id	sid	tid	token	lemma	pos
ejpam-5903	1	1	european	european	PROPN
ejpam-5903	1	2	journal	journal	PROPN
ejpam-5903	1	3	of	of	ADP
ejpam-5903	1	4	pure	pure	ADJ
ejpam-5903	1	5	and	and	CCONJ
ejpam-5903	1	6	applied	applied	ADJ
ejpam-5903	1	7	mathematics	mathematic	NOUN
ejpam-5903	1	8	2025	2025	NUM
ejpam-5903	1	9	,	,	PUNCT
ejpam-5903	1	10	vol	vol	NOUN
ejpam-5903	1	11	.	.	PROPN
ejpam-5903	1	12	18	18	NUM
ejpam-5903	1	13	,	,	PUNCT
ejpam-5903	1	14	issue	issue	NOUN
ejpam-5903	1	15	2	2	NUM
ejpam-5903	1	16	,	,	PUNCT
ejpam-5903	1	17	article	article	NOUN
ejpam-5903	1	18	number	number	NOUN
ejpam-5903	1	19	5903	5903	NUM
ejpam-5903	1	20	issn	issn	VERB
ejpam-5903	1	21	1307	1307	NUM
ejpam-5903	1	22	-	-	SYM
ejpam-5903	1	23	5543	5543	NUM
ejpam-5903	1	24	–	–	PUNCT
ejpam-5903	1	25	ejpam.com	ejpam.com	X
ejpam-5903	1	26	published	publish	VERB
ejpam-5903	1	27	by	by	ADP
ejpam-5903	1	28	new	new	PROPN
ejpam-5903	1	29	york	york	PROPN
ejpam-5903	1	30	business	business	PROPN
ejpam-5903	1	31	global	global	PROPN
ejpam-5903	1	32	k	k	PROPN
ejpam-5903	1	33	-	-	ADJ
ejpam-5903	1	34	geodetic	geodetic	ADJ
ejpam-5903	1	35	hop	hop	NOUN
ejpam-5903	1	36	domination	domination	NOUN
ejpam-5903	1	37	defect	defect	NOUN
ejpam-5903	1	38	in	in	ADP
ejpam-5903	1	39	a	a	DET
ejpam-5903	1	40	graph	graph	NOUN
ejpam-5903	1	41	jesica	jesica	PROPN
ejpam-5903	1	42	m.	m.	NOUN
ejpam-5903	1	43	anoche1,2,∗	anoche1,2,∗	PROPN
ejpam-5903	1	44	,	,	PUNCT
ejpam-5903	1	45	sergio	sergio	PROPN
ejpam-5903	1	46	r.	r.	PROPN
ejpam-5903	1	47	canoy	canoy	PROPN
ejpam-5903	1	48	,	,	PUNCT
ejpam-5903	1	49	jr.1,2	jr.1,2	ADJ
ejpam-5903	1	50	1	1	NUM
ejpam-5903	1	51	department	department	NOUN
ejpam-5903	1	52	of	of	ADP
ejpam-5903	1	53	mathematics	mathematic	NOUN
ejpam-5903	1	54	and	and	CCONJ
ejpam-5903	1	55	statistics	statistic	NOUN
ejpam-5903	1	56	,	,	PUNCT
ejpam-5903	1	57	college	college	NOUN
ejpam-5903	1	58	of	of	ADP
ejpam-5903	1	59	science	science	NOUN
ejpam-5903	1	60	and	and	CCONJ
ejpam-5903	1	61	mathematics	mathematic	NOUN
ejpam-5903	1	62	,	,	PUNCT
ejpam-5903	1	63	msu	msu	PROPN
ejpam-5903	1	64	-	-	PUNCT
ejpam-5903	1	65	iligan	iligan	PROPN
ejpam-5903	1	66	institute	institute	PROPN
ejpam-5903	1	67	of	of	ADP
ejpam-5903	1	68	technology	technology	PROPN
ejpam-5903	1	69	,	,	PUNCT
ejpam-5903	1	70	9200	9200	NUM
ejpam-5903	1	71	iligan	iligan	ADJ
ejpam-5903	1	72	city	city	NOUN
ejpam-5903	1	73	,	,	PUNCT
ejpam-5903	1	74	philippines	philippine	NOUN
ejpam-5903	1	75	2	2	NUM
ejpam-5903	1	76	center	center	NOUN
ejpam-5903	1	77	of	of	ADP
ejpam-5903	1	78	mathematical	mathematical	ADJ
ejpam-5903	1	79	and	and	CCONJ
ejpam-5903	1	80	theoretical	theoretical	ADJ
ejpam-5903	1	81	physical	physical	ADJ
ejpam-5903	1	82	sciences	science	NOUN
ejpam-5903	1	83	-	-	PUNCT
ejpam-5903	1	84	prism	prism	NOUN
ejpam-5903	1	85	,	,	PUNCT
ejpam-5903	1	86	msu	msu	PROPN
ejpam-5903	1	87	-	-	PUNCT
ejpam-5903	1	88	iligan	iligan	PROPN
ejpam-5903	1	89	institute	institute	PROPN
ejpam-5903	1	90	of	of	ADP
ejpam-5903	1	91	technology	technology	PROPN
ejpam-5903	1	92	,	,	PUNCT
ejpam-5903	1	93	9200	9200	NUM
ejpam-5903	1	94	iligan	iligan	ADJ
ejpam-5903	1	95	city	city	NOUN
ejpam-5903	1	96	,	,	PUNCT
ejpam-5903	1	97	philippines	philippine	NOUN
ejpam-5903	1	98	abstract	abstract	ADJ
ejpam-5903	1	99	.	.	PUNCT
ejpam-5903	2	1	let	let	VERB
ejpam-5903	2	2	g	g	PROPN
ejpam-5903	2	3	=	=	SYM
ejpam-5903	2	4	(	(	PUNCT
ejpam-5903	2	5	v	v	NOUN
ejpam-5903	2	6	(	(	PUNCT
ejpam-5903	2	7	g	g	NOUN
ejpam-5903	2	8	)	)	PUNCT
ejpam-5903	2	9	,	,	PUNCT
ejpam-5903	2	10	e(g	e(g	PROPN
ejpam-5903	2	11	)	)	PUNCT
ejpam-5903	2	12	)	)	PUNCT
ejpam-5903	3	1	be	be	AUX
ejpam-5903	3	2	a	a	DET
ejpam-5903	3	3	simple	simple	ADJ
ejpam-5903	3	4	undirected	undirected	ADJ
ejpam-5903	3	5	graph	graph	NOUN
ejpam-5903	3	6	.	.	PUNCT
ejpam-5903	4	1	a	a	DET
ejpam-5903	4	2	set	set	NOUN
ejpam-5903	4	3	s	s	NOUN
ejpam-5903	4	4	⊆	⊆	NUM
ejpam-5903	4	5	v	v	NOUN
ejpam-5903	4	6	(	(	PUNCT
ejpam-5903	4	7	g	g	NOUN
ejpam-5903	4	8	)	)	PUNCT
ejpam-5903	4	9	is	be	AUX
ejpam-5903	4	10	a	a	DET
ejpam-5903	4	11	geodetic	geodetic	ADJ
ejpam-5903	4	12	hop	hop	NOUN
ejpam-5903	4	13	dominating	dominating	NOUN
ejpam-5903	4	14	set	set	VERB
ejpam-5903	4	15	in	in	ADP
ejpam-5903	4	16	g	g	PROPN
ejpam-5903	4	17	if	if	SCONJ
ejpam-5903	4	18	for	for	ADP
ejpam-5903	4	19	every	every	DET
ejpam-5903	4	20	v	v	NUM
ejpam-5903	4	21	∈	∈	NOUN
ejpam-5903	4	22	v	v	NOUN
ejpam-5903	4	23	(	(	PUNCT
ejpam-5903	4	24	g)\s	g)\s	NOUN
ejpam-5903	4	25	,	,	PUNCT
ejpam-5903	4	26	there	there	PRON
ejpam-5903	4	27	exist	exist	VERB
ejpam-5903	4	28	vertices	vertex	NOUN
ejpam-5903	4	29	x	x	X
ejpam-5903	4	30	,	,	PUNCT
ejpam-5903	4	31	y	y	PROPN
ejpam-5903	4	32	,	,	PUNCT
ejpam-5903	4	33	z	z	PROPN
ejpam-5903	4	34	∈	∈	PROPN
ejpam-5903	4	35	s	s	VERB
ejpam-5903	4	36	such	such	ADJ
ejpam-5903	4	37	that	that	DET
ejpam-5903	4	38	dg(x	dg(x	ADJ
ejpam-5903	4	39	,	,	PUNCT
ejpam-5903	4	40	v	v	NOUN
ejpam-5903	4	41	)	)	PUNCT
ejpam-5903	4	42	=	=	SYM
ejpam-5903	4	43	2	2	NUM
ejpam-5903	4	44	and	and	CCONJ
ejpam-5903	4	45	v	v	NOUN
ejpam-5903	4	46	lies	lie	NOUN
ejpam-5903	4	47	in	in	ADP
ejpam-5903	4	48	a	a	DET
ejpam-5903	4	49	y	y	PROPN
ejpam-5903	4	50	-	-	PROPN
ejpam-5903	4	51	z	z	NOUN
ejpam-5903	4	52	geodesic	geodesic	NOUN
ejpam-5903	4	53	,	,	PUNCT
ejpam-5903	4	54	that	that	ADV
ejpam-5903	4	55	is	is	ADV
ejpam-5903	4	56	,	,	PUNCT
ejpam-5903	4	57	v	v	PROPN
ejpam-5903	4	58	∈	∈	PROPN
ejpam-5903	4	59	ig(y	ig(y	NOUN
ejpam-5903	4	60	,	,	PUNCT
ejpam-5903	4	61	z	z	NOUN
ejpam-5903	4	62	)	)	PUNCT
ejpam-5903	4	63	.	.	PUNCT
ejpam-5903	5	1	the	the	DET
ejpam-5903	5	2	minimum	minimum	ADJ
ejpam-5903	5	3	cardinality	cardinality	NOUN
ejpam-5903	5	4	of	of	ADP
ejpam-5903	5	5	a	a	DET
ejpam-5903	5	6	geodetic	geodetic	ADJ
ejpam-5903	5	7	hop	hop	NOUN
ejpam-5903	5	8	dominating	dominating	NOUN
ejpam-5903	5	9	set	set	NOUN
ejpam-5903	5	10	of	of	ADP
ejpam-5903	5	11	g	g	NOUN
ejpam-5903	5	12	,	,	PUNCT
ejpam-5903	5	13	denoted	denote	VERB
ejpam-5903	5	14	by	by	ADP
ejpam-5903	5	15	γhg(g	γhg(g	PROPN
ejpam-5903	5	16	)	)	PUNCT
ejpam-5903	5	17	,	,	PUNCT
ejpam-5903	5	18	is	be	AUX
ejpam-5903	5	19	called	call	VERB
ejpam-5903	5	20	the	the	DET
ejpam-5903	5	21	geodetic	geodetic	ADJ
ejpam-5903	5	22	hop	hop	NOUN
ejpam-5903	5	23	domination	domination	NOUN
ejpam-5903	5	24	number	number	NOUN
ejpam-5903	5	25	of	of	ADP
ejpam-5903	5	26	g.	g.	PROPN
ejpam-5903	5	27	the	the	DET
ejpam-5903	5	28	minimality	minimality	NOUN
ejpam-5903	5	29	of	of	ADP
ejpam-5903	5	30	γhg(g	γhg(g	PROPN
ejpam-5903	5	31	)	)	PUNCT
ejpam-5903	5	32	implies	imply	VERB
ejpam-5903	5	33	that	that	SCONJ
ejpam-5903	5	34	if	if	SCONJ
ejpam-5903	5	35	s	s	VERB
ejpam-5903	5	36	⊆	⊆	NUM
ejpam-5903	5	37	v	v	NOUN
ejpam-5903	5	38	(	(	PUNCT
ejpam-5903	5	39	g	g	NOUN
ejpam-5903	5	40	)	)	PUNCT
ejpam-5903	5	41	such	such	ADJ
ejpam-5903	5	42	that	that	SCONJ
ejpam-5903	5	43	|s|	|s|	VERB
ejpam-5903	5	44	<	<	X
ejpam-5903	5	45	γhg(g	γhg(g	PROPN
ejpam-5903	5	46	)	)	PUNCT
ejpam-5903	5	47	,	,	PUNCT
ejpam-5903	5	48	then	then	ADV
ejpam-5903	5	49	there	there	PRON
ejpam-5903	5	50	is	be	VERB
ejpam-5903	5	51	at	at	ADV
ejpam-5903	5	52	least	least	ADJ
ejpam-5903	5	53	one	one	NUM
ejpam-5903	5	54	vertex	vertex	NOUN
ejpam-5903	5	55	of	of	ADP
ejpam-5903	5	56	g	g	NOUN
ejpam-5903	5	57	that	that	PRON
ejpam-5903	5	58	is	be	AUX
ejpam-5903	5	59	not	not	PART
ejpam-5903	5	60	geodetically	geodetically	ADV
ejpam-5903	5	61	hop	hop	NOUN
ejpam-5903	5	62	-	-	PUNCT
ejpam-5903	5	63	dominated	dominate	VERB
ejpam-5903	5	64	by	by	ADP
ejpam-5903	5	65	s.	s.	PROPN
ejpam-5903	5	66	the	the	DET
ejpam-5903	5	67	k	k	PROPN
ejpam-5903	5	68	-	-	ADJ
ejpam-5903	5	69	geodetic	geodetic	ADJ
ejpam-5903	5	70	hop	hop	NOUN
ejpam-5903	5	71	domination	domination	NOUN
ejpam-5903	5	72	defect	defect	NOUN
ejpam-5903	5	73	of	of	ADP
ejpam-5903	5	74	g	g	NOUN
ejpam-5903	5	75	,	,	PUNCT
ejpam-5903	5	76	denoted	denote	VERB
ejpam-5903	5	77	by	by	ADP
ejpam-5903	5	78	ζhgk	ζhgk	NOUN
ejpam-5903	5	79	(	(	PUNCT
ejpam-5903	5	80	g	g	NOUN
ejpam-5903	5	81	)	)	PUNCT
ejpam-5903	5	82	,	,	PUNCT
ejpam-5903	5	83	is	be	AUX
ejpam-5903	5	84	the	the	DET
ejpam-5903	5	85	minimum	minimum	ADJ
ejpam-5903	5	86	number	number	NOUN
ejpam-5903	5	87	of	of	ADP
ejpam-5903	5	88	vertices	vertex	NOUN
ejpam-5903	5	89	of	of	ADP
ejpam-5903	5	90	g	g	NOUN
ejpam-5903	5	91	that	that	PRON
ejpam-5903	5	92	is	be	AUX
ejpam-5903	5	93	not	not	PART
ejpam-5903	5	94	geodetically	geodetically	ADV
ejpam-5903	5	95	hop	hop	NOUN
ejpam-5903	5	96	-	-	PUNCT
ejpam-5903	5	97	dominated	dominate	VERB
ejpam-5903	5	98	by	by	ADP
ejpam-5903	5	99	any	any	DET
ejpam-5903	5	100	subset	subset	NOUN
ejpam-5903	5	101	of	of	ADP
ejpam-5903	5	102	vertices	vertex	NOUN
ejpam-5903	5	103	of	of	ADP
ejpam-5903	5	104	g	g	NOUN
ejpam-5903	5	105	with	with	ADP
ejpam-5903	5	106	cardinality	cardinality	PROPN
ejpam-5903	5	107	γhg(g	γhg(g	PROPN
ejpam-5903	5	108	)	)	PUNCT
ejpam-5903	6	1	−	−	PROPN
ejpam-5903	6	2	k.	k.	NOUN
ejpam-5903	7	1	a	a	DET
ejpam-5903	7	2	set	set	NOUN
ejpam-5903	7	3	s	s	PROPN
ejpam-5903	7	4	⊆	⊆	NUM
ejpam-5903	7	5	v	v	NOUN
ejpam-5903	7	6	(	(	PUNCT
ejpam-5903	7	7	g	g	NOUN
ejpam-5903	7	8	)	)	PUNCT
ejpam-5903	7	9	of	of	ADP
ejpam-5903	7	10	cardinality	cardinality	NOUN
ejpam-5903	7	11	γhg(g)−k	γhg(g)−k	PROPN
ejpam-5903	7	12	for	for	ADP
ejpam-5903	7	13	which	which	PRON
ejpam-5903	7	14	|v	|v	PUNCT
ejpam-5903	7	15	(	(	PUNCT
ejpam-5903	7	16	g)\nhg	g)\nhg	PROPN
ejpam-5903	7	17	g	g	PROPN
ejpam-5903	7	18	[	[	X
ejpam-5903	7	19	s]|	s]|	X
ejpam-5903	7	20	=	=	SYM
ejpam-5903	7	21	ζhgk	ζhgk	NOUN
ejpam-5903	7	22	(	(	PUNCT
ejpam-5903	7	23	g	g	NOUN
ejpam-5903	7	24	)	)	PUNCT
ejpam-5903	7	25	,	,	PUNCT
ejpam-5903	7	26	where	where	SCONJ
ejpam-5903	7	27	nhg	nhg	NOUN
ejpam-5903	7	28	g	g	PROPN
ejpam-5903	7	29	[	[	X
ejpam-5903	7	30	s	s	X
ejpam-5903	7	31	]	]	X
ejpam-5903	7	32	=	=	SYM
ejpam-5903	7	33	n2	n2	ADJ
ejpam-5903	7	34	g[s]∩ig[s	g[s]∩ig[s	PROPN
ejpam-5903	7	35	]	]	PUNCT
ejpam-5903	7	36	,	,	PUNCT
ejpam-5903	7	37	is	be	AUX
ejpam-5903	7	38	called	call	VERB
ejpam-5903	7	39	a	a	DET
ejpam-5903	7	40	ζhgk	ζhgk	NOUN
ejpam-5903	7	41	-set	-set	ADJ
ejpam-5903	7	42	of	of	ADP
ejpam-5903	7	43	g.	g.	PROPN
ejpam-5903	7	44	in	in	ADP
ejpam-5903	7	45	this	this	DET
ejpam-5903	7	46	paper	paper	NOUN
ejpam-5903	7	47	,	,	PUNCT
ejpam-5903	7	48	we	we	PRON
ejpam-5903	7	49	initiate	initiate	VERB
ejpam-5903	7	50	the	the	DET
ejpam-5903	7	51	study	study	NOUN
ejpam-5903	7	52	of	of	ADP
ejpam-5903	7	53	the	the	DET
ejpam-5903	7	54	concept	concept	NOUN
ejpam-5903	7	55	of	of	ADP
ejpam-5903	7	56	k	k	ADJ
ejpam-5903	7	57	-	-	ADJ
ejpam-5903	7	58	geodetic	geodetic	ADJ
ejpam-5903	7	59	hop	hop	NOUN
ejpam-5903	7	60	domination	domination	NOUN
ejpam-5903	7	61	defect	defect	NOUN
ejpam-5903	7	62	of	of	ADP
ejpam-5903	7	63	a	a	DET
ejpam-5903	7	64	non	non	ADJ
ejpam-5903	7	65	-	-	ADJ
ejpam-5903	7	66	trivial	trivial	ADJ
ejpam-5903	7	67	graph	graph	NOUN
ejpam-5903	7	68	g	g	NOUN
ejpam-5903	7	69	and	and	CCONJ
ejpam-5903	7	70	investigate	investigate	VERB
ejpam-5903	7	71	it	it	PRON
ejpam-5903	7	72	for	for	ADP
ejpam-5903	7	73	some	some	DET
ejpam-5903	7	74	known	know	VERB
ejpam-5903	7	75	classes	class	NOUN
ejpam-5903	7	76	of	of	ADP
ejpam-5903	7	77	graphs	graph	NOUN
ejpam-5903	7	78	.	.	PUNCT
ejpam-5903	8	1	2020	2020	NUM
ejpam-5903	8	2	mathematics	mathematic	NOUN
ejpam-5903	8	3	subject	subject	NOUN
ejpam-5903	8	4	classifications	classification	NOUN
ejpam-5903	8	5	:	:	PUNCT
ejpam-5903	8	6	05c69	05c69	X
ejpam-5903	8	7	key	key	ADJ
ejpam-5903	8	8	words	word	NOUN
ejpam-5903	8	9	and	and	CCONJ
ejpam-5903	8	10	phrases	phrase	NOUN
ejpam-5903	8	11	:	:	PUNCT
ejpam-5903	8	12	geodetic	geodetic	ADJ
ejpam-5903	8	13	set	set	NOUN
ejpam-5903	8	14	,	,	PUNCT
ejpam-5903	8	15	hop	hop	NOUN
ejpam-5903	8	16	domination	domination	NOUN
ejpam-5903	8	17	,	,	PUNCT
ejpam-5903	8	18	geodetic	geodetic	ADJ
ejpam-5903	8	19	hop	hop	NOUN
ejpam-5903	8	20	domination	domination	NOUN
ejpam-5903	8	21	,	,	PUNCT
ejpam-5903	8	22	k	k	ADJ
ejpam-5903	8	23	-	-	ADJ
ejpam-5903	8	24	geodetic	geodetic	ADJ
ejpam-5903	8	25	hop	hop	NOUN
ejpam-5903	8	26	domination	domination	NOUN
ejpam-5903	8	27	defect	defect	NOUN
ejpam-5903	8	28	1	1	NUM
ejpam-5903	8	29	.	.	PUNCT
ejpam-5903	9	1	introduction	introduction	NOUN
ejpam-5903	9	2	the	the	DET
ejpam-5903	9	3	domination	domination	NOUN
ejpam-5903	9	4	number	number	NOUN
ejpam-5903	9	5	γ(g	γ(g	PROPN
ejpam-5903	9	6	)	)	PUNCT
ejpam-5903	9	7	of	of	ADP
ejpam-5903	9	8	a	a	DET
ejpam-5903	9	9	graph	graph	NOUN
ejpam-5903	9	10	g	g	NOUN
ejpam-5903	9	11	refers	refer	VERB
ejpam-5903	9	12	to	to	ADP
ejpam-5903	9	13	the	the	DET
ejpam-5903	9	14	smallest	small	ADJ
ejpam-5903	9	15	number	number	NOUN
ejpam-5903	9	16	of	of	ADP
ejpam-5903	9	17	vertices	vertex	NOUN
ejpam-5903	9	18	required	require	VERB
ejpam-5903	9	19	to	to	PART
ejpam-5903	9	20	dominate	dominate	VERB
ejpam-5903	9	21	all	all	DET
ejpam-5903	9	22	the	the	DET
ejpam-5903	9	23	vertices	vertex	NOUN
ejpam-5903	9	24	of	of	ADP
ejpam-5903	9	25	g.	g.	PROPN
ejpam-5903	9	26	hence	hence	ADV
ejpam-5903	9	27	,	,	PUNCT
ejpam-5903	9	28	if	if	SCONJ
ejpam-5903	9	29	a	a	DET
ejpam-5903	9	30	set	set	NOUN
ejpam-5903	9	31	s	s	NOUN
ejpam-5903	9	32	of	of	ADP
ejpam-5903	9	33	vertices	vertex	NOUN
ejpam-5903	9	34	of	of	ADP
ejpam-5903	9	35	g	g	PROPN
ejpam-5903	9	36	has	have	VERB
ejpam-5903	9	37	cardinality	cardinality	NOUN
ejpam-5903	9	38	strictly	strictly	ADV
ejpam-5903	9	39	less	less	ADJ
ejpam-5903	9	40	than	than	ADP
ejpam-5903	9	41	γ(g	γ(g	PROPN
ejpam-5903	9	42	)	)	PUNCT
ejpam-5903	9	43	,	,	PUNCT
ejpam-5903	9	44	then	then	ADV
ejpam-5903	9	45	definitely	definitely	ADV
ejpam-5903	9	46	,	,	PUNCT
ejpam-5903	9	47	there	there	PRON
ejpam-5903	9	48	will	will	AUX
ejpam-5903	9	49	be	be	AUX
ejpam-5903	9	50	vertices	vertex	NOUN
ejpam-5903	9	51	ofg	ofg	PROPN
ejpam-5903	9	52	that	that	PRON
ejpam-5903	9	53	will	will	AUX
ejpam-5903	9	54	not	not	PART
ejpam-5903	9	55	be	be	AUX
ejpam-5903	9	56	dominated	dominate	VERB
ejpam-5903	9	57	by	by	ADP
ejpam-5903	9	58	any	any	PRON
ejpam-5903	9	59	of	of	ADP
ejpam-5903	9	60	the	the	DET
ejpam-5903	9	61	vertices	vertex	NOUN
ejpam-5903	9	62	in	in	ADP
ejpam-5903	9	63	s.	s.	PROPN
ejpam-5903	9	64	recently	recently	ADV
ejpam-5903	9	65	,	,	PUNCT
ejpam-5903	9	66	das	das	PROPN
ejpam-5903	9	67	et	et	PROPN
ejpam-5903	9	68	al	al	PROPN
ejpam-5903	9	69	.	.	PUNCT
ejpam-5903	10	1	[	[	X
ejpam-5903	10	2	1	1	X
ejpam-5903	10	3	]	]	PUNCT
ejpam-5903	10	4	introduced	introduce	VERB
ejpam-5903	10	5	and	and	CCONJ
ejpam-5903	10	6	studied	study	VERB
ejpam-5903	10	7	the	the	DET
ejpam-5903	10	8	notion	notion	NOUN
ejpam-5903	10	9	of	of	ADP
ejpam-5903	10	10	k	k	ADJ
ejpam-5903	10	11	-	-	PUNCT
ejpam-5903	10	12	domination	domination	NOUN
ejpam-5903	10	13	defect	defect	NOUN
ejpam-5903	10	14	of	of	ADP
ejpam-5903	10	15	a	a	DET
ejpam-5903	10	16	graph	graph	NOUN
ejpam-5903	10	17	,	,	PUNCT
ejpam-5903	10	18	where	where	SCONJ
ejpam-5903	10	19	k	k	PROPN
ejpam-5903	10	20	is	be	AUX
ejpam-5903	10	21	a	a	DET
ejpam-5903	10	22	positive	positive	ADJ
ejpam-5903	10	23	integer	integer	NOUN
ejpam-5903	10	24	strictly	strictly	ADV
ejpam-5903	10	25	less	less	ADJ
ejpam-5903	10	26	than	than	ADP
ejpam-5903	10	27	the	the	DET
ejpam-5903	10	28	domination	domination	NOUN
ejpam-5903	10	29	number	number	NOUN
ejpam-5903	10	30	of	of	ADP
ejpam-5903	10	31	the	the	DET
ejpam-5903	10	32	graph	graph	NOUN
ejpam-5903	10	33	.	.	PUNCT
ejpam-5903	11	1	the	the	DET
ejpam-5903	11	2	authors	author	NOUN
ejpam-5903	11	3	in	in	ADP
ejpam-5903	11	4	this	this	DET
ejpam-5903	11	5	study	study	NOUN
ejpam-5903	11	6	established	establish	VERB
ejpam-5903	11	7	various	various	ADJ
ejpam-5903	11	8	bounds	bound	NOUN
ejpam-5903	11	9	on	on	ADP
ejpam-5903	11	10	the	the	DET
ejpam-5903	11	11	k	k	ADJ
ejpam-5903	11	12	-	-	PUNCT
ejpam-5903	11	13	domination	domination	NOUN
ejpam-5903	11	14	defect	defect	NOUN
ejpam-5903	11	15	of	of	ADP
ejpam-5903	11	16	a	a	DET
ejpam-5903	11	17	graph	graph	NOUN
ejpam-5903	11	18	in	in	ADP
ejpam-5903	11	19	terms	term	NOUN
ejpam-5903	11	20	of	of	ADP
ejpam-5903	11	21	the	the	DET
ejpam-5903	11	22	maximum	maximum	ADJ
ejpam-5903	11	23	degree	degree	NOUN
ejpam-5903	11	24	and	and	CCONJ
ejpam-5903	11	25	domination	domination	NOUN
ejpam-5903	11	26	number	number	NOUN
ejpam-5903	11	27	of	of	ADP
ejpam-5903	11	28	the	the	DET
ejpam-5903	11	29	graph	graph	NOUN
ejpam-5903	11	30	,	,	PUNCT
ejpam-5903	11	31	and	and	CCONJ
ejpam-5903	11	32	other	other	ADJ
ejpam-5903	11	33	parameters	parameter	NOUN
ejpam-5903	11	34	.	.	PUNCT
ejpam-5903	12	1	∗corresponding	∗corresponde	VERB
ejpam-5903	12	2	author	author	NOUN
ejpam-5903	12	3	.	.	PUNCT
ejpam-5903	13	1	doi	doi	NOUN
ejpam-5903	13	2	:	:	PUNCT
ejpam-5903	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5903	https://doi.org/10.29020/nybg.ejpam.v18i2.5903	ADJ
ejpam-5903	13	4	email	email	NOUN
ejpam-5903	13	5	addresses	address	NOUN
ejpam-5903	13	6	:	:	PUNCT
ejpam-5903	13	7	jesica.anoche@g.msuiit.edu.ph	jesica.anoche@g.msuiit.edu.ph	PROPN
ejpam-5903	13	8	(	(	PUNCT
ejpam-5903	13	9	j.	j.	PROPN
ejpam-5903	13	10	anoche	anoche	PROPN
ejpam-5903	13	11	)	)	PUNCT
ejpam-5903	13	12	,	,	PUNCT
ejpam-5903	13	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5903	13	14	(	(	PUNCT
ejpam-5903	13	15	s.	s.	PROPN
ejpam-5903	13	16	canoy	canoy	PROPN
ejpam-5903	13	17	,	,	PUNCT
ejpam-5903	13	18	jr	jr	PROPN
ejpam-5903	13	19	.	.	PUNCT
ejpam-5903	13	20	)	)	PUNCT
ejpam-5903	13	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5903	14	1	1	1	NUM
ejpam-5903	14	2	copyright	copyright	NOUN
ejpam-5903	14	3	:	:	PUNCT
ejpam-5903	14	4	©	©	PROPN
ejpam-5903	14	5	2025	2025	NUM
ejpam-5903	14	6	the	the	DET
ejpam-5903	14	7	author(s	author(s	NOUN
ejpam-5903	14	8	)	)	PUNCT
ejpam-5903	14	9	.	.	PUNCT
ejpam-5903	15	1	(	(	PUNCT
ejpam-5903	15	2	cc	cc	NOUN
ejpam-5903	15	3	by	by	ADP
ejpam-5903	15	4	-	-	PUNCT
ejpam-5903	15	5	nc	nc	PROPN
ejpam-5903	15	6	4.0	4.0	NUM
ejpam-5903	15	7	)	)	PUNCT
ejpam-5903	15	8	j.	j.	PROPN
ejpam-5903	15	9	anoche	anoche	PROPN
ejpam-5903	15	10	,	,	PUNCT
ejpam-5903	15	11	s.	s.	PROPN
ejpam-5903	15	12	canoy	canoy	PROPN
ejpam-5903	15	13	,	,	PUNCT
ejpam-5903	15	14	jr	jr	PROPN
ejpam-5903	15	15	.	.	PROPN
ejpam-5903	15	16	/	/	SYM
ejpam-5903	15	17	eur	eur	PROPN
ejpam-5903	15	18	.	.	PUNCT
ejpam-5903	16	1	j.	j.	PROPN
ejpam-5903	16	2	pure	pure	PROPN
ejpam-5903	16	3	appl	appl	PROPN
ejpam-5903	16	4	.	.	PROPN
ejpam-5903	16	5	math	math	PROPN
ejpam-5903	16	6	,	,	PUNCT
ejpam-5903	16	7	18	18	NUM
ejpam-5903	16	8	(	(	PUNCT
ejpam-5903	16	9	2	2	NUM
ejpam-5903	16	10	)	)	PUNCT
ejpam-5903	16	11	(	(	PUNCT
ejpam-5903	16	12	2025	2025	NUM
ejpam-5903	16	13	)	)	PUNCT
ejpam-5903	16	14	,	,	PUNCT
ejpam-5903	16	15	5903	5903	NUM
ejpam-5903	16	16	2	2	NUM
ejpam-5903	16	17	of	of	ADP
ejpam-5903	16	18	17	17	NUM
ejpam-5903	16	19	for	for	ADP
ejpam-5903	16	20	hop	hop	PROPN
ejpam-5903	16	21	domination	domination	NOUN
ejpam-5903	16	22	,	,	PUNCT
ejpam-5903	16	23	a	a	DET
ejpam-5903	16	24	concept	concept	NOUN
ejpam-5903	16	25	which	which	PRON
ejpam-5903	16	26	is	be	AUX
ejpam-5903	16	27	studied	study	VERB
ejpam-5903	16	28	by	by	ADP
ejpam-5903	16	29	many	many	ADJ
ejpam-5903	16	30	researchers	researcher	NOUN
ejpam-5903	16	31	(	(	PUNCT
ejpam-5903	16	32	see	see	VERB
ejpam-5903	16	33	for	for	ADP
ejpam-5903	16	34	example	example	NOUN
ejpam-5903	16	35	,	,	PUNCT
ejpam-5903	17	1	[	[	X
ejpam-5903	17	2	2	2	NUM
ejpam-5903	17	3	]	]	PUNCT
ejpam-5903	17	4	,	,	PUNCT
ejpam-5903	17	5	[	[	X
ejpam-5903	17	6	3	3	NUM
ejpam-5903	17	7	]	]	PUNCT
ejpam-5903	17	8	,	,	PUNCT
ejpam-5903	17	9	[	[	X
ejpam-5903	17	10	4	4	NUM
ejpam-5903	17	11	]	]	PUNCT
ejpam-5903	17	12	,	,	PUNCT
ejpam-5903	17	13	[	[	X
ejpam-5903	17	14	5	5	NUM
ejpam-5903	17	15	]	]	PUNCT
ejpam-5903	17	16	,	,	PUNCT
ejpam-5903	18	1	[	[	X
ejpam-5903	18	2	6	6	NUM
ejpam-5903	18	3	]	]	PUNCT
ejpam-5903	18	4	,	,	PUNCT
ejpam-5903	18	5	and	and	CCONJ
ejpam-5903	18	6	[	[	X
ejpam-5903	18	7	7	7	NUM
ejpam-5903	18	8	]	]	NUM
ejpam-5903	18	9	)	)	PUNCT
ejpam-5903	18	10	,	,	PUNCT
ejpam-5903	18	11	anoche	anoche	PROPN
ejpam-5903	18	12	et	et	PROPN
ejpam-5903	18	13	al	al	PROPN
ejpam-5903	18	14	.	.	PUNCT
ejpam-5903	19	1	[	[	X
ejpam-5903	19	2	8	8	NUM
ejpam-5903	19	3	]	]	PUNCT
ejpam-5903	19	4	introduced	introduce	VERB
ejpam-5903	19	5	and	and	CCONJ
ejpam-5903	19	6	studied	study	VERB
ejpam-5903	19	7	the	the	DET
ejpam-5903	19	8	notion	notion	NOUN
ejpam-5903	19	9	of	of	ADP
ejpam-5903	19	10	k	k	ADJ
ejpam-5903	19	11	-	-	PUNCT
ejpam-5903	19	12	hop	hop	NOUN
ejpam-5903	19	13	domination	domination	NOUN
ejpam-5903	19	14	defect	defect	NOUN
ejpam-5903	19	15	in	in	ADP
ejpam-5903	19	16	a	a	DET
ejpam-5903	19	17	graph	graph	NOUN
ejpam-5903	19	18	.	.	PUNCT
ejpam-5903	20	1	the	the	DET
ejpam-5903	20	2	study	study	NOUN
ejpam-5903	20	3	obtained	obtain	VERB
ejpam-5903	20	4	some	some	DET
ejpam-5903	20	5	bounds	bound	NOUN
ejpam-5903	20	6	on	on	ADP
ejpam-5903	20	7	the	the	DET
ejpam-5903	20	8	k	k	ADJ
ejpam-5903	20	9	-	-	PUNCT
ejpam-5903	20	10	hop	hop	NOUN
ejpam-5903	20	11	domination	domination	NOUN
ejpam-5903	20	12	defect	defect	NOUN
ejpam-5903	20	13	of	of	ADP
ejpam-5903	20	14	a	a	DET
ejpam-5903	20	15	graph	graph	NOUN
ejpam-5903	20	16	in	in	ADP
ejpam-5903	20	17	terms	term	NOUN
ejpam-5903	20	18	of	of	ADP
ejpam-5903	20	19	its	its	PRON
ejpam-5903	20	20	order	order	NOUN
ejpam-5903	20	21	and	and	CCONJ
ejpam-5903	20	22	maximum	maximum	ADJ
ejpam-5903	20	23	hop	hop	NOUN
ejpam-5903	20	24	degree	degree	NOUN
ejpam-5903	20	25	.	.	PUNCT
ejpam-5903	21	1	moreover	moreover	ADV
ejpam-5903	21	2	,	,	PUNCT
ejpam-5903	21	3	the	the	DET
ejpam-5903	21	4	k	k	ADJ
ejpam-5903	21	5	-	-	PUNCT
ejpam-5903	21	6	hop	hop	NOUN
ejpam-5903	21	7	domination	domination	NOUN
ejpam-5903	21	8	defects	defect	NOUN
ejpam-5903	21	9	of	of	ADP
ejpam-5903	21	10	some	some	DET
ejpam-5903	21	11	classes	class	NOUN
ejpam-5903	21	12	of	of	ADP
ejpam-5903	21	13	graphs	graph	NOUN
ejpam-5903	21	14	have	have	AUX
ejpam-5903	21	15	been	be	AUX
ejpam-5903	21	16	determined	determine	VERB
ejpam-5903	21	17	.	.	PUNCT
ejpam-5903	22	1	some	some	DET
ejpam-5903	22	2	variants	variant	NOUN
ejpam-5903	22	3	of	of	ADP
ejpam-5903	22	4	domination	domination	NOUN
ejpam-5903	22	5	and	and	CCONJ
ejpam-5903	22	6	hop	hop	NOUN
ejpam-5903	22	7	domination	domination	NOUN
ejpam-5903	22	8	utilize	utilize	VERB
ejpam-5903	22	9	the	the	DET
ejpam-5903	22	10	concept	concept	NOUN
ejpam-5903	22	11	of	of	ADP
ejpam-5903	22	12	geodetic	geodetic	ADJ
ejpam-5903	22	13	set	set	NOUN
ejpam-5903	22	14	.	.	PUNCT
ejpam-5903	23	1	the	the	DET
ejpam-5903	23	2	associated	associated	ADJ
ejpam-5903	23	3	term	term	NOUN
ejpam-5903	23	4	geodetic	geodetic	ADJ
ejpam-5903	23	5	number	number	NOUN
ejpam-5903	23	6	of	of	ADP
ejpam-5903	23	7	a	a	DET
ejpam-5903	23	8	graph	graph	NOUN
ejpam-5903	23	9	was	be	AUX
ejpam-5903	23	10	introduced	introduce	VERB
ejpam-5903	23	11	by	by	ADP
ejpam-5903	23	12	harary	harary	PROPN
ejpam-5903	23	13	et	et	PROPN
ejpam-5903	23	14	al	al	PROPN
ejpam-5903	23	15	.	.	PUNCT
ejpam-5903	24	1	[	[	X
ejpam-5903	24	2	9	9	NUM
ejpam-5903	24	3	]	]	PUNCT
ejpam-5903	24	4	.	.	PUNCT
ejpam-5903	25	1	geodetic	geodetic	ADJ
ejpam-5903	25	2	number	number	NOUN
ejpam-5903	25	3	and	and	CCONJ
ejpam-5903	25	4	geodetic	geodetic	ADJ
ejpam-5903	25	5	domination	domination	NOUN
ejpam-5903	25	6	were	be	AUX
ejpam-5903	25	7	considered	consider	VERB
ejpam-5903	25	8	in	in	ADP
ejpam-5903	25	9	[	[	X
ejpam-5903	25	10	10	10	NUM
ejpam-5903	25	11	]	]	PUNCT
ejpam-5903	25	12	,	,	PUNCT
ejpam-5903	25	13	[	[	X
ejpam-5903	25	14	11	11	NUM
ejpam-5903	25	15	]	]	PUNCT
ejpam-5903	25	16	,	,	PUNCT
ejpam-5903	25	17	[	[	X
ejpam-5903	25	18	12	12	NUM
ejpam-5903	25	19	]	]	PUNCT
ejpam-5903	25	20	,	,	PUNCT
ejpam-5903	25	21	[	[	X
ejpam-5903	25	22	13	13	NUM
ejpam-5903	25	23	]	]	PUNCT
ejpam-5903	25	24	,	,	PUNCT
ejpam-5903	25	25	and	and	CCONJ
ejpam-5903	25	26	[	[	X
ejpam-5903	25	27	14	14	NUM
ejpam-5903	25	28	]	]	PUNCT
ejpam-5903	25	29	.	.	PUNCT
ejpam-5903	26	1	recently	recently	ADV
ejpam-5903	26	2	,	,	PUNCT
ejpam-5903	26	3	anoche	anoche	PROPN
ejpam-5903	26	4	et	et	PROPN
ejpam-5903	26	5	al	al	PROPN
ejpam-5903	26	6	.	.	PUNCT
ejpam-5903	27	1	[	[	X
ejpam-5903	27	2	15	15	NUM
ejpam-5903	27	3	]	]	PUNCT
ejpam-5903	27	4	introduced	introduce	VERB
ejpam-5903	27	5	and	and	CCONJ
ejpam-5903	27	6	studied	study	VERB
ejpam-5903	27	7	the	the	DET
ejpam-5903	27	8	notion	notion	NOUN
ejpam-5903	27	9	of	of	ADP
ejpam-5903	27	10	k	k	ADJ
ejpam-5903	27	11	-	-	ADJ
ejpam-5903	27	12	geodetic	geodetic	ADJ
ejpam-5903	27	13	domination	domination	NOUN
ejpam-5903	27	14	defect	defect	NOUN
ejpam-5903	27	15	of	of	ADP
ejpam-5903	27	16	a	a	DET
ejpam-5903	27	17	graph	graph	NOUN
ejpam-5903	27	18	.	.	PUNCT
ejpam-5903	28	1	the	the	DET
ejpam-5903	28	2	authors	author	NOUN
ejpam-5903	28	3	in	in	ADP
ejpam-5903	28	4	this	this	DET
ejpam-5903	28	5	study	study	NOUN
ejpam-5903	28	6	established	establish	VERB
ejpam-5903	28	7	some	some	DET
ejpam-5903	28	8	sharp	sharp	ADJ
ejpam-5903	28	9	bounds	bound	NOUN
ejpam-5903	28	10	on	on	ADP
ejpam-5903	28	11	the	the	DET
ejpam-5903	28	12	kgeodetic	kgeodetic	ADJ
ejpam-5903	28	13	domination	domination	NOUN
ejpam-5903	28	14	defect	defect	NOUN
ejpam-5903	28	15	of	of	ADP
ejpam-5903	28	16	a	a	DET
ejpam-5903	28	17	graph	graph	NOUN
ejpam-5903	28	18	and	and	CCONJ
ejpam-5903	28	19	computed	compute	VERB
ejpam-5903	28	20	its	its	PRON
ejpam-5903	28	21	values	value	NOUN
ejpam-5903	28	22	for	for	ADP
ejpam-5903	28	23	several	several	ADJ
ejpam-5903	28	24	well	well	ADV
ejpam-5903	28	25	-	-	PUNCT
ejpam-5903	28	26	known	know	VERB
ejpam-5903	28	27	graphs	graph	NOUN
ejpam-5903	28	28	.	.	PUNCT
ejpam-5903	29	1	on	on	ADP
ejpam-5903	29	2	the	the	DET
ejpam-5903	29	3	other	other	ADJ
ejpam-5903	29	4	hand	hand	NOUN
ejpam-5903	29	5	,	,	PUNCT
ejpam-5903	29	6	the	the	DET
ejpam-5903	29	7	notion	notion	NOUN
ejpam-5903	29	8	of	of	ADP
ejpam-5903	29	9	geodetic	geodetic	ADJ
ejpam-5903	29	10	hop	hop	NOUN
ejpam-5903	29	11	domination	domination	NOUN
ejpam-5903	29	12	was	be	AUX
ejpam-5903	29	13	introduced	introduce	VERB
ejpam-5903	29	14	and	and	CCONJ
ejpam-5903	29	15	investigated	investigate	VERB
ejpam-5903	29	16	in	in	ADP
ejpam-5903	29	17	[	[	X
ejpam-5903	29	18	16	16	NUM
ejpam-5903	29	19	]	]	PUNCT
ejpam-5903	29	20	,	,	PUNCT
ejpam-5903	29	21	[	[	X
ejpam-5903	29	22	17	17	NUM
ejpam-5903	29	23	]	]	PUNCT
ejpam-5903	29	24	,	,	PUNCT
ejpam-5903	29	25	[	[	X
ejpam-5903	29	26	18	18	NUM
ejpam-5903	29	27	]	]	PUNCT
ejpam-5903	29	28	and	and	CCONJ
ejpam-5903	29	29	[	[	X
ejpam-5903	29	30	19	19	NUM
ejpam-5903	29	31	]	]	PUNCT
ejpam-5903	29	32	.	.	PUNCT
ejpam-5903	30	1	note	note	VERB
ejpam-5903	30	2	that	that	SCONJ
ejpam-5903	30	3	if	if	SCONJ
ejpam-5903	30	4	g	g	PROPN
ejpam-5903	30	5	is	be	AUX
ejpam-5903	30	6	a	a	DET
ejpam-5903	30	7	graph	graph	NOUN
ejpam-5903	30	8	and	and	CCONJ
ejpam-5903	30	9	s	s	NOUN
ejpam-5903	30	10	is	be	AUX
ejpam-5903	30	11	a	a	DET
ejpam-5903	30	12	set	set	NOUN
ejpam-5903	30	13	of	of	ADP
ejpam-5903	30	14	vertices	vertex	NOUN
ejpam-5903	30	15	of	of	ADP
ejpam-5903	30	16	g	g	NOUN
ejpam-5903	30	17	with	with	ADP
ejpam-5903	30	18	cardinality	cardinality	NOUN
ejpam-5903	30	19	strictly	strictly	ADV
ejpam-5903	30	20	less	less	ADJ
ejpam-5903	30	21	than	than	ADP
ejpam-5903	30	22	the	the	DET
ejpam-5903	30	23	geodetic	geodetic	ADJ
ejpam-5903	30	24	hop	hop	NOUN
ejpam-5903	30	25	domination	domination	NOUN
ejpam-5903	30	26	number	number	NOUN
ejpam-5903	30	27	γhg(g	γhg(g	PROPN
ejpam-5903	30	28	)	)	PUNCT
ejpam-5903	30	29	of	of	ADP
ejpam-5903	30	30	g	g	PROPN
ejpam-5903	30	31	,	,	PUNCT
ejpam-5903	30	32	then	then	ADV
ejpam-5903	30	33	there	there	PRON
ejpam-5903	30	34	is	be	VERB
ejpam-5903	30	35	at	at	ADV
ejpam-5903	30	36	least	least	ADJ
ejpam-5903	30	37	one	one	NUM
ejpam-5903	30	38	vertex	vertex	NOUN
ejpam-5903	30	39	outside	outside	ADP
ejpam-5903	30	40	s	s	PRON
ejpam-5903	30	41	that	that	PRON
ejpam-5903	30	42	is	be	AUX
ejpam-5903	30	43	not	not	PART
ejpam-5903	30	44	geodetically	geodetically	ADV
ejpam-5903	30	45	hop	hop	ADV
ejpam-5903	30	46	-	-	PUNCT
ejpam-5903	30	47	dominated	dominate	VERB
ejpam-5903	30	48	,	,	PUNCT
ejpam-5903	30	49	that	that	ADV
ejpam-5903	30	50	is	is	ADV
ejpam-5903	30	51	,	,	PUNCT
ejpam-5903	30	52	has	have	VERB
ejpam-5903	30	53	no	no	DET
ejpam-5903	30	54	hop	hop	NOUN
ejpam-5903	30	55	neighbor	neighbor	NOUN
ejpam-5903	30	56	in	in	ADP
ejpam-5903	30	57	s	s	PRON
ejpam-5903	30	58	or	or	CCONJ
ejpam-5903	30	59	is	be	AUX
ejpam-5903	30	60	not	not	PART
ejpam-5903	30	61	in	in	ADP
ejpam-5903	30	62	any	any	DET
ejpam-5903	30	63	shortest	short	ADJ
ejpam-5903	30	64	path	path	NOUN
ejpam-5903	30	65	joining	join	VERB
ejpam-5903	30	66	any	any	DET
ejpam-5903	30	67	two	two	NUM
ejpam-5903	30	68	vertices	vertex	NOUN
ejpam-5903	30	69	in	in	ADP
ejpam-5903	30	70	s.	s.	PROPN
ejpam-5903	30	71	in	in	ADP
ejpam-5903	30	72	this	this	DET
ejpam-5903	30	73	paper	paper	NOUN
ejpam-5903	30	74	,	,	PUNCT
ejpam-5903	30	75	we	we	PRON
ejpam-5903	30	76	introduce	introduce	VERB
ejpam-5903	30	77	the	the	DET
ejpam-5903	30	78	notion	notion	NOUN
ejpam-5903	30	79	k	k	ADJ
ejpam-5903	30	80	-	-	ADJ
ejpam-5903	30	81	geodetic	geodetic	ADJ
ejpam-5903	30	82	hop	hop	NOUN
ejpam-5903	30	83	domination	domination	NOUN
ejpam-5903	30	84	defect	defect	NOUN
ejpam-5903	30	85	and	and	CCONJ
ejpam-5903	30	86	study	study	VERB
ejpam-5903	30	87	it	it	PRON
ejpam-5903	30	88	for	for	ADP
ejpam-5903	30	89	some	some	DET
ejpam-5903	30	90	classes	class	NOUN
ejpam-5903	30	91	of	of	ADP
ejpam-5903	30	92	graphs	graph	NOUN
ejpam-5903	30	93	.	.	PUNCT
ejpam-5903	31	1	for	for	ADP
ejpam-5903	31	2	a	a	DET
ejpam-5903	31	3	motivation	motivation	NOUN
ejpam-5903	31	4	of	of	ADP
ejpam-5903	31	5	the	the	DET
ejpam-5903	31	6	study	study	NOUN
ejpam-5903	31	7	,	,	PUNCT
ejpam-5903	31	8	consider	consider	VERB
ejpam-5903	31	9	an	an	DET
ejpam-5903	31	10	establishment	establishment	NOUN
ejpam-5903	31	11	with	with	ADP
ejpam-5903	31	12	a	a	DET
ejpam-5903	31	13	large	large	ADJ
ejpam-5903	31	14	number	number	NOUN
ejpam-5903	31	15	of	of	ADP
ejpam-5903	31	16	employees	employee	NOUN
ejpam-5903	31	17	which	which	PRON
ejpam-5903	31	18	needs	need	VERB
ejpam-5903	31	19	to	to	PART
ejpam-5903	31	20	make	make	VERB
ejpam-5903	31	21	an	an	DET
ejpam-5903	31	22	annual	annual	ADJ
ejpam-5903	31	23	evaluation	evaluation	NOUN
ejpam-5903	31	24	of	of	ADP
ejpam-5903	31	25	their	their	PRON
ejpam-5903	31	26	workers	worker	NOUN
ejpam-5903	31	27	.	.	PUNCT
ejpam-5903	32	1	the	the	DET
ejpam-5903	32	2	manager	manager	NOUN
ejpam-5903	32	3	chooses	choose	VERB
ejpam-5903	32	4	some	some	DET
ejpam-5903	32	5	workers	worker	NOUN
ejpam-5903	32	6	to	to	PART
ejpam-5903	32	7	form	form	VERB
ejpam-5903	32	8	a	a	DET
ejpam-5903	32	9	team	team	NOUN
ejpam-5903	32	10	of	of	ADP
ejpam-5903	32	11	assessors	assessor	NOUN
ejpam-5903	32	12	to	to	PART
ejpam-5903	32	13	evaluate	evaluate	VERB
ejpam-5903	32	14	the	the	DET
ejpam-5903	32	15	performance	performance	NOUN
ejpam-5903	32	16	of	of	ADP
ejpam-5903	32	17	their	their	PRON
ejpam-5903	32	18	co	co	NOUN
ejpam-5903	32	19	-	-	NOUN
ejpam-5903	32	20	workers	worker	NOUN
ejpam-5903	32	21	.	.	PUNCT
ejpam-5903	33	1	to	to	PART
ejpam-5903	33	2	be	be	AUX
ejpam-5903	33	3	cost	cost	VERB
ejpam-5903	33	4	effective	effective	ADJ
ejpam-5903	33	5	or	or	CCONJ
ejpam-5903	33	6	to	to	PART
ejpam-5903	33	7	minimize	minimize	VERB
ejpam-5903	33	8	costs	cost	NOUN
ejpam-5903	34	1	,	,	PUNCT
ejpam-5903	34	2	the	the	DET
ejpam-5903	34	3	manager	manager	NOUN
ejpam-5903	34	4	ensures	ensure	VERB
ejpam-5903	34	5	that	that	SCONJ
ejpam-5903	34	6	this	this	DET
ejpam-5903	34	7	team	team	NOUN
ejpam-5903	34	8	will	will	AUX
ejpam-5903	34	9	consist	consist	VERB
ejpam-5903	34	10	of	of	ADP
ejpam-5903	34	11	the	the	DET
ejpam-5903	34	12	smallest	small	ADJ
ejpam-5903	34	13	number	number	NOUN
ejpam-5903	34	14	of	of	ADP
ejpam-5903	34	15	members	member	NOUN
ejpam-5903	34	16	that	that	PRON
ejpam-5903	34	17	can	can	AUX
ejpam-5903	34	18	do	do	VERB
ejpam-5903	34	19	the	the	DET
ejpam-5903	34	20	task	task	NOUN
ejpam-5903	34	21	.	.	PUNCT
ejpam-5903	35	1	moreover	moreover	ADV
ejpam-5903	35	2	,	,	PUNCT
ejpam-5903	35	3	to	to	PART
ejpam-5903	35	4	avoid	avoid	VERB
ejpam-5903	35	5	bias	bias	NOUN
ejpam-5903	35	6	in	in	ADP
ejpam-5903	35	7	the	the	DET
ejpam-5903	35	8	assessment	assessment	NOUN
ejpam-5903	35	9	,	,	PUNCT
ejpam-5903	35	10	an	an	DET
ejpam-5903	35	11	inspector	inspector	NOUN
ejpam-5903	35	12	should	should	AUX
ejpam-5903	35	13	be	be	AUX
ejpam-5903	35	14	non	non	ADJ
ejpam-5903	35	15	-	-	ADJ
ejpam-5903	35	16	biased	biased	ADJ
ejpam-5903	35	17	,	,	PUNCT
ejpam-5903	35	18	that	that	ADV
ejpam-5903	35	19	is	is	ADV
ejpam-5903	35	20	,	,	PUNCT
ejpam-5903	35	21	neither	neither	CCONJ
ejpam-5903	35	22	be	be	AUX
ejpam-5903	35	23	close	close	ADJ
ejpam-5903	35	24	friends	friend	NOUN
ejpam-5903	35	25	nor	nor	CCONJ
ejpam-5903	35	26	enemies	enemy	NOUN
ejpam-5903	35	27	with	with	ADP
ejpam-5903	35	28	any	any	PRON
ejpam-5903	35	29	of	of	ADP
ejpam-5903	35	30	the	the	DET
ejpam-5903	35	31	workers	worker	NOUN
ejpam-5903	36	1	he	he	PRON
ejpam-5903	36	2	or	or	CCONJ
ejpam-5903	36	3	she	she	PRON
ejpam-5903	36	4	is	be	AUX
ejpam-5903	36	5	assigned	assign	VERB
ejpam-5903	36	6	to	to	PART
ejpam-5903	36	7	assess	assess	VERB
ejpam-5903	36	8	.	.	PUNCT
ejpam-5903	37	1	this	this	DET
ejpam-5903	37	2	situation	situation	NOUN
ejpam-5903	37	3	can	can	AUX
ejpam-5903	37	4	be	be	AUX
ejpam-5903	37	5	modeled	model	VERB
ejpam-5903	37	6	by	by	ADP
ejpam-5903	37	7	constructing	construct	VERB
ejpam-5903	37	8	a	a	DET
ejpam-5903	37	9	graph	graph	NOUN
ejpam-5903	37	10	where	where	SCONJ
ejpam-5903	37	11	each	each	DET
ejpam-5903	37	12	vertex	vertex	NOUN
ejpam-5903	37	13	represents	represent	VERB
ejpam-5903	37	14	a	a	DET
ejpam-5903	37	15	worker	worker	NOUN
ejpam-5903	37	16	and	and	CCONJ
ejpam-5903	37	17	an	an	DET
ejpam-5903	37	18	edge	edge	NOUN
ejpam-5903	37	19	between	between	ADP
ejpam-5903	37	20	two	two	NUM
ejpam-5903	37	21	workers	worker	NOUN
ejpam-5903	37	22	represents	represent	VERB
ejpam-5903	37	23	possible	possible	ADJ
ejpam-5903	37	24	bias	bias	NOUN
ejpam-5903	37	25	,	,	PUNCT
ejpam-5903	37	26	that	that	ADV
ejpam-5903	37	27	is	is	ADV
ejpam-5903	37	28	,	,	PUNCT
ejpam-5903	37	29	if	if	SCONJ
ejpam-5903	37	30	the	the	DET
ejpam-5903	37	31	two	two	NUM
ejpam-5903	37	32	workers	worker	NOUN
ejpam-5903	37	33	are	be	AUX
ejpam-5903	37	34	either	either	CCONJ
ejpam-5903	37	35	close	close	ADJ
ejpam-5903	37	36	friends	friend	NOUN
ejpam-5903	37	37	or	or	CCONJ
ejpam-5903	37	38	enemies	enemy	NOUN
ejpam-5903	37	39	.	.	PUNCT
ejpam-5903	38	1	here	here	ADV
ejpam-5903	38	2	,	,	PUNCT
ejpam-5903	38	3	every	every	DET
ejpam-5903	38	4	worker	worker	NOUN
ejpam-5903	38	5	who	who	PRON
ejpam-5903	38	6	is	be	AUX
ejpam-5903	38	7	not	not	PART
ejpam-5903	38	8	in	in	ADP
ejpam-5903	38	9	the	the	DET
ejpam-5903	38	10	team	team	NOUN
ejpam-5903	38	11	will	will	AUX
ejpam-5903	38	12	be	be	AUX
ejpam-5903	38	13	evaluated	evaluate	VERB
ejpam-5903	38	14	by	by	ADP
ejpam-5903	38	15	a	a	DET
ejpam-5903	38	16	non	non	ADJ
ejpam-5903	38	17	-	-	ADJ
ejpam-5903	38	18	biased	biased	ADJ
ejpam-5903	38	19	inspector	inspector	NOUN
ejpam-5903	38	20	who	who	PRON
ejpam-5903	38	21	is	be	AUX
ejpam-5903	38	22	at	at	ADP
ejpam-5903	38	23	a	a	DET
ejpam-5903	38	24	distance	distance	NOUN
ejpam-5903	38	25	two	two	NUM
ejpam-5903	38	26	from	from	ADP
ejpam-5903	38	27	him	he	PRON
ejpam-5903	38	28	/	/	SYM
ejpam-5903	38	29	her	she	PRON
ejpam-5903	38	30	.	.	PUNCT
ejpam-5903	39	1	moreover	moreover	ADV
ejpam-5903	39	2	,	,	PUNCT
ejpam-5903	39	3	for	for	ADP
ejpam-5903	39	4	the	the	DET
ejpam-5903	39	5	purpose	purpose	NOUN
ejpam-5903	39	6	of	of	ADP
ejpam-5903	39	7	visibility	visibility	NOUN
ejpam-5903	39	8	and	and	CCONJ
ejpam-5903	39	9	monitoring	monitoring	NOUN
ejpam-5903	39	10	that	that	SCONJ
ejpam-5903	39	11	the	the	DET
ejpam-5903	39	12	policy	policy	NOUN
ejpam-5903	39	13	is	be	AUX
ejpam-5903	39	14	strictly	strictly	ADV
ejpam-5903	39	15	followed	follow	VERB
ejpam-5903	39	16	,	,	PUNCT
ejpam-5903	39	17	it	it	PRON
ejpam-5903	39	18	is	be	AUX
ejpam-5903	39	19	imposed	impose	VERB
ejpam-5903	39	20	that	that	SCONJ
ejpam-5903	39	21	every	every	DET
ejpam-5903	39	22	worker	worker	NOUN
ejpam-5903	39	23	must	must	AUX
ejpam-5903	39	24	be	be	AUX
ejpam-5903	39	25	in	in	ADP
ejpam-5903	39	26	a	a	DET
ejpam-5903	39	27	shortest	short	ADJ
ejpam-5903	39	28	path	path	NOUN
ejpam-5903	39	29	connecting	connect	VERB
ejpam-5903	39	30	two	two	NUM
ejpam-5903	39	31	members	member	NOUN
ejpam-5903	39	32	of	of	ADP
ejpam-5903	39	33	the	the	DET
ejpam-5903	39	34	team	team	NOUN
ejpam-5903	39	35	.	.	PUNCT
ejpam-5903	40	1	however	however	ADV
ejpam-5903	40	2	,	,	PUNCT
ejpam-5903	40	3	due	due	ADP
ejpam-5903	40	4	to	to	ADP
ejpam-5903	40	5	possible	possible	ADJ
ejpam-5903	40	6	budgetary	budgetary	ADJ
ejpam-5903	40	7	constraints	constraint	NOUN
ejpam-5903	40	8	,	,	PUNCT
ejpam-5903	40	9	the	the	DET
ejpam-5903	40	10	required	require	VERB
ejpam-5903	40	11	minimum	minimum	ADJ
ejpam-5903	40	12	number	number	NOUN
ejpam-5903	40	13	of	of	ADP
ejpam-5903	40	14	evaluators	evaluator	NOUN
ejpam-5903	40	15	may	may	AUX
ejpam-5903	40	16	not	not	PART
ejpam-5903	40	17	always	always	ADV
ejpam-5903	40	18	be	be	AUX
ejpam-5903	40	19	attained	attain	VERB
ejpam-5903	40	20	or	or	CCONJ
ejpam-5903	40	21	sometimes	sometimes	ADV
ejpam-5903	40	22	,	,	PUNCT
ejpam-5903	40	23	it	it	PRON
ejpam-5903	40	24	may	may	AUX
ejpam-5903	40	25	happen	happen	VERB
ejpam-5903	40	26	that	that	SCONJ
ejpam-5903	40	27	during	during	ADP
ejpam-5903	40	28	the	the	DET
ejpam-5903	40	29	course	course	NOUN
ejpam-5903	40	30	of	of	ADP
ejpam-5903	40	31	the	the	DET
ejpam-5903	40	32	evaluation	evaluation	NOUN
ejpam-5903	40	33	process	process	NOUN
ejpam-5903	40	34	an	an	DET
ejpam-5903	40	35	evaluator	evaluator	NOUN
ejpam-5903	40	36	may	may	AUX
ejpam-5903	40	37	be	be	AUX
ejpam-5903	40	38	absent	absent	ADJ
ejpam-5903	40	39	and	and	CCONJ
ejpam-5903	40	40	,	,	PUNCT
ejpam-5903	40	41	subsequently	subsequently	ADV
ejpam-5903	40	42	,	,	PUNCT
ejpam-5903	40	43	unable	unable	ADJ
ejpam-5903	40	44	to	to	PART
ejpam-5903	40	45	perform	perform	VERB
ejpam-5903	40	46	his	his	PRON
ejpam-5903	40	47	or	or	CCONJ
ejpam-5903	40	48	her	her	PRON
ejpam-5903	40	49	task	task	NOUN
ejpam-5903	40	50	.	.	PUNCT
ejpam-5903	41	1	consequently	consequently	ADV
ejpam-5903	41	2	,	,	PUNCT
ejpam-5903	41	3	some	some	DET
ejpam-5903	41	4	workers	worker	NOUN
ejpam-5903	41	5	may	may	AUX
ejpam-5903	41	6	not	not	PART
ejpam-5903	41	7	be	be	AUX
ejpam-5903	41	8	evaluated	evaluate	VERB
ejpam-5903	41	9	accordingly	accordingly	ADV
ejpam-5903	41	10	.	.	PUNCT
ejpam-5903	42	1	finding	find	VERB
ejpam-5903	42	2	the	the	DET
ejpam-5903	42	3	number	number	NOUN
ejpam-5903	42	4	of	of	ADP
ejpam-5903	42	5	unevaluated	unevaluated	ADJ
ejpam-5903	42	6	workers	worker	NOUN
ejpam-5903	42	7	with	with	ADP
ejpam-5903	42	8	respect	respect	NOUN
ejpam-5903	42	9	to	to	ADP
ejpam-5903	42	10	a	a	DET
ejpam-5903	42	11	given	give	VERB
ejpam-5903	42	12	team	team	NOUN
ejpam-5903	42	13	of	of	ADP
ejpam-5903	42	14	evaluators	evaluator	NOUN
ejpam-5903	42	15	not	not	PART
ejpam-5903	42	16	reaching	reach	VERB
ejpam-5903	42	17	the	the	DET
ejpam-5903	42	18	required	require	VERB
ejpam-5903	42	19	minimum	minimum	ADJ
ejpam-5903	42	20	number	number	NOUN
ejpam-5903	42	21	of	of	ADP
ejpam-5903	42	22	membership	membership	NOUN
ejpam-5903	42	23	may	may	AUX
ejpam-5903	42	24	be	be	AUX
ejpam-5903	42	25	of	of	ADP
ejpam-5903	42	26	help	help	NOUN
ejpam-5903	42	27	to	to	ADP
ejpam-5903	42	28	the	the	DET
ejpam-5903	42	29	management	management	NOUN
ejpam-5903	42	30	.	.	PUNCT
ejpam-5903	43	1	situations	situation	NOUN
ejpam-5903	43	2	such	such	ADJ
ejpam-5903	43	3	as	as	ADP
ejpam-5903	43	4	this	this	PRON
ejpam-5903	43	5	led	lead	VERB
ejpam-5903	43	6	us	we	PRON
ejpam-5903	43	7	to	to	PART
ejpam-5903	43	8	introduce	introduce	VERB
ejpam-5903	43	9	the	the	DET
ejpam-5903	43	10	concept	concept	NOUN
ejpam-5903	43	11	of	of	ADP
ejpam-5903	43	12	geodetic	geodetic	ADJ
ejpam-5903	43	13	hop	hop	NOUN
ejpam-5903	43	14	domination	domination	NOUN
ejpam-5903	43	15	defect	defect	NOUN
ejpam-5903	43	16	in	in	ADP
ejpam-5903	43	17	a	a	DET
ejpam-5903	43	18	graph	graph	NOUN
ejpam-5903	43	19	.	.	PUNCT
ejpam-5903	44	1	2	2	X
ejpam-5903	44	2	.	.	X
ejpam-5903	44	3	terminology	terminology	NOUN
ejpam-5903	44	4	and	and	CCONJ
ejpam-5903	44	5	notation	notation	NOUN
ejpam-5903	44	6	for	for	ADP
ejpam-5903	44	7	any	any	DET
ejpam-5903	44	8	two	two	NUM
ejpam-5903	44	9	vertices	vertex	NOUN
ejpam-5903	44	10	u	u	NOUN
ejpam-5903	44	11	and	and	CCONJ
ejpam-5903	44	12	v	v	NOUN
ejpam-5903	44	13	in	in	ADP
ejpam-5903	44	14	an	an	DET
ejpam-5903	44	15	undirected	undirected	ADJ
ejpam-5903	44	16	connected	connected	ADJ
ejpam-5903	44	17	graph	graph	NOUN
ejpam-5903	44	18	g	g	PROPN
ejpam-5903	44	19	,	,	PUNCT
ejpam-5903	44	20	the	the	DET
ejpam-5903	44	21	distance	distance	NOUN
ejpam-5903	44	22	dg(u	dg(u	X
ejpam-5903	44	23	,	,	PUNCT
ejpam-5903	44	24	v	v	NOUN
ejpam-5903	44	25	)	)	PUNCT
ejpam-5903	44	26	is	be	AUX
ejpam-5903	44	27	the	the	DET
ejpam-5903	44	28	length	length	NOUN
ejpam-5903	44	29	of	of	ADP
ejpam-5903	44	30	a	a	DET
ejpam-5903	44	31	shortest	short	ADJ
ejpam-5903	44	32	path	path	NOUN
ejpam-5903	44	33	joining	join	VERB
ejpam-5903	44	34	u	u	NOUN
ejpam-5903	44	35	and	and	CCONJ
ejpam-5903	44	36	v.	v.	ADP
ejpam-5903	44	37	any	any	DET
ejpam-5903	44	38	u	u	NOUN
ejpam-5903	44	39	-	-	NOUN
ejpam-5903	44	40	v	v	ADJ
ejpam-5903	44	41	path	path	NOUN
ejpam-5903	44	42	of	of	ADP
ejpam-5903	44	43	length	length	NOUN
ejpam-5903	44	44	dg(u	dg(u	PROPN
ejpam-5903	44	45	,	,	PUNCT
ejpam-5903	44	46	v	v	NOUN
ejpam-5903	44	47	)	)	PUNCT
ejpam-5903	44	48	is	be	AUX
ejpam-5903	44	49	j.	j.	PROPN
ejpam-5903	44	50	anoche	anoche	PROPN
ejpam-5903	44	51	,	,	PUNCT
ejpam-5903	44	52	s.	s.	PROPN
ejpam-5903	44	53	canoy	canoy	PROPN
ejpam-5903	44	54	,	,	PUNCT
ejpam-5903	44	55	jr	jr	PROPN
ejpam-5903	44	56	.	.	PROPN
ejpam-5903	44	57	/	/	SYM
ejpam-5903	44	58	eur	eur	PROPN
ejpam-5903	44	59	.	.	PUNCT
ejpam-5903	45	1	j.	j.	PROPN
ejpam-5903	45	2	pure	pure	PROPN
ejpam-5903	45	3	appl	appl	PROPN
ejpam-5903	45	4	.	.	PROPN
ejpam-5903	45	5	math	math	PROPN
ejpam-5903	45	6	,	,	PUNCT
ejpam-5903	45	7	18	18	NUM
ejpam-5903	45	8	(	(	PUNCT
ejpam-5903	45	9	2	2	NUM
ejpam-5903	45	10	)	)	PUNCT
ejpam-5903	45	11	(	(	PUNCT
ejpam-5903	45	12	2025	2025	NUM
ejpam-5903	45	13	)	)	PUNCT
ejpam-5903	45	14	,	,	PUNCT
ejpam-5903	45	15	5903	5903	NUM
ejpam-5903	45	16	3	3	NUM
ejpam-5903	45	17	of	of	ADP
ejpam-5903	45	18	17	17	NUM
ejpam-5903	45	19	called	call	VERB
ejpam-5903	45	20	a	a	DET
ejpam-5903	45	21	u	u	NOUN
ejpam-5903	45	22	-	-	NOUN
ejpam-5903	45	23	v	v	ADJ
ejpam-5903	45	24	geodesic	geodesic	NOUN
ejpam-5903	45	25	.	.	PUNCT
ejpam-5903	46	1	the	the	DET
ejpam-5903	46	2	distance	distance	NOUN
ejpam-5903	46	3	between	between	ADP
ejpam-5903	46	4	two	two	NUM
ejpam-5903	46	5	subsets	subset	NOUN
ejpam-5903	46	6	a	a	PRON
ejpam-5903	46	7	and	and	CCONJ
ejpam-5903	46	8	b	b	NOUN
ejpam-5903	46	9	of	of	ADP
ejpam-5903	46	10	v	v	NOUN
ejpam-5903	46	11	(	(	PUNCT
ejpam-5903	46	12	g	g	NOUN
ejpam-5903	46	13	)	)	PUNCT
ejpam-5903	46	14	is	be	AUX
ejpam-5903	46	15	given	give	VERB
ejpam-5903	46	16	by	by	ADP
ejpam-5903	46	17	dg(a	dg(a	PROPN
ejpam-5903	46	18	,	,	PUNCT
ejpam-5903	46	19	b	b	NOUN
ejpam-5903	46	20	)	)	PUNCT
ejpam-5903	46	21	=	=	SYM
ejpam-5903	46	22	min{dg(a	min{dg(a	PROPN
ejpam-5903	46	23	,	,	PUNCT
ejpam-5903	46	24	b	b	NOUN
ejpam-5903	46	25	)	)	PUNCT
ejpam-5903	46	26	:	:	PUNCT
ejpam-5903	46	27	a	a	DET
ejpam-5903	46	28	∈	∈	PROPN
ejpam-5903	46	29	a	a	PRON
ejpam-5903	46	30	and	and	CCONJ
ejpam-5903	46	31	b	b	NOUN
ejpam-5903	46	32	∈	∈	PROPN
ejpam-5903	46	33	b	b	NOUN
ejpam-5903	46	34	}	}	PUNCT
ejpam-5903	46	35	.	.	PUNCT
ejpam-5903	47	1	the	the	DET
ejpam-5903	47	2	open	open	ADJ
ejpam-5903	47	3	neighborhood	neighborhood	NOUN
ejpam-5903	47	4	of	of	ADP
ejpam-5903	47	5	a	a	DET
ejpam-5903	47	6	point	point	NOUN
ejpam-5903	47	7	u	u	NOUN
ejpam-5903	47	8	is	be	AUX
ejpam-5903	47	9	the	the	DET
ejpam-5903	47	10	set	set	NOUN
ejpam-5903	47	11	ng(u	ng(u	NOUN
ejpam-5903	47	12	)	)	PUNCT
ejpam-5903	47	13	consisting	consist	VERB
ejpam-5903	47	14	of	of	ADP
ejpam-5903	47	15	all	all	DET
ejpam-5903	47	16	points	point	NOUN
ejpam-5903	47	17	v	v	NUM
ejpam-5903	47	18	which	which	PRON
ejpam-5903	47	19	are	be	AUX
ejpam-5903	47	20	adjacent	adjacent	ADJ
ejpam-5903	47	21	to	to	PART
ejpam-5903	47	22	u.	u.	VERB
ejpam-5903	47	23	the	the	DET
ejpam-5903	47	24	closed	closed	ADJ
ejpam-5903	47	25	neighborhood	neighborhood	NOUN
ejpam-5903	47	26	of	of	ADP
ejpam-5903	47	27	u	u	NOUN
ejpam-5903	47	28	is	be	AUX
ejpam-5903	47	29	ng[u	ng[u	PROPN
ejpam-5903	47	30	]	]	X
ejpam-5903	47	31	=	=	SYM
ejpam-5903	47	32	ng(u	ng(u	PROPN
ejpam-5903	47	33	)	)	PUNCT
ejpam-5903	47	34	∪	∪	NOUN
ejpam-5903	47	35	{	{	PUNCT
ejpam-5903	47	36	u	u	NOUN
ejpam-5903	47	37	}	}	PUNCT
ejpam-5903	47	38	.	.	PUNCT
ejpam-5903	48	1	for	for	ADP
ejpam-5903	48	2	any	any	DET
ejpam-5903	48	3	a	a	DET
ejpam-5903	48	4	⊆	⊆	NUM
ejpam-5903	48	5	v	v	NOUN
ejpam-5903	48	6	(	(	PUNCT
ejpam-5903	48	7	g	g	NOUN
ejpam-5903	48	8	)	)	PUNCT
ejpam-5903	48	9	,	,	PUNCT
ejpam-5903	48	10	ng(a	ng(a	X
ejpam-5903	48	11	)	)	PUNCT
ejpam-5903	48	12	=	=	PUNCT
ejpam-5903	48	13	⋃	⋃	NOUN
ejpam-5903	48	14	v∈a	v∈a	NOUN
ejpam-5903	48	15	ng(v	ng(v	PUNCT
ejpam-5903	48	16	)	)	PUNCT
ejpam-5903	48	17	is	be	AUX
ejpam-5903	48	18	called	call	VERB
ejpam-5903	48	19	the	the	DET
ejpam-5903	48	20	open	open	ADJ
ejpam-5903	48	21	neighborhood	neighborhood	NOUN
ejpam-5903	48	22	of	of	ADP
ejpam-5903	48	23	a	a	PRON
ejpam-5903	48	24	and	and	CCONJ
ejpam-5903	48	25	ng[a	ng[a	NOUN
ejpam-5903	48	26	]	]	X
ejpam-5903	48	27	=	=	PUNCT
ejpam-5903	48	28	ng(a	ng(a	X
ejpam-5903	48	29	)	)	PUNCT
ejpam-5903	48	30	∪	∪	ADP
ejpam-5903	48	31	a	a	PRON
ejpam-5903	48	32	is	be	AUX
ejpam-5903	48	33	called	call	VERB
ejpam-5903	48	34	the	the	DET
ejpam-5903	48	35	closed	closed	ADJ
ejpam-5903	48	36	neighborhood	neighborhood	NOUN
ejpam-5903	48	37	of	of	ADP
ejpam-5903	48	38	a.	a.	NOUN
ejpam-5903	48	39	a	a	DET
ejpam-5903	48	40	vertex	vertex	NOUN
ejpam-5903	48	41	v	v	NOUN
ejpam-5903	48	42	of	of	ADP
ejpam-5903	48	43	g	g	PROPN
ejpam-5903	48	44	is	be	AUX
ejpam-5903	48	45	isolated	isolate	VERB
ejpam-5903	48	46	if	if	SCONJ
ejpam-5903	48	47	|ng(v)|	|ng(v)|	NOUN
ejpam-5903	48	48	=	=	SYM
ejpam-5903	48	49	0	0	NUM
ejpam-5903	48	50	.	.	PUNCT
ejpam-5903	49	1	the	the	DET
ejpam-5903	49	2	set	set	NOUN
ejpam-5903	49	3	containing	contain	VERB
ejpam-5903	49	4	all	all	DET
ejpam-5903	49	5	the	the	DET
ejpam-5903	49	6	isolated	isolated	ADJ
ejpam-5903	49	7	vertices	vertex	NOUN
ejpam-5903	49	8	of	of	ADP
ejpam-5903	49	9	g	g	PROPN
ejpam-5903	49	10	is	be	AUX
ejpam-5903	49	11	denoted	denote	VERB
ejpam-5903	49	12	by	by	ADP
ejpam-5903	49	13	i(g	i(g	NOUN
ejpam-5903	49	14	)	)	PUNCT
ejpam-5903	49	15	.	.	PUNCT
ejpam-5903	50	1	the	the	DET
ejpam-5903	50	2	open	open	ADJ
ejpam-5903	50	3	hop	hop	NOUN
ejpam-5903	50	4	neighborhood	neighborhood	NOUN
ejpam-5903	50	5	of	of	ADP
ejpam-5903	50	6	a	a	DET
ejpam-5903	50	7	point	point	NOUN
ejpam-5903	50	8	u	u	NOUN
ejpam-5903	50	9	is	be	AUX
ejpam-5903	50	10	the	the	DET
ejpam-5903	50	11	set	set	ADJ
ejpam-5903	50	12	n2	n2	ADJ
ejpam-5903	50	13	g(u	g(u	PROPN
ejpam-5903	50	14	)	)	PUNCT
ejpam-5903	50	15	=	=	PRON
ejpam-5903	50	16	{	{	PUNCT
ejpam-5903	50	17	v	v	NUM
ejpam-5903	50	18	∈	∈	NOUN
ejpam-5903	50	19	v	v	NOUN
ejpam-5903	50	20	(	(	PUNCT
ejpam-5903	50	21	g	g	NOUN
ejpam-5903	50	22	)	)	PUNCT
ejpam-5903	50	23	:	:	PUNCT
ejpam-5903	50	24	dg(v	dg(v	X
ejpam-5903	50	25	,	,	PUNCT
ejpam-5903	50	26	u	u	NOUN
ejpam-5903	50	27	)	)	PUNCT
ejpam-5903	50	28	=	=	SYM
ejpam-5903	50	29	2	2	NUM
ejpam-5903	50	30	}	}	PUNCT
ejpam-5903	50	31	.	.	PUNCT
ejpam-5903	51	1	the	the	DET
ejpam-5903	51	2	closed	closed	ADJ
ejpam-5903	51	3	hop	hop	NOUN
ejpam-5903	51	4	neighborhood	neighborhood	NOUN
ejpam-5903	51	5	of	of	ADP
ejpam-5903	51	6	u	u	NOUN
ejpam-5903	51	7	is	be	AUX
ejpam-5903	51	8	n2	n2	ADJ
ejpam-5903	51	9	g[u	g[u	X
ejpam-5903	51	10	]	]	X
ejpam-5903	51	11	=	=	SYM
ejpam-5903	51	12	n2	n2	ADJ
ejpam-5903	51	13	g(u	g(u	PROPN
ejpam-5903	51	14	)	)	PUNCT
ejpam-5903	51	15	∪	∪	NOUN
ejpam-5903	51	16	{	{	PUNCT
ejpam-5903	51	17	u	u	NOUN
ejpam-5903	51	18	}	}	PUNCT
ejpam-5903	51	19	.	.	PUNCT
ejpam-5903	52	1	for	for	ADP
ejpam-5903	52	2	any	any	DET
ejpam-5903	52	3	a	a	DET
ejpam-5903	52	4	⊆	⊆	NUM
ejpam-5903	52	5	v	v	NOUN
ejpam-5903	52	6	(	(	PUNCT
ejpam-5903	52	7	g	g	NOUN
ejpam-5903	52	8	)	)	PUNCT
ejpam-5903	52	9	,	,	PUNCT
ejpam-5903	52	10	n2	n2	PROPN
ejpam-5903	52	11	g(a	g(a	PROPN
ejpam-5903	52	12	)	)	PUNCT
ejpam-5903	52	13	=	=	SYM
ejpam-5903	52	14	⋃	⋃	NOUN
ejpam-5903	52	15	v∈a	v∈a	NOUN
ejpam-5903	52	16	n2	n2	ADJ
ejpam-5903	52	17	g(v	g(v	PROPN
ejpam-5903	52	18	)	)	PUNCT
ejpam-5903	52	19	is	be	AUX
ejpam-5903	52	20	called	call	VERB
ejpam-5903	52	21	the	the	DET
ejpam-5903	52	22	open	open	ADJ
ejpam-5903	52	23	hop	hop	NOUN
ejpam-5903	52	24	neighborhood	neighborhood	NOUN
ejpam-5903	52	25	of	of	ADP
ejpam-5903	52	26	a	a	DET
ejpam-5903	52	27	and	and	CCONJ
ejpam-5903	52	28	n2	n2	ADJ
ejpam-5903	52	29	g[a	g[a	NOUN
ejpam-5903	52	30	]	]	X
ejpam-5903	52	31	=	=	SYM
ejpam-5903	52	32	n2	n2	PROPN
ejpam-5903	52	33	g(a	g(a	PROPN
ejpam-5903	52	34	)	)	PUNCT
ejpam-5903	52	35	∪a	∪a	NUM
ejpam-5903	52	36	is	be	AUX
ejpam-5903	52	37	called	call	VERB
ejpam-5903	52	38	the	the	DET
ejpam-5903	52	39	closed	closed	ADJ
ejpam-5903	52	40	hop	hop	NOUN
ejpam-5903	52	41	neighborhood	neighborhood	NOUN
ejpam-5903	52	42	of	of	ADP
ejpam-5903	52	43	a.	a.	NOUN
ejpam-5903	52	44	a	a	DET
ejpam-5903	52	45	set	set	NOUN
ejpam-5903	52	46	s	s	NOUN
ejpam-5903	52	47	⊆	⊆	NUM
ejpam-5903	52	48	v	v	NOUN
ejpam-5903	52	49	(	(	PUNCT
ejpam-5903	52	50	g	g	NOUN
ejpam-5903	52	51	)	)	PUNCT
ejpam-5903	52	52	is	be	AUX
ejpam-5903	52	53	a	a	DET
ejpam-5903	52	54	dominating	dominating	NOUN
ejpam-5903	52	55	set	set	NOUN
ejpam-5903	52	56	of	of	ADP
ejpam-5903	52	57	g	g	PROPN
ejpam-5903	52	58	if	if	SCONJ
ejpam-5903	52	59	ng[s	ng[	NOUN
ejpam-5903	52	60	]	]	PUNCT
ejpam-5903	52	61	=	=	SYM
ejpam-5903	52	62	v	v	NOUN
ejpam-5903	52	63	(	(	PUNCT
ejpam-5903	52	64	g	g	NOUN
ejpam-5903	52	65	)	)	PUNCT
ejpam-5903	52	66	.	.	PUNCT
ejpam-5903	53	1	the	the	DET
ejpam-5903	53	2	smallest	small	ADJ
ejpam-5903	53	3	cardinality	cardinality	NOUN
ejpam-5903	53	4	of	of	ADP
ejpam-5903	53	5	a	a	DET
ejpam-5903	53	6	dominating	dominating	NOUN
ejpam-5903	53	7	set	set	NOUN
ejpam-5903	53	8	of	of	ADP
ejpam-5903	53	9	g	g	NOUN
ejpam-5903	53	10	,	,	PUNCT
ejpam-5903	53	11	denoted	denote	VERB
ejpam-5903	53	12	by	by	ADP
ejpam-5903	53	13	γ(g	γ(g	PROPN
ejpam-5903	53	14	)	)	PUNCT
ejpam-5903	53	15	,	,	PUNCT
ejpam-5903	53	16	is	be	AUX
ejpam-5903	53	17	called	call	VERB
ejpam-5903	53	18	the	the	DET
ejpam-5903	53	19	domination	domination	NOUN
ejpam-5903	53	20	number	number	NOUN
ejpam-5903	53	21	of	of	ADP
ejpam-5903	53	22	g.	g.	PROPN
ejpam-5903	53	23	a	a	DET
ejpam-5903	53	24	dominating	dominating	NOUN
ejpam-5903	53	25	set	set	NOUN
ejpam-5903	53	26	s	s	NOUN
ejpam-5903	53	27	of	of	ADP
ejpam-5903	53	28	g	g	NOUN
ejpam-5903	53	29	with	with	ADP
ejpam-5903	53	30	|s|	|s|	PROPN
ejpam-5903	53	31	=	=	SYM
ejpam-5903	53	32	γ(g	γ(g	PROPN
ejpam-5903	53	33	)	)	PUNCT
ejpam-5903	53	34	,	,	PUNCT
ejpam-5903	53	35	is	be	AUX
ejpam-5903	53	36	called	call	VERB
ejpam-5903	53	37	a	a	DET
ejpam-5903	53	38	γ	γ	NOUN
ejpam-5903	53	39	-	-	PUNCT
ejpam-5903	53	40	set	set	NOUN
ejpam-5903	53	41	of	of	ADP
ejpam-5903	53	42	g.	g.	PROPN
ejpam-5903	53	43	the	the	DET
ejpam-5903	53	44	geodetic	geodetic	ADJ
ejpam-5903	53	45	closure	closure	NOUN
ejpam-5903	53	46	of	of	ADP
ejpam-5903	53	47	a	a	DET
ejpam-5903	53	48	set	set	NOUN
ejpam-5903	53	49	s	s	NOUN
ejpam-5903	53	50	⊆	⊆	NUM
ejpam-5903	53	51	v	v	NOUN
ejpam-5903	53	52	(	(	PUNCT
ejpam-5903	53	53	g	g	NOUN
ejpam-5903	53	54	)	)	PUNCT
ejpam-5903	53	55	,	,	PUNCT
ejpam-5903	53	56	denoted	denote	VERB
ejpam-5903	53	57	by	by	ADP
ejpam-5903	53	58	ig[s	ig[	NOUN
ejpam-5903	53	59	]	]	PUNCT
ejpam-5903	53	60	,	,	PUNCT
ejpam-5903	53	61	is	be	AUX
ejpam-5903	53	62	the	the	DET
ejpam-5903	53	63	union	union	NOUN
ejpam-5903	53	64	of	of	ADP
ejpam-5903	53	65	the	the	DET
ejpam-5903	53	66	intervals	interval	NOUN
ejpam-5903	53	67	ig[u	ig[u	VERB
ejpam-5903	53	68	,	,	PUNCT
ejpam-5903	53	69	v	v	NOUN
ejpam-5903	53	70	]	]	X
ejpam-5903	53	71	,	,	PUNCT
ejpam-5903	53	72	where	where	SCONJ
ejpam-5903	53	73	u	u	NOUN
ejpam-5903	53	74	,	,	PUNCT
ejpam-5903	53	75	v	v	ADP
ejpam-5903	53	76	∈	∈	PROPN
ejpam-5903	53	77	s.	s.	PROPN
ejpam-5903	54	1	the	the	DET
ejpam-5903	54	2	set	set	PROPN
ejpam-5903	54	3	s	s	VERB
ejpam-5903	54	4	is	be	AUX
ejpam-5903	54	5	a	a	DET
ejpam-5903	54	6	geodetic	geodetic	ADJ
ejpam-5903	54	7	set	set	NOUN
ejpam-5903	54	8	in	in	ADP
ejpam-5903	54	9	g	g	PROPN
ejpam-5903	54	10	if	if	SCONJ
ejpam-5903	54	11	ig[s	ig[	NOUN
ejpam-5903	54	12	]	]	X
ejpam-5903	54	13	=	=	SYM
ejpam-5903	54	14	v	v	X
ejpam-5903	54	15	(	(	PUNCT
ejpam-5903	54	16	g	g	NOUN
ejpam-5903	54	17	)	)	PUNCT
ejpam-5903	54	18	.	.	PUNCT
ejpam-5903	55	1	the	the	DET
ejpam-5903	55	2	smallest	small	ADJ
ejpam-5903	55	3	cardinality	cardinality	NOUN
ejpam-5903	55	4	among	among	ADP
ejpam-5903	55	5	all	all	DET
ejpam-5903	55	6	geodetic	geodetic	ADJ
ejpam-5903	55	7	sets	set	NOUN
ejpam-5903	55	8	in	in	ADP
ejpam-5903	55	9	g	g	NOUN
ejpam-5903	55	10	,	,	PUNCT
ejpam-5903	55	11	denoted	denote	VERB
ejpam-5903	55	12	by	by	ADP
ejpam-5903	55	13	g(g	g(g	PROPN
ejpam-5903	55	14	)	)	PUNCT
ejpam-5903	55	15	,	,	PUNCT
ejpam-5903	55	16	is	be	AUX
ejpam-5903	55	17	called	call	VERB
ejpam-5903	55	18	the	the	DET
ejpam-5903	55	19	geodetic	geodetic	ADJ
ejpam-5903	55	20	number	number	NOUN
ejpam-5903	55	21	of	of	ADP
ejpam-5903	55	22	g.	g.	PROPN
ejpam-5903	55	23	a	a	DET
ejpam-5903	55	24	geodetic	geodetic	ADJ
ejpam-5903	55	25	set	set	NOUN
ejpam-5903	55	26	of	of	ADP
ejpam-5903	55	27	cardinality	cardinality	PROPN
ejpam-5903	55	28	g(g	g(g	PROPN
ejpam-5903	55	29	)	)	PUNCT
ejpam-5903	55	30	is	be	AUX
ejpam-5903	55	31	called	call	VERB
ejpam-5903	55	32	a	a	DET
ejpam-5903	55	33	g	g	NOUN
ejpam-5903	55	34	-	-	PUNCT
ejpam-5903	55	35	set	set	NOUN
ejpam-5903	55	36	of	of	ADP
ejpam-5903	55	37	g.	g.	PROPN
ejpam-5903	55	38	a	a	DET
ejpam-5903	55	39	set	set	NOUN
ejpam-5903	55	40	s	s	PROPN
ejpam-5903	55	41	⊆	⊆	NUM
ejpam-5903	55	42	v	v	NOUN
ejpam-5903	55	43	(	(	PUNCT
ejpam-5903	55	44	g	g	NOUN
ejpam-5903	55	45	)	)	PUNCT
ejpam-5903	55	46	is	be	AUX
ejpam-5903	55	47	a	a	DET
ejpam-5903	55	48	geodetic	geodetic	ADJ
ejpam-5903	55	49	dominating	dominating	NOUN
ejpam-5903	55	50	set	set	VERB
ejpam-5903	55	51	in	in	ADP
ejpam-5903	55	52	g	g	PROPN
ejpam-5903	55	53	if	if	SCONJ
ejpam-5903	55	54	it	it	PRON
ejpam-5903	55	55	is	be	AUX
ejpam-5903	55	56	both	both	CCONJ
ejpam-5903	55	57	a	a	DET
ejpam-5903	55	58	dominating	dominating	NOUN
ejpam-5903	55	59	and	and	CCONJ
ejpam-5903	55	60	a	a	DET
ejpam-5903	55	61	geodetic	geodetic	ADJ
ejpam-5903	55	62	set	set	NOUN
ejpam-5903	55	63	.	.	PUNCT
ejpam-5903	56	1	a	a	DET
ejpam-5903	56	2	set	set	NOUN
ejpam-5903	56	3	s	s	NOUN
ejpam-5903	56	4	⊆	⊆	NUM
ejpam-5903	56	5	v	v	NOUN
ejpam-5903	56	6	(	(	PUNCT
ejpam-5903	56	7	g	g	NOUN
ejpam-5903	56	8	)	)	PUNCT
ejpam-5903	56	9	is	be	AUX
ejpam-5903	56	10	a	a	DET
ejpam-5903	56	11	hop	hop	NOUN
ejpam-5903	56	12	dominating	dominating	NOUN
ejpam-5903	56	13	set	set	NOUN
ejpam-5903	56	14	of	of	ADP
ejpam-5903	56	15	g	g	PROPN
ejpam-5903	56	16	if	if	SCONJ
ejpam-5903	56	17	for	for	ADP
ejpam-5903	56	18	each	each	DET
ejpam-5903	56	19	x	x	SYM
ejpam-5903	56	20	∈	∈	PROPN
ejpam-5903	56	21	v	v	ADP
ejpam-5903	56	22	(	(	PUNCT
ejpam-5903	56	23	g	g	NOUN
ejpam-5903	56	24	)	)	PUNCT
ejpam-5903	56	25	\	\	PROPN
ejpam-5903	57	1	s	s	X
ejpam-5903	57	2	,	,	PUNCT
ejpam-5903	57	3	there	there	PRON
ejpam-5903	57	4	exists	exist	VERB
ejpam-5903	57	5	z	z	PROPN
ejpam-5903	57	6	∈	∈	PROPN
ejpam-5903	57	7	s	s	VERB
ejpam-5903	57	8	such	such	ADJ
ejpam-5903	57	9	that	that	PRON
ejpam-5903	57	10	dg(x	dg(x	NOUN
ejpam-5903	57	11	,	,	PUNCT
ejpam-5903	57	12	z	z	NOUN
ejpam-5903	57	13	)	)	PUNCT
ejpam-5903	57	14	=	=	SYM
ejpam-5903	57	15	2	2	X
ejpam-5903	57	16	.	.	X
ejpam-5903	57	17	the	the	DET
ejpam-5903	57	18	smallest	small	ADJ
ejpam-5903	57	19	cardinality	cardinality	NOUN
ejpam-5903	57	20	of	of	ADP
ejpam-5903	57	21	a	a	DET
ejpam-5903	57	22	hop	hop	NOUN
ejpam-5903	57	23	dominating	dominating	NOUN
ejpam-5903	57	24	set	set	NOUN
ejpam-5903	57	25	of	of	ADP
ejpam-5903	57	26	g	g	NOUN
ejpam-5903	57	27	,	,	PUNCT
ejpam-5903	57	28	denoted	denote	VERB
ejpam-5903	57	29	by	by	ADP
ejpam-5903	57	30	γh(g	γh(g	NOUN
ejpam-5903	57	31	)	)	PUNCT
ejpam-5903	57	32	,	,	PUNCT
ejpam-5903	57	33	is	be	AUX
ejpam-5903	57	34	called	call	VERB
ejpam-5903	57	35	the	the	DET
ejpam-5903	57	36	hop	hop	NOUN
ejpam-5903	57	37	domination	domination	NOUN
ejpam-5903	57	38	number	number	NOUN
ejpam-5903	57	39	of	of	ADP
ejpam-5903	57	40	g.	g.	PROPN
ejpam-5903	57	41	a	a	DET
ejpam-5903	57	42	hop	hop	NOUN
ejpam-5903	57	43	dominating	dominating	NOUN
ejpam-5903	57	44	set	set	NOUN
ejpam-5903	57	45	s	s	NOUN
ejpam-5903	57	46	of	of	ADP
ejpam-5903	57	47	g	g	NOUN
ejpam-5903	57	48	with	with	ADP
ejpam-5903	57	49	|s|	|s|	NOUN
ejpam-5903	57	50	=	=	NOUN
ejpam-5903	57	51	γh(g	γh(g	NOUN
ejpam-5903	57	52	)	)	PUNCT
ejpam-5903	57	53	is	be	AUX
ejpam-5903	57	54	called	call	VERB
ejpam-5903	57	55	a	a	DET
ejpam-5903	57	56	γh	γh	ADV
ejpam-5903	57	57	-	-	PUNCT
ejpam-5903	57	58	set	set	NOUN
ejpam-5903	57	59	of	of	ADP
ejpam-5903	57	60	g.	g.	PROPN
ejpam-5903	57	61	a	a	DET
ejpam-5903	57	62	set	set	NOUN
ejpam-5903	57	63	s	s	PROPN
ejpam-5903	57	64	⊆	⊆	NUM
ejpam-5903	57	65	v	v	NOUN
ejpam-5903	57	66	(	(	PUNCT
ejpam-5903	57	67	g	g	NOUN
ejpam-5903	57	68	)	)	PUNCT
ejpam-5903	57	69	is	be	AUX
ejpam-5903	57	70	geodetic	geodetic	ADJ
ejpam-5903	57	71	hop	hop	NOUN
ejpam-5903	57	72	dominating	dominating	NOUN
ejpam-5903	57	73	if	if	SCONJ
ejpam-5903	57	74	it	it	PRON
ejpam-5903	57	75	is	be	AUX
ejpam-5903	57	76	both	both	CCONJ
ejpam-5903	57	77	a	a	DET
ejpam-5903	57	78	geodetic	geodetic	ADJ
ejpam-5903	57	79	and	and	CCONJ
ejpam-5903	57	80	a	a	DET
ejpam-5903	57	81	hop	hop	NOUN
ejpam-5903	57	82	dominating	dominating	NOUN
ejpam-5903	57	83	set	set	NOUN
ejpam-5903	57	84	.	.	PUNCT
ejpam-5903	58	1	the	the	DET
ejpam-5903	58	2	geodetic	geodetic	ADJ
ejpam-5903	58	3	hop	hop	NOUN
ejpam-5903	58	4	domination	domination	NOUN
ejpam-5903	58	5	number	number	NOUN
ejpam-5903	58	6	γhg(g	γhg(g	PROPN
ejpam-5903	58	7	)	)	PUNCT
ejpam-5903	58	8	of	of	ADP
ejpam-5903	58	9	g	g	PROPN
ejpam-5903	58	10	is	be	AUX
ejpam-5903	58	11	the	the	DET
ejpam-5903	58	12	minimum	minimum	ADJ
ejpam-5903	58	13	cardinality	cardinality	NOUN
ejpam-5903	58	14	among	among	ADP
ejpam-5903	58	15	all	all	DET
ejpam-5903	58	16	geodetic	geodetic	ADJ
ejpam-5903	58	17	hop	hop	NOUN
ejpam-5903	58	18	dominating	dominating	NOUN
ejpam-5903	58	19	sets	set	NOUN
ejpam-5903	58	20	in	in	ADP
ejpam-5903	58	21	g.	g.	PROPN
ejpam-5903	58	22	any	any	DET
ejpam-5903	58	23	geodetic	geodetic	ADJ
ejpam-5903	58	24	hop	hop	NOUN
ejpam-5903	58	25	dominating	dominating	NOUN
ejpam-5903	58	26	set	set	NOUN
ejpam-5903	58	27	of	of	ADP
ejpam-5903	58	28	g	g	PROPN
ejpam-5903	58	29	with	with	ADP
ejpam-5903	58	30	cardinality	cardinality	PROPN
ejpam-5903	58	31	γhg(g	γhg(g	PROPN
ejpam-5903	58	32	)	)	PUNCT
ejpam-5903	58	33	is	be	AUX
ejpam-5903	58	34	called	call	VERB
ejpam-5903	58	35	a	a	DET
ejpam-5903	58	36	γhg	γhg	NOUN
ejpam-5903	58	37	-	-	PUNCT
ejpam-5903	58	38	set	set	NOUN
ejpam-5903	58	39	.	.	PUNCT
ejpam-5903	59	1	let	let	VERB
ejpam-5903	59	2	g	g	PRON
ejpam-5903	59	3	be	be	AUX
ejpam-5903	59	4	a	a	DET
ejpam-5903	59	5	non	non	ADJ
ejpam-5903	59	6	-	-	ADJ
ejpam-5903	59	7	trivial	trivial	ADJ
ejpam-5903	59	8	graph	graph	NOUN
ejpam-5903	59	9	of	of	ADP
ejpam-5903	59	10	order	order	NOUN
ejpam-5903	59	11	n	n	NOUN
ejpam-5903	59	12	and	and	CCONJ
ejpam-5903	59	13	let	let	VERB
ejpam-5903	59	14	1	1	NUM
ejpam-5903	59	15	≤	≤	NOUN
ejpam-5903	59	16	k	k	X
ejpam-5903	59	17	<	<	X
ejpam-5903	59	18	γhg(g	γhg(g	PROPN
ejpam-5903	59	19	)	)	PUNCT
ejpam-5903	59	20	.	.	PUNCT
ejpam-5903	60	1	let	let	VERB
ejpam-5903	60	2	s	s	PRON
ejpam-5903	60	3	⊆	⊆	NUM
ejpam-5903	60	4	v	v	NOUN
ejpam-5903	60	5	(	(	PUNCT
ejpam-5903	60	6	g	g	NOUN
ejpam-5903	60	7	)	)	PUNCT
ejpam-5903	60	8	with	with	ADP
ejpam-5903	60	9	cardinality	cardinality	NOUN
ejpam-5903	60	10	|s|	|s|	NOUN
ejpam-5903	60	11	=	=	SYM
ejpam-5903	60	12	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	60	13	k	k	PROPN
ejpam-5903	60	14	and	and	CCONJ
ejpam-5903	60	15	let	let	VERB
ejpam-5903	60	16	nhg	nhg	NOUN
ejpam-5903	60	17	g	g	PROPN
ejpam-5903	61	1	[	[	X
ejpam-5903	61	2	s	s	X
ejpam-5903	61	3	]	]	X
ejpam-5903	61	4	=	=	SYM
ejpam-5903	61	5	n2	n2	PROPN
ejpam-5903	61	6	g[s	g[s	PROPN
ejpam-5903	61	7	]	]	PUNCT
ejpam-5903	61	8	∩	∩	ADJ
ejpam-5903	61	9	ig[s	ig[s	PROPN
ejpam-5903	61	10	]	]	PUNCT
ejpam-5903	61	11	,	,	PUNCT
ejpam-5903	61	12	the	the	DET
ejpam-5903	61	13	set	set	NOUN
ejpam-5903	61	14	of	of	ADP
ejpam-5903	61	15	geodetically	geodetically	ADV
ejpam-5903	61	16	hopdominated	hopdominate	VERB
ejpam-5903	61	17	set	set	NOUN
ejpam-5903	61	18	of	of	ADP
ejpam-5903	61	19	vertices	vertex	NOUN
ejpam-5903	61	20	of	of	ADP
ejpam-5903	61	21	g.	g.	PROPN
ejpam-5903	61	22	the	the	DET
ejpam-5903	61	23	set	set	NOUN
ejpam-5903	61	24	v	v	NOUN
ejpam-5903	61	25	(	(	PUNCT
ejpam-5903	61	26	g	g	NOUN
ejpam-5903	61	27	)	)	PUNCT
ejpam-5903	61	28	\	\	NOUN
ejpam-5903	62	1	nhg	nhg	PROPN
ejpam-5903	62	2	g	g	PROPN
ejpam-5903	63	1	[	[	X
ejpam-5903	63	2	s	s	X
ejpam-5903	63	3	]	]	X
ejpam-5903	63	4	is	be	AUX
ejpam-5903	63	5	called	call	VERB
ejpam-5903	63	6	the	the	DET
ejpam-5903	63	7	k	k	ADJ
ejpam-5903	63	8	-	-	ADJ
ejpam-5903	63	9	geodetic	geodetic	ADJ
ejpam-5903	63	10	hop	hop	NOUN
ejpam-5903	63	11	domination	domination	NOUN
ejpam-5903	63	12	defect	defect	NOUN
ejpam-5903	63	13	set	set	NOUN
ejpam-5903	63	14	of	of	ADP
ejpam-5903	63	15	s	s	PRON
ejpam-5903	63	16	and	and	CCONJ
ejpam-5903	63	17	the	the	DET
ejpam-5903	63	18	k	k	ADJ
ejpam-5903	63	19	-	-	ADJ
ejpam-5903	63	20	geodetic	geodetic	ADJ
ejpam-5903	63	21	hop	hop	NOUN
ejpam-5903	63	22	domination	domination	NOUN
ejpam-5903	63	23	defect	defect	NOUN
ejpam-5903	63	24	of	of	ADP
ejpam-5903	63	25	s	s	NOUN
ejpam-5903	63	26	is	be	AUX
ejpam-5903	63	27	ζhgk	ζhgk	NOUN
ejpam-5903	63	28	(	(	PUNCT
ejpam-5903	63	29	s	s	X
ejpam-5903	63	30	)	)	PUNCT
ejpam-5903	63	31	=	=	SYM
ejpam-5903	63	32	|v	|v	X
ejpam-5903	63	33	(	(	PUNCT
ejpam-5903	63	34	g	g	NOUN
ejpam-5903	63	35	)	)	PUNCT
ejpam-5903	63	36	\	\	NOUN
ejpam-5903	63	37	nhg	nhg	PROPN
ejpam-5903	63	38	g	g	PROPN
ejpam-5903	64	1	[	[	X
ejpam-5903	64	2	s]|	s]|	X
ejpam-5903	64	3	=	=	SYM
ejpam-5903	64	4	n	n	PRON
ejpam-5903	64	5	−	−	PROPN
ejpam-5903	64	6	|nhg	|nhg	PROPN
ejpam-5903	64	7	g	g	PROPN
ejpam-5903	64	8	[	[	X
ejpam-5903	64	9	s]|	s]|	PROPN
ejpam-5903	64	10	.	.	PUNCT
ejpam-5903	65	1	the	the	DET
ejpam-5903	65	2	minimum	minimum	ADJ
ejpam-5903	65	3	cardinality	cardinality	NOUN
ejpam-5903	65	4	of	of	ADP
ejpam-5903	65	5	a	a	DET
ejpam-5903	65	6	k	k	ADJ
ejpam-5903	65	7	-	-	ADJ
ejpam-5903	65	8	geodetic	geodetic	ADJ
ejpam-5903	65	9	hop	hop	NOUN
ejpam-5903	65	10	domination	domination	NOUN
ejpam-5903	65	11	defect	defect	NOUN
ejpam-5903	65	12	set	set	VERB
ejpam-5903	65	13	in	in	ADP
ejpam-5903	65	14	g	g	NOUN
ejpam-5903	65	15	,	,	PUNCT
ejpam-5903	65	16	denoted	denote	VERB
ejpam-5903	65	17	by	by	ADP
ejpam-5903	65	18	ζhgk	ζhgk	NOUN
ejpam-5903	65	19	(	(	PUNCT
ejpam-5903	65	20	g	g	NOUN
ejpam-5903	65	21	)	)	PUNCT
ejpam-5903	65	22	,	,	PUNCT
ejpam-5903	65	23	is	be	AUX
ejpam-5903	65	24	called	call	VERB
ejpam-5903	65	25	the	the	DET
ejpam-5903	65	26	k	k	ADJ
ejpam-5903	65	27	-	-	ADJ
ejpam-5903	65	28	geodetic	geodetic	ADJ
ejpam-5903	65	29	hop	hop	NOUN
ejpam-5903	65	30	domination	domination	NOUN
ejpam-5903	65	31	defect	defect	NOUN
ejpam-5903	65	32	of	of	ADP
ejpam-5903	65	33	g	g	NOUN
ejpam-5903	65	34	,	,	PUNCT
ejpam-5903	65	35	i.e.	i.e.	X
ejpam-5903	65	36	,	,	PUNCT
ejpam-5903	65	37	ζhgk	ζhgk	NOUN
ejpam-5903	65	38	(	(	PUNCT
ejpam-5903	65	39	g	g	NOUN
ejpam-5903	65	40	)	)	PUNCT
ejpam-5903	65	41	=	=	VERB
ejpam-5903	66	1	min{ζhgk	min{ζhgk	X
ejpam-5903	66	2	(	(	PUNCT
ejpam-5903	66	3	s	s	X
ejpam-5903	66	4	)	)	PUNCT
ejpam-5903	66	5	:	:	PUNCT
ejpam-5903	66	6	s	s	VERB
ejpam-5903	66	7	⊆	⊆	NUM
ejpam-5903	66	8	v	v	NOUN
ejpam-5903	66	9	(	(	PUNCT
ejpam-5903	66	10	g	g	NOUN
ejpam-5903	66	11	)	)	PUNCT
ejpam-5903	66	12	with	with	ADP
ejpam-5903	66	13	|s|	|s|	PROPN
ejpam-5903	66	14	=	=	SYM
ejpam-5903	66	15	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	66	16	k	k	NOUN
ejpam-5903	66	17	}	}	PUNCT
ejpam-5903	66	18	.	.	PUNCT
ejpam-5903	67	1	a	a	DET
ejpam-5903	67	2	set	set	NOUN
ejpam-5903	67	3	s	s	NOUN
ejpam-5903	67	4	⊆	⊆	NUM
ejpam-5903	67	5	v	v	NOUN
ejpam-5903	67	6	(	(	PUNCT
ejpam-5903	67	7	g	g	NOUN
ejpam-5903	67	8	)	)	PUNCT
ejpam-5903	67	9	of	of	ADP
ejpam-5903	67	10	cardinality	cardinality	NOUN
ejpam-5903	67	11	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	67	12	k	k	PROPN
ejpam-5903	67	13	for	for	ADP
ejpam-5903	67	14	which	which	PRON
ejpam-5903	67	15	|v	|v	PROPN
ejpam-5903	67	16	(	(	PUNCT
ejpam-5903	67	17	g	g	NOUN
ejpam-5903	67	18	)	)	PUNCT
ejpam-5903	68	1	\nhg	\nhg	ADP
ejpam-5903	68	2	g	g	NOUN
ejpam-5903	68	3	[	[	X
ejpam-5903	68	4	s]|	s]|	X
ejpam-5903	68	5	=	=	SYM
ejpam-5903	68	6	ζhgk	ζhgk	NOUN
ejpam-5903	68	7	(	(	PUNCT
ejpam-5903	68	8	g	g	NOUN
ejpam-5903	68	9	)	)	PUNCT
ejpam-5903	68	10	is	be	AUX
ejpam-5903	68	11	called	call	VERB
ejpam-5903	68	12	a	a	DET
ejpam-5903	68	13	ζhgk	ζhgk	NOUN
ejpam-5903	68	14	-set	-set	PUNCT
ejpam-5903	68	15	of	of	ADP
ejpam-5903	68	16	g.	g.	PROPN
ejpam-5903	68	17	thus	thus	ADV
ejpam-5903	68	18	,	,	PUNCT
ejpam-5903	68	19	〈	〈	PROPN
ejpam-5903	68	20	nhg	nhg	NOUN
ejpam-5903	68	21	g	g	PROPN
ejpam-5903	69	1	[	[	X
ejpam-5903	69	2	s	s	X
ejpam-5903	69	3	]	]	X
ejpam-5903	69	4	〉	〉	NOUN
ejpam-5903	69	5	is	be	AUX
ejpam-5903	69	6	an	an	DET
ejpam-5903	69	7	induced	induced	ADJ
ejpam-5903	69	8	subgraph	subgraph	NOUN
ejpam-5903	69	9	of	of	ADP
ejpam-5903	69	10	g	g	PROPN
ejpam-5903	69	11	with	with	ADP
ejpam-5903	69	12	n−	n−	NOUN
ejpam-5903	69	13	ζhgk	ζhgk	NOUN
ejpam-5903	69	14	(	(	PUNCT
ejpam-5903	69	15	g	g	NOUN
ejpam-5903	69	16	)	)	PUNCT
ejpam-5903	69	17	vertices	vertex	NOUN
ejpam-5903	69	18	and	and	CCONJ
ejpam-5903	69	19	geodetic	geodetic	ADJ
ejpam-5903	69	20	hop	hop	NOUN
ejpam-5903	69	21	domination	domination	NOUN
ejpam-5903	69	22	number	number	NOUN
ejpam-5903	69	23	γhg	γhg	PROPN
ejpam-5903	69	24	−	−	PROPN
ejpam-5903	69	25	k.	k.	PROPN
ejpam-5903	69	26	consider	consider	VERB
ejpam-5903	69	27	the	the	DET
ejpam-5903	69	28	graph	graph	NOUN
ejpam-5903	69	29	g	g	NOUN
ejpam-5903	69	30	in	in	ADP
ejpam-5903	69	31	figure	figure	NOUN
ejpam-5903	69	32	1	1	NUM
ejpam-5903	69	33	.	.	PUNCT
ejpam-5903	70	1	then	then	ADV
ejpam-5903	70	2	d	d	PROPN
ejpam-5903	70	3	=	=	PUNCT
ejpam-5903	70	4	{	{	PUNCT
ejpam-5903	70	5	a	a	PRON
ejpam-5903	70	6	,	,	PUNCT
ejpam-5903	70	7	b	b	NOUN
ejpam-5903	70	8	,	,	PUNCT
ejpam-5903	70	9	x	x	NOUN
ejpam-5903	70	10	,	,	PUNCT
ejpam-5903	70	11	y	y	PRON
ejpam-5903	70	12	}	}	PUNCT
ejpam-5903	70	13	is	be	AUX
ejpam-5903	70	14	a	a	DET
ejpam-5903	70	15	γhg	γhg	NOUN
ejpam-5903	70	16	-	-	PUNCT
ejpam-5903	70	17	set	set	NOUN
ejpam-5903	70	18	of	of	ADP
ejpam-5903	70	19	g	g	NOUN
ejpam-5903	70	20	,	,	PUNCT
ejpam-5903	70	21	i.e.	i.e.	X
ejpam-5903	70	22	,	,	PUNCT
ejpam-5903	70	23	j.	j.	PROPN
ejpam-5903	70	24	anoche	anoche	PROPN
ejpam-5903	70	25	,	,	PUNCT
ejpam-5903	70	26	s.	s.	PROPN
ejpam-5903	70	27	canoy	canoy	PROPN
ejpam-5903	70	28	,	,	PUNCT
ejpam-5903	70	29	jr	jr	PROPN
ejpam-5903	70	30	.	.	PROPN
ejpam-5903	70	31	/	/	SYM
ejpam-5903	70	32	eur	eur	PROPN
ejpam-5903	70	33	.	.	PUNCT
ejpam-5903	71	1	j.	j.	PROPN
ejpam-5903	71	2	pure	pure	PROPN
ejpam-5903	71	3	appl	appl	PROPN
ejpam-5903	71	4	.	.	PROPN
ejpam-5903	71	5	math	math	PROPN
ejpam-5903	71	6	,	,	PUNCT
ejpam-5903	71	7	18	18	NUM
ejpam-5903	71	8	(	(	PUNCT
ejpam-5903	71	9	2	2	NUM
ejpam-5903	71	10	)	)	PUNCT
ejpam-5903	71	11	(	(	PUNCT
ejpam-5903	71	12	2025	2025	NUM
ejpam-5903	71	13	)	)	PUNCT
ejpam-5903	71	14	,	,	PUNCT
ejpam-5903	71	15	5903	5903	NUM
ejpam-5903	71	16	4	4	NUM
ejpam-5903	71	17	of	of	ADP
ejpam-5903	71	18	17	17	NUM
ejpam-5903	71	19	γhg(g	γhg(g	NUM
ejpam-5903	71	20	)	)	PUNCT
ejpam-5903	71	21	=	=	SYM
ejpam-5903	72	1	4	4	X
ejpam-5903	72	2	.	.	PUNCT
ejpam-5903	73	1	if	if	SCONJ
ejpam-5903	73	2	k	k	PROPN
ejpam-5903	73	3	=	=	SYM
ejpam-5903	73	4	1	1	NUM
ejpam-5903	73	5	,	,	PUNCT
ejpam-5903	73	6	then	then	ADV
ejpam-5903	73	7	s1	s1	PROPN
ejpam-5903	73	8	=	=	PUNCT
ejpam-5903	73	9	{	{	PUNCT
ejpam-5903	73	10	a	a	PRON
ejpam-5903	73	11	,	,	PUNCT
ejpam-5903	73	12	b	b	NOUN
ejpam-5903	73	13	,	,	PUNCT
ejpam-5903	73	14	x	x	PRON
ejpam-5903	73	15	}	}	PUNCT
ejpam-5903	73	16	is	be	AUX
ejpam-5903	73	17	a	a	DET
ejpam-5903	73	18	ζhg1	ζhg1	PROPN
ejpam-5903	73	19	-set	-set	PUNCT
ejpam-5903	73	20	ofg	ofg	PROPN
ejpam-5903	73	21	.	.	PROPN
ejpam-5903	74	1	sincenhg	sincenhg	VERB
ejpam-5903	74	2	g	g	PROPN
ejpam-5903	75	1	[	[	X
ejpam-5903	75	2	s1	s1	X
ejpam-5903	75	3	]	]	X
ejpam-5903	75	4	=	=	X
ejpam-5903	75	5	{	{	PUNCT
ejpam-5903	75	6	a	a	PRON
ejpam-5903	75	7	,	,	PUNCT
ejpam-5903	75	8	b	b	NOUN
ejpam-5903	75	9	,	,	PUNCT
ejpam-5903	75	10	c	c	NOUN
ejpam-5903	75	11	,	,	PUNCT
ejpam-5903	75	12	d	d	NOUN
ejpam-5903	75	13	,	,	PUNCT
ejpam-5903	75	14	u	u	NOUN
ejpam-5903	75	15	,	,	PUNCT
ejpam-5903	75	16	v	v	NOUN
ejpam-5903	75	17	,	,	PUNCT
ejpam-5903	75	18	x	x	NOUN
ejpam-5903	75	19	}	}	PUNCT
ejpam-5903	75	20	,	,	PUNCT
ejpam-5903	75	21	it	it	PRON
ejpam-5903	75	22	follows	follow	VERB
ejpam-5903	75	23	that	that	DET
ejpam-5903	75	24	ζhg1	ζhg1	PROPN
ejpam-5903	75	25	(	(	PUNCT
ejpam-5903	75	26	g	g	NOUN
ejpam-5903	75	27	)	)	PUNCT
ejpam-5903	75	28	=	=	SYM
ejpam-5903	75	29	ζhg1	ζhg1	PROPN
ejpam-5903	75	30	(	(	PUNCT
ejpam-5903	75	31	s	s	NOUN
ejpam-5903	75	32	)	)	PUNCT
ejpam-5903	75	33	=	=	SYM
ejpam-5903	75	34	|v	|v	PROPN
ejpam-5903	75	35	(	(	PUNCT
ejpam-5903	75	36	g)|	g)|	NOUN
ejpam-5903	75	37	−	−	PROPN
ejpam-5903	75	38	|nhg	|nhg	PROPN
ejpam-5903	75	39	g	g	NOUN
ejpam-5903	76	1	[	[	X
ejpam-5903	76	2	s1]|	s1]|	X
ejpam-5903	76	3	=	=	SYM
ejpam-5903	76	4	8−	8−	NUM
ejpam-5903	76	5	7	7	NUM
ejpam-5903	76	6	=	=	SYM
ejpam-5903	76	7	1	1	NUM
ejpam-5903	76	8	.	.	PUNCT
ejpam-5903	77	1	clearly	clearly	ADV
ejpam-5903	77	2	,	,	PUNCT
ejpam-5903	77	3	the	the	DET
ejpam-5903	77	4	set	set	NOUN
ejpam-5903	77	5	{	{	PUNCT
ejpam-5903	77	6	a	a	PRON
ejpam-5903	77	7	,	,	PUNCT
ejpam-5903	77	8	b	b	NOUN
ejpam-5903	77	9	,	,	PUNCT
ejpam-5903	77	10	d	d	NOUN
ejpam-5903	77	11	}	}	PUNCT
ejpam-5903	77	12	is	be	AUX
ejpam-5903	77	13	not	not	PART
ejpam-5903	77	14	a	a	DET
ejpam-5903	77	15	ζhg1	ζhg1	NOUN
ejpam-5903	77	16	-set	-set	PUNCT
ejpam-5903	77	17	of	of	ADP
ejpam-5903	77	18	g	g	PROPN
ejpam-5903	77	19	because	because	SCONJ
ejpam-5903	77	20	nhg	nhg	PROPN
ejpam-5903	77	21	g	g	PROPN
ejpam-5903	78	1	[	[	X
ejpam-5903	78	2	{	{	PUNCT
ejpam-5903	78	3	a	a	PRON
ejpam-5903	78	4	,	,	PUNCT
ejpam-5903	78	5	b	b	NOUN
ejpam-5903	78	6	,	,	PUNCT
ejpam-5903	78	7	d	d	NOUN
ejpam-5903	78	8	}	}	PUNCT
ejpam-5903	78	9	]	]	PUNCT
ejpam-5903	79	1	=	=	X
ejpam-5903	79	2	{	{	PUNCT
ejpam-5903	79	3	a	a	PRON
ejpam-5903	79	4	,	,	PUNCT
ejpam-5903	79	5	b	b	NOUN
ejpam-5903	79	6	,	,	PUNCT
ejpam-5903	79	7	c	c	NOUN
ejpam-5903	79	8	,	,	PUNCT
ejpam-5903	79	9	d	d	NOUN
ejpam-5903	79	10	,	,	PUNCT
ejpam-5903	79	11	u	u	NOUN
ejpam-5903	79	12	,	,	PUNCT
ejpam-5903	79	13	v	v	NOUN
ejpam-5903	79	14	}	}	PUNCT
ejpam-5903	79	15	,	,	PUNCT
ejpam-5903	79	16	i.e.	i.e.	X
ejpam-5903	79	17	,	,	PUNCT
ejpam-5903	79	18	ζhg1	ζhg1	PROPN
ejpam-5903	79	19	(	(	PUNCT
ejpam-5903	79	20	{	{	PUNCT
ejpam-5903	79	21	a	a	PRON
ejpam-5903	79	22	,	,	PUNCT
ejpam-5903	79	23	b	b	NOUN
ejpam-5903	79	24	,	,	PUNCT
ejpam-5903	79	25	d	d	NOUN
ejpam-5903	79	26	}	}	PUNCT
ejpam-5903	79	27	)	)	PUNCT
ejpam-5903	79	28	=	=	SYM
ejpam-5903	79	29	8	8	NUM
ejpam-5903	79	30	−	−	NUM
ejpam-5903	79	31	6	6	NUM
ejpam-5903	79	32	=	=	SYM
ejpam-5903	79	33	2	2	NUM
ejpam-5903	79	34	.	.	PUNCT
ejpam-5903	80	1	if	if	SCONJ
ejpam-5903	80	2	k	k	PROPN
ejpam-5903	80	3	=	=	SYM
ejpam-5903	80	4	2	2	NUM
ejpam-5903	80	5	,	,	PUNCT
ejpam-5903	80	6	then	then	ADV
ejpam-5903	80	7	s2	s2	VERB
ejpam-5903	80	8	=	=	PUNCT
ejpam-5903	80	9	{	{	PUNCT
ejpam-5903	80	10	a	a	DET
ejpam-5903	80	11	,	,	PUNCT
ejpam-5903	80	12	v	v	NOUN
ejpam-5903	80	13	}	}	PUNCT
ejpam-5903	80	14	is	be	AUX
ejpam-5903	80	15	a	a	DET
ejpam-5903	80	16	ζhg2	ζhg2	PROPN
ejpam-5903	80	17	-set	-set	PUNCT
ejpam-5903	80	18	of	of	ADP
ejpam-5903	80	19	g	g	PROPN
ejpam-5903	80	20	and	and	CCONJ
ejpam-5903	80	21	nhg	nhg	VERB
ejpam-5903	80	22	g	g	PROPN
ejpam-5903	81	1	[	[	X
ejpam-5903	81	2	s2	s2	X
ejpam-5903	81	3	]	]	X
ejpam-5903	81	4	=	=	X
ejpam-5903	81	5	{	{	PUNCT
ejpam-5903	81	6	a	a	X
ejpam-5903	81	7	,	,	PUNCT
ejpam-5903	81	8	c	c	NOUN
ejpam-5903	81	9	,	,	PUNCT
ejpam-5903	81	10	d	d	NOUN
ejpam-5903	81	11	,	,	PUNCT
ejpam-5903	81	12	u	u	NOUN
ejpam-5903	81	13	,	,	PUNCT
ejpam-5903	81	14	v	v	NOUN
ejpam-5903	81	15	}	}	PUNCT
ejpam-5903	81	16	.	.	PUNCT
ejpam-5903	82	1	hence	hence	ADV
ejpam-5903	82	2	,	,	PUNCT
ejpam-5903	82	3	ζhg2	ζhg2	PROPN
ejpam-5903	82	4	(	(	PUNCT
ejpam-5903	82	5	g	g	NOUN
ejpam-5903	82	6	)	)	PUNCT
ejpam-5903	82	7	=	=	SYM
ejpam-5903	83	1	8	8	NUM
ejpam-5903	83	2	−	−	NUM
ejpam-5903	83	3	5	5	NUM
ejpam-5903	83	4	=	=	SYM
ejpam-5903	83	5	3	3	X
ejpam-5903	83	6	.	.	X
ejpam-5903	83	7	observe	observe	VERB
ejpam-5903	83	8	that	that	SCONJ
ejpam-5903	83	9	the	the	DET
ejpam-5903	83	10	sets	set	NOUN
ejpam-5903	83	11	{	{	PUNCT
ejpam-5903	83	12	a	a	PRON
ejpam-5903	83	13	,	,	PUNCT
ejpam-5903	83	14	x	x	NOUN
ejpam-5903	83	15	}	}	PUNCT
ejpam-5903	83	16	and	and	CCONJ
ejpam-5903	83	17	{	{	PUNCT
ejpam-5903	83	18	b	b	NOUN
ejpam-5903	83	19	,	,	PUNCT
ejpam-5903	83	20	x	x	PRON
ejpam-5903	83	21	}	}	PUNCT
ejpam-5903	83	22	are	be	AUX
ejpam-5903	83	23	not	not	PART
ejpam-5903	83	24	ζhg2	ζhg2	PROPN
ejpam-5903	83	25	-sets	-set	NOUN
ejpam-5903	83	26	of	of	ADP
ejpam-5903	83	27	g.	g.	NOUN
ejpam-5903	83	28	finally	finally	ADV
ejpam-5903	83	29	,	,	PUNCT
ejpam-5903	83	30	if	if	SCONJ
ejpam-5903	83	31	k	k	PROPN
ejpam-5903	83	32	=	=	SYM
ejpam-5903	83	33	3	3	NUM
ejpam-5903	83	34	,	,	PUNCT
ejpam-5903	83	35	then	then	ADV
ejpam-5903	83	36	any	any	DET
ejpam-5903	83	37	1	1	NUM
ejpam-5903	83	38	-	-	PUNCT
ejpam-5903	83	39	element	element	NOUN
ejpam-5903	83	40	subset	subset	NOUN
ejpam-5903	83	41	s3	s3	PROPN
ejpam-5903	83	42	of	of	ADP
ejpam-5903	83	43	v	v	PROPN
ejpam-5903	83	44	(	(	PUNCT
ejpam-5903	83	45	g	g	NOUN
ejpam-5903	83	46	)	)	PUNCT
ejpam-5903	83	47	is	be	AUX
ejpam-5903	83	48	a	a	DET
ejpam-5903	83	49	ζhg3	ζhg3	NOUN
ejpam-5903	83	50	-set	-set	ADJ
ejpam-5903	83	51	of	of	ADP
ejpam-5903	83	52	g.	g.	PROPN
ejpam-5903	83	53	since	since	SCONJ
ejpam-5903	83	54	nhg	nhg	PROPN
ejpam-5903	83	55	g	g	PROPN
ejpam-5903	84	1	[	[	X
ejpam-5903	84	2	s3	s3	PROPN
ejpam-5903	84	3	]	]	X
ejpam-5903	84	4	=	=	SYM
ejpam-5903	84	5	s3	s3	PROPN
ejpam-5903	84	6	,	,	PUNCT
ejpam-5903	84	7	it	it	PRON
ejpam-5903	84	8	follows	follow	VERB
ejpam-5903	84	9	that	that	SCONJ
ejpam-5903	84	10	ζ	ζ	NOUN
ejpam-5903	84	11	hg	hg	NOUN
ejpam-5903	84	12	3	3	NUM
ejpam-5903	84	13	(	(	PUNCT
ejpam-5903	84	14	g	g	NOUN
ejpam-5903	84	15	)	)	PUNCT
ejpam-5903	84	16	=	=	SYM
ejpam-5903	85	1	|v	|v	X
ejpam-5903	85	2	(	(	PUNCT
ejpam-5903	85	3	g)|−	g)|−	PRON
ejpam-5903	85	4	|nhg	|nhg	ADJ
ejpam-5903	85	5	g	g	X
ejpam-5903	86	1	[	[	X
ejpam-5903	86	2	s3]|	s3]|	ADP
ejpam-5903	86	3	=	=	SYM
ejpam-5903	86	4	8−	8−	NUM
ejpam-5903	86	5	1	1	NUM
ejpam-5903	86	6	=	=	SYM
ejpam-5903	86	7	7	7	NUM
ejpam-5903	86	8	.	.	PUNCT
ejpam-5903	86	9	................................................................................................................	................................................................................................................	PROPN
ejpam-5903	86	10	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	87	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	87	2	....................................	....................................	PUNCT
ejpam-5903	88	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	88	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	89	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	89	2	....................................	....................................	PUNCT
ejpam-5903	89	3	.........	.........	PUNCT
ejpam-5903	90	1	........	........	PUNCT
ejpam-5903	90	2	........	........	PUNCT
ejpam-5903	90	3	........	........	PUNCT
ejpam-5903	90	4	........	........	PUNCT
ejpam-5903	90	5	........	........	PUNCT
ejpam-5903	90	6	........	........	PUNCT
ejpam-5903	90	7	........	........	PUNCT
ejpam-5903	90	8	........	........	PUNCT
ejpam-5903	90	9	...	...	PUNCT
ejpam-5903	91	1	....................................	....................................	PUNCT
ejpam-5903	91	2	....................................	....................................	PUNCT
ejpam-5903	91	3	.........	.........	PUNCT
ejpam-5903	91	4	........	........	PUNCT
ejpam-5903	91	5	........	........	PUNCT
ejpam-5903	91	6	........	........	PUNCT
ejpam-5903	91	7	........	........	PUNCT
ejpam-5903	91	8	........	........	PUNCT
ejpam-5903	91	9	........	........	PUNCT
ejpam-5903	91	10	........	........	PUNCT
ejpam-5903	91	11	........	........	PUNCT
ejpam-5903	91	12	...	...	PUNCT
ejpam-5903	92	1	....................................	....................................	PUNCT
ejpam-5903	92	2	....................................	....................................	PUNCT
ejpam-5903	93	1	a	a	DET
ejpam-5903	93	2	b	b	X
ejpam-5903	93	3	x	x	SYM
ejpam-5903	93	4	y	y	NOUN
ejpam-5903	93	5	c	c	NOUN
ejpam-5903	93	6	u	u	PROPN
ejpam-5903	93	7	d	d	X
ejpam-5903	93	8	v	v	NUM
ejpam-5903	93	9	figure	figure	NOUN
ejpam-5903	93	10	1	1	NUM
ejpam-5903	93	11	:	:	PUNCT
ejpam-5903	93	12	graph	graph	VERB
ejpam-5903	93	13	g	g	NOUN
ejpam-5903	93	14	with	with	ADP
ejpam-5903	93	15	γhg(g	γhg(g	PROPN
ejpam-5903	93	16	)	)	PUNCT
ejpam-5903	93	17	=	=	NOUN
ejpam-5903	93	18	4	4	NUM
ejpam-5903	93	19	3	3	NUM
ejpam-5903	93	20	.	.	PUNCT
ejpam-5903	93	21	results	result	NOUN
ejpam-5903	93	22	theorem	theorem	VERB
ejpam-5903	93	23	1	1	NUM
ejpam-5903	93	24	(	(	PUNCT
ejpam-5903	93	25	[	[	X
ejpam-5903	93	26	19	19	NUM
ejpam-5903	93	27	]	]	NUM
ejpam-5903	93	28	)	)	PUNCT
ejpam-5903	93	29	.	.	PUNCT
ejpam-5903	94	1	let	let	VERB
ejpam-5903	94	2	n	n	PRON
ejpam-5903	94	3	be	be	AUX
ejpam-5903	94	4	positive	positive	ADJ
ejpam-5903	94	5	integer	integer	NOUN
ejpam-5903	94	6	.	.	PUNCT
ejpam-5903	95	1	then	then	ADV
ejpam-5903	95	2	each	each	PRON
ejpam-5903	95	3	of	of	ADP
ejpam-5903	95	4	the	the	DET
ejpam-5903	95	5	following	follow	VERB
ejpam-5903	95	6	holds	hold	NOUN
ejpam-5903	95	7	.	.	PUNCT
ejpam-5903	96	1	(	(	PUNCT
ejpam-5903	96	2	i	i	NOUN
ejpam-5903	96	3	)	)	PUNCT
ejpam-5903	96	4	for	for	ADP
ejpam-5903	96	5	a	a	DET
ejpam-5903	96	6	path	path	NOUN
ejpam-5903	96	7	pn	pn	NOUN
ejpam-5903	96	8	on	on	ADP
ejpam-5903	96	9	n	n	PRON
ejpam-5903	96	10	vertices	vertex	NOUN
ejpam-5903	96	11	,	,	PUNCT
ejpam-5903	96	12	we	we	PRON
ejpam-5903	96	13	have	have	VERB
ejpam-5903	96	14	γhg(pn	γhg(pn	NOUN
ejpam-5903	96	15	)	)	PUNCT
ejpam-5903	96	16	=	=	PUNCT
ejpam-5903	97	1			VERB
ejpam-5903	97	2	n	n	CCONJ
ejpam-5903	97	3	if	if	SCONJ
ejpam-5903	97	4	n	n	NOUN
ejpam-5903	97	5	=	=	SYM
ejpam-5903	97	6	1	1	NUM
ejpam-5903	97	7	,	,	PUNCT
ejpam-5903	97	8	2	2	NUM
ejpam-5903	97	9	n+6	n+6	NUM
ejpam-5903	97	10	3	3	NUM
ejpam-5903	97	11	if	if	SCONJ
ejpam-5903	97	12	n	n	PRON
ejpam-5903	97	13	≡	≡	PROPN
ejpam-5903	97	14	0(mod	0(mod	NOUN
ejpam-5903	97	15	3	3	X
ejpam-5903	97	16	)	)	PUNCT
ejpam-5903	97	17	n+2	n+2	ADV
ejpam-5903	97	18	3	3	NUM
ejpam-5903	97	19	if	if	SCONJ
ejpam-5903	97	20	n	n	PRON
ejpam-5903	97	21	≡	≡	PROPN
ejpam-5903	97	22	1(mod	1(mod	NUM
ejpam-5903	97	23	3	3	X
ejpam-5903	97	24	)	)	PUNCT
ejpam-5903	97	25	n+4	n+4	NUM
ejpam-5903	97	26	3	3	NUM
ejpam-5903	97	27	if	if	SCONJ
ejpam-5903	97	28	n	n	PRON
ejpam-5903	97	29	≡	≡	PROPN
ejpam-5903	97	30	2(mod	2(mod	NUM
ejpam-5903	97	31	3	3	NUM
ejpam-5903	97	32	)	)	PUNCT
ejpam-5903	97	33	.	.	PUNCT
ejpam-5903	98	1	(	(	PUNCT
ejpam-5903	98	2	ii	ii	NOUN
ejpam-5903	98	3	)	)	PUNCT
ejpam-5903	98	4	for	for	ADP
ejpam-5903	98	5	a	a	DET
ejpam-5903	98	6	cycle	cycle	NOUN
ejpam-5903	98	7	cn	cn	NOUN
ejpam-5903	98	8	on	on	ADP
ejpam-5903	98	9	n	n	PRON
ejpam-5903	98	10	vertices	vertex	NOUN
ejpam-5903	98	11	,	,	PUNCT
ejpam-5903	98	12	we	we	PRON
ejpam-5903	98	13	have	have	VERB
ejpam-5903	98	14	γhg(cn	γhg(cn	NOUN
ejpam-5903	98	15	)	)	PUNCT
ejpam-5903	98	16	=	=	PUNCT
ejpam-5903	98	17			NOUN
ejpam-5903	98	18	3	3	NUM
ejpam-5903	98	19	if	if	SCONJ
ejpam-5903	98	20	n	n	NOUN
ejpam-5903	98	21	=	=	SYM
ejpam-5903	98	22	3	3	NUM
ejpam-5903	98	23	,	,	PUNCT
ejpam-5903	98	24	4	4	NUM
ejpam-5903	98	25	,	,	PUNCT
ejpam-5903	98	26	5	5	NUM
ejpam-5903	98	27	n	n	SYM
ejpam-5903	98	28	3	3	NUM
ejpam-5903	98	29	if	if	SCONJ
ejpam-5903	98	30	n	n	PRON
ejpam-5903	98	31	≡	≡	PROPN
ejpam-5903	98	32	0(mod	0(mod	NOUN
ejpam-5903	98	33	3	3	X
ejpam-5903	98	34	)	)	PUNCT
ejpam-5903	98	35	n+2	n+2	ADV
ejpam-5903	98	36	3	3	NUM
ejpam-5903	98	37	if	if	SCONJ
ejpam-5903	98	38	n	n	PRON
ejpam-5903	98	39	≡	≡	PROPN
ejpam-5903	98	40	1(mod	1(mod	NUM
ejpam-5903	98	41	3	3	X
ejpam-5903	98	42	)	)	PUNCT
ejpam-5903	98	43	n+4	n+4	NUM
ejpam-5903	98	44	3	3	NUM
ejpam-5903	98	45	if	if	SCONJ
ejpam-5903	98	46	n	n	PRON
ejpam-5903	98	47	≡	≡	PROPN
ejpam-5903	98	48	2(mod	2(mod	NUM
ejpam-5903	98	49	3	3	NUM
ejpam-5903	98	50	)	)	PUNCT
ejpam-5903	98	51	.	.	PUNCT
ejpam-5903	99	1	(	(	PUNCT
ejpam-5903	99	2	iii	iii	X
ejpam-5903	99	3	)	)	PUNCT
ejpam-5903	99	4	for	for	ADP
ejpam-5903	99	5	a	a	DET
ejpam-5903	99	6	complete	complete	ADJ
ejpam-5903	99	7	graph	graph	NOUN
ejpam-5903	99	8	kn	kn	PROPN
ejpam-5903	99	9	,	,	PUNCT
ejpam-5903	99	10	we	we	PRON
ejpam-5903	99	11	have	have	VERB
ejpam-5903	99	12	γhg(kn	γhg(kn	NOUN
ejpam-5903	99	13	)	)	PUNCT
ejpam-5903	100	1	=	=	VERB
ejpam-5903	100	2	n.	n.	NOUN
ejpam-5903	100	3	corollary	corollary	NOUN
ejpam-5903	100	4	1	1	NUM
ejpam-5903	100	5	(	(	PUNCT
ejpam-5903	100	6	[	[	X
ejpam-5903	100	7	18	18	NUM
ejpam-5903	100	8	]	]	NUM
ejpam-5903	100	9	)	)	PUNCT
ejpam-5903	100	10	.	.	PUNCT
ejpam-5903	101	1	let	let	VERB
ejpam-5903	101	2	g	g	NOUN
ejpam-5903	101	3	and	and	CCONJ
ejpam-5903	101	4	h	h	NOUN
ejpam-5903	101	5	be	be	VERB
ejpam-5903	101	6	any	any	DET
ejpam-5903	101	7	two	two	NUM
ejpam-5903	101	8	graphs	graph	NOUN
ejpam-5903	101	9	of	of	ADP
ejpam-5903	101	10	orders	order	NOUN
ejpam-5903	101	11	m	m	VERB
ejpam-5903	101	12	and	and	CCONJ
ejpam-5903	101	13	n	n	CCONJ
ejpam-5903	101	14	,	,	PUNCT
ejpam-5903	101	15	respectively	respectively	ADV
ejpam-5903	101	16	.	.	PUNCT
ejpam-5903	102	1	then	then	ADV
ejpam-5903	102	2	(	(	PUNCT
ejpam-5903	102	3	i	i	NOUN
ejpam-5903	102	4	)	)	PUNCT
ejpam-5903	102	5	γhg(g+h	γhg(g+h	NOUN
ejpam-5903	102	6	)	)	PUNCT
ejpam-5903	103	1	=	=	PUNCT
ejpam-5903	104	1	m+	m+	NUM
ejpam-5903	104	2	n	n	NOUN
ejpam-5903	104	3	if	if	SCONJ
ejpam-5903	104	4	g	g	PROPN
ejpam-5903	104	5	and	and	CCONJ
ejpam-5903	104	6	h	h	NOUN
ejpam-5903	104	7	are	be	AUX
ejpam-5903	104	8	complete	complete	ADJ
ejpam-5903	104	9	;	;	PUNCT
ejpam-5903	104	10	j.	j.	PROPN
ejpam-5903	104	11	anoche	anoche	PROPN
ejpam-5903	104	12	,	,	PUNCT
ejpam-5903	104	13	s.	s.	PROPN
ejpam-5903	104	14	canoy	canoy	PROPN
ejpam-5903	104	15	,	,	PUNCT
ejpam-5903	104	16	jr	jr	PROPN
ejpam-5903	104	17	.	.	PROPN
ejpam-5903	104	18	/	/	SYM
ejpam-5903	104	19	eur	eur	PROPN
ejpam-5903	104	20	.	.	PUNCT
ejpam-5903	105	1	j.	j.	PROPN
ejpam-5903	105	2	pure	pure	PROPN
ejpam-5903	105	3	appl	appl	PROPN
ejpam-5903	105	4	.	.	PROPN
ejpam-5903	105	5	math	math	PROPN
ejpam-5903	105	6	,	,	PUNCT
ejpam-5903	105	7	18	18	NUM
ejpam-5903	105	8	(	(	PUNCT
ejpam-5903	105	9	2	2	NUM
ejpam-5903	105	10	)	)	PUNCT
ejpam-5903	105	11	(	(	PUNCT
ejpam-5903	105	12	2025	2025	NUM
ejpam-5903	105	13	)	)	PUNCT
ejpam-5903	105	14	,	,	PUNCT
ejpam-5903	105	15	5903	5903	NUM
ejpam-5903	105	16	5	5	NUM
ejpam-5903	105	17	of	of	ADP
ejpam-5903	105	18	17	17	NUM
ejpam-5903	105	19	(	(	PUNCT
ejpam-5903	105	20	ii	ii	NOUN
ejpam-5903	105	21	)	)	PUNCT
ejpam-5903	106	1	γhg(k1	γhg(k1	ADV
ejpam-5903	106	2	,	,	PUNCT
ejpam-5903	106	3	n−	n−	NOUN
ejpam-5903	106	4	1	1	NUM
ejpam-5903	106	5	)	)	PUNCT
ejpam-5903	106	6	=	=	PUNCT
ejpam-5903	107	1	γhg(k1	γhg(k1	PROPN
ejpam-5903	107	2	+	+	SYM
ejpam-5903	107	3	kn−1	kn−1	PROPN
ejpam-5903	107	4	)	)	PUNCT
ejpam-5903	107	5	=	=	SYM
ejpam-5903	108	1	n	n	PROPN
ejpam-5903	108	2	for	for	ADP
ejpam-5903	108	3	n	n	PRON
ejpam-5903	108	4	≥	≥	NOUN
ejpam-5903	108	5	2	2	NUM
ejpam-5903	108	6	;	;	PUNCT
ejpam-5903	108	7	(	(	PUNCT
ejpam-5903	108	8	iii	iii	NOUN
ejpam-5903	108	9	)	)	PUNCT
ejpam-5903	108	10	γhg(fn	γhg(fn	NOUN
ejpam-5903	108	11	)	)	PUNCT
ejpam-5903	108	12	=	=	SYM
ejpam-5903	108	13	1	1	NUM
ejpam-5903	108	14	+	+	NUM
ejpam-5903	108	15	ρ2pnd(pn	ρ2pnd(pn	NUM
ejpam-5903	108	16	)	)	PUNCT
ejpam-5903	108	17	;	;	PUNCT
ejpam-5903	108	18	(	(	PUNCT
ejpam-5903	108	19	iv	iv	X
ejpam-5903	108	20	)	)	PUNCT
ejpam-5903	108	21	γhg(wn	γhg(wn	NOUN
ejpam-5903	108	22	)	)	PUNCT
ejpam-5903	108	23	=	=	SYM
ejpam-5903	108	24	1	1	NUM
ejpam-5903	108	25	+	+	NUM
ejpam-5903	108	26	ρ2pnd(cn	ρ2pnd(cn	NOUN
ejpam-5903	108	27	)	)	PUNCT
ejpam-5903	108	28	;	;	PUNCT
ejpam-5903	108	29	and	and	CCONJ
ejpam-5903	108	30	(	(	PUNCT
ejpam-5903	108	31	v	v	NOUN
ejpam-5903	108	32	)	)	PUNCT
ejpam-5903	108	33	γhg(km	γhg(km	NOUN
ejpam-5903	108	34	,	,	PUNCT
ejpam-5903	108	35	n	n	CCONJ
ejpam-5903	108	36	)	)	PUNCT
ejpam-5903	109	1	=	=	PRON
ejpam-5903	109	2	{	{	PUNCT
ejpam-5903	109	3	3	3	NUM
ejpam-5903	109	4	if	if	SCONJ
ejpam-5903	109	5	m	m	VERB
ejpam-5903	109	6	=	=	SYM
ejpam-5903	109	7	2	2	NUM
ejpam-5903	109	8	or	or	CCONJ
ejpam-5903	109	9	n	n	NOUN
ejpam-5903	109	10	=	=	SYM
ejpam-5903	109	11	2	2	NUM
ejpam-5903	109	12	4	4	NUM
ejpam-5903	109	13	otherwise	otherwise	ADV
ejpam-5903	109	14	.	.	PUNCT
ejpam-5903	110	1	remark	remark	PROPN
ejpam-5903	110	2	1	1	NUM
ejpam-5903	110	3	.	.	PUNCT
ejpam-5903	111	1	let	let	VERB
ejpam-5903	111	2	g1	g1	PROPN
ejpam-5903	111	3	,	,	PUNCT
ejpam-5903	111	4	g2	g2	PROPN
ejpam-5903	111	5	,	,	PUNCT
ejpam-5903	111	6	·	·	PUNCT
ejpam-5903	111	7	·	·	PUNCT
ejpam-5903	111	8	·	·	PUNCT
ejpam-5903	111	9	,	,	PUNCT
ejpam-5903	111	10	gr	gr	INTJ
ejpam-5903	111	11	be	be	AUX
ejpam-5903	111	12	the	the	DET
ejpam-5903	111	13	components	component	NOUN
ejpam-5903	111	14	of	of	ADP
ejpam-5903	111	15	a	a	DET
ejpam-5903	111	16	graph	graph	NOUN
ejpam-5903	111	17	g.	g.	NOUN
ejpam-5903	112	1	then	then	ADV
ejpam-5903	112	2	each	each	PRON
ejpam-5903	112	3	of	of	ADP
ejpam-5903	112	4	the	the	DET
ejpam-5903	112	5	following	follow	VERB
ejpam-5903	112	6	holds	hold	VERB
ejpam-5903	112	7	:	:	PUNCT
ejpam-5903	112	8	(	(	PUNCT
ejpam-5903	112	9	i	i	NOUN
ejpam-5903	112	10	)	)	PUNCT
ejpam-5903	112	11	γhg(g	γhg(g	PROPN
ejpam-5903	112	12	)	)	PUNCT
ejpam-5903	113	1	=	=	PUNCT
ejpam-5903	114	1	∑r	∑r	PROPN
ejpam-5903	114	2	j=1	j=1	PROPN
ejpam-5903	114	3	γhg(gj	γhg(gj	NOUN
ejpam-5903	114	4	)	)	PUNCT
ejpam-5903	114	5	.	.	PUNCT
ejpam-5903	115	1	(	(	PUNCT
ejpam-5903	115	2	ii	ii	NOUN
ejpam-5903	115	3	)	)	PUNCT
ejpam-5903	115	4	if	if	SCONJ
ejpam-5903	115	5	aj	aj	PROPN
ejpam-5903	115	6	⊆	⊆	NUM
ejpam-5903	115	7	v	v	NOUN
ejpam-5903	115	8	(	(	PUNCT
ejpam-5903	115	9	gj	gj	NOUN
ejpam-5903	115	10	)	)	PUNCT
ejpam-5903	115	11	for	for	ADP
ejpam-5903	115	12	each	each	DET
ejpam-5903	115	13	j	j	PROPN
ejpam-5903	115	14	∈	∈	PROPN
ejpam-5903	116	1	[	[	X
ejpam-5903	116	2	r	r	X
ejpam-5903	116	3	]	]	X
ejpam-5903	116	4	=	=	PUNCT
ejpam-5903	116	5	{	{	PUNCT
ejpam-5903	116	6	1	1	NUM
ejpam-5903	116	7	,	,	PUNCT
ejpam-5903	116	8	2	2	NUM
ejpam-5903	116	9	,	,	PUNCT
ejpam-5903	116	10	·	·	PUNCT
ejpam-5903	116	11	·	·	PUNCT
ejpam-5903	116	12	·	·	PUNCT
ejpam-5903	116	13	,	,	PUNCT
ejpam-5903	116	14	r	r	X
ejpam-5903	116	15	}	}	PUNCT
ejpam-5903	116	16	and	and	CCONJ
ejpam-5903	116	17	a	a	DET
ejpam-5903	116	18	=	=	X
ejpam-5903	116	19	∪r	∪r	NUM
ejpam-5903	116	20	j=1aj	j=1aj	X
ejpam-5903	116	21	,	,	PUNCT
ejpam-5903	116	22	then	then	ADV
ejpam-5903	116	23	nhg	nhg	VERB
ejpam-5903	116	24	g	g	PROPN
ejpam-5903	117	1	[	[	X
ejpam-5903	117	2	a	a	X
ejpam-5903	117	3	]	]	X
ejpam-5903	117	4	=	=	PUNCT
ejpam-5903	117	5	∪r	∪r	PUNCT
ejpam-5903	117	6	j=1n	j=1n	VERB
ejpam-5903	117	7	hg	hg	PROPN
ejpam-5903	117	8	g	g	PROPN
ejpam-5903	118	1	[	[	X
ejpam-5903	118	2	aj	aj	PROPN
ejpam-5903	118	3	]	]	X
ejpam-5903	118	4	(	(	PUNCT
ejpam-5903	118	5	a	a	DET
ejpam-5903	118	6	disjoint	disjoint	NOUN
ejpam-5903	118	7	union	union	NOUN
ejpam-5903	118	8	)	)	PUNCT
ejpam-5903	118	9	.	.	PUNCT
ejpam-5903	119	1	theorem	theorem	NOUN
ejpam-5903	119	2	2	2	NUM
ejpam-5903	119	3	.	.	PUNCT
ejpam-5903	119	4	let	let	VERB
ejpam-5903	119	5	g1	g1	PROPN
ejpam-5903	119	6	,	,	PUNCT
ejpam-5903	119	7	g2	g2	PROPN
ejpam-5903	119	8	,	,	PUNCT
ejpam-5903	119	9	·	·	PUNCT
ejpam-5903	119	10	·	·	PUNCT
ejpam-5903	119	11	·	·	PUNCT
ejpam-5903	119	12	,	,	PUNCT
ejpam-5903	119	13	gr	gr	INTJ
ejpam-5903	119	14	be	be	AUX
ejpam-5903	119	15	the	the	DET
ejpam-5903	119	16	components	component	NOUN
ejpam-5903	119	17	of	of	ADP
ejpam-5903	119	18	graph	graph	NOUN
ejpam-5903	119	19	g	g	PROPN
ejpam-5903	119	20	and	and	CCONJ
ejpam-5903	119	21	let	let	VERB
ejpam-5903	119	22	ζhg1	ζhg1	PROPN
ejpam-5903	119	23	(	(	PUNCT
ejpam-5903	119	24	gi	gi	INTJ
ejpam-5903	119	25	)	)	PUNCT
ejpam-5903	119	26	be	be	AUX
ejpam-5903	119	27	the	the	DET
ejpam-5903	119	28	1	1	NUM
ejpam-5903	119	29	-	-	PUNCT
ejpam-5903	119	30	geodetic	geodetic	ADJ
ejpam-5903	119	31	hop	hop	NOUN
ejpam-5903	119	32	domination	domination	NOUN
ejpam-5903	119	33	defect	defect	NOUN
ejpam-5903	119	34	of	of	ADP
ejpam-5903	119	35	gi	gi	NOUN
ejpam-5903	119	36	for	for	ADP
ejpam-5903	119	37	each	each	DET
ejpam-5903	119	38	i	i	PRON
ejpam-5903	119	39	∈	∈	PROPN
ejpam-5903	120	1	[	[	X
ejpam-5903	120	2	r	r	X
ejpam-5903	120	3	]	]	X
ejpam-5903	120	4	=	=	PUNCT
ejpam-5903	120	5	{	{	PUNCT
ejpam-5903	120	6	1	1	NUM
ejpam-5903	120	7	,	,	PUNCT
ejpam-5903	120	8	2	2	NUM
ejpam-5903	120	9	,	,	PUNCT
ejpam-5903	120	10	·	·	PUNCT
ejpam-5903	120	11	·	·	PUNCT
ejpam-5903	120	12	·	·	PUNCT
ejpam-5903	120	13	,	,	PUNCT
ejpam-5903	120	14	r	r	NOUN
ejpam-5903	120	15	}	}	PUNCT
ejpam-5903	120	16	.	.	PUNCT
ejpam-5903	121	1	then	then	ADV
ejpam-5903	121	2	ζhg1	ζhg1	PROPN
ejpam-5903	121	3	(	(	PUNCT
ejpam-5903	121	4	g	g	NOUN
ejpam-5903	121	5	)	)	PUNCT
ejpam-5903	121	6	=	=	SYM
ejpam-5903	121	7	min{ζhg1	min{ζhg1	PROPN
ejpam-5903	121	8	(	(	PUNCT
ejpam-5903	121	9	gi	gi	NOUN
ejpam-5903	121	10	)	)	PUNCT
ejpam-5903	121	11	:	:	PUNCT
ejpam-5903	122	1	i	i	PRON
ejpam-5903	122	2	∈	∈	VERB
ejpam-5903	123	1	[	[	X
ejpam-5903	123	2	r	r	X
ejpam-5903	123	3	]	]	PUNCT
ejpam-5903	123	4	}	}	PUNCT
ejpam-5903	123	5	.	.	PUNCT
ejpam-5903	124	1	proof	proof	NOUN
ejpam-5903	124	2	.	.	PUNCT
ejpam-5903	125	1	let	let	VERB
ejpam-5903	125	2	γhg(gi	γhg(gi	NUM
ejpam-5903	125	3	)	)	PUNCT
ejpam-5903	125	4	and	and	CCONJ
ejpam-5903	125	5	γhg(g	γhg(g	X
ejpam-5903	125	6	)	)	PUNCT
ejpam-5903	125	7	be	be	VERB
ejpam-5903	125	8	the	the	DET
ejpam-5903	125	9	geodetic	geodetic	ADJ
ejpam-5903	125	10	hop	hop	NOUN
ejpam-5903	125	11	domination	domination	NOUN
ejpam-5903	125	12	numbers	number	NOUN
ejpam-5903	125	13	of	of	ADP
ejpam-5903	125	14	gi	gi	NOUN
ejpam-5903	125	15	and	and	CCONJ
ejpam-5903	125	16	g	g	NOUN
ejpam-5903	125	17	,	,	PUNCT
ejpam-5903	125	18	respectively	respectively	ADV
ejpam-5903	125	19	.	.	PUNCT
ejpam-5903	126	1	by	by	ADP
ejpam-5903	126	2	remark	remark	NOUN
ejpam-5903	126	3	1(i	1(i	NUM
ejpam-5903	126	4	)	)	PUNCT
ejpam-5903	126	5	,	,	PUNCT
ejpam-5903	126	6	γhg(g	γhg(g	PROPN
ejpam-5903	126	7	)	)	PUNCT
ejpam-5903	127	1	=	=	PUNCT
ejpam-5903	127	2	∑r	∑r	PROPN
ejpam-5903	127	3	i=1	i=1	PROPN
ejpam-5903	127	4	γhg(gi	γhg(gi	PROPN
ejpam-5903	127	5	)	)	PUNCT
ejpam-5903	127	6	.	.	PUNCT
ejpam-5903	128	1	for	for	ADP
ejpam-5903	128	2	each	each	DET
ejpam-5903	128	3	i	i	PRON
ejpam-5903	128	4	∈	∈	PROPN
ejpam-5903	129	1	[	[	X
ejpam-5903	129	2	r	r	X
ejpam-5903	129	3	]	]	PUNCT
ejpam-5903	129	4	,	,	PUNCT
ejpam-5903	129	5	let	let	VERB
ejpam-5903	129	6	di	di	PART
ejpam-5903	129	7	be	be	AUX
ejpam-5903	129	8	a	a	DET
ejpam-5903	129	9	ζhg1	ζhg1	NOUN
ejpam-5903	129	10	-set	-set	ADJ
ejpam-5903	129	11	of	of	ADP
ejpam-5903	129	12	gi	gi	PROPN
ejpam-5903	129	13	.	.	PUNCT
ejpam-5903	130	1	then	then	ADV
ejpam-5903	130	2	|di|	|di|	PROPN
ejpam-5903	130	3	=	=	SYM
ejpam-5903	130	4	γhg(gi	γhg(gi	NUM
ejpam-5903	130	5	)	)	PUNCT
ejpam-5903	131	1	−	−	ADP
ejpam-5903	131	2	1	1	NUM
ejpam-5903	131	3	and	and	CCONJ
ejpam-5903	131	4	ζhg1	ζhg1	PROPN
ejpam-5903	131	5	(	(	PUNCT
ejpam-5903	131	6	gi	gi	INTJ
ejpam-5903	131	7	)	)	PUNCT
ejpam-5903	131	8	=	=	SYM
ejpam-5903	132	1	|v	|v	PROPN
ejpam-5903	132	2	(	(	PUNCT
ejpam-5903	132	3	gi	gi	INTJ
ejpam-5903	132	4	)	)	PUNCT
ejpam-5903	132	5	−	−	NOUN
ejpam-5903	132	6	nhg	nhg	VERB
ejpam-5903	132	7	g	g	PROPN
ejpam-5903	133	1	[	[	X
ejpam-5903	134	1	di]|	di]|	PROPN
ejpam-5903	134	2	.	.	PUNCT
ejpam-5903	135	1	let	let	VERB
ejpam-5903	135	2	j	j	PROPN
ejpam-5903	135	3	∈	∈	PROPN
ejpam-5903	136	1	[	[	X
ejpam-5903	136	2	r	r	X
ejpam-5903	136	3	]	]	PUNCT
ejpam-5903	136	4	be	be	AUX
ejpam-5903	136	5	such	such	ADJ
ejpam-5903	136	6	that	that	DET
ejpam-5903	136	7	ζhg1	ζhg1	NOUN
ejpam-5903	136	8	(	(	PUNCT
ejpam-5903	136	9	gj	gj	NOUN
ejpam-5903	136	10	)	)	PUNCT
ejpam-5903	136	11	=	=	SYM
ejpam-5903	137	1	min{ζhg1	min{ζhg1	PROPN
ejpam-5903	137	2	(	(	PUNCT
ejpam-5903	137	3	gi	gi	NOUN
ejpam-5903	137	4	)	)	PUNCT
ejpam-5903	137	5	:	:	PUNCT
ejpam-5903	138	1	i	i	PRON
ejpam-5903	138	2	∈	∈	VERB
ejpam-5903	139	1	[	[	X
ejpam-5903	139	2	r	r	X
ejpam-5903	139	3	]	]	PUNCT
ejpam-5903	139	4	}	}	PUNCT
ejpam-5903	139	5	.	.	PUNCT
ejpam-5903	140	1	let	let	VERB
ejpam-5903	140	2	si	si	X
ejpam-5903	140	3	be	be	AUX
ejpam-5903	140	4	a	a	DET
ejpam-5903	140	5	γhg	γhg	NOUN
ejpam-5903	140	6	-	-	PUNCT
ejpam-5903	140	7	set	set	VERB
ejpam-5903	140	8	in	in	ADP
ejpam-5903	140	9	gi	gi	NOUN
ejpam-5903	140	10	for	for	ADP
ejpam-5903	140	11	each	each	DET
ejpam-5903	140	12	i	i	PRON
ejpam-5903	140	13	∈	∈	PROPN
ejpam-5903	141	1	[	[	X
ejpam-5903	141	2	r	r	X
ejpam-5903	141	3	]	]	PUNCT
ejpam-5903	141	4	and	and	CCONJ
ejpam-5903	141	5	let	let	VERB
ejpam-5903	141	6	s	s	PRON
ejpam-5903	141	7	=	=	PUNCT
ejpam-5903	141	8	(	(	PUNCT
ejpam-5903	141	9	∪i∈[r]\{j}si	∪i∈[r]\{j}si	NOUN
ejpam-5903	141	10	)	)	PUNCT
ejpam-5903	141	11	∪dj	∪dj	NOUN
ejpam-5903	141	12	.	.	PUNCT
ejpam-5903	142	1	then	then	ADV
ejpam-5903	142	2	|s|	|s|	PROPN
ejpam-5903	142	3	=	=	SYM
ejpam-5903	142	4	∑	∑	SYM
ejpam-5903	142	5	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5903	142	6	}	}	PUNCT
ejpam-5903	142	7	|si|+	|si|+	NOUN
ejpam-5903	142	8	|dj	|dj	PUNCT
ejpam-5903	142	9	|	|	ADV
ejpam-5903	142	10	=	=	SYM
ejpam-5903	142	11	γhg(g)−	γhg(g)−	ADJ
ejpam-5903	142	12	1	1	NUM
ejpam-5903	142	13	and	and	CCONJ
ejpam-5903	142	14	,	,	PUNCT
ejpam-5903	142	15	by	by	ADP
ejpam-5903	142	16	remark	remark	NOUN
ejpam-5903	142	17	1(ii	1(ii	NUM
ejpam-5903	142	18	)	)	PUNCT
ejpam-5903	142	19	,	,	PUNCT
ejpam-5903	142	20	|nhg	|nhg	VERB
ejpam-5903	143	1	g	g	PROPN
ejpam-5903	143	2	[	[	X
ejpam-5903	143	3	s]|	s]|	X
ejpam-5903	143	4	=	=	SYM
ejpam-5903	143	5	|nhg	|nhg	PROPN
ejpam-5903	143	6	gj	gj	NOUN
ejpam-5903	143	7	[	[	X
ejpam-5903	143	8	dj	dj	X
ejpam-5903	143	9	]	]	X
ejpam-5903	143	10	|+	|+	NOUN
ejpam-5903	143	11	∑	∑	ADV
ejpam-5903	143	12	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5903	143	13	}	}	PUNCT
ejpam-5903	143	14	|nhg	|nhg	NOUN
ejpam-5903	143	15	gi	gi	X
ejpam-5903	144	1	[	[	X
ejpam-5903	144	2	si]|	si]|	ADP
ejpam-5903	144	3	=	=	SYM
ejpam-5903	144	4	|v	|v	X
ejpam-5903	144	5	(	(	PUNCT
ejpam-5903	144	6	gj)|	gj)|	PROPN
ejpam-5903	144	7	−	−	PROPN
ejpam-5903	144	8	ζhg1	ζhg1	PROPN
ejpam-5903	144	9	(	(	PUNCT
ejpam-5903	144	10	gj	gj	PROPN
ejpam-5903	144	11	)	)	PUNCT
ejpam-5903	144	12	+	+	CCONJ
ejpam-5903	144	13	∑	∑	PUNCT
ejpam-5903	144	14	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5903	144	15	}	}	PUNCT
ejpam-5903	144	16	|v	|v	NOUN
ejpam-5903	144	17	(	(	PUNCT
ejpam-5903	144	18	gi)|	gi)|	X
ejpam-5903	144	19	=	=	PUNCT
ejpam-5903	144	20	r∑	r∑	NOUN
ejpam-5903	144	21	i=1	i=1	PROPN
ejpam-5903	144	22	|v	|v	X
ejpam-5903	144	23	(	(	PUNCT
ejpam-5903	144	24	gi)|	gi)|	INTJ
ejpam-5903	144	25	−	−	PROPN
ejpam-5903	144	26	ζhg1	ζhg1	PROPN
ejpam-5903	144	27	(	(	PUNCT
ejpam-5903	144	28	gj	gj	PROPN
ejpam-5903	144	29	)	)	PUNCT
ejpam-5903	144	30	.	.	PUNCT
ejpam-5903	145	1	thus	thus	ADV
ejpam-5903	145	2	,	,	PUNCT
ejpam-5903	145	3	in	in	ADP
ejpam-5903	145	4	g	g	NOUN
ejpam-5903	145	5	,	,	PUNCT
ejpam-5903	145	6	ζhg1	ζhg1	PROPN
ejpam-5903	145	7	(	(	PUNCT
ejpam-5903	145	8	s	s	NOUN
ejpam-5903	145	9	)	)	PUNCT
ejpam-5903	145	10	=	=	SYM
ejpam-5903	145	11	|v	|v	PROPN
ejpam-5903	145	12	(	(	PUNCT
ejpam-5903	145	13	g)|	g)|	NOUN
ejpam-5903	145	14	−	−	PROPN
ejpam-5903	145	15	|nhg	|nhg	PROPN
ejpam-5903	145	16	g	g	PROPN
ejpam-5903	145	17	[	[	X
ejpam-5903	145	18	s]|	s]|	PROPN
ejpam-5903	145	19	=	=	SYM
ejpam-5903	145	20	ζhg1	ζhg1	PROPN
ejpam-5903	145	21	(	(	PUNCT
ejpam-5903	145	22	gj	gj	PROPN
ejpam-5903	145	23	)	)	PUNCT
ejpam-5903	145	24	.	.	PUNCT
ejpam-5903	146	1	we	we	PRON
ejpam-5903	146	2	claim	claim	VERB
ejpam-5903	146	3	that	that	SCONJ
ejpam-5903	146	4	ζhg1	ζhg1	PROPN
ejpam-5903	146	5	(	(	PUNCT
ejpam-5903	146	6	s	s	X
ejpam-5903	146	7	)	)	PUNCT
ejpam-5903	146	8	is	be	AUX
ejpam-5903	146	9	the	the	DET
ejpam-5903	146	10	minimum	minimum	NOUN
ejpam-5903	146	11	among	among	ADP
ejpam-5903	146	12	all	all	DET
ejpam-5903	146	13	subsets	subset	NOUN
ejpam-5903	146	14	of	of	ADP
ejpam-5903	146	15	v	v	NOUN
ejpam-5903	146	16	(	(	PUNCT
ejpam-5903	146	17	g	g	NOUN
ejpam-5903	146	18	)	)	PUNCT
ejpam-5903	146	19	with	with	ADP
ejpam-5903	146	20	cardinality	cardinality	NOUN
ejpam-5903	146	21	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	146	22	1	1	NUM
ejpam-5903	146	23	.	.	PUNCT
ejpam-5903	146	24	to	to	ADP
ejpam-5903	146	25	this	this	DET
ejpam-5903	146	26	end	end	NOUN
ejpam-5903	146	27	,	,	PUNCT
ejpam-5903	146	28	suppose	suppose	VERB
ejpam-5903	146	29	there	there	PRON
ejpam-5903	146	30	exists	exist	VERB
ejpam-5903	146	31	q	q	PROPN
ejpam-5903	146	32	⊆	⊆	NUM
ejpam-5903	146	33	v	v	NOUN
ejpam-5903	146	34	(	(	PUNCT
ejpam-5903	146	35	g	g	NOUN
ejpam-5903	146	36	)	)	PUNCT
ejpam-5903	146	37	such	such	ADJ
ejpam-5903	146	38	that	that	SCONJ
ejpam-5903	146	39	|q|	|q|	VERB
ejpam-5903	146	40	=	=	SYM
ejpam-5903	146	41	γhg(g)−	γhg(g)−	ADJ
ejpam-5903	146	42	1	1	NUM
ejpam-5903	146	43	and	and	CCONJ
ejpam-5903	146	44	ζhg1	ζhg1	PROPN
ejpam-5903	146	45	(	(	PUNCT
ejpam-5903	146	46	q	q	X
ejpam-5903	146	47	)	)	PUNCT
ejpam-5903	146	48	<	<	X
ejpam-5903	146	49	ζhg1	ζhg1	PROPN
ejpam-5903	146	50	(	(	PUNCT
ejpam-5903	146	51	s	s	NOUN
ejpam-5903	146	52	)	)	PUNCT
ejpam-5903	146	53	.	.	PUNCT
ejpam-5903	147	1	let	let	VERB
ejpam-5903	147	2	q	q	NOUN
ejpam-5903	147	3	=	=	PROPN
ejpam-5903	147	4	q1	q1	PROPN
ejpam-5903	147	5	∪q2	∪q2	NOUN
ejpam-5903	147	6	∪	∪	X
ejpam-5903	147	7	·	·	PUNCT
ejpam-5903	147	8	·	·	PUNCT
ejpam-5903	147	9	·	·	PUNCT
ejpam-5903	147	10	∪qr	∪qr	NOUN
ejpam-5903	147	11	where	where	SCONJ
ejpam-5903	147	12	qi	qi	PROPN
ejpam-5903	147	13	⊆	⊆	PROPN
ejpam-5903	147	14	v	v	NOUN
ejpam-5903	147	15	(	(	PUNCT
ejpam-5903	147	16	gi	gi	INTJ
ejpam-5903	147	17	)	)	PUNCT
ejpam-5903	147	18	for	for	ADP
ejpam-5903	147	19	each	each	DET
ejpam-5903	147	20	i	i	PRON
ejpam-5903	147	21	∈	∈	PROPN
ejpam-5903	148	1	[	[	X
ejpam-5903	148	2	r	r	X
ejpam-5903	148	3	]	]	X
ejpam-5903	148	4	.	.	PUNCT
ejpam-5903	149	1	since	since	SCONJ
ejpam-5903	149	2	|q|	|q|	PROPN
ejpam-5903	149	3	=	=	SYM
ejpam-5903	149	4	γhg(g	γhg(g	PROPN
ejpam-5903	149	5	)	)	PUNCT
ejpam-5903	149	6	−	−	NOUN
ejpam-5903	149	7	1	1	NUM
ejpam-5903	149	8	,	,	PUNCT
ejpam-5903	149	9	at	at	ADV
ejpam-5903	149	10	least	least	ADV
ejpam-5903	149	11	one	one	NUM
ejpam-5903	149	12	qt	qt	NOUN
ejpam-5903	149	13	is	be	AUX
ejpam-5903	149	14	not	not	PART
ejpam-5903	149	15	j.	j.	PROPN
ejpam-5903	149	16	anoche	anoche	PROPN
ejpam-5903	149	17	,	,	PUNCT
ejpam-5903	149	18	s.	s.	PROPN
ejpam-5903	149	19	canoy	canoy	PROPN
ejpam-5903	149	20	,	,	PUNCT
ejpam-5903	149	21	jr	jr	PROPN
ejpam-5903	149	22	.	.	PROPN
ejpam-5903	149	23	/	/	SYM
ejpam-5903	149	24	eur	eur	PROPN
ejpam-5903	149	25	.	.	PUNCT
ejpam-5903	150	1	j.	j.	PROPN
ejpam-5903	150	2	pure	pure	PROPN
ejpam-5903	150	3	appl	appl	PROPN
ejpam-5903	150	4	.	.	PROPN
ejpam-5903	150	5	math	math	PROPN
ejpam-5903	150	6	,	,	PUNCT
ejpam-5903	150	7	18	18	NUM
ejpam-5903	150	8	(	(	PUNCT
ejpam-5903	150	9	2	2	NUM
ejpam-5903	150	10	)	)	PUNCT
ejpam-5903	150	11	(	(	PUNCT
ejpam-5903	150	12	2025	2025	NUM
ejpam-5903	150	13	)	)	PUNCT
ejpam-5903	150	14	,	,	PUNCT
ejpam-5903	150	15	5903	5903	NUM
ejpam-5903	150	16	6	6	NUM
ejpam-5903	150	17	of	of	ADP
ejpam-5903	150	18	17	17	NUM
ejpam-5903	150	19	a	a	DET
ejpam-5903	150	20	geodetic	geodetic	ADJ
ejpam-5903	150	21	hop	hop	NOUN
ejpam-5903	150	22	dominating	dominating	NOUN
ejpam-5903	150	23	set	set	NOUN
ejpam-5903	150	24	of	of	ADP
ejpam-5903	150	25	gt	gt	PROPN
ejpam-5903	150	26	by	by	ADP
ejpam-5903	150	27	remark	remark	NOUN
ejpam-5903	150	28	1(i	1(i	NUM
ejpam-5903	150	29	)	)	PUNCT
ejpam-5903	150	30	.	.	PUNCT
ejpam-5903	151	1	thus	thus	ADV
ejpam-5903	151	2	,	,	PUNCT
ejpam-5903	151	3	|qt|	|qt|	PROPN
ejpam-5903	151	4	=	=	SYM
ejpam-5903	151	5	γhg(gt	γhg(gt	PROPN
ejpam-5903	151	6	)	)	PUNCT
ejpam-5903	151	7	−	−	PROPN
ejpam-5903	151	8	1	1	NUM
ejpam-5903	151	9	and	and	CCONJ
ejpam-5903	151	10	ζhg1	ζhg1	PROPN
ejpam-5903	151	11	(	(	PUNCT
ejpam-5903	151	12	qt	qt	PROPN
ejpam-5903	151	13	)	)	PUNCT
ejpam-5903	151	14	≥	≥	NOUN
ejpam-5903	151	15	ζhg1	ζhg1	PROPN
ejpam-5903	151	16	(	(	PUNCT
ejpam-5903	151	17	gt	gt	PROPN
ejpam-5903	151	18	)	)	PUNCT
ejpam-5903	151	19	≥	≥	NOUN
ejpam-5903	151	20	ζhg1	ζhg1	PROPN
ejpam-5903	151	21	(	(	PUNCT
ejpam-5903	151	22	gj	gj	PROPN
ejpam-5903	151	23	)	)	PUNCT
ejpam-5903	151	24	.	.	PUNCT
ejpam-5903	152	1	hence	hence	ADV
ejpam-5903	152	2	,	,	PUNCT
ejpam-5903	152	3	ζhg1	ζhg1	PROPN
ejpam-5903	152	4	(	(	PUNCT
ejpam-5903	152	5	q	q	X
ejpam-5903	152	6	)	)	PUNCT
ejpam-5903	152	7	=	=	SYM
ejpam-5903	152	8	|v	|v	PROPN
ejpam-5903	152	9	(	(	PUNCT
ejpam-5903	152	10	g)|	g)|	NOUN
ejpam-5903	152	11	−	−	PROPN
ejpam-5903	152	12	|nhg	|nhg	PROPN
ejpam-5903	152	13	g	g	NOUN
ejpam-5903	153	1	[	[	X
ejpam-5903	153	2	q]|	q]|	PROPN
ejpam-5903	153	3	=	=	PUNCT
ejpam-5903	153	4	r∑	r∑	NOUN
ejpam-5903	154	1	i=1	i=1	PROPN
ejpam-5903	154	2	(	(	PUNCT
ejpam-5903	154	3	|v	|v	X
ejpam-5903	154	4	(	(	PUNCT
ejpam-5903	154	5	gi)|	gi)|	INTJ
ejpam-5903	154	6	−	−	PROPN
ejpam-5903	154	7	|nhg	|nhg	PROPN
ejpam-5903	154	8	gi	gi	X
ejpam-5903	155	1	[	[	X
ejpam-5903	155	2	qi]|	qi]|	NUM
ejpam-5903	155	3	)	)	PUNCT
ejpam-5903	155	4	≥	≥	NOUN
ejpam-5903	155	5	|v	|v	NOUN
ejpam-5903	155	6	(	(	PUNCT
ejpam-5903	155	7	gt)|	gt)|	PROPN
ejpam-5903	155	8	−	−	PROPN
ejpam-5903	156	1	|nhg	|nhg	PROPN
ejpam-5903	156	2	gt	gt	PROPN
ejpam-5903	157	1	[	[	X
ejpam-5903	157	2	qt]|	qt]|	NOUN
ejpam-5903	157	3	=	=	SYM
ejpam-5903	157	4	ζhg1	ζhg1	PROPN
ejpam-5903	157	5	(	(	PUNCT
ejpam-5903	157	6	qt	qt	PROPN
ejpam-5903	157	7	)	)	PUNCT
ejpam-5903	157	8	≥	≥	NOUN
ejpam-5903	157	9	ζhg1	ζhg1	PROPN
ejpam-5903	157	10	(	(	PUNCT
ejpam-5903	157	11	gj	gj	NOUN
ejpam-5903	157	12	)	)	PUNCT
ejpam-5903	157	13	=	=	SYM
ejpam-5903	157	14	ζhg1	ζhg1	PROPN
ejpam-5903	157	15	(	(	PUNCT
ejpam-5903	157	16	s	s	NOUN
ejpam-5903	157	17	)	)	PUNCT
ejpam-5903	157	18	,	,	PUNCT
ejpam-5903	157	19	contrary	contrary	ADV
ejpam-5903	157	20	to	to	ADP
ejpam-5903	157	21	the	the	DET
ejpam-5903	157	22	assumption	assumption	NOUN
ejpam-5903	157	23	that	that	SCONJ
ejpam-5903	157	24	ζhg1	ζhg1	PROPN
ejpam-5903	157	25	(	(	PUNCT
ejpam-5903	157	26	q	q	X
ejpam-5903	157	27	)	)	PUNCT
ejpam-5903	157	28	<	<	X
ejpam-5903	157	29	ζhg1	ζhg1	PROPN
ejpam-5903	157	30	(	(	PUNCT
ejpam-5903	157	31	s	s	NOUN
ejpam-5903	157	32	)	)	PUNCT
ejpam-5903	157	33	.	.	PUNCT
ejpam-5903	158	1	therefore	therefore	ADV
ejpam-5903	158	2	,	,	PUNCT
ejpam-5903	158	3	ζhg1	ζhg1	PROPN
ejpam-5903	158	4	(	(	PUNCT
ejpam-5903	158	5	g	g	NOUN
ejpam-5903	158	6	)	)	PUNCT
ejpam-5903	158	7	=	=	SYM
ejpam-5903	158	8	ζhg1	ζhg1	PROPN
ejpam-5903	158	9	(	(	PUNCT
ejpam-5903	158	10	s	s	NOUN
ejpam-5903	158	11	)	)	PUNCT
ejpam-5903	158	12	=	=	SYM
ejpam-5903	158	13	ζhg1	ζhg1	PROPN
ejpam-5903	158	14	(	(	PUNCT
ejpam-5903	158	15	gj	gj	PROPN
ejpam-5903	158	16	)	)	PUNCT
ejpam-5903	158	17	.	.	PUNCT
ejpam-5903	159	1	theorem	theorem	NOUN
ejpam-5903	159	2	3	3	X
ejpam-5903	159	3	.	.	PUNCT
ejpam-5903	160	1	let	let	VERB
ejpam-5903	160	2	g	g	PRON
ejpam-5903	160	3	be	be	AUX
ejpam-5903	160	4	a	a	DET
ejpam-5903	160	5	graph	graph	NOUN
ejpam-5903	160	6	with	with	ADP
ejpam-5903	160	7	i(g	i(g	NOUN
ejpam-5903	160	8	)	)	PUNCT
ejpam-5903	161	1	̸=	̸=	NOUN
ejpam-5903	161	2	∅	∅	NOUN
ejpam-5903	161	3	and	and	CCONJ
ejpam-5903	161	4	suppose	suppose	VERB
ejpam-5903	161	5	|i(g)|	|i(g)|	NOUN
ejpam-5903	161	6	=	=	PROPN
ejpam-5903	161	7	r.	r.	PROPN
ejpam-5903	161	8	then	then	ADV
ejpam-5903	161	9	ζhgj	ζhgj	ADV
ejpam-5903	161	10	(	(	PUNCT
ejpam-5903	161	11	g	g	NOUN
ejpam-5903	161	12	)	)	PUNCT
ejpam-5903	161	13	=	=	SYM
ejpam-5903	162	1	j	j	PROPN
ejpam-5903	162	2	for	for	ADP
ejpam-5903	162	3	every	every	DET
ejpam-5903	162	4	j	j	PROPN
ejpam-5903	162	5	∈	∈	PROPN
ejpam-5903	163	1	[	[	X
ejpam-5903	163	2	r	r	X
ejpam-5903	163	3	]	]	X
ejpam-5903	163	4	=	=	PUNCT
ejpam-5903	163	5	{	{	PUNCT
ejpam-5903	163	6	1	1	NUM
ejpam-5903	163	7	,	,	PUNCT
ejpam-5903	163	8	2	2	NUM
ejpam-5903	163	9	,	,	PUNCT
ejpam-5903	163	10	·	·	PUNCT
ejpam-5903	163	11	·	·	PUNCT
ejpam-5903	163	12	·	·	PUNCT
ejpam-5903	163	13	,	,	PUNCT
ejpam-5903	163	14	r	r	NOUN
ejpam-5903	163	15	}	}	PUNCT
ejpam-5903	163	16	and	and	CCONJ
ejpam-5903	163	17	ζhgk	ζhgk	NOUN
ejpam-5903	163	18	(	(	PUNCT
ejpam-5903	163	19	g	g	NOUN
ejpam-5903	163	20	)	)	PUNCT
ejpam-5903	163	21	=	=	SYM
ejpam-5903	164	1	r	r	NOUN
ejpam-5903	164	2	+	+	NUM
ejpam-5903	164	3	ζhgk−r(g	ζhgk−r(g	PROPN
ejpam-5903	164	4	′	′	NUM
ejpam-5903	164	5	)	)	PUNCT
ejpam-5903	164	6	for	for	ADP
ejpam-5903	164	7	every	every	DET
ejpam-5903	164	8	k	k	PROPN
ejpam-5903	164	9	∈	∈	PROPN
ejpam-5903	164	10	{	{	PUNCT
ejpam-5903	164	11	r	r	NOUN
ejpam-5903	164	12	+	+	PROPN
ejpam-5903	164	13	1	1	NUM
ejpam-5903	164	14	,	,	PUNCT
ejpam-5903	164	15	·	·	PUNCT
ejpam-5903	164	16	·	·	PUNCT
ejpam-5903	164	17	·	·	PUNCT
ejpam-5903	164	18	,	,	PUNCT
ejpam-5903	164	19	γhg(g)−	γhg(g)−	VERB
ejpam-5903	164	20	1	1	NUM
ejpam-5903	164	21	}	}	PUNCT
ejpam-5903	164	22	,	,	PUNCT
ejpam-5903	164	23	where	where	SCONJ
ejpam-5903	164	24	g′	g′	NOUN
ejpam-5903	164	25	=	=	SYM
ejpam-5903	164	26	⟨v	⟨v	PUNCT
ejpam-5903	164	27	(	(	PUNCT
ejpam-5903	164	28	g	g	NOUN
ejpam-5903	164	29	)	)	PUNCT
ejpam-5903	164	30	\	\	NOUN
ejpam-5903	164	31	i(g)⟩.	i(g)⟩.	VERB
ejpam-5903	164	32	proof	proof	NOUN
ejpam-5903	164	33	.	.	PUNCT
ejpam-5903	165	1	let	let	VERB
ejpam-5903	165	2	i(g	i(g	NOUN
ejpam-5903	165	3	)	)	PUNCT
ejpam-5903	166	1	=	=	PRON
ejpam-5903	166	2	{	{	PUNCT
ejpam-5903	166	3	v1	v1	PROPN
ejpam-5903	166	4	,	,	PUNCT
ejpam-5903	166	5	v2	v2	PROPN
ejpam-5903	166	6	,	,	PUNCT
ejpam-5903	166	7	·	·	PUNCT
ejpam-5903	166	8	·	·	PUNCT
ejpam-5903	166	9	·	·	PUNCT
ejpam-5903	166	10	,	,	PUNCT
ejpam-5903	166	11	vr	vr	NOUN
ejpam-5903	166	12	}	}	PUNCT
ejpam-5903	166	13	and	and	CCONJ
ejpam-5903	166	14	let	let	VERB
ejpam-5903	166	15	s	s	PRON
ejpam-5903	166	16	be	be	AUX
ejpam-5903	166	17	a	a	DET
ejpam-5903	166	18	γhg	γhg	NOUN
ejpam-5903	166	19	-	-	PUNCT
ejpam-5903	166	20	set	set	NOUN
ejpam-5903	166	21	in	in	ADP
ejpam-5903	166	22	g.	g.	PROPN
ejpam-5903	166	23	then	then	ADV
ejpam-5903	166	24	i(g	i(g	ADV
ejpam-5903	166	25	)	)	PUNCT
ejpam-5903	167	1	⊆	⊆	NUM
ejpam-5903	167	2	s.	s.	PROPN
ejpam-5903	167	3	let	let	VERB
ejpam-5903	167	4	j	j	PROPN
ejpam-5903	167	5	∈	∈	PROPN
ejpam-5903	168	1	[	[	X
ejpam-5903	168	2	r	r	X
ejpam-5903	168	3	]	]	PUNCT
ejpam-5903	168	4	.	.	PUNCT
ejpam-5903	169	1	then	then	ADV
ejpam-5903	169	2	d	d	X
ejpam-5903	169	3	=	=	SYM
ejpam-5903	169	4	s	s	PART
ejpam-5903	169	5	\	\	X
ejpam-5903	169	6	{	{	PUNCT
ejpam-5903	169	7	v1	v1	NOUN
ejpam-5903	169	8	,	,	PUNCT
ejpam-5903	169	9	v2	v2	PROPN
ejpam-5903	169	10	,	,	PUNCT
ejpam-5903	169	11	·	·	PUNCT
ejpam-5903	169	12	·	·	PUNCT
ejpam-5903	169	13	·	·	PUNCT
ejpam-5903	169	14	,	,	PUNCT
ejpam-5903	169	15	vj	vj	INTJ
ejpam-5903	169	16	}	}	PUNCT
ejpam-5903	169	17	is	be	AUX
ejpam-5903	169	18	a	a	DET
ejpam-5903	169	19	ζhgj	ζhgj	NOUN
ejpam-5903	169	20	-set	-set	PUNCT
ejpam-5903	169	21	of	of	ADP
ejpam-5903	169	22	g	g	PROPN
ejpam-5903	169	23	and	and	CCONJ
ejpam-5903	169	24	|nhg	|nhg	ADJ
ejpam-5903	170	1	g	g	PROPN
ejpam-5903	170	2	[	[	X
ejpam-5903	170	3	d]|	d]|	X
ejpam-5903	170	4	=	=	SYM
ejpam-5903	170	5	|nhg	|nhg	PROPN
ejpam-5903	171	1	g	g	X
ejpam-5903	171	2	[	[	X
ejpam-5903	171	3	s]|	s]|	X
ejpam-5903	171	4	−	−	PROPN
ejpam-5903	172	1	|nhg	|nhg	PROPN
ejpam-5903	172	2	g	g	NOUN
ejpam-5903	172	3	[	[	X
ejpam-5903	172	4	{	{	PUNCT
ejpam-5903	172	5	v1	v1	NOUN
ejpam-5903	172	6	,	,	PUNCT
ejpam-5903	172	7	v2	v2	PROPN
ejpam-5903	172	8	,	,	PUNCT
ejpam-5903	172	9	·	·	PUNCT
ejpam-5903	172	10	·	·	PUNCT
ejpam-5903	172	11	·	·	PUNCT
ejpam-5903	172	12	,	,	PUNCT
ejpam-5903	172	13	vj}]|	vj}]|	NOUN
ejpam-5903	172	14	=	=	SYM
ejpam-5903	172	15	|v	|v	PROPN
ejpam-5903	172	16	(	(	PUNCT
ejpam-5903	172	17	g)|	g)|	PROPN
ejpam-5903	172	18	−	−	PROPN
ejpam-5903	172	19	j.	j.	PROPN
ejpam-5903	172	20	hence	hence	PROPN
ejpam-5903	172	21	,	,	PUNCT
ejpam-5903	172	22	ζhgj	ζhgj	ADV
ejpam-5903	172	23	(	(	PUNCT
ejpam-5903	172	24	g	g	NOUN
ejpam-5903	172	25	)	)	PUNCT
ejpam-5903	173	1	=	=	SYM
ejpam-5903	173	2	|v	|v	PROPN
ejpam-5903	173	3	(	(	PUNCT
ejpam-5903	173	4	g)|	g)|	INTJ
ejpam-5903	173	5	−	−	PROPN
ejpam-5903	173	6	(	(	PUNCT
ejpam-5903	173	7	|v	|v	PROPN
ejpam-5903	173	8	(	(	PUNCT
ejpam-5903	173	9	g)|	g)|	PROPN
ejpam-5903	173	10	−	−	PROPN
ejpam-5903	173	11	j	j	PROPN
ejpam-5903	173	12	)	)	PUNCT
ejpam-5903	173	13	=	=	PUNCT
ejpam-5903	174	1	j.	j.	PROPN
ejpam-5903	174	2	next	next	ADV
ejpam-5903	174	3	,	,	PUNCT
ejpam-5903	174	4	let	let	VERB
ejpam-5903	174	5	k	k	PROPN
ejpam-5903	174	6	∈	∈	PROPN
ejpam-5903	174	7	{	{	PUNCT
ejpam-5903	174	8	r	r	NOUN
ejpam-5903	174	9	+	+	PROPN
ejpam-5903	174	10	1	1	NUM
ejpam-5903	174	11	,	,	PUNCT
ejpam-5903	174	12	·	·	PUNCT
ejpam-5903	174	13	·	·	PUNCT
ejpam-5903	174	14	·	·	PUNCT
ejpam-5903	174	15	,	,	PUNCT
ejpam-5903	174	16	γhg(g	γhg(g	PROPN
ejpam-5903	174	17	)	)	PUNCT
ejpam-5903	174	18	−	−	NOUN
ejpam-5903	174	19	1	1	NUM
ejpam-5903	174	20	}	}	PUNCT
ejpam-5903	174	21	.	.	PUNCT
ejpam-5903	175	1	then	then	ADV
ejpam-5903	175	2	s0	s0	PROPN
ejpam-5903	175	3	=	=	PUNCT
ejpam-5903	175	4	s	s	PART
ejpam-5903	175	5	\	\	PROPN
ejpam-5903	175	6	i(g	i(g	NOUN
ejpam-5903	175	7	)	)	PUNCT
ejpam-5903	175	8	is	be	AUX
ejpam-5903	175	9	γhg	γhg	ADV
ejpam-5903	175	10	-	-	PUNCT
ejpam-5903	175	11	set	set	VERB
ejpam-5903	175	12	in	in	ADP
ejpam-5903	175	13	g′	g′	NOUN
ejpam-5903	175	14	=	=	SYM
ejpam-5903	175	15	⟨v	⟨v	PUNCT
ejpam-5903	175	16	(	(	PUNCT
ejpam-5903	175	17	g	g	NOUN
ejpam-5903	175	18	)	)	PUNCT
ejpam-5903	175	19	\	\	NOUN
ejpam-5903	175	20	i(g)⟩.	i(g)⟩.	VERB
ejpam-5903	175	21	hence	hence	ADV
ejpam-5903	175	22	,	,	PUNCT
ejpam-5903	175	23	γhg(g	γhg(g	PROPN
ejpam-5903	175	24	′	′	NUM
ejpam-5903	175	25	)	)	PUNCT
ejpam-5903	175	26	=	=	SYM
ejpam-5903	175	27	γhg(g	γhg(g	PROPN
ejpam-5903	175	28	)	)	PUNCT
ejpam-5903	175	29	−	−	PROPN
ejpam-5903	175	30	r.	r.	PROPN
ejpam-5903	175	31	since	since	SCONJ
ejpam-5903	175	32	k	k	PROPN
ejpam-5903	175	33	≤	≤	PROPN
ejpam-5903	175	34	γhg(g	γhg(g	PROPN
ejpam-5903	175	35	)	)	PUNCT
ejpam-5903	176	1	−	−	PROPN
ejpam-5903	176	2	1	1	NUM
ejpam-5903	176	3	,	,	PUNCT
ejpam-5903	176	4	k	k	PROPN
ejpam-5903	176	5	−	−	NOUN
ejpam-5903	176	6	r	r	NOUN
ejpam-5903	176	7	≤	≤	NUM
ejpam-5903	176	8	γhg(g	γhg(g	PROPN
ejpam-5903	176	9	)	)	PUNCT
ejpam-5903	176	10	−	−	PROPN
ejpam-5903	177	1	(	(	PUNCT
ejpam-5903	177	2	r	r	NOUN
ejpam-5903	177	3	+	+	NOUN
ejpam-5903	177	4	1	1	NUM
ejpam-5903	177	5	)	)	PUNCT
ejpam-5903	177	6	<	<	X
ejpam-5903	177	7	γhg(g	γhg(g	PROPN
ejpam-5903	177	8	)	)	PUNCT
ejpam-5903	177	9	−	−	PROPN
ejpam-5903	178	1	r.	r.	PROPN
ejpam-5903	178	2	let	let	VERB
ejpam-5903	178	3	s′	s′	PROPN
ejpam-5903	178	4	be	be	AUX
ejpam-5903	178	5	a	a	DET
ejpam-5903	178	6	ζhgk−r	ζhgk−r	NOUN
ejpam-5903	178	7	-	-	PUNCT
ejpam-5903	178	8	set	set	NOUN
ejpam-5903	178	9	of	of	ADP
ejpam-5903	178	10	g′.	g′.	PROPN
ejpam-5903	178	11	then	then	ADV
ejpam-5903	178	12	|s′|	|s′|	NOUN
ejpam-5903	178	13	=	=	SYM
ejpam-5903	178	14	(	(	PUNCT
ejpam-5903	178	15	γhg(g	γhg(g	PROPN
ejpam-5903	178	16	)	)	PUNCT
ejpam-5903	178	17	−	−	NOUN
ejpam-5903	179	1	r	r	NOUN
ejpam-5903	179	2	)	)	PUNCT
ejpam-5903	179	3	−	−	PROPN
ejpam-5903	179	4	(	(	PUNCT
ejpam-5903	179	5	k	k	NOUN
ejpam-5903	179	6	−	−	X
ejpam-5903	179	7	r	r	NOUN
ejpam-5903	179	8	)	)	PUNCT
ejpam-5903	179	9	=	=	SYM
ejpam-5903	179	10	γhg(g	γhg(g	PROPN
ejpam-5903	179	11	)	)	PUNCT
ejpam-5903	180	1	−	−	PROPN
ejpam-5903	181	1	k	k	PROPN
ejpam-5903	181	2	and	and	CCONJ
ejpam-5903	181	3	ζhgk−r(g	ζhgk−r(g	PROPN
ejpam-5903	181	4	′	′	NUM
ejpam-5903	181	5	)	)	PUNCT
ejpam-5903	182	1	=	=	PUNCT
ejpam-5903	182	2	|v	|v	PROPN
ejpam-5903	182	3	(	(	PUNCT
ejpam-5903	182	4	g′)|	g′)|	NOUN
ejpam-5903	182	5	−	−	PROPN
ejpam-5903	182	6	|nhg	|nhg	ADJ
ejpam-5903	182	7	g′	g′	NOUN
ejpam-5903	183	1	[	[	X
ejpam-5903	183	2	s′]|	s′]|	NOUN
ejpam-5903	183	3	=	=	SYM
ejpam-5903	183	4	(	(	PUNCT
ejpam-5903	183	5	|v	|v	X
ejpam-5903	183	6	(	(	PUNCT
ejpam-5903	183	7	g)|	g)|	INTJ
ejpam-5903	183	8	−	−	NOUN
ejpam-5903	183	9	r	r	NOUN
ejpam-5903	183	10	)	)	PUNCT
ejpam-5903	183	11	−	−	PROPN
ejpam-5903	184	1	|nhg	|nhg	VERB
ejpam-5903	184	2	g	g	NOUN
ejpam-5903	185	1	[	[	X
ejpam-5903	185	2	s′]|	s′]|	NOUN
ejpam-5903	185	3	.	.	PUNCT
ejpam-5903	186	1	this	this	PRON
ejpam-5903	186	2	implies	imply	VERB
ejpam-5903	186	3	that	that	SCONJ
ejpam-5903	186	4	|v	|v	PROPN
ejpam-5903	186	5	(	(	PUNCT
ejpam-5903	186	6	g)|	g)|	NOUN
ejpam-5903	186	7	−	−	PROPN
ejpam-5903	186	8	|nhg	|nhg	PROPN
ejpam-5903	186	9	g	g	NOUN
ejpam-5903	187	1	[	[	X
ejpam-5903	187	2	s′]|	s′]|	X
ejpam-5903	188	1	=	=	PUNCT
ejpam-5903	188	2	r	r	NOUN
ejpam-5903	188	3	+	+	NUM
ejpam-5903	188	4	ζhgk−r(g	ζhgk−r(g	PROPN
ejpam-5903	188	5	′	′	NUM
ejpam-5903	188	6	)	)	PUNCT
ejpam-5903	188	7	.	.	PUNCT
ejpam-5903	189	1	therefore	therefore	ADV
ejpam-5903	189	2	,	,	PUNCT
ejpam-5903	189	3	since	since	SCONJ
ejpam-5903	189	4	s′	s′	ADJ
ejpam-5903	189	5	is	be	AUX
ejpam-5903	189	6	also	also	ADV
ejpam-5903	189	7	a	a	DET
ejpam-5903	189	8	ζhgk	ζhgk	NOUN
ejpam-5903	189	9	-set	-set	ADJ
ejpam-5903	189	10	of	of	ADP
ejpam-5903	189	11	g	g	PROPN
ejpam-5903	189	12	,	,	PUNCT
ejpam-5903	189	13	ζhgk	ζhgk	NOUN
ejpam-5903	189	14	(	(	PUNCT
ejpam-5903	189	15	g	g	NOUN
ejpam-5903	189	16	)	)	PUNCT
ejpam-5903	189	17	=	=	SYM
ejpam-5903	190	1	r	r	NOUN
ejpam-5903	190	2	+	+	NUM
ejpam-5903	190	3	ζhgk−r(g	ζhgk−r(g	PROPN
ejpam-5903	190	4	′	′	NUM
ejpam-5903	190	5	)	)	PUNCT
ejpam-5903	190	6	.	.	PUNCT
ejpam-5903	191	1	theorem	theorem	ADJ
ejpam-5903	191	2	4	4	NUM
ejpam-5903	191	3	.	.	PUNCT
ejpam-5903	192	1	let	let	VERB
ejpam-5903	192	2	g	g	PRON
ejpam-5903	192	3	be	be	AUX
ejpam-5903	192	4	a	a	DET
ejpam-5903	192	5	non	non	ADJ
ejpam-5903	192	6	-	-	ADJ
ejpam-5903	192	7	trivial	trivial	ADJ
ejpam-5903	192	8	graph	graph	NOUN
ejpam-5903	192	9	of	of	ADP
ejpam-5903	192	10	order	order	NOUN
ejpam-5903	192	11	n	n	NOUN
ejpam-5903	192	12	and	and	CCONJ
ejpam-5903	192	13	let	let	VERB
ejpam-5903	192	14	k	k	PRON
ejpam-5903	192	15	be	be	AUX
ejpam-5903	192	16	a	a	DET
ejpam-5903	192	17	positive	positive	ADJ
ejpam-5903	192	18	integer	integer	NOUN
ejpam-5903	192	19	with	with	ADP
ejpam-5903	192	20	k	k	PROPN
ejpam-5903	192	21	≤	≤	PROPN
ejpam-5903	192	22	γhg(g)−	γhg(g)−	ADJ
ejpam-5903	192	23	1	1	NUM
ejpam-5903	192	24	.	.	PUNCT
ejpam-5903	193	1	then	then	ADV
ejpam-5903	193	2	ζhgk	ζhgk	NOUN
ejpam-5903	193	3	(	(	PUNCT
ejpam-5903	193	4	g	g	NOUN
ejpam-5903	193	5	)	)	PUNCT
ejpam-5903	193	6	≤	≤	NUM
ejpam-5903	193	7	n−	n−	NOUN
ejpam-5903	193	8	γhg(g	γhg(g	PROPN
ejpam-5903	193	9	)	)	PUNCT
ejpam-5903	194	1	+	+	CCONJ
ejpam-5903	194	2	k.	k.	PROPN
ejpam-5903	194	3	proof	proof	NOUN
ejpam-5903	194	4	.	.	PUNCT
ejpam-5903	195	1	let	let	VERB
ejpam-5903	195	2	k	k	PRON
ejpam-5903	195	3	be	be	AUX
ejpam-5903	195	4	a	a	DET
ejpam-5903	195	5	positive	positive	ADJ
ejpam-5903	195	6	integer	integer	NOUN
ejpam-5903	195	7	with	with	ADP
ejpam-5903	195	8	k	k	PROPN
ejpam-5903	195	9	≤	≤	NUM
ejpam-5903	195	10	γhg(g	γhg(g	PROPN
ejpam-5903	195	11	)	)	PUNCT
ejpam-5903	195	12	−	−	NOUN
ejpam-5903	195	13	1	1	NUM
ejpam-5903	195	14	and	and	CCONJ
ejpam-5903	195	15	let	let	VERB
ejpam-5903	195	16	s	s	PRON
ejpam-5903	195	17	be	be	AUX
ejpam-5903	195	18	a	a	DET
ejpam-5903	195	19	ζhgk	ζhgk	NOUN
ejpam-5903	195	20	-set	-set	ADJ
ejpam-5903	195	21	of	of	ADP
ejpam-5903	195	22	g.	g.	PROPN
ejpam-5903	195	23	then	then	ADV
ejpam-5903	195	24	|s|	|s|	PROPN
ejpam-5903	195	25	=	=	SYM
ejpam-5903	195	26	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	195	27	k	k	PROPN
ejpam-5903	195	28	and	and	CCONJ
ejpam-5903	195	29	ζhgk	ζhgk	NOUN
ejpam-5903	195	30	(	(	PUNCT
ejpam-5903	195	31	g	g	NOUN
ejpam-5903	195	32	)	)	PUNCT
ejpam-5903	195	33	=	=	SYM
ejpam-5903	195	34	n−	n−	NOUN
ejpam-5903	195	35	|nhg	|nhg	VERB
ejpam-5903	195	36	g	g	PROPN
ejpam-5903	195	37	[	[	X
ejpam-5903	195	38	s]|	s]|	PROPN
ejpam-5903	195	39	.	.	PUNCT
ejpam-5903	196	1	since	since	SCONJ
ejpam-5903	196	2	s	s	NOUN
ejpam-5903	196	3	⊆	⊆	NUM
ejpam-5903	196	4	nhg	nhg	NOUN
ejpam-5903	196	5	g	g	PROPN
ejpam-5903	196	6	[	[	X
ejpam-5903	196	7	s	s	X
ejpam-5903	196	8	]	]	X
ejpam-5903	196	9	,	,	PUNCT
ejpam-5903	196	10	it	it	PRON
ejpam-5903	196	11	follows	follow	VERB
ejpam-5903	196	12	that	that	SCONJ
ejpam-5903	196	13	ζhgk	ζhgk	NOUN
ejpam-5903	196	14	(	(	PUNCT
ejpam-5903	196	15	g	g	NOUN
ejpam-5903	196	16	)	)	PUNCT
ejpam-5903	197	1	=	=	SYM
ejpam-5903	197	2	n−	n−	NOUN
ejpam-5903	197	3	|nhg	|nhg	VERB
ejpam-5903	197	4	g	g	NOUN
ejpam-5903	198	1	[	[	X
ejpam-5903	198	2	s]|	s]|	X
ejpam-5903	198	3	≤	≤	NUM
ejpam-5903	198	4	n−	n−	NOUN
ejpam-5903	198	5	|s|	|s|	NOUN
ejpam-5903	198	6	=	=	SYM
ejpam-5903	198	7	n−	n−	PROPN
ejpam-5903	198	8	(	(	PUNCT
ejpam-5903	198	9	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	198	10	k	k	PROPN
ejpam-5903	198	11	)	)	PUNCT
ejpam-5903	198	12	=	=	PUNCT
ejpam-5903	198	13	n−	n−	NOUN
ejpam-5903	198	14	γhg(g	γhg(g	PROPN
ejpam-5903	198	15	)	)	PUNCT
ejpam-5903	199	1	+	+	CCONJ
ejpam-5903	199	2	k.	k.	NOUN
ejpam-5903	199	3	this	this	PRON
ejpam-5903	199	4	proves	prove	VERB
ejpam-5903	199	5	the	the	DET
ejpam-5903	199	6	assertion	assertion	NOUN
ejpam-5903	199	7	.	.	PUNCT
ejpam-5903	200	1	remark	remark	NOUN
ejpam-5903	200	2	2	2	NUM
ejpam-5903	200	3	.	.	PUNCT
ejpam-5903	201	1	the	the	DET
ejpam-5903	201	2	bound	bind	VERB
ejpam-5903	201	3	in	in	ADP
ejpam-5903	201	4	theorem	theorem	NOUN
ejpam-5903	201	5	4	4	NUM
ejpam-5903	201	6	is	be	AUX
ejpam-5903	201	7	sharp	sharp	ADJ
ejpam-5903	201	8	.	.	PUNCT
ejpam-5903	202	1	strict	strict	ADJ
ejpam-5903	202	2	inequality	inequality	NOUN
ejpam-5903	202	3	is	be	AUX
ejpam-5903	202	4	also	also	ADV
ejpam-5903	202	5	possible	possible	ADJ
ejpam-5903	202	6	.	.	PUNCT
ejpam-5903	203	1	to	to	PART
ejpam-5903	203	2	see	see	VERB
ejpam-5903	203	3	this	this	PRON
ejpam-5903	203	4	,	,	PUNCT
ejpam-5903	203	5	consider	consider	VERB
ejpam-5903	203	6	the	the	DET
ejpam-5903	203	7	graph	graph	NOUN
ejpam-5903	203	8	g	g	PROPN
ejpam-5903	203	9	=	=	PROPN
ejpam-5903	203	10	c5	c5	PROPN
ejpam-5903	203	11	in	in	ADP
ejpam-5903	203	12	figure	figure	NOUN
ejpam-5903	203	13	2	2	NUM
ejpam-5903	203	14	.	.	PUNCT
ejpam-5903	203	15	by	by	ADP
ejpam-5903	203	16	theorem	theorem	NOUN
ejpam-5903	203	17	1(ii	1(ii	NUM
ejpam-5903	203	18	)	)	PUNCT
ejpam-5903	203	19	,	,	PUNCT
ejpam-5903	203	20	γhg(g	γhg(g	PROPN
ejpam-5903	203	21	)	)	PUNCT
ejpam-5903	203	22	=	=	SYM
ejpam-5903	204	1	3	3	X
ejpam-5903	204	2	.	.	PUNCT
ejpam-5903	204	3	let	let	VERB
ejpam-5903	204	4	k	k	NOUN
ejpam-5903	205	1	=	=	SYM
ejpam-5903	205	2	1	1	X
ejpam-5903	205	3	.	.	PUNCT
ejpam-5903	206	1	then	then	ADV
ejpam-5903	206	2	any	any	DET
ejpam-5903	206	3	set	set	NOUN
ejpam-5903	206	4	s1	s1	NOUN
ejpam-5903	206	5	⊆	⊆	NUM
ejpam-5903	206	6	v	v	NOUN
ejpam-5903	206	7	(	(	PUNCT
ejpam-5903	206	8	g	g	NOUN
ejpam-5903	206	9	)	)	PUNCT
ejpam-5903	206	10	with	with	ADP
ejpam-5903	206	11	|s1|	|s1|	NOUN
ejpam-5903	206	12	=	=	SYM
ejpam-5903	206	13	2	2	NUM
ejpam-5903	206	14	is	be	AUX
ejpam-5903	206	15	a	a	DET
ejpam-5903	206	16	ζhg1	ζhg1	NOUN
ejpam-5903	206	17	-set	-set	PUNCT
ejpam-5903	206	18	of	of	ADP
ejpam-5903	206	19	g	g	PROPN
ejpam-5903	206	20	and	and	CCONJ
ejpam-5903	206	21	nhg	nhg	VERB
ejpam-5903	206	22	g	g	PROPN
ejpam-5903	207	1	[	[	X
ejpam-5903	207	2	s1	s1	X
ejpam-5903	207	3	]	]	X
ejpam-5903	207	4	=	=	SYM
ejpam-5903	207	5	s1	s1	PROPN
ejpam-5903	207	6	.	.	PUNCT
ejpam-5903	208	1	j.	j.	PROPN
ejpam-5903	208	2	anoche	anoche	PROPN
ejpam-5903	208	3	,	,	PUNCT
ejpam-5903	208	4	s.	s.	PROPN
ejpam-5903	208	5	canoy	canoy	PROPN
ejpam-5903	208	6	,	,	PUNCT
ejpam-5903	208	7	jr	jr	PROPN
ejpam-5903	208	8	.	.	PROPN
ejpam-5903	208	9	/	/	SYM
ejpam-5903	208	10	eur	eur	PROPN
ejpam-5903	208	11	.	.	PUNCT
ejpam-5903	209	1	j.	j.	PROPN
ejpam-5903	209	2	pure	pure	PROPN
ejpam-5903	209	3	appl	appl	PROPN
ejpam-5903	209	4	.	.	PROPN
ejpam-5903	209	5	math	math	PROPN
ejpam-5903	209	6	,	,	PUNCT
ejpam-5903	209	7	18	18	NUM
ejpam-5903	209	8	(	(	PUNCT
ejpam-5903	209	9	2	2	NUM
ejpam-5903	209	10	)	)	PUNCT
ejpam-5903	209	11	(	(	PUNCT
ejpam-5903	209	12	2025	2025	NUM
ejpam-5903	209	13	)	)	PUNCT
ejpam-5903	209	14	,	,	PUNCT
ejpam-5903	209	15	5903	5903	NUM
ejpam-5903	209	16	7	7	NUM
ejpam-5903	209	17	of	of	ADP
ejpam-5903	209	18	17	17	NUM
ejpam-5903	209	19	thus	thus	ADV
ejpam-5903	209	20	,	,	PUNCT
ejpam-5903	209	21	ζhg1	ζhg1	PROPN
ejpam-5903	209	22	(	(	PUNCT
ejpam-5903	209	23	g	g	NOUN
ejpam-5903	209	24	)	)	PUNCT
ejpam-5903	209	25	=	=	SYM
ejpam-5903	210	1	|v	|v	PROPN
ejpam-5903	210	2	(	(	PUNCT
ejpam-5903	210	3	g)|	g)|	INTJ
ejpam-5903	210	4	−	−	PROPN
ejpam-5903	210	5	γhg(g	γhg(g	PROPN
ejpam-5903	210	6	)	)	PUNCT
ejpam-5903	211	1	+	+	CCONJ
ejpam-5903	212	1	k	k	X
ejpam-5903	212	2	=	=	SYM
ejpam-5903	212	3	5−	5−	NUM
ejpam-5903	212	4	3	3	NUM
ejpam-5903	212	5	+	+	CCONJ
ejpam-5903	212	6	1	1	NUM
ejpam-5903	212	7	=	=	SYM
ejpam-5903	212	8	3	3	X
ejpam-5903	212	9	.	.	PUNCT
ejpam-5903	213	1	if	if	SCONJ
ejpam-5903	213	2	k	k	PROPN
ejpam-5903	213	3	=	=	SYM
ejpam-5903	213	4	2	2	NUM
ejpam-5903	213	5	,	,	PUNCT
ejpam-5903	213	6	then	then	ADV
ejpam-5903	213	7	any	any	DET
ejpam-5903	213	8	1	1	NUM
ejpam-5903	213	9	-	-	PUNCT
ejpam-5903	213	10	element	element	NOUN
ejpam-5903	213	11	subset	subset	NOUN
ejpam-5903	213	12	s2	s2	NOUN
ejpam-5903	213	13	is	be	AUX
ejpam-5903	213	14	a	a	DET
ejpam-5903	213	15	ζhg2	ζhg2	PROPN
ejpam-5903	213	16	-set	-set	PUNCT
ejpam-5903	213	17	of	of	ADP
ejpam-5903	213	18	g	g	PROPN
ejpam-5903	213	19	and	and	CCONJ
ejpam-5903	213	20	nhg	nhg	VERB
ejpam-5903	213	21	g	g	PROPN
ejpam-5903	214	1	[	[	X
ejpam-5903	214	2	s2	s2	X
ejpam-5903	214	3	]	]	X
ejpam-5903	214	4	=	=	SYM
ejpam-5903	214	5	s2	s2	PROPN
ejpam-5903	214	6	.	.	PUNCT
ejpam-5903	215	1	thus	thus	ADV
ejpam-5903	215	2	,	,	PUNCT
ejpam-5903	215	3	ζhg2	ζhg2	PROPN
ejpam-5903	215	4	(	(	PUNCT
ejpam-5903	215	5	g	g	NOUN
ejpam-5903	215	6	)	)	PUNCT
ejpam-5903	215	7	=	=	SYM
ejpam-5903	215	8	5	5	NUM
ejpam-5903	215	9	−	−	NOUN
ejpam-5903	215	10	1	1	NUM
ejpam-5903	215	11	=	=	SYM
ejpam-5903	215	12	4	4	NUM
ejpam-5903	215	13	.	.	PUNCT
ejpam-5903	216	1	since	since	SCONJ
ejpam-5903	216	2	|v	|v	PROPN
ejpam-5903	216	3	(	(	PUNCT
ejpam-5903	216	4	g)|	g)|	INTJ
ejpam-5903	216	5	−	−	PROPN
ejpam-5903	216	6	γhg(g	γhg(g	PROPN
ejpam-5903	216	7	)	)	PUNCT
ejpam-5903	217	1	+	+	CCONJ
ejpam-5903	218	1	k	k	X
ejpam-5903	218	2	=	=	SYM
ejpam-5903	218	3	5	5	NUM
ejpam-5903	218	4	−	−	NOUN
ejpam-5903	218	5	3	3	NUM
ejpam-5903	218	6	+	+	CCONJ
ejpam-5903	218	7	k	k	NOUN
ejpam-5903	218	8	=	=	SYM
ejpam-5903	218	9	4	4	NUM
ejpam-5903	218	10	,	,	PUNCT
ejpam-5903	218	11	the	the	DET
ejpam-5903	218	12	equality	equality	NOUN
ejpam-5903	218	13	ζhgk	ζhgk	NOUN
ejpam-5903	218	14	(	(	PUNCT
ejpam-5903	218	15	c5	c5	PROPN
ejpam-5903	218	16	)	)	PUNCT
ejpam-5903	219	1	=	=	NUM
ejpam-5903	219	2	n−	n−	NOUN
ejpam-5903	219	3	γhg(c5	γhg(c5	PROPN
ejpam-5903	219	4	)	)	PUNCT
ejpam-5903	220	1	+	+	CCONJ
ejpam-5903	220	2	k	k	PROPN
ejpam-5903	220	3	holds	hold	VERB
ejpam-5903	220	4	.	.	PUNCT
ejpam-5903	220	5	..............	..............	PUNCT
ejpam-5903	220	6	.............	.............	PUNCT
ejpam-5903	220	7	.............	.............	PUNCT
ejpam-5903	220	8	.............	.............	PUNCT
ejpam-5903	220	9	.............	.............	PUNCT
ejpam-5903	220	10	.............	.............	PUNCT
ejpam-5903	220	11	.............	.............	PUNCT
ejpam-5903	220	12	.............	.............	PUNCT
ejpam-5903	220	13	.............	.............	PUNCT
ejpam-5903	220	14	.............	.............	PUNCT
ejpam-5903	220	15	..	..	PUNCT
ejpam-5903	220	16	....................................	....................................	PUNCT
ejpam-5903	220	17	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-5903	220	18	....................................	....................................	PUNCT
ejpam-5903	220	19	...........	...........	PUNCT
ejpam-5903	220	20	..........	..........	PUNCT
ejpam-5903	221	1	..........	..........	PUNCT
ejpam-5903	221	2	..........	..........	PUNCT
ejpam-5903	222	1	..........	..........	PUNCT
ejpam-5903	222	2	..........	..........	PUNCT
ejpam-5903	223	1	..........	..........	PUNCT
ejpam-5903	223	2	..........	..........	PUNCT
ejpam-5903	224	1	..........	..........	PUNCT
ejpam-5903	224	2	..	..	PUNCT
ejpam-5903	224	3	..	..	PUNCT
ejpam-5903	224	4	..................................	..................................	PUNCT
ejpam-5903	225	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-5903	225	2	....................................	....................................	PUNCT
ejpam-5903	226	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-5903	226	2	....................................	....................................	PUNCT
ejpam-5903	227	1	....................................	....................................	PUNCT
ejpam-5903	228	1	a	a	DET
ejpam-5903	228	2	b	b	X
ejpam-5903	228	3	c	c	X
ejpam-5903	228	4	de	de	X
ejpam-5903	228	5	figure	figure	NOUN
ejpam-5903	228	6	2	2	NUM
ejpam-5903	228	7	:	:	PUNCT
ejpam-5903	228	8	g	g	PROPN
ejpam-5903	228	9	=	=	PROPN
ejpam-5903	228	10	c5	c5	PROPN
ejpam-5903	228	11	and	and	CCONJ
ejpam-5903	228	12	γhg(g	γhg(g	PROPN
ejpam-5903	228	13	)	)	PUNCT
ejpam-5903	228	14	=	=	SYM
ejpam-5903	228	15	3	3	NUM
ejpam-5903	228	16	for	for	ADP
ejpam-5903	228	17	strict	strict	ADJ
ejpam-5903	228	18	inequality	inequality	NOUN
ejpam-5903	228	19	,	,	PUNCT
ejpam-5903	228	20	consider	consider	VERB
ejpam-5903	228	21	h	h	NOUN
ejpam-5903	228	22	=	=	PUNCT
ejpam-5903	228	23	p10	p10	NOUN
ejpam-5903	228	24	in	in	ADP
ejpam-5903	228	25	figure	figure	NOUN
ejpam-5903	228	26	3	3	NUM
ejpam-5903	228	27	.	.	PUNCT
ejpam-5903	229	1	by	by	ADP
ejpam-5903	229	2	theorem	theorem	NOUN
ejpam-5903	229	3	1(i	1(i	NUM
ejpam-5903	229	4	)	)	PUNCT
ejpam-5903	229	5	,	,	PUNCT
ejpam-5903	229	6	γhg(h	γhg(h	PROPN
ejpam-5903	229	7	)	)	PUNCT
ejpam-5903	229	8	=	=	SYM
ejpam-5903	229	9	4	4	X
ejpam-5903	229	10	.	.	PUNCT
ejpam-5903	229	11	let	let	VERB
ejpam-5903	229	12	p10	p10	NOUN
ejpam-5903	229	13	=	=	PUNCT
ejpam-5903	230	1	[	[	X
ejpam-5903	230	2	v1	v1	NOUN
ejpam-5903	230	3	,	,	PUNCT
ejpam-5903	230	4	v2	v2	PROPN
ejpam-5903	230	5	,	,	PUNCT
ejpam-5903	230	6	·	·	PUNCT
ejpam-5903	230	7	·	·	PUNCT
ejpam-5903	230	8	·	·	PUNCT
ejpam-5903	230	9	,	,	PUNCT
ejpam-5903	230	10	v10	v10	PROPN
ejpam-5903	230	11	]	]	PUNCT
ejpam-5903	230	12	and	and	CCONJ
ejpam-5903	230	13	let	let	VERB
ejpam-5903	230	14	k	k	NOUN
ejpam-5903	230	15	=	=	NOUN
ejpam-5903	230	16	1	1	X
ejpam-5903	230	17	.	.	PUNCT
ejpam-5903	231	1	it	it	PRON
ejpam-5903	231	2	can	can	AUX
ejpam-5903	231	3	easily	easily	ADV
ejpam-5903	231	4	be	be	AUX
ejpam-5903	231	5	verified	verify	VERB
ejpam-5903	231	6	that	that	SCONJ
ejpam-5903	231	7	s1	s1	NOUN
ejpam-5903	231	8	=	=	PUNCT
ejpam-5903	231	9	{	{	PUNCT
ejpam-5903	231	10	v1	v1	PROPN
ejpam-5903	231	11	,	,	PUNCT
ejpam-5903	231	12	v4	v4	NOUN
ejpam-5903	231	13	,	,	PUNCT
ejpam-5903	231	14	v7	v7	NOUN
ejpam-5903	231	15	}	}	PUNCT
ejpam-5903	231	16	is	be	AUX
ejpam-5903	231	17	a	a	DET
ejpam-5903	231	18	ζhg1	ζhg1	NOUN
ejpam-5903	231	19	-set	-set	PUNCT
ejpam-5903	231	20	of	of	ADP
ejpam-5903	231	21	h	h	PROPN
ejpam-5903	231	22	and	and	CCONJ
ejpam-5903	231	23	nhg	nhg	PROPN
ejpam-5903	231	24	h	h	NOUN
ejpam-5903	232	1	[	[	X
ejpam-5903	232	2	s1	s1	X
ejpam-5903	232	3	]	]	X
ejpam-5903	232	4	=	=	SYM
ejpam-5903	232	5	{	{	PUNCT
ejpam-5903	232	6	v1	v1	PROPN
ejpam-5903	232	7	,	,	PUNCT
ejpam-5903	232	8	v2	v2	PROPN
ejpam-5903	232	9	,	,	PUNCT
ejpam-5903	232	10	v3	v3	PROPN
ejpam-5903	232	11	,	,	PUNCT
ejpam-5903	232	12	·	·	PUNCT
ejpam-5903	232	13	·	·	PUNCT
ejpam-5903	232	14	·	·	PUNCT
ejpam-5903	232	15	,	,	PUNCT
ejpam-5903	232	16	v7	v7	VERB
ejpam-5903	232	17	}	}	PUNCT
ejpam-5903	232	18	.	.	PUNCT
ejpam-5903	233	1	hence	hence	ADV
ejpam-5903	233	2	,	,	PUNCT
ejpam-5903	233	3	ζhg1	ζhg1	PROPN
ejpam-5903	233	4	(	(	PUNCT
ejpam-5903	233	5	h	h	NOUN
ejpam-5903	233	6	)	)	PUNCT
ejpam-5903	233	7	=	=	NOUN
ejpam-5903	233	8	10−	10−	NOUN
ejpam-5903	233	9	7	7	NUM
ejpam-5903	233	10	=	=	SYM
ejpam-5903	233	11	3	3	NUM
ejpam-5903	233	12	<	<	SYM
ejpam-5903	233	13	7	7	NUM
ejpam-5903	233	14	=	=	SYM
ejpam-5903	233	15	|v	|v	X
ejpam-5903	233	16	(	(	PUNCT
ejpam-5903	233	17	h)|	h)|	NOUN
ejpam-5903	233	18	−	−	PROPN
ejpam-5903	233	19	γhg(h	γhg(h	PROPN
ejpam-5903	233	20	)	)	PUNCT
ejpam-5903	234	1	+	+	CCONJ
ejpam-5903	234	2	k.	k.	NOUN
ejpam-5903	235	1	if	if	SCONJ
ejpam-5903	235	2	k	k	PROPN
ejpam-5903	235	3	=	=	SYM
ejpam-5903	235	4	2	2	NUM
ejpam-5903	235	5	,	,	PUNCT
ejpam-5903	235	6	then	then	ADV
ejpam-5903	235	7	s2	s2	VERB
ejpam-5903	235	8	=	=	SYM
ejpam-5903	235	9	{	{	PUNCT
ejpam-5903	235	10	v1	v1	PROPN
ejpam-5903	235	11	,	,	PUNCT
ejpam-5903	235	12	v4	v4	PROPN
ejpam-5903	235	13	}	}	PUNCT
ejpam-5903	235	14	is	be	AUX
ejpam-5903	235	15	a	a	DET
ejpam-5903	235	16	ζhg2	ζhg2	PROPN
ejpam-5903	235	17	-set	-set	PUNCT
ejpam-5903	235	18	of	of	ADP
ejpam-5903	235	19	h	h	PROPN
ejpam-5903	235	20	and	and	CCONJ
ejpam-5903	235	21	nhg	nhg	PROPN
ejpam-5903	235	22	h	h	PROPN
ejpam-5903	236	1	[	[	X
ejpam-5903	236	2	s2	s2	X
ejpam-5903	236	3	]	]	X
ejpam-5903	236	4	=	=	SYM
ejpam-5903	236	5	{	{	PUNCT
ejpam-5903	236	6	v1	v1	PROPN
ejpam-5903	236	7	,	,	PUNCT
ejpam-5903	236	8	v2	v2	PROPN
ejpam-5903	236	9	,	,	PUNCT
ejpam-5903	236	10	v3	v3	PROPN
ejpam-5903	236	11	,	,	PUNCT
ejpam-5903	236	12	v4	v4	PROPN
ejpam-5903	236	13	}	}	PUNCT
ejpam-5903	236	14	.	.	PUNCT
ejpam-5903	237	1	this	this	PRON
ejpam-5903	237	2	implies	imply	VERB
ejpam-5903	237	3	that	that	SCONJ
ejpam-5903	237	4	ζhg2	ζhg2	PROPN
ejpam-5903	237	5	(	(	PUNCT
ejpam-5903	237	6	h	h	NOUN
ejpam-5903	237	7	)	)	PUNCT
ejpam-5903	237	8	=	=	PUNCT
ejpam-5903	237	9	6	6	NUM
ejpam-5903	237	10	<	<	SYM
ejpam-5903	237	11	8	8	NUM
ejpam-5903	237	12	=	=	SYM
ejpam-5903	237	13	|v	|v	X
ejpam-5903	237	14	(	(	PUNCT
ejpam-5903	237	15	h)|	h)|	NOUN
ejpam-5903	237	16	−	−	PROPN
ejpam-5903	237	17	γhg(h	γhg(h	PROPN
ejpam-5903	237	18	)	)	PUNCT
ejpam-5903	237	19	+	+	CCONJ
ejpam-5903	237	20	k.	k.	PROPN
ejpam-5903	237	21	................................................................................................................	................................................................................................................	PROPN
ejpam-5903	237	22	................................................................................................................	................................................................................................................	PROPN
ejpam-5903	238	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	238	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	239	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	239	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	240	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	240	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	241	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5903	242	1	....................................	....................................	PUNCT
ejpam-5903	243	1	v1	v1	VERB
ejpam-5903	243	2	v2	v2	PROPN
ejpam-5903	243	3	v3	v3	PROPN
ejpam-5903	243	4	v4	v4	PROPN
ejpam-5903	243	5	v5	v5	PROPN
ejpam-5903	243	6	v6	v6	NOUN
ejpam-5903	243	7	v7	v7	VERB
ejpam-5903	243	8	v8	v8	PROPN
ejpam-5903	243	9	v9	v9	PROPN
ejpam-5903	243	10	v10	v10	NOUN
ejpam-5903	243	11	figure	figure	NOUN
ejpam-5903	243	12	3	3	NUM
ejpam-5903	243	13	:	:	PUNCT
ejpam-5903	243	14	h	h	NOUN
ejpam-5903	243	15	=	=	PUNCT
ejpam-5903	243	16	p10	p10	PROPN
ejpam-5903	243	17	and	and	CCONJ
ejpam-5903	243	18	γhg(h	γhg(h	PROPN
ejpam-5903	243	19	)	)	PUNCT
ejpam-5903	243	20	=	=	SYM
ejpam-5903	243	21	4	4	NUM
ejpam-5903	243	22	theorem	theorem	NOUN
ejpam-5903	243	23	5	5	NUM
ejpam-5903	243	24	.	.	PUNCT
ejpam-5903	244	1	let	let	VERB
ejpam-5903	244	2	g	g	PRON
ejpam-5903	244	3	be	be	AUX
ejpam-5903	244	4	a	a	DET
ejpam-5903	244	5	graph	graph	NOUN
ejpam-5903	244	6	of	of	ADP
ejpam-5903	244	7	order	order	NOUN
ejpam-5903	244	8	n	n	PRON
ejpam-5903	244	9	≥	≥	NOUN
ejpam-5903	244	10	2	2	NUM
ejpam-5903	244	11	and	and	CCONJ
ejpam-5903	244	12	k	k	PROPN
ejpam-5903	244	13	≤	≤	NUM
ejpam-5903	244	14	γhg(g)−1	γhg(g)−1	NOUN
ejpam-5903	244	15	,	,	PUNCT
ejpam-5903	244	16	then	then	ADV
ejpam-5903	244	17	1	1	NUM
ejpam-5903	244	18	≤	≤	NOUN
ejpam-5903	244	19	ζhgk	ζhgk	NOUN
ejpam-5903	244	20	(	(	PUNCT
ejpam-5903	244	21	g	g	NOUN
ejpam-5903	244	22	)	)	PUNCT
ejpam-5903	244	23	≤	≤	NOUN
ejpam-5903	245	1	n−1	n−1	PROPN
ejpam-5903	245	2	.	.	PUNCT
ejpam-5903	245	3	proof	proof	NOUN
ejpam-5903	245	4	.	.	PUNCT
ejpam-5903	246	1	let	let	VERB
ejpam-5903	246	2	s	s	PRON
ejpam-5903	246	3	be	be	AUX
ejpam-5903	246	4	a	a	DET
ejpam-5903	246	5	ζhgk	ζhgk	NOUN
ejpam-5903	246	6	-set	-set	ADJ
ejpam-5903	246	7	of	of	ADP
ejpam-5903	246	8	g.	g.	PROPN
ejpam-5903	246	9	then	then	ADV
ejpam-5903	246	10	|s|	|s|	PROPN
ejpam-5903	246	11	=	=	SYM
ejpam-5903	246	12	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	246	13	k.	k.	PROPN
ejpam-5903	246	14	hence	hence	ADV
ejpam-5903	246	15	,	,	PUNCT
ejpam-5903	246	16	v	v	X
ejpam-5903	246	17	(	(	PUNCT
ejpam-5903	246	18	g	g	NOUN
ejpam-5903	246	19	)	)	PUNCT
ejpam-5903	247	1	\nhg	\nhg	ADP
ejpam-5903	247	2	g	g	NOUN
ejpam-5903	247	3	[	[	X
ejpam-5903	247	4	s	s	X
ejpam-5903	247	5	]	]	X
ejpam-5903	247	6	̸=	̸=	PROPN
ejpam-5903	247	7	∅.	∅.	NOUN
ejpam-5903	247	8	it	it	PRON
ejpam-5903	247	9	follows	follow	VERB
ejpam-5903	247	10	that	that	SCONJ
ejpam-5903	247	11	ζhgk	ζhgk	NOUN
ejpam-5903	247	12	(	(	PUNCT
ejpam-5903	247	13	g	g	NOUN
ejpam-5903	247	14	)	)	PUNCT
ejpam-5903	248	1	=	=	SYM
ejpam-5903	248	2	|v	|v	PROPN
ejpam-5903	248	3	(	(	PUNCT
ejpam-5903	248	4	g)|	g)|	NOUN
ejpam-5903	248	5	−	−	PROPN
ejpam-5903	248	6	|nhg	|nhg	PROPN
ejpam-5903	248	7	g	g	NOUN
ejpam-5903	248	8	[	[	X
ejpam-5903	248	9	s]|	s]|	PROPN
ejpam-5903	248	10	≥	≥	NUM
ejpam-5903	248	11	1	1	NUM
ejpam-5903	248	12	.	.	PUNCT
ejpam-5903	249	1	also	also	ADV
ejpam-5903	249	2	,	,	PUNCT
ejpam-5903	249	3	since	since	SCONJ
ejpam-5903	249	4	|nhg	|nhg	PROPN
ejpam-5903	249	5	g	g	PROPN
ejpam-5903	250	1	[	[	X
ejpam-5903	250	2	s]|	s]|	PROPN
ejpam-5903	250	3	≥	≥	NUM
ejpam-5903	250	4	1	1	NUM
ejpam-5903	250	5	,	,	PUNCT
ejpam-5903	250	6	ζhgk	ζhgk	NOUN
ejpam-5903	250	7	(	(	PUNCT
ejpam-5903	250	8	g	g	NOUN
ejpam-5903	250	9	)	)	PUNCT
ejpam-5903	250	10	=	=	SYM
ejpam-5903	250	11	|v	|v	PROPN
ejpam-5903	250	12	(	(	PUNCT
ejpam-5903	250	13	g)|	g)|	NOUN
ejpam-5903	250	14	−	−	PROPN
ejpam-5903	250	15	|nhg	|nhg	PROPN
ejpam-5903	250	16	g	g	NOUN
ejpam-5903	250	17	[	[	X
ejpam-5903	250	18	s]|	s]|	X
ejpam-5903	250	19	≤	≤	NUM
ejpam-5903	250	20	n−	n−	PROPN
ejpam-5903	250	21	1	1	NUM
ejpam-5903	250	22	.	.	PUNCT
ejpam-5903	251	1	this	this	PRON
ejpam-5903	251	2	proves	prove	VERB
ejpam-5903	251	3	the	the	DET
ejpam-5903	251	4	assertion	assertion	NOUN
ejpam-5903	251	5	.	.	PUNCT
ejpam-5903	252	1	theorem	theorem	ADJ
ejpam-5903	252	2	6	6	NUM
ejpam-5903	252	3	.	.	PUNCT
ejpam-5903	253	1	let	let	VERB
ejpam-5903	253	2	g	g	PRON
ejpam-5903	253	3	be	be	AUX
ejpam-5903	253	4	a	a	DET
ejpam-5903	253	5	non	non	ADJ
ejpam-5903	253	6	-	-	ADJ
ejpam-5903	253	7	trivial	trivial	ADJ
ejpam-5903	253	8	graph	graph	NOUN
ejpam-5903	253	9	of	of	ADP
ejpam-5903	253	10	order	order	NOUN
ejpam-5903	253	11	n.	n.	NOUN
ejpam-5903	253	12	then	then	ADV
ejpam-5903	253	13	ζhg1	ζhg1	PROPN
ejpam-5903	253	14	(	(	PUNCT
ejpam-5903	253	15	g	g	NOUN
ejpam-5903	253	16	)	)	PUNCT
ejpam-5903	253	17	=	=	SYM
ejpam-5903	253	18	1	1	NUM
ejpam-5903	253	19	if	if	SCONJ
ejpam-5903	253	20	and	and	CCONJ
ejpam-5903	253	21	only	only	ADV
ejpam-5903	253	22	if	if	SCONJ
ejpam-5903	253	23	there	there	PRON
ejpam-5903	253	24	exists	exist	VERB
ejpam-5903	253	25	v	v	ADP
ejpam-5903	253	26	∈	∈	PROPN
ejpam-5903	253	27	v	v	NOUN
ejpam-5903	253	28	(	(	PUNCT
ejpam-5903	253	29	g	g	NOUN
ejpam-5903	253	30	)	)	PUNCT
ejpam-5903	253	31	such	such	ADJ
ejpam-5903	253	32	that	that	SCONJ
ejpam-5903	253	33	γhg(g−	γhg(g−	PROPN
ejpam-5903	253	34	v	v	NOUN
ejpam-5903	253	35	)	)	PUNCT
ejpam-5903	253	36	=	=	PUNCT
ejpam-5903	253	37	γhg(g)−	γhg(g)−	ADJ
ejpam-5903	253	38	1	1	NUM
ejpam-5903	253	39	.	.	PUNCT
ejpam-5903	254	1	proof	proof	NOUN
ejpam-5903	254	2	.	.	PUNCT
ejpam-5903	255	1	suppose	suppose	VERB
ejpam-5903	255	2	ζhg1	ζhg1	PROPN
ejpam-5903	255	3	(	(	PUNCT
ejpam-5903	255	4	g	g	NOUN
ejpam-5903	255	5	)	)	PUNCT
ejpam-5903	255	6	=	=	SYM
ejpam-5903	255	7	1	1	NUM
ejpam-5903	255	8	and	and	CCONJ
ejpam-5903	255	9	let	let	VERB
ejpam-5903	255	10	s	s	PRON
ejpam-5903	255	11	be	be	AUX
ejpam-5903	255	12	a	a	DET
ejpam-5903	255	13	ζhg1	ζhg1	NOUN
ejpam-5903	255	14	-set	-set	PUNCT
ejpam-5903	255	15	of	of	ADP
ejpam-5903	255	16	g.	g.	PROPN
ejpam-5903	255	17	then	then	ADV
ejpam-5903	255	18	|s|	|s|	PROPN
ejpam-5903	255	19	=	=	SYM
ejpam-5903	255	20	γhg(g	γhg(g	PROPN
ejpam-5903	255	21	)	)	PUNCT
ejpam-5903	256	1	−	−	NOUN
ejpam-5903	256	2	1	1	NUM
ejpam-5903	256	3	and	and	CCONJ
ejpam-5903	256	4	ζhgk	ζhgk	NOUN
ejpam-5903	256	5	(	(	PUNCT
ejpam-5903	256	6	g	g	NOUN
ejpam-5903	256	7	)	)	PUNCT
ejpam-5903	256	8	=	=	SYM
ejpam-5903	257	1	|v	|v	X
ejpam-5903	257	2	(	(	PUNCT
ejpam-5903	257	3	g	g	NOUN
ejpam-5903	257	4	)	)	PUNCT
ejpam-5903	257	5	\	\	NOUN
ejpam-5903	257	6	nhg	nhg	PROPN
ejpam-5903	257	7	g	g	PROPN
ejpam-5903	258	1	[	[	X
ejpam-5903	258	2	s]|	s]|	X
ejpam-5903	258	3	=	=	SYM
ejpam-5903	258	4	1	1	X
ejpam-5903	258	5	.	.	PUNCT
ejpam-5903	258	6	let	let	VERB
ejpam-5903	258	7	v	v	NUM
ejpam-5903	258	8	∈	∈	PROPN
ejpam-5903	258	9	v	v	NOUN
ejpam-5903	258	10	(	(	PUNCT
ejpam-5903	258	11	g	g	NOUN
ejpam-5903	258	12	)	)	PUNCT
ejpam-5903	258	13	\	\	NOUN
ejpam-5903	258	14	nhg	nhg	PROPN
ejpam-5903	259	1	g	g	PROPN
ejpam-5903	260	1	[	[	X
ejpam-5903	260	2	s	s	X
ejpam-5903	260	3	]	]	X
ejpam-5903	260	4	.	.	PUNCT
ejpam-5903	261	1	then	then	ADV
ejpam-5903	261	2	nhg	nhg	VERB
ejpam-5903	261	3	g	g	PROPN
ejpam-5903	262	1	[	[	X
ejpam-5903	262	2	s	s	X
ejpam-5903	262	3	]	]	X
ejpam-5903	262	4	=	=	SYM
ejpam-5903	262	5	v	v	X
ejpam-5903	262	6	(	(	PUNCT
ejpam-5903	262	7	g	g	NOUN
ejpam-5903	262	8	)	)	PUNCT
ejpam-5903	262	9	\	\	NOUN
ejpam-5903	262	10	{	{	PUNCT
ejpam-5903	262	11	v	v	NOUN
ejpam-5903	262	12	}	}	PUNCT
ejpam-5903	262	13	.	.	PUNCT
ejpam-5903	263	1	therefore	therefore	ADV
ejpam-5903	263	2	,	,	PUNCT
ejpam-5903	263	3	γhg(g−	γhg(g−	PROPN
ejpam-5903	263	4	v	v	NOUN
ejpam-5903	263	5	)	)	PUNCT
ejpam-5903	263	6	=	=	SYM
ejpam-5903	263	7	γhg	γhg	PROPN
ejpam-5903	263	8	(	(	PUNCT
ejpam-5903	263	9	〈	〈	PROPN
ejpam-5903	263	10	nhg	nhg	NOUN
ejpam-5903	263	11	g	g	PROPN
ejpam-5903	264	1	[	[	X
ejpam-5903	264	2	s	s	X
ejpam-5903	264	3	]	]	X
ejpam-5903	264	4	〉	〉	NOUN
ejpam-5903	264	5	)	)	PUNCT
ejpam-5903	265	1	=	=	PUNCT
ejpam-5903	265	2	γhg(g)−	γhg(g)−	ADJ
ejpam-5903	265	3	1	1	NUM
ejpam-5903	265	4	.	.	PUNCT
ejpam-5903	266	1	j.	j.	PROPN
ejpam-5903	266	2	anoche	anoche	PROPN
ejpam-5903	266	3	,	,	PUNCT
ejpam-5903	266	4	s.	s.	PROPN
ejpam-5903	266	5	canoy	canoy	PROPN
ejpam-5903	266	6	,	,	PUNCT
ejpam-5903	266	7	jr	jr	PROPN
ejpam-5903	266	8	.	.	PROPN
ejpam-5903	266	9	/	/	SYM
ejpam-5903	266	10	eur	eur	PROPN
ejpam-5903	266	11	.	.	PUNCT
ejpam-5903	267	1	j.	j.	PROPN
ejpam-5903	267	2	pure	pure	PROPN
ejpam-5903	267	3	appl	appl	PROPN
ejpam-5903	267	4	.	.	PROPN
ejpam-5903	267	5	math	math	PROPN
ejpam-5903	267	6	,	,	PUNCT
ejpam-5903	267	7	18	18	NUM
ejpam-5903	267	8	(	(	PUNCT
ejpam-5903	267	9	2	2	NUM
ejpam-5903	267	10	)	)	PUNCT
ejpam-5903	267	11	(	(	PUNCT
ejpam-5903	267	12	2025	2025	NUM
ejpam-5903	267	13	)	)	PUNCT
ejpam-5903	267	14	,	,	PUNCT
ejpam-5903	267	15	5903	5903	NUM
ejpam-5903	267	16	8	8	NUM
ejpam-5903	267	17	of	of	ADP
ejpam-5903	267	18	17	17	NUM
ejpam-5903	267	19	conversely	conversely	ADV
ejpam-5903	267	20	,	,	PUNCT
ejpam-5903	267	21	let	let	VERB
ejpam-5903	267	22	v	v	NUM
ejpam-5903	267	23	∈	∈	PROPN
ejpam-5903	267	24	v	v	NOUN
ejpam-5903	267	25	(	(	PUNCT
ejpam-5903	267	26	g	g	NOUN
ejpam-5903	267	27	)	)	PUNCT
ejpam-5903	267	28	such	such	ADJ
ejpam-5903	267	29	that	that	PRON
ejpam-5903	267	30	γhg(g	γhg(g	PROPN
ejpam-5903	268	1	−	−	NUM
ejpam-5903	268	2	v	v	NOUN
ejpam-5903	268	3	)	)	PUNCT
ejpam-5903	268	4	=	=	SYM
ejpam-5903	268	5	γhg(g	γhg(g	PROPN
ejpam-5903	268	6	)	)	PUNCT
ejpam-5903	268	7	−	−	PROPN
ejpam-5903	269	1	1	1	X
ejpam-5903	269	2	.	.	PUNCT
ejpam-5903	269	3	then	then	ADV
ejpam-5903	269	4	there	there	PRON
ejpam-5903	269	5	exists	exist	VERB
ejpam-5903	269	6	d	d	PROPN
ejpam-5903	269	7	⊆	⊆	NUM
ejpam-5903	269	8	v	v	ADP
ejpam-5903	269	9	(	(	PUNCT
ejpam-5903	269	10	g	g	NOUN
ejpam-5903	269	11	)	)	PUNCT
ejpam-5903	269	12	with	with	ADP
ejpam-5903	269	13	|d|	|d|	PROPN
ejpam-5903	269	14	=	=	SYM
ejpam-5903	269	15	γhg(g	γhg(g	PROPN
ejpam-5903	269	16	)	)	PUNCT
ejpam-5903	269	17	−	−	NOUN
ejpam-5903	269	18	1	1	NUM
ejpam-5903	269	19	and	and	CCONJ
ejpam-5903	269	20	nhg	nhg	VERB
ejpam-5903	269	21	g	g	PROPN
ejpam-5903	270	1	[	[	X
ejpam-5903	270	2	d	d	X
ejpam-5903	270	3	]	]	X
ejpam-5903	270	4	=	=	SYM
ejpam-5903	270	5	v	v	X
ejpam-5903	270	6	(	(	PUNCT
ejpam-5903	270	7	g	g	NOUN
ejpam-5903	270	8	)	)	PUNCT
ejpam-5903	270	9	\	\	NOUN
ejpam-5903	270	10	{	{	PUNCT
ejpam-5903	270	11	v	v	NOUN
ejpam-5903	270	12	}	}	PUNCT
ejpam-5903	270	13	.	.	PUNCT
ejpam-5903	271	1	this	this	PRON
ejpam-5903	271	2	implies	imply	VERB
ejpam-5903	271	3	that	that	DET
ejpam-5903	271	4	ζhg1	ζhg1	PROPN
ejpam-5903	271	5	(	(	PUNCT
ejpam-5903	271	6	g	g	NOUN
ejpam-5903	271	7	)	)	PUNCT
ejpam-5903	271	8	=	=	SYM
ejpam-5903	272	1	|v	|v	X
ejpam-5903	272	2	(	(	PUNCT
ejpam-5903	272	3	g	g	NOUN
ejpam-5903	272	4	)	)	PUNCT
ejpam-5903	273	1	\nhg	\nhg	ADP
ejpam-5903	273	2	g	g	X
ejpam-5903	274	1	[	[	X
ejpam-5903	274	2	d]|	d]|	X
ejpam-5903	274	3	=	=	SYM
ejpam-5903	274	4	|{v}|	|{v}|	PUNCT
ejpam-5903	274	5	=	=	SYM
ejpam-5903	274	6	1	1	X
ejpam-5903	274	7	.	.	X
ejpam-5903	274	8	therefore	therefore	ADV
ejpam-5903	274	9	,	,	PUNCT
ejpam-5903	274	10	ζhg1	ζhg1	PROPN
ejpam-5903	274	11	(	(	PUNCT
ejpam-5903	274	12	g	g	NOUN
ejpam-5903	274	13	)	)	PUNCT
ejpam-5903	274	14	=	=	SYM
ejpam-5903	274	15	1	1	X
ejpam-5903	274	16	.	.	PUNCT
ejpam-5903	274	17	lemma	lemma	PROPN
ejpam-5903	274	18	1	1	X
ejpam-5903	274	19	.	.	PUNCT
ejpam-5903	275	1	let	let	VERB
ejpam-5903	275	2	g	g	PRON
ejpam-5903	275	3	be	be	AUX
ejpam-5903	275	4	a	a	DET
ejpam-5903	275	5	non	non	ADJ
ejpam-5903	275	6	-	-	ADJ
ejpam-5903	275	7	trivial	trivial	ADJ
ejpam-5903	275	8	graph	graph	NOUN
ejpam-5903	275	9	of	of	ADP
ejpam-5903	275	10	order	order	NOUN
ejpam-5903	275	11	n.	n.	VERB
ejpam-5903	275	12	if	if	SCONJ
ejpam-5903	275	13	k	k	PROPN
ejpam-5903	275	14	=	=	PUNCT
ejpam-5903	275	15	γhg(g)−1	γhg(g)−1	PROPN
ejpam-5903	275	16	,	,	PUNCT
ejpam-5903	275	17	then	then	ADV
ejpam-5903	275	18	ζhgk	ζhgk	NOUN
ejpam-5903	275	19	(	(	PUNCT
ejpam-5903	275	20	g	g	NOUN
ejpam-5903	275	21	)	)	PUNCT
ejpam-5903	276	1	=	=	SYM
ejpam-5903	276	2	n−1	n−1	PROPN
ejpam-5903	276	3	.	.	PUNCT
ejpam-5903	276	4	proof	proof	NOUN
ejpam-5903	276	5	.	.	PUNCT
ejpam-5903	277	1	let	let	VERB
ejpam-5903	277	2	k	k	NOUN
ejpam-5903	277	3	=	=	SYM
ejpam-5903	277	4	γhg(g	γhg(g	PROPN
ejpam-5903	277	5	)	)	PUNCT
ejpam-5903	277	6	−	−	NOUN
ejpam-5903	277	7	1	1	NUM
ejpam-5903	277	8	and	and	CCONJ
ejpam-5903	277	9	let	let	VERB
ejpam-5903	277	10	s	s	PRON
ejpam-5903	277	11	be	be	AUX
ejpam-5903	277	12	a	a	DET
ejpam-5903	277	13	ζhgk	ζhgk	NOUN
ejpam-5903	277	14	-set	-set	ADJ
ejpam-5903	277	15	of	of	ADP
ejpam-5903	277	16	g.	g.	PROPN
ejpam-5903	277	17	then	then	ADV
ejpam-5903	277	18	|s|	|s|	PROPN
ejpam-5903	277	19	=	=	SYM
ejpam-5903	277	20	1	1	NUM
ejpam-5903	277	21	,	,	PUNCT
ejpam-5903	277	22	say	say	VERB
ejpam-5903	277	23	,	,	PUNCT
ejpam-5903	277	24	s	s	PART
ejpam-5903	277	25	=	=	PUNCT
ejpam-5903	277	26	{	{	PUNCT
ejpam-5903	277	27	x	x	NOUN
ejpam-5903	277	28	}	}	PUNCT
ejpam-5903	277	29	and	and	CCONJ
ejpam-5903	277	30	ζhgk	ζhgk	NOUN
ejpam-5903	277	31	(	(	PUNCT
ejpam-5903	277	32	g	g	NOUN
ejpam-5903	277	33	)	)	PUNCT
ejpam-5903	277	34	=	=	VERB
ejpam-5903	277	35	ζhgk	ζhgk	NOUN
ejpam-5903	277	36	(	(	PUNCT
ejpam-5903	277	37	s	s	NOUN
ejpam-5903	277	38	)	)	PUNCT
ejpam-5903	277	39	=	=	SYM
ejpam-5903	277	40	n	n	PRON
ejpam-5903	277	41	−	−	PROPN
ejpam-5903	277	42	|nhg	|nhg	PROPN
ejpam-5903	277	43	g	g	PROPN
ejpam-5903	277	44	[	[	X
ejpam-5903	277	45	s]|	s]|	PROPN
ejpam-5903	277	46	.	.	PUNCT
ejpam-5903	278	1	since	since	SCONJ
ejpam-5903	278	2	x	x	PROPN
ejpam-5903	278	3	∈	∈	PROPN
ejpam-5903	278	4	n2	n2	NOUN
ejpam-5903	278	5	g[s	g[s	PROPN
ejpam-5903	278	6	]	]	PUNCT
ejpam-5903	278	7	and	and	CCONJ
ejpam-5903	278	8	ig[s	ig[s	PROPN
ejpam-5903	278	9	]	]	PUNCT
ejpam-5903	278	10	=	=	SYM
ejpam-5903	278	11	s	s	X
ejpam-5903	278	12	,	,	PUNCT
ejpam-5903	278	13	it	it	PRON
ejpam-5903	278	14	follows	follow	VERB
ejpam-5903	278	15	that	that	DET
ejpam-5903	278	16	nhg	nhg	NOUN
ejpam-5903	278	17	g	g	PROPN
ejpam-5903	279	1	[	[	X
ejpam-5903	279	2	s	s	X
ejpam-5903	279	3	]	]	X
ejpam-5903	279	4	=	=	PUNCT
ejpam-5903	279	5	s.	s.	PROPN
ejpam-5903	279	6	it	it	PRON
ejpam-5903	279	7	follows	follow	VERB
ejpam-5903	279	8	that	that	SCONJ
ejpam-5903	279	9	ζhgk	ζhgk	NOUN
ejpam-5903	279	10	(	(	PUNCT
ejpam-5903	279	11	g	g	NOUN
ejpam-5903	279	12	)	)	PUNCT
ejpam-5903	279	13	=	=	SYM
ejpam-5903	279	14	n−	n−	NOUN
ejpam-5903	279	15	|nhg	|nhg	VERB
ejpam-5903	279	16	g	g	PROPN
ejpam-5903	280	1	[	[	X
ejpam-5903	280	2	s]|	s]|	X
ejpam-5903	280	3	=	=	SYM
ejpam-5903	280	4	n−	n−	NOUN
ejpam-5903	280	5	1	1	NUM
ejpam-5903	280	6	.	.	PUNCT
ejpam-5903	281	1	lemma	lemma	PROPN
ejpam-5903	281	2	2	2	X
ejpam-5903	281	3	.	.	PUNCT
ejpam-5903	282	1	let	let	VERB
ejpam-5903	282	2	g	g	PRON
ejpam-5903	282	3	be	be	AUX
ejpam-5903	282	4	a	a	DET
ejpam-5903	282	5	connected	connected	ADJ
ejpam-5903	282	6	graph	graph	NOUN
ejpam-5903	282	7	of	of	ADP
ejpam-5903	282	8	order	order	NOUN
ejpam-5903	282	9	n.	n.	NOUN
ejpam-5903	282	10	if	if	SCONJ
ejpam-5903	282	11	s	s	VERB
ejpam-5903	282	12	is	be	AUX
ejpam-5903	282	13	a	a	DET
ejpam-5903	282	14	clique	clique	NOUN
ejpam-5903	282	15	in	in	ADP
ejpam-5903	282	16	g	g	PROPN
ejpam-5903	282	17	,	,	PUNCT
ejpam-5903	282	18	then	then	ADV
ejpam-5903	282	19	nhg	nhg	VERB
ejpam-5903	282	20	g	g	PROPN
ejpam-5903	283	1	[	[	X
ejpam-5903	283	2	s	s	X
ejpam-5903	283	3	]	]	X
ejpam-5903	283	4	=	=	PUNCT
ejpam-5903	283	5	s.	s.	PROPN
ejpam-5903	283	6	proof	proof	NOUN
ejpam-5903	283	7	.	.	PUNCT
ejpam-5903	284	1	let	let	VERB
ejpam-5903	284	2	s	s	PRON
ejpam-5903	284	3	is	be	AUX
ejpam-5903	284	4	be	be	AUX
ejpam-5903	284	5	clique	clique	ADJ
ejpam-5903	284	6	in	in	ADP
ejpam-5903	284	7	g.	g.	PROPN
ejpam-5903	284	8	then	then	ADV
ejpam-5903	284	9	n2	n2	PROPN
ejpam-5903	284	10	g[s	g[s	PROPN
ejpam-5903	284	11	]	]	X
ejpam-5903	284	12	=	=	SYM
ejpam-5903	284	13	ig[s	ig[s	PROPN
ejpam-5903	284	14	]	]	PUNCT
ejpam-5903	284	15	=	=	PUNCT
ejpam-5903	284	16	s.	s.	PROPN
ejpam-5903	284	17	thus	thus	ADV
ejpam-5903	284	18	,	,	PUNCT
ejpam-5903	284	19	nhg	nhg	NOUN
ejpam-5903	284	20	g	g	PROPN
ejpam-5903	285	1	[	[	X
ejpam-5903	285	2	s	s	X
ejpam-5903	285	3	]	]	X
ejpam-5903	285	4	=	=	SYM
ejpam-5903	285	5	n2	n2	PROPN
ejpam-5903	285	6	g[s	g[s	PROPN
ejpam-5903	285	7	]	]	PUNCT
ejpam-5903	285	8	∩	∩	ADJ
ejpam-5903	285	9	ig[s	ig[s	PROPN
ejpam-5903	285	10	]	]	PUNCT
ejpam-5903	285	11	=	=	PUNCT
ejpam-5903	285	12	s.	s.	PROPN
ejpam-5903	285	13	the	the	DET
ejpam-5903	285	14	next	next	ADJ
ejpam-5903	285	15	result	result	NOUN
ejpam-5903	285	16	shows	show	VERB
ejpam-5903	285	17	that	that	SCONJ
ejpam-5903	285	18	the	the	DET
ejpam-5903	285	19	bound	bind	VERB
ejpam-5903	285	20	given	give	VERB
ejpam-5903	285	21	in	in	ADP
ejpam-5903	285	22	theorem	theorem	ADJ
ejpam-5903	285	23	4	4	NUM
ejpam-5903	285	24	is	be	AUX
ejpam-5903	285	25	sharp	sharp	ADJ
ejpam-5903	285	26	.	.	PUNCT
ejpam-5903	286	1	theorem	theorem	VERB
ejpam-5903	286	2	7	7	NUM
ejpam-5903	286	3	.	.	PUNCT
ejpam-5903	287	1	if	if	SCONJ
ejpam-5903	287	2	kn	kn	PROPN
ejpam-5903	287	3	is	be	AUX
ejpam-5903	287	4	a	a	DET
ejpam-5903	287	5	complete	complete	ADJ
ejpam-5903	287	6	graph	graph	NOUN
ejpam-5903	287	7	on	on	ADP
ejpam-5903	287	8	n	n	DET
ejpam-5903	287	9	vertices	vertex	NOUN
ejpam-5903	287	10	,	,	PUNCT
ejpam-5903	287	11	where	where	SCONJ
ejpam-5903	287	12	n	n	PRON
ejpam-5903	287	13	≥	≥	NOUN
ejpam-5903	287	14	2	2	NUM
ejpam-5903	287	15	,	,	PUNCT
ejpam-5903	287	16	and	and	CCONJ
ejpam-5903	287	17	1	1	NUM
ejpam-5903	287	18	≤	≤	NUM
ejpam-5903	287	19	k	k	NOUN
ejpam-5903	287	20	≤	≤	NUM
ejpam-5903	287	21	n	n	CCONJ
ejpam-5903	287	22	−	−	PROPN
ejpam-5903	287	23	1	1	NUM
ejpam-5903	287	24	,	,	PUNCT
ejpam-5903	287	25	then	then	ADV
ejpam-5903	287	26	ζhgk	ζhgk	NOUN
ejpam-5903	287	27	(	(	PUNCT
ejpam-5903	287	28	kn	kn	PROPN
ejpam-5903	287	29	)	)	PUNCT
ejpam-5903	287	30	=	=	PUNCT
ejpam-5903	287	31	k.	k.	PROPN
ejpam-5903	287	32	proof	proof	NOUN
ejpam-5903	287	33	.	.	PUNCT
ejpam-5903	288	1	let	let	VERB
ejpam-5903	288	2	k	k	PRON
ejpam-5903	288	3	be	be	AUX
ejpam-5903	288	4	a	a	DET
ejpam-5903	288	5	positive	positive	ADJ
ejpam-5903	288	6	integer	integer	NOUN
ejpam-5903	288	7	with	with	ADP
ejpam-5903	288	8	k	k	PROPN
ejpam-5903	288	9	≤	≤	PROPN
ejpam-5903	288	10	γhg(kn)−1	γhg(kn)−1	PROPN
ejpam-5903	288	11	.	.	PUNCT
ejpam-5903	289	1	since	since	SCONJ
ejpam-5903	289	2	γhg(kn	γhg(kn	NOUN
ejpam-5903	289	3	)	)	PUNCT
ejpam-5903	289	4	=	=	SYM
ejpam-5903	289	5	n	n	CCONJ
ejpam-5903	289	6	,	,	PUNCT
ejpam-5903	289	7	k	k	PROPN
ejpam-5903	289	8	≤	≤	PROPN
ejpam-5903	289	9	n−1	n−1	PROPN
ejpam-5903	289	10	.	.	PUNCT
ejpam-5903	290	1	let	let	VERB
ejpam-5903	290	2	s	s	PRON
ejpam-5903	290	3	be	be	AUX
ejpam-5903	290	4	a	a	DET
ejpam-5903	290	5	ζhgk	ζhgk	NOUN
ejpam-5903	290	6	-set	-set	ADJ
ejpam-5903	290	7	of	of	ADP
ejpam-5903	290	8	kn	kn	PROPN
ejpam-5903	290	9	.	.	PUNCT
ejpam-5903	291	1	then	then	ADV
ejpam-5903	291	2	s	s	VERB
ejpam-5903	291	3	is	be	AUX
ejpam-5903	291	4	a	a	DET
ejpam-5903	291	5	clique	clique	NOUN
ejpam-5903	291	6	,	,	PUNCT
ejpam-5903	291	7	|s|	|s|	NOUN
ejpam-5903	291	8	=	=	SYM
ejpam-5903	291	9	n	n	CCONJ
ejpam-5903	291	10	−	−	PROPN
ejpam-5903	291	11	k	k	NOUN
ejpam-5903	291	12	and	and	CCONJ
ejpam-5903	291	13	ζhgk	ζhgk	NOUN
ejpam-5903	291	14	(	(	PUNCT
ejpam-5903	291	15	g	g	NOUN
ejpam-5903	291	16	)	)	PUNCT
ejpam-5903	291	17	=	=	SYM
ejpam-5903	291	18	n	n	PRON
ejpam-5903	291	19	−	−	PROPN
ejpam-5903	291	20	|nhg	|nhg	PROPN
ejpam-5903	291	21	g	g	PROPN
ejpam-5903	291	22	[	[	X
ejpam-5903	291	23	s]|	s]|	PROPN
ejpam-5903	291	24	.	.	PUNCT
ejpam-5903	292	1	therefore	therefore	ADV
ejpam-5903	292	2	,	,	PUNCT
ejpam-5903	292	3	by	by	ADP
ejpam-5903	292	4	lemma	lemma	PROPN
ejpam-5903	292	5	2	2	NUM
ejpam-5903	292	6	,	,	PUNCT
ejpam-5903	292	7	ζhgk	ζhgk	NOUN
ejpam-5903	292	8	(	(	PUNCT
ejpam-5903	292	9	g	g	NOUN
ejpam-5903	292	10	)	)	PUNCT
ejpam-5903	292	11	=	=	VERB
ejpam-5903	292	12	n−	n−	NOUN
ejpam-5903	292	13	(	(	PUNCT
ejpam-5903	292	14	n−	n−	NOUN
ejpam-5903	292	15	k	k	NOUN
ejpam-5903	292	16	)	)	PUNCT
ejpam-5903	292	17	=	=	SYM
ejpam-5903	292	18	k.	k.	PROPN
ejpam-5903	292	19	theorem	theorem	VERB
ejpam-5903	292	20	8	8	NUM
ejpam-5903	292	21	.	.	PUNCT
ejpam-5903	293	1	for	for	ADP
ejpam-5903	293	2	a	a	DET
ejpam-5903	293	3	path	path	NOUN
ejpam-5903	293	4	pn	pn	NOUN
ejpam-5903	293	5	with	with	ADP
ejpam-5903	293	6	n	n	ADP
ejpam-5903	293	7	vertices	vertex	NOUN
ejpam-5903	293	8	,	,	PUNCT
ejpam-5903	293	9	ζhgk	ζhgk	NOUN
ejpam-5903	293	10	(	(	PUNCT
ejpam-5903	293	11	pn	pn	NOUN
ejpam-5903	293	12	)	)	PUNCT
ejpam-5903	293	13	=	=	PUNCT
ejpam-5903	293	14			NOUN
ejpam-5903	293	15	1	1	NUM
ejpam-5903	293	16	if	if	SCONJ
ejpam-5903	293	17	n	n	NOUN
ejpam-5903	293	18	=	=	SYM
ejpam-5903	293	19	2	2	NUM
ejpam-5903	293	20	or	or	CCONJ
ejpam-5903	293	21	n	n	NOUN
ejpam-5903	293	22	=	=	NOUN
ejpam-5903	293	23	3r	3r	NUM
ejpam-5903	293	24	and	and	CCONJ
ejpam-5903	293	25	k	k	NOUN
ejpam-5903	293	26	=	=	NOUN
ejpam-5903	293	27	1	1	NUM
ejpam-5903	293	28	3k	3k	NOUN
ejpam-5903	293	29	−	−	NOUN
ejpam-5903	293	30	4	4	NUM
ejpam-5903	293	31	if	if	SCONJ
ejpam-5903	293	32	n	n	NOUN
ejpam-5903	293	33	=	=	NOUN
ejpam-5903	293	34	3r	3r	NUM
ejpam-5903	293	35	and	and	CCONJ
ejpam-5903	293	36	k	k	NOUN
ejpam-5903	293	37	≥	≥	NUM
ejpam-5903	293	38	2	2	NUM
ejpam-5903	293	39	3k	3k	NUM
ejpam-5903	293	40	if	if	SCONJ
ejpam-5903	293	41	n	n	NOUN
ejpam-5903	293	42	=	=	NOUN
ejpam-5903	293	43	3r	3r	NUM
ejpam-5903	293	44	+	+	CCONJ
ejpam-5903	293	45	1	1	NUM
ejpam-5903	293	46	and	and	CCONJ
ejpam-5903	293	47	k	k	PROPN
ejpam-5903	293	48	≤	≤	NUM
ejpam-5903	293	49	r	r	NOUN
ejpam-5903	293	50	3k	3k	NUM
ejpam-5903	294	1	−	−	NOUN
ejpam-5903	294	2	2	2	NUM
ejpam-5903	294	3	if	if	SCONJ
ejpam-5903	294	4	n	n	NOUN
ejpam-5903	294	5	=	=	NOUN
ejpam-5903	294	6	3r	3r	NUM
ejpam-5903	294	7	+	+	CCONJ
ejpam-5903	294	8	2	2	NUM
ejpam-5903	294	9	and	and	CCONJ
ejpam-5903	294	10	k	k	PROPN
ejpam-5903	294	11	≤	≤	PROPN
ejpam-5903	294	12	r	r	NOUN
ejpam-5903	294	13	+	+	NOUN
ejpam-5903	294	14	1	1	NUM
ejpam-5903	294	15	.	.	X
ejpam-5903	294	16	proof	proof	NOUN
ejpam-5903	294	17	.	.	PUNCT
ejpam-5903	295	1	let	let	VERB
ejpam-5903	295	2	pn	pn	VERB
ejpam-5903	295	3	=	=	PUNCT
ejpam-5903	296	1	[	[	X
ejpam-5903	296	2	v1	v1	NOUN
ejpam-5903	296	3	,	,	PUNCT
ejpam-5903	296	4	v2	v2	PROPN
ejpam-5903	296	5	,	,	PUNCT
ejpam-5903	296	6	·	·	PUNCT
ejpam-5903	296	7	·	·	PUNCT
ejpam-5903	296	8	·	·	PUNCT
ejpam-5903	296	9	,	,	PUNCT
ejpam-5903	296	10	vn	vn	X
ejpam-5903	296	11	]	]	PUNCT
ejpam-5903	296	12	and	and	CCONJ
ejpam-5903	296	13	let	let	VERB
ejpam-5903	296	14	r	r	PRON
ejpam-5903	296	15	≥	≥	NUM
ejpam-5903	296	16	1	1	NUM
ejpam-5903	296	17	.	.	PUNCT
ejpam-5903	296	18	consider	consider	VERB
ejpam-5903	296	19	the	the	DET
ejpam-5903	296	20	following	follow	VERB
ejpam-5903	296	21	cases	case	NOUN
ejpam-5903	296	22	:	:	PUNCT
ejpam-5903	296	23	case	case	NOUN
ejpam-5903	296	24	1	1	NUM
ejpam-5903	296	25	:	:	PUNCT
ejpam-5903	296	26	n	n	NOUN
ejpam-5903	296	27	=	=	NOUN
ejpam-5903	296	28	3r	3r	NUM
ejpam-5903	296	29	.	.	PUNCT
ejpam-5903	297	1	by	by	ADP
ejpam-5903	297	2	theorem	theorem	NOUN
ejpam-5903	297	3	1	1	NUM
ejpam-5903	297	4	(	(	PUNCT
ejpam-5903	297	5	i	i	NOUN
ejpam-5903	297	6	)	)	PUNCT
ejpam-5903	297	7	,	,	PUNCT
ejpam-5903	297	8	γhg(pn	γhg(pn	NOUN
ejpam-5903	297	9	)	)	PUNCT
ejpam-5903	297	10	=	=	SYM
ejpam-5903	297	11	3r+6	3r+6	NUM
ejpam-5903	297	12	3	3	NUM
ejpam-5903	297	13	.	.	PUNCT
ejpam-5903	298	1	let	let	VERB
ejpam-5903	298	2	k	k	NOUN
ejpam-5903	298	3	=	=	PUNCT
ejpam-5903	298	4	1	1	NUM
ejpam-5903	298	5	and	and	CCONJ
ejpam-5903	298	6	let	let	VERB
ejpam-5903	298	7	s1	s1	PROPN
ejpam-5903	298	8	=	=	SYM
ejpam-5903	298	9	{	{	PUNCT
ejpam-5903	298	10	v1	v1	PROPN
ejpam-5903	298	11	,	,	PUNCT
ejpam-5903	298	12	v4	v4	NOUN
ejpam-5903	298	13	,	,	PUNCT
ejpam-5903	298	14	·	·	PUNCT
ejpam-5903	298	15	·	·	PUNCT
ejpam-5903	298	16	·	·	PUNCT
ejpam-5903	298	17	,	,	PUNCT
ejpam-5903	298	18	v3r−2	v3r−2	PROPN
ejpam-5903	298	19	}	}	PUNCT
ejpam-5903	298	20	∪	∪	X
ejpam-5903	298	21	{	{	PUNCT
ejpam-5903	298	22	v3r−1	v3r−1	PROPN
ejpam-5903	298	23	}	}	PUNCT
ejpam-5903	298	24	.	.	PUNCT
ejpam-5903	299	1	then	then	ADV
ejpam-5903	299	2	nhg	nhg	VERB
ejpam-5903	299	3	g	g	PROPN
ejpam-5903	300	1	[	[	X
ejpam-5903	300	2	s1	s1	X
ejpam-5903	300	3	]	]	X
ejpam-5903	300	4	=	=	SYM
ejpam-5903	300	5	v	v	X
ejpam-5903	300	6	(	(	PUNCT
ejpam-5903	300	7	pn	pn	NOUN
ejpam-5903	300	8	)	)	PUNCT
ejpam-5903	300	9	\	\	NOUN
ejpam-5903	300	10	{	{	PUNCT
ejpam-5903	300	11	v3r	v3r	NOUN
ejpam-5903	300	12	}	}	PUNCT
ejpam-5903	300	13	.	.	PUNCT
ejpam-5903	301	1	hence	hence	ADV
ejpam-5903	301	2	,	,	PUNCT
ejpam-5903	301	3	ζhgk	ζhgk	PROPN
ejpam-5903	301	4	(	(	PUNCT
ejpam-5903	301	5	s1	s1	NOUN
ejpam-5903	301	6	)	)	PUNCT
ejpam-5903	301	7	=	=	SYM
ejpam-5903	301	8	n	n	PRON
ejpam-5903	301	9	−	−	PROPN
ejpam-5903	301	10	|nhg	|nhg	PROPN
ejpam-5903	301	11	g	g	X
ejpam-5903	302	1	[	[	X
ejpam-5903	302	2	s1]|	s1]|	X
ejpam-5903	302	3	=	=	SYM
ejpam-5903	302	4	3r	3r	NUM
ejpam-5903	302	5	−	−	NOUN
ejpam-5903	302	6	(	(	PUNCT
ejpam-5903	302	7	3r	3r	NUM
ejpam-5903	302	8	−	−	NOUN
ejpam-5903	302	9	1	1	NUM
ejpam-5903	302	10	)	)	PUNCT
ejpam-5903	302	11	=	=	SYM
ejpam-5903	302	12	1	1	X
ejpam-5903	302	13	.	.	PUNCT
ejpam-5903	303	1	thus	thus	ADV
ejpam-5903	303	2	,	,	PUNCT
ejpam-5903	303	3	ζhgk	ζhgk	PROPN
ejpam-5903	303	4	(	(	PUNCT
ejpam-5903	303	5	pn	pn	NOUN
ejpam-5903	303	6	)	)	PUNCT
ejpam-5903	303	7	=	=	SYM
ejpam-5903	303	8	1	1	X
ejpam-5903	303	9	.	.	PUNCT
ejpam-5903	304	1	next	next	ADV
ejpam-5903	304	2	,	,	PUNCT
ejpam-5903	304	3	let	let	VERB
ejpam-5903	304	4	k	k	PROPN
ejpam-5903	304	5	≥	≥	NUM
ejpam-5903	304	6	2	2	NUM
ejpam-5903	304	7	.	.	PUNCT
ejpam-5903	305	1	then	then	ADV
ejpam-5903	305	2	3r+6	3r+6	PROPN
ejpam-5903	305	3	3	3	NUM
ejpam-5903	305	4	−	−	PROPN
ejpam-5903	306	1	k	k	NOUN
ejpam-5903	306	2	=	=	PUNCT
ejpam-5903	306	3	r	r	NOUN
ejpam-5903	306	4	−	−	PROPN
ejpam-5903	307	1	k	k	NOUN
ejpam-5903	307	2	+	+	PROPN
ejpam-5903	307	3	2	2	X
ejpam-5903	307	4	.	.	X
ejpam-5903	307	5	choose	choose	VERB
ejpam-5903	307	6	an	an	DET
ejpam-5903	307	7	(	(	PUNCT
ejpam-5903	307	8	r	r	NOUN
ejpam-5903	307	9	−	−	PROPN
ejpam-5903	307	10	k	k	PROPN
ejpam-5903	308	1	+	+	PROPN
ejpam-5903	308	2	2)-element	2)-element	NUM
ejpam-5903	308	3	set	set	NOUN
ejpam-5903	308	4	s2	s2	NOUN
ejpam-5903	308	5	=	=	SYM
ejpam-5903	308	6	{	{	PUNCT
ejpam-5903	308	7	v1	v1	PROPN
ejpam-5903	308	8	,	,	PUNCT
ejpam-5903	308	9	v4	v4	NOUN
ejpam-5903	308	10	,	,	PUNCT
ejpam-5903	308	11	·	·	PUNCT
ejpam-5903	308	12	·	·	PUNCT
ejpam-5903	308	13	·	·	PUNCT
ejpam-5903	308	14	,	,	PUNCT
ejpam-5903	308	15	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	308	16	}	}	PUNCT
ejpam-5903	308	17	.	.	PUNCT
ejpam-5903	309	1	then	then	ADV
ejpam-5903	309	2	s2	s2	PROPN
ejpam-5903	309	3	is	be	AUX
ejpam-5903	309	4	a	a	DET
ejpam-5903	309	5	ζhgk	ζhgk	NOUN
ejpam-5903	309	6	-set	-set	ADJ
ejpam-5903	309	7	of	of	ADP
ejpam-5903	309	8	pn	pn	PROPN
ejpam-5903	309	9	and	and	CCONJ
ejpam-5903	309	10	nhg	nhg	VERB
ejpam-5903	309	11	g	g	PROPN
ejpam-5903	310	1	[	[	X
ejpam-5903	310	2	s2	s2	X
ejpam-5903	310	3	]	]	X
ejpam-5903	310	4	=	=	SYM
ejpam-5903	310	5	{	{	PUNCT
ejpam-5903	310	6	v1	v1	PROPN
ejpam-5903	310	7	,	,	PUNCT
ejpam-5903	310	8	v2	v2	PROPN
ejpam-5903	310	9	,	,	PUNCT
ejpam-5903	310	10	v3	v3	PROPN
ejpam-5903	310	11	,	,	PUNCT
ejpam-5903	310	12	v4	v4	PROPN
ejpam-5903	310	13	,	,	PUNCT
ejpam-5903	310	14	·	·	PUNCT
ejpam-5903	310	15	·	·	PUNCT
ejpam-5903	310	16	·	·	PUNCT
ejpam-5903	310	17	,	,	PUNCT
ejpam-5903	310	18	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	310	19	}	}	PUNCT
ejpam-5903	310	20	.	.	PUNCT
ejpam-5903	311	1	this	this	PRON
ejpam-5903	311	2	implies	imply	VERB
ejpam-5903	311	3	that	that	SCONJ
ejpam-5903	311	4	ζhgk	ζhgk	NOUN
ejpam-5903	311	5	(	(	PUNCT
ejpam-5903	311	6	pn	pn	NOUN
ejpam-5903	311	7	)	)	PUNCT
ejpam-5903	311	8	=	=	NOUN
ejpam-5903	311	9	ζhgk	ζhgk	NOUN
ejpam-5903	311	10	(	(	PUNCT
ejpam-5903	311	11	s2	s2	PROPN
ejpam-5903	311	12	)	)	PUNCT
ejpam-5903	311	13	=	=	SYM
ejpam-5903	311	14	n−	n−	NOUN
ejpam-5903	311	15	|nhg	|nhg	VERB
ejpam-5903	311	16	g	g	NOUN
ejpam-5903	312	1	[	[	X
ejpam-5903	312	2	s2]|	s2]|	NOUN
ejpam-5903	312	3	=	=	SYM
ejpam-5903	312	4	3r	3r	NUM
ejpam-5903	312	5	−	−	NOUN
ejpam-5903	312	6	(	(	PUNCT
ejpam-5903	312	7	3r	3r	NUM
ejpam-5903	312	8	−	−	NOUN
ejpam-5903	312	9	3k	3k	NOUN
ejpam-5903	312	10	+	+	CCONJ
ejpam-5903	312	11	4	4	X
ejpam-5903	312	12	)	)	PUNCT
ejpam-5903	312	13	=	=	PUNCT
ejpam-5903	313	1	3k	3k	X
ejpam-5903	314	1	−	−	NOUN
ejpam-5903	314	2	4	4	X
ejpam-5903	314	3	.	.	PUNCT
ejpam-5903	314	4	case	case	NOUN
ejpam-5903	314	5	2	2	NUM
ejpam-5903	314	6	:	:	SYM
ejpam-5903	314	7	n	n	NOUN
ejpam-5903	314	8	=	=	SYM
ejpam-5903	314	9	3r	3r	NUM
ejpam-5903	314	10	+	+	CCONJ
ejpam-5903	314	11	1	1	X
ejpam-5903	314	12	.	.	PUNCT
ejpam-5903	314	13	by	by	ADP
ejpam-5903	314	14	theorem	theorem	NOUN
ejpam-5903	314	15	1	1	NUM
ejpam-5903	314	16	(	(	PUNCT
ejpam-5903	314	17	i	i	NOUN
ejpam-5903	314	18	)	)	PUNCT
ejpam-5903	314	19	,	,	PUNCT
ejpam-5903	314	20	γhg(pn	γhg(pn	NOUN
ejpam-5903	314	21	)	)	PUNCT
ejpam-5903	314	22	=	=	SYM
ejpam-5903	315	1	3r+3	3r+3	NOUN
ejpam-5903	315	2	3	3	NUM
ejpam-5903	315	3	.	.	PUNCT
ejpam-5903	316	1	then	then	ADV
ejpam-5903	316	2	k	k	PROPN
ejpam-5903	316	3	≤	≤	ADJ
ejpam-5903	316	4	r	r	NOUN
ejpam-5903	316	5	and	and	CCONJ
ejpam-5903	316	6	3r+3	3r+3	PROPN
ejpam-5903	316	7	3	3	NUM
ejpam-5903	316	8	−	−	PROPN
ejpam-5903	317	1	k	k	NOUN
ejpam-5903	318	1	=	=	PUNCT
ejpam-5903	319	1	r	r	NOUN
ejpam-5903	319	2	−	−	PROPN
ejpam-5903	320	1	k	k	NOUN
ejpam-5903	320	2	+	+	NOUN
ejpam-5903	320	3	1	1	X
ejpam-5903	320	4	.	.	X
ejpam-5903	320	5	choose	choose	VERB
ejpam-5903	320	6	j.	j.	PROPN
ejpam-5903	320	7	anoche	anoche	PROPN
ejpam-5903	320	8	,	,	PUNCT
ejpam-5903	320	9	s.	s.	PROPN
ejpam-5903	320	10	canoy	canoy	PROPN
ejpam-5903	320	11	,	,	PUNCT
ejpam-5903	320	12	jr	jr	PROPN
ejpam-5903	320	13	.	.	PROPN
ejpam-5903	320	14	/	/	SYM
ejpam-5903	320	15	eur	eur	PROPN
ejpam-5903	320	16	.	.	PUNCT
ejpam-5903	321	1	j.	j.	PROPN
ejpam-5903	321	2	pure	pure	PROPN
ejpam-5903	321	3	appl	appl	PROPN
ejpam-5903	321	4	.	.	PROPN
ejpam-5903	321	5	math	math	PROPN
ejpam-5903	321	6	,	,	PUNCT
ejpam-5903	321	7	18	18	NUM
ejpam-5903	321	8	(	(	PUNCT
ejpam-5903	321	9	2	2	NUM
ejpam-5903	321	10	)	)	PUNCT
ejpam-5903	321	11	(	(	PUNCT
ejpam-5903	321	12	2025	2025	NUM
ejpam-5903	321	13	)	)	PUNCT
ejpam-5903	321	14	,	,	PUNCT
ejpam-5903	321	15	5903	5903	NUM
ejpam-5903	321	16	9	9	NUM
ejpam-5903	321	17	of	of	ADP
ejpam-5903	321	18	17	17	NUM
ejpam-5903	321	19	an	an	DET
ejpam-5903	321	20	(	(	PUNCT
ejpam-5903	321	21	r	r	NOUN
ejpam-5903	321	22	−	−	PROPN
ejpam-5903	321	23	k	k	PROPN
ejpam-5903	322	1	+	+	PROPN
ejpam-5903	322	2	1)-element	1)-element	NUM
ejpam-5903	322	3	set	set	NOUN
ejpam-5903	322	4	s3	s3	NOUN
ejpam-5903	322	5	=	=	SYM
ejpam-5903	322	6	{	{	PUNCT
ejpam-5903	322	7	v1	v1	PROPN
ejpam-5903	322	8	,	,	PUNCT
ejpam-5903	322	9	v4	v4	NOUN
ejpam-5903	322	10	,	,	PUNCT
ejpam-5903	322	11	·	·	PUNCT
ejpam-5903	322	12	·	·	PUNCT
ejpam-5903	322	13	·	·	PUNCT
ejpam-5903	322	14	,	,	PUNCT
ejpam-5903	322	15	v3r−3k+1	v3r−3k+1	NOUN
ejpam-5903	322	16	}	}	PUNCT
ejpam-5903	322	17	.	.	PUNCT
ejpam-5903	323	1	then	then	ADV
ejpam-5903	323	2	s3	s3	PROPN
ejpam-5903	323	3	is	be	AUX
ejpam-5903	323	4	a	a	DET
ejpam-5903	323	5	ζhgk	ζhgk	NOUN
ejpam-5903	323	6	-set	-set	ADJ
ejpam-5903	323	7	of	of	ADP
ejpam-5903	323	8	pn	pn	PROPN
ejpam-5903	323	9	and	and	CCONJ
ejpam-5903	323	10	nhg	nhg	VERB
ejpam-5903	323	11	g	g	PROPN
ejpam-5903	324	1	[	[	X
ejpam-5903	324	2	s3	s3	PROPN
ejpam-5903	324	3	]	]	X
ejpam-5903	324	4	=	=	SYM
ejpam-5903	324	5	{	{	PUNCT
ejpam-5903	324	6	v1	v1	PROPN
ejpam-5903	324	7	,	,	PUNCT
ejpam-5903	324	8	v2	v2	PROPN
ejpam-5903	324	9	,	,	PUNCT
ejpam-5903	324	10	v3	v3	PROPN
ejpam-5903	324	11	,	,	PUNCT
ejpam-5903	324	12	v4	v4	PROPN
ejpam-5903	324	13	,	,	PUNCT
ejpam-5903	324	14	·	·	PUNCT
ejpam-5903	324	15	·	·	PUNCT
ejpam-5903	324	16	·	·	PUNCT
ejpam-5903	324	17	,	,	PUNCT
ejpam-5903	324	18	v3r−3k+1	v3r−3k+1	NOUN
ejpam-5903	324	19	}	}	PUNCT
ejpam-5903	324	20	.	.	PUNCT
ejpam-5903	325	1	thus	thus	ADV
ejpam-5903	325	2	,	,	PUNCT
ejpam-5903	325	3	ζhgk	ζhgk	PROPN
ejpam-5903	325	4	(	(	PUNCT
ejpam-5903	325	5	pn	pn	NOUN
ejpam-5903	325	6	)	)	PUNCT
ejpam-5903	325	7	=	=	NOUN
ejpam-5903	325	8	ζhgk	ζhgk	NOUN
ejpam-5903	325	9	(	(	PUNCT
ejpam-5903	325	10	s3	s3	PROPN
ejpam-5903	325	11	)	)	PUNCT
ejpam-5903	325	12	=	=	SYM
ejpam-5903	325	13	n−	n−	NOUN
ejpam-5903	325	14	|nhg	|nhg	VERB
ejpam-5903	325	15	g	g	NOUN
ejpam-5903	326	1	[	[	X
ejpam-5903	326	2	s3]|	s3]|	VERB
ejpam-5903	326	3	=	=	SYM
ejpam-5903	326	4	(	(	PUNCT
ejpam-5903	326	5	3r	3r	NUM
ejpam-5903	326	6	+	+	SYM
ejpam-5903	326	7	1)−	1)−	NUM
ejpam-5903	326	8	(	(	PUNCT
ejpam-5903	326	9	3r	3r	NUM
ejpam-5903	326	10	−	−	NOUN
ejpam-5903	326	11	3k	3k	NOUN
ejpam-5903	326	12	+	+	CCONJ
ejpam-5903	326	13	1	1	X
ejpam-5903	326	14	)	)	PUNCT
ejpam-5903	326	15	=	=	SYM
ejpam-5903	326	16	3k	3k	X
ejpam-5903	326	17	.	.	PUNCT
ejpam-5903	327	1	case	case	NOUN
ejpam-5903	327	2	3	3	NUM
ejpam-5903	327	3	:	:	PUNCT
ejpam-5903	327	4	n	n	NOUN
ejpam-5903	327	5	=	=	SYM
ejpam-5903	327	6	3r	3r	NUM
ejpam-5903	327	7	+	+	CCONJ
ejpam-5903	327	8	2	2	X
ejpam-5903	327	9	.	.	PUNCT
ejpam-5903	327	10	by	by	ADP
ejpam-5903	327	11	theorem	theorem	NOUN
ejpam-5903	327	12	1	1	NUM
ejpam-5903	327	13	(	(	PUNCT
ejpam-5903	327	14	i	i	NOUN
ejpam-5903	327	15	)	)	PUNCT
ejpam-5903	327	16	,	,	PUNCT
ejpam-5903	327	17	γhg(pn	γhg(pn	NOUN
ejpam-5903	327	18	)	)	PUNCT
ejpam-5903	327	19	=	=	SYM
ejpam-5903	328	1	3r+6	3r+6	NUM
ejpam-5903	328	2	3	3	NUM
ejpam-5903	328	3	=	=	SYM
ejpam-5903	328	4	r	r	NOUN
ejpam-5903	328	5	+	+	NOUN
ejpam-5903	328	6	2	2	NUM
ejpam-5903	328	7	.	.	PUNCT
ejpam-5903	329	1	here	here	ADV
ejpam-5903	329	2	,	,	PUNCT
ejpam-5903	329	3	k	k	PROPN
ejpam-5903	329	4	≤	≤	PROPN
ejpam-5903	329	5	r	r	NOUN
ejpam-5903	329	6	+	+	CCONJ
ejpam-5903	329	7	1	1	NUM
ejpam-5903	329	8	and	and	CCONJ
ejpam-5903	329	9	γhg(pn)−	γhg(pn)−	PROPN
ejpam-5903	329	10	k	k	X
ejpam-5903	330	1	=	=	PUNCT
ejpam-5903	330	2	r	r	NOUN
ejpam-5903	330	3	−	−	PROPN
ejpam-5903	331	1	k	k	NOUN
ejpam-5903	331	2	+	+	NOUN
ejpam-5903	331	3	2	2	X
ejpam-5903	331	4	.	.	X
ejpam-5903	331	5	consider	consider	VERB
ejpam-5903	331	6	an	an	DET
ejpam-5903	331	7	(	(	PUNCT
ejpam-5903	331	8	r−	r−	PROPN
ejpam-5903	331	9	k+2)-element	k+2)-element	NOUN
ejpam-5903	331	10	set	set	VERB
ejpam-5903	331	11	s4	s4	PROPN
ejpam-5903	331	12	=	=	SYM
ejpam-5903	331	13	{	{	PUNCT
ejpam-5903	331	14	v1	v1	PROPN
ejpam-5903	331	15	,	,	PUNCT
ejpam-5903	331	16	v4	v4	NOUN
ejpam-5903	331	17	,	,	PUNCT
ejpam-5903	331	18	·	·	PUNCT
ejpam-5903	331	19	·	·	PUNCT
ejpam-5903	331	20	·	·	PUNCT
ejpam-5903	331	21	,	,	PUNCT
ejpam-5903	331	22	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	331	23	}	}	PUNCT
ejpam-5903	331	24	.	.	PUNCT
ejpam-5903	332	1	the	the	DET
ejpam-5903	332	2	set	set	NOUN
ejpam-5903	332	3	s4	s4	PROPN
ejpam-5903	332	4	is	be	AUX
ejpam-5903	332	5	a	a	DET
ejpam-5903	332	6	ζhgk	ζhgk	NOUN
ejpam-5903	332	7	-set	-set	ADJ
ejpam-5903	332	8	of	of	ADP
ejpam-5903	332	9	pn	pn	PROPN
ejpam-5903	332	10	and	and	CCONJ
ejpam-5903	332	11	nhg	nhg	VERB
ejpam-5903	332	12	g	g	PROPN
ejpam-5903	333	1	[	[	X
ejpam-5903	333	2	s4	s4	X
ejpam-5903	333	3	]	]	X
ejpam-5903	333	4	=	=	SYM
ejpam-5903	333	5	{	{	PUNCT
ejpam-5903	333	6	v1	v1	PROPN
ejpam-5903	333	7	,	,	PUNCT
ejpam-5903	333	8	v2	v2	PROPN
ejpam-5903	333	9	,	,	PUNCT
ejpam-5903	333	10	v3	v3	PROPN
ejpam-5903	333	11	,	,	PUNCT
ejpam-5903	333	12	v4	v4	PROPN
ejpam-5903	333	13	,	,	PUNCT
ejpam-5903	333	14	·	·	PUNCT
ejpam-5903	333	15	·	·	PUNCT
ejpam-5903	333	16	·	·	PUNCT
ejpam-5903	333	17	,	,	PUNCT
ejpam-5903	333	18	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	333	19	}	}	PUNCT
ejpam-5903	333	20	.	.	PUNCT
ejpam-5903	334	1	therefore	therefore	ADV
ejpam-5903	334	2	,	,	PUNCT
ejpam-5903	334	3	ζhgk	ζhgk	PROPN
ejpam-5903	334	4	(	(	PUNCT
ejpam-5903	334	5	pn	pn	NOUN
ejpam-5903	334	6	)	)	PUNCT
ejpam-5903	334	7	=	=	NOUN
ejpam-5903	334	8	ζhgk	ζhgk	NOUN
ejpam-5903	334	9	(	(	PUNCT
ejpam-5903	334	10	s4	s4	PROPN
ejpam-5903	334	11	)	)	PUNCT
ejpam-5903	335	1	=	=	SYM
ejpam-5903	335	2	n−	n−	NOUN
ejpam-5903	335	3	|nhg	|nhg	VERB
ejpam-5903	335	4	g	g	NOUN
ejpam-5903	335	5	[	[	X
ejpam-5903	335	6	s4]|	s4]|	NOUN
ejpam-5903	335	7	=	=	SYM
ejpam-5903	335	8	3r	3r	NUM
ejpam-5903	335	9	+	+	CCONJ
ejpam-5903	335	10	2−	2−	NUM
ejpam-5903	335	11	(	(	PUNCT
ejpam-5903	335	12	3r	3r	NUM
ejpam-5903	335	13	−	−	NOUN
ejpam-5903	335	14	3k	3k	NOUN
ejpam-5903	335	15	+	+	CCONJ
ejpam-5903	335	16	4	4	X
ejpam-5903	335	17	)	)	PUNCT
ejpam-5903	335	18	=	=	PUNCT
ejpam-5903	336	1	3k	3k	X
ejpam-5903	337	1	−	−	NOUN
ejpam-5903	337	2	2	2	X
ejpam-5903	337	3	.	.	PUNCT
ejpam-5903	337	4	theorem	theorem	NOUN
ejpam-5903	337	5	9	9	NUM
ejpam-5903	337	6	.	.	PUNCT
ejpam-5903	338	1	if	if	SCONJ
ejpam-5903	338	2	cn	cn	PROPN
ejpam-5903	338	3	is	be	AUX
ejpam-5903	338	4	the	the	DET
ejpam-5903	338	5	cycle	cycle	NOUN
ejpam-5903	338	6	with	with	ADP
ejpam-5903	338	7	n	n	ADP
ejpam-5903	338	8	vertices	vertex	NOUN
ejpam-5903	338	9	and	and	CCONJ
ejpam-5903	338	10	k	k	PROPN
ejpam-5903	338	11	≤	≤	PROPN
ejpam-5903	338	12	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	338	13	1	1	NUM
ejpam-5903	338	14	,	,	PUNCT
ejpam-5903	338	15	then	then	ADV
ejpam-5903	338	16	ζhgk	ζhgk	NOUN
ejpam-5903	338	17	(	(	PUNCT
ejpam-5903	338	18	cn	cn	PROPN
ejpam-5903	338	19	)	)	PUNCT
ejpam-5903	338	20	=	=	SYM
ejpam-5903	338	21			NUM
ejpam-5903	338	22	n+	n+	PUNCT
ejpam-5903	339	1	k	k	PROPN
ejpam-5903	339	2	−	−	NOUN
ejpam-5903	339	3	3	3	NUM
ejpam-5903	339	4	if	if	SCONJ
ejpam-5903	339	5	n	n	X
ejpam-5903	339	6	=	=	SYM
ejpam-5903	339	7	3	3	NUM
ejpam-5903	339	8	,	,	PUNCT
ejpam-5903	339	9	4	4	NUM
ejpam-5903	339	10	,	,	PUNCT
ejpam-5903	339	11	5	5	NUM
ejpam-5903	339	12	3k	3k	NUM
ejpam-5903	339	13	+	+	CCONJ
ejpam-5903	339	14	2	2	NUM
ejpam-5903	339	15	if	if	SCONJ
ejpam-5903	339	16	n	n	NOUN
ejpam-5903	339	17	=	=	NOUN
ejpam-5903	339	18	3r	3r	NUM
ejpam-5903	339	19	,	,	PUNCT
ejpam-5903	339	20	r	r	NOUN
ejpam-5903	339	21	≥	≥	NUM
ejpam-5903	339	22	2	2	NUM
ejpam-5903	339	23	and	and	CCONJ
ejpam-5903	339	24	k	k	PROPN
ejpam-5903	339	25	=	=	SYM
ejpam-5903	339	26	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	339	27	1	1	NUM
ejpam-5903	339	28	or	or	CCONJ
ejpam-5903	339	29	r	r	NOUN
ejpam-5903	339	30	is	be	AUX
ejpam-5903	339	31	odd	odd	ADJ
ejpam-5903	339	32	,	,	PUNCT
ejpam-5903	339	33	r	r	NOUN
ejpam-5903	339	34	≥	≥	NOUN
ejpam-5903	339	35	3	3	NUM
ejpam-5903	339	36	,	,	PUNCT
ejpam-5903	339	37	and	and	CCONJ
ejpam-5903	339	38	k	k	PROPN
ejpam-5903	339	39	=	=	SYM
ejpam-5903	339	40	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	339	41	2	2	NUM
ejpam-5903	339	42	3k	3k	NOUN
ejpam-5903	339	43	if	if	SCONJ
ejpam-5903	339	44	n	n	NOUN
ejpam-5903	339	45	=	=	NOUN
ejpam-5903	339	46	3r	3r	NUM
ejpam-5903	339	47	,	,	PUNCT
ejpam-5903	339	48	r	r	NOUN
ejpam-5903	339	49	≥	≥	NOUN
ejpam-5903	339	50	4	4	NUM
ejpam-5903	339	51	and	and	CCONJ
ejpam-5903	339	52	,	,	PUNCT
ejpam-5903	339	53	1	1	NUM
ejpam-5903	339	54	≤	≤	NUM
ejpam-5903	339	55	k	k	X
ejpam-5903	339	56	≤	≤	PROPN
ejpam-5903	340	1	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	340	2	3	3	NUM
ejpam-5903	340	3	or	or	CCONJ
ejpam-5903	340	4	n	n	NOUN
ejpam-5903	340	5	=	=	NOUN
ejpam-5903	340	6	3r	3r	NUM
ejpam-5903	340	7	,	,	PUNCT
ejpam-5903	340	8	r	r	NOUN
ejpam-5903	340	9	is	be	AUX
ejpam-5903	340	10	even	even	ADV
ejpam-5903	340	11	,	,	PUNCT
ejpam-5903	341	1	r	r	NOUN
ejpam-5903	341	2	≥	≥	NOUN
ejpam-5903	341	3	4	4	NUM
ejpam-5903	341	4	,	,	PUNCT
ejpam-5903	341	5	and	and	CCONJ
ejpam-5903	341	6	k	k	PROPN
ejpam-5903	341	7	=	=	SYM
ejpam-5903	341	8	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	341	9	2	2	NUM
ejpam-5903	341	10	or	or	CCONJ
ejpam-5903	341	11	n	n	NOUN
ejpam-5903	341	12	=	=	NOUN
ejpam-5903	341	13	3r	3r	NUM
ejpam-5903	341	14	+	+	CCONJ
ejpam-5903	341	15	1	1	NUM
ejpam-5903	341	16	and	and	CCONJ
ejpam-5903	341	17	k	k	PROPN
ejpam-5903	341	18	=	=	SYM
ejpam-5903	341	19	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	341	20	1	1	NUM
ejpam-5903	341	21	or	or	CCONJ
ejpam-5903	341	22	n	n	NOUN
ejpam-5903	341	23	=	=	NOUN
ejpam-5903	341	24	3r	3r	NUM
ejpam-5903	341	25	+	+	CCONJ
ejpam-5903	341	26	1	1	NUM
ejpam-5903	341	27	,	,	PUNCT
ejpam-5903	341	28	r	r	NOUN
ejpam-5903	341	29	is	be	AUX
ejpam-5903	341	30	even	even	ADV
ejpam-5903	341	31	,	,	PUNCT
ejpam-5903	341	32	and	and	CCONJ
ejpam-5903	341	33	k	k	PROPN
ejpam-5903	341	34	=	=	SYM
ejpam-5903	341	35	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	341	36	2	2	NUM
ejpam-5903	341	37	1	1	NUM
ejpam-5903	341	38	if	if	SCONJ
ejpam-5903	341	39	n	n	NOUN
ejpam-5903	341	40	=	=	NOUN
ejpam-5903	341	41	3r	3r	NUM
ejpam-5903	341	42	+	+	CCONJ
ejpam-5903	341	43	2	2	NUM
ejpam-5903	341	44	,	,	PUNCT
ejpam-5903	341	45	r	r	NOUN
ejpam-5903	341	46	≥	≥	NOUN
ejpam-5903	341	47	2	2	NUM
ejpam-5903	341	48	,	,	PUNCT
ejpam-5903	341	49	and	and	CCONJ
ejpam-5903	341	50	k	k	X
ejpam-5903	341	51	=	=	NOUN
ejpam-5903	341	52	1	1	NUM
ejpam-5903	341	53	2	2	NUM
ejpam-5903	341	54	if	if	SCONJ
ejpam-5903	341	55	n	n	NOUN
ejpam-5903	341	56	=	=	NOUN
ejpam-5903	341	57	3r	3r	NUM
ejpam-5903	341	58	+	+	CCONJ
ejpam-5903	341	59	1	1	NUM
ejpam-5903	341	60	,	,	PUNCT
ejpam-5903	341	61	r	r	NOUN
ejpam-5903	341	62	≥	≥	NUM
ejpam-5903	341	63	3	3	NUM
ejpam-5903	341	64	and	and	CCONJ
ejpam-5903	341	65	k	k	NOUN
ejpam-5903	342	1	=	=	SYM
ejpam-5903	342	2	1	1	NUM
ejpam-5903	342	3	3k	3k	NUM
ejpam-5903	342	4	−	−	NOUN
ejpam-5903	342	5	2	2	NUM
ejpam-5903	342	6	if	if	SCONJ
ejpam-5903	342	7	n	n	NOUN
ejpam-5903	342	8	=	=	NOUN
ejpam-5903	342	9	3r	3r	NUM
ejpam-5903	342	10	+	+	CCONJ
ejpam-5903	342	11	1	1	NUM
ejpam-5903	342	12	,	,	PUNCT
ejpam-5903	342	13	r	r	NOUN
ejpam-5903	342	14	≥	≥	NOUN
ejpam-5903	342	15	4	4	NUM
ejpam-5903	342	16	,	,	PUNCT
ejpam-5903	342	17	and	and	CCONJ
ejpam-5903	342	18	2	2	NUM
ejpam-5903	342	19	≤	≤	NUM
ejpam-5903	342	20	k	k	PROPN
ejpam-5903	342	21	≤	≤	PROPN
ejpam-5903	342	22	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	342	23	3	3	NUM
ejpam-5903	342	24	or	or	CCONJ
ejpam-5903	342	25	n	n	NOUN
ejpam-5903	342	26	=	=	NOUN
ejpam-5903	342	27	3r	3r	NUM
ejpam-5903	342	28	+	+	CCONJ
ejpam-5903	342	29	1	1	NUM
ejpam-5903	342	30	,	,	PUNCT
ejpam-5903	342	31	r	r	NOUN
ejpam-5903	342	32	is	be	AUX
ejpam-5903	342	33	odd	odd	ADJ
ejpam-5903	342	34	,	,	PUNCT
ejpam-5903	342	35	r	r	NOUN
ejpam-5903	342	36	≥	≥	NOUN
ejpam-5903	342	37	3	3	NUM
ejpam-5903	342	38	,	,	PUNCT
ejpam-5903	342	39	and	and	CCONJ
ejpam-5903	342	40	k	k	PROPN
ejpam-5903	342	41	=	=	SYM
ejpam-5903	342	42	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	342	43	2	2	NUM
ejpam-5903	342	44	or	or	CCONJ
ejpam-5903	342	45	n	n	NOUN
ejpam-5903	342	46	=	=	NOUN
ejpam-5903	342	47	3r	3r	NUM
ejpam-5903	342	48	+	+	CCONJ
ejpam-5903	342	49	2	2	NUM
ejpam-5903	342	50	and	and	CCONJ
ejpam-5903	342	51	k	k	PROPN
ejpam-5903	343	1	=	=	SYM
ejpam-5903	343	2	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	343	3	1	1	NUM
ejpam-5903	343	4	or	or	CCONJ
ejpam-5903	343	5	n	n	NOUN
ejpam-5903	343	6	=	=	NOUN
ejpam-5903	343	7	3r	3r	NUM
ejpam-5903	343	8	+	+	CCONJ
ejpam-5903	343	9	2	2	NUM
ejpam-5903	343	10	,	,	PUNCT
ejpam-5903	343	11	r	r	NOUN
ejpam-5903	343	12	is	be	AUX
ejpam-5903	343	13	odd	odd	ADJ
ejpam-5903	343	14	,	,	PUNCT
ejpam-5903	343	15	r	r	NOUN
ejpam-5903	343	16	≥	≥	NOUN
ejpam-5903	343	17	3	3	NUM
ejpam-5903	343	18	,	,	PUNCT
ejpam-5903	343	19	and	and	CCONJ
ejpam-5903	343	20	k	k	PROPN
ejpam-5903	343	21	=	=	SYM
ejpam-5903	343	22	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	343	23	2	2	NUM
ejpam-5903	343	24	or	or	CCONJ
ejpam-5903	343	25	n	n	NOUN
ejpam-5903	343	26	=	=	NOUN
ejpam-5903	343	27	3r	3r	NUM
ejpam-5903	344	1	+	+	CCONJ
ejpam-5903	344	2	2	2	NUM
ejpam-5903	344	3	,	,	PUNCT
ejpam-5903	344	4	r	r	NOUN
ejpam-5903	344	5	=	=	SYM
ejpam-5903	344	6	2	2	NUM
ejpam-5903	344	7	,	,	PUNCT
ejpam-5903	344	8	and	and	CCONJ
ejpam-5903	344	9	k	k	PROPN
ejpam-5903	345	1	=	=	SYM
ejpam-5903	345	2	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	345	3	2	2	NUM
ejpam-5903	345	4	3k	3k	NOUN
ejpam-5903	345	5	−	−	NOUN
ejpam-5903	345	6	4	4	NUM
ejpam-5903	345	7	if	if	SCONJ
ejpam-5903	345	8	n	n	NOUN
ejpam-5903	345	9	=	=	NOUN
ejpam-5903	345	10	3r	3r	NUM
ejpam-5903	345	11	+	+	CCONJ
ejpam-5903	345	12	2	2	NUM
ejpam-5903	345	13	,	,	PUNCT
ejpam-5903	345	14	r	r	NOUN
ejpam-5903	345	15	≥	≥	NOUN
ejpam-5903	345	16	3	3	NUM
ejpam-5903	345	17	and	and	CCONJ
ejpam-5903	345	18	2	2	NUM
ejpam-5903	345	19	≤	≤	NOUN
ejpam-5903	345	20	k	k	PROPN
ejpam-5903	345	21	≤	≤	PROPN
ejpam-5903	345	22	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	345	23	3	3	NUM
ejpam-5903	345	24	or	or	CCONJ
ejpam-5903	345	25	n	n	NOUN
ejpam-5903	345	26	=	=	NOUN
ejpam-5903	345	27	3r	3r	NUM
ejpam-5903	345	28	+	+	CCONJ
ejpam-5903	345	29	2	2	NUM
ejpam-5903	345	30	,	,	PUNCT
ejpam-5903	345	31	r	r	NOUN
ejpam-5903	345	32	is	be	AUX
ejpam-5903	345	33	even	even	ADV
ejpam-5903	345	34	,	,	PUNCT
ejpam-5903	345	35	r	r	NOUN
ejpam-5903	345	36	≥	≥	NOUN
ejpam-5903	345	37	4	4	NUM
ejpam-5903	345	38	,	,	PUNCT
ejpam-5903	345	39	and	and	CCONJ
ejpam-5903	345	40	k	k	PROPN
ejpam-5903	345	41	=	=	SYM
ejpam-5903	345	42	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	345	43	2	2	NUM
ejpam-5903	345	44	proof	proof	NOUN
ejpam-5903	345	45	.	.	PUNCT
ejpam-5903	346	1	let	let	VERB
ejpam-5903	346	2	cn	cn	PROPN
ejpam-5903	346	3	=	=	PUNCT
ejpam-5903	347	1	[	[	X
ejpam-5903	347	2	v1	v1	NOUN
ejpam-5903	347	3	,	,	PUNCT
ejpam-5903	347	4	v2	v2	PROPN
ejpam-5903	347	5	,	,	PUNCT
ejpam-5903	347	6	·	·	PUNCT
ejpam-5903	347	7	·	·	PUNCT
ejpam-5903	347	8	·	·	PUNCT
ejpam-5903	347	9	,	,	PUNCT
ejpam-5903	347	10	vn	vn	X
ejpam-5903	347	11	,	,	PUNCT
ejpam-5903	347	12	v1	v1	PROPN
ejpam-5903	347	13	]	]	PUNCT
ejpam-5903	347	14	and	and	CCONJ
ejpam-5903	347	15	let	let	VERB
ejpam-5903	347	16	k	k	PROPN
ejpam-5903	347	17	≤	≤	NUM
ejpam-5903	347	18	γhg(cn	γhg(cn	NOUN
ejpam-5903	347	19	)	)	PUNCT
ejpam-5903	347	20	−	−	PROPN
ejpam-5903	347	21	1	1	X
ejpam-5903	347	22	.	.	PUNCT
ejpam-5903	347	23	consider	consider	VERB
ejpam-5903	347	24	the	the	DET
ejpam-5903	347	25	following	follow	VERB
ejpam-5903	347	26	cases	case	NOUN
ejpam-5903	347	27	:	:	PUNCT
ejpam-5903	347	28	case	case	NOUN
ejpam-5903	347	29	1	1	NUM
ejpam-5903	347	30	:	:	PUNCT
ejpam-5903	347	31	n	n	PROPN
ejpam-5903	347	32	=	=	SYM
ejpam-5903	347	33	3	3	NUM
ejpam-5903	347	34	or	or	CCONJ
ejpam-5903	347	35	4	4	NUM
ejpam-5903	347	36	,	,	PUNCT
ejpam-5903	347	37	or	or	CCONJ
ejpam-5903	347	38	5	5	NUM
ejpam-5903	347	39	.	.	PUNCT
ejpam-5903	347	40	by	by	ADP
ejpam-5903	347	41	theorem	theorem	NOUN
ejpam-5903	347	42	1(ii	1(ii	NUM
ejpam-5903	347	43	)	)	PUNCT
ejpam-5903	347	44	,	,	PUNCT
ejpam-5903	347	45	γhg(cn	γhg(cn	NOUN
ejpam-5903	347	46	)	)	PUNCT
ejpam-5903	347	47	=	=	SYM
ejpam-5903	347	48	3	3	X
ejpam-5903	347	49	.	.	X
ejpam-5903	347	50	choose	choose	VERB
ejpam-5903	347	51	a	a	DET
ejpam-5903	347	52	(	(	PUNCT
ejpam-5903	347	53	3	3	NUM
ejpam-5903	347	54	−	−	NOUN
ejpam-5903	347	55	k)-element	k)-element	PUNCT
ejpam-5903	347	56	set	set	VERB
ejpam-5903	347	57	d1	d1	PROPN
ejpam-5903	347	58	=	=	SYM
ejpam-5903	347	59	{	{	PUNCT
ejpam-5903	347	60	v1	v1	PROPN
ejpam-5903	347	61	,	,	PUNCT
ejpam-5903	347	62	v3−k	v3−k	X
ejpam-5903	347	63	}	}	PUNCT
ejpam-5903	347	64	.	.	PUNCT
ejpam-5903	348	1	this	this	DET
ejpam-5903	348	2	j.	j.	PROPN
ejpam-5903	348	3	anoche	anoche	PROPN
ejpam-5903	348	4	,	,	PUNCT
ejpam-5903	348	5	s.	s.	PROPN
ejpam-5903	348	6	canoy	canoy	PROPN
ejpam-5903	348	7	,	,	PUNCT
ejpam-5903	348	8	jr	jr	PROPN
ejpam-5903	348	9	.	.	PROPN
ejpam-5903	348	10	/	/	SYM
ejpam-5903	348	11	eur	eur	PROPN
ejpam-5903	348	12	.	.	PUNCT
ejpam-5903	349	1	j.	j.	PROPN
ejpam-5903	349	2	pure	pure	PROPN
ejpam-5903	349	3	appl	appl	PROPN
ejpam-5903	349	4	.	.	PROPN
ejpam-5903	349	5	math	math	PROPN
ejpam-5903	349	6	,	,	PUNCT
ejpam-5903	349	7	18	18	NUM
ejpam-5903	349	8	(	(	PUNCT
ejpam-5903	349	9	2	2	NUM
ejpam-5903	349	10	)	)	PUNCT
ejpam-5903	349	11	(	(	PUNCT
ejpam-5903	349	12	2025	2025	NUM
ejpam-5903	349	13	)	)	PUNCT
ejpam-5903	349	14	,	,	PUNCT
ejpam-5903	349	15	5903	5903	NUM
ejpam-5903	349	16	10	10	NUM
ejpam-5903	349	17	of	of	ADP
ejpam-5903	349	18	17	17	NUM
ejpam-5903	349	19	set	set	NOUN
ejpam-5903	349	20	is	be	AUX
ejpam-5903	349	21	a	a	DET
ejpam-5903	349	22	ζhgk	ζhgk	NOUN
ejpam-5903	349	23	-set	-set	ADJ
ejpam-5903	349	24	of	of	ADP
ejpam-5903	349	25	cn	cn	PROPN
ejpam-5903	349	26	.	.	PUNCT
ejpam-5903	350	1	since	since	SCONJ
ejpam-5903	350	2	d1	d1	PROPN
ejpam-5903	350	3	is	be	AUX
ejpam-5903	350	4	a	a	DET
ejpam-5903	350	5	clique	clique	NOUN
ejpam-5903	350	6	,	,	PUNCT
ejpam-5903	350	7	nhg	nhg	NOUN
ejpam-5903	350	8	g	g	PROPN
ejpam-5903	351	1	[	[	X
ejpam-5903	351	2	d1	d1	PROPN
ejpam-5903	351	3	]	]	X
ejpam-5903	351	4	=	=	SYM
ejpam-5903	351	5	d1	d1	NOUN
ejpam-5903	351	6	.	.	PUNCT
ejpam-5903	352	1	hence	hence	ADV
ejpam-5903	352	2	,	,	PUNCT
ejpam-5903	352	3	ζhgk	ζhgk	PROPN
ejpam-5903	352	4	(	(	PUNCT
ejpam-5903	352	5	cn	cn	NOUN
ejpam-5903	352	6	)	)	PUNCT
ejpam-5903	352	7	=	=	VERB
ejpam-5903	352	8	ζhgk	ζhgk	NOUN
ejpam-5903	352	9	(	(	PUNCT
ejpam-5903	352	10	d1	d1	NOUN
ejpam-5903	352	11	)	)	PUNCT
ejpam-5903	352	12	=	=	SYM
ejpam-5903	352	13	n−	n−	NOUN
ejpam-5903	352	14	|nhg	|nhg	VERB
ejpam-5903	352	15	g	g	PROPN
ejpam-5903	352	16	[	[	X
ejpam-5903	352	17	d1]|	d1]|	X
ejpam-5903	352	18	=	=	SYM
ejpam-5903	352	19	n−	n−	PROPN
ejpam-5903	352	20	(	(	PUNCT
ejpam-5903	352	21	3−	3−	NUM
ejpam-5903	352	22	k	k	NOUN
ejpam-5903	352	23	)	)	PUNCT
ejpam-5903	352	24	=	=	SYM
ejpam-5903	353	1	n+	n+	PUNCT
ejpam-5903	354	1	k	k	X
ejpam-5903	355	1	−	−	NOUN
ejpam-5903	356	1	3	3	X
ejpam-5903	356	2	.	.	PUNCT
ejpam-5903	356	3	case	case	NOUN
ejpam-5903	356	4	2	2	NUM
ejpam-5903	356	5	:	:	PUNCT
ejpam-5903	356	6	n	n	PROPN
ejpam-5903	356	7	=	=	NOUN
ejpam-5903	356	8	3r	3r	NUM
ejpam-5903	356	9	where	where	SCONJ
ejpam-5903	356	10	r	r	NOUN
ejpam-5903	356	11	≥	≥	NOUN
ejpam-5903	356	12	2	2	NUM
ejpam-5903	356	13	.	.	PUNCT
ejpam-5903	356	14	by	by	ADP
ejpam-5903	356	15	theorem	theorem	NOUN
ejpam-5903	356	16	1(ii	1(ii	NUM
ejpam-5903	356	17	)	)	PUNCT
ejpam-5903	356	18	,	,	PUNCT
ejpam-5903	356	19	γhg(cn	γhg(cn	NOUN
ejpam-5903	356	20	)	)	PUNCT
ejpam-5903	356	21	=	=	SYM
ejpam-5903	356	22	3r	3r	NUM
ejpam-5903	356	23	3	3	NUM
ejpam-5903	356	24	=	=	SYM
ejpam-5903	356	25	r.	r.	PROPN
ejpam-5903	356	26	thus	thus	ADV
ejpam-5903	356	27	,	,	PUNCT
ejpam-5903	356	28	k	k	PROPN
ejpam-5903	356	29	≤	≤	PROPN
ejpam-5903	356	30	r−1	r−1	PROPN
ejpam-5903	356	31	.	.	PUNCT
ejpam-5903	357	1	consider	consider	VERB
ejpam-5903	357	2	the	the	DET
ejpam-5903	357	3	following	follow	VERB
ejpam-5903	357	4	subcases	subcase	NOUN
ejpam-5903	357	5	:	:	PUNCT
ejpam-5903	357	6	subcase	subcase	NOUN
ejpam-5903	357	7	1	1	NUM
ejpam-5903	357	8	:	:	PUNCT
ejpam-5903	357	9	k	k	PROPN
ejpam-5903	357	10	=	=	SYM
ejpam-5903	357	11	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	357	12	1	1	NUM
ejpam-5903	357	13	.	.	PUNCT
ejpam-5903	358	1	by	by	ADP
ejpam-5903	358	2	lemma	lemma	PROPN
ejpam-5903	358	3	1	1	NUM
ejpam-5903	358	4	,	,	PUNCT
ejpam-5903	358	5	ζhgk	ζhgk	NOUN
ejpam-5903	358	6	(	(	PUNCT
ejpam-5903	358	7	cn	cn	NOUN
ejpam-5903	358	8	)	)	PUNCT
ejpam-5903	358	9	=	=	PUNCT
ejpam-5903	358	10	n−	n−	NOUN
ejpam-5903	358	11	1	1	NUM
ejpam-5903	358	12	=	=	SYM
ejpam-5903	358	13	3r	3r	NUM
ejpam-5903	358	14	−	−	NOUN
ejpam-5903	358	15	1	1	NUM
ejpam-5903	358	16	=	=	SYM
ejpam-5903	358	17	3k	3k	NOUN
ejpam-5903	358	18	+	+	CCONJ
ejpam-5903	358	19	2	2	X
ejpam-5903	358	20	.	.	X
ejpam-5903	358	21	subcase	subcase	NOUN
ejpam-5903	358	22	2	2	NUM
ejpam-5903	358	23	:	:	PUNCT
ejpam-5903	358	24	r	r	NOUN
ejpam-5903	358	25	is	be	AUX
ejpam-5903	358	26	odd	odd	ADJ
ejpam-5903	358	27	and	and	CCONJ
ejpam-5903	358	28	k	k	PROPN
ejpam-5903	358	29	=	=	SYM
ejpam-5903	358	30	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	358	31	2	2	X
ejpam-5903	358	32	.	.	PUNCT
ejpam-5903	359	1	let	let	VERB
ejpam-5903	359	2	d2	d2	PROPN
ejpam-5903	359	3	=	=	SYM
ejpam-5903	359	4	{	{	PUNCT
ejpam-5903	359	5	v1	v1	PROPN
ejpam-5903	359	6	,	,	PUNCT
ejpam-5903	359	7	v4	v4	NOUN
ejpam-5903	359	8	}	}	PUNCT
ejpam-5903	359	9	.	.	PUNCT
ejpam-5903	360	1	then	then	ADV
ejpam-5903	360	2	d2	d2	PROPN
ejpam-5903	360	3	is	be	AUX
ejpam-5903	360	4	a	a	DET
ejpam-5903	360	5	ζhgk	ζhgk	NOUN
ejpam-5903	360	6	-set	-set	ADJ
ejpam-5903	360	7	of	of	ADP
ejpam-5903	360	8	cn	cn	PROPN
ejpam-5903	360	9	and	and	CCONJ
ejpam-5903	360	10	nhg	nhg	VERB
ejpam-5903	360	11	g	g	PROPN
ejpam-5903	361	1	[	[	X
ejpam-5903	361	2	d2	d2	X
ejpam-5903	361	3	]	]	X
ejpam-5903	361	4	=	=	SYM
ejpam-5903	361	5	{	{	PUNCT
ejpam-5903	361	6	v1	v1	PROPN
ejpam-5903	361	7	,	,	PUNCT
ejpam-5903	361	8	v2	v2	PROPN
ejpam-5903	361	9	,	,	PUNCT
ejpam-5903	361	10	v3	v3	PROPN
ejpam-5903	361	11	,	,	PUNCT
ejpam-5903	361	12	v4	v4	PROPN
ejpam-5903	361	13	}	}	PUNCT
ejpam-5903	361	14	.	.	PUNCT
ejpam-5903	362	1	thus	thus	ADV
ejpam-5903	362	2	,	,	PUNCT
ejpam-5903	362	3	ζhgk	ζhgk	PROPN
ejpam-5903	362	4	(	(	PUNCT
ejpam-5903	362	5	cn	cn	NOUN
ejpam-5903	362	6	)	)	PUNCT
ejpam-5903	362	7	=	=	NOUN
ejpam-5903	362	8	ζhgk	ζhgk	NOUN
ejpam-5903	362	9	(	(	PUNCT
ejpam-5903	362	10	d2	d2	PROPN
ejpam-5903	362	11	)	)	PUNCT
ejpam-5903	362	12	=	=	SYM
ejpam-5903	362	13	3r	3r	NUM
ejpam-5903	362	14	−	−	PROPN
ejpam-5903	362	15	|nhg	|nhg	PROPN
ejpam-5903	362	16	g	g	X
ejpam-5903	363	1	[	[	X
ejpam-5903	363	2	d2]|	d2]|	NOUN
ejpam-5903	363	3	=	=	NOUN
ejpam-5903	363	4	3r	3r	NUM
ejpam-5903	363	5	−	−	NOUN
ejpam-5903	363	6	4	4	NUM
ejpam-5903	363	7	=	=	SYM
ejpam-5903	363	8	3k	3k	NOUN
ejpam-5903	364	1	+	+	CCONJ
ejpam-5903	364	2	2	2	X
ejpam-5903	364	3	.	.	X
ejpam-5903	364	4	subcase	subcase	NOUN
ejpam-5903	364	5	3	3	NUM
ejpam-5903	364	6	:	:	PUNCT
ejpam-5903	364	7	r	r	NOUN
ejpam-5903	364	8	≥	≥	NOUN
ejpam-5903	364	9	4	4	NUM
ejpam-5903	364	10	is	be	AUX
ejpam-5903	364	11	even	even	ADV
ejpam-5903	364	12	and	and	CCONJ
ejpam-5903	364	13	k	k	PROPN
ejpam-5903	364	14	=	=	SYM
ejpam-5903	364	15	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	365	1	2	2	X
ejpam-5903	365	2	.	.	PUNCT
ejpam-5903	365	3	let	let	VERB
ejpam-5903	365	4	d3	d3	PROPN
ejpam-5903	365	5	=	=	SYM
ejpam-5903	365	6	{	{	PUNCT
ejpam-5903	365	7	v1	v1	PROPN
ejpam-5903	365	8	,	,	PUNCT
ejpam-5903	365	9	v	v	ADP
ejpam-5903	365	10	3r+2	3r+2	NUM
ejpam-5903	365	11	2	2	NUM
ejpam-5903	365	12	}	}	PUNCT
ejpam-5903	365	13	.	.	PUNCT
ejpam-5903	366	1	then	then	ADV
ejpam-5903	366	2	d3	d3	PROPN
ejpam-5903	366	3	is	be	AUX
ejpam-5903	366	4	a	a	DET
ejpam-5903	366	5	ζhgk	ζhgk	NOUN
ejpam-5903	366	6	-set	-set	X
ejpam-5903	366	7	of	of	ADP
ejpam-5903	366	8	cn	cn	PROPN
ejpam-5903	366	9	and	and	CCONJ
ejpam-5903	366	10	nhg	nhg	VERB
ejpam-5903	366	11	g	g	PROPN
ejpam-5903	367	1	[	[	X
ejpam-5903	367	2	d3	d3	X
ejpam-5903	367	3	]	]	X
ejpam-5903	367	4	=	=	PRON
ejpam-5903	367	5	{	{	PUNCT
ejpam-5903	367	6	v1	v1	PROPN
ejpam-5903	367	7	,	,	PUNCT
ejpam-5903	367	8	v3	v3	PROPN
ejpam-5903	367	9	,	,	PUNCT
ejpam-5903	367	10	v	v	ADP
ejpam-5903	367	11	3r−2	3r−2	NUM
ejpam-5903	367	12	2	2	NUM
ejpam-5903	367	13	,	,	PUNCT
ejpam-5903	367	14	v	v	ADP
ejpam-5903	367	15	3r+2	3r+2	NUM
ejpam-5903	367	16	2	2	NUM
ejpam-5903	367	17	,	,	PUNCT
ejpam-5903	367	18	v	v	PRON
ejpam-5903	367	19	3r+6	3r+6	NUM
ejpam-5903	367	20	2	2	NUM
ejpam-5903	367	21	,	,	PUNCT
ejpam-5903	367	22	v3r−1	v3r−1	PROPN
ejpam-5903	367	23	}	}	PUNCT
ejpam-5903	367	24	.	.	PUNCT
ejpam-5903	368	1	hence	hence	ADV
ejpam-5903	368	2	,	,	PUNCT
ejpam-5903	368	3	ζhgk	ζhgk	PROPN
ejpam-5903	368	4	(	(	PUNCT
ejpam-5903	368	5	cn	cn	NOUN
ejpam-5903	368	6	)	)	PUNCT
ejpam-5903	368	7	=	=	VERB
ejpam-5903	368	8	ζhgk	ζhgk	NOUN
ejpam-5903	368	9	(	(	PUNCT
ejpam-5903	368	10	d3	d3	PROPN
ejpam-5903	368	11	)	)	PUNCT
ejpam-5903	368	12	=	=	SYM
ejpam-5903	368	13	3r	3r	NUM
ejpam-5903	368	14	+	+	SYM
ejpam-5903	368	15	1−	1−	NUM
ejpam-5903	368	16	|nhg	|nhg	VERB
ejpam-5903	368	17	g	g	X
ejpam-5903	369	1	[	[	X
ejpam-5903	369	2	d3]|	d3]|	NOUN
ejpam-5903	369	3	=	=	SYM
ejpam-5903	369	4	3r	3r	NUM
ejpam-5903	369	5	−	−	NOUN
ejpam-5903	369	6	6	6	NUM
ejpam-5903	369	7	=	=	SYM
ejpam-5903	369	8	3k	3k	NUM
ejpam-5903	369	9	.	.	PUNCT
ejpam-5903	370	1	subcase	subcase	PROPN
ejpam-5903	370	2	4	4	NUM
ejpam-5903	370	3	:	:	PUNCT
ejpam-5903	370	4	r	r	NOUN
ejpam-5903	370	5	≥	≥	NUM
ejpam-5903	370	6	4	4	NUM
ejpam-5903	370	7	and	and	CCONJ
ejpam-5903	370	8	1	1	NUM
ejpam-5903	370	9	≤	≤	NUM
ejpam-5903	370	10	k	k	PROPN
ejpam-5903	370	11	≤	≤	PROPN
ejpam-5903	370	12	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	371	1	3	3	X
ejpam-5903	371	2	.	.	PUNCT
ejpam-5903	371	3	let	let	VERB
ejpam-5903	371	4	k	k	PROPN
ejpam-5903	371	5	≤	≤	X
ejpam-5903	371	6	⌊γhg(cn)−2	⌊γhg(cn)−2	ADP
ejpam-5903	371	7	2	2	NUM
ejpam-5903	371	8	⌋	⌋	NOUN
ejpam-5903	371	9	and	and	CCONJ
ejpam-5903	371	10	let	let	VERB
ejpam-5903	371	11	d4	d4	PROPN
ejpam-5903	371	12	=	=	SYM
ejpam-5903	371	13	{	{	PUNCT
ejpam-5903	371	14	v1	v1	PROPN
ejpam-5903	371	15	,	,	PUNCT
ejpam-5903	371	16	v4	v4	NOUN
ejpam-5903	371	17	,	,	PUNCT
ejpam-5903	371	18	·	·	PUNCT
ejpam-5903	371	19	·	·	PUNCT
ejpam-5903	371	20	·	·	PUNCT
ejpam-5903	371	21	,	,	PUNCT
ejpam-5903	371	22	v3r−3k−2	v3r−3k−2	NOUN
ejpam-5903	371	23	}	}	PUNCT
ejpam-5903	371	24	.	.	PUNCT
ejpam-5903	372	1	then	then	ADV
ejpam-5903	372	2	d4	d4	PROPN
ejpam-5903	372	3	is	be	AUX
ejpam-5903	372	4	a	a	DET
ejpam-5903	372	5	ζhgk	ζhgk	NOUN
ejpam-5903	372	6	-set	-set	X
ejpam-5903	372	7	of	of	ADP
ejpam-5903	372	8	cn	cn	PROPN
ejpam-5903	372	9	and	and	CCONJ
ejpam-5903	372	10	nhg	nhg	VERB
ejpam-5903	372	11	g	g	PROPN
ejpam-5903	373	1	[	[	X
ejpam-5903	373	2	d4	d4	PROPN
ejpam-5903	373	3	]	]	X
ejpam-5903	373	4	=	=	SYM
ejpam-5903	373	5	{	{	PUNCT
ejpam-5903	373	6	v1	v1	PROPN
ejpam-5903	373	7	,	,	PUNCT
ejpam-5903	373	8	v2	v2	PROPN
ejpam-5903	373	9	,	,	PUNCT
ejpam-5903	373	10	v3	v3	PROPN
ejpam-5903	373	11	,	,	PUNCT
ejpam-5903	373	12	v4	v4	PROPN
ejpam-5903	373	13	,	,	PUNCT
ejpam-5903	373	14	·	·	PUNCT
ejpam-5903	373	15	·	·	PUNCT
ejpam-5903	373	16	·	·	PUNCT
ejpam-5903	373	17	,	,	PUNCT
ejpam-5903	373	18	v3r−3k−2	v3r−3k−2	NOUN
ejpam-5903	373	19	,	,	PUNCT
ejpam-5903	373	20	v3r−3k	v3r−3k	PROPN
ejpam-5903	373	21	,	,	PUNCT
ejpam-5903	373	22	v3r−1	v3r−1	PROPN
ejpam-5903	373	23	}	}	PUNCT
ejpam-5903	373	24	.	.	PUNCT
ejpam-5903	374	1	thus	thus	ADV
ejpam-5903	374	2	,	,	PUNCT
ejpam-5903	374	3	ζhgk	ζhgk	PROPN
ejpam-5903	374	4	(	(	PUNCT
ejpam-5903	374	5	cn	cn	NOUN
ejpam-5903	374	6	)	)	PUNCT
ejpam-5903	374	7	=	=	NOUN
ejpam-5903	374	8	ζhgk	ζhgk	NOUN
ejpam-5903	374	9	(	(	PUNCT
ejpam-5903	374	10	d4	d4	PROPN
ejpam-5903	374	11	)	)	PUNCT
ejpam-5903	374	12	=	=	SYM
ejpam-5903	374	13	n	n	PRON
ejpam-5903	374	14	−	−	PROPN
ejpam-5903	374	15	|nhg	|nhg	PROPN
ejpam-5903	374	16	g	g	X
ejpam-5903	374	17	[	[	X
ejpam-5903	374	18	d4]|	d4]|	NOUN
ejpam-5903	374	19	=	=	NOUN
ejpam-5903	374	20	3r	3r	NUM
ejpam-5903	374	21	−	−	PROPN
ejpam-5903	375	1	[	[	X
ejpam-5903	375	2	(	(	PUNCT
ejpam-5903	375	3	3r	3r	NUM
ejpam-5903	375	4	−	−	NOUN
ejpam-5903	375	5	3k	3k	NOUN
ejpam-5903	375	6	−	−	PROPN
ejpam-5903	375	7	2	2	NUM
ejpam-5903	375	8	)	)	PUNCT
ejpam-5903	375	9	+	+	CCONJ
ejpam-5903	375	10	2	2	X
ejpam-5903	375	11	]	]	PUNCT
ejpam-5903	375	12	=	=	SYM
ejpam-5903	375	13	3k	3k	X
ejpam-5903	375	14	.	.	PUNCT
ejpam-5903	376	1	next	next	ADV
ejpam-5903	376	2	,	,	PUNCT
ejpam-5903	376	3	let	let	VERB
ejpam-5903	376	4	⌊γhg(cn)−2	⌊γhg(cn)−2	ADP
ejpam-5903	376	5	2	2	NUM
ejpam-5903	376	6	⌋	⌋	NOUN
ejpam-5903	376	7	<	<	X
ejpam-5903	376	8	k	k	PROPN
ejpam-5903	376	9	≤	≤	PROPN
ejpam-5903	376	10	γhg(cn	γhg(cn	NOUN
ejpam-5903	376	11	)	)	PUNCT
ejpam-5903	376	12	−	−	PROPN
ejpam-5903	376	13	3	3	X
ejpam-5903	376	14	.	.	PUNCT
ejpam-5903	376	15	choose	choose	VERB
ejpam-5903	376	16	an	an	DET
ejpam-5903	376	17	(	(	PUNCT
ejpam-5903	376	18	r	r	NOUN
ejpam-5903	376	19	−	−	PROPN
ejpam-5903	376	20	k)-element	k)-element	PUNCT
ejpam-5903	376	21	set	set	NOUN
ejpam-5903	376	22	d5	d5	NOUN
ejpam-5903	376	23	=	=	PUNCT
ejpam-5903	376	24	{	{	PUNCT
ejpam-5903	376	25	v⌈	v⌈	NOUN
ejpam-5903	376	26	3r+2	3r+2	PROPN
ejpam-5903	376	27	2	2	NUM
ejpam-5903	376	28	⌉	⌉	NOUN
ejpam-5903	376	29	,	,	PUNCT
ejpam-5903	376	30	v1	v1	NOUN
ejpam-5903	376	31	,	,	PUNCT
ejpam-5903	376	32	v4	v4	NOUN
ejpam-5903	376	33	,	,	PUNCT
ejpam-5903	376	34	·	·	PUNCT
ejpam-5903	376	35	·	·	PUNCT
ejpam-5903	376	36	·	·	PUNCT
ejpam-5903	376	37	,	,	PUNCT
ejpam-5903	376	38	v3r−3k−5	v3r−3k−5	VERB
ejpam-5903	376	39	}	}	PUNCT
ejpam-5903	376	40	.	.	PUNCT
ejpam-5903	377	1	then	then	ADV
ejpam-5903	377	2	d5	d5	NOUN
ejpam-5903	377	3	is	be	AUX
ejpam-5903	377	4	a	a	DET
ejpam-5903	377	5	ζhgk	ζhgk	NOUN
ejpam-5903	377	6	-set	-set	X
ejpam-5903	377	7	of	of	ADP
ejpam-5903	377	8	cn	cn	PROPN
ejpam-5903	377	9	and	and	CCONJ
ejpam-5903	377	10	nhg	nhg	VERB
ejpam-5903	377	11	g	g	PROPN
ejpam-5903	378	1	[	[	X
ejpam-5903	378	2	d5	d5	NOUN
ejpam-5903	378	3	]	]	X
ejpam-5903	378	4	=	=	SYM
ejpam-5903	378	5	{	{	PUNCT
ejpam-5903	378	6	v1	v1	PROPN
ejpam-5903	378	7	,	,	PUNCT
ejpam-5903	378	8	v2	v2	PROPN
ejpam-5903	378	9	,	,	PUNCT
ejpam-5903	378	10	v3	v3	PROPN
ejpam-5903	378	11	,	,	PUNCT
ejpam-5903	378	12	v4	v4	PROPN
ejpam-5903	378	13	,	,	PUNCT
ejpam-5903	378	14	·	·	PUNCT
ejpam-5903	378	15	·	·	PUNCT
ejpam-5903	378	16	·	·	PUNCT
ejpam-5903	378	17	,	,	PUNCT
ejpam-5903	378	18	v3r−3k−5	v3r−3k−5	NUM
ejpam-5903	378	19	,	,	PUNCT
ejpam-5903	378	20	v3r−3k−3	v3r−3k−3	NOUN
ejpam-5903	378	21	,	,	PUNCT
ejpam-5903	378	22	v⌈	v⌈	NOUN
ejpam-5903	378	23	3r+2	3r+2	PROPN
ejpam-5903	378	24	2	2	NUM
ejpam-5903	378	25	⌉−2	⌉−2	NOUN
ejpam-5903	378	26	,	,	PUNCT
ejpam-5903	378	27	v⌈	v⌈	NOUN
ejpam-5903	378	28	3r+2	3r+2	PROPN
ejpam-5903	378	29	2	2	NUM
ejpam-5903	378	30	⌉	⌉	NOUN
ejpam-5903	378	31	,	,	PUNCT
ejpam-5903	378	32	v⌈	v⌈	NOUN
ejpam-5903	378	33	3r+2	3r+2	PROPN
ejpam-5903	378	34	2	2	NUM
ejpam-5903	378	35	⌉+2	⌉+2	PROPN
ejpam-5903	378	36	,	,	PUNCT
ejpam-5903	378	37	v3r−1	v3r−1	PROPN
ejpam-5903	378	38	}	}	PUNCT
ejpam-5903	378	39	.	.	PUNCT
ejpam-5903	379	1	this	this	PRON
ejpam-5903	379	2	implies	imply	VERB
ejpam-5903	379	3	that	that	SCONJ
ejpam-5903	379	4	ζhgk	ζhgk	NOUN
ejpam-5903	379	5	(	(	PUNCT
ejpam-5903	379	6	cn	cn	NOUN
ejpam-5903	379	7	)	)	PUNCT
ejpam-5903	379	8	=	=	NOUN
ejpam-5903	379	9	ζhgk	ζhgk	NOUN
ejpam-5903	379	10	(	(	PUNCT
ejpam-5903	379	11	d5	d5	NOUN
ejpam-5903	379	12	)	)	PUNCT
ejpam-5903	379	13	=	=	SYM
ejpam-5903	379	14	n−	n−	NOUN
ejpam-5903	379	15	|nhg	|nhg	VERB
ejpam-5903	379	16	g	g	NOUN
ejpam-5903	379	17	[	[	X
ejpam-5903	379	18	d5]|	d5]|	NOUN
ejpam-5903	379	19	=	=	SYM
ejpam-5903	379	20	3r	3r	NUM
ejpam-5903	379	21	−	−	PROPN
ejpam-5903	380	1	[	[	X
ejpam-5903	380	2	(	(	PUNCT
ejpam-5903	380	3	3r	3r	NUM
ejpam-5903	380	4	−	−	NOUN
ejpam-5903	380	5	3k	3k	NOUN
ejpam-5903	380	6	−	−	PROPN
ejpam-5903	380	7	5	5	NUM
ejpam-5903	380	8	)	)	PUNCT
ejpam-5903	380	9	+	+	CCONJ
ejpam-5903	380	10	5	5	X
ejpam-5903	380	11	]	]	PUNCT
ejpam-5903	380	12	=	=	SYM
ejpam-5903	380	13	3k	3k	X
ejpam-5903	380	14	.	.	PUNCT
ejpam-5903	381	1	case	case	NOUN
ejpam-5903	381	2	3	3	NUM
ejpam-5903	381	3	:	:	PUNCT
ejpam-5903	381	4	n	n	NOUN
ejpam-5903	381	5	=	=	SYM
ejpam-5903	381	6	3r	3r	NUM
ejpam-5903	381	7	+	+	CCONJ
ejpam-5903	381	8	1	1	X
ejpam-5903	381	9	.	.	PUNCT
ejpam-5903	381	10	by	by	ADP
ejpam-5903	381	11	theorem	theorem	NOUN
ejpam-5903	381	12	1(ii	1(ii	NUM
ejpam-5903	381	13	)	)	PUNCT
ejpam-5903	381	14	,	,	PUNCT
ejpam-5903	381	15	γhg(cn	γhg(cn	NOUN
ejpam-5903	381	16	)	)	PUNCT
ejpam-5903	381	17	=	=	SYM
ejpam-5903	382	1	3r+1	3r+1	NUM
ejpam-5903	382	2	+	+	PROPN
ejpam-5903	382	3	2	2	NUM
ejpam-5903	382	4	3	3	NUM
ejpam-5903	382	5	=	=	SYM
ejpam-5903	382	6	r	r	NOUN
ejpam-5903	382	7	+	+	NOUN
ejpam-5903	382	8	1	1	NUM
ejpam-5903	382	9	.	.	PUNCT
ejpam-5903	383	1	thus	thus	ADV
ejpam-5903	383	2	,	,	PUNCT
ejpam-5903	383	3	k	k	PROPN
ejpam-5903	383	4	≤	≤	PROPN
ejpam-5903	383	5	r.	r.	PROPN
ejpam-5903	383	6	consider	consider	VERB
ejpam-5903	383	7	the	the	DET
ejpam-5903	383	8	following	follow	VERB
ejpam-5903	383	9	subcases	subcase	NOUN
ejpam-5903	383	10	:	:	PUNCT
ejpam-5903	383	11	j.	j.	PROPN
ejpam-5903	383	12	anoche	anoche	PROPN
ejpam-5903	383	13	,	,	PUNCT
ejpam-5903	383	14	s.	s.	PROPN
ejpam-5903	383	15	canoy	canoy	PROPN
ejpam-5903	383	16	,	,	PUNCT
ejpam-5903	383	17	jr	jr	PROPN
ejpam-5903	383	18	.	.	PROPN
ejpam-5903	383	19	/	/	SYM
ejpam-5903	383	20	eur	eur	PROPN
ejpam-5903	383	21	.	.	PUNCT
ejpam-5903	384	1	j.	j.	PROPN
ejpam-5903	384	2	pure	pure	PROPN
ejpam-5903	384	3	appl	appl	PROPN
ejpam-5903	384	4	.	.	PROPN
ejpam-5903	384	5	math	math	PROPN
ejpam-5903	384	6	,	,	PUNCT
ejpam-5903	384	7	18	18	NUM
ejpam-5903	384	8	(	(	PUNCT
ejpam-5903	384	9	2	2	NUM
ejpam-5903	384	10	)	)	PUNCT
ejpam-5903	384	11	(	(	PUNCT
ejpam-5903	384	12	2025	2025	NUM
ejpam-5903	384	13	)	)	PUNCT
ejpam-5903	384	14	,	,	PUNCT
ejpam-5903	384	15	5903	5903	NUM
ejpam-5903	384	16	11	11	NUM
ejpam-5903	384	17	of	of	ADP
ejpam-5903	384	18	17	17	NUM
ejpam-5903	384	19	subcase	subcase	NOUN
ejpam-5903	384	20	1	1	NUM
ejpam-5903	384	21	:	:	PUNCT
ejpam-5903	384	22	k	k	PROPN
ejpam-5903	384	23	=	=	SYM
ejpam-5903	384	24	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	384	25	1	1	NUM
ejpam-5903	384	26	.	.	PUNCT
ejpam-5903	385	1	by	by	ADP
ejpam-5903	385	2	lemma	lemma	PROPN
ejpam-5903	385	3	1	1	NUM
ejpam-5903	385	4	,	,	PUNCT
ejpam-5903	385	5	ζhgk	ζhgk	NOUN
ejpam-5903	385	6	(	(	PUNCT
ejpam-5903	385	7	cn	cn	NOUN
ejpam-5903	385	8	)	)	PUNCT
ejpam-5903	385	9	=	=	PUNCT
ejpam-5903	385	10	n−	n−	NOUN
ejpam-5903	385	11	1	1	NUM
ejpam-5903	385	12	=	=	SYM
ejpam-5903	385	13	3r	3r	NUM
ejpam-5903	385	14	+	+	CCONJ
ejpam-5903	385	15	1−	1−	NUM
ejpam-5903	385	16	1	1	NUM
ejpam-5903	385	17	=	=	SYM
ejpam-5903	385	18	3r	3r	NUM
ejpam-5903	385	19	=	=	SYM
ejpam-5903	385	20	3k	3k	X
ejpam-5903	385	21	.	.	PUNCT
ejpam-5903	386	1	subcase	subcase	PROPN
ejpam-5903	386	2	2	2	NUM
ejpam-5903	386	3	:	:	PUNCT
ejpam-5903	386	4	r	r	NOUN
ejpam-5903	386	5	is	be	AUX
ejpam-5903	386	6	even	even	ADV
ejpam-5903	386	7	and	and	CCONJ
ejpam-5903	386	8	k	k	PROPN
ejpam-5903	386	9	=	=	SYM
ejpam-5903	386	10	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	386	11	2	2	X
ejpam-5903	386	12	.	.	PUNCT
ejpam-5903	387	1	let	let	VERB
ejpam-5903	387	2	d6	d6	NOUN
ejpam-5903	387	3	=	=	SYM
ejpam-5903	387	4	{	{	PUNCT
ejpam-5903	387	5	v1	v1	NOUN
ejpam-5903	387	6	,	,	PUNCT
ejpam-5903	387	7	v4	v4	NOUN
ejpam-5903	387	8	}	}	PUNCT
ejpam-5903	387	9	.	.	PUNCT
ejpam-5903	388	1	then	then	ADV
ejpam-5903	388	2	d6	d6	NOUN
ejpam-5903	388	3	is	be	AUX
ejpam-5903	388	4	a	a	DET
ejpam-5903	388	5	ζhgk	ζhgk	NOUN
ejpam-5903	388	6	-set	-set	ADJ
ejpam-5903	388	7	of	of	ADP
ejpam-5903	388	8	cn	cn	PROPN
ejpam-5903	388	9	and	and	CCONJ
ejpam-5903	388	10	nhg	nhg	VERB
ejpam-5903	388	11	g	g	PROPN
ejpam-5903	389	1	[	[	X
ejpam-5903	389	2	d6	d6	X
ejpam-5903	389	3	]	]	X
ejpam-5903	389	4	=	=	SYM
ejpam-5903	389	5	{	{	PUNCT
ejpam-5903	389	6	v1	v1	PROPN
ejpam-5903	389	7	,	,	PUNCT
ejpam-5903	389	8	v2	v2	PROPN
ejpam-5903	389	9	,	,	PUNCT
ejpam-5903	389	10	v3	v3	PROPN
ejpam-5903	389	11	,	,	PUNCT
ejpam-5903	389	12	v4	v4	PROPN
ejpam-5903	389	13	}	}	PUNCT
ejpam-5903	389	14	.	.	PUNCT
ejpam-5903	390	1	hence	hence	ADV
ejpam-5903	390	2	,	,	PUNCT
ejpam-5903	390	3	ζhgk	ζhgk	PROPN
ejpam-5903	390	4	(	(	PUNCT
ejpam-5903	390	5	cn	cn	NOUN
ejpam-5903	390	6	)	)	PUNCT
ejpam-5903	390	7	=	=	NOUN
ejpam-5903	390	8	ζhgk	ζhgk	NOUN
ejpam-5903	390	9	(	(	PUNCT
ejpam-5903	390	10	d6	d6	NOUN
ejpam-5903	390	11	)	)	PUNCT
ejpam-5903	390	12	=	=	SYM
ejpam-5903	390	13	3r	3r	NUM
ejpam-5903	390	14	+	+	SYM
ejpam-5903	390	15	1−	1−	NUM
ejpam-5903	391	1	|nhg	|nhg	VERB
ejpam-5903	391	2	g	g	X
ejpam-5903	391	3	[	[	X
ejpam-5903	391	4	d6]|	d6]|	VERB
ejpam-5903	391	5	=	=	SYM
ejpam-5903	391	6	3r	3r	NUM
ejpam-5903	391	7	+	+	CCONJ
ejpam-5903	391	8	1−	1−	NUM
ejpam-5903	391	9	4	4	NUM
ejpam-5903	391	10	=	=	SYM
ejpam-5903	391	11	3k	3k	NUM
ejpam-5903	391	12	.	.	PUNCT
ejpam-5903	392	1	subcase	subcase	PROPN
ejpam-5903	392	2	3	3	NUM
ejpam-5903	392	3	:	:	PUNCT
ejpam-5903	392	4	r	r	NOUN
ejpam-5903	392	5	≥	≥	NUM
ejpam-5903	392	6	3	3	NUM
ejpam-5903	392	7	and	and	CCONJ
ejpam-5903	392	8	k	k	NOUN
ejpam-5903	393	1	=	=	NOUN
ejpam-5903	393	2	1	1	X
ejpam-5903	393	3	.	.	PUNCT
ejpam-5903	393	4	let	let	VERB
ejpam-5903	393	5	d7	d7	PROPN
ejpam-5903	393	6	=	=	PUNCT
ejpam-5903	393	7	{	{	PUNCT
ejpam-5903	393	8	v1	v1	PROPN
ejpam-5903	393	9	,	,	PUNCT
ejpam-5903	393	10	v4	v4	NOUN
ejpam-5903	393	11	,	,	PUNCT
ejpam-5903	393	12	v7	v7	VERB
ejpam-5903	393	13	,	,	PUNCT
ejpam-5903	393	14	·	·	PUNCT
ejpam-5903	393	15	·	·	PUNCT
ejpam-5903	393	16	·	·	PUNCT
ejpam-5903	393	17	,	,	PUNCT
ejpam-5903	393	18	v3r−2	v3r−2	AUX
ejpam-5903	393	19	}	}	PUNCT
ejpam-5903	393	20	be	be	AUX
ejpam-5903	393	21	an	an	DET
ejpam-5903	393	22	r	r	NOUN
ejpam-5903	393	23	-	-	PUNCT
ejpam-5903	393	24	element	element	NOUN
ejpam-5903	393	25	set	set	NOUN
ejpam-5903	393	26	.	.	PUNCT
ejpam-5903	394	1	then	then	ADV
ejpam-5903	394	2	nhg	nhg	VERB
ejpam-5903	394	3	g	g	PROPN
ejpam-5903	395	1	[	[	X
ejpam-5903	395	2	d7	d7	X
ejpam-5903	395	3	]	]	X
ejpam-5903	395	4	=	=	SYM
ejpam-5903	395	5	{	{	PUNCT
ejpam-5903	395	6	v1	v1	PROPN
ejpam-5903	395	7	,	,	PUNCT
ejpam-5903	395	8	v2	v2	PROPN
ejpam-5903	395	9	,	,	PUNCT
ejpam-5903	395	10	v3	v3	PROPN
ejpam-5903	395	11	,	,	PUNCT
ejpam-5903	395	12	v4	v4	PROPN
ejpam-5903	395	13	,	,	PUNCT
ejpam-5903	395	14	·	·	PUNCT
ejpam-5903	395	15	·	·	PUNCT
ejpam-5903	395	16	·	·	PUNCT
ejpam-5903	395	17	,	,	PUNCT
ejpam-5903	395	18	v3r−2	v3r−2	PROPN
ejpam-5903	395	19	,	,	PUNCT
ejpam-5903	395	20	v3r	v3r	PROPN
ejpam-5903	395	21	}	}	PUNCT
ejpam-5903	395	22	.	.	PUNCT
ejpam-5903	396	1	thus	thus	ADV
ejpam-5903	396	2	,	,	PUNCT
ejpam-5903	396	3	d7	d7	PROPN
ejpam-5903	396	4	is	be	AUX
ejpam-5903	396	5	a	a	DET
ejpam-5903	396	6	ζhg1	ζhg1	NOUN
ejpam-5903	396	7	-set	-set	PUNCT
ejpam-5903	396	8	of	of	ADP
ejpam-5903	396	9	cn	cn	PROPN
ejpam-5903	396	10	.	.	PUNCT
ejpam-5903	397	1	hence	hence	ADV
ejpam-5903	397	2	,	,	PUNCT
ejpam-5903	397	3	ζhg1	ζhg1	PROPN
ejpam-5903	397	4	(	(	PUNCT
ejpam-5903	397	5	cn	cn	PROPN
ejpam-5903	397	6	)	)	PUNCT
ejpam-5903	397	7	=	=	SYM
ejpam-5903	397	8	ζhg1	ζhg1	PROPN
ejpam-5903	397	9	(	(	PUNCT
ejpam-5903	397	10	d7	d7	PROPN
ejpam-5903	397	11	)	)	PUNCT
ejpam-5903	397	12	=	=	SYM
ejpam-5903	397	13	n−	n−	NOUN
ejpam-5903	397	14	|nhg	|nhg	VERB
ejpam-5903	397	15	g	g	PROPN
ejpam-5903	398	1	[	[	X
ejpam-5903	398	2	d7]|	d7]|	NOUN
ejpam-5903	398	3	=	=	NOUN
ejpam-5903	398	4	3r	3r	NUM
ejpam-5903	398	5	+	+	SYM
ejpam-5903	398	6	1−	1−	NUM
ejpam-5903	398	7	(	(	PUNCT
ejpam-5903	398	8	3r	3r	NUM
ejpam-5903	398	9	−	−	NOUN
ejpam-5903	398	10	1	1	NUM
ejpam-5903	398	11	)	)	PUNCT
ejpam-5903	398	12	=	=	SYM
ejpam-5903	398	13	2	2	X
ejpam-5903	398	14	.	.	X
ejpam-5903	398	15	subcase	subcase	NOUN
ejpam-5903	398	16	4	4	NUM
ejpam-5903	398	17	:	:	PUNCT
ejpam-5903	399	1	r	r	NOUN
ejpam-5903	399	2	≥	≥	NUM
ejpam-5903	399	3	4	4	NUM
ejpam-5903	399	4	and	and	CCONJ
ejpam-5903	399	5	2	2	NUM
ejpam-5903	399	6	≤	≤	NOUN
ejpam-5903	399	7	k	k	PROPN
ejpam-5903	399	8	≤	≤	PROPN
ejpam-5903	399	9	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	399	10	3	3	X
ejpam-5903	399	11	.	.	PUNCT
ejpam-5903	400	1	let	let	VERB
ejpam-5903	400	2	k	k	PROPN
ejpam-5903	400	3	≤	≤	X
ejpam-5903	400	4	⌊γhg(cn)−2	⌊γhg(cn)−2	PUNCT
ejpam-5903	400	5	2	2	NUM
ejpam-5903	400	6	⌋	⌋	NOUN
ejpam-5903	400	7	and	and	CCONJ
ejpam-5903	400	8	d8	d8	PROPN
ejpam-5903	400	9	=	=	SYM
ejpam-5903	400	10	{	{	PUNCT
ejpam-5903	400	11	v1	v1	PROPN
ejpam-5903	400	12	,	,	PUNCT
ejpam-5903	400	13	v4	v4	NOUN
ejpam-5903	400	14	,	,	PUNCT
ejpam-5903	400	15	·	·	PUNCT
ejpam-5903	400	16	·	·	PUNCT
ejpam-5903	400	17	·	·	PUNCT
ejpam-5903	400	18	,	,	PUNCT
ejpam-5903	400	19	v3r−3k+1	v3r−3k+1	NOUN
ejpam-5903	400	20	}	}	PUNCT
ejpam-5903	400	21	.	.	PUNCT
ejpam-5903	401	1	then	then	ADV
ejpam-5903	401	2	d8	d8	PROPN
ejpam-5903	401	3	is	be	AUX
ejpam-5903	401	4	a	a	DET
ejpam-5903	401	5	ζhgk	ζhgk	NOUN
ejpam-5903	401	6	-set	-set	ADJ
ejpam-5903	401	7	of	of	ADP
ejpam-5903	401	8	cn	cn	PROPN
ejpam-5903	401	9	and	and	CCONJ
ejpam-5903	401	10	nhg	nhg	VERB
ejpam-5903	401	11	g	g	PROPN
ejpam-5903	402	1	[	[	X
ejpam-5903	402	2	d8	d8	X
ejpam-5903	402	3	]	]	X
ejpam-5903	402	4	=	=	SYM
ejpam-5903	402	5	{	{	PUNCT
ejpam-5903	402	6	v1	v1	PROPN
ejpam-5903	402	7	,	,	PUNCT
ejpam-5903	402	8	v2	v2	PROPN
ejpam-5903	402	9	,	,	PUNCT
ejpam-5903	402	10	v3	v3	PROPN
ejpam-5903	402	11	,	,	PUNCT
ejpam-5903	402	12	v4	v4	PROPN
ejpam-5903	402	13	,	,	PUNCT
ejpam-5903	402	14	·	·	PUNCT
ejpam-5903	402	15	·	·	PUNCT
ejpam-5903	402	16	·	·	PUNCT
ejpam-5903	402	17	,	,	PUNCT
ejpam-5903	402	18	v3r−3k+1	v3r−3k+1	NOUN
ejpam-5903	402	19	,	,	PUNCT
ejpam-5903	402	20	v3r−3k+3	v3r−3k+3	NOUN
ejpam-5903	402	21	,	,	PUNCT
ejpam-5903	402	22	v3r	v3r	PROPN
ejpam-5903	402	23	}	}	PUNCT
ejpam-5903	402	24	.	.	PUNCT
ejpam-5903	403	1	this	this	PRON
ejpam-5903	403	2	implies	imply	VERB
ejpam-5903	403	3	that	that	SCONJ
ejpam-5903	403	4	ζhgk	ζhgk	NOUN
ejpam-5903	403	5	(	(	PUNCT
ejpam-5903	403	6	cn	cn	NOUN
ejpam-5903	403	7	)	)	PUNCT
ejpam-5903	403	8	=	=	SYM
ejpam-5903	403	9	ζhgk	ζhgk	NOUN
ejpam-5903	403	10	(	(	PUNCT
ejpam-5903	403	11	d8	d8	PROPN
ejpam-5903	403	12	)	)	PUNCT
ejpam-5903	403	13	=	=	PUNCT
ejpam-5903	404	1	n−|nhg	n−|nhg	ADJ
ejpam-5903	404	2	g	g	NOUN
ejpam-5903	405	1	[	[	X
ejpam-5903	405	2	d8]|	d8]|	X
ejpam-5903	405	3	=	=	SYM
ejpam-5903	405	4	3r+1−	3r+1−	NUM
ejpam-5903	406	1	[	[	X
ejpam-5903	406	2	(	(	PUNCT
ejpam-5903	406	3	3r−3k+1)+2	3r−3k+1)+2	NUM
ejpam-5903	406	4	]	]	X
ejpam-5903	406	5	=	=	SYM
ejpam-5903	406	6	3k−2	3k−2	PROPN
ejpam-5903	406	7	.	.	PUNCT
ejpam-5903	407	1	hence	hence	ADV
ejpam-5903	407	2	,	,	PUNCT
ejpam-5903	407	3	ζhgk	ζhgk	PROPN
ejpam-5903	407	4	(	(	PUNCT
ejpam-5903	407	5	cn	cn	PROPN
ejpam-5903	407	6	)	)	PUNCT
ejpam-5903	407	7	=	=	PUNCT
ejpam-5903	408	1	3k−	3k−	NUM
ejpam-5903	408	2	2	2	NUM
ejpam-5903	408	3	.	.	PUNCT
ejpam-5903	409	1	next	next	ADV
ejpam-5903	409	2	,	,	PUNCT
ejpam-5903	409	3	let	let	VERB
ejpam-5903	409	4	⌊γhg(cn)−2	⌊γhg(cn)−2	ADP
ejpam-5903	409	5	2	2	NUM
ejpam-5903	409	6	⌋	⌋	NOUN
ejpam-5903	409	7	<	<	X
ejpam-5903	409	8	k	k	PROPN
ejpam-5903	409	9	≤	≤	PROPN
ejpam-5903	409	10	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	410	1	3	3	X
ejpam-5903	410	2	.	.	PUNCT
ejpam-5903	410	3	choose	choose	VERB
ejpam-5903	410	4	an	an	DET
ejpam-5903	410	5	(	(	PUNCT
ejpam-5903	410	6	r−	r−	NOUN
ejpam-5903	410	7	k+1)element	k+1)element	PROPN
ejpam-5903	410	8	set	set	VERB
ejpam-5903	410	9	d9	d9	PROPN
ejpam-5903	410	10	=	=	PUNCT
ejpam-5903	410	11	{	{	PUNCT
ejpam-5903	410	12	v⌈	v⌈	NOUN
ejpam-5903	410	13	3r+3	3r+3	PROPN
ejpam-5903	410	14	2	2	NUM
ejpam-5903	410	15	⌉	⌉	NOUN
ejpam-5903	410	16	,	,	PUNCT
ejpam-5903	410	17	v1	v1	NOUN
ejpam-5903	410	18	,	,	PUNCT
ejpam-5903	410	19	v4	v4	NOUN
ejpam-5903	410	20	,	,	PUNCT
ejpam-5903	410	21	·	·	PUNCT
ejpam-5903	410	22	·	·	PUNCT
ejpam-5903	410	23	·	·	PUNCT
ejpam-5903	410	24	,	,	PUNCT
ejpam-5903	410	25	v3r−3k−2	v3r−3k−2	NOUN
ejpam-5903	410	26	}	}	PUNCT
ejpam-5903	410	27	.	.	PUNCT
ejpam-5903	411	1	then	then	ADV
ejpam-5903	411	2	d9	d9	PROPN
ejpam-5903	411	3	is	be	AUX
ejpam-5903	411	4	a	a	DET
ejpam-5903	411	5	ζhgk	ζhgk	NOUN
ejpam-5903	411	6	-set	-set	ADJ
ejpam-5903	411	7	of	of	ADP
ejpam-5903	411	8	cn	cn	PROPN
ejpam-5903	411	9	and	and	CCONJ
ejpam-5903	411	10	nhg	nhg	VERB
ejpam-5903	411	11	g	g	PROPN
ejpam-5903	412	1	[	[	X
ejpam-5903	412	2	d9	d9	X
ejpam-5903	412	3	]	]	X
ejpam-5903	412	4	=	=	SYM
ejpam-5903	412	5	{	{	PUNCT
ejpam-5903	412	6	v1	v1	PROPN
ejpam-5903	412	7	,	,	PUNCT
ejpam-5903	412	8	v2	v2	PROPN
ejpam-5903	412	9	,	,	PUNCT
ejpam-5903	412	10	v3	v3	PROPN
ejpam-5903	412	11	,	,	PUNCT
ejpam-5903	412	12	v4	v4	PROPN
ejpam-5903	412	13	,	,	PUNCT
ejpam-5903	412	14	·	·	PUNCT
ejpam-5903	412	15	·	·	PUNCT
ejpam-5903	412	16	·	·	PUNCT
ejpam-5903	412	17	,	,	PUNCT
ejpam-5903	412	18	v3r−3k−2	v3r−3k−2	NOUN
ejpam-5903	412	19	,	,	PUNCT
ejpam-5903	412	20	v3r−3k	v3r−3k	PROPN
ejpam-5903	412	21	,	,	PUNCT
ejpam-5903	412	22	v⌈	v⌈	NOUN
ejpam-5903	412	23	3r+3	3r+3	PROPN
ejpam-5903	412	24	2	2	NUM
ejpam-5903	412	25	⌉−2	⌉−2	NOUN
ejpam-5903	412	26	,	,	PUNCT
ejpam-5903	412	27	v⌈	v⌈	NOUN
ejpam-5903	412	28	3r+3	3r+3	PROPN
ejpam-5903	412	29	2	2	NUM
ejpam-5903	412	30	⌉	⌉	NOUN
ejpam-5903	412	31	,	,	PUNCT
ejpam-5903	412	32	v⌈	v⌈	NOUN
ejpam-5903	412	33	3r+3	3r+3	PROPN
ejpam-5903	412	34	2	2	NUM
ejpam-5903	412	35	⌉+2	⌉+2	PROPN
ejpam-5903	412	36	,	,	PUNCT
ejpam-5903	412	37	v3r	v3r	NOUN
ejpam-5903	412	38	}	}	PUNCT
ejpam-5903	412	39	.	.	PUNCT
ejpam-5903	413	1	this	this	PRON
ejpam-5903	413	2	implies	imply	VERB
ejpam-5903	413	3	that	that	SCONJ
ejpam-5903	413	4	ζhgk	ζhgk	NOUN
ejpam-5903	413	5	(	(	PUNCT
ejpam-5903	413	6	cn	cn	NOUN
ejpam-5903	413	7	)	)	PUNCT
ejpam-5903	413	8	=	=	VERB
ejpam-5903	413	9	ζhgk	ζhgk	NOUN
ejpam-5903	413	10	(	(	PUNCT
ejpam-5903	413	11	d9	d9	PROPN
ejpam-5903	413	12	)	)	PUNCT
ejpam-5903	413	13	=	=	PUNCT
ejpam-5903	414	1	n−|nhg	n−|nhg	ADJ
ejpam-5903	414	2	g	g	X
ejpam-5903	415	1	[	[	X
ejpam-5903	415	2	d9]|	d9]|	X
ejpam-5903	415	3	=	=	SYM
ejpam-5903	415	4	3r+1−	3r+1−	NUM
ejpam-5903	416	1	[	[	X
ejpam-5903	416	2	(	(	PUNCT
ejpam-5903	416	3	3r−3k−2)+5	3r−3k−2)+5	NUM
ejpam-5903	416	4	]	]	X
ejpam-5903	416	5	=	=	SYM
ejpam-5903	416	6	3k−2	3k−2	PROPN
ejpam-5903	416	7	.	.	PUNCT
ejpam-5903	417	1	hence	hence	ADV
ejpam-5903	417	2	,	,	PUNCT
ejpam-5903	417	3	ζhgk	ζhgk	PROPN
ejpam-5903	417	4	(	(	PUNCT
ejpam-5903	417	5	cn	cn	PROPN
ejpam-5903	417	6	)	)	PUNCT
ejpam-5903	417	7	=	=	SYM
ejpam-5903	417	8	3k	3k	PRON
ejpam-5903	417	9	−	−	NOUN
ejpam-5903	417	10	2	2	X
ejpam-5903	417	11	.	.	X
ejpam-5903	417	12	subcase	subcase	NOUN
ejpam-5903	417	13	5	5	NUM
ejpam-5903	417	14	:	:	PUNCT
ejpam-5903	418	1	r	r	NOUN
ejpam-5903	418	2	≥	≥	NUM
ejpam-5903	418	3	3	3	NUM
ejpam-5903	418	4	is	be	AUX
ejpam-5903	418	5	odd	odd	ADJ
ejpam-5903	418	6	and	and	CCONJ
ejpam-5903	418	7	k	k	PROPN
ejpam-5903	418	8	=	=	SYM
ejpam-5903	418	9	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	418	10	2	2	X
ejpam-5903	418	11	.	.	PUNCT
ejpam-5903	419	1	let	let	VERB
ejpam-5903	419	2	d10	d10	X
ejpam-5903	419	3	=	=	SYM
ejpam-5903	419	4	{	{	PUNCT
ejpam-5903	419	5	v1	v1	PROPN
ejpam-5903	419	6	,	,	PUNCT
ejpam-5903	419	7	v	v	NOUN
ejpam-5903	419	8	3r+3	3r+3	PROPN
ejpam-5903	419	9	2	2	NUM
ejpam-5903	419	10	}	}	PUNCT
ejpam-5903	419	11	.	.	PUNCT
ejpam-5903	420	1	then	then	ADV
ejpam-5903	420	2	d10	d10	PROPN
ejpam-5903	420	3	is	be	AUX
ejpam-5903	420	4	a	a	DET
ejpam-5903	420	5	ζhgk	ζhgk	NOUN
ejpam-5903	420	6	-set	-set	X
ejpam-5903	420	7	of	of	ADP
ejpam-5903	420	8	cn	cn	PROPN
ejpam-5903	420	9	and	and	CCONJ
ejpam-5903	420	10	nhg	nhg	VERB
ejpam-5903	420	11	g	g	PROPN
ejpam-5903	421	1	[	[	X
ejpam-5903	421	2	d10	d10	X
ejpam-5903	421	3	]	]	X
ejpam-5903	421	4	=	=	SYM
ejpam-5903	421	5	{	{	PUNCT
ejpam-5903	421	6	v1	v1	PROPN
ejpam-5903	421	7	,	,	PUNCT
ejpam-5903	421	8	v3	v3	PROPN
ejpam-5903	421	9	,	,	PUNCT
ejpam-5903	421	10	v	v	ADP
ejpam-5903	421	11	3r−1	3r−1	NUM
ejpam-5903	421	12	2	2	NUM
ejpam-5903	421	13	,	,	PUNCT
ejpam-5903	421	14	v	v	NOUN
ejpam-5903	421	15	3r+3	3r+3	PROPN
ejpam-5903	421	16	2	2	NUM
ejpam-5903	421	17	,	,	PUNCT
ejpam-5903	421	18	v	v	NOUN
ejpam-5903	421	19	3r+7	3r+7	PROPN
ejpam-5903	421	20	2	2	NUM
ejpam-5903	421	21	,	,	PUNCT
ejpam-5903	421	22	v3r	v3r	NOUN
ejpam-5903	421	23	}	}	PUNCT
ejpam-5903	421	24	.	.	PUNCT
ejpam-5903	422	1	hence	hence	ADV
ejpam-5903	422	2	,	,	PUNCT
ejpam-5903	422	3	ζhgk	ζhgk	PROPN
ejpam-5903	422	4	(	(	PUNCT
ejpam-5903	422	5	cn	cn	NOUN
ejpam-5903	422	6	)	)	PUNCT
ejpam-5903	422	7	=	=	VERB
ejpam-5903	422	8	ζhgk	ζhgk	NOUN
ejpam-5903	422	9	(	(	PUNCT
ejpam-5903	422	10	d10	d10	PROPN
ejpam-5903	422	11	)	)	PUNCT
ejpam-5903	422	12	=	=	SYM
ejpam-5903	422	13	3r	3r	NUM
ejpam-5903	422	14	+	+	SYM
ejpam-5903	422	15	1−	1−	NUM
ejpam-5903	423	1	|nhg	|nhg	VERB
ejpam-5903	423	2	g	g	X
ejpam-5903	423	3	[	[	X
ejpam-5903	423	4	d10]|	d10]|	NOUN
ejpam-5903	423	5	=	=	SYM
ejpam-5903	423	6	3r	3r	NUM
ejpam-5903	423	7	+	+	CCONJ
ejpam-5903	423	8	1−	1−	NUM
ejpam-5903	423	9	6	6	NUM
ejpam-5903	423	10	=	=	SYM
ejpam-5903	423	11	3k	3k	NOUN
ejpam-5903	423	12	−	−	NOUN
ejpam-5903	423	13	2	2	X
ejpam-5903	423	14	.	.	PUNCT
ejpam-5903	423	15	case	case	NOUN
ejpam-5903	423	16	4	4	NUM
ejpam-5903	423	17	:	:	SYM
ejpam-5903	424	1	n	n	NOUN
ejpam-5903	424	2	=	=	SYM
ejpam-5903	424	3	3r	3r	NUM
ejpam-5903	424	4	+	+	CCONJ
ejpam-5903	424	5	2	2	NUM
ejpam-5903	424	6	where	where	SCONJ
ejpam-5903	424	7	r	r	NOUN
ejpam-5903	424	8	≥	≥	NOUN
ejpam-5903	424	9	2	2	NUM
ejpam-5903	424	10	.	.	PUNCT
ejpam-5903	424	11	by	by	ADP
ejpam-5903	424	12	theorem	theorem	NOUN
ejpam-5903	424	13	1(ii	1(ii	NUM
ejpam-5903	424	14	)	)	PUNCT
ejpam-5903	424	15	,	,	PUNCT
ejpam-5903	424	16	γhg(cn	γhg(cn	NOUN
ejpam-5903	424	17	)	)	PUNCT
ejpam-5903	424	18	=	=	SYM
ejpam-5903	425	1	3r+6	3r+6	NUM
ejpam-5903	425	2	3	3	NUM
ejpam-5903	426	1	=	=	SYM
ejpam-5903	426	2	r	r	NOUN
ejpam-5903	426	3	+	+	NOUN
ejpam-5903	426	4	2	2	NUM
ejpam-5903	426	5	.	.	PUNCT
ejpam-5903	427	1	thus	thus	ADV
ejpam-5903	427	2	,	,	PUNCT
ejpam-5903	427	3	k	k	PROPN
ejpam-5903	427	4	≤	≤	PROPN
ejpam-5903	427	5	r	r	NOUN
ejpam-5903	427	6	+	+	NOUN
ejpam-5903	427	7	1	1	X
ejpam-5903	427	8	.	.	X
ejpam-5903	427	9	consider	consider	VERB
ejpam-5903	427	10	the	the	DET
ejpam-5903	427	11	following	follow	VERB
ejpam-5903	427	12	subcases	subcase	NOUN
ejpam-5903	427	13	:	:	PUNCT
ejpam-5903	427	14	j.	j.	PROPN
ejpam-5903	427	15	anoche	anoche	PROPN
ejpam-5903	427	16	,	,	PUNCT
ejpam-5903	427	17	s.	s.	PROPN
ejpam-5903	427	18	canoy	canoy	PROPN
ejpam-5903	427	19	,	,	PUNCT
ejpam-5903	427	20	jr	jr	PROPN
ejpam-5903	427	21	.	.	PROPN
ejpam-5903	427	22	/	/	SYM
ejpam-5903	427	23	eur	eur	PROPN
ejpam-5903	427	24	.	.	PUNCT
ejpam-5903	428	1	j.	j.	PROPN
ejpam-5903	428	2	pure	pure	PROPN
ejpam-5903	428	3	appl	appl	PROPN
ejpam-5903	428	4	.	.	PROPN
ejpam-5903	428	5	math	math	PROPN
ejpam-5903	428	6	,	,	PUNCT
ejpam-5903	428	7	18	18	NUM
ejpam-5903	428	8	(	(	PUNCT
ejpam-5903	428	9	2	2	NUM
ejpam-5903	428	10	)	)	PUNCT
ejpam-5903	428	11	(	(	PUNCT
ejpam-5903	428	12	2025	2025	NUM
ejpam-5903	428	13	)	)	PUNCT
ejpam-5903	428	14	,	,	PUNCT
ejpam-5903	428	15	5903	5903	NUM
ejpam-5903	428	16	12	12	NUM
ejpam-5903	428	17	of	of	ADP
ejpam-5903	428	18	17	17	NUM
ejpam-5903	428	19	subcase	subcase	NOUN
ejpam-5903	428	20	1	1	NUM
ejpam-5903	428	21	:	:	PUNCT
ejpam-5903	428	22	k	k	X
ejpam-5903	429	1	=	=	SYM
ejpam-5903	429	2	1	1	X
ejpam-5903	429	3	.	.	PUNCT
ejpam-5903	429	4	let	let	VERB
ejpam-5903	429	5	d11	d11	PROPN
ejpam-5903	429	6	=	=	SYM
ejpam-5903	429	7	{	{	PUNCT
ejpam-5903	429	8	v1	v1	PROPN
ejpam-5903	429	9	,	,	PUNCT
ejpam-5903	429	10	v4	v4	NOUN
ejpam-5903	429	11	,	,	PUNCT
ejpam-5903	429	12	·	·	PUNCT
ejpam-5903	429	13	·	·	PUNCT
ejpam-5903	429	14	·	·	PUNCT
ejpam-5903	429	15	,	,	PUNCT
ejpam-5903	429	16	v3r−2	v3r−2	PROPN
ejpam-5903	429	17	,	,	PUNCT
ejpam-5903	429	18	v3r+1	v3r+1	PROPN
ejpam-5903	429	19	}	}	PUNCT
ejpam-5903	429	20	be	be	AUX
ejpam-5903	429	21	an	an	DET
ejpam-5903	429	22	(	(	PUNCT
ejpam-5903	429	23	r	r	NOUN
ejpam-5903	429	24	+	+	NOUN
ejpam-5903	429	25	1)-element	1)-element	NUM
ejpam-5903	429	26	set	set	NOUN
ejpam-5903	429	27	.	.	PUNCT
ejpam-5903	430	1	then	then	ADV
ejpam-5903	430	2	nhg	nhg	VERB
ejpam-5903	430	3	g	g	PROPN
ejpam-5903	431	1	[	[	X
ejpam-5903	431	2	d11	d11	X
ejpam-5903	431	3	]	]	X
ejpam-5903	431	4	=	=	SYM
ejpam-5903	431	5	v	v	X
ejpam-5903	431	6	(	(	PUNCT
ejpam-5903	431	7	cn	cn	PROPN
ejpam-5903	431	8	)	)	PUNCT
ejpam-5903	431	9	\	\	PROPN
ejpam-5903	431	10	{	{	PUNCT
ejpam-5903	431	11	v3r+2	v3r+2	NOUN
ejpam-5903	431	12	}	}	PUNCT
ejpam-5903	431	13	.	.	PUNCT
ejpam-5903	432	1	thus	thus	ADV
ejpam-5903	432	2	,	,	PUNCT
ejpam-5903	432	3	d11	d11	PROPN
ejpam-5903	432	4	is	be	AUX
ejpam-5903	432	5	a	a	DET
ejpam-5903	432	6	ζhg1	ζhg1	NOUN
ejpam-5903	432	7	-set	-set	PUNCT
ejpam-5903	432	8	of	of	ADP
ejpam-5903	432	9	cn	cn	PROPN
ejpam-5903	432	10	.	.	PUNCT
ejpam-5903	433	1	hence	hence	ADV
ejpam-5903	433	2	,	,	PUNCT
ejpam-5903	433	3	ζhg1	ζhg1	PROPN
ejpam-5903	433	4	(	(	PUNCT
ejpam-5903	433	5	cn	cn	PROPN
ejpam-5903	433	6	)	)	PUNCT
ejpam-5903	433	7	=	=	SYM
ejpam-5903	433	8	ζhg1	ζhg1	PROPN
ejpam-5903	433	9	(	(	PUNCT
ejpam-5903	433	10	d11	d11	PROPN
ejpam-5903	433	11	)	)	PUNCT
ejpam-5903	433	12	=	=	SYM
ejpam-5903	433	13	n	n	PRON
ejpam-5903	433	14	−	−	PROPN
ejpam-5903	434	1	|nhg	|nhg	PROPN
ejpam-5903	434	2	g	g	PROPN
ejpam-5903	434	3	[	[	X
ejpam-5903	434	4	d11]|	d11]|	X
ejpam-5903	434	5	=	=	PUNCT
ejpam-5903	434	6	3r	3r	NUM
ejpam-5903	434	7	+	+	CCONJ
ejpam-5903	434	8	2−	2−	NUM
ejpam-5903	434	9	(	(	PUNCT
ejpam-5903	434	10	3r	3r	NUM
ejpam-5903	434	11	+	+	CCONJ
ejpam-5903	434	12	1	1	NUM
ejpam-5903	434	13	)	)	PUNCT
ejpam-5903	434	14	=	=	SYM
ejpam-5903	434	15	1	1	X
ejpam-5903	434	16	.	.	X
ejpam-5903	434	17	subcase	subcase	NOUN
ejpam-5903	434	18	2	2	NUM
ejpam-5903	434	19	:	:	PUNCT
ejpam-5903	434	20	k	k	PROPN
ejpam-5903	434	21	=	=	SYM
ejpam-5903	434	22	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	434	23	1	1	NUM
ejpam-5903	434	24	.	.	PUNCT
ejpam-5903	434	25	by	by	ADP
ejpam-5903	434	26	lemma	lemma	PROPN
ejpam-5903	434	27	1	1	NUM
ejpam-5903	434	28	,	,	PUNCT
ejpam-5903	434	29	ζhgk	ζhgk	NOUN
ejpam-5903	434	30	(	(	PUNCT
ejpam-5903	434	31	cn	cn	NOUN
ejpam-5903	434	32	)	)	PUNCT
ejpam-5903	434	33	=	=	PUNCT
ejpam-5903	435	1	n−	n−	NOUN
ejpam-5903	435	2	1	1	NUM
ejpam-5903	435	3	=	=	SYM
ejpam-5903	435	4	3r	3r	NUM
ejpam-5903	435	5	+	+	CCONJ
ejpam-5903	435	6	2−	2−	NUM
ejpam-5903	435	7	1	1	NUM
ejpam-5903	435	8	=	=	NOUN
ejpam-5903	435	9	3r	3r	NUM
ejpam-5903	435	10	+	+	CCONJ
ejpam-5903	435	11	1	1	NUM
ejpam-5903	435	12	=	=	SYM
ejpam-5903	435	13	3k	3k	X
ejpam-5903	435	14	−	−	NOUN
ejpam-5903	435	15	2	2	X
ejpam-5903	435	16	.	.	X
ejpam-5903	435	17	subcase	subcase	PROPN
ejpam-5903	435	18	3	3	NUM
ejpam-5903	435	19	:	:	PUNCT
ejpam-5903	435	20	r	r	NOUN
ejpam-5903	435	21	is	be	AUX
ejpam-5903	435	22	odd	odd	ADJ
ejpam-5903	435	23	and	and	CCONJ
ejpam-5903	435	24	k	k	PROPN
ejpam-5903	435	25	=	=	SYM
ejpam-5903	435	26	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	435	27	2	2	X
ejpam-5903	435	28	.	.	PUNCT
ejpam-5903	436	1	let	let	VERB
ejpam-5903	436	2	d12	d12	NOUN
ejpam-5903	436	3	=	=	SYM
ejpam-5903	436	4	{	{	PUNCT
ejpam-5903	436	5	v1	v1	PROPN
ejpam-5903	436	6	,	,	PUNCT
ejpam-5903	436	7	v4	v4	NOUN
ejpam-5903	436	8	}	}	PUNCT
ejpam-5903	436	9	.	.	PUNCT
ejpam-5903	437	1	then	then	ADV
ejpam-5903	437	2	d12	d12	PROPN
ejpam-5903	437	3	is	be	AUX
ejpam-5903	437	4	a	a	DET
ejpam-5903	437	5	ζhgk	ζhgk	NOUN
ejpam-5903	437	6	-set	-set	ADJ
ejpam-5903	437	7	of	of	ADP
ejpam-5903	437	8	cn	cn	PROPN
ejpam-5903	437	9	and	and	CCONJ
ejpam-5903	437	10	nhg	nhg	VERB
ejpam-5903	437	11	g	g	PROPN
ejpam-5903	438	1	[	[	X
ejpam-5903	438	2	d12	d12	X
ejpam-5903	438	3	]	]	X
ejpam-5903	438	4	=	=	SYM
ejpam-5903	438	5	{	{	PUNCT
ejpam-5903	438	6	v1	v1	PROPN
ejpam-5903	438	7	,	,	PUNCT
ejpam-5903	438	8	v2	v2	PROPN
ejpam-5903	438	9	,	,	PUNCT
ejpam-5903	438	10	v3	v3	PROPN
ejpam-5903	438	11	,	,	PUNCT
ejpam-5903	438	12	v4	v4	PROPN
ejpam-5903	438	13	}	}	PUNCT
ejpam-5903	438	14	.	.	PUNCT
ejpam-5903	439	1	hence	hence	ADV
ejpam-5903	439	2	,	,	PUNCT
ejpam-5903	439	3	ζhgk	ζhgk	PROPN
ejpam-5903	439	4	(	(	PUNCT
ejpam-5903	439	5	cn	cn	NOUN
ejpam-5903	439	6	)	)	PUNCT
ejpam-5903	439	7	=	=	VERB
ejpam-5903	439	8	ζhgk	ζhgk	NOUN
ejpam-5903	439	9	(	(	PUNCT
ejpam-5903	439	10	d12	d12	PROPN
ejpam-5903	439	11	)	)	PUNCT
ejpam-5903	439	12	=	=	NOUN
ejpam-5903	439	13	3r	3r	NUM
ejpam-5903	439	14	+	+	NUM
ejpam-5903	439	15	2−	2−	NUM
ejpam-5903	439	16	|nhg	|nhg	NOUN
ejpam-5903	439	17	g	g	X
ejpam-5903	440	1	[	[	X
ejpam-5903	440	2	d12]|	d12]|	X
ejpam-5903	440	3	=	=	PUNCT
ejpam-5903	440	4	3r	3r	NUM
ejpam-5903	440	5	+	+	CCONJ
ejpam-5903	440	6	2−	2−	NUM
ejpam-5903	440	7	4	4	NUM
ejpam-5903	440	8	=	=	SYM
ejpam-5903	440	9	3k	3k	NOUN
ejpam-5903	440	10	−	−	NOUN
ejpam-5903	440	11	2	2	X
ejpam-5903	440	12	.	.	X
ejpam-5903	440	13	subcase	subcase	PROPN
ejpam-5903	440	14	4	4	NUM
ejpam-5903	440	15	:	:	PUNCT
ejpam-5903	440	16	r	r	NOUN
ejpam-5903	440	17	is	be	AUX
ejpam-5903	440	18	even	even	ADV
ejpam-5903	440	19	and	and	CCONJ
ejpam-5903	440	20	k	k	PROPN
ejpam-5903	440	21	=	=	SYM
ejpam-5903	440	22	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	440	23	2	2	X
ejpam-5903	440	24	.	.	PUNCT
ejpam-5903	441	1	let	let	VERB
ejpam-5903	441	2	r	r	NOUN
ejpam-5903	441	3	=	=	SYM
ejpam-5903	441	4	2	2	NUM
ejpam-5903	441	5	.	.	PUNCT
ejpam-5903	441	6	then	then	ADV
ejpam-5903	441	7	d13	d13	NOUN
ejpam-5903	441	8	=	=	SYM
ejpam-5903	441	9	{	{	PUNCT
ejpam-5903	441	10	v1	v1	PROPN
ejpam-5903	441	11	,	,	PUNCT
ejpam-5903	441	12	v4	v4	PROPN
ejpam-5903	441	13	}	}	PUNCT
ejpam-5903	441	14	is	be	AUX
ejpam-5903	441	15	a	a	DET
ejpam-5903	441	16	ζhgk	ζhgk	NOUN
ejpam-5903	441	17	-set	-set	ADJ
ejpam-5903	441	18	of	of	ADP
ejpam-5903	441	19	cn	cn	PROPN
ejpam-5903	441	20	and	and	CCONJ
ejpam-5903	441	21	nhg	nhg	VERB
ejpam-5903	441	22	g	g	PROPN
ejpam-5903	442	1	[	[	X
ejpam-5903	442	2	d13	d13	X
ejpam-5903	442	3	]	]	X
ejpam-5903	442	4	=	=	SYM
ejpam-5903	442	5	{	{	PUNCT
ejpam-5903	442	6	v1	v1	PROPN
ejpam-5903	442	7	,	,	PUNCT
ejpam-5903	442	8	v2	v2	PROPN
ejpam-5903	442	9	,	,	PUNCT
ejpam-5903	442	10	v3	v3	PROPN
ejpam-5903	442	11	,	,	PUNCT
ejpam-5903	442	12	v4	v4	PROPN
ejpam-5903	442	13	}	}	PUNCT
ejpam-5903	442	14	.	.	PUNCT
ejpam-5903	443	1	hence	hence	ADV
ejpam-5903	443	2	,	,	PUNCT
ejpam-5903	443	3	ζhgk	ζhgk	PROPN
ejpam-5903	443	4	(	(	PUNCT
ejpam-5903	443	5	cn	cn	NOUN
ejpam-5903	443	6	)	)	PUNCT
ejpam-5903	443	7	=	=	VERB
ejpam-5903	443	8	ζhgk	ζhgk	NOUN
ejpam-5903	443	9	(	(	PUNCT
ejpam-5903	443	10	d13	d13	NOUN
ejpam-5903	443	11	)	)	PUNCT
ejpam-5903	443	12	=	=	SYM
ejpam-5903	443	13	3r	3r	NUM
ejpam-5903	443	14	+	+	NUM
ejpam-5903	443	15	2−	2−	NUM
ejpam-5903	443	16	|nhg	|nhg	NOUN
ejpam-5903	443	17	g	g	X
ejpam-5903	444	1	[	[	X
ejpam-5903	444	2	d13]|	d13]|	X
ejpam-5903	444	3	=	=	SYM
ejpam-5903	444	4	3r	3r	NUM
ejpam-5903	444	5	+	+	CCONJ
ejpam-5903	444	6	2−	2−	NUM
ejpam-5903	444	7	4	4	NUM
ejpam-5903	444	8	=	=	SYM
ejpam-5903	444	9	3k	3k	NOUN
ejpam-5903	445	1	−	−	NOUN
ejpam-5903	445	2	2	2	X
ejpam-5903	445	3	.	.	PUNCT
ejpam-5903	445	4	suppose	suppose	VERB
ejpam-5903	445	5	r	r	NOUN
ejpam-5903	445	6	≥	≥	NUM
ejpam-5903	445	7	4	4	NUM
ejpam-5903	445	8	.	.	PUNCT
ejpam-5903	446	1	then	then	ADV
ejpam-5903	446	2	d14	d14	VERB
ejpam-5903	446	3	=	=	SYM
ejpam-5903	446	4	{	{	PUNCT
ejpam-5903	446	5	v1	v1	PROPN
ejpam-5903	446	6	,	,	PUNCT
ejpam-5903	446	7	v	v	X
ejpam-5903	446	8	3r+4	3r+4	NUM
ejpam-5903	446	9	2	2	NUM
ejpam-5903	446	10	}	}	PUNCT
ejpam-5903	446	11	is	be	AUX
ejpam-5903	446	12	a	a	DET
ejpam-5903	446	13	ζhgk	ζhgk	NOUN
ejpam-5903	446	14	-set	-set	ADJ
ejpam-5903	446	15	of	of	ADP
ejpam-5903	446	16	cn	cn	PROPN
ejpam-5903	446	17	and	and	CCONJ
ejpam-5903	446	18	nhg	nhg	VERB
ejpam-5903	446	19	g	g	PROPN
ejpam-5903	447	1	[	[	X
ejpam-5903	447	2	d14	d14	X
ejpam-5903	447	3	]	]	X
ejpam-5903	447	4	=	=	SYM
ejpam-5903	447	5	{	{	PUNCT
ejpam-5903	447	6	v1	v1	PROPN
ejpam-5903	447	7	,	,	PUNCT
ejpam-5903	447	8	v3	v3	PROPN
ejpam-5903	447	9	,	,	PUNCT
ejpam-5903	447	10	v	v	NOUN
ejpam-5903	447	11	3r+3	3r+3	PROPN
ejpam-5903	447	12	2	2	NUM
ejpam-5903	447	13	−2	−2	NOUN
ejpam-5903	447	14	,	,	PUNCT
ejpam-5903	447	15	v	v	NOUN
ejpam-5903	447	16	3r+3	3r+3	PROPN
ejpam-5903	447	17	2	2	NUM
ejpam-5903	447	18	,	,	PUNCT
ejpam-5903	447	19	v	v	NOUN
ejpam-5903	447	20	3r+3	3r+3	PROPN
ejpam-5903	447	21	2	2	NUM
ejpam-5903	447	22	+2	+2	NOUN
ejpam-5903	447	23	,	,	PUNCT
ejpam-5903	447	24	v3r+1	v3r+1	NOUN
ejpam-5903	447	25	}	}	PUNCT
ejpam-5903	447	26	.	.	PUNCT
ejpam-5903	448	1	hence	hence	ADV
ejpam-5903	448	2	,	,	PUNCT
ejpam-5903	448	3	ζhgk	ζhgk	PROPN
ejpam-5903	448	4	(	(	PUNCT
ejpam-5903	448	5	cn	cn	NOUN
ejpam-5903	448	6	)	)	PUNCT
ejpam-5903	448	7	=	=	VERB
ejpam-5903	448	8	ζhgk	ζhgk	NOUN
ejpam-5903	448	9	(	(	PUNCT
ejpam-5903	448	10	d14	d14	NOUN
ejpam-5903	448	11	)	)	PUNCT
ejpam-5903	448	12	=	=	SYM
ejpam-5903	448	13	3r	3r	NUM
ejpam-5903	448	14	+	+	SYM
ejpam-5903	448	15	1−	1−	NUM
ejpam-5903	449	1	|nhg	|nhg	VERB
ejpam-5903	449	2	g	g	X
ejpam-5903	449	3	[	[	X
ejpam-5903	449	4	d14]|	d14]|	NOUN
ejpam-5903	449	5	=	=	NOUN
ejpam-5903	449	6	3r	3r	NUM
ejpam-5903	449	7	+	+	CCONJ
ejpam-5903	450	1	2−	2−	NUM
ejpam-5903	450	2	6	6	NUM
ejpam-5903	450	3	=	=	SYM
ejpam-5903	450	4	3k	3k	NOUN
ejpam-5903	450	5	−	−	NOUN
ejpam-5903	450	6	4	4	X
ejpam-5903	450	7	.	.	PUNCT
ejpam-5903	450	8	subcase	subcase	PROPN
ejpam-5903	450	9	5	5	NUM
ejpam-5903	450	10	:	:	PUNCT
ejpam-5903	451	1	r	r	NOUN
ejpam-5903	451	2	≥	≥	NUM
ejpam-5903	451	3	3	3	NUM
ejpam-5903	451	4	and	and	CCONJ
ejpam-5903	451	5	2	2	NUM
ejpam-5903	451	6	≤	≤	NOUN
ejpam-5903	451	7	k	k	PROPN
ejpam-5903	451	8	≤	≤	PROPN
ejpam-5903	451	9	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	451	10	3	3	X
ejpam-5903	451	11	.	.	PUNCT
ejpam-5903	452	1	let	let	VERB
ejpam-5903	452	2	k	k	PROPN
ejpam-5903	452	3	≤	≤	X
ejpam-5903	452	4	⌊γhg(cn)−2	⌊γhg(cn)−2	ADP
ejpam-5903	452	5	2	2	NUM
ejpam-5903	452	6	⌋	⌋	NOUN
ejpam-5903	452	7	and	and	CCONJ
ejpam-5903	452	8	let	let	VERB
ejpam-5903	452	9	d15	d15	NOUN
ejpam-5903	452	10	=	=	SYM
ejpam-5903	452	11	{	{	PUNCT
ejpam-5903	452	12	v1	v1	PROPN
ejpam-5903	452	13	,	,	PUNCT
ejpam-5903	452	14	v4	v4	NOUN
ejpam-5903	452	15	,	,	PUNCT
ejpam-5903	452	16	·	·	PUNCT
ejpam-5903	452	17	·	·	PUNCT
ejpam-5903	452	18	·	·	PUNCT
ejpam-5903	452	19	,	,	PUNCT
ejpam-5903	452	20	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	452	21	}	}	PUNCT
ejpam-5903	452	22	.	.	PUNCT
ejpam-5903	453	1	then	then	ADV
ejpam-5903	453	2	d15	d15	PROPN
ejpam-5903	453	3	is	be	AUX
ejpam-5903	453	4	a	a	DET
ejpam-5903	453	5	ζhgk	ζhgk	NOUN
ejpam-5903	453	6	-set	-set	ADJ
ejpam-5903	453	7	of	of	ADP
ejpam-5903	453	8	cn	cn	PROPN
ejpam-5903	453	9	and	and	CCONJ
ejpam-5903	453	10	nhg	nhg	VERB
ejpam-5903	453	11	g	g	PROPN
ejpam-5903	454	1	[	[	X
ejpam-5903	454	2	d15	d15	X
ejpam-5903	454	3	]	]	X
ejpam-5903	454	4	=	=	SYM
ejpam-5903	454	5	{	{	PUNCT
ejpam-5903	454	6	v1	v1	PROPN
ejpam-5903	454	7	,	,	PUNCT
ejpam-5903	454	8	v2	v2	PROPN
ejpam-5903	454	9	,	,	PUNCT
ejpam-5903	454	10	v3	v3	PROPN
ejpam-5903	454	11	,	,	PUNCT
ejpam-5903	454	12	v4	v4	PROPN
ejpam-5903	454	13	,	,	PUNCT
ejpam-5903	454	14	·	·	PUNCT
ejpam-5903	454	15	·	·	PUNCT
ejpam-5903	454	16	·	·	PUNCT
ejpam-5903	454	17	,	,	PUNCT
ejpam-5903	454	18	v3r−3k+4	v3r−3k+4	VERB
ejpam-5903	454	19	,	,	PUNCT
ejpam-5903	454	20	v3r−3k+6	v3r−3k+6	NOUN
ejpam-5903	454	21	,	,	PUNCT
ejpam-5903	454	22	v3r+1	v3r+1	ADJ
ejpam-5903	454	23	}	}	PUNCT
ejpam-5903	454	24	.	.	PUNCT
ejpam-5903	455	1	thus	thus	ADV
ejpam-5903	455	2	,	,	PUNCT
ejpam-5903	455	3	ζhgk	ζhgk	PROPN
ejpam-5903	455	4	(	(	PUNCT
ejpam-5903	455	5	cn	cn	NOUN
ejpam-5903	455	6	)	)	PUNCT
ejpam-5903	455	7	=	=	VERB
ejpam-5903	455	8	ζhgk	ζhgk	NOUN
ejpam-5903	455	9	(	(	PUNCT
ejpam-5903	455	10	d15	d15	NOUN
ejpam-5903	455	11	)	)	PUNCT
ejpam-5903	455	12	=	=	SYM
ejpam-5903	455	13	n−	n−	NOUN
ejpam-5903	455	14	|nhg	|nhg	VERB
ejpam-5903	455	15	g	g	ADP
ejpam-5903	456	1	[	[	X
ejpam-5903	456	2	d15]|	d15]|	X
ejpam-5903	456	3	=	=	PUNCT
ejpam-5903	457	1	3r+2−	3r+2−	NUM
ejpam-5903	458	1	[	[	X
ejpam-5903	458	2	(	(	PUNCT
ejpam-5903	458	3	3r−	3r−	PROPN
ejpam-5903	458	4	3k+4)+2	3k+4)+2	NUM
ejpam-5903	458	5	]	]	X
ejpam-5903	458	6	=	=	PUNCT
ejpam-5903	458	7	3k−	3k−	NUM
ejpam-5903	458	8	4	4	NUM
ejpam-5903	458	9	.	.	PUNCT
ejpam-5903	459	1	next	next	ADV
ejpam-5903	459	2	,	,	PUNCT
ejpam-5903	459	3	let	let	VERB
ejpam-5903	459	4	⌊γhg(cn)−2	⌊γhg(cn)−2	ADP
ejpam-5903	459	5	2	2	NUM
ejpam-5903	459	6	⌋	⌋	NOUN
ejpam-5903	459	7	<	<	X
ejpam-5903	459	8	k	k	PROPN
ejpam-5903	459	9	≤	≤	PROPN
ejpam-5903	459	10	γhg(cn)−	γhg(cn)−	PROPN
ejpam-5903	460	1	3	3	X
ejpam-5903	460	2	.	.	PUNCT
ejpam-5903	460	3	choose	choose	VERB
ejpam-5903	460	4	an	an	DET
ejpam-5903	460	5	(	(	PUNCT
ejpam-5903	460	6	r	r	NOUN
ejpam-5903	460	7	−	−	PROPN
ejpam-5903	460	8	k	k	PROPN
ejpam-5903	461	1	+	+	PROPN
ejpam-5903	461	2	2)-element	2)-element	NUM
ejpam-5903	461	3	set	set	VERB
ejpam-5903	461	4	d16	d16	NOUN
ejpam-5903	461	5	=	=	NOUN
ejpam-5903	461	6	{	{	PUNCT
ejpam-5903	461	7	v⌈	v⌈	NOUN
ejpam-5903	461	8	3r+5	3r+5	PROPN
ejpam-5903	461	9	2	2	NUM
ejpam-5903	461	10	⌉	⌉	X
ejpam-5903	461	11	,	,	PUNCT
ejpam-5903	461	12	v1	v1	NOUN
ejpam-5903	461	13	,	,	PUNCT
ejpam-5903	461	14	v4	v4	NOUN
ejpam-5903	461	15	,	,	PUNCT
ejpam-5903	461	16	·	·	PUNCT
ejpam-5903	461	17	·	·	PUNCT
ejpam-5903	461	18	·	·	PUNCT
ejpam-5903	461	19	,	,	PUNCT
ejpam-5903	461	20	v3r−3k+1	v3r−3k+1	NOUN
ejpam-5903	461	21	}	}	PUNCT
ejpam-5903	461	22	.	.	PUNCT
ejpam-5903	462	1	then	then	ADV
ejpam-5903	462	2	d16	d16	PROPN
ejpam-5903	462	3	is	be	AUX
ejpam-5903	462	4	a	a	DET
ejpam-5903	462	5	ζhgk	ζhgk	NOUN
ejpam-5903	462	6	-set	-set	X
ejpam-5903	462	7	of	of	ADP
ejpam-5903	462	8	cn	cn	PROPN
ejpam-5903	462	9	and	and	CCONJ
ejpam-5903	462	10	nhg	nhg	VERB
ejpam-5903	462	11	g	g	PROPN
ejpam-5903	463	1	[	[	X
ejpam-5903	463	2	d16	d16	X
ejpam-5903	463	3	]	]	X
ejpam-5903	463	4	=	=	SYM
ejpam-5903	463	5	{	{	PUNCT
ejpam-5903	463	6	v1	v1	PROPN
ejpam-5903	463	7	,	,	PUNCT
ejpam-5903	463	8	v2	v2	PROPN
ejpam-5903	463	9	,	,	PUNCT
ejpam-5903	463	10	v3	v3	PROPN
ejpam-5903	463	11	,	,	PUNCT
ejpam-5903	463	12	v4	v4	PROPN
ejpam-5903	463	13	,	,	PUNCT
ejpam-5903	463	14	·	·	PUNCT
ejpam-5903	463	15	·	·	PUNCT
ejpam-5903	463	16	·	·	PUNCT
ejpam-5903	463	17	,	,	PUNCT
ejpam-5903	463	18	v3r−3k+1	v3r−3k+1	PROPN
ejpam-5903	463	19	,	,	PUNCT
ejpam-5903	463	20	v3r−3k+3	v3r−3k+3	PROPN
ejpam-5903	463	21	,	,	PUNCT
ejpam-5903	463	22	v⌈	v⌈	PROPN
ejpam-5903	463	23	3r+5	3r+5	PROPN
ejpam-5903	463	24	2	2	NUM
ejpam-5903	463	25	⌉−2	⌉−2	NOUN
ejpam-5903	463	26	,	,	PUNCT
ejpam-5903	463	27	v⌈	v⌈	NOUN
ejpam-5903	463	28	3r+5	3r+5	PROPN
ejpam-5903	463	29	2	2	NUM
ejpam-5903	463	30	⌉	⌉	NOUN
ejpam-5903	463	31	,	,	PUNCT
ejpam-5903	463	32	v⌈	v⌈	NOUN
ejpam-5903	463	33	3r+5	3r+5	PROPN
ejpam-5903	463	34	2	2	NUM
ejpam-5903	463	35	⌉+2	⌉+2	PROPN
ejpam-5903	463	36	,	,	PUNCT
ejpam-5903	463	37	v3r+1	v3r+1	PROPN
ejpam-5903	463	38	}	}	PUNCT
ejpam-5903	463	39	.	.	PUNCT
ejpam-5903	464	1	this	this	PRON
ejpam-5903	464	2	implies	imply	VERB
ejpam-5903	464	3	that	that	SCONJ
ejpam-5903	464	4	ζhgk	ζhgk	NOUN
ejpam-5903	464	5	(	(	PUNCT
ejpam-5903	464	6	cn	cn	NOUN
ejpam-5903	464	7	)	)	PUNCT
ejpam-5903	464	8	=	=	VERB
ejpam-5903	464	9	ζhgk	ζhgk	NOUN
ejpam-5903	464	10	(	(	PUNCT
ejpam-5903	464	11	d16	d16	NOUN
ejpam-5903	464	12	)	)	PUNCT
ejpam-5903	464	13	=	=	SYM
ejpam-5903	464	14	n−	n−	NOUN
ejpam-5903	464	15	|nhg	|nhg	VERB
ejpam-5903	464	16	g	g	NOUN
ejpam-5903	464	17	[	[	X
ejpam-5903	464	18	d16]|	d16]|	NOUN
ejpam-5903	464	19	=	=	NOUN
ejpam-5903	464	20	3r	3r	NUM
ejpam-5903	464	21	+	+	CCONJ
ejpam-5903	464	22	2−	2−	NUM
ejpam-5903	464	23	[	[	X
ejpam-5903	464	24	(	(	PUNCT
ejpam-5903	464	25	3r	3r	NUM
ejpam-5903	464	26	−	−	NOUN
ejpam-5903	464	27	3k	3k	NOUN
ejpam-5903	465	1	+	+	CCONJ
ejpam-5903	465	2	1	1	X
ejpam-5903	465	3	)	)	PUNCT
ejpam-5903	465	4	+	+	CCONJ
ejpam-5903	465	5	5	5	X
ejpam-5903	465	6	]	]	PUNCT
ejpam-5903	465	7	=	=	SYM
ejpam-5903	465	8	3k	3k	X
ejpam-5903	466	1	−	−	NOUN
ejpam-5903	466	2	4	4	X
ejpam-5903	466	3	.	.	PUNCT
ejpam-5903	467	1	this	this	PRON
ejpam-5903	467	2	proves	prove	VERB
ejpam-5903	467	3	the	the	DET
ejpam-5903	467	4	assertion	assertion	NOUN
ejpam-5903	467	5	.	.	PUNCT
ejpam-5903	468	1	j.	j.	PROPN
ejpam-5903	468	2	anoche	anoche	PROPN
ejpam-5903	468	3	,	,	PUNCT
ejpam-5903	468	4	s.	s.	PROPN
ejpam-5903	468	5	canoy	canoy	PROPN
ejpam-5903	468	6	,	,	PUNCT
ejpam-5903	468	7	jr	jr	PROPN
ejpam-5903	468	8	.	.	PROPN
ejpam-5903	468	9	/	/	SYM
ejpam-5903	468	10	eur	eur	PROPN
ejpam-5903	468	11	.	.	PUNCT
ejpam-5903	469	1	j.	j.	PROPN
ejpam-5903	469	2	pure	pure	PROPN
ejpam-5903	469	3	appl	appl	PROPN
ejpam-5903	469	4	.	.	PROPN
ejpam-5903	469	5	math	math	PROPN
ejpam-5903	469	6	,	,	PUNCT
ejpam-5903	469	7	18	18	NUM
ejpam-5903	469	8	(	(	PUNCT
ejpam-5903	469	9	2	2	NUM
ejpam-5903	469	10	)	)	PUNCT
ejpam-5903	469	11	(	(	PUNCT
ejpam-5903	469	12	2025	2025	NUM
ejpam-5903	469	13	)	)	PUNCT
ejpam-5903	469	14	,	,	PUNCT
ejpam-5903	469	15	5903	5903	NUM
ejpam-5903	469	16	13	13	NUM
ejpam-5903	469	17	of	of	ADP
ejpam-5903	469	18	17	17	NUM
ejpam-5903	469	19	theorem	theorem	NOUN
ejpam-5903	469	20	10	10	NUM
ejpam-5903	469	21	.	.	PUNCT
ejpam-5903	470	1	if	if	SCONJ
ejpam-5903	470	2	g	g	PROPN
ejpam-5903	470	3	=	=	SYM
ejpam-5903	470	4	km	km	PROPN
ejpam-5903	470	5	,	,	PUNCT
ejpam-5903	470	6	n	n	PRON
ejpam-5903	470	7	is	be	AUX
ejpam-5903	470	8	a	a	DET
ejpam-5903	470	9	complete	complete	ADJ
ejpam-5903	470	10	bipartite	bipartite	NOUN
ejpam-5903	470	11	graph	graph	NOUN
ejpam-5903	470	12	with	with	ADP
ejpam-5903	470	13	1	1	NUM
ejpam-5903	470	14	≤	≤	NUM
ejpam-5903	470	15	m	m	VERB
ejpam-5903	470	16	≤	≤	NOUN
ejpam-5903	470	17	n	n	PRON
ejpam-5903	470	18	and	and	CCONJ
ejpam-5903	470	19	k	k	PROPN
ejpam-5903	470	20	is	be	AUX
ejpam-5903	470	21	a	a	DET
ejpam-5903	470	22	postive	postive	ADJ
ejpam-5903	470	23	integer	integer	NOUN
ejpam-5903	470	24	with	with	ADP
ejpam-5903	470	25	k	k	PROPN
ejpam-5903	470	26	≤	≤	PROPN
ejpam-5903	470	27	γhg(km	γhg(km	PROPN
ejpam-5903	470	28	,	,	PUNCT
ejpam-5903	470	29	n)−	n)−	PROPN
ejpam-5903	470	30	1	1	NUM
ejpam-5903	470	31	,	,	PUNCT
ejpam-5903	470	32	then	then	ADV
ejpam-5903	470	33	ζhgk	ζhgk	NOUN
ejpam-5903	470	34	(	(	PUNCT
ejpam-5903	470	35	g	g	NOUN
ejpam-5903	470	36	)	)	PUNCT
ejpam-5903	470	37	=	=	PUNCT
ejpam-5903	471	1			PROPN
ejpam-5903	471	2	k	k	NOUN
ejpam-5903	472	1	if	if	SCONJ
ejpam-5903	472	2	m	m	VERB
ejpam-5903	472	3	=	=	NOUN
ejpam-5903	472	4	1	1	NUM
ejpam-5903	472	5	and	and	CCONJ
ejpam-5903	472	6	k	k	PROPN
ejpam-5903	472	7	≤	≤	PROPN
ejpam-5903	472	8	n	n	PROPN
ejpam-5903	472	9	n+	n+	NUM
ejpam-5903	473	1	k	k	NOUN
ejpam-5903	473	2	−	−	NOUN
ejpam-5903	473	3	1	1	NUM
ejpam-5903	473	4	if	if	SCONJ
ejpam-5903	473	5	m	m	VERB
ejpam-5903	473	6	=	=	SYM
ejpam-5903	473	7	2	2	NUM
ejpam-5903	473	8	and	and	CCONJ
ejpam-5903	473	9	k	k	PROPN
ejpam-5903	473	10	≤	≤	ADV
ejpam-5903	473	11	2	2	NUM
ejpam-5903	473	12	m−	m−	PROPN
ejpam-5903	473	13	2	2	NUM
ejpam-5903	473	14	if	if	SCONJ
ejpam-5903	473	15	m	m	PROPN
ejpam-5903	473	16	≥	≥	VERB
ejpam-5903	473	17	3	3	NUM
ejpam-5903	473	18	and	and	CCONJ
ejpam-5903	473	19	k	k	NOUN
ejpam-5903	473	20	=	=	SYM
ejpam-5903	473	21	1	1	NUM
ejpam-5903	473	22	m+	m+	NUM
ejpam-5903	473	23	n+	n+	PUNCT
ejpam-5903	473	24	k	k	PROPN
ejpam-5903	474	1	−	−	NOUN
ejpam-5903	474	2	4	4	NUM
ejpam-5903	474	3	if	if	SCONJ
ejpam-5903	474	4	m	m	PROPN
ejpam-5903	474	5	≥	≥	NOUN
ejpam-5903	474	6	3	3	NUM
ejpam-5903	474	7	and	and	CCONJ
ejpam-5903	474	8	k	k	NOUN
ejpam-5903	474	9	=	=	SYM
ejpam-5903	474	10	2	2	NUM
ejpam-5903	474	11	,	,	PUNCT
ejpam-5903	474	12	3	3	NUM
ejpam-5903	474	13	.	.	PUNCT
ejpam-5903	474	14	proof	proof	NOUN
ejpam-5903	474	15	.	.	PUNCT
ejpam-5903	475	1	let	let	VERB
ejpam-5903	475	2	k	k	PROPN
ejpam-5903	475	3	≤	≤	PROPN
ejpam-5903	475	4	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	475	5	1	1	NUM
ejpam-5903	475	6	.	.	PUNCT
ejpam-5903	475	7	consider	consider	VERB
ejpam-5903	475	8	the	the	DET
ejpam-5903	475	9	following	follow	VERB
ejpam-5903	475	10	cases	case	NOUN
ejpam-5903	475	11	:	:	PUNCT
ejpam-5903	475	12	case	case	NOUN
ejpam-5903	475	13	1	1	NUM
ejpam-5903	475	14	:	:	PUNCT
ejpam-5903	475	15	m	m	VERB
ejpam-5903	475	16	=	=	NOUN
ejpam-5903	476	1	1	1	X
ejpam-5903	476	2	.	.	PUNCT
ejpam-5903	477	1	if	if	SCONJ
ejpam-5903	477	2	n	n	NOUN
ejpam-5903	477	3	=	=	SYM
ejpam-5903	477	4	1	1	NUM
ejpam-5903	477	5	,	,	PUNCT
ejpam-5903	477	6	then	then	ADV
ejpam-5903	477	7	k	k	PROPN
ejpam-5903	477	8	=	=	SYM
ejpam-5903	477	9	1	1	NUM
ejpam-5903	477	10	and	and	CCONJ
ejpam-5903	477	11	ζhg1	ζhg1	PROPN
ejpam-5903	477	12	(	(	PUNCT
ejpam-5903	477	13	g	g	NOUN
ejpam-5903	477	14	)	)	PUNCT
ejpam-5903	477	15	=	=	SYM
ejpam-5903	478	1	1	1	X
ejpam-5903	478	2	.	.	PUNCT
ejpam-5903	478	3	suppose	suppose	VERB
ejpam-5903	478	4	n	n	PRON
ejpam-5903	478	5	≥	≥	NOUN
ejpam-5903	478	6	2	2	NUM
ejpam-5903	478	7	.	.	PUNCT
ejpam-5903	478	8	by	by	ADP
ejpam-5903	478	9	corollary	corollary	ADJ
ejpam-5903	478	10	1(ii	1(ii	NUM
ejpam-5903	478	11	)	)	PUNCT
ejpam-5903	478	12	,	,	PUNCT
ejpam-5903	478	13	γhg(g	γhg(g	PROPN
ejpam-5903	478	14	)	)	PUNCT
ejpam-5903	478	15	=	=	PUNCT
ejpam-5903	478	16	n+	n+	PUNCT
ejpam-5903	478	17	1	1	X
ejpam-5903	478	18	.	.	PUNCT
ejpam-5903	478	19	let	let	VERB
ejpam-5903	478	20	k	k	PROPN
ejpam-5903	478	21	≤	≤	PROPN
ejpam-5903	478	22	n	n	CCONJ
ejpam-5903	478	23	and	and	CCONJ
ejpam-5903	478	24	let	let	VERB
ejpam-5903	478	25	s	s	PRON
ejpam-5903	478	26	⊆	⊆	NUM
ejpam-5903	478	27	v	v	NOUN
ejpam-5903	478	28	(	(	PUNCT
ejpam-5903	478	29	k1,n	k1,n	PROPN
ejpam-5903	478	30	)	)	PUNCT
ejpam-5903	478	31	with	with	ADP
ejpam-5903	478	32	|s|	|s|	PROPN
ejpam-5903	478	33	=	=	SYM
ejpam-5903	478	34	n−	n−	PROPN
ejpam-5903	478	35	k	k	NOUN
ejpam-5903	479	1	+	+	NOUN
ejpam-5903	479	2	1	1	X
ejpam-5903	479	3	.	.	PUNCT
ejpam-5903	479	4	let	let	VERB
ejpam-5903	479	5	v0	v0	NOUN
ejpam-5903	479	6	be	be	AUX
ejpam-5903	479	7	the	the	DET
ejpam-5903	479	8	central	central	ADJ
ejpam-5903	479	9	vertex	vertex	NOUN
ejpam-5903	479	10	of	of	ADP
ejpam-5903	479	11	k1,n	k1,n	PROPN
ejpam-5903	479	12	and	and	CCONJ
ejpam-5903	479	13	v	v	NOUN
ejpam-5903	479	14	(	(	PUNCT
ejpam-5903	479	15	k1,n	k1,n	PROPN
ejpam-5903	479	16	)	)	PUNCT
ejpam-5903	479	17	=	=	PROPN
ejpam-5903	479	18	{	{	PUNCT
ejpam-5903	479	19	v0	v0	PROPN
ejpam-5903	479	20	,	,	PUNCT
ejpam-5903	479	21	w1	w1	NOUN
ejpam-5903	479	22	,	,	PUNCT
ejpam-5903	479	23	w2	w2	NOUN
ejpam-5903	479	24	,	,	PUNCT
ejpam-5903	479	25	·	·	PUNCT
ejpam-5903	479	26	·	·	PUNCT
ejpam-5903	479	27	·	·	PUNCT
ejpam-5903	479	28	,	,	PUNCT
ejpam-5903	479	29	wn	wn	PROPN
ejpam-5903	479	30	}	}	PUNCT
ejpam-5903	479	31	.	.	PUNCT
ejpam-5903	480	1	suppose	suppose	VERB
ejpam-5903	480	2	wj	wj	PROPN
ejpam-5903	480	3	∈	∈	PROPN
ejpam-5903	480	4	v	v	PROPN
ejpam-5903	480	5	(	(	PUNCT
ejpam-5903	480	6	g	g	NOUN
ejpam-5903	480	7	)	)	PUNCT
ejpam-5903	480	8	\	\	PROPN
ejpam-5903	481	1	s	s	VERB
ejpam-5903	481	2	for	for	ADP
ejpam-5903	481	3	some	some	DET
ejpam-5903	481	4	1	1	NUM
ejpam-5903	481	5	≤	≤	NUM
ejpam-5903	481	6	j	j	PROPN
ejpam-5903	481	7	≤	≤	PROPN
ejpam-5903	481	8	n.	n.	NOUN
ejpam-5903	481	9	since	since	SCONJ
ejpam-5903	481	10	wj	wj	PROPN
ejpam-5903	481	11	/∈	/∈	PUNCT
ejpam-5903	482	1	ig[s	ig[s	PROPN
ejpam-5903	482	2	]	]	PUNCT
ejpam-5903	482	3	,	,	PUNCT
ejpam-5903	482	4	wj	wj	PROPN
ejpam-5903	482	5	/∈	/∈	PUNCT
ejpam-5903	483	1	nhg	nhg	PROPN
ejpam-5903	483	2	g	g	PROPN
ejpam-5903	484	1	[	[	X
ejpam-5903	484	2	s	s	X
ejpam-5903	484	3	]	]	PUNCT
ejpam-5903	484	4	.	.	PUNCT
ejpam-5903	485	1	suppose	suppose	VERB
ejpam-5903	486	1	v0	v0	PROPN
ejpam-5903	486	2	/∈	/∈	PUNCT
ejpam-5903	486	3	s.	s.	PROPN
ejpam-5903	486	4	since	since	SCONJ
ejpam-5903	486	5	v0	v0	PROPN
ejpam-5903	486	6	/∈	/∈	PUNCT
ejpam-5903	486	7	n2	n2	PROPN
ejpam-5903	486	8	g[s	g[s	PROPN
ejpam-5903	486	9	]	]	PUNCT
ejpam-5903	486	10	,	,	PUNCT
ejpam-5903	486	11	v0	v0	PROPN
ejpam-5903	486	12	/∈	/∈	PUNCT
ejpam-5903	487	1	nhg	nhg	PROPN
ejpam-5903	487	2	g	g	PROPN
ejpam-5903	488	1	[	[	X
ejpam-5903	488	2	s	s	X
ejpam-5903	488	3	]	]	X
ejpam-5903	488	4	.	.	PUNCT
ejpam-5903	489	1	therefore	therefore	ADV
ejpam-5903	489	2	,	,	PUNCT
ejpam-5903	489	3	nhg	nhg	NOUN
ejpam-5903	489	4	g	g	PROPN
ejpam-5903	490	1	[	[	X
ejpam-5903	490	2	s	s	X
ejpam-5903	490	3	]	]	X
ejpam-5903	490	4	∩	∩	NOUN
ejpam-5903	490	5	(	(	PUNCT
ejpam-5903	490	6	v	v	NOUN
ejpam-5903	490	7	(	(	PUNCT
ejpam-5903	490	8	g	g	NOUN
ejpam-5903	490	9	)	)	PUNCT
ejpam-5903	490	10	\	\	PROPN
ejpam-5903	491	1	s	s	X
ejpam-5903	491	2	)	)	PUNCT
ejpam-5903	491	3	=	=	SYM
ejpam-5903	491	4	∅	∅	NOUN
ejpam-5903	491	5	,	,	PUNCT
ejpam-5903	491	6	i.e.	i.e.	X
ejpam-5903	491	7	,	,	PUNCT
ejpam-5903	491	8	nhg	nhg	NOUN
ejpam-5903	491	9	g	g	PROPN
ejpam-5903	492	1	[	[	X
ejpam-5903	492	2	s	s	X
ejpam-5903	492	3	]	]	X
ejpam-5903	492	4	=	=	PUNCT
ejpam-5903	492	5	s.	s.	PROPN
ejpam-5903	492	6	this	this	PRON
ejpam-5903	492	7	implies	imply	VERB
ejpam-5903	492	8	that	that	SCONJ
ejpam-5903	492	9	ζhgk	ζhgk	NOUN
ejpam-5903	492	10	(	(	PUNCT
ejpam-5903	492	11	g	g	NOUN
ejpam-5903	492	12	)	)	PUNCT
ejpam-5903	492	13	=	=	VERB
ejpam-5903	492	14	ζhgk	ζhgk	NOUN
ejpam-5903	492	15	(	(	PUNCT
ejpam-5903	492	16	s	s	NOUN
ejpam-5903	492	17	)	)	PUNCT
ejpam-5903	493	1	=	=	SYM
ejpam-5903	493	2	|v	|v	PROPN
ejpam-5903	493	3	(	(	PUNCT
ejpam-5903	493	4	g)|	g)|	NOUN
ejpam-5903	493	5	−	−	PROPN
ejpam-5903	493	6	|nhg	|nhg	PROPN
ejpam-5903	493	7	g	g	PROPN
ejpam-5903	494	1	[	[	X
ejpam-5903	494	2	s]|	s]|	X
ejpam-5903	494	3	=	=	SYM
ejpam-5903	494	4	(	(	PUNCT
ejpam-5903	494	5	n+	n+	NUM
ejpam-5903	494	6	1)−	1)−	NUM
ejpam-5903	494	7	(	(	PUNCT
ejpam-5903	494	8	n−	n−	NOUN
ejpam-5903	494	9	k	k	NOUN
ejpam-5903	495	1	+	+	CCONJ
ejpam-5903	495	2	1	1	X
ejpam-5903	495	3	)	)	PUNCT
ejpam-5903	495	4	=	=	PUNCT
ejpam-5903	495	5	k.	k.	NOUN
ejpam-5903	495	6	case	case	NOUN
ejpam-5903	495	7	2	2	NUM
ejpam-5903	495	8	:	:	PUNCT
ejpam-5903	495	9	m	m	VERB
ejpam-5903	495	10	=	=	SYM
ejpam-5903	495	11	2	2	X
ejpam-5903	495	12	.	.	PUNCT
ejpam-5903	495	13	by	by	ADP
ejpam-5903	495	14	corollary	corollary	ADJ
ejpam-5903	495	15	1(v	1(v	NUM
ejpam-5903	495	16	)	)	PUNCT
ejpam-5903	495	17	,	,	PUNCT
ejpam-5903	495	18	γhg(g	γhg(g	PROPN
ejpam-5903	495	19	)	)	PUNCT
ejpam-5903	495	20	=	=	SYM
ejpam-5903	496	1	3	3	X
ejpam-5903	496	2	.	.	X
ejpam-5903	497	1	hence	hence	ADV
ejpam-5903	497	2	,	,	PUNCT
ejpam-5903	497	3	k	k	PROPN
ejpam-5903	497	4	≤	≤	ADV
ejpam-5903	497	5	2	2	NUM
ejpam-5903	497	6	and	and	CCONJ
ejpam-5903	497	7	any	any	DET
ejpam-5903	497	8	set	set	NOUN
ejpam-5903	497	9	s	s	NOUN
ejpam-5903	497	10	⊆	⊆	NUM
ejpam-5903	497	11	v	v	NOUN
ejpam-5903	497	12	(	(	PUNCT
ejpam-5903	497	13	g	g	NOUN
ejpam-5903	497	14	)	)	PUNCT
ejpam-5903	497	15	with	with	ADP
ejpam-5903	497	16	|s|	|s|	PROPN
ejpam-5903	497	17	=	=	SYM
ejpam-5903	497	18	3−	3−	NUM
ejpam-5903	497	19	k	k	NOUN
ejpam-5903	497	20	is	be	AUX
ejpam-5903	497	21	a	a	DET
ejpam-5903	497	22	ζhgk	ζhgk	NOUN
ejpam-5903	497	23	-set	-set	ADJ
ejpam-5903	497	24	of	of	ADP
ejpam-5903	497	25	g.	g.	PROPN
ejpam-5903	497	26	clearly	clearly	ADV
ejpam-5903	497	27	,	,	PUNCT
ejpam-5903	497	28	nhg	nhg	VERB
ejpam-5903	497	29	g	g	PROPN
ejpam-5903	498	1	[	[	X
ejpam-5903	498	2	s	s	X
ejpam-5903	498	3	]	]	X
ejpam-5903	498	4	=	=	PUNCT
ejpam-5903	498	5	s.	s.	PROPN
ejpam-5903	498	6	hence	hence	ADV
ejpam-5903	498	7	,	,	PUNCT
ejpam-5903	498	8	ζhgk	ζhgk	NOUN
ejpam-5903	498	9	(	(	PUNCT
ejpam-5903	498	10	g	g	NOUN
ejpam-5903	498	11	)	)	PUNCT
ejpam-5903	498	12	=	=	SYM
ejpam-5903	498	13	(	(	PUNCT
ejpam-5903	498	14	n+	n+	NUM
ejpam-5903	498	15	2)−	2)−	NUM
ejpam-5903	498	16	(	(	PUNCT
ejpam-5903	498	17	3−	3−	NUM
ejpam-5903	498	18	k	k	NOUN
ejpam-5903	498	19	)	)	PUNCT
ejpam-5903	498	20	=	=	SYM
ejpam-5903	498	21	n+	n+	PUNCT
ejpam-5903	499	1	k	k	X
ejpam-5903	499	2	−	−	NOUN
ejpam-5903	500	1	1	1	X
ejpam-5903	500	2	.	.	PUNCT
ejpam-5903	500	3	case	case	NOUN
ejpam-5903	500	4	3	3	NUM
ejpam-5903	500	5	:	:	PUNCT
ejpam-5903	500	6	m	m	VERB
ejpam-5903	500	7	≥	≥	NOUN
ejpam-5903	500	8	3	3	NUM
ejpam-5903	500	9	.	.	PUNCT
ejpam-5903	500	10	by	by	ADP
ejpam-5903	500	11	corollary	corollary	ADJ
ejpam-5903	500	12	1(v	1(v	NUM
ejpam-5903	500	13	)	)	PUNCT
ejpam-5903	500	14	,	,	PUNCT
ejpam-5903	500	15	γhg(g	γhg(g	PROPN
ejpam-5903	500	16	)	)	PUNCT
ejpam-5903	500	17	=	=	SYM
ejpam-5903	501	1	4	4	X
ejpam-5903	501	2	.	.	PUNCT
ejpam-5903	501	3	this	this	PRON
ejpam-5903	501	4	implies	imply	VERB
ejpam-5903	501	5	that	that	SCONJ
ejpam-5903	501	6	k	k	PROPN
ejpam-5903	501	7	≤	≤	ADV
ejpam-5903	501	8	3	3	X
ejpam-5903	501	9	.	.	PUNCT
ejpam-5903	502	1	if	if	SCONJ
ejpam-5903	502	2	k	k	PROPN
ejpam-5903	502	3	=	=	SYM
ejpam-5903	502	4	3	3	NUM
ejpam-5903	502	5	,	,	PUNCT
ejpam-5903	502	6	then	then	ADV
ejpam-5903	502	7	ζhg3	ζhg3	PROPN
ejpam-5903	502	8	(	(	PUNCT
ejpam-5903	502	9	g	g	NOUN
ejpam-5903	502	10	)	)	PUNCT
ejpam-5903	502	11	=	=	SYM
ejpam-5903	503	1	m+n−	m+n−	NOUN
ejpam-5903	503	2	1	1	NUM
ejpam-5903	503	3	=	=	SYM
ejpam-5903	503	4	m+n+k−	m+n+k−	X
ejpam-5903	503	5	4	4	NUM
ejpam-5903	503	6	by	by	ADP
ejpam-5903	503	7	lemma	lemma	PROPN
ejpam-5903	503	8	1	1	NUM
ejpam-5903	503	9	.	.	PUNCT
ejpam-5903	504	1	if	if	SCONJ
ejpam-5903	504	2	k	k	PROPN
ejpam-5903	504	3	=	=	SYM
ejpam-5903	504	4	2	2	NUM
ejpam-5903	504	5	,	,	PUNCT
ejpam-5903	504	6	then	then	ADV
ejpam-5903	504	7	any	any	DET
ejpam-5903	504	8	set	set	NOUN
ejpam-5903	504	9	s	s	NOUN
ejpam-5903	504	10	⊆	⊆	NUM
ejpam-5903	504	11	v	v	NOUN
ejpam-5903	504	12	(	(	PUNCT
ejpam-5903	504	13	g	g	NOUN
ejpam-5903	504	14	)	)	PUNCT
ejpam-5903	504	15	with	with	ADP
ejpam-5903	504	16	|s|	|s|	PROPN
ejpam-5903	504	17	=	=	SYM
ejpam-5903	504	18	2	2	NUM
ejpam-5903	504	19	is	be	AUX
ejpam-5903	504	20	a	a	DET
ejpam-5903	504	21	ζhg2	ζhg2	PROPN
ejpam-5903	504	22	-set	-set	PUNCT
ejpam-5903	504	23	of	of	ADP
ejpam-5903	504	24	g	g	PROPN
ejpam-5903	504	25	and	and	CCONJ
ejpam-5903	504	26	nhg	nhg	VERB
ejpam-5903	504	27	g	g	PROPN
ejpam-5903	505	1	[	[	X
ejpam-5903	505	2	s	s	X
ejpam-5903	505	3	]	]	X
ejpam-5903	505	4	=	=	PUNCT
ejpam-5903	505	5	s.	s.	PROPN
ejpam-5903	505	6	hence	hence	ADV
ejpam-5903	505	7	,	,	PUNCT
ejpam-5903	505	8	ζhg2	ζhg2	PROPN
ejpam-5903	505	9	(	(	PUNCT
ejpam-5903	505	10	g	g	NOUN
ejpam-5903	505	11	)	)	PUNCT
ejpam-5903	505	12	=	=	SYM
ejpam-5903	506	1	m+	m+	NUM
ejpam-5903	506	2	n−	n−	PROPN
ejpam-5903	506	3	|s|	|s|	PROPN
ejpam-5903	506	4	=	=	SYM
ejpam-5903	506	5	m+	m+	NUM
ejpam-5903	506	6	n−	n−	NOUN
ejpam-5903	506	7	2	2	NUM
ejpam-5903	506	8	=	=	SYM
ejpam-5903	506	9	m+	m+	NUM
ejpam-5903	506	10	n+	n+	NUM
ejpam-5903	506	11	k−	k−	PROPN
ejpam-5903	506	12	4	4	NUM
ejpam-5903	506	13	.	.	PUNCT
ejpam-5903	506	14	suppose	suppose	VERB
ejpam-5903	506	15	k	k	PROPN
ejpam-5903	506	16	=	=	SYM
ejpam-5903	506	17	1	1	X
ejpam-5903	506	18	.	.	PUNCT
ejpam-5903	506	19	let	let	VERB
ejpam-5903	506	20	a	a	PRON
ejpam-5903	506	21	and	and	CCONJ
ejpam-5903	506	22	b	b	NOUN
ejpam-5903	506	23	be	be	AUX
ejpam-5903	506	24	the	the	DET
ejpam-5903	506	25	partite	partite	ADJ
ejpam-5903	506	26	sets	set	NOUN
ejpam-5903	506	27	of	of	ADP
ejpam-5903	506	28	g	g	NOUN
ejpam-5903	506	29	with	with	ADP
ejpam-5903	506	30	|a|	|a|	PROPN
ejpam-5903	506	31	=	=	PROPN
ejpam-5903	506	32	m	m	PROPN
ejpam-5903	506	33	and	and	CCONJ
ejpam-5903	506	34	|b|	|b|	PROPN
ejpam-5903	506	35	=	=	SYM
ejpam-5903	506	36	n	n	CCONJ
ejpam-5903	506	37	,	,	PUNCT
ejpam-5903	506	38	respectively	respectively	ADV
ejpam-5903	506	39	,	,	PUNCT
ejpam-5903	506	40	and	and	CCONJ
ejpam-5903	506	41	let	let	VERB
ejpam-5903	506	42	s	s	PRON
ejpam-5903	506	43	be	be	AUX
ejpam-5903	506	44	a	a	DET
ejpam-5903	506	45	set	set	NOUN
ejpam-5903	506	46	of	of	ADP
ejpam-5903	506	47	vertices	vertex	NOUN
ejpam-5903	506	48	of	of	ADP
ejpam-5903	506	49	g	g	NOUN
ejpam-5903	506	50	with	with	ADP
ejpam-5903	506	51	|s|	|s|	NOUN
ejpam-5903	506	52	=	=	SYM
ejpam-5903	506	53	3	3	X
ejpam-5903	506	54	.	.	PUNCT
ejpam-5903	506	55	consider	consider	VERB
ejpam-5903	506	56	the	the	DET
ejpam-5903	506	57	following	follow	VERB
ejpam-5903	506	58	subcases	subcase	NOUN
ejpam-5903	506	59	:	:	PUNCT
ejpam-5903	506	60	subcase	subcase	NOUN
ejpam-5903	506	61	1	1	NUM
ejpam-5903	506	62	:	:	PUNCT
ejpam-5903	506	63	s	s	VERB
ejpam-5903	506	64	⊂	⊂	PROPN
ejpam-5903	506	65	a	a	PRON
ejpam-5903	506	66	or	or	CCONJ
ejpam-5903	506	67	s	s	PROPN
ejpam-5903	506	68	⊂	⊂	PROPN
ejpam-5903	506	69	b.	b.	PROPN
ejpam-5903	507	1	then	then	ADV
ejpam-5903	507	2	nhg	nhg	VERB
ejpam-5903	507	3	g	g	PROPN
ejpam-5903	508	1	[	[	X
ejpam-5903	508	2	s	s	X
ejpam-5903	508	3	]	]	X
ejpam-5903	508	4	=	=	SYM
ejpam-5903	508	5	s	s	PROPN
ejpam-5903	508	6	and	and	CCONJ
ejpam-5903	508	7	ζhg1	ζhg1	PROPN
ejpam-5903	508	8	(	(	PUNCT
ejpam-5903	508	9	s	s	NOUN
ejpam-5903	508	10	)	)	PUNCT
ejpam-5903	508	11	=	=	SYM
ejpam-5903	509	1	m+	m+	NUM
ejpam-5903	509	2	n−	n−	NOUN
ejpam-5903	509	3	3	3	NUM
ejpam-5903	509	4	.	.	PUNCT
ejpam-5903	510	1	subcase	subcase	PROPN
ejpam-5903	510	2	2	2	NUM
ejpam-5903	510	3	:	:	PUNCT
ejpam-5903	510	4	|s	|s	PROPN
ejpam-5903	510	5	∩a|	∩a|	PUNCT
ejpam-5903	511	1	=	=	SYM
ejpam-5903	511	2	1	1	NUM
ejpam-5903	511	3	and	and	CCONJ
ejpam-5903	511	4	|s	|s	PROPN
ejpam-5903	511	5	∩b|	∩b|	PROPN
ejpam-5903	512	1	=	=	SYM
ejpam-5903	512	2	2	2	X
ejpam-5903	512	3	.	.	PUNCT
ejpam-5903	512	4	then	then	ADV
ejpam-5903	512	5	nhg	nhg	VERB
ejpam-5903	512	6	g	g	PROPN
ejpam-5903	513	1	[	[	X
ejpam-5903	513	2	s	s	X
ejpam-5903	513	3	]	]	X
ejpam-5903	513	4	=	=	SYM
ejpam-5903	513	5	a∪(s∩b	a∪(s∩b	NOUN
ejpam-5903	513	6	)	)	PUNCT
ejpam-5903	513	7	.	.	PUNCT
ejpam-5903	514	1	thus	thus	ADV
ejpam-5903	514	2	,	,	PUNCT
ejpam-5903	514	3	nhg	nhg	NOUN
ejpam-5903	514	4	g	g	PROPN
ejpam-5903	515	1	[	[	X
ejpam-5903	515	2	s	s	X
ejpam-5903	515	3	]	]	X
ejpam-5903	515	4	=	=	SYM
ejpam-5903	515	5	m+2	m+2	NOUN
ejpam-5903	515	6	.	.	PUNCT
ejpam-5903	516	1	hence	hence	ADV
ejpam-5903	516	2	,	,	PUNCT
ejpam-5903	516	3	ζhg1	ζhg1	PROPN
ejpam-5903	516	4	(	(	PUNCT
ejpam-5903	516	5	s	s	NOUN
ejpam-5903	516	6	)	)	PUNCT
ejpam-5903	516	7	=	=	SYM
ejpam-5903	516	8	m+n−(m+2	m+n−(m+2	NOUN
ejpam-5903	516	9	)	)	PUNCT
ejpam-5903	516	10	=	=	SYM
ejpam-5903	517	1	j.	j.	PROPN
ejpam-5903	517	2	anoche	anoche	PROPN
ejpam-5903	517	3	,	,	PUNCT
ejpam-5903	517	4	s.	s.	PROPN
ejpam-5903	517	5	canoy	canoy	PROPN
ejpam-5903	517	6	,	,	PUNCT
ejpam-5903	517	7	jr	jr	PROPN
ejpam-5903	517	8	.	.	PROPN
ejpam-5903	517	9	/	/	SYM
ejpam-5903	517	10	eur	eur	PROPN
ejpam-5903	517	11	.	.	PUNCT
ejpam-5903	518	1	j.	j.	PROPN
ejpam-5903	518	2	pure	pure	PROPN
ejpam-5903	518	3	appl	appl	PROPN
ejpam-5903	518	4	.	.	PROPN
ejpam-5903	518	5	math	math	PROPN
ejpam-5903	518	6	,	,	PUNCT
ejpam-5903	518	7	18	18	NUM
ejpam-5903	518	8	(	(	PUNCT
ejpam-5903	518	9	2	2	NUM
ejpam-5903	518	10	)	)	PUNCT
ejpam-5903	518	11	(	(	PUNCT
ejpam-5903	518	12	2025	2025	NUM
ejpam-5903	518	13	)	)	PUNCT
ejpam-5903	518	14	,	,	PUNCT
ejpam-5903	518	15	5903	5903	NUM
ejpam-5903	518	16	14	14	NUM
ejpam-5903	518	17	of	of	ADP
ejpam-5903	518	18	17	17	NUM
ejpam-5903	518	19	n−	n−	NOUN
ejpam-5903	518	20	2	2	NUM
ejpam-5903	518	21	.	.	NOUN
ejpam-5903	518	22	subcase	subcase	PROPN
ejpam-5903	518	23	3	3	NUM
ejpam-5903	518	24	:	:	PUNCT
ejpam-5903	518	25	|s	|s	PROPN
ejpam-5903	518	26	∩a|	∩a|	PUNCT
ejpam-5903	519	1	=	=	SYM
ejpam-5903	519	2	2	2	NUM
ejpam-5903	519	3	and	and	CCONJ
ejpam-5903	519	4	|s	|s	PROPN
ejpam-5903	519	5	∩b|	∩b|	NUM
ejpam-5903	519	6	=	=	SYM
ejpam-5903	520	1	1	1	X
ejpam-5903	520	2	.	.	PUNCT
ejpam-5903	520	3	then	then	ADV
ejpam-5903	520	4	nhg	nhg	VERB
ejpam-5903	520	5	g	g	PROPN
ejpam-5903	521	1	[	[	X
ejpam-5903	521	2	s	s	X
ejpam-5903	521	3	]	]	X
ejpam-5903	521	4	=	=	SYM
ejpam-5903	521	5	(	(	PUNCT
ejpam-5903	521	6	s∩a)∪b	s∩a)∪b	PROPN
ejpam-5903	521	7	.	.	PUNCT
ejpam-5903	522	1	thus	thus	ADV
ejpam-5903	522	2	,	,	PUNCT
ejpam-5903	522	3	nhg	nhg	NOUN
ejpam-5903	522	4	g	g	PROPN
ejpam-5903	523	1	[	[	X
ejpam-5903	523	2	s	s	X
ejpam-5903	523	3	]	]	X
ejpam-5903	523	4	=	=	SYM
ejpam-5903	523	5	2+n	2+n	NUM
ejpam-5903	523	6	.	.	PUNCT
ejpam-5903	524	1	hence	hence	ADV
ejpam-5903	524	2	,	,	PUNCT
ejpam-5903	524	3	ζhg1	ζhg1	PROPN
ejpam-5903	524	4	(	(	PUNCT
ejpam-5903	524	5	s	s	NOUN
ejpam-5903	524	6	)	)	PUNCT
ejpam-5903	524	7	=	=	SYM
ejpam-5903	524	8	m+n−	m+n−	NOUN
ejpam-5903	524	9	(	(	PUNCT
ejpam-5903	524	10	n+2	n+2	NUM
ejpam-5903	524	11	)	)	PUNCT
ejpam-5903	524	12	=	=	NOUN
ejpam-5903	524	13	m−	m−	PROPN
ejpam-5903	524	14	2	2	NUM
ejpam-5903	524	15	.	.	PUNCT
ejpam-5903	525	1	therefore	therefore	ADV
ejpam-5903	525	2	,	,	PUNCT
ejpam-5903	525	3	s	s	VERB
ejpam-5903	525	4	is	be	AUX
ejpam-5903	525	5	a	a	DET
ejpam-5903	525	6	ζhg1	ζhg1	NOUN
ejpam-5903	525	7	-set	-set	PUNCT
ejpam-5903	525	8	ofg	ofg	PROPN
ejpam-5903	525	9	if	if	SCONJ
ejpam-5903	525	10	|s∩a|	|s∩a|	VERB
ejpam-5903	525	11	=	=	SYM
ejpam-5903	525	12	2	2	NUM
ejpam-5903	525	13	and	and	CCONJ
ejpam-5903	525	14	|s∩b|	|s∩b|	NOUN
ejpam-5903	525	15	=	=	SYM
ejpam-5903	525	16	1	1	NUM
ejpam-5903	525	17	becausem−2	becausem−2	NUM
ejpam-5903	525	18	≤	≤	ADV
ejpam-5903	525	19	n−2	n−2	PROPN
ejpam-5903	525	20	≤	≤	PROPN
ejpam-5903	525	21	m+n−3	m+n−3	PROPN
ejpam-5903	525	22	.	.	PUNCT
ejpam-5903	526	1	accordingly	accordingly	ADV
ejpam-5903	526	2	,	,	PUNCT
ejpam-5903	526	3	ζhg1	ζhg1	PROPN
ejpam-5903	526	4	(	(	PUNCT
ejpam-5903	526	5	g	g	NOUN
ejpam-5903	526	6	)	)	PUNCT
ejpam-5903	526	7	=	=	SYM
ejpam-5903	527	1	m−	m−	PROPN
ejpam-5903	527	2	2	2	NUM
ejpam-5903	527	3	.	.	PUNCT
ejpam-5903	527	4	theorem	theorem	VERB
ejpam-5903	527	5	11	11	NUM
ejpam-5903	527	6	.	.	PUNCT
ejpam-5903	528	1	if	if	SCONJ
ejpam-5903	528	2	g	g	PROPN
ejpam-5903	528	3	=	=	SYM
ejpam-5903	528	4	km1,m2	km1,m2	PROPN
ejpam-5903	528	5	,	,	PUNCT
ejpam-5903	528	6	·	·	PUNCT
ejpam-5903	528	7	·	·	PUNCT
ejpam-5903	528	8	·	·	PUNCT
ejpam-5903	528	9	,	,	PUNCT
ejpam-5903	528	10	mr	mr	PROPN
ejpam-5903	528	11	is	be	AUX
ejpam-5903	528	12	a	a	DET
ejpam-5903	528	13	complete	complete	ADJ
ejpam-5903	528	14	multipartite	multipartite	ADJ
ejpam-5903	528	15	graph	graph	NOUN
ejpam-5903	528	16	with	with	ADP
ejpam-5903	528	17	2	2	NUM
ejpam-5903	528	18	≤	≤	NOUN
ejpam-5903	528	19	m1	m1	NOUN
ejpam-5903	528	20	≤	≤	NUM
ejpam-5903	528	21	m2	m2	PROPN
ejpam-5903	528	22	≤	≤	NOUN
ejpam-5903	528	23	·	·	PUNCT
ejpam-5903	528	24	·	·	PUNCT
ejpam-5903	528	25	·	·	PUNCT
ejpam-5903	529	1	≤	≤	NUM
ejpam-5903	530	1	mr	mr	PROPN
ejpam-5903	530	2	,	,	PUNCT
ejpam-5903	530	3	where	where	SCONJ
ejpam-5903	530	4	r	r	NOUN
ejpam-5903	530	5	≥	≥	NOUN
ejpam-5903	530	6	3	3	NUM
ejpam-5903	530	7	,	,	PUNCT
ejpam-5903	530	8	then	then	ADV
ejpam-5903	530	9	γhg(g	γhg(g	PROPN
ejpam-5903	530	10	)	)	PUNCT
ejpam-5903	530	11	=	=	PRON
ejpam-5903	530	12	{	{	PUNCT
ejpam-5903	530	13	r	r	NOUN
ejpam-5903	530	14	+	+	NOUN
ejpam-5903	530	15	1	1	NUM
ejpam-5903	530	16	if	if	SCONJ
ejpam-5903	530	17	m1	m1	NOUN
ejpam-5903	530	18	=	=	SYM
ejpam-5903	530	19	2	2	NUM
ejpam-5903	530	20	r	r	NOUN
ejpam-5903	530	21	+	+	NUM
ejpam-5903	530	22	2	2	NUM
ejpam-5903	530	23	if	if	SCONJ
ejpam-5903	530	24	m1	m1	PROPN
ejpam-5903	530	25	≥	≥	NOUN
ejpam-5903	530	26	3	3	X
ejpam-5903	530	27	.	.	PUNCT
ejpam-5903	531	1	proof	proof	NOUN
ejpam-5903	531	2	.	.	PUNCT
ejpam-5903	532	1	let	let	VERB
ejpam-5903	532	2	q1	q1	PROPN
ejpam-5903	532	3	,	,	PUNCT
ejpam-5903	532	4	q2	q2	NOUN
ejpam-5903	532	5	,	,	PUNCT
ejpam-5903	532	6	·	·	PUNCT
ejpam-5903	532	7	·	·	PUNCT
ejpam-5903	532	8	·	·	PUNCT
ejpam-5903	532	9	,	,	PUNCT
ejpam-5903	532	10	qr	qr	INTJ
ejpam-5903	532	11	be	be	AUX
ejpam-5903	532	12	the	the	DET
ejpam-5903	532	13	partite	partite	ADJ
ejpam-5903	532	14	sets	set	NOUN
ejpam-5903	532	15	of	of	ADP
ejpam-5903	532	16	g	g	NOUN
ejpam-5903	532	17	with	with	ADP
ejpam-5903	532	18	|qj	|qj	NUM
ejpam-5903	532	19	|	|	ADV
ejpam-5903	532	20	=	=	SYM
ejpam-5903	532	21	mj	mj	PROPN
ejpam-5903	532	22	for	for	ADP
ejpam-5903	532	23	each	each	DET
ejpam-5903	532	24	j	j	PROPN
ejpam-5903	532	25	∈	∈	PROPN
ejpam-5903	533	1	[	[	X
ejpam-5903	533	2	r	r	X
ejpam-5903	533	3	]	]	PUNCT
ejpam-5903	533	4	.	.	PUNCT
ejpam-5903	534	1	let	let	VERB
ejpam-5903	534	2	s	s	PRON
ejpam-5903	534	3	be	be	AUX
ejpam-5903	534	4	a	a	DET
ejpam-5903	534	5	geodetic	geodetic	ADJ
ejpam-5903	534	6	hop	hop	NOUN
ejpam-5903	534	7	dominating	dominating	NOUN
ejpam-5903	534	8	set	set	NOUN
ejpam-5903	534	9	of	of	ADP
ejpam-5903	534	10	g.	g.	PROPN
ejpam-5903	534	11	suppose	suppose	VERB
ejpam-5903	534	12	there	there	PRON
ejpam-5903	534	13	exists	exist	VERB
ejpam-5903	534	14	j	j	PROPN
ejpam-5903	534	15	∈	∈	PROPN
ejpam-5903	534	16	[	[	X
ejpam-5903	534	17	r	r	X
ejpam-5903	534	18	]	]	X
ejpam-5903	534	19	=	=	PUNCT
ejpam-5903	534	20	{	{	PUNCT
ejpam-5903	534	21	1	1	NUM
ejpam-5903	534	22	,	,	PUNCT
ejpam-5903	534	23	2	2	NUM
ejpam-5903	534	24	,	,	PUNCT
ejpam-5903	534	25	·	·	PUNCT
ejpam-5903	534	26	·	·	PUNCT
ejpam-5903	534	27	·	·	PUNCT
ejpam-5903	534	28	,	,	PUNCT
ejpam-5903	534	29	r	r	X
ejpam-5903	534	30	}	}	PUNCT
ejpam-5903	534	31	such	such	ADJ
ejpam-5903	534	32	that	that	PRON
ejpam-5903	534	33	s	s	VERB
ejpam-5903	534	34	∩qj	∩qj	NOUN
ejpam-5903	534	35	=	=	VERB
ejpam-5903	534	36	∅.	∅.	NOUN
ejpam-5903	534	37	then	then	ADV
ejpam-5903	534	38	qj	qj	PROPN
ejpam-5903	534	39	⊆	⊆	NUM
ejpam-5903	534	40	ng(s	ng(s	NUM
ejpam-5903	534	41	)	)	PUNCT
ejpam-5903	534	42	.	.	PUNCT
ejpam-5903	535	1	this	this	PRON
ejpam-5903	535	2	implies	imply	VERB
ejpam-5903	535	3	that	that	SCONJ
ejpam-5903	535	4	qj	qj	PROPN
ejpam-5903	535	5	∩n2	∩n2	PROPN
ejpam-5903	535	6	g(s	g(s	PROPN
ejpam-5903	535	7	)	)	PUNCT
ejpam-5903	535	8	=	=	SYM
ejpam-5903	535	9	∅	∅	NOUN
ejpam-5903	535	10	,	,	PUNCT
ejpam-5903	535	11	contrary	contrary	ADJ
ejpam-5903	535	12	to	to	ADP
ejpam-5903	535	13	the	the	DET
ejpam-5903	535	14	assumption	assumption	NOUN
ejpam-5903	535	15	that	that	SCONJ
ejpam-5903	535	16	s	s	VERB
ejpam-5903	535	17	is	be	AUX
ejpam-5903	535	18	a	a	DET
ejpam-5903	535	19	hop	hop	NOUN
ejpam-5903	535	20	dominating	dominating	NOUN
ejpam-5903	535	21	set	set	NOUN
ejpam-5903	535	22	.	.	PUNCT
ejpam-5903	536	1	therefore	therefore	ADV
ejpam-5903	536	2	,	,	PUNCT
ejpam-5903	536	3	s	s	VERB
ejpam-5903	536	4	∩qj	∩qj	NOUN
ejpam-5903	536	5	̸=	̸=	PROPN
ejpam-5903	536	6	∅	∅	NOUN
ejpam-5903	536	7	for	for	ADP
ejpam-5903	536	8	each	each	DET
ejpam-5903	536	9	j	j	PROPN
ejpam-5903	536	10	∈	∈	PROPN
ejpam-5903	537	1	[	[	X
ejpam-5903	537	2	r	r	X
ejpam-5903	537	3	]	]	PUNCT
ejpam-5903	537	4	.	.	PUNCT
ejpam-5903	538	1	suppose	suppose	VERB
ejpam-5903	538	2	|s	|s	PROPN
ejpam-5903	538	3	∩qj	∩qj	NOUN
ejpam-5903	538	4	|	|	NOUN
ejpam-5903	538	5	=	=	NOUN
ejpam-5903	538	6	1	1	NUM
ejpam-5903	538	7	for	for	ADP
ejpam-5903	538	8	each	each	DET
ejpam-5903	538	9	j	j	PROPN
ejpam-5903	538	10	∈	∈	PROPN
ejpam-5903	539	1	[	[	X
ejpam-5903	539	2	r	r	X
ejpam-5903	539	3	]	]	PUNCT
ejpam-5903	539	4	.	.	PUNCT
ejpam-5903	540	1	then	then	ADV
ejpam-5903	540	2	[	[	X
ejpam-5903	540	3	q1	q1	X
ejpam-5903	540	4	\	\	PUNCT
ejpam-5903	541	1	(	(	PUNCT
ejpam-5903	541	2	s	s	NOUN
ejpam-5903	541	3	∩q1	∩q1	PROPN
ejpam-5903	541	4	)	)	PUNCT
ejpam-5903	541	5	]	]	PUNCT
ejpam-5903	542	1	∩	∩	X
ejpam-5903	542	2	ig[s	ig[s	PROPN
ejpam-5903	542	3	]	]	PUNCT
ejpam-5903	542	4	=	=	SYM
ejpam-5903	542	5	∅	∅	NOUN
ejpam-5903	542	6	,	,	PUNCT
ejpam-5903	542	7	contrary	contrary	ADJ
ejpam-5903	542	8	to	to	ADP
ejpam-5903	542	9	the	the	DET
ejpam-5903	542	10	assumption	assumption	NOUN
ejpam-5903	542	11	that	that	SCONJ
ejpam-5903	542	12	s	s	VERB
ejpam-5903	542	13	is	be	AUX
ejpam-5903	542	14	a	a	DET
ejpam-5903	542	15	geodetic	geodetic	ADJ
ejpam-5903	542	16	set	set	NOUN
ejpam-5903	542	17	.	.	PUNCT
ejpam-5903	543	1	thus	thus	ADV
ejpam-5903	543	2	,	,	PUNCT
ejpam-5903	543	3	there	there	PRON
ejpam-5903	543	4	exists	exist	VERB
ejpam-5903	543	5	t	t	PROPN
ejpam-5903	543	6	∈	∈	PROPN
ejpam-5903	544	1	[	[	X
ejpam-5903	544	2	r	r	X
ejpam-5903	544	3	]	]	PUNCT
ejpam-5903	544	4	such	such	ADJ
ejpam-5903	544	5	that	that	SCONJ
ejpam-5903	544	6	|s	|s	PROPN
ejpam-5903	544	7	∩	∩	PROPN
ejpam-5903	544	8	qt|	qt|	PRON
ejpam-5903	544	9	≥	≥	NOUN
ejpam-5903	544	10	2	2	X
ejpam-5903	544	11	.	.	PUNCT
ejpam-5903	545	1	this	this	PRON
ejpam-5903	545	2	implies	imply	VERB
ejpam-5903	545	3	that	that	SCONJ
ejpam-5903	545	4	γhg(g	γhg(g	PROPN
ejpam-5903	545	5	)	)	PUNCT
ejpam-5903	545	6	≥	≥	NOUN
ejpam-5903	545	7	r	r	NOUN
ejpam-5903	545	8	+	+	NOUN
ejpam-5903	545	9	1	1	NUM
ejpam-5903	545	10	.	.	PUNCT
ejpam-5903	546	1	if	if	SCONJ
ejpam-5903	546	2	m1	m1	PROPN
ejpam-5903	546	3	=	=	SYM
ejpam-5903	546	4	2	2	NUM
ejpam-5903	546	5	,	,	PUNCT
ejpam-5903	546	6	then	then	ADV
ejpam-5903	546	7	choose	choose	VERB
ejpam-5903	546	8	s1	s1	NOUN
ejpam-5903	546	9	such	such	ADJ
ejpam-5903	546	10	that	that	PRON
ejpam-5903	546	11	|s1	|s1	NOUN
ejpam-5903	546	12	∩q1|	∩q1|	ADV
ejpam-5903	546	13	=	=	SYM
ejpam-5903	546	14	2	2	NUM
ejpam-5903	546	15	and	and	CCONJ
ejpam-5903	546	16	|s1	|s1	NOUN
ejpam-5903	546	17	∩	∩	X
ejpam-5903	546	18	qj	qj	PROPN
ejpam-5903	547	1	|	|	NOUN
ejpam-5903	547	2	=	=	NOUN
ejpam-5903	547	3	1	1	NUM
ejpam-5903	547	4	for	for	ADP
ejpam-5903	547	5	each	each	DET
ejpam-5903	547	6	j	j	PROPN
ejpam-5903	547	7	∈	∈	PROPN
ejpam-5903	548	1	[	[	X
ejpam-5903	548	2	r	r	X
ejpam-5903	548	3	]	]	PUNCT
ejpam-5903	548	4	\	\	PUNCT
ejpam-5903	548	5	{	{	PUNCT
ejpam-5903	548	6	1	1	NUM
ejpam-5903	548	7	}	}	PUNCT
ejpam-5903	548	8	.	.	PUNCT
ejpam-5903	549	1	then	then	ADV
ejpam-5903	549	2	s1	s1	PROPN
ejpam-5903	549	3	is	be	AUX
ejpam-5903	549	4	a	a	DET
ejpam-5903	549	5	γhg	γhg	NOUN
ejpam-5903	549	6	-	-	PUNCT
ejpam-5903	549	7	set	set	NOUN
ejpam-5903	549	8	of	of	ADP
ejpam-5903	549	9	g.	g.	PROPN
ejpam-5903	549	10	hence	hence	ADV
ejpam-5903	549	11	,	,	PUNCT
ejpam-5903	549	12	γhg(g	γhg(g	PROPN
ejpam-5903	549	13	)	)	PUNCT
ejpam-5903	550	1	=	=	SYM
ejpam-5903	550	2	r	r	NOUN
ejpam-5903	550	3	+	+	NOUN
ejpam-5903	550	4	1	1	NUM
ejpam-5903	550	5	.	.	X
ejpam-5903	550	6	supposem1	supposem1	PROPN
ejpam-5903	550	7	≥	≥	NUM
ejpam-5903	550	8	3	3	X
ejpam-5903	550	9	.	.	PUNCT
ejpam-5903	551	1	let	let	VERB
ejpam-5903	551	2	s2	s2	PROPN
ejpam-5903	551	3	be	be	AUX
ejpam-5903	551	4	a	a	DET
ejpam-5903	551	5	γhg	γhg	NOUN
ejpam-5903	551	6	-	-	PUNCT
ejpam-5903	551	7	set	set	NOUN
ejpam-5903	551	8	of	of	ADP
ejpam-5903	551	9	g.	g.	PROPN
ejpam-5903	551	10	suppose	suppose	VERB
ejpam-5903	551	11	there	there	PRON
ejpam-5903	551	12	exists	exist	VERB
ejpam-5903	551	13	exactly	exactly	ADV
ejpam-5903	551	14	a	a	DET
ejpam-5903	551	15	single	single	ADJ
ejpam-5903	551	16	set	set	NOUN
ejpam-5903	551	17	qt	qt	NOUN
ejpam-5903	551	18	with	with	ADP
ejpam-5903	551	19	|s2	|s2	NUM
ejpam-5903	551	20	∩qt|	∩qt|	NOUN
ejpam-5903	551	21	=	=	SYM
ejpam-5903	551	22	2	2	X
ejpam-5903	551	23	.	.	PUNCT
ejpam-5903	552	1	then	then	ADV
ejpam-5903	552	2	[	[	X
ejpam-5903	552	3	q1	q1	NOUN
ejpam-5903	552	4	\	\	PUNCT
ejpam-5903	553	1	(	(	PUNCT
ejpam-5903	553	2	s2	s2	PROPN
ejpam-5903	553	3	∩q1)]∩	∩q1)]∩	NOUN
ejpam-5903	553	4	ig[s2	ig[s2	PROPN
ejpam-5903	553	5	]	]	PUNCT
ejpam-5903	553	6	=	=	SYM
ejpam-5903	553	7	∅	∅	NOUN
ejpam-5903	553	8	,	,	PUNCT
ejpam-5903	553	9	a	a	DET
ejpam-5903	553	10	contradiction	contradiction	NOUN
ejpam-5903	553	11	.	.	PUNCT
ejpam-5903	554	1	this	this	PRON
ejpam-5903	554	2	would	would	AUX
ejpam-5903	554	3	imply	imply	VERB
ejpam-5903	554	4	that	that	PRON
ejpam-5903	554	5	γhg(g	γhg(g	PROPN
ejpam-5903	554	6	)	)	PUNCT
ejpam-5903	555	1	=	=	PRON
ejpam-5903	555	2	|s2|	|s2|	NOUN
ejpam-5903	555	3	≥	≥	NOUN
ejpam-5903	555	4	r	r	NOUN
ejpam-5903	555	5	+	+	NUM
ejpam-5903	555	6	2	2	NUM
ejpam-5903	555	7	.	.	X
ejpam-5903	555	8	consider	consider	VERB
ejpam-5903	555	9	a	a	DET
ejpam-5903	555	10	set	set	NOUN
ejpam-5903	555	11	d	d	NOUN
ejpam-5903	555	12	with	with	ADP
ejpam-5903	555	13	the	the	DET
ejpam-5903	555	14	property	property	NOUN
ejpam-5903	555	15	that	that	PRON
ejpam-5903	555	16	|d	|d	NOUN
ejpam-5903	555	17	∩q1|	∩q1|	ADV
ejpam-5903	555	18	=	=	SYM
ejpam-5903	555	19	|d	|d	NOUN
ejpam-5903	555	20	∩q2|	∩q2|	PROPN
ejpam-5903	555	21	=	=	SYM
ejpam-5903	555	22	2	2	NUM
ejpam-5903	555	23	and	and	CCONJ
ejpam-5903	555	24	|d	|d	NOUN
ejpam-5903	555	25	∩qj	∩qj	NOUN
ejpam-5903	555	26	|	|	NOUN
ejpam-5903	555	27	=	=	NOUN
ejpam-5903	555	28	1	1	NUM
ejpam-5903	555	29	for	for	ADP
ejpam-5903	555	30	each	each	DET
ejpam-5903	555	31	j	j	PROPN
ejpam-5903	555	32	∈	∈	PROPN
ejpam-5903	556	1	[	[	X
ejpam-5903	556	2	r	r	X
ejpam-5903	556	3	]	]	PUNCT
ejpam-5903	556	4	\	\	PUNCT
ejpam-5903	556	5	{	{	PUNCT
ejpam-5903	556	6	1	1	NUM
ejpam-5903	556	7	,	,	PUNCT
ejpam-5903	556	8	2	2	NUM
ejpam-5903	556	9	}	}	PUNCT
ejpam-5903	556	10	.	.	PUNCT
ejpam-5903	557	1	then	then	ADV
ejpam-5903	557	2	d	d	X
ejpam-5903	557	3	is	be	AUX
ejpam-5903	557	4	a	a	DET
ejpam-5903	557	5	geodetic	geodetic	ADJ
ejpam-5903	557	6	hop	hop	NOUN
ejpam-5903	557	7	dominating	dominating	NOUN
ejpam-5903	557	8	set	set	NOUN
ejpam-5903	557	9	of	of	ADP
ejpam-5903	557	10	g	g	PROPN
ejpam-5903	557	11	and	and	CCONJ
ejpam-5903	557	12	|d|	|d|	PROPN
ejpam-5903	557	13	=	=	SYM
ejpam-5903	557	14	r+2	r+2	PROPN
ejpam-5903	557	15	.	.	NOUN
ejpam-5903	558	1	since	since	SCONJ
ejpam-5903	558	2	s2	s2	PROPN
ejpam-5903	558	3	is	be	AUX
ejpam-5903	558	4	a	a	DET
ejpam-5903	558	5	γhg	γhg	NOUN
ejpam-5903	558	6	-	-	PUNCT
ejpam-5903	558	7	set	set	NOUN
ejpam-5903	558	8	of	of	ADP
ejpam-5903	558	9	g	g	NOUN
ejpam-5903	558	10	,	,	PUNCT
ejpam-5903	558	11	it	it	PRON
ejpam-5903	558	12	follows	follow	VERB
ejpam-5903	558	13	that	that	SCONJ
ejpam-5903	558	14	γhg(g	γhg(g	PROPN
ejpam-5903	558	15	)	)	PUNCT
ejpam-5903	559	1	=	=	SYM
ejpam-5903	559	2	|s2|	|s2|	NOUN
ejpam-5903	559	3	=	=	SYM
ejpam-5903	559	4	|d|	|d|	PROPN
ejpam-5903	559	5	=	=	SYM
ejpam-5903	559	6	r+2	r+2	PROPN
ejpam-5903	559	7	.	.	X
ejpam-5903	559	8	theorem	theorem	VERB
ejpam-5903	559	9	12	12	NUM
ejpam-5903	559	10	.	.	PUNCT
ejpam-5903	560	1	for	for	ADP
ejpam-5903	560	2	a	a	DET
ejpam-5903	560	3	complete	complete	ADJ
ejpam-5903	560	4	multipartite	multipartite	ADJ
ejpam-5903	560	5	graph	graph	NOUN
ejpam-5903	560	6	g	g	PROPN
ejpam-5903	560	7	=	=	PUNCT
ejpam-5903	560	8	km1,m2	km1,m2	PROPN
ejpam-5903	560	9	,	,	PUNCT
ejpam-5903	560	10	·	·	PUNCT
ejpam-5903	560	11	·	·	PUNCT
ejpam-5903	560	12	·	·	PUNCT
ejpam-5903	560	13	,	,	PUNCT
ejpam-5903	560	14	mr	mr	PROPN
ejpam-5903	560	15	where	where	SCONJ
ejpam-5903	560	16	r	r	NOUN
ejpam-5903	560	17	≥	≥	NUM
ejpam-5903	560	18	3	3	NUM
ejpam-5903	560	19	and	and	CCONJ
ejpam-5903	560	20	2	2	NUM
ejpam-5903	560	21	≤	≤	NOUN
ejpam-5903	560	22	m1	m1	NOUN
ejpam-5903	560	23	≤	≤	NUM
ejpam-5903	560	24	m2	m2	PROPN
ejpam-5903	560	25	≤	≤	NOUN
ejpam-5903	560	26	·	·	PUNCT
ejpam-5903	560	27	·	·	PUNCT
ejpam-5903	560	28	·	·	PUNCT
ejpam-5903	560	29	≤	≤	NUM
ejpam-5903	561	1	mr	mr	PROPN
ejpam-5903	561	2	,	,	PUNCT
ejpam-5903	561	3	we	we	PRON
ejpam-5903	561	4	have	have	VERB
ejpam-5903	561	5	ζhgk	ζhgk	NOUN
ejpam-5903	561	6	(	(	PUNCT
ejpam-5903	561	7	g	g	NOUN
ejpam-5903	561	8	)	)	PUNCT
ejpam-5903	561	9	=	=	PUNCT
ejpam-5903	562	1			PRON
ejpam-5903	562	2	n−	n−	NOUN
ejpam-5903	562	3	1	1	NUM
ejpam-5903	562	4	if	if	SCONJ
ejpam-5903	562	5	k	k	NOUN
ejpam-5903	562	6	=	=	PRON
ejpam-5903	562	7	γhg(g)−	γhg(g)−	VERB
ejpam-5903	562	8	1	1	NUM
ejpam-5903	562	9	n−	n−	NOUN
ejpam-5903	562	10	2	2	NUM
ejpam-5903	562	11	if	if	SCONJ
ejpam-5903	562	12	k	k	NOUN
ejpam-5903	562	13	=	=	PUNCT
ejpam-5903	562	14	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	562	15	2∑k+1	2∑k+1	NUM
ejpam-5903	562	16	j=2	j=2	PROPN
ejpam-5903	562	17	mj	mj	NOUN
ejpam-5903	562	18	if	if	SCONJ
ejpam-5903	562	19	m1	m1	PROPN
ejpam-5903	562	20	=	=	SYM
ejpam-5903	562	21	2	2	NUM
ejpam-5903	562	22	and	and	CCONJ
ejpam-5903	562	23	1	1	NUM
ejpam-5903	562	24	≤	≤	NUM
ejpam-5903	562	25	k	k	NOUN
ejpam-5903	562	26	≤	≤	NUM
ejpam-5903	562	27	r	r	NOUN
ejpam-5903	562	28	−	−	PROPN
ejpam-5903	562	29	2∑k	2∑k	NUM
ejpam-5903	562	30	j=1mj	j=1mj	NOUN
ejpam-5903	563	1	−	−	NOUN
ejpam-5903	563	2	2	2	NUM
ejpam-5903	563	3	if	if	SCONJ
ejpam-5903	563	4	m1	m1	PROPN
ejpam-5903	563	5	≥	≥	NUM
ejpam-5903	563	6	3	3	NUM
ejpam-5903	563	7	and	and	CCONJ
ejpam-5903	563	8	1	1	NUM
ejpam-5903	563	9	≤	≤	NUM
ejpam-5903	563	10	k	k	NOUN
ejpam-5903	563	11	≤	≤	NUM
ejpam-5903	563	12	r	r	NOUN
ejpam-5903	563	13	−	−	PROPN
ejpam-5903	563	14	2	2	NUM
ejpam-5903	563	15	,	,	PUNCT
ejpam-5903	563	16	where	where	SCONJ
ejpam-5903	563	17	n	n	PROPN
ejpam-5903	563	18	=	=	SYM
ejpam-5903	563	19	∑r	∑r	PROPN
ejpam-5903	563	20	j=1mj	j=1mj	PROPN
ejpam-5903	563	21	.	.	PUNCT
ejpam-5903	564	1	proof	proof	NOUN
ejpam-5903	564	2	.	.	PUNCT
ejpam-5903	565	1	let	let	VERB
ejpam-5903	565	2	q1	q1	PROPN
ejpam-5903	565	3	,	,	PUNCT
ejpam-5903	565	4	q2	q2	NOUN
ejpam-5903	565	5	,	,	PUNCT
ejpam-5903	565	6	·	·	PUNCT
ejpam-5903	565	7	·	·	PUNCT
ejpam-5903	565	8	·	·	PUNCT
ejpam-5903	565	9	,	,	PUNCT
ejpam-5903	565	10	qr	qr	INTJ
ejpam-5903	565	11	be	be	AUX
ejpam-5903	565	12	the	the	DET
ejpam-5903	565	13	partite	partite	ADJ
ejpam-5903	565	14	sets	set	NOUN
ejpam-5903	565	15	of	of	ADP
ejpam-5903	565	16	g	g	NOUN
ejpam-5903	565	17	with	with	ADP
ejpam-5903	565	18	|qj	|qj	NUM
ejpam-5903	565	19	|	|	ADV
ejpam-5903	565	20	=	=	SYM
ejpam-5903	565	21	mj	mj	PROPN
ejpam-5903	565	22	for	for	ADP
ejpam-5903	565	23	each	each	DET
ejpam-5903	565	24	j	j	PROPN
ejpam-5903	565	25	∈	∈	PROPN
ejpam-5903	566	1	[	[	X
ejpam-5903	566	2	r	r	X
ejpam-5903	566	3	]	]	PUNCT
ejpam-5903	566	4	.	.	PUNCT
ejpam-5903	567	1	consider	consider	VERB
ejpam-5903	567	2	the	the	DET
ejpam-5903	567	3	following	follow	VERB
ejpam-5903	567	4	cases	case	NOUN
ejpam-5903	567	5	:	:	PUNCT
ejpam-5903	567	6	j.	j.	PROPN
ejpam-5903	567	7	anoche	anoche	PROPN
ejpam-5903	567	8	,	,	PUNCT
ejpam-5903	567	9	s.	s.	PROPN
ejpam-5903	567	10	canoy	canoy	PROPN
ejpam-5903	567	11	,	,	PUNCT
ejpam-5903	567	12	jr	jr	PROPN
ejpam-5903	567	13	.	.	PROPN
ejpam-5903	567	14	/	/	SYM
ejpam-5903	567	15	eur	eur	PROPN
ejpam-5903	567	16	.	.	PUNCT
ejpam-5903	568	1	j.	j.	PROPN
ejpam-5903	568	2	pure	pure	PROPN
ejpam-5903	568	3	appl	appl	PROPN
ejpam-5903	568	4	.	.	PROPN
ejpam-5903	568	5	math	math	PROPN
ejpam-5903	568	6	,	,	PUNCT
ejpam-5903	568	7	18	18	NUM
ejpam-5903	568	8	(	(	PUNCT
ejpam-5903	568	9	2	2	NUM
ejpam-5903	568	10	)	)	PUNCT
ejpam-5903	568	11	(	(	PUNCT
ejpam-5903	568	12	2025	2025	NUM
ejpam-5903	568	13	)	)	PUNCT
ejpam-5903	568	14	,	,	PUNCT
ejpam-5903	568	15	5903	5903	NUM
ejpam-5903	568	16	15	15	NUM
ejpam-5903	568	17	of	of	ADP
ejpam-5903	568	18	17	17	NUM
ejpam-5903	568	19	case	case	NOUN
ejpam-5903	568	20	1	1	NUM
ejpam-5903	568	21	:	:	PUNCT
ejpam-5903	568	22	k	k	NOUN
ejpam-5903	568	23	=	=	PUNCT
ejpam-5903	568	24	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	568	25	1	1	NUM
ejpam-5903	568	26	.	.	PUNCT
ejpam-5903	568	27	by	by	ADP
ejpam-5903	568	28	lemma	lemma	PROPN
ejpam-5903	568	29	1	1	NUM
ejpam-5903	568	30	,	,	PUNCT
ejpam-5903	568	31	ζhgk	ζhgk	NOUN
ejpam-5903	568	32	(	(	PUNCT
ejpam-5903	568	33	g	g	NOUN
ejpam-5903	568	34	)	)	PUNCT
ejpam-5903	568	35	=	=	PUNCT
ejpam-5903	569	1	n−	n−	NOUN
ejpam-5903	569	2	1	1	NUM
ejpam-5903	569	3	=	=	SYM
ejpam-5903	569	4	∑r	∑r	PROPN
ejpam-5903	569	5	j=1mj	j=1mj	X
ejpam-5903	570	1	−	−	NOUN
ejpam-5903	570	2	1	1	X
ejpam-5903	570	3	.	.	PUNCT
ejpam-5903	570	4	case	case	NOUN
ejpam-5903	570	5	2	2	NUM
ejpam-5903	570	6	:	:	PUNCT
ejpam-5903	570	7	k	k	NOUN
ejpam-5903	570	8	=	=	PUNCT
ejpam-5903	570	9	γhg(g)−	γhg(g)−	PROPN
ejpam-5903	570	10	2	2	NUM
ejpam-5903	570	11	.	.	PUNCT
ejpam-5903	571	1	then	then	ADV
ejpam-5903	571	2	any	any	DET
ejpam-5903	571	3	2	2	NUM
ejpam-5903	571	4	-	-	PUNCT
ejpam-5903	571	5	element	element	NOUN
ejpam-5903	571	6	subset	subset	NOUN
ejpam-5903	571	7	s	s	PROPN
ejpam-5903	571	8	of	of	ADP
ejpam-5903	571	9	v	v	NOUN
ejpam-5903	571	10	(	(	PUNCT
ejpam-5903	571	11	g	g	NOUN
ejpam-5903	571	12	)	)	PUNCT
ejpam-5903	571	13	is	be	AUX
ejpam-5903	571	14	a	a	DET
ejpam-5903	571	15	ζhgk	ζhgk	NOUN
ejpam-5903	571	16	-set	-set	ADJ
ejpam-5903	571	17	of	of	ADP
ejpam-5903	571	18	g	g	PROPN
ejpam-5903	571	19	and	and	CCONJ
ejpam-5903	571	20	nhg	nhg	VERB
ejpam-5903	571	21	g	g	PROPN
ejpam-5903	572	1	[	[	X
ejpam-5903	572	2	s	s	X
ejpam-5903	572	3	]	]	X
ejpam-5903	572	4	=	=	PUNCT
ejpam-5903	572	5	s.	s.	PROPN
ejpam-5903	572	6	hence	hence	ADV
ejpam-5903	572	7	,	,	PUNCT
ejpam-5903	572	8	ζhgk	ζhgk	NOUN
ejpam-5903	572	9	(	(	PUNCT
ejpam-5903	572	10	g	g	NOUN
ejpam-5903	572	11	)	)	PUNCT
ejpam-5903	572	12	=	=	VERB
ejpam-5903	572	13	ζhgk	ζhgk	NOUN
ejpam-5903	572	14	(	(	PUNCT
ejpam-5903	572	15	s	s	NOUN
ejpam-5903	572	16	)	)	PUNCT
ejpam-5903	572	17	=	=	SYM
ejpam-5903	572	18	n−	n−	NOUN
ejpam-5903	572	19	|nhg	|nhg	VERB
ejpam-5903	572	20	g	g	PROPN
ejpam-5903	573	1	[	[	X
ejpam-5903	573	2	s]|	s]|	X
ejpam-5903	573	3	=	=	SYM
ejpam-5903	573	4	n−	n−	NOUN
ejpam-5903	573	5	2	2	NUM
ejpam-5903	573	6	=	=	SYM
ejpam-5903	573	7	∑r	∑r	PROPN
ejpam-5903	573	8	j=1mj	j=1mj	X
ejpam-5903	574	1	−	−	NOUN
ejpam-5903	574	2	2	2	X
ejpam-5903	574	3	.	.	PUNCT
ejpam-5903	574	4	case	case	NOUN
ejpam-5903	574	5	3	3	NUM
ejpam-5903	574	6	:	:	PUNCT
ejpam-5903	574	7	m1	m1	PROPN
ejpam-5903	574	8	=	=	SYM
ejpam-5903	574	9	2	2	NUM
ejpam-5903	574	10	and	and	CCONJ
ejpam-5903	574	11	1	1	NUM
ejpam-5903	574	12	≤	≤	NUM
ejpam-5903	574	13	k	k	NOUN
ejpam-5903	575	1	≤	≤	NUM
ejpam-5903	575	2	r	r	NOUN
ejpam-5903	575	3	−	−	NOUN
ejpam-5903	575	4	2	2	NUM
ejpam-5903	575	5	.	.	PUNCT
ejpam-5903	575	6	by	by	ADP
ejpam-5903	575	7	theorem	theorem	NOUN
ejpam-5903	575	8	11	11	NUM
ejpam-5903	575	9	,	,	PUNCT
ejpam-5903	575	10	γhg(g	γhg(g	PROPN
ejpam-5903	575	11	)	)	PUNCT
ejpam-5903	576	1	=	=	SYM
ejpam-5903	577	1	r	r	NOUN
ejpam-5903	577	2	+	+	NOUN
ejpam-5903	577	3	1	1	X
ejpam-5903	577	4	.	.	X
ejpam-5903	577	5	consider	consider	VERB
ejpam-5903	577	6	the	the	DET
ejpam-5903	577	7	set	set	NOUN
ejpam-5903	577	8	d	d	PROPN
ejpam-5903	577	9	=	=	PUNCT
ejpam-5903	577	10	{	{	PUNCT
ejpam-5903	577	11	q11	q11	NOUN
ejpam-5903	577	12	,	,	PUNCT
ejpam-5903	577	13	q21	q21	NOUN
ejpam-5903	577	14	,	,	PUNCT
ejpam-5903	577	15	q1k+2	q1k+2	NOUN
ejpam-5903	577	16	,	,	PUNCT
ejpam-5903	577	17	q	q	PROPN
ejpam-5903	577	18	1	1	NUM
ejpam-5903	577	19	k+3	k+3	PROPN
ejpam-5903	577	20	,	,	PUNCT
ejpam-5903	577	21	·	·	PUNCT
ejpam-5903	577	22	·	·	PUNCT
ejpam-5903	577	23	·	·	PUNCT
ejpam-5903	577	24	,	,	PUNCT
ejpam-5903	577	25	q1r	q1r	ADV
ejpam-5903	577	26	}	}	PUNCT
ejpam-5903	577	27	where	where	SCONJ
ejpam-5903	577	28	qtj	qtj	PROPN
ejpam-5903	577	29	∈	∈	PROPN
ejpam-5903	577	30	qj	qj	PROPN
ejpam-5903	577	31	for	for	ADP
ejpam-5903	577	32	each	each	DET
ejpam-5903	577	33	j	j	PROPN
ejpam-5903	577	34	∈	∈	PROPN
ejpam-5903	577	35	{	{	PUNCT
ejpam-5903	577	36	1	1	NUM
ejpam-5903	577	37	,	,	PUNCT
ejpam-5903	577	38	k	k	PROPN
ejpam-5903	578	1	+	+	PROPN
ejpam-5903	578	2	2	2	NUM
ejpam-5903	578	3	,	,	PUNCT
ejpam-5903	578	4	k	k	PROPN
ejpam-5903	578	5	+	+	PROPN
ejpam-5903	578	6	3	3	NUM
ejpam-5903	578	7	,	,	PUNCT
ejpam-5903	578	8	·	·	PUNCT
ejpam-5903	578	9	·	·	PUNCT
ejpam-5903	578	10	·	·	PUNCT
ejpam-5903	578	11	,	,	PUNCT
ejpam-5903	578	12	r	r	NOUN
ejpam-5903	578	13	}	}	PUNCT
ejpam-5903	578	14	and	and	CCONJ
ejpam-5903	578	15	t	t	PROPN
ejpam-5903	578	16	∈	∈	PROPN
ejpam-5903	578	17	{	{	PUNCT
ejpam-5903	578	18	1	1	NUM
ejpam-5903	578	19	,	,	PUNCT
ejpam-5903	578	20	2	2	NUM
ejpam-5903	578	21	}	}	PUNCT
ejpam-5903	578	22	.	.	PUNCT
ejpam-5903	579	1	then	then	ADV
ejpam-5903	579	2	nhg	nhg	VERB
ejpam-5903	579	3	g	g	PROPN
ejpam-5903	580	1	[	[	X
ejpam-5903	580	2	d	d	X
ejpam-5903	580	3	]	]	X
ejpam-5903	580	4	=	=	PUNCT
ejpam-5903	580	5	∪r	∪r	NUM
ejpam-5903	580	6	j	j	PROPN
ejpam-5903	581	1	=	=	NOUN
ejpam-5903	581	2	k+2qj	k+2qj	NOUN
ejpam-5903	581	3	∪	∪	X
ejpam-5903	581	4	{	{	PUNCT
ejpam-5903	581	5	q11	q11	NOUN
ejpam-5903	581	6	,	,	PUNCT
ejpam-5903	581	7	q21	q21	PROPN
ejpam-5903	581	8	}	}	PUNCT
ejpam-5903	581	9	.	.	PUNCT
ejpam-5903	582	1	it	it	PRON
ejpam-5903	582	2	follows	follow	VERB
ejpam-5903	582	3	that	that	DET
ejpam-5903	582	4	ζhgk	ζhgk	NOUN
ejpam-5903	582	5	(	(	PUNCT
ejpam-5903	582	6	g	g	NOUN
ejpam-5903	582	7	)	)	PUNCT
ejpam-5903	582	8	≤	≤	NOUN
ejpam-5903	582	9	ζhgk	ζhgk	NOUN
ejpam-5903	582	10	(	(	PUNCT
ejpam-5903	582	11	d	d	NOUN
ejpam-5903	582	12	)	)	PUNCT
ejpam-5903	582	13	=	=	SYM
ejpam-5903	582	14	|v	|v	PROPN
ejpam-5903	582	15	(	(	PUNCT
ejpam-5903	582	16	g)|	g)|	NOUN
ejpam-5903	582	17	−	−	PROPN
ejpam-5903	582	18	|nhg	|nhg	PROPN
ejpam-5903	582	19	g	g	NOUN
ejpam-5903	583	1	[	[	X
ejpam-5903	583	2	d]|	d]|	X
ejpam-5903	583	3	=	=	SYM
ejpam-5903	583	4	r∑	r∑	NOUN
ejpam-5903	583	5	j=1	j=1	PROPN
ejpam-5903	583	6	mj	mj	PROPN
ejpam-5903	583	7	−	−	PROPN
ejpam-5903	584	1	[	[	PUNCT
ejpam-5903	584	2	r∑	r∑	X
ejpam-5903	584	3	j	j	X
ejpam-5903	584	4	=	=	SYM
ejpam-5903	584	5	k+2	k+2	PROPN
ejpam-5903	584	6	mj	mj	PROPN
ejpam-5903	584	7	+	+	PROPN
ejpam-5903	584	8	2	2	NUM
ejpam-5903	584	9	]	]	PUNCT
ejpam-5903	584	10	=	=	PUNCT
ejpam-5903	585	1	[	[	X
ejpam-5903	585	2	2	2	NUM
ejpam-5903	585	3	+	+	CCONJ
ejpam-5903	585	4	r∑	r∑	NOUN
ejpam-5903	585	5	j=2	j=2	PROPN
ejpam-5903	585	6	mj	mj	NOUN
ejpam-5903	585	7	]	]	X
ejpam-5903	585	8	−	−	X
ejpam-5903	586	1	[	[	PUNCT
ejpam-5903	586	2	r∑	r∑	NOUN
ejpam-5903	586	3	j	j	X
ejpam-5903	586	4	=	=	SYM
ejpam-5903	586	5	k+2	k+2	PROPN
ejpam-5903	586	6	mj	mj	PROPN
ejpam-5903	586	7	+	+	PROPN
ejpam-5903	586	8	2	2	NUM
ejpam-5903	586	9	]	]	X
ejpam-5903	586	10	=	=	SYM
ejpam-5903	586	11	k+1∑	k+1∑	PROPN
ejpam-5903	586	12	j=2	j=2	PROPN
ejpam-5903	586	13	mj	mj	INTJ
ejpam-5903	586	14	.	.	PUNCT
ejpam-5903	587	1	next	next	ADV
ejpam-5903	587	2	,	,	PUNCT
ejpam-5903	587	3	let	let	VERB
ejpam-5903	587	4	s	s	PRON
ejpam-5903	587	5	be	be	AUX
ejpam-5903	587	6	a	a	DET
ejpam-5903	587	7	ζhgk	ζhgk	NOUN
ejpam-5903	587	8	-set	-set	ADJ
ejpam-5903	587	9	of	of	ADP
ejpam-5903	587	10	g.	g.	PROPN
ejpam-5903	587	11	then	then	ADV
ejpam-5903	587	12	|s|	|s|	PROPN
ejpam-5903	588	1	=	=	SYM
ejpam-5903	588	2	r	r	NOUN
ejpam-5903	588	3	−	−	PROPN
ejpam-5903	589	1	k	k	NOUN
ejpam-5903	589	2	+	+	CCONJ
ejpam-5903	589	3	1	1	NUM
ejpam-5903	589	4	and	and	CCONJ
ejpam-5903	589	5	ζhgk	ζhgk	NOUN
ejpam-5903	589	6	(	(	PUNCT
ejpam-5903	589	7	g	g	NOUN
ejpam-5903	589	8	)	)	PUNCT
ejpam-5903	589	9	=	=	VERB
ejpam-5903	590	1	ζhgk	ζhgk	NOUN
ejpam-5903	590	2	(	(	PUNCT
ejpam-5903	590	3	s	s	NOUN
ejpam-5903	590	4	)	)	PUNCT
ejpam-5903	590	5	.	.	PUNCT
ejpam-5903	591	1	suppose	suppose	VERB
ejpam-5903	591	2	s	s	VERB
ejpam-5903	591	3	⊆	⊆	NUM
ejpam-5903	591	4	qj	qj	NOUN
ejpam-5903	591	5	for	for	ADP
ejpam-5903	591	6	some	some	DET
ejpam-5903	591	7	j	j	PROPN
ejpam-5903	591	8	∈	∈	PROPN
ejpam-5903	592	1	[	[	X
ejpam-5903	592	2	r	r	X
ejpam-5903	592	3	]	]	PUNCT
ejpam-5903	592	4	.	.	PUNCT
ejpam-5903	593	1	then	then	ADV
ejpam-5903	593	2	nhg	nhg	VERB
ejpam-5903	593	3	g	g	PROPN
ejpam-5903	594	1	[	[	X
ejpam-5903	594	2	s	s	X
ejpam-5903	594	3	]	]	X
ejpam-5903	594	4	=	=	SYM
ejpam-5903	594	5	s	s	PROPN
ejpam-5903	594	6	and	and	CCONJ
ejpam-5903	594	7	ζhgk	ζhgk	NOUN
ejpam-5903	594	8	(	(	PUNCT
ejpam-5903	594	9	s	s	NOUN
ejpam-5903	594	10	)	)	PUNCT
ejpam-5903	594	11	=	=	SYM
ejpam-5903	594	12	n	n	CCONJ
ejpam-5903	594	13	−	−	NOUN
ejpam-5903	595	1	r	r	NOUN
ejpam-5903	595	2	+	+	CCONJ
ejpam-5903	596	1	k	k	PROPN
ejpam-5903	596	2	−	−	NOUN
ejpam-5903	596	3	1	1	X
ejpam-5903	596	4	.	.	PUNCT
ejpam-5903	596	5	suppose	suppose	VERB
ejpam-5903	596	6	|s	|s	PROPN
ejpam-5903	596	7	∩	∩	ADJ
ejpam-5903	596	8	qi|	qi|	X
ejpam-5903	596	9	=	=	NOUN
ejpam-5903	596	10	1	1	NUM
ejpam-5903	596	11	for	for	ADP
ejpam-5903	596	12	each	each	DET
ejpam-5903	596	13	i	i	PRON
ejpam-5903	596	14	∈	∈	NOUN
ejpam-5903	596	15	r	r	NOUN
ejpam-5903	596	16	=	=	PUNCT
ejpam-5903	596	17	{	{	PUNCT
ejpam-5903	596	18	t	t	NOUN
ejpam-5903	596	19	∈	∈	PROPN
ejpam-5903	597	1	[	[	X
ejpam-5903	597	2	r	r	X
ejpam-5903	597	3	]	]	X
ejpam-5903	597	4	:	:	PUNCT
ejpam-5903	597	5	s	s	X
ejpam-5903	597	6	∩	∩	X
ejpam-5903	597	7	qt	qt	ADP
ejpam-5903	597	8	̸=	̸=	PROPN
ejpam-5903	597	9	∅	∅	NOUN
ejpam-5903	597	10	}	}	PUNCT
ejpam-5903	597	11	.	.	PUNCT
ejpam-5903	598	1	then	then	ADV
ejpam-5903	598	2	|r|	|r|	PROPN
ejpam-5903	598	3	=	=	SYM
ejpam-5903	598	4	|s|	|s|	PROPN
ejpam-5903	598	5	,	,	PUNCT
ejpam-5903	598	6	nhg	nhg	NOUN
ejpam-5903	598	7	g	g	PROPN
ejpam-5903	599	1	[	[	X
ejpam-5903	599	2	s	s	X
ejpam-5903	599	3	]	]	X
ejpam-5903	599	4	=	=	SYM
ejpam-5903	599	5	s	s	PROPN
ejpam-5903	599	6	and	and	CCONJ
ejpam-5903	599	7	ζhgk	ζhgk	NOUN
ejpam-5903	599	8	(	(	PUNCT
ejpam-5903	599	9	s	s	NOUN
ejpam-5903	599	10	)	)	PUNCT
ejpam-5903	600	1	=	=	SYM
ejpam-5903	600	2	n−	n−	NOUN
ejpam-5903	600	3	r	r	NOUN
ejpam-5903	600	4	+	+	CCONJ
ejpam-5903	601	1	k	k	PROPN
ejpam-5903	601	2	−	−	PROPN
ejpam-5903	601	3	1	1	X
ejpam-5903	601	4	.	.	PUNCT
ejpam-5903	602	1	for	for	ADP
ejpam-5903	602	2	both	both	DET
ejpam-5903	602	3	cases	case	NOUN
ejpam-5903	602	4	,	,	PUNCT
ejpam-5903	602	5	we	we	PRON
ejpam-5903	602	6	have	have	VERB
ejpam-5903	602	7	ζhgk	ζhgk	NOUN
ejpam-5903	602	8	(	(	PUNCT
ejpam-5903	602	9	g	g	NOUN
ejpam-5903	602	10	)	)	PUNCT
ejpam-5903	603	1	=	=	VERB
ejpam-5903	603	2	ζhgk	ζhgk	NOUN
ejpam-5903	603	3	(	(	PUNCT
ejpam-5903	603	4	s	s	NOUN
ejpam-5903	603	5	)	)	PUNCT
ejpam-5903	603	6	=	=	VERB
ejpam-5903	603	7	n−	n−	NOUN
ejpam-5903	603	8	r+	r+	PUNCT
ejpam-5903	603	9	k−	k−	PROPN
ejpam-5903	603	10	1	1	NUM
ejpam-5903	603	11	=	=	PUNCT
ejpam-5903	603	12	[	[	PUNCT
ejpam-5903	603	13	k+1∑	k+1∑	PROPN
ejpam-5903	603	14	j=2	j=2	PROPN
ejpam-5903	603	15	mj	mj	PROPN
ejpam-5903	603	16	+2+mk+2	+2+mk+2	PROPN
ejpam-5903	603	17	+	+	X
ejpam-5903	603	18	·	·	PUNCT
ejpam-5903	603	19	·	·	PUNCT
ejpam-5903	603	20	·	·	PUNCT
ejpam-5903	603	21	+	+	SYM
ejpam-5903	603	22	mr]−	mr]−	PRON
ejpam-5903	603	23	(	(	PUNCT
ejpam-5903	603	24	r−	r−	PROPN
ejpam-5903	603	25	k+1	k+1	PROPN
ejpam-5903	603	26	)	)	PUNCT
ejpam-5903	603	27	≥	≥	NOUN
ejpam-5903	603	28	k+1∑	k+1∑	PROPN
ejpam-5903	603	29	j=2	j=2	PROPN
ejpam-5903	604	1	mj	mj	INTJ
ejpam-5903	604	2	.	.	PUNCT
ejpam-5903	605	1	since	since	SCONJ
ejpam-5903	605	2	only	only	ADV
ejpam-5903	605	3	two	two	NUM
ejpam-5903	605	4	vertices	vertex	NOUN
ejpam-5903	605	5	,	,	PUNCT
ejpam-5903	605	6	say	say	VERB
ejpam-5903	605	7	x	x	PUNCT
ejpam-5903	605	8	and	and	CCONJ
ejpam-5903	605	9	y	y	PROPN
ejpam-5903	605	10	,	,	PUNCT
ejpam-5903	605	11	from	from	ADP
ejpam-5903	605	12	a	a	DET
ejpam-5903	605	13	partite	partite	ADJ
ejpam-5903	605	14	set	set	NOUN
ejpam-5903	605	15	are	be	AUX
ejpam-5903	605	16	needed	need	VERB
ejpam-5903	605	17	for	for	SCONJ
ejpam-5903	605	18	the	the	DET
ejpam-5903	605	19	elements	element	NOUN
ejpam-5903	605	20	of	of	ADP
ejpam-5903	605	21	the	the	DET
ejpam-5903	605	22	other	other	ADJ
ejpam-5903	605	23	partite	partite	ADJ
ejpam-5903	605	24	sets	set	NOUN
ejpam-5903	605	25	to	to	PART
ejpam-5903	605	26	be	be	AUX
ejpam-5903	605	27	in	in	ADP
ejpam-5903	605	28	the	the	DET
ejpam-5903	605	29	interval	interval	NOUN
ejpam-5903	605	30	ig(x	ig(x	PUNCT
ejpam-5903	605	31	,	,	PUNCT
ejpam-5903	605	32	y	y	PROPN
ejpam-5903	605	33	)	)	PUNCT
ejpam-5903	605	34	,	,	PUNCT
ejpam-5903	605	35	it	it	PRON
ejpam-5903	605	36	can	can	AUX
ejpam-5903	605	37	be	be	AUX
ejpam-5903	605	38	shown	show	VERB
ejpam-5903	605	39	that	that	SCONJ
ejpam-5903	605	40	s	s	VERB
ejpam-5903	605	41	always	always	ADV
ejpam-5903	605	42	yields	yield	VERB
ejpam-5903	605	43	a	a	DET
ejpam-5903	605	44	k	k	ADJ
ejpam-5903	605	45	-	-	ADJ
ejpam-5903	605	46	geodetic	geodetic	ADJ
ejpam-5903	605	47	hop	hop	NOUN
ejpam-5903	605	48	domination	domination	NOUN
ejpam-5903	605	49	defect	defect	VERB
ejpam-5903	605	50	greater	great	ADJ
ejpam-5903	605	51	than	than	ADP
ejpam-5903	605	52	or	or	CCONJ
ejpam-5903	605	53	equal	equal	ADJ
ejpam-5903	605	54	to	to	ADP
ejpam-5903	605	55	∑k+1	∑k+1	PROPN
ejpam-5903	605	56	j=2	j=2	PROPN
ejpam-5903	605	57	mj	mj	PROPN
ejpam-5903	605	58	.	.	PUNCT
ejpam-5903	606	1	therefore	therefore	ADV
ejpam-5903	606	2	,	,	PUNCT
ejpam-5903	606	3	ζhgk	ζhgk	NOUN
ejpam-5903	606	4	(	(	PUNCT
ejpam-5903	606	5	g	g	NOUN
ejpam-5903	606	6	)	)	PUNCT
ejpam-5903	606	7	=	=	VERB
ejpam-5903	606	8	ζhgk	ζhgk	NOUN
ejpam-5903	606	9	(	(	PUNCT
ejpam-5903	606	10	s	s	X
ejpam-5903	606	11	)	)	PUNCT
ejpam-5903	606	12	=	=	PUNCT
ejpam-5903	606	13	∑k+1	∑k+1	PROPN
ejpam-5903	606	14	j=2	j=2	PROPN
ejpam-5903	606	15	mj	mj	PROPN
ejpam-5903	606	16	.	.	PUNCT
ejpam-5903	607	1	case	case	NOUN
ejpam-5903	607	2	4	4	NUM
ejpam-5903	607	3	:	:	PUNCT
ejpam-5903	607	4	m1	m1	NOUN
ejpam-5903	607	5	≥	≥	NUM
ejpam-5903	607	6	3	3	NUM
ejpam-5903	607	7	and	and	CCONJ
ejpam-5903	607	8	1	1	NUM
ejpam-5903	607	9	≤	≤	NUM
ejpam-5903	607	10	k	k	NOUN
ejpam-5903	608	1	≤	≤	NUM
ejpam-5903	608	2	r	r	NOUN
ejpam-5903	608	3	−	−	NOUN
ejpam-5903	608	4	2	2	NUM
ejpam-5903	608	5	.	.	PUNCT
ejpam-5903	608	6	j.	j.	PROPN
ejpam-5903	608	7	anoche	anoche	PROPN
ejpam-5903	608	8	,	,	PUNCT
ejpam-5903	608	9	s.	s.	PROPN
ejpam-5903	608	10	canoy	canoy	PROPN
ejpam-5903	608	11	,	,	PUNCT
ejpam-5903	608	12	jr	jr	PROPN
ejpam-5903	608	13	.	.	PROPN
ejpam-5903	608	14	/	/	SYM
ejpam-5903	608	15	eur	eur	PROPN
ejpam-5903	608	16	.	.	PUNCT
ejpam-5903	609	1	j.	j.	PROPN
ejpam-5903	609	2	pure	pure	PROPN
ejpam-5903	609	3	appl	appl	PROPN
ejpam-5903	609	4	.	.	PROPN
ejpam-5903	609	5	math	math	PROPN
ejpam-5903	609	6	,	,	PUNCT
ejpam-5903	609	7	18	18	NUM
ejpam-5903	609	8	(	(	PUNCT
ejpam-5903	609	9	2	2	NUM
ejpam-5903	609	10	)	)	PUNCT
ejpam-5903	609	11	(	(	PUNCT
ejpam-5903	609	12	2025	2025	NUM
ejpam-5903	609	13	)	)	PUNCT
ejpam-5903	609	14	,	,	PUNCT
ejpam-5903	609	15	5903	5903	NUM
ejpam-5903	609	16	16	16	NUM
ejpam-5903	609	17	of	of	ADP
ejpam-5903	609	18	17	17	NUM
ejpam-5903	609	19	by	by	ADP
ejpam-5903	609	20	theorem	theorem	NOUN
ejpam-5903	609	21	11	11	NUM
ejpam-5903	609	22	,	,	PUNCT
ejpam-5903	609	23	γhg(g	γhg(g	PROPN
ejpam-5903	609	24	)	)	PUNCT
ejpam-5903	610	1	=	=	SYM
ejpam-5903	610	2	r	r	NOUN
ejpam-5903	610	3	+	+	NOUN
ejpam-5903	610	4	2	2	X
ejpam-5903	610	5	.	.	X
ejpam-5903	610	6	consider	consider	VERB
ejpam-5903	610	7	the	the	DET
ejpam-5903	610	8	set	set	NOUN
ejpam-5903	610	9	d′	d′	X
ejpam-5903	610	10	=	=	PUNCT
ejpam-5903	610	11	{	{	PUNCT
ejpam-5903	610	12	q11	q11	NOUN
ejpam-5903	610	13	,	,	PUNCT
ejpam-5903	610	14	q21	q21	NOUN
ejpam-5903	610	15	,	,	PUNCT
ejpam-5903	610	16	q1k+1	q1k+1	NOUN
ejpam-5903	610	17	,	,	PUNCT
ejpam-5903	610	18	q	q	PROPN
ejpam-5903	610	19	1	1	NUM
ejpam-5903	610	20	k+2	k+2	NUM
ejpam-5903	610	21	,	,	PUNCT
ejpam-5903	610	22	·	·	PUNCT
ejpam-5903	610	23	·	·	PUNCT
ejpam-5903	610	24	·	·	PUNCT
ejpam-5903	610	25	,	,	PUNCT
ejpam-5903	610	26	q1r	q1r	ADV
ejpam-5903	610	27	}	}	PUNCT
ejpam-5903	610	28	where	where	SCONJ
ejpam-5903	610	29	qtj	qtj	PROPN
ejpam-5903	610	30	∈	∈	PROPN
ejpam-5903	610	31	qj	qj	PROPN
ejpam-5903	610	32	for	for	ADP
ejpam-5903	610	33	each	each	DET
ejpam-5903	610	34	j	j	PROPN
ejpam-5903	610	35	∈	∈	PROPN
ejpam-5903	610	36	{	{	PUNCT
ejpam-5903	610	37	1	1	NUM
ejpam-5903	610	38	,	,	PUNCT
ejpam-5903	610	39	k	k	PROPN
ejpam-5903	611	1	+	+	PROPN
ejpam-5903	611	2	1	1	NUM
ejpam-5903	611	3	,	,	PUNCT
ejpam-5903	611	4	k	k	PROPN
ejpam-5903	611	5	+	+	PROPN
ejpam-5903	611	6	2	2	NUM
ejpam-5903	611	7	,	,	PUNCT
ejpam-5903	611	8	·	·	PUNCT
ejpam-5903	611	9	·	·	PUNCT
ejpam-5903	611	10	·	·	PUNCT
ejpam-5903	611	11	,	,	PUNCT
ejpam-5903	611	12	r	r	NOUN
ejpam-5903	611	13	}	}	PUNCT
ejpam-5903	611	14	and	and	CCONJ
ejpam-5903	611	15	t	t	PROPN
ejpam-5903	611	16	∈	∈	PROPN
ejpam-5903	611	17	{	{	PUNCT
ejpam-5903	611	18	1	1	NUM
ejpam-5903	611	19	,	,	PUNCT
ejpam-5903	611	20	2	2	NUM
ejpam-5903	611	21	}	}	PUNCT
ejpam-5903	611	22	.	.	PUNCT
ejpam-5903	612	1	then	then	ADV
ejpam-5903	612	2	nhg	nhg	VERB
ejpam-5903	612	3	g	g	PROPN
ejpam-5903	613	1	[	[	X
ejpam-5903	613	2	d′	d′	X
ejpam-5903	613	3	]	]	X
ejpam-5903	613	4	=	=	SYM
ejpam-5903	613	5	∪r	∪r	PUNCT
ejpam-5903	613	6	j	j	X
ejpam-5903	613	7	=	=	NOUN
ejpam-5903	613	8	k+1qj	k+1qj	NOUN
ejpam-5903	613	9	∪	∪	VERB
ejpam-5903	613	10	{	{	PUNCT
ejpam-5903	613	11	q11	q11	NOUN
ejpam-5903	613	12	,	,	PUNCT
ejpam-5903	613	13	q21	q21	PROPN
ejpam-5903	613	14	}	}	PUNCT
ejpam-5903	613	15	.	.	PUNCT
ejpam-5903	614	1	it	it	PRON
ejpam-5903	614	2	follows	follow	VERB
ejpam-5903	614	3	that	that	DET
ejpam-5903	614	4	ζhgk	ζhgk	NOUN
ejpam-5903	614	5	(	(	PUNCT
ejpam-5903	614	6	g	g	NOUN
ejpam-5903	614	7	)	)	PUNCT
ejpam-5903	614	8	≤	≤	NOUN
ejpam-5903	614	9	ζhgk	ζhgk	NOUN
ejpam-5903	614	10	(	(	PUNCT
ejpam-5903	614	11	d′	d′	X
ejpam-5903	614	12	)	)	PUNCT
ejpam-5903	615	1	=	=	SYM
ejpam-5903	615	2	|v	|v	PROPN
ejpam-5903	615	3	(	(	PUNCT
ejpam-5903	615	4	g)|	g)|	NOUN
ejpam-5903	615	5	−	−	PROPN
ejpam-5903	615	6	|nhg	|nhg	PROPN
ejpam-5903	615	7	g	g	X
ejpam-5903	616	1	[	[	X
ejpam-5903	616	2	d′]|	d′]|	NOUN
ejpam-5903	616	3	=	=	PUNCT
ejpam-5903	616	4	r∑	r∑	NOUN
ejpam-5903	616	5	j=1	j=1	PROPN
ejpam-5903	616	6	mj	mj	PROPN
ejpam-5903	617	1	−	−	PROPN
ejpam-5903	618	1	[	[	PUNCT
ejpam-5903	618	2	r∑	r∑	ADP
ejpam-5903	618	3	j	j	X
ejpam-5903	618	4	=	=	NOUN
ejpam-5903	618	5	k+1	k+1	X
ejpam-5903	618	6	mj	mj	NOUN
ejpam-5903	619	1	+	+	NOUN
ejpam-5903	619	2	2	2	X
ejpam-5903	619	3	]	]	PUNCT
ejpam-5903	619	4	=	=	PUNCT
ejpam-5903	619	5	k∑	k∑	PROPN
ejpam-5903	620	1	j=1	j=1	PROPN
ejpam-5903	620	2	mj	mj	PROPN
ejpam-5903	621	1	−	−	PROPN
ejpam-5903	621	2	2	2	X
ejpam-5903	621	3	.	.	PUNCT
ejpam-5903	621	4	by	by	ADP
ejpam-5903	621	5	following	follow	VERB
ejpam-5903	621	6	the	the	DET
ejpam-5903	621	7	arguments	argument	NOUN
ejpam-5903	621	8	of	of	ADP
ejpam-5903	621	9	the	the	DET
ejpam-5903	621	10	preceding	precede	VERB
ejpam-5903	621	11	case	case	NOUN
ejpam-5903	621	12	,	,	PUNCT
ejpam-5903	621	13	it	it	PRON
ejpam-5903	621	14	can	can	AUX
ejpam-5903	621	15	be	be	AUX
ejpam-5903	621	16	shown	show	VERB
ejpam-5903	621	17	that	that	SCONJ
ejpam-5903	621	18	if	if	SCONJ
ejpam-5903	621	19	s′	s′	ADJ
ejpam-5903	621	20	is	be	AUX
ejpam-5903	621	21	a	a	DET
ejpam-5903	621	22	ζhgk	ζhgk	NOUN
ejpam-5903	621	23	-set	-set	ADJ
ejpam-5903	621	24	of	of	ADP
ejpam-5903	621	25	g	g	PROPN
ejpam-5903	621	26	,	,	PUNCT
ejpam-5903	621	27	then	then	ADV
ejpam-5903	621	28	ζhgk	ζhgk	NOUN
ejpam-5903	621	29	(	(	PUNCT
ejpam-5903	621	30	g	g	NOUN
ejpam-5903	621	31	)	)	PUNCT
ejpam-5903	621	32	=	=	VERB
ejpam-5903	621	33	ζhgk	ζhgk	NOUN
ejpam-5903	621	34	(	(	PUNCT
ejpam-5903	621	35	s′	s′	X
ejpam-5903	621	36	)	)	PUNCT
ejpam-5903	621	37	≥	≥	PROPN
ejpam-5903	622	1	∑k	∑k	PROPN
ejpam-5903	622	2	j=1mj	j=1mj	PROPN
ejpam-5903	622	3	−	−	NOUN
ejpam-5903	623	1	2	2	X
ejpam-5903	623	2	.	.	PUNCT
ejpam-5903	624	1	therefore	therefore	ADV
ejpam-5903	624	2	,	,	PUNCT
ejpam-5903	624	3	ζhgk	ζhgk	NOUN
ejpam-5903	624	4	(	(	PUNCT
ejpam-5903	624	5	g	g	NOUN
ejpam-5903	624	6	)	)	PUNCT
ejpam-5903	624	7	=	=	PUNCT
ejpam-5903	625	1	∑k	∑k	PROPN
ejpam-5903	625	2	j=1mj	j=1mj	X
ejpam-5903	625	3	−	−	NOUN
ejpam-5903	626	1	2	2	NUM
ejpam-5903	626	2	.	.	SYM
ejpam-5903	626	3	4	4	NUM
ejpam-5903	626	4	.	.	X
ejpam-5903	626	5	conclusion	conclusion	NOUN
ejpam-5903	626	6	in	in	ADP
ejpam-5903	626	7	this	this	DET
ejpam-5903	626	8	paper	paper	NOUN
ejpam-5903	626	9	,	,	PUNCT
ejpam-5903	626	10	we	we	PRON
ejpam-5903	626	11	introduced	introduce	VERB
ejpam-5903	626	12	a	a	DET
ejpam-5903	626	13	new	new	ADJ
ejpam-5903	626	14	graph	graph	NOUN
ejpam-5903	626	15	invariant	invariant	NOUN
ejpam-5903	626	16	called	call	VERB
ejpam-5903	626	17	the	the	DET
ejpam-5903	626	18	k	k	ADJ
ejpam-5903	626	19	-	-	ADJ
ejpam-5903	626	20	geodetic	geodetic	ADJ
ejpam-5903	626	21	hop	hop	NOUN
ejpam-5903	626	22	domination	domination	NOUN
ejpam-5903	626	23	defect	defect	NOUN
ejpam-5903	626	24	.	.	PUNCT
ejpam-5903	627	1	some	some	DET
ejpam-5903	627	2	bounds	bound	NOUN
ejpam-5903	627	3	of	of	ADP
ejpam-5903	627	4	the	the	DET
ejpam-5903	627	5	parameter	parameter	NOUN
ejpam-5903	627	6	were	be	AUX
ejpam-5903	627	7	obtained	obtain	VERB
ejpam-5903	627	8	.	.	PUNCT
ejpam-5903	628	1	also	also	ADV
ejpam-5903	628	2	,	,	PUNCT
ejpam-5903	628	3	we	we	PRON
ejpam-5903	628	4	computed	compute	VERB
ejpam-5903	628	5	the	the	DET
ejpam-5903	628	6	k	k	ADJ
ejpam-5903	628	7	-	-	ADJ
ejpam-5903	628	8	geodetic	geodetic	ADJ
ejpam-5903	628	9	hop	hop	NOUN
ejpam-5903	628	10	domination	domination	NOUN
ejpam-5903	628	11	defects	defect	NOUN
ejpam-5903	628	12	of	of	ADP
ejpam-5903	628	13	several	several	ADJ
ejpam-5903	628	14	well	well	ADV
ejpam-5903	628	15	-	-	PUNCT
ejpam-5903	628	16	known	know	VERB
ejpam-5903	628	17	graphs	graph	NOUN
ejpam-5903	628	18	.	.	PUNCT
ejpam-5903	629	1	it	it	PRON
ejpam-5903	629	2	is	be	AUX
ejpam-5903	629	3	recommended	recommend	VERB
ejpam-5903	629	4	that	that	SCONJ
ejpam-5903	629	5	further	further	ADJ
ejpam-5903	629	6	investigation	investigation	NOUN
ejpam-5903	629	7	of	of	ADP
ejpam-5903	629	8	this	this	DET
ejpam-5903	629	9	newly	newly	ADV
ejpam-5903	629	10	defined	define	VERB
ejpam-5903	629	11	parameter	parameter	NOUN
ejpam-5903	629	12	be	be	AUX
ejpam-5903	629	13	done	do	VERB
ejpam-5903	629	14	especially	especially	ADV
ejpam-5903	629	15	on	on	ADP
ejpam-5903	629	16	graphs	graph	NOUN
ejpam-5903	629	17	trees	tree	NOUN
ejpam-5903	629	18	and	and	CCONJ
ejpam-5903	629	19	graphs	graph	NOUN
ejpam-5903	629	20	resulting	result	VERB
ejpam-5903	629	21	from	from	ADP
ejpam-5903	629	22	some	some	DET
ejpam-5903	629	23	graph	graph	NOUN
ejpam-5903	629	24	operations	operation	NOUN
ejpam-5903	629	25	.	.	PUNCT
ejpam-5903	630	1	moreover	moreover	ADV
ejpam-5903	630	2	,	,	PUNCT
ejpam-5903	630	3	complexity	complexity	NOUN
ejpam-5903	630	4	of	of	ADP
ejpam-5903	630	5	the	the	DET
ejpam-5903	630	6	k	k	ADJ
ejpam-5903	630	7	-	-	ADJ
ejpam-5903	630	8	geodetic	geodetic	ADJ
ejpam-5903	630	9	hop	hop	NOUN
ejpam-5903	630	10	domination	domination	NOUN
ejpam-5903	630	11	defect	defect	NOUN
ejpam-5903	630	12	may	may	AUX
ejpam-5903	630	13	be	be	AUX
ejpam-5903	630	14	a	a	DET
ejpam-5903	630	15	worthwhile	worthwhile	ADJ
ejpam-5903	630	16	aspect	aspect	NOUN
ejpam-5903	630	17	to	to	PART
ejpam-5903	630	18	study	study	VERB
ejpam-5903	630	19	.	.	PUNCT
ejpam-5903	631	1	acknowledgements	acknowledgement	NOUN
ejpam-5903	631	2	the	the	DET
ejpam-5903	631	3	authors	author	NOUN
ejpam-5903	631	4	would	would	AUX
ejpam-5903	631	5	like	like	VERB
ejpam-5903	631	6	to	to	PART
ejpam-5903	631	7	thank	thank	VERB
ejpam-5903	631	8	the	the	DET
ejpam-5903	631	9	department	department	NOUN
ejpam-5903	631	10	of	of	ADP
ejpam-5903	631	11	science	science	NOUN
ejpam-5903	631	12	and	and	CCONJ
ejpam-5903	631	13	technology	technology	NOUN
ejpam-5903	631	14	accelerated	accelerate	VERB
ejpam-5903	631	15	science	science	NOUN
ejpam-5903	631	16	and	and	CCONJ
ejpam-5903	631	17	technology	technology	NOUN
ejpam-5903	631	18	human	human	ADJ
ejpam-5903	631	19	resource	resource	NOUN
ejpam-5903	631	20	development	development	NOUN
ejpam-5903	631	21	program	program	NOUN
ejpam-5903	631	22	(	(	PUNCT
ejpam-5903	631	23	dost	dost	NOUN
ejpam-5903	631	24	-	-	PUNCT
ejpam-5903	631	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5903	631	26	,	,	PUNCT
ejpam-5903	631	27	and	and	CCONJ
ejpam-5903	631	28	msu	msu	PROPN
ejpam-5903	631	29	-	-	PUNCT
ejpam-5903	631	30	iligan	iligan	PROPN
ejpam-5903	631	31	institute	institute	PROPN
ejpam-5903	631	32	of	of	ADP
ejpam-5903	631	33	technology	technology	PROPN
ejpam-5903	631	34	,	,	PUNCT
ejpam-5903	631	35	philippines	philippine	NOUN
ejpam-5903	631	36	for	for	ADP
ejpam-5903	631	37	funding	fund	VERB
ejpam-5903	631	38	this	this	DET
ejpam-5903	631	39	research	research	NOUN
ejpam-5903	631	40	.	.	PUNCT
ejpam-5903	632	1	references	reference	NOUN
ejpam-5903	632	2	[	[	X
ejpam-5903	632	3	1	1	NUM
ejpam-5903	632	4	]	]	PUNCT
ejpam-5903	632	5	a.	a.	NOUN
ejpam-5903	632	6	das	das	PROPN
ejpam-5903	632	7	and	and	CCONJ
ejpam-5903	632	8	w.	w.	PROPN
ejpam-5903	632	9	j.	j.	PROPN
ejpam-5903	632	10	desormeaux	desormeaux	PROPN
ejpam-5903	632	11	.	.	PUNCT
ejpam-5903	633	1	domination	domination	NOUN
ejpam-5903	633	2	defect	defect	NOUN
ejpam-5903	633	3	in	in	ADP
ejpam-5903	633	4	graphs	graph	NOUN
ejpam-5903	633	5	:	:	PUNCT
ejpam-5903	633	6	guarding	guard	VERB
ejpam-5903	633	7	with	with	ADP
ejpam-5903	633	8	fewer	few	ADJ
ejpam-5903	633	9	guards	guard	NOUN
ejpam-5903	633	10	.	.	PUNCT
ejpam-5903	634	1	indian	indian	PROPN
ejpam-5903	634	2	j.	j.	PROPN
ejpam-5903	634	3	pure	pure	PROPN
ejpam-5903	634	4	appl	appl	PROPN
ejpam-5903	634	5	.	.	PUNCT
ejpam-5903	634	6	math	math	PROPN
ejpam-5903	634	7	.	.	PUNCT
ejpam-5903	634	8	,	,	PUNCT
ejpam-5903	635	1	49(2):349–364	49(2):349–364	NOUN
ejpam-5903	635	2	,	,	PUNCT
ejpam-5903	635	3	2018	2018	NUM
ejpam-5903	635	4	.	.	PUNCT
ejpam-5903	636	1	[	[	X
ejpam-5903	636	2	2	2	NUM
ejpam-5903	636	3	]	]	PUNCT
ejpam-5903	636	4	s.	s.	PROPN
ejpam-5903	636	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5903	636	6	,	,	PUNCT
ejpam-5903	636	7	b.	b.	PROPN
ejpam-5903	636	8	krishnakumari	krishnakumari	PROPN
ejpam-5903	636	9	,	,	PUNCT
ejpam-5903	636	10	b.	b.	PROPN
ejpam-5903	636	11	natarjan	natarjan	PROPN
ejpam-5903	636	12	,	,	PUNCT
ejpam-5903	636	13	and	and	CCONJ
ejpam-5903	636	14	y.	y.	PROPN
ejpam-5903	636	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-5903	636	16	.	.	PUNCT
ejpam-5903	637	1	bounds	bound	NOUN
ejpam-5903	637	2	on	on	ADP
ejpam-5903	637	3	the	the	DET
ejpam-5903	637	4	hop	hop	NOUN
ejpam-5903	637	5	domination	domination	NOUN
ejpam-5903	637	6	number	number	NOUN
ejpam-5903	637	7	of	of	ADP
ejpam-5903	637	8	a	a	DET
ejpam-5903	637	9	tree	tree	NOUN
ejpam-5903	637	10	.	.	PUNCT
ejpam-5903	638	1	proceedings	proceeding	NOUN
ejpam-5903	638	2	-	-	PUNCT
ejpam-5903	638	3	mathematical	mathematical	ADJ
ejpam-5903	638	4	sciences	science	NOUN
ejpam-5903	638	5	,	,	PUNCT
ejpam-5903	638	6	125(4):449	125(4):449	NUM
ejpam-5903	638	7	–	–	PUNCT
ejpam-5903	638	8	455	455	NUM
ejpam-5903	638	9	,	,	PUNCT
ejpam-5903	638	10	2015	2015	NUM
ejpam-5903	638	11	.	.	PUNCT
ejpam-5903	639	1	[	[	X
ejpam-5903	639	2	3	3	NUM
ejpam-5903	639	3	]	]	X
ejpam-5903	639	4	m.	m.	NOUN
ejpam-5903	639	5	henning	henning	PROPN
ejpam-5903	639	6	and	and	CCONJ
ejpam-5903	639	7	n.	n.	PROPN
ejpam-5903	639	8	rad	rad	PROPN
ejpam-5903	639	9	.	.	PROPN
ejpam-5903	640	1	on	on	ADP
ejpam-5903	640	2	2	2	NUM
ejpam-5903	640	3	-	-	PUNCT
ejpam-5903	640	4	step	step	NOUN
ejpam-5903	640	5	and	and	CCONJ
ejpam-5903	640	6	hop	hop	NOUN
ejpam-5903	640	7	dominating	dominating	NOUN
ejpam-5903	640	8	sets	set	NOUN
ejpam-5903	640	9	in	in	ADP
ejpam-5903	640	10	graphs	graph	NOUN
ejpam-5903	640	11	.	.	PUNCT
ejpam-5903	641	1	graphs	graph	NOUN
ejpam-5903	641	2	and	and	CCONJ
ejpam-5903	641	3	combinatorics	combinatoric	NOUN
ejpam-5903	641	4	.	.	PUNCT
ejpam-5903	641	5	,	,	PUNCT
ejpam-5903	641	6	33(4):913–927	33(4):913–927	PROPN
ejpam-5903	641	7	,	,	PUNCT
ejpam-5903	641	8	2017	2017	NUM
ejpam-5903	641	9	.	.	PUNCT
ejpam-5903	642	1	[	[	X
ejpam-5903	642	2	4	4	X
ejpam-5903	642	3	]	]	X
ejpam-5903	642	4	s.	s.	PROPN
ejpam-5903	642	5	canoy	canoy	PROPN
ejpam-5903	642	6	jr	jr	PROPN
ejpam-5903	642	7	.	.	PROPN
ejpam-5903	642	8	,	,	PUNCT
ejpam-5903	642	9	r.	r.	PROPN
ejpam-5903	642	10	mollejon	mollejon	NOUN
ejpam-5903	642	11	,	,	PUNCT
ejpam-5903	642	12	and	and	CCONJ
ejpam-5903	642	13	j.	j.	PROPN
ejpam-5903	642	14	g.	g.	PROPN
ejpam-5903	642	15	canoy	canoy	PROPN
ejpam-5903	642	16	.	.	PUNCT
ejpam-5903	643	1	hop	hop	PROPN
ejpam-5903	643	2	dominating	dominating	NOUN
ejpam-5903	643	3	sets	set	NOUN
ejpam-5903	643	4	in	in	ADP
ejpam-5903	643	5	graphs	graph	NOUN
ejpam-5903	643	6	under	under	ADP
ejpam-5903	643	7	binary	binary	ADJ
ejpam-5903	643	8	operations	operation	NOUN
ejpam-5903	643	9	.	.	PUNCT
ejpam-5903	644	1	eur	eur	PROPN
ejpam-5903	644	2	.	.	PUNCT
ejpam-5903	645	1	j.	j.	PROPN
ejpam-5903	645	2	pure	pure	PROPN
ejpam-5903	645	3	appl	appl	PROPN
ejpam-5903	645	4	.	.	PUNCT
ejpam-5903	645	5	math	math	PROPN
ejpam-5903	645	6	.	.	PUNCT
ejpam-5903	645	7	,	,	PUNCT
ejpam-5903	646	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-5903	646	2	,	,	PUNCT
ejpam-5903	646	3	2019	2019	NUM
ejpam-5903	646	4	.	.	PUNCT
ejpam-5903	647	1	j.	j.	PROPN
ejpam-5903	647	2	anoche	anoche	PROPN
ejpam-5903	647	3	,	,	PUNCT
ejpam-5903	647	4	s.	s.	PROPN
ejpam-5903	647	5	canoy	canoy	PROPN
ejpam-5903	647	6	,	,	PUNCT
ejpam-5903	647	7	jr	jr	PROPN
ejpam-5903	647	8	.	.	PROPN
ejpam-5903	647	9	/	/	SYM
ejpam-5903	647	10	eur	eur	PROPN
ejpam-5903	647	11	.	.	PUNCT
ejpam-5903	648	1	j.	j.	PROPN
ejpam-5903	648	2	pure	pure	PROPN
ejpam-5903	648	3	appl	appl	PROPN
ejpam-5903	648	4	.	.	PROPN
ejpam-5903	648	5	math	math	PROPN
ejpam-5903	648	6	,	,	PUNCT
ejpam-5903	648	7	18	18	NUM
ejpam-5903	648	8	(	(	PUNCT
ejpam-5903	648	9	2	2	NUM
ejpam-5903	648	10	)	)	PUNCT
ejpam-5903	648	11	(	(	PUNCT
ejpam-5903	648	12	2025	2025	NUM
ejpam-5903	648	13	)	)	PUNCT
ejpam-5903	648	14	,	,	PUNCT
ejpam-5903	648	15	5903	5903	NUM
ejpam-5903	648	16	17	17	NUM
ejpam-5903	648	17	of	of	ADP
ejpam-5903	648	18	17	17	NUM
ejpam-5903	648	19	[	[	SYM
ejpam-5903	648	20	5	5	NUM
ejpam-5903	648	21	]	]	PUNCT
ejpam-5903	648	22	s.	s.	PROPN
ejpam-5903	648	23	canoy	canoy	PROPN
ejpam-5903	648	24	jr	jr	PROPN
ejpam-5903	648	25	.	.	PROPN
ejpam-5903	648	26	and	and	CCONJ
ejpam-5903	648	27	g.	g.	PROPN
ejpam-5903	648	28	salasalan	salasalan	NOUN
ejpam-5903	648	29	.	.	PUNCT
ejpam-5903	649	1	locating	locate	VERB
ejpam-5903	649	2	-	-	PUNCT
ejpam-5903	649	3	hop	hop	NOUN
ejpam-5903	649	4	domination	domination	NOUN
ejpam-5903	649	5	in	in	ADP
ejpam-5903	649	6	graphs	graph	NOUN
ejpam-5903	649	7	.	.	PUNCT
ejpam-5903	650	1	kyungpook	kyungpook	PROPN
ejpam-5903	650	2	mathematical	mathematical	PROPN
ejpam-5903	650	3	journal	journal	PROPN
ejpam-5903	650	4	,	,	PUNCT
ejpam-5903	650	5	62:193–204	62:193–204	PROPN
ejpam-5903	650	6	,	,	PUNCT
ejpam-5903	650	7	2022	2022	NUM
ejpam-5903	650	8	.	.	PUNCT
ejpam-5903	651	1	[	[	X
ejpam-5903	651	2	6	6	NUM
ejpam-5903	651	3	]	]	PUNCT
ejpam-5903	651	4	c.	c.	PROPN
ejpam-5903	651	5	natarajan	natarajan	PROPN
ejpam-5903	651	6	and	and	CCONJ
ejpam-5903	651	7	s.	s.	PROPN
ejpam-5903	651	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5903	651	9	.	.	PUNCT
ejpam-5903	652	1	hop	hop	PROPN
ejpam-5903	652	2	domination	domination	NOUN
ejpam-5903	652	3	in	in	ADP
ejpam-5903	652	4	graphs	graphs	PROPN
ejpam-5903	652	5	ii	ii	PROPN
ejpam-5903	652	6	.	.	PUNCT
ejpam-5903	652	7	versita	versita	PROPN
ejpam-5903	652	8	,	,	PUNCT
ejpam-5903	652	9	23(2):187	23(2):187	NUM
ejpam-5903	652	10	–	–	PUNCT
ejpam-5903	652	11	199	199	NUM
ejpam-5903	652	12	,	,	PUNCT
ejpam-5903	652	13	2015	2015	NUM
ejpam-5903	652	14	.	.	PUNCT
ejpam-5903	653	1	[	[	X
ejpam-5903	653	2	7	7	X
ejpam-5903	653	3	]	]	X
ejpam-5903	653	4	g.	g.	NOUN
ejpam-5903	653	5	salasalan	salasalan	NOUN
ejpam-5903	653	6	and	and	CCONJ
ejpam-5903	653	7	s.	s.	PROPN
ejpam-5903	653	8	canoy	canoy	PROPN
ejpam-5903	653	9	jr	jr	PROPN
ejpam-5903	653	10	.	.	PROPN
ejpam-5903	653	11	global	global	PROPN
ejpam-5903	653	12	hop	hop	PROPN
ejpam-5903	653	13	domination	domination	PROPN
ejpam-5903	653	14	numbers	number	NOUN
ejpam-5903	653	15	of	of	ADP
ejpam-5903	653	16	graphs	graph	NOUN
ejpam-5903	653	17	.	.	PUNCT
ejpam-5903	654	1	eur	eur	PROPN
ejpam-5903	654	2	.	.	PUNCT
ejpam-5903	655	1	j.	j.	PROPN
ejpam-5903	655	2	pure	pure	PROPN
ejpam-5903	655	3	appl	appl	PROPN
ejpam-5903	655	4	.	.	PUNCT
ejpam-5903	655	5	math	math	PROPN
ejpam-5903	655	6	.	.	PUNCT
ejpam-5903	655	7	,	,	PUNCT
ejpam-5903	655	8	14(1):112–125	14(1):112–125	NUM
ejpam-5903	655	9	,	,	PUNCT
ejpam-5903	655	10	2021	2021	NUM
ejpam-5903	655	11	.	.	PUNCT
ejpam-5903	656	1	[	[	X
ejpam-5903	656	2	8	8	X
ejpam-5903	656	3	]	]	X
ejpam-5903	656	4	j.	j.	PROPN
ejpam-5903	656	5	anoche	anoche	PROPN
ejpam-5903	656	6	and	and	CCONJ
ejpam-5903	656	7	s.	s.	PROPN
ejpam-5903	656	8	canoy	canoy	PROPN
ejpam-5903	656	9	jr	jr	PROPN
ejpam-5903	656	10	.	.	PUNCT
ejpam-5903	657	1	k	k	ADJ
ejpam-5903	657	2	-	-	PUNCT
ejpam-5903	657	3	hop	hop	NOUN
ejpam-5903	657	4	domination	domination	NOUN
ejpam-5903	657	5	defect	defect	NOUN
ejpam-5903	657	6	in	in	ADP
ejpam-5903	657	7	a	a	DET
ejpam-5903	657	8	graph	graph	NOUN
ejpam-5903	657	9	.	.	PUNCT
ejpam-5903	658	1	eur	eur	PROPN
ejpam-5903	658	2	.	.	PUNCT
ejpam-5903	659	1	j.	j.	PROPN
ejpam-5903	659	2	pure	pure	PROPN
ejpam-5903	659	3	appl	appl	PROPN
ejpam-5903	659	4	.	.	PUNCT
ejpam-5903	659	5	math	math	PROPN
ejpam-5903	659	6	.	.	PUNCT
ejpam-5903	659	7	,	,	PUNCT
ejpam-5903	659	8	18(1	18(1	NUM
ejpam-5903	659	9	)	)	PUNCT
ejpam-5903	659	10	,	,	PUNCT
ejpam-5903	659	11	2025	2025	NUM
ejpam-5903	659	12	.	.	PUNCT
ejpam-5903	660	1	[	[	X
ejpam-5903	660	2	9	9	NUM
ejpam-5903	660	3	]	]	PUNCT
ejpam-5903	660	4	f.	f.	PROPN
ejpam-5903	660	5	harary	harary	PROPN
ejpam-5903	660	6	,	,	PUNCT
ejpam-5903	660	7	e.	e.	PROPN
ejpam-5903	660	8	loukakis	loukakis	PROPN
ejpam-5903	660	9	,	,	PUNCT
ejpam-5903	660	10	and	and	CCONJ
ejpam-5903	660	11	c.	c.	PROPN
ejpam-5903	660	12	tsouros	tsouros	PROPN
ejpam-5903	660	13	.	.	PUNCT
ejpam-5903	661	1	the	the	DET
ejpam-5903	661	2	geodetic	geodetic	ADJ
ejpam-5903	661	3	number	number	NOUN
ejpam-5903	661	4	of	of	ADP
ejpam-5903	661	5	a	a	DET
ejpam-5903	661	6	graph	graph	NOUN
ejpam-5903	661	7	.	.	PUNCT
ejpam-5903	662	1	mathl	mathl	NOUN
ejpam-5903	662	2	.	.	PUNCT
ejpam-5903	663	1	comput	comput	NOUN
ejpam-5903	663	2	.	.	PUNCT
ejpam-5903	664	1	modelling	modelling	NOUN
ejpam-5903	664	2	,	,	PUNCT
ejpam-5903	664	3	17(11):89–95	17(11):89–95	NUM
ejpam-5903	664	4	,	,	PUNCT
ejpam-5903	664	5	1993	1993	NUM
ejpam-5903	664	6	.	.	PUNCT
ejpam-5903	665	1	[	[	X
ejpam-5903	665	2	10	10	NUM
ejpam-5903	665	3	]	]	PUNCT
ejpam-5903	665	4	g.	g.	PROPN
ejpam-5903	665	5	cagaanan	cagaanan	PROPN
ejpam-5903	665	6	and	and	CCONJ
ejpam-5903	665	7	s.	s.	PROPN
ejpam-5903	665	8	canoy	canoy	PROPN
ejpam-5903	665	9	jr	jr	PROPN
ejpam-5903	665	10	.	.	PROPN
ejpam-5903	665	11	on	on	ADP
ejpam-5903	665	12	the	the	DET
ejpam-5903	665	13	geodesic	geodesic	ADJ
ejpam-5903	665	14	and	and	CCONJ
ejpam-5903	665	15	hull	hull	NOUN
ejpam-5903	665	16	numbers	number	NOUN
ejpam-5903	665	17	of	of	ADP
ejpam-5903	665	18	the	the	DET
ejpam-5903	665	19	sum	sum	NOUN
ejpam-5903	665	20	of	of	ADP
ejpam-5903	665	21	graphs	graph	NOUN
ejpam-5903	665	22	.	.	PUNCT
ejpam-5903	666	1	congresus	congresus	PROPN
ejpam-5903	666	2	numerantium	numerantium	PROPN
ejpam-5903	666	3	,	,	PUNCT
ejpam-5903	666	4	161:97–104	161:97–104	NUM
ejpam-5903	666	5	,	,	PUNCT
ejpam-5903	666	6	2003	2003	NUM
ejpam-5903	666	7	.	.	PUNCT
ejpam-5903	667	1	[	[	X
ejpam-5903	667	2	11	11	NUM
ejpam-5903	667	3	]	]	PUNCT
ejpam-5903	667	4	g.	g.	PROPN
ejpam-5903	667	5	cagaanan	cagaanan	PROPN
ejpam-5903	667	6	and	and	CCONJ
ejpam-5903	667	7	s.	s.	PROPN
ejpam-5903	667	8	canoy	canoy	PROPN
ejpam-5903	667	9	jr	jr	PROPN
ejpam-5903	667	10	.	.	PROPN
ejpam-5903	667	11	on	on	ADP
ejpam-5903	667	12	the	the	DET
ejpam-5903	667	13	geodetic	geodetic	ADJ
ejpam-5903	667	14	covers	cover	NOUN
ejpam-5903	667	15	and	and	CCONJ
ejpam-5903	667	16	geodetic	geodetic	ADJ
ejpam-5903	667	17	bases	basis	NOUN
ejpam-5903	667	18	of	of	ADP
ejpam-5903	667	19	the	the	DET
ejpam-5903	667	20	composition	composition	NOUN
ejpam-5903	668	1	g	g	PROPN
ejpam-5903	668	2	[	[	X
ejpam-5903	668	3	km	km	X
ejpam-5903	668	4	]	]	PUNCT
ejpam-5903	668	5	.	.	PUNCT
ejpam-5903	669	1	ars	ars	PROPN
ejpam-5903	669	2	combinatoria	combinatoria	PROPN
ejpam-5903	669	3	,	,	PUNCT
ejpam-5903	669	4	79:33–45	79:33–45	NUM
ejpam-5903	669	5	,	,	PUNCT
ejpam-5903	669	6	2006	2006	NUM
ejpam-5903	669	7	.	.	PUNCT
ejpam-5903	670	1	[	[	X
ejpam-5903	670	2	12	12	NUM
ejpam-5903	670	3	]	]	PUNCT
ejpam-5903	670	4	g.	g.	PROPN
ejpam-5903	670	5	cagaanan	cagaanan	PROPN
ejpam-5903	670	6	and	and	CCONJ
ejpam-5903	670	7	s.	s.	PROPN
ejpam-5903	670	8	canoy	canoy	PROPN
ejpam-5903	670	9	jr	jr	PROPN
ejpam-5903	670	10	.	.	PROPN
ejpam-5903	670	11	bounds	bound	VERB
ejpam-5903	670	12	for	for	ADP
ejpam-5903	670	13	the	the	DET
ejpam-5903	670	14	geodetic	geodetic	ADJ
ejpam-5903	670	15	number	number	NOUN
ejpam-5903	670	16	of	of	ADP
ejpam-5903	670	17	the	the	DET
ejpam-5903	670	18	cartesian	cartesian	ADJ
ejpam-5903	670	19	product	product	NOUN
ejpam-5903	670	20	of	of	ADP
ejpam-5903	670	21	graphs	graph	NOUN
ejpam-5903	670	22	.	.	PUNCT
ejpam-5903	671	1	utilitas	utilitas	PROPN
ejpam-5903	671	2	mathematica	mathematica	PROPN
ejpam-5903	671	3	,	,	PUNCT
ejpam-5903	671	4	79:9	79:9	NUM
ejpam-5903	671	5	,	,	PUNCT
ejpam-5903	671	6	2009	2009	NUM
ejpam-5903	671	7	.	.	PUNCT
ejpam-5903	672	1	[	[	X
ejpam-5903	672	2	13	13	NUM
ejpam-5903	672	3	]	]	PUNCT
ejpam-5903	672	4	g.	g.	PROPN
ejpam-5903	672	5	chartrand	chartrand	PROPN
ejpam-5903	672	6	,	,	PUNCT
ejpam-5903	672	7	f.	f.	PROPN
ejpam-5903	672	8	harary	harary	PROPN
ejpam-5903	672	9	,	,	PUNCT
ejpam-5903	672	10	and	and	CCONJ
ejpam-5903	672	11	p.	p.	PROPN
ejpam-5903	672	12	zhang	zhang	PROPN
ejpam-5903	672	13	.	.	PUNCT
ejpam-5903	673	1	the	the	DET
ejpam-5903	673	2	geodetic	geodetic	ADJ
ejpam-5903	673	3	number	number	NOUN
ejpam-5903	673	4	of	of	ADP
ejpam-5903	673	5	a	a	DET
ejpam-5903	673	6	graph	graph	NOUN
ejpam-5903	673	7	.	.	PUNCT
ejpam-5903	674	1	networks	network	NOUN
ejpam-5903	674	2	:	:	PUNCT
ejpam-5903	674	3	an	an	DET
ejpam-5903	674	4	international	international	ADJ
ejpam-5903	674	5	journal	journal	NOUN
ejpam-5903	674	6	,	,	PUNCT
ejpam-5903	674	7	39(1):1–6	39(1):1–6	NUM
ejpam-5903	674	8	,	,	PUNCT
ejpam-5903	674	9	2002	2002	NUM
ejpam-5903	674	10	.	.	PUNCT
ejpam-5903	675	1	[	[	X
ejpam-5903	675	2	14	14	NUM
ejpam-5903	675	3	]	]	X
ejpam-5903	675	4	h.	h.	NOUN
ejpam-5903	675	5	escuardo	escuardo	PROPN
ejpam-5903	675	6	,	,	PUNCT
ejpam-5903	675	7	r.	r.	PROPN
ejpam-5903	675	8	gera	gera	PROPN
ejpam-5903	675	9	,	,	PUNCT
ejpam-5903	675	10	a.	a.	NOUN
ejpam-5903	675	11	hansberg	hansberg	PROPN
ejpam-5903	675	12	,	,	PUNCT
ejpam-5903	675	13	n.	n.	PROPN
ejpam-5903	675	14	jafari	jafari	PROPN
ejpam-5903	675	15	rad	rad	PROPN
ejpam-5903	675	16	,	,	PUNCT
ejpam-5903	675	17	and	and	CCONJ
ejpam-5903	675	18	l.	l.	PROPN
ejpam-5903	675	19	volkmann	volkmann	PROPN
ejpam-5903	675	20	.	.	PUNCT
ejpam-5903	676	1	geodetic	geodetic	ADJ
ejpam-5903	676	2	domination	domination	NOUN
ejpam-5903	676	3	in	in	ADP
ejpam-5903	676	4	graphs	graph	NOUN
ejpam-5903	676	5	.	.	PUNCT
ejpam-5903	677	1	combin	combin	NOUN
ejpam-5903	677	2	.	.	PUNCT
ejpam-5903	677	3	math	math	NOUN
ejpam-5903	677	4	.	.	PUNCT
ejpam-5903	678	1	combin	combin	NOUN
ejpam-5903	678	2	.	.	PUNCT
ejpam-5903	679	1	comput	comput	NOUN
ejpam-5903	679	2	.	.	PUNCT
ejpam-5903	679	3	,	,	PUNCT
ejpam-5903	680	1	77(1):89–101	77(1):89–101	NUM
ejpam-5903	680	2	,	,	PUNCT
ejpam-5903	680	3	2022	2022	NUM
ejpam-5903	680	4	.	.	PUNCT
ejpam-5903	681	1	[	[	X
ejpam-5903	681	2	15	15	NUM
ejpam-5903	681	3	]	]	X
ejpam-5903	681	4	s.	s.	PROPN
ejpam-5903	681	5	canoy	canoy	PROPN
ejpam-5903	681	6	jr	jr	PROPN
ejpam-5903	681	7	.	.	PROPN
ejpam-5903	681	8	and	and	CCONJ
ejpam-5903	681	9	j.	j.	PROPN
ejpam-5903	681	10	anoche	anoche	PROPN
ejpam-5903	681	11	.	.	PUNCT
ejpam-5903	682	1	geodetically	geodetically	ADV
ejpam-5903	682	2	undominated	undominate	VERB
ejpam-5903	682	3	vertices	vertex	NOUN
ejpam-5903	682	4	in	in	ADP
ejpam-5903	682	5	a	a	DET
ejpam-5903	682	6	graph	graph	NOUN
ejpam-5903	682	7	.	.	PUNCT
ejpam-5903	683	1	eur	eur	PROPN
ejpam-5903	683	2	.	.	PUNCT
ejpam-5903	684	1	j.	j.	PROPN
ejpam-5903	684	2	pure	pure	PROPN
ejpam-5903	684	3	appl	appl	PROPN
ejpam-5903	684	4	.	.	PUNCT
ejpam-5903	684	5	math	math	PROPN
ejpam-5903	684	6	.	.	PUNCT
ejpam-5903	684	7	,	,	PUNCT
ejpam-5903	684	8	18(1	18(1	NUM
ejpam-5903	684	9	)	)	PUNCT
ejpam-5903	684	10	,	,	PUNCT
ejpam-5903	684	11	2025	2025	NUM
ejpam-5903	684	12	.	.	PUNCT
ejpam-5903	685	1	[	[	X
ejpam-5903	685	2	16	16	NUM
ejpam-5903	685	3	]	]	X
ejpam-5903	685	4	d.	d.	PROPN
ejpam-5903	685	5	anusha	anusha	PROPN
ejpam-5903	685	6	and	and	CCONJ
ejpam-5903	685	7	s.	s.	PROPN
ejpam-5903	685	8	joseph	joseph	PROPN
ejpam-5903	685	9	robin	robin	PROPN
ejpam-5903	685	10	.	.	PUNCT
ejpam-5903	686	1	geodetic	geodetic	ADJ
ejpam-5903	686	2	hop	hop	NOUN
ejpam-5903	686	3	domination	domination	NOUN
ejpam-5903	686	4	in	in	ADP
ejpam-5903	686	5	join	join	NOUN
ejpam-5903	686	6	and	and	CCONJ
ejpam-5903	686	7	corona	corona	NOUN
ejpam-5903	686	8	of	of	ADP
ejpam-5903	686	9	graphs	graph	NOUN
ejpam-5903	686	10	.	.	PUNCT
ejpam-5903	687	1	journal	journal	NOUN
ejpam-5903	687	2	of	of	ADP
ejpam-5903	687	3	combinatorial	combinatorial	ADJ
ejpam-5903	687	4	mathematics	mathematic	NOUN
ejpam-5903	687	5	and	and	CCONJ
ejpam-5903	687	6	combinatorial	combinatorial	ADJ
ejpam-5903	687	7	computing	computing	NOUN
ejpam-5903	687	8	,	,	PUNCT
ejpam-5903	687	9	21(3):1117–1127	21(3):1117–1127	NUM
ejpam-5903	687	10	,	,	PUNCT
ejpam-5903	687	11	2011	2011	NUM
ejpam-5903	687	12	.	.	PUNCT
ejpam-5903	688	1	[	[	X
ejpam-5903	688	2	17	17	NUM
ejpam-5903	688	3	]	]	X
ejpam-5903	688	4	d.	d.	PROPN
ejpam-5903	688	5	anusha	anusha	PROPN
ejpam-5903	688	6	and	and	CCONJ
ejpam-5903	688	7	s.	s.	PROPN
ejpam-5903	688	8	joseph	joseph	PROPN
ejpam-5903	688	9	robin	robin	PROPN
ejpam-5903	688	10	.	.	PUNCT
ejpam-5903	689	1	the	the	DET
ejpam-5903	689	2	geodetic	geodetic	ADJ
ejpam-5903	689	3	hop	hop	NOUN
ejpam-5903	689	4	domination	domination	NOUN
ejpam-5903	689	5	number	number	NOUN
ejpam-5903	689	6	of	of	ADP
ejpam-5903	689	7	complementary	complementary	ADJ
ejpam-5903	689	8	prisms	prism	NOUN
ejpam-5903	689	9	.	.	PUNCT
ejpam-5903	690	1	discrete	discrete	ADJ
ejpam-5903	690	2	mathematics	mathematic	NOUN
ejpam-5903	690	3	,	,	PUNCT
ejpam-5903	690	4	algorithms	algorithm	NOUN
ejpam-5903	690	5	and	and	CCONJ
ejpam-5903	690	6	applications	application	NOUN
ejpam-5903	690	7	,	,	PUNCT
ejpam-5903	690	8	13(6):doi.org/10.1142	13(6):doi.org/10.1142	NUM
ejpam-5903	690	9	/	/	SYM
ejpam-5903	690	10	s1793830921500774	s1793830921500774	NOUN
ejpam-5903	690	11	,	,	PUNCT
ejpam-5903	690	12	2021	2021	NUM
ejpam-5903	690	13	.	.	PUNCT
ejpam-5903	691	1	[	[	X
ejpam-5903	691	2	18	18	NUM
ejpam-5903	691	3	]	]	X
ejpam-5903	691	4	c.j	c.j	PROPN
ejpam-5903	691	5	.	.	PROPN
ejpam-5903	691	6	saromines	saromine	NOUN
ejpam-5903	691	7	and	and	CCONJ
ejpam-5903	691	8	s.	s.	PROPN
ejpam-5903	691	9	canoy	canoy	PROPN
ejpam-5903	691	10	jr	jr	PROPN
ejpam-5903	691	11	.	.	PUNCT
ejpam-5903	692	1	another	another	DET
ejpam-5903	692	2	look	look	NOUN
ejpam-5903	692	3	at	at	ADP
ejpam-5903	692	4	geodetic	geodetic	ADJ
ejpam-5903	692	5	hop	hop	NOUN
ejpam-5903	692	6	domination	domination	NOUN
ejpam-5903	692	7	in	in	ADP
ejpam-5903	692	8	a	a	DET
ejpam-5903	692	9	graph	graph	NOUN
ejpam-5903	692	10	.	.	PUNCT
ejpam-5903	693	1	eur	eur	PROPN
ejpam-5903	693	2	.	.	PUNCT
ejpam-5903	694	1	j.	j.	PROPN
ejpam-5903	694	2	pure	pure	PROPN
ejpam-5903	694	3	appl	appl	PROPN
ejpam-5903	694	4	.	.	PUNCT
ejpam-5903	694	5	math	math	PROPN
ejpam-5903	694	6	.	.	PUNCT
ejpam-5903	694	7	,	,	PUNCT
ejpam-5903	694	8	16(3):1568–1579	16(3):1568–1579	NUM
ejpam-5903	694	9	,	,	PUNCT
ejpam-5903	694	10	2023	2023	NUM
ejpam-5903	694	11	.	.	PUNCT
ejpam-5903	695	1	[	[	X
ejpam-5903	695	2	19	19	NUM
ejpam-5903	695	3	]	]	X
ejpam-5903	695	4	c.j	c.j	PROPN
ejpam-5903	695	5	.	.	PROPN
ejpam-5903	695	6	saromines	saromine	NOUN
ejpam-5903	695	7	and	and	CCONJ
ejpam-5903	695	8	s.	s.	PROPN
ejpam-5903	695	9	canoy	canoy	PROPN
ejpam-5903	695	10	jr	jr	PROPN
ejpam-5903	695	11	.	.	PROPN
ejpam-5903	695	12	geodetic	geodetic	ADJ
ejpam-5903	695	13	hop	hop	NOUN
ejpam-5903	695	14	dominating	dominating	NOUN
ejpam-5903	695	15	sets	set	NOUN
ejpam-5903	695	16	in	in	ADP
ejpam-5903	695	17	a	a	DET
ejpam-5903	695	18	graph	graph	NOUN
ejpam-5903	695	19	.	.	PUNCT
ejpam-5903	696	1	eur	eur	PROPN
ejpam-5903	696	2	.	.	PUNCT
ejpam-5903	697	1	j.	j.	PROPN
ejpam-5903	697	2	pure	pure	PROPN
ejpam-5903	697	3	appl	appl	PROPN
ejpam-5903	697	4	.	.	PUNCT
ejpam-5903	697	5	math	math	PROPN
ejpam-5903	697	6	.	.	PUNCT
ejpam-5903	697	7	,	,	PUNCT
ejpam-5903	697	8	16(1):5–17	16(1):5–17	NUM
ejpam-5903	697	9	,	,	PUNCT
ejpam-5903	697	10	2023	2023	NUM
ejpam-5903	697	11	.	.	PUNCT