+3	PROPN
ejpam-6040	557	43	2	2	NUM
ejpam-6040	557	44	⌉+1	⌉+1	PROPN
ejpam-6040	557	45	,	,	PUNCT
ejpam-6040	557	46	v3r+1	v3r+1	NOUN
ejpam-6040	557	47	}	}	PUNCT
ejpam-6040	557	48	.	.	PUNCT
ejpam-6040	558	1	this	this	PRON
ejpam-6040	558	2	implies	imply	VERB
ejpam-6040	558	3	that	that	DET
ejpam-6040	558	4	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	558	5	)	)	PUNCT
ejpam-6040	558	6	=	=	SYM
ejpam-6040	558	7	ζgk(d9	ζgk(d9	NOUN
ejpam-6040	558	8	)	)	PUNCT
ejpam-6040	558	9	=	=	SYM
ejpam-6040	558	10	n−	n−	NOUN
ejpam-6040	558	11	|ng	|ng	X
ejpam-6040	558	12	g[d9]|	g[d9]|	X
ejpam-6040	558	13	=	=	PUNCT
ejpam-6040	559	1	3r+1−	3r+1−	NUM
ejpam-6040	559	2	[	[	X
ejpam-6040	559	3	(	(	PUNCT
ejpam-6040	559	4	3r−	3r−	PROPN
ejpam-6040	559	5	3k−	3k−	NUM
ejpam-6040	559	6	1)+	1)+	NUM
ejpam-6040	559	7	4	4	NUM
ejpam-6040	559	8	]	]	PUNCT
ejpam-6040	559	9	=	=	PUNCT
ejpam-6040	560	1	3k−	3k−	NUM
ejpam-6040	560	2	2	2	NUM
ejpam-6040	560	3	.	.	PUNCT
ejpam-6040	561	1	hence	hence	ADV
ejpam-6040	561	2	,	,	PUNCT
ejpam-6040	561	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	561	4	)	)	PUNCT
ejpam-6040	561	5	=	=	PUNCT
ejpam-6040	562	1	3k	3k	X
ejpam-6040	563	1	−	−	NOUN
ejpam-6040	563	2	2	2	X
ejpam-6040	563	3	.	.	PUNCT
ejpam-6040	563	4	s.	s.	PROPN
ejpam-6040	563	5	canoy	canoy	PROPN
ejpam-6040	563	6	,	,	PUNCT
ejpam-6040	563	7	jr	jr	PROPN
ejpam-6040	563	8	.	.	PROPN
ejpam-6040	563	9	,	,	PUNCT
ejpam-6040	563	10	j.	j.	PROPN
ejpam-6040	563	11	anoche	anoche	PROPN
ejpam-6040	563	12	/	/	SYM
ejpam-6040	563	13	eur	eur	PROPN
ejpam-6040	563	14	.	.	PUNCT
ejpam-6040	564	1	j.	j.	PROPN
ejpam-6040	564	2	pure	pure	PROPN
ejpam-6040	564	3	appl	appl	PROPN
ejpam-6040	564	4	.	.	PROPN
ejpam-6040	564	5	math	math	PROPN
ejpam-6040	564	6	,	,	PUNCT
ejpam-6040	564	7	18	18	NUM
ejpam-6040	564	8	(	(	PUNCT
ejpam-6040	564	9	2	2	NUM
ejpam-6040	564	10	)	)	PUNCT
ejpam-6040	564	11	(	(	PUNCT
ejpam-6040	564	12	2025	2025	NUM
ejpam-6040	564	13	)	)	PUNCT
ejpam-6040	564	14	,	,	PUNCT
ejpam-6040	564	15	6040	6040	NUM
ejpam-6040	564	16	14	14	NUM
ejpam-6040	564	17	of	of	ADP
ejpam-6040	564	18	16	16	NUM
ejpam-6040	564	19	subcase	subcase	NOUN
ejpam-6040	564	20	4	4	NUM
ejpam-6040	564	21	:	:	PUNCT
ejpam-6040	564	22	r	r	NOUN
ejpam-6040	564	23	≥	≥	NUM
ejpam-6040	564	24	3	3	NUM
ejpam-6040	564	25	is	be	AUX
ejpam-6040	564	26	odd	odd	ADJ
ejpam-6040	564	27	and	and	CCONJ
ejpam-6040	564	28	k	k	NOUN
ejpam-6040	564	29	=	=	SYM
ejpam-6040	565	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	565	2	2	2	NUM
ejpam-6040	565	3	=	=	SYM
ejpam-6040	565	4	r	r	NOUN
ejpam-6040	565	5	−	−	NOUN
ejpam-6040	565	6	1	1	NUM
ejpam-6040	565	7	.	.	PUNCT
ejpam-6040	566	1	let	let	VERB
ejpam-6040	566	2	d10	d10	PROPN
ejpam-6040	566	3	=	=	SYM
ejpam-6040	566	4	{	{	PUNCT
ejpam-6040	566	5	v1	v1	PROPN
ejpam-6040	566	6	,	,	PUNCT
ejpam-6040	566	7	v	v	NOUN
ejpam-6040	566	8	3r+3	3r+3	PROPN
ejpam-6040	566	9	2	2	NUM
ejpam-6040	566	10	}	}	PUNCT
ejpam-6040	566	11	.	.	PUNCT
ejpam-6040	567	1	then	then	ADV
ejpam-6040	567	2	d10	d10	PROPN
ejpam-6040	567	3	is	be	AUX
ejpam-6040	567	4	a	a	DET
ejpam-6040	567	5	ζgk	ζgk	ADJ
ejpam-6040	567	6	-set	-set	ADJ
ejpam-6040	567	7	of	of	ADP
ejpam-6040	567	8	cn	cn	PROPN
ejpam-6040	567	9	and	and	CCONJ
ejpam-6040	567	10	ng	ng	PROPN
ejpam-6040	567	11	g[d10	g[d10	PROPN
ejpam-6040	567	12	]	]	X
ejpam-6040	568	1	=	=	PRON
ejpam-6040	568	2	{	{	PUNCT
ejpam-6040	568	3	v1	v1	PROPN
ejpam-6040	568	4	,	,	PUNCT
ejpam-6040	568	5	v2	v2	PROPN
ejpam-6040	568	6	,	,	PUNCT
ejpam-6040	568	7	v	v	X
ejpam-6040	568	8	3r+1	3r+1	PROPN
ejpam-6040	568	9	2	2	NUM
ejpam-6040	568	10	,	,	PUNCT
ejpam-6040	568	11	v	v	NOUN
ejpam-6040	568	12	3r+3	3r+3	PROPN
ejpam-6040	568	13	2	2	NUM
ejpam-6040	568	14	,	,	PUNCT
ejpam-6040	568	15	v	v	ADP
ejpam-6040	568	16	3r+5	3r+5	PROPN
ejpam-6040	568	17	2	2	NUM
ejpam-6040	568	18	,	,	PUNCT
ejpam-6040	568	19	v3r+1	v3r+1	PROPN
ejpam-6040	568	20	}	}	PUNCT
ejpam-6040	568	21	.	.	PUNCT
ejpam-6040	569	1	hence	hence	ADV
ejpam-6040	569	2	,	,	PUNCT
ejpam-6040	569	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	569	4	)	)	PUNCT
ejpam-6040	569	5	=	=	SYM
ejpam-6040	569	6	ζgk(d10	ζgk(d10	X
ejpam-6040	569	7	)	)	PUNCT
ejpam-6040	569	8	=	=	SYM
ejpam-6040	570	1	3r	3r	NUM
ejpam-6040	570	2	+	+	CCONJ
ejpam-6040	570	3	1−	1−	NUM
ejpam-6040	570	4	|ng	|ng	X
ejpam-6040	570	5	g[d10]|	g[d10]|	NOUN
ejpam-6040	570	6	=	=	SYM
ejpam-6040	570	7	3r	3r	NUM
ejpam-6040	570	8	+	+	CCONJ
ejpam-6040	570	9	1−	1−	NUM
ejpam-6040	570	10	6	6	NUM
ejpam-6040	570	11	=	=	SYM
ejpam-6040	570	12	3k	3k	NOUN
ejpam-6040	571	1	−	−	NOUN
ejpam-6040	571	2	2	2	X
ejpam-6040	571	3	.	.	PUNCT
ejpam-6040	571	4	case	case	NOUN
ejpam-6040	571	5	3	3	NUM
ejpam-6040	571	6	:	:	PUNCT
ejpam-6040	571	7	n	n	NOUN
ejpam-6040	571	8	=	=	SYM
ejpam-6040	571	9	3r	3r	NUM
ejpam-6040	571	10	+	+	CCONJ
ejpam-6040	571	11	2	2	NUM
ejpam-6040	571	12	where	where	SCONJ
ejpam-6040	571	13	r	r	NOUN
ejpam-6040	571	14	≥	≥	NOUN
ejpam-6040	571	15	2	2	NUM
ejpam-6040	571	16	.	.	PUNCT
ejpam-6040	571	17	by	by	ADP
ejpam-6040	571	18	theorem	theorem	NOUN
ejpam-6040	571	19	1(v	1(v	NUM
ejpam-6040	571	20	)	)	PUNCT
ejpam-6040	571	21	,	,	PUNCT
ejpam-6040	571	22	γg(cn	γg(cn	NOUN
ejpam-6040	571	23	)	)	PUNCT
ejpam-6040	571	24	=	=	PUNCT
ejpam-6040	571	25	⌈n3	⌈n3	X
ejpam-6040	571	26	⌉	⌉	PRON
ejpam-6040	571	27	=	=	SYM
ejpam-6040	571	28	r+1	r+1	PROPN
ejpam-6040	571	29	.	.	PUNCT
ejpam-6040	572	1	thus	thus	ADV
ejpam-6040	572	2	,	,	PUNCT
ejpam-6040	572	3	k	k	PROPN
ejpam-6040	572	4	≤	≤	PROPN
ejpam-6040	572	5	r.	r.	PROPN
ejpam-6040	572	6	consider	consider	VERB
ejpam-6040	572	7	the	the	DET
ejpam-6040	572	8	following	follow	VERB
ejpam-6040	572	9	subcases	subcase	NOUN
ejpam-6040	572	10	:	:	PUNCT
ejpam-6040	572	11	subcase	subcase	NOUN
ejpam-6040	572	12	1	1	NUM
ejpam-6040	572	13	:	:	PUNCT
ejpam-6040	573	1	r	r	NOUN
ejpam-6040	573	2	≥	≥	NUM
ejpam-6040	573	3	3	3	NUM
ejpam-6040	573	4	and	and	CCONJ
ejpam-6040	573	5	k	k	NOUN
ejpam-6040	573	6	=	=	NOUN
ejpam-6040	573	7	1	1	X
ejpam-6040	573	8	.	.	PUNCT
ejpam-6040	573	9	letd11	letd11	NOUN
ejpam-6040	574	1	=	=	PRON
ejpam-6040	574	2	{	{	PUNCT
ejpam-6040	574	3	v1	v1	PROPN
ejpam-6040	574	4	,	,	PUNCT
ejpam-6040	574	5	v4	v4	NOUN
ejpam-6040	574	6	,	,	PUNCT
ejpam-6040	574	7	·	·	PUNCT
ejpam-6040	574	8	·	·	PUNCT
ejpam-6040	574	9	·	·	PUNCT
ejpam-6040	574	10	,	,	PUNCT
ejpam-6040	574	11	v3r−2	v3r−2	AUX
ejpam-6040	574	12	}	}	PUNCT
ejpam-6040	574	13	be	be	VERB
ejpam-6040	574	14	an	an	DET
ejpam-6040	574	15	(	(	PUNCT
ejpam-6040	574	16	r)-element	r)-element	ADJ
ejpam-6040	574	17	set	set	NOUN
ejpam-6040	574	18	.	.	PUNCT
ejpam-6040	575	1	thenng	thenng	PROPN
ejpam-6040	575	2	g[d11	g[d11	PROPN
ejpam-6040	575	3	]	]	X
ejpam-6040	575	4	=	=	PRON
ejpam-6040	575	5	{	{	PUNCT
ejpam-6040	575	6	v1	v1	PROPN
ejpam-6040	575	7	,	,	PUNCT
ejpam-6040	575	8	v2	v2	PROPN
ejpam-6040	575	9	,	,	PUNCT
ejpam-6040	575	10	·	·	PUNCT
ejpam-6040	575	11	·	·	PUNCT
ejpam-6040	575	12	·	·	PUNCT
ejpam-6040	575	13	,	,	PUNCT
ejpam-6040	575	14	v3r−2	v3r−2	PROPN
ejpam-6040	575	15	,	,	PUNCT
ejpam-6040	575	16	v3r−1	v3r−1	PROPN
ejpam-6040	575	17	,	,	PUNCT
ejpam-6040	575	18	v3r+2	v3r+2	ADJ
ejpam-6040	575	19	}	}	PUNCT
ejpam-6040	575	20	.	.	PUNCT
ejpam-6040	576	1	thus	thus	ADV
ejpam-6040	576	2	,	,	PUNCT
ejpam-6040	576	3	d11	d11	PROPN
ejpam-6040	576	4	is	be	AUX
ejpam-6040	576	5	a	a	DET
ejpam-6040	576	6	ζg1	ζg1	PROPN
ejpam-6040	576	7	-set	-set	ADJ
ejpam-6040	576	8	of	of	ADP
ejpam-6040	576	9	cn	cn	PROPN
ejpam-6040	576	10	.	.	PUNCT
ejpam-6040	577	1	hence	hence	ADV
ejpam-6040	577	2	,	,	PUNCT
ejpam-6040	577	3	ζg1	ζg1	X
ejpam-6040	577	4	(	(	PUNCT
ejpam-6040	577	5	cn	cn	PROPN
ejpam-6040	577	6	)	)	PUNCT
ejpam-6040	577	7	=	=	PUNCT
ejpam-6040	577	8	ζg1	ζg1	X
ejpam-6040	577	9	(	(	PUNCT
ejpam-6040	577	10	d11	d11	PROPN
ejpam-6040	577	11	)	)	PUNCT
ejpam-6040	578	1	=	=	PUNCT
ejpam-6040	578	2	n−	n−	NOUN
ejpam-6040	578	3	|ng	|ng	PUNCT
ejpam-6040	578	4	g[d11]|	g[d11]|	X
ejpam-6040	578	5	=	=	PUNCT
ejpam-6040	578	6	3r	3r	NUM
ejpam-6040	578	7	+	+	CCONJ
ejpam-6040	578	8	2−	2−	NUM
ejpam-6040	579	1	[	[	X
ejpam-6040	579	2	(	(	PUNCT
ejpam-6040	579	3	3r	3r	NUM
ejpam-6040	579	4	−	−	NOUN
ejpam-6040	579	5	1	1	NUM
ejpam-6040	579	6	)	)	PUNCT
ejpam-6040	579	7	+	+	CCONJ
ejpam-6040	579	8	1	1	X
ejpam-6040	579	9	]	]	X
ejpam-6040	579	10	=	=	SYM
ejpam-6040	579	11	2	2	NUM
ejpam-6040	579	12	=	=	SYM
ejpam-6040	579	13	3k	3k	NOUN
ejpam-6040	579	14	−	−	NOUN
ejpam-6040	579	15	1	1	X
ejpam-6040	579	16	.	.	PUNCT
ejpam-6040	579	17	subcase	subcase	PROPN
ejpam-6040	579	18	2	2	NUM
ejpam-6040	579	19	:	:	PUNCT
ejpam-6040	579	20	k	k	X
ejpam-6040	579	21	=	=	PUNCT
ejpam-6040	579	22	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	579	23	1	1	NUM
ejpam-6040	579	24	=	=	SYM
ejpam-6040	579	25	r.	r.	X
ejpam-6040	579	26	by	by	ADP
ejpam-6040	579	27	lemma	lemma	PROPN
ejpam-6040	579	28	1	1	NUM
ejpam-6040	579	29	,	,	PUNCT
ejpam-6040	579	30	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	579	31	)	)	PUNCT
ejpam-6040	579	32	=	=	PUNCT
ejpam-6040	580	1	n−	n−	NOUN
ejpam-6040	580	2	1	1	NUM
ejpam-6040	580	3	=	=	SYM
ejpam-6040	580	4	3r	3r	NUM
ejpam-6040	580	5	+	+	CCONJ
ejpam-6040	580	6	2−	2−	NUM
ejpam-6040	580	7	1	1	NUM
ejpam-6040	580	8	=	=	NOUN
ejpam-6040	580	9	3r	3r	NUM
ejpam-6040	580	10	+	+	CCONJ
ejpam-6040	580	11	1	1	NUM
ejpam-6040	580	12	=	=	SYM
ejpam-6040	580	13	3k	3k	NOUN
ejpam-6040	581	1	+	+	NOUN
ejpam-6040	581	2	1	1	X
ejpam-6040	581	3	.	.	X
ejpam-6040	581	4	subcase	subcase	NOUN
ejpam-6040	581	5	3	3	NUM
ejpam-6040	581	6	:	:	PUNCT
ejpam-6040	581	7	r	r	NOUN
ejpam-6040	581	8	is	be	AUX
ejpam-6040	581	9	odd	odd	ADJ
ejpam-6040	581	10	and	and	CCONJ
ejpam-6040	581	11	k	k	NOUN
ejpam-6040	581	12	=	=	SYM
ejpam-6040	582	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	582	2	2	2	NUM
ejpam-6040	582	3	=	=	SYM
ejpam-6040	582	4	r	r	NOUN
ejpam-6040	582	5	−	−	NOUN
ejpam-6040	582	6	1	1	NUM
ejpam-6040	582	7	.	.	PUNCT
ejpam-6040	583	1	let	let	VERB
ejpam-6040	583	2	d12	d12	NOUN
ejpam-6040	583	3	=	=	SYM
ejpam-6040	583	4	{	{	PUNCT
ejpam-6040	583	5	v1	v1	PROPN
ejpam-6040	583	6	,	,	PUNCT
ejpam-6040	583	7	v4	v4	NOUN
ejpam-6040	583	8	}	}	PUNCT
ejpam-6040	583	9	.	.	PUNCT
ejpam-6040	584	1	then	then	ADV
ejpam-6040	584	2	d12	d12	PROPN
ejpam-6040	584	3	is	be	AUX
ejpam-6040	584	4	a	a	DET
ejpam-6040	584	5	ζgk	ζgk	ADJ
ejpam-6040	584	6	-set	-set	ADJ
ejpam-6040	584	7	of	of	ADP
ejpam-6040	584	8	cn	cn	PROPN
ejpam-6040	584	9	and	and	CCONJ
ejpam-6040	584	10	ng	ng	PROPN
ejpam-6040	584	11	g[d12	g[d12	PROPN
ejpam-6040	584	12	]	]	X
ejpam-6040	584	13	=	=	PRON
ejpam-6040	584	14	{	{	PUNCT
ejpam-6040	584	15	v1	v1	PROPN
ejpam-6040	584	16	,	,	PUNCT
ejpam-6040	584	17	v2	v2	PROPN
ejpam-6040	584	18	,	,	PUNCT
ejpam-6040	584	19	v3	v3	PROPN
ejpam-6040	584	20	,	,	PUNCT
ejpam-6040	584	21	v4	v4	PROPN
ejpam-6040	584	22	}	}	PUNCT
ejpam-6040	584	23	.	.	PUNCT
ejpam-6040	585	1	hence	hence	ADV
ejpam-6040	585	2	,	,	PUNCT
ejpam-6040	585	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	585	4	)	)	PUNCT
ejpam-6040	585	5	=	=	SYM
ejpam-6040	585	6	ζgk(d12	ζgk(d12	X
ejpam-6040	585	7	)	)	PUNCT
ejpam-6040	586	1	=	=	NOUN
ejpam-6040	586	2	3r	3r	NUM
ejpam-6040	586	3	+	+	CCONJ
ejpam-6040	586	4	2−	2−	NUM
ejpam-6040	586	5	|ng	|ng	NOUN
ejpam-6040	586	6	g[d12]|	g[d12]|	NOUN
ejpam-6040	586	7	=	=	NOUN
ejpam-6040	586	8	3r	3r	NUM
ejpam-6040	586	9	+	+	CCONJ
ejpam-6040	586	10	2−	2−	NUM
ejpam-6040	586	11	4	4	NUM
ejpam-6040	586	12	=	=	SYM
ejpam-6040	586	13	3k	3k	NOUN
ejpam-6040	587	1	+	+	NOUN
ejpam-6040	587	2	1	1	X
ejpam-6040	587	3	.	.	X
ejpam-6040	587	4	subcase	subcase	NOUN
ejpam-6040	587	5	4	4	NUM
ejpam-6040	587	6	:	:	PUNCT
ejpam-6040	587	7	r	r	NOUN
ejpam-6040	587	8	is	be	AUX
ejpam-6040	587	9	even	even	ADV
ejpam-6040	587	10	and	and	CCONJ
ejpam-6040	587	11	k	k	PROPN
ejpam-6040	587	12	=	=	SYM
ejpam-6040	588	1	γg(cn)−	γg(cn)−	ADJ
ejpam-6040	588	2	2	2	NUM
ejpam-6040	588	3	=	=	SYM
ejpam-6040	588	4	r	r	NOUN
ejpam-6040	588	5	−	−	NOUN
ejpam-6040	588	6	1	1	NUM
ejpam-6040	588	7	.	.	PUNCT
ejpam-6040	588	8	letd14	letd14	NOUN
ejpam-6040	588	9	=	=	SYM
ejpam-6040	588	10	{	{	PUNCT
ejpam-6040	588	11	v1	v1	PROPN
ejpam-6040	588	12	,	,	PUNCT
ejpam-6040	588	13	v	v	X
ejpam-6040	588	14	3r+4	3r+4	NUM
ejpam-6040	588	15	2	2	NUM
ejpam-6040	588	16	}	}	PUNCT
ejpam-6040	588	17	is	be	AUX
ejpam-6040	588	18	a	a	DET
ejpam-6040	588	19	ζgk	ζgk	ADJ
ejpam-6040	588	20	-set	-set	ADJ
ejpam-6040	588	21	of	of	ADP
ejpam-6040	588	22	cn	cn	PROPN
ejpam-6040	588	23	andng	andng	PROPN
ejpam-6040	588	24	g[d14	g[d14	PROPN
ejpam-6040	588	25	]	]	X
ejpam-6040	588	26	=	=	SYM
ejpam-6040	588	27	{	{	PUNCT
ejpam-6040	588	28	v1	v1	PROPN
ejpam-6040	588	29	,	,	PUNCT
ejpam-6040	588	30	v2	v2	PROPN
ejpam-6040	588	31	,	,	PUNCT
ejpam-6040	588	32	v	v	ADP
ejpam-6040	588	33	3r+2	3r+2	NUM
ejpam-6040	588	34	2	2	NUM
ejpam-6040	588	35	,	,	PUNCT
ejpam-6040	588	36	v	v	ADP
ejpam-6040	588	37	3r+4	3r+4	PROPN
ejpam-6040	588	38	2	2	NUM
ejpam-6040	588	39	,	,	PUNCT
ejpam-6040	588	40	v	v	PRON
ejpam-6040	588	41	3r+6	3r+6	NUM
ejpam-6040	588	42	2	2	NUM
ejpam-6040	588	43	,	,	PUNCT
ejpam-6040	588	44	v3r+2	v3r+2	ADJ
ejpam-6040	588	45	}	}	PUNCT
ejpam-6040	588	46	.	.	PUNCT
ejpam-6040	589	1	hence	hence	ADV
ejpam-6040	589	2	,	,	PUNCT
ejpam-6040	589	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	589	4	)	)	PUNCT
ejpam-6040	589	5	=	=	SYM
ejpam-6040	590	1	ζgk(d14	ζgk(d14	X
ejpam-6040	590	2	)	)	PUNCT
ejpam-6040	590	3	=	=	SYM
ejpam-6040	590	4	3r	3r	NUM
ejpam-6040	590	5	+	+	CCONJ
ejpam-6040	590	6	2−	2−	NUM
ejpam-6040	590	7	|ng	|ng	NOUN
ejpam-6040	590	8	g[d14]|	g[d14]|	NOUN
ejpam-6040	590	9	=	=	NOUN
ejpam-6040	590	10	3r	3r	NUM
ejpam-6040	590	11	+	+	CCONJ
ejpam-6040	590	12	2−	2−	NUM
ejpam-6040	590	13	6	6	NUM
ejpam-6040	590	14	=	=	SYM
ejpam-6040	590	15	3k	3k	NOUN
ejpam-6040	590	16	−	−	NOUN
ejpam-6040	590	17	1	1	X
ejpam-6040	590	18	.	.	PUNCT
ejpam-6040	590	19	subcase	subcase	PROPN
ejpam-6040	590	20	5	5	NUM
ejpam-6040	590	21	:	:	PUNCT
ejpam-6040	590	22	r	r	NOUN
ejpam-6040	590	23	≥	≥	NUM
ejpam-6040	590	24	4	4	NUM
ejpam-6040	590	25	and	and	CCONJ
ejpam-6040	590	26	2	2	NUM
ejpam-6040	590	27	≤	≤	NOUN
ejpam-6040	590	28	k	k	NOUN
ejpam-6040	590	29	≤	≤	NUM
ejpam-6040	591	1	γg(cn)−	γg(cn)−	INTJ
ejpam-6040	591	2	3	3	X
ejpam-6040	591	3	.	.	PUNCT
ejpam-6040	592	1	let	let	VERB
ejpam-6040	592	2	k	k	PROPN
ejpam-6040	592	3	≤	≤	X
ejpam-6040	592	4	⌊γg(cn)−2	⌊γg(cn)−2	PUNCT
ejpam-6040	592	5	2	2	NUM
ejpam-6040	592	6	⌋	⌋	NOUN
ejpam-6040	592	7	and	and	CCONJ
ejpam-6040	592	8	let	let	VERB
ejpam-6040	592	9	d15	d15	NOUN
ejpam-6040	592	10	=	=	SYM
ejpam-6040	592	11	{	{	PUNCT
ejpam-6040	592	12	v1	v1	PROPN
ejpam-6040	592	13	,	,	PUNCT
ejpam-6040	592	14	v4	v4	NOUN
ejpam-6040	592	15	,	,	PUNCT
ejpam-6040	592	16	·	·	PUNCT
ejpam-6040	592	17	·	·	PUNCT
ejpam-6040	592	18	·	·	PUNCT
ejpam-6040	592	19	,	,	PUNCT
ejpam-6040	592	20	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	592	21	}	}	PUNCT
ejpam-6040	592	22	.	.	PUNCT
ejpam-6040	593	1	then	then	ADV
ejpam-6040	593	2	d15	d15	PROPN
ejpam-6040	593	3	is	be	AUX
ejpam-6040	593	4	a	a	DET
ejpam-6040	593	5	ζgk	ζgk	ADJ
ejpam-6040	593	6	-set	-set	ADJ
ejpam-6040	593	7	of	of	ADP
ejpam-6040	593	8	cn	cn	PROPN
ejpam-6040	593	9	and	and	CCONJ
ejpam-6040	593	10	ng	ng	PROPN
ejpam-6040	593	11	g[d15	g[d15	PROPN
ejpam-6040	593	12	]	]	X
ejpam-6040	594	1	=	=	PRON
ejpam-6040	594	2	{	{	PUNCT
ejpam-6040	594	3	v1	v1	PROPN
ejpam-6040	594	4	,	,	PUNCT
ejpam-6040	594	5	v2	v2	PROPN
ejpam-6040	594	6	,	,	PUNCT
ejpam-6040	594	7	v3	v3	PROPN
ejpam-6040	594	8	,	,	PUNCT
ejpam-6040	594	9	v4	v4	PROPN
ejpam-6040	594	10	,	,	PUNCT
ejpam-6040	594	11	·	·	PUNCT
ejpam-6040	594	12	·	·	PUNCT
ejpam-6040	594	13	·	·	PUNCT
ejpam-6040	594	14	,	,	PUNCT
ejpam-6040	594	15	v3r−3k+1	v3r−3k+1	NOUN
ejpam-6040	594	16	,	,	PUNCT
ejpam-6040	594	17	v3r−3k+2	v3r−3k+2	NOUN
ejpam-6040	594	18	,	,	PUNCT
ejpam-6040	594	19	v3r+2	v3r+2	ADJ
ejpam-6040	594	20	}	}	PUNCT
ejpam-6040	594	21	.	.	PUNCT
ejpam-6040	595	1	thus	thus	ADV
ejpam-6040	595	2	,	,	PUNCT
ejpam-6040	595	3	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	595	4	)	)	PUNCT
ejpam-6040	595	5	=	=	SYM
ejpam-6040	595	6	ζgk(d15	ζgk(d15	X
ejpam-6040	595	7	)	)	PUNCT
ejpam-6040	595	8	=	=	SYM
ejpam-6040	595	9	n−|ng	n−|ng	NOUN
ejpam-6040	595	10	g[d15]|	g[d15]|	NOUN
ejpam-6040	595	11	=	=	SYM
ejpam-6040	596	1	3r+2−	3r+2−	NUM
ejpam-6040	597	1	[	[	X
ejpam-6040	597	2	(	(	PUNCT
ejpam-6040	597	3	3r−3k+2)+1	3r−3k+2)+1	NUM
ejpam-6040	597	4	]	]	X
ejpam-6040	597	5	=	=	SYM
ejpam-6040	597	6	3k−1	3k−1	PROPN
ejpam-6040	597	7	.	.	PUNCT
ejpam-6040	598	1	next	next	ADV
ejpam-6040	598	2	,	,	PUNCT
ejpam-6040	598	3	let	let	VERB
ejpam-6040	598	4	⌊γg(cn)−2	⌊γg(cn)−2	ADP
ejpam-6040	598	5	2	2	NUM
ejpam-6040	598	6	⌋	⌋	NOUN
ejpam-6040	598	7	<	<	X
ejpam-6040	598	8	k	k	PROPN
ejpam-6040	598	9	≤	≤	PROPN
ejpam-6040	598	10	γg(cn)−3	γg(cn)−3	NOUN
ejpam-6040	598	11	.	.	PUNCT
ejpam-6040	599	1	choose	choose	VERB
ejpam-6040	599	2	an	an	DET
ejpam-6040	599	3	(	(	PUNCT
ejpam-6040	599	4	r	r	NOUN
ejpam-6040	599	5	−	−	PROPN
ejpam-6040	599	6	k	k	PROPN
ejpam-6040	600	1	+	+	PROPN
ejpam-6040	600	2	1)-element	1)-element	NUM
ejpam-6040	600	3	set	set	VERB
ejpam-6040	600	4	d16	d16	NOUN
ejpam-6040	600	5	=	=	NOUN
ejpam-6040	600	6	{	{	PUNCT
ejpam-6040	600	7	v⌈	v⌈	NOUN
ejpam-6040	600	8	3r+5	3r+5	PROPN
ejpam-6040	600	9	2	2	NUM
ejpam-6040	600	10	⌉	⌉	X
ejpam-6040	600	11	,	,	PUNCT
ejpam-6040	600	12	v1	v1	NOUN
ejpam-6040	600	13	,	,	PUNCT
ejpam-6040	600	14	v4	v4	NOUN
ejpam-6040	600	15	,	,	PUNCT
ejpam-6040	600	16	·	·	PUNCT
ejpam-6040	600	17	·	·	PUNCT
ejpam-6040	600	18	·	·	PUNCT
ejpam-6040	600	19	,	,	PUNCT
ejpam-6040	600	20	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	600	21	}	}	PUNCT
ejpam-6040	600	22	.	.	PUNCT
ejpam-6040	601	1	then	then	ADV
ejpam-6040	601	2	d16	d16	PROPN
ejpam-6040	601	3	is	be	AUX
ejpam-6040	601	4	a	a	DET
ejpam-6040	601	5	ζgk	ζgk	ADJ
ejpam-6040	601	6	-set	-set	ADJ
ejpam-6040	601	7	of	of	ADP
ejpam-6040	601	8	cn	cn	PROPN
ejpam-6040	601	9	and	and	CCONJ
ejpam-6040	601	10	ng	ng	PROPN
ejpam-6040	601	11	g[d16	g[d16	PROPN
ejpam-6040	601	12	]	]	X
ejpam-6040	602	1	=	=	PRON
ejpam-6040	602	2	{	{	PUNCT
ejpam-6040	602	3	v1	v1	PROPN
ejpam-6040	602	4	,	,	PUNCT
ejpam-6040	602	5	v2	v2	PROPN
ejpam-6040	602	6	,	,	PUNCT
ejpam-6040	602	7	v3	v3	PROPN
ejpam-6040	602	8	,	,	PUNCT
ejpam-6040	602	9	v4	v4	PROPN
ejpam-6040	602	10	,	,	PUNCT
ejpam-6040	602	11	·	·	PUNCT
ejpam-6040	602	12	·	·	PUNCT
ejpam-6040	602	13	·	·	PUNCT
ejpam-6040	602	14	,	,	PUNCT
ejpam-6040	602	15	v3r−3k−2	v3r−3k−2	NOUN
ejpam-6040	602	16	,	,	PUNCT
ejpam-6040	602	17	v3r−3k−1	v3r−3k−1	NOUN
ejpam-6040	602	18	,	,	PUNCT
ejpam-6040	602	19	v⌈	v⌈	NOUN
ejpam-6040	602	20	3r+5	3r+5	PROPN
ejpam-6040	602	21	2	2	NUM
ejpam-6040	602	22	⌉−1	⌉−1	PROPN
ejpam-6040	602	23	,	,	PUNCT
ejpam-6040	602	24	v⌈	v⌈	NOUN
ejpam-6040	602	25	3r+5	3r+5	PROPN
ejpam-6040	602	26	2	2	NUM
ejpam-6040	602	27	⌉	⌉	NOUN
ejpam-6040	602	28	,	,	PUNCT
ejpam-6040	602	29	v⌈	v⌈	NOUN
ejpam-6040	602	30	3r+5	3r+5	PROPN
ejpam-6040	602	31	2	2	NUM
ejpam-6040	602	32	⌉+1	⌉+1	PROPN
ejpam-6040	602	33	,	,	PUNCT
ejpam-6040	602	34	v3r+2	v3r+2	ADJ
ejpam-6040	602	35	}	}	PUNCT
ejpam-6040	602	36	.	.	PUNCT
ejpam-6040	603	1	s.	s.	PROPN
ejpam-6040	603	2	canoy	canoy	PROPN
ejpam-6040	603	3	,	,	PUNCT
ejpam-6040	603	4	jr	jr	PROPN
ejpam-6040	603	5	.	.	PROPN
ejpam-6040	603	6	,	,	PUNCT
ejpam-6040	603	7	j.	j.	PROPN
ejpam-6040	603	8	anoche	anoche	PROPN
ejpam-6040	603	9	/	/	SYM
ejpam-6040	603	10	eur	eur	PROPN
ejpam-6040	603	11	.	.	PUNCT
ejpam-6040	604	1	j.	j.	PROPN
ejpam-6040	604	2	pure	pure	PROPN
ejpam-6040	604	3	appl	appl	PROPN
ejpam-6040	604	4	.	.	PROPN
ejpam-6040	604	5	math	math	PROPN
ejpam-6040	604	6	,	,	PUNCT
ejpam-6040	604	7	18	18	NUM
ejpam-6040	604	8	(	(	PUNCT
ejpam-6040	604	9	2	2	NUM
ejpam-6040	604	10	)	)	PUNCT
ejpam-6040	604	11	(	(	PUNCT
ejpam-6040	604	12	2025	2025	NUM
ejpam-6040	604	13	)	)	PUNCT
ejpam-6040	604	14	,	,	PUNCT
ejpam-6040	604	15	6040	6040	NUM
ejpam-6040	604	16	15	15	NUM
ejpam-6040	604	17	of	of	ADP
ejpam-6040	604	18	16	16	NUM
ejpam-6040	604	19	this	this	PRON
ejpam-6040	604	20	implies	imply	VERB
ejpam-6040	604	21	that	that	DET
ejpam-6040	604	22	ζgk(cn	ζgk(cn	NOUN
ejpam-6040	604	23	)	)	PUNCT
ejpam-6040	604	24	=	=	SYM
ejpam-6040	604	25	ζgk(d16	ζgk(d16	PROPN
ejpam-6040	604	26	)	)	PUNCT
ejpam-6040	604	27	=	=	SYM
ejpam-6040	605	1	n−	n−	NOUN
ejpam-6040	605	2	|ng	|ng	NOUN
ejpam-6040	605	3	g[d16]|	g[d16]|	X
ejpam-6040	605	4	=	=	NOUN
ejpam-6040	605	5	3r	3r	NUM
ejpam-6040	605	6	+	+	CCONJ
ejpam-6040	605	7	2−	2−	NUM
ejpam-6040	606	1	[	[	X
ejpam-6040	606	2	(	(	PUNCT
ejpam-6040	606	3	3r	3r	NUM
ejpam-6040	606	4	−	−	NOUN
ejpam-6040	606	5	3k	3k	NOUN
ejpam-6040	606	6	−	−	NOUN
ejpam-6040	606	7	1	1	NUM
ejpam-6040	606	8	)	)	PUNCT
ejpam-6040	606	9	+	+	CCONJ
ejpam-6040	606	10	4	4	X
ejpam-6040	606	11	]	]	PUNCT
ejpam-6040	606	12	=	=	SYM
ejpam-6040	606	13	3k	3k	X
ejpam-6040	606	14	−	−	NOUN
ejpam-6040	607	1	1	1	X
ejpam-6040	607	2	.	.	PUNCT
ejpam-6040	608	1	this	this	PRON
ejpam-6040	608	2	shows	show	VERB
ejpam-6040	608	3	that	that	SCONJ
ejpam-6040	608	4	the	the	DET
ejpam-6040	608	5	assertion	assertion	NOUN
ejpam-6040	608	6	holds	hold	VERB
ejpam-6040	608	7	.	.	PUNCT
ejpam-6040	609	1	4	4	X
ejpam-6040	609	2	.	.	X
ejpam-6040	609	3	conclusion	conclusion	NOUN
ejpam-6040	609	4	in	in	ADP
ejpam-6040	609	5	this	this	DET
ejpam-6040	609	6	paper	paper	NOUN
ejpam-6040	609	7	,	,	PUNCT
ejpam-6040	609	8	we	we	PRON
ejpam-6040	609	9	introduced	introduce	VERB
ejpam-6040	609	10	the	the	DET
ejpam-6040	609	11	concept	concept	NOUN
ejpam-6040	609	12	of	of	ADP
ejpam-6040	609	13	k	k	ADJ
ejpam-6040	609	14	-	-	ADJ
ejpam-6040	609	15	geodetic	geodetic	ADJ
ejpam-6040	609	16	domination	domination	NOUN
ejpam-6040	609	17	defect	defect	NOUN
ejpam-6040	609	18	of	of	ADP
ejpam-6040	609	19	a	a	DET
ejpam-6040	609	20	graph	graph	NOUN
ejpam-6040	609	21	and	and	CCONJ
ejpam-6040	609	22	computed	compute	VERB
ejpam-6040	609	23	its	its	PRON
ejpam-6040	609	24	values	value	NOUN
ejpam-6040	609	25	for	for	ADP
ejpam-6040	609	26	several	several	ADJ
ejpam-6040	609	27	well	well	ADV
ejpam-6040	609	28	-	-	PUNCT
ejpam-6040	609	29	known	know	VERB
ejpam-6040	609	30	graphs	graph	NOUN
ejpam-6040	609	31	.	.	PUNCT
ejpam-6040	610	1	additionally	additionally	ADV
ejpam-6040	610	2	,	,	PUNCT
ejpam-6040	610	3	we	we	PRON
ejpam-6040	610	4	established	establish	VERB
ejpam-6040	610	5	some	some	DET
ejpam-6040	610	6	sharp	sharp	ADJ
ejpam-6040	610	7	bounds	bound	NOUN
ejpam-6040	610	8	of	of	ADP
ejpam-6040	610	9	this	this	DET
ejpam-6040	610	10	parameter	parameter	NOUN
ejpam-6040	610	11	.	.	PUNCT
ejpam-6040	611	1	it	it	PRON
ejpam-6040	611	2	is	be	AUX
ejpam-6040	611	3	recommended	recommend	VERB
ejpam-6040	611	4	that	that	SCONJ
ejpam-6040	611	5	further	further	ADJ
ejpam-6040	611	6	investigation	investigation	NOUN
ejpam-6040	611	7	of	of	ADP
ejpam-6040	611	8	this	this	DET
ejpam-6040	611	9	newly	newly	ADV
ejpam-6040	611	10	defined	define	VERB
ejpam-6040	611	11	parameter	parameter	NOUN
ejpam-6040	611	12	be	be	AUX
ejpam-6040	611	13	done	do	VERB
ejpam-6040	611	14	especially	especially	ADV
ejpam-6040	611	15	on	on	ADP
ejpam-6040	611	16	graphs	graph	NOUN
ejpam-6040	611	17	resulting	result	VERB
ejpam-6040	611	18	from	from	ADP
ejpam-6040	611	19	some	some	DET
ejpam-6040	611	20	graph	graph	NOUN
ejpam-6040	611	21	operations	operation	NOUN
ejpam-6040	611	22	.	.	PUNCT
ejpam-6040	612	1	acknowledgements	acknowledgement	NOUN
ejpam-6040	612	2	the	the	DET
ejpam-6040	612	3	authors	author	NOUN
ejpam-6040	612	4	would	would	AUX
ejpam-6040	612	5	like	like	VERB
ejpam-6040	612	6	to	to	PART
ejpam-6040	612	7	thank	thank	VERB
ejpam-6040	612	8	the	the	DET
ejpam-6040	612	9	referees	referee	NOUN
ejpam-6040	612	10	for	for	ADP
ejpam-6040	612	11	the	the	DET
ejpam-6040	612	12	comments	comment	NOUN
ejpam-6040	612	13	and	and	CCONJ
ejpam-6040	612	14	suggestions	suggestion	NOUN
ejpam-6040	612	15	they	they	PRON
ejpam-6040	612	16	offered	offer	VERB
ejpam-6040	612	17	us	we	PRON
ejpam-6040	612	18	which	which	PRON
ejpam-6040	612	19	led	lead	VERB
ejpam-6040	612	20	to	to	ADP
ejpam-6040	612	21	the	the	DET
ejpam-6040	612	22	improvement	improvement	NOUN
ejpam-6040	612	23	of	of	ADP
ejpam-6040	612	24	the	the	DET
ejpam-6040	612	25	paper	paper	NOUN
ejpam-6040	612	26	.	.	PUNCT
ejpam-6040	613	1	also	also	ADV
ejpam-6040	613	2	,	,	PUNCT
ejpam-6040	613	3	the	the	DET
ejpam-6040	613	4	authors	author	NOUN
ejpam-6040	613	5	would	would	AUX
ejpam-6040	613	6	like	like	VERB
ejpam-6040	613	7	to	to	PART
ejpam-6040	613	8	thank	thank	VERB
ejpam-6040	613	9	the	the	DET
ejpam-6040	613	10	department	department	NOUN
ejpam-6040	613	11	of	of	ADP
ejpam-6040	613	12	science	science	NOUN
ejpam-6040	613	13	and	and	CCONJ
ejpam-6040	613	14	technology	technology	NOUN
ejpam-6040	613	15	accelerated	accelerate	VERB
ejpam-6040	613	16	science	science	NOUN
ejpam-6040	613	17	and	and	CCONJ
ejpam-6040	613	18	technology	technology	NOUN
ejpam-6040	613	19	human	human	ADJ
ejpam-6040	613	20	resource	resource	NOUN
ejpam-6040	613	21	development	development	NOUN
ejpam-6040	613	22	program	program	NOUN
ejpam-6040	613	23	(	(	PUNCT
ejpam-6040	613	24	dost	dost	NOUN
ejpam-6040	613	25	-	-	PUNCT
ejpam-6040	613	26	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-6040	613	27	,	,	PUNCT
ejpam-6040	613	28	and	and	CCONJ
ejpam-6040	613	29	msu	msu	PROPN
ejpam-6040	613	30	-	-	PUNCT
ejpam-6040	613	31	iligan	iligan	PROPN
ejpam-6040	613	32	institute	institute	PROPN
ejpam-6040	613	33	of	of	ADP
ejpam-6040	613	34	technology	technology	NOUN
ejpam-6040	613	35	for	for	ADP
ejpam-6040	613	36	funding	fund	VERB
ejpam-6040	613	37	this	this	DET
ejpam-6040	613	38	research	research	NOUN
ejpam-6040	613	39	.	.	PUNCT
ejpam-6040	614	1	references	reference	NOUN
ejpam-6040	614	2	[	[	X
ejpam-6040	614	3	1	1	NUM
ejpam-6040	614	4	]	]	PUNCT
ejpam-6040	614	5	e.	e.	PROPN
ejpam-6040	614	6	cockayne	cockayne	PROPN
ejpam-6040	614	7	and	and	CCONJ
ejpam-6040	614	8	s.	s.	PROPN
ejpam-6040	614	9	hedetniemi	hedetniemi	PROPN
ejpam-6040	614	10	.	.	PUNCT
ejpam-6040	615	1	towards	towards	ADP
ejpam-6040	615	2	a	a	DET
ejpam-6040	615	3	theory	theory	NOUN
ejpam-6040	615	4	of	of	ADP
ejpam-6040	615	5	domination	domination	NOUN
ejpam-6040	615	6	in	in	ADP
ejpam-6040	615	7	graphs	graph	NOUN
ejpam-6040	615	8	.	.	PUNCT
ejpam-6040	616	1	marcel	marcel	PROPN
ejpam-6040	616	2	dekker	dekker	PROPN
ejpam-6040	616	3	,	,	PUNCT
ejpam-6040	616	4	inc	inc	PROPN
ejpam-6040	616	5	.	.	PROPN
ejpam-6040	616	6	new	new	PROPN
ejpam-6040	616	7	york	york	PROPN
ejpam-6040	616	8	,	,	PUNCT
ejpam-6040	616	9	7(3):247–261	7(3):247–261	PROPN
ejpam-6040	616	10	,	,	PUNCT
ejpam-6040	616	11	1977	1977	NUM
ejpam-6040	616	12	.	.	PUNCT
ejpam-6040	617	1	[	[	X
ejpam-6040	617	2	2	2	X
ejpam-6040	617	3	]	]	X
ejpam-6040	617	4	t.w	t.w	PROPN
ejpam-6040	617	5	.	.	PROPN
ejpam-6040	617	6	haynes	haynes	PROPN
ejpam-6040	617	7	,	,	PUNCT
ejpam-6040	617	8	s.t	s.t	PROPN
ejpam-6040	617	9	.	.	PROPN
ejpam-6040	617	10	hedetniemi	hedetniemi	PROPN
ejpam-6040	617	11	,	,	PUNCT
ejpam-6040	617	12	and	and	CCONJ
ejpam-6040	617	13	p.j	p.j	PROPN
ejpam-6040	617	14	.	.	PROPN
ejpam-6040	617	15	slater	slater	PROPN
ejpam-6040	617	16	.	.	PUNCT
ejpam-6040	618	1	fundamentals	fundamental	NOUN
ejpam-6040	618	2	of	of	ADP
ejpam-6040	618	3	domination	domination	NOUN
ejpam-6040	618	4	in	in	ADP
ejpam-6040	618	5	graphs	graph	NOUN
ejpam-6040	618	6	.	.	PUNCT
ejpam-6040	619	1	networks	network	NOUN
ejpam-6040	619	2	,	,	PUNCT
ejpam-6040	619	3	1998	1998	NUM
ejpam-6040	619	4	.	.	PUNCT
ejpam-6040	620	1	[	[	X
ejpam-6040	620	2	3	3	NUM
ejpam-6040	620	3	]	]	PUNCT
ejpam-6040	620	4	a.	a.	NOUN
ejpam-6040	620	5	das	das	PROPN
ejpam-6040	620	6	and	and	CCONJ
ejpam-6040	620	7	w.	w.	PROPN
ejpam-6040	620	8	j.	j.	PROPN
ejpam-6040	620	9	desormeaux	desormeaux	PROPN
ejpam-6040	620	10	.	.	PUNCT
ejpam-6040	621	1	domination	domination	NOUN
ejpam-6040	621	2	defect	defect	NOUN
ejpam-6040	621	3	in	in	ADP
ejpam-6040	621	4	graphs	graph	NOUN
ejpam-6040	621	5	:	:	PUNCT
ejpam-6040	621	6	guarding	guard	VERB
ejpam-6040	621	7	with	with	ADP
ejpam-6040	621	8	fewer	few	ADJ
ejpam-6040	621	9	guards	guard	NOUN
ejpam-6040	621	10	.	.	PUNCT
ejpam-6040	622	1	indian	indian	PROPN
ejpam-6040	622	2	j.	j.	PROPN
ejpam-6040	622	3	pure	pure	PROPN
ejpam-6040	622	4	appl	appl	PROPN
ejpam-6040	622	5	.	.	PUNCT
ejpam-6040	622	6	math	math	PROPN
ejpam-6040	622	7	.	.	PUNCT
ejpam-6040	622	8	,	,	PUNCT
ejpam-6040	623	1	49(2):349–364	49(2):349–364	NOUN
ejpam-6040	623	2	,	,	PUNCT
ejpam-6040	623	3	2018	2018	NUM
ejpam-6040	623	4	.	.	PUNCT
ejpam-6040	624	1	[	[	X
ejpam-6040	624	2	4	4	NUM
ejpam-6040	624	3	]	]	PUNCT
ejpam-6040	624	4	a.	a.	NOUN
ejpam-6040	624	5	miranda	miranda	PROPN
ejpam-6040	624	6	and	and	CCONJ
ejpam-6040	624	7	r.	r.	PROPN
ejpam-6040	624	8	eballe	eballe	PROPN
ejpam-6040	624	9	.	.	PUNCT
ejpam-6040	625	1	domination	domination	NOUN
ejpam-6040	625	2	defect	defect	NOUN
ejpam-6040	625	3	for	for	ADP
ejpam-6040	625	4	the	the	DET
ejpam-6040	625	5	join	join	NOUN
ejpam-6040	625	6	and	and	CCONJ
ejpam-6040	625	7	corona	corona	NOUN
ejpam-6040	625	8	of	of	ADP
ejpam-6040	625	9	graphs	graph	NOUN
ejpam-6040	625	10	.	.	PUNCT
ejpam-6040	626	1	applied	apply	VERB
ejpam-6040	626	2	mathematical	mathematical	ADJ
ejpam-6040	626	3	sciences	science	NOUN
ejpam-6040	626	4	,	,	PUNCT
ejpam-6040	626	5	15(12):615	15(12):615	NUM
ejpam-6040	626	6	–	–	PUNCT
ejpam-6040	626	7	623	623	NUM
ejpam-6040	626	8	,	,	PUNCT
ejpam-6040	626	9	2021	2021	NUM
ejpam-6040	626	10	.	.	PUNCT
ejpam-6040	627	1	[	[	X
ejpam-6040	627	2	5	5	NUM
ejpam-6040	627	3	]	]	PUNCT
ejpam-6040	627	4	a.	a.	NOUN
ejpam-6040	627	5	miranda	miranda	PROPN
ejpam-6040	627	6	and	and	CCONJ
ejpam-6040	627	7	r.	r.	PROPN
ejpam-6040	627	8	eballe	eballe	PROPN
ejpam-6040	627	9	.	.	PUNCT
ejpam-6040	628	1	domination	domination	NOUN
ejpam-6040	628	2	defect	defect	NOUN
ejpam-6040	628	3	in	in	ADP
ejpam-6040	628	4	the	the	DET
ejpam-6040	628	5	edge	edge	NOUN
ejpam-6040	628	6	corona	corona	NOUN
ejpam-6040	628	7	of	of	ADP
ejpam-6040	628	8	graphs	graph	NOUN
ejpam-6040	628	9	.	.	PUNCT
ejpam-6040	629	1	asian	asian	ADJ
ejpam-6040	629	2	research	research	PROPN
ejpam-6040	629	3	journal	journal	NOUN
ejpam-6040	629	4	of	of	ADP
ejpam-6040	629	5	mathematics	mathematic	NOUN
ejpam-6040	629	6	,	,	PUNCT
ejpam-6040	629	7	18(12):95–101	18(12):95–101	PROPN
ejpam-6040	629	8	,	,	PUNCT
ejpam-6040	629	9	2022	2022	NUM
ejpam-6040	629	10	.	.	PUNCT
ejpam-6040	630	1	[	[	X
ejpam-6040	630	2	6	6	NUM
ejpam-6040	630	3	]	]	PUNCT
ejpam-6040	630	4	a.	a.	NOUN
ejpam-6040	630	5	miranda	miranda	PROPN
ejpam-6040	630	6	and	and	CCONJ
ejpam-6040	630	7	r.	r.	PROPN
ejpam-6040	630	8	eballe	eballe	PROPN
ejpam-6040	630	9	.	.	PUNCT
ejpam-6040	631	1	domination	domination	NOUN
ejpam-6040	631	2	defect	defect	NOUN
ejpam-6040	631	3	in	in	ADP
ejpam-6040	631	4	the	the	DET
ejpam-6040	631	5	composition	composition	NOUN
ejpam-6040	631	6	of	of	ADP
ejpam-6040	631	7	graphs	graph	NOUN
ejpam-6040	631	8	.	.	PUNCT
ejpam-6040	632	1	advances	advance	NOUN
ejpam-6040	632	2	and	and	CCONJ
ejpam-6040	632	3	applications	application	NOUN
ejpam-6040	632	4	in	in	ADP
ejpam-6040	632	5	discrete	discrete	ADJ
ejpam-6040	632	6	mathematics	mathematic	NOUN
ejpam-6040	632	7	,	,	PUNCT
ejpam-6040	632	8	39(2):209–219	39(2):209–219	PROPN
ejpam-6040	632	9	,	,	PUNCT
ejpam-6040	632	10	2023	2023	NUM
ejpam-6040	632	11	.	.	PUNCT
ejpam-6040	633	1	[	[	X
ejpam-6040	633	2	7	7	X
ejpam-6040	633	3	]	]	X
ejpam-6040	633	4	j.	j.	PROPN
ejpam-6040	633	5	anoche	anoche	PROPN
ejpam-6040	633	6	and	and	CCONJ
ejpam-6040	633	7	s.	s.	PROPN
ejpam-6040	633	8	canoy	canoy	PROPN
ejpam-6040	633	9	jr	jr	PROPN
ejpam-6040	633	10	.	.	PUNCT
ejpam-6040	634	1	k	k	ADJ
ejpam-6040	634	2	-	-	PUNCT
ejpam-6040	634	3	hop	hop	NOUN
ejpam-6040	634	4	domination	domination	NOUN
ejpam-6040	634	5	defect	defect	NOUN
ejpam-6040	634	6	in	in	ADP
ejpam-6040	634	7	a	a	DET
ejpam-6040	634	8	graph	graph	NOUN
ejpam-6040	634	9	.	.	PUNCT
ejpam-6040	635	1	eur	eur	PROPN
ejpam-6040	635	2	.	.	PUNCT
ejpam-6040	636	1	j.	j.	PROPN
ejpam-6040	636	2	pure	pure	PROPN
ejpam-6040	636	3	appl	appl	PROPN
ejpam-6040	636	4	.	.	PUNCT
ejpam-6040	636	5	math	math	PROPN
ejpam-6040	636	6	.	.	PUNCT
ejpam-6040	636	7	,	,	PUNCT
ejpam-6040	636	8	18(2):5716	18(2):5716	NUM
ejpam-6040	636	9	,	,	PUNCT
ejpam-6040	636	10	2025	2025	NUM
ejpam-6040	636	11	.	.	PUNCT
ejpam-6040	637	1	[	[	X
ejpam-6040	637	2	8	8	NUM
ejpam-6040	637	3	]	]	X
ejpam-6040	637	4	i.	i.	NOUN
ejpam-6040	637	5	aniversario	aniversario	PROPN
ejpam-6040	637	6	,	,	PUNCT
ejpam-6040	637	7	f.	f.	PROPN
ejpam-6040	637	8	jamil	jamil	PROPN
ejpam-6040	637	9	,	,	PUNCT
ejpam-6040	637	10	and	and	CCONJ
ejpam-6040	637	11	s.	s.	PROPN
ejpam-6040	637	12	canoy	canoy	PROPN
ejpam-6040	637	13	jr	jr	PROPN
ejpam-6040	637	14	.	.	PUNCT
ejpam-6040	638	1	the	the	DET
ejpam-6040	638	2	closed	closed	ADJ
ejpam-6040	638	3	geodetic	geodetic	ADJ
ejpam-6040	638	4	numbers	number	NOUN
ejpam-6040	638	5	of	of	ADP
ejpam-6040	638	6	graphs	graph	NOUN
ejpam-6040	638	7	.	.	PUNCT
ejpam-6040	639	1	utilitas	utilitas	PROPN
ejpam-6040	639	2	mathematica	mathematica	PROPN
ejpam-6040	639	3	,	,	PUNCT
ejpam-6040	639	4	74:3–18	74:3–18	NUM
ejpam-6040	639	5	,	,	PUNCT
ejpam-6040	639	6	2007	2007	NUM
ejpam-6040	639	7	.	.	PUNCT
ejpam-6040	640	1	[	[	X
ejpam-6040	640	2	9	9	NUM
ejpam-6040	640	3	]	]	PUNCT
ejpam-6040	640	4	a.	a.	NOUN
ejpam-6040	640	5	hansberg	hansberg	PROPN
ejpam-6040	640	6	and	and	CCONJ
ejpam-6040	640	7	l.	l.	PROPN
ejpam-6040	640	8	volkmann	volkmann	PROPN
ejpam-6040	640	9	.	.	PUNCT
ejpam-6040	641	1	on	on	ADP
ejpam-6040	641	2	the	the	DET
ejpam-6040	641	3	geodetic	geodetic	ADJ
ejpam-6040	641	4	and	and	CCONJ
ejpam-6040	641	5	geodetic	geodetic	ADJ
ejpam-6040	641	6	domination	domination	NOUN
ejpam-6040	641	7	numbers	number	NOUN
ejpam-6040	641	8	of	of	ADP
ejpam-6040	641	9	a	a	DET
ejpam-6040	641	10	graph	graph	NOUN
ejpam-6040	641	11	.	.	PUNCT
ejpam-6040	641	12	discrete	discrete	ADJ
ejpam-6040	641	13	mathematics	mathematic	NOUN
ejpam-6040	641	14	,	,	PUNCT
ejpam-6040	641	15	310(15	310(15	PROPN
ejpam-6040	641	16	-	-	SYM
ejpam-6040	641	17	6):2140	6):2140	ADJ
ejpam-6040	641	18	–	–	PUNCT
ejpam-6040	641	19	2146	2146	NUM
ejpam-6040	641	20	,	,	PUNCT
ejpam-6040	641	21	2010	2010	NUM
ejpam-6040	641	22	.	.	PUNCT
ejpam-6040	642	1	[	[	X
ejpam-6040	642	2	10	10	NUM
ejpam-6040	642	3	]	]	X
ejpam-6040	642	4	f.	f.	PROPN
ejpam-6040	642	5	jamil	jamil	PROPN
ejpam-6040	642	6	,	,	PUNCT
ejpam-6040	642	7	i.	i.	PROPN
ejpam-6040	642	8	aniversario	aniversario	PROPN
ejpam-6040	642	9	,	,	PUNCT
ejpam-6040	642	10	and	and	CCONJ
ejpam-6040	642	11	s.	s.	PROPN
ejpam-6040	642	12	canoy	canoy	PROPN
ejpam-6040	642	13	jr	jr	PROPN
ejpam-6040	642	14	.	.	PROPN
ejpam-6040	642	15	on	on	ADP
ejpam-6040	642	16	closed	closed	ADJ
ejpam-6040	642	17	and	and	CCONJ
ejpam-6040	642	18	upper	upper	ADJ
ejpam-6040	642	19	closed	closed	ADJ
ejpam-6040	642	20	geodetic	geodetic	ADJ
ejpam-6040	642	21	numbers	number	NOUN
ejpam-6040	642	22	of	of	ADP
ejpam-6040	642	23	graphs	graph	NOUN
ejpam-6040	642	24	.	.	PUNCT
ejpam-6040	643	1	ars	ar	NOUN
ejpam-6040	643	2	combinatoria	combinatoria	NOUN
ejpam-6040	643	3	,	,	PUNCT
ejpam-6040	643	4	84:191–203	84:191–203	NUM
ejpam-6040	643	5	,	,	PUNCT
ejpam-6040	643	6	2007	2007	NUM
ejpam-6040	643	7	.	.	PUNCT
ejpam-6040	644	1	s.	s.	PROPN
ejpam-6040	644	2	canoy	canoy	PROPN
ejpam-6040	644	3	,	,	PUNCT
ejpam-6040	644	4	jr	jr	PROPN
ejpam-6040	644	5	.	.	PROPN
ejpam-6040	644	6	,	,	PUNCT
ejpam-6040	644	7	j.	j.	PROPN
ejpam-6040	644	8	anoche	anoche	PROPN
ejpam-6040	644	9	/	/	SYM
ejpam-6040	644	10	eur	eur	PROPN
ejpam-6040	644	11	.	.	PUNCT
ejpam-6040	645	1	j.	j.	PROPN
ejpam-6040	645	2	pure	pure	PROPN
ejpam-6040	645	3	appl	appl	PROPN
ejpam-6040	645	4	.	.	PROPN
ejpam-6040	645	5	math	math	PROPN
ejpam-6040	645	6	,	,	PUNCT
ejpam-6040	645	7	18	18	NUM
ejpam-6040	645	8	(	(	PUNCT
ejpam-6040	645	9	2	2	NUM
ejpam-6040	645	10	)	)	PUNCT
ejpam-6040	645	11	(	(	PUNCT
ejpam-6040	645	12	2025	2025	NUM
ejpam-6040	645	13	)	)	PUNCT
ejpam-6040	645	14	,	,	PUNCT
ejpam-6040	645	15	6040	6040	NUM
ejpam-6040	645	16	16	16	NUM
ejpam-6040	645	17	of	of	ADP
ejpam-6040	645	18	16	16	NUM
ejpam-6040	646	1	[	[	X
ejpam-6040	646	2	11	11	NUM
ejpam-6040	646	3	]	]	X
ejpam-6040	646	4	j.j	j.j	PROPN
ejpam-6040	646	5	.	.	PROPN
ejpam-6040	646	6	mulloor	mulloor	PROPN
ejpam-6040	646	7	and	and	CCONJ
ejpam-6040	646	8	v.	v.	ADP
ejpam-6040	646	9	sangeetha	sangeetha	PROPN
ejpam-6040	646	10	.	.	PUNCT
ejpam-6040	647	1	restrained	restrain	VERB
ejpam-6040	647	2	geodetic	geodetic	ADJ
ejpam-6040	647	3	domination	domination	NOUN
ejpam-6040	647	4	in	in	ADP
ejpam-6040	647	5	graphs	graph	NOUN
ejpam-6040	647	6	.	.	PUNCT
ejpam-6040	648	1	discrete	discrete	ADJ
ejpam-6040	648	2	mathematics	mathematic	NOUN
ejpam-6040	648	3	,	,	PUNCT
ejpam-6040	648	4	algorithms	algorithm	NOUN
ejpam-6040	648	5	and	and	CCONJ
ejpam-6040	648	6	applications	application	NOUN
ejpam-6040	648	7	,	,	PUNCT
ejpam-6040	648	8	12(6):https://doi.org/10.1142	12(6):https://doi.org/10.1142	PROPN
ejpam-6040	648	9	/	/	SYM
ejpam-6040	648	10	s1793830920500846c	s1793830920500846c	ADJ
ejpam-6040	648	11	,	,	PUNCT
ejpam-6040	648	12	2020	2020	NUM
ejpam-6040	648	13	.	.	PUNCT
ejpam-6040	649	1	[	[	X
ejpam-6040	649	2	12	12	NUM
ejpam-6040	649	3	]	]	X
ejpam-6040	649	4	d.	d.	PROPN
ejpam-6040	649	5	stalin	stalin	PROPN
ejpam-6040	649	6	and	and	CCONJ
ejpam-6040	649	7	j.	j.	PROPN
ejpam-6040	649	8	john	john	PROPN
ejpam-6040	649	9	.	.	PROPN
ejpam-6040	649	10	edge	edge	PROPN
ejpam-6040	649	11	geodetic	geodetic	ADJ
ejpam-6040	649	12	dominations	domination	NOUN
ejpam-6040	649	13	in	in	ADP
ejpam-6040	649	14	graphs	graph	NOUN
ejpam-6040	649	15	.	.	PUNCT
ejpam-6040	650	1	international	international	ADJ
ejpam-6040	650	2	journal	journal	NOUN
ejpam-6040	650	3	of	of	ADP
ejpam-6040	650	4	pure	pure	ADJ
ejpam-6040	650	5	and	and	CCONJ
ejpam-6040	650	6	applied	applied	ADJ
ejpam-6040	650	7	mathematics	mathematic	NOUN
ejpam-6040	650	8	,	,	PUNCT
ejpam-6040	650	9	116(22):31–40	116(22):31–40	NUM
ejpam-6040	650	10	,	,	PUNCT
ejpam-6040	650	11	2017	2017	NUM
ejpam-6040	650	12	.	.	PUNCT
ejpam-6040	651	1	[	[	X
ejpam-6040	651	2	13	13	NUM
ejpam-6040	651	3	]	]	X
ejpam-6040	651	4	f.	f.	PROPN
ejpam-6040	651	5	harary	harary	PROPN
ejpam-6040	651	6	,	,	PUNCT
ejpam-6040	651	7	e.	e.	PROPN
ejpam-6040	651	8	loukakis	loukakis	PROPN
ejpam-6040	651	9	,	,	PUNCT
ejpam-6040	651	10	and	and	CCONJ
ejpam-6040	651	11	c.	c.	PROPN
ejpam-6040	651	12	tsouros	tsouros	PROPN
ejpam-6040	651	13	.	.	PUNCT
ejpam-6040	652	1	the	the	DET
ejpam-6040	652	2	geodetic	geodetic	ADJ
ejpam-6040	652	3	number	number	NOUN
ejpam-6040	652	4	of	of	ADP
ejpam-6040	652	5	a	a	DET
ejpam-6040	652	6	graph	graph	NOUN
ejpam-6040	652	7	.	.	PUNCT
ejpam-6040	653	1	mathl	mathl	NOUN
ejpam-6040	653	2	.	.	PUNCT
ejpam-6040	654	1	comput	comput	NOUN
ejpam-6040	654	2	.	.	PUNCT
ejpam-6040	655	1	modelling	modelling	NOUN
ejpam-6040	655	2	,	,	PUNCT
ejpam-6040	655	3	17(11):89–95	17(11):89–95	NUM
ejpam-6040	655	4	,	,	PUNCT
ejpam-6040	655	5	1993	1993	NUM
ejpam-6040	655	6	.	.	PUNCT
ejpam-6040	656	1	[	[	X
ejpam-6040	656	2	14	14	NUM
ejpam-6040	656	3	]	]	X
ejpam-6040	656	4	g.	g.	PROPN
ejpam-6040	656	5	cagaanan	cagaanan	PROPN
ejpam-6040	656	6	and	and	CCONJ
ejpam-6040	656	7	s.	s.	PROPN
ejpam-6040	656	8	canoy	canoy	PROPN
ejpam-6040	656	9	jr	jr	PROPN
ejpam-6040	656	10	.	.	PROPN
ejpam-6040	656	11	on	on	ADP
ejpam-6040	656	12	the	the	DET
ejpam-6040	656	13	geodesic	geodesic	ADJ
ejpam-6040	656	14	and	and	CCONJ
ejpam-6040	656	15	hull	hull	NOUN
ejpam-6040	656	16	numbers	number	NOUN
ejpam-6040	656	17	of	of	ADP
ejpam-6040	656	18	the	the	DET
ejpam-6040	656	19	sum	sum	NOUN
ejpam-6040	656	20	of	of	ADP
ejpam-6040	656	21	graphs	graph	NOUN
ejpam-6040	656	22	.	.	PUNCT
ejpam-6040	657	1	congresus	congresus	PROPN
ejpam-6040	657	2	numerantium	numerantium	PROPN
ejpam-6040	657	3	,	,	PUNCT
ejpam-6040	657	4	161:97–104	161:97–104	NUM
ejpam-6040	657	5	,	,	PUNCT
ejpam-6040	657	6	2003	2003	NUM
ejpam-6040	657	7	.	.	PUNCT
ejpam-6040	658	1	[	[	X
ejpam-6040	658	2	15	15	NUM
ejpam-6040	658	3	]	]	X
ejpam-6040	658	4	g.	g.	NOUN
ejpam-6040	658	5	cagaanan	cagaanan	PROPN
ejpam-6040	658	6	and	and	CCONJ
ejpam-6040	658	7	s.	s.	PROPN
ejpam-6040	658	8	canoy	canoy	PROPN
ejpam-6040	658	9	jr	jr	PROPN
ejpam-6040	658	10	.	.	PROPN
ejpam-6040	658	11	on	on	ADP
ejpam-6040	658	12	the	the	DET
ejpam-6040	658	13	geodetic	geodetic	ADJ
ejpam-6040	658	14	covers	cover	NOUN
ejpam-6040	658	15	and	and	CCONJ
ejpam-6040	658	16	geodetic	geodetic	ADJ
ejpam-6040	658	17	bases	basis	NOUN
ejpam-6040	658	18	of	of	ADP
ejpam-6040	658	19	the	the	DET
ejpam-6040	658	20	composition	composition	NOUN
ejpam-6040	658	21	g[km	g[km	PROPN
ejpam-6040	658	22	]	]	PUNCT
ejpam-6040	658	23	.	.	PUNCT
ejpam-6040	658	24	ars	ars	PROPN
ejpam-6040	658	25	combinatoria	combinatoria	PROPN
ejpam-6040	658	26	,	,	PUNCT
ejpam-6040	658	27	79:33–45	79:33–45	NUM
ejpam-6040	658	28	,	,	PUNCT
ejpam-6040	658	29	2006	2006	NUM
ejpam-6040	658	30	.	.	PUNCT
ejpam-6040	659	1	[	[	X
ejpam-6040	659	2	16	16	NUM
ejpam-6040	659	3	]	]	X
ejpam-6040	659	4	g.	g.	PROPN
ejpam-6040	659	5	cagaanan	cagaanan	PROPN
ejpam-6040	659	6	and	and	CCONJ
ejpam-6040	659	7	s.	s.	PROPN
ejpam-6040	659	8	canoy	canoy	PROPN
ejpam-6040	659	9	jr	jr	PROPN
ejpam-6040	659	10	.	.	PROPN
ejpam-6040	659	11	bounds	bound	VERB
ejpam-6040	659	12	for	for	ADP
ejpam-6040	659	13	the	the	DET
ejpam-6040	659	14	geodetic	geodetic	ADJ
ejpam-6040	659	15	number	number	NOUN
ejpam-6040	659	16	of	of	ADP
ejpam-6040	659	17	the	the	DET
ejpam-6040	659	18	cartesian	cartesian	ADJ
ejpam-6040	659	19	product	product	NOUN
ejpam-6040	659	20	of	of	ADP
ejpam-6040	659	21	graphs	graph	NOUN
ejpam-6040	659	22	.	.	PUNCT
ejpam-6040	660	1	utilitas	utilitas	PROPN
ejpam-6040	660	2	mathematica	mathematica	PROPN
ejpam-6040	660	3	,	,	PUNCT
ejpam-6040	660	4	79:9	79:9	NUM
ejpam-6040	660	5	,	,	PUNCT
ejpam-6040	660	6	2009	2009	NUM
ejpam-6040	660	7	.	.	PUNCT
ejpam-6040	661	1	[	[	X
ejpam-6040	661	2	17	17	NUM
ejpam-6040	661	3	]	]	X
ejpam-6040	661	4	g.	g.	PROPN
ejpam-6040	661	5	chartrand	chartrand	PROPN
ejpam-6040	661	6	,	,	PUNCT
ejpam-6040	661	7	f.	f.	PROPN
ejpam-6040	661	8	harary	harary	PROPN
ejpam-6040	661	9	,	,	PUNCT
ejpam-6040	661	10	and	and	CCONJ
ejpam-6040	661	11	p.	p.	PROPN
ejpam-6040	661	12	zhang	zhang	PROPN
ejpam-6040	661	13	.	.	PUNCT
ejpam-6040	662	1	the	the	DET
ejpam-6040	662	2	geodetic	geodetic	ADJ
ejpam-6040	662	3	number	number	NOUN
ejpam-6040	662	4	of	of	ADP
ejpam-6040	662	5	a	a	DET
ejpam-6040	662	6	graph	graph	NOUN
ejpam-6040	662	7	.	.	PUNCT
ejpam-6040	663	1	networks	network	NOUN
ejpam-6040	663	2	:	:	PUNCT
ejpam-6040	663	3	an	an	DET
ejpam-6040	663	4	international	international	ADJ
ejpam-6040	663	5	journal	journal	NOUN
ejpam-6040	663	6	,	,	PUNCT
ejpam-6040	663	7	39(1):1–6	39(1):1–6	NUM
ejpam-6040	663	8	,	,	PUNCT
ejpam-6040	663	9	2002	2002	NUM
ejpam-6040	663	10	.	.	PUNCT
ejpam-6040	664	1	[	[	X
ejpam-6040	664	2	18	18	NUM
ejpam-6040	664	3	]	]	X
ejpam-6040	664	4	h.	h.	NOUN
ejpam-6040	664	5	escuardo	escuardo	PROPN
ejpam-6040	664	6	,	,	PUNCT
ejpam-6040	664	7	r.	r.	PROPN
ejpam-6040	664	8	gera	gera	PROPN
ejpam-6040	664	9	,	,	PUNCT
ejpam-6040	664	10	a.	a.	NOUN
ejpam-6040	664	11	hansberg	hansberg	PROPN
ejpam-6040	664	12	,	,	PUNCT
ejpam-6040	664	13	n.	n.	PROPN
ejpam-6040	664	14	jafari	jafari	PROPN
ejpam-6040	664	15	rad	rad	PROPN
ejpam-6040	664	16	,	,	PUNCT
ejpam-6040	664	17	and	and	CCONJ
ejpam-6040	664	18	l.	l.	PROPN
ejpam-6040	664	19	volkmann	volkmann	PROPN
ejpam-6040	664	20	.	.	PUNCT
ejpam-6040	665	1	geodetic	geodetic	ADJ
ejpam-6040	665	2	domination	domination	NOUN
ejpam-6040	665	3	in	in	ADP
ejpam-6040	665	4	graphs	graph	NOUN
ejpam-6040	665	5	.	.	PUNCT
ejpam-6040	666	1	combin	combin	NOUN
ejpam-6040	666	2	.	.	PUNCT
ejpam-6040	666	3	math	math	NOUN
ejpam-6040	666	4	.	.	PUNCT
ejpam-6040	667	1	combin	combin	NOUN
ejpam-6040	667	2	.	.	PUNCT
ejpam-6040	668	1	comput	comput	NOUN
ejpam-6040	668	2	.	.	PUNCT
ejpam-6040	668	3	,	,	PUNCT
ejpam-6040	669	1	77(1):89–101	77(1):89–101	NUM
ejpam-6040	669	2	,	,	PUNCT
ejpam-6040	669	3	2022	2022	NUM
ejpam-6040	669	4	.	.	PUNCT
ejpam-6040	670	1	[	[	X
ejpam-6040	670	2	19	19	NUM
ejpam-6040	670	3	]	]	X
ejpam-6040	670	4	s.	s.	PROPN
ejpam-6040	670	5	canoy	canoy	PROPN
ejpam-6040	670	6	jr	jr	PROPN
ejpam-6040	670	7	.	.	PROPN
ejpam-6040	670	8	,	,	PUNCT
ejpam-6040	670	9	g.	g.	PROPN
ejpam-6040	670	10	cagaanan	cagaanan	PROPN
ejpam-6040	670	11	,	,	PUNCT
ejpam-6040	670	12	and	and	CCONJ
ejpam-6040	670	13	s.	s.	PROPN
ejpam-6040	670	14	gervacio	gervacio	PROPN
ejpam-6040	670	15	.	.	PUNCT
ejpam-6040	671	1	convexity	convexity	PROPN
ejpam-6040	671	2	,	,	PUNCT
ejpam-6040	671	3	geodetic	geodetic	ADJ
ejpam-6040	671	4	,	,	PUNCT
ejpam-6040	671	5	and	and	CCONJ
ejpam-6040	671	6	hull	hull	NOUN
ejpam-6040	671	7	numbers	number	NOUN
ejpam-6040	671	8	of	of	ADP
ejpam-6040	671	9	the	the	DET
ejpam-6040	671	10	join	join	NOUN
ejpam-6040	671	11	of	of	ADP
ejpam-6040	671	12	graphs	graph	NOUN
ejpam-6040	671	13	.	.	PUNCT
ejpam-6040	672	1	utilitas	utilitas	PROPN
ejpam-6040	672	2	mathematica	mathematica	PROPN
ejpam-6040	672	3	,	,	PUNCT
ejpam-6040	672	4	71:143–159	71:143–159	PROPN
ejpam-6040	672	5	,	,	PUNCT
ejpam-6040	672	6	2006	2006	NUM
ejpam-6040	672	7	.	.	PUNCT
ejpam-6040	673	1	[	[	X
ejpam-6040	673	2	20	20	NUM
ejpam-6040	673	3	]	]	PUNCT
ejpam-6040	673	4	s.	s.	PROPN
ejpam-6040	673	5	robinson	robinson	PROPN
ejpam-6040	673	6	chellathurai	chellathurai	PROPN
ejpam-6040	673	7	and	and	CCONJ
ejpam-6040	673	8	s.	s.	PROPN
ejpam-6040	673	9	padma	padma	PROPN
ejpam-6040	673	10	vijaya	vijaya	PROPN
ejpam-6040	673	11	.	.	PUNCT
ejpam-6040	674	1	the	the	DET
ejpam-6040	674	2	geodetic	geodetic	ADJ
ejpam-6040	674	3	domination	domination	NOUN
ejpam-6040	674	4	number	number	NOUN
ejpam-6040	674	5	for	for	ADP
ejpam-6040	674	6	the	the	DET
ejpam-6040	674	7	product	product	NOUN
ejpam-6040	674	8	of	of	ADP
ejpam-6040	674	9	graphs	graph	NOUN
ejpam-6040	674	10	.	.	PUNCT
ejpam-6040	675	1	transactions	transaction	NOUN
ejpam-6040	675	2	on	on	ADP
ejpam-6040	675	3	combinatorics	combinatoric	NOUN
ejpam-6040	675	4	,	,	PUNCT
ejpam-6040	675	5	3(4):19–30	3(4):19–30	NUM
ejpam-6040	675	6	,	,	PUNCT
ejpam-6040	675	7	2014	2014	NUM
ejpam-6040	675	8	.	.	PUNCT