id	sid	tid	token	lemma	pos
ejpam-5716	1	1	european	european	PROPN
ejpam-5716	1	2	journal	journal	PROPN
ejpam-5716	1	3	of	of	ADP
ejpam-5716	1	4	pure	pure	ADJ
ejpam-5716	1	5	and	and	CCONJ
ejpam-5716	1	6	applied	applied	ADJ
ejpam-5716	1	7	mathematics	mathematic	NOUN
ejpam-5716	1	8	2025	2025	NUM
ejpam-5716	1	9	,	,	PUNCT
ejpam-5716	1	10	vol	vol	NOUN
ejpam-5716	1	11	.	.	PROPN
ejpam-5716	1	12	18	18	NUM
ejpam-5716	1	13	,	,	PUNCT
ejpam-5716	1	14	issue	issue	NOUN
ejpam-5716	1	15	1	1	NUM
ejpam-5716	1	16	,	,	PUNCT
ejpam-5716	1	17	article	article	NOUN
ejpam-5716	1	18	number	number	NOUN
ejpam-5716	1	19	5716	5716	NUM
ejpam-5716	1	20	issn	issn	PROPN
ejpam-5716	1	21	1307	1307	NUM
ejpam-5716	1	22	-	-	SYM
ejpam-5716	1	23	5543	5543	NUM
ejpam-5716	1	24	–	–	PUNCT
ejpam-5716	1	25	ejpam.com	ejpam.com	X
ejpam-5716	1	26	published	publish	VERB
ejpam-5716	1	27	by	by	ADP
ejpam-5716	1	28	new	new	PROPN
ejpam-5716	1	29	york	york	PROPN
ejpam-5716	1	30	business	business	PROPN
ejpam-5716	1	31	global	global	PROPN
ejpam-5716	1	32	k	k	PROPN
ejpam-5716	1	33	-	-	PUNCT
ejpam-5716	1	34	hop	hop	NOUN
ejpam-5716	1	35	domination	domination	NOUN
ejpam-5716	1	36	defect	defect	NOUN
ejpam-5716	1	37	in	in	ADP
ejpam-5716	1	38	a	a	DET
ejpam-5716	1	39	graph	graph	NOUN
ejpam-5716	1	40	jesica	jesica	PROPN
ejpam-5716	1	41	m.	m.	NOUN
ejpam-5716	1	42	anoche	anoche	PROPN
ejpam-5716	1	43	1	1	NUM
ejpam-5716	1	44	,	,	PUNCT
ejpam-5716	1	45	sergio	sergio	PROPN
ejpam-5716	1	46	r.	r.	PROPN
ejpam-5716	1	47	canoy	canoy	PROPN
ejpam-5716	1	48	,	,	PUNCT
ejpam-5716	1	49	jr.1,2	jr.1,2	ADJ
ejpam-5716	1	50	1	1	NUM
ejpam-5716	1	51	department	department	NOUN
ejpam-5716	1	52	of	of	ADP
ejpam-5716	1	53	mathematics	mathematic	NOUN
ejpam-5716	1	54	and	and	CCONJ
ejpam-5716	1	55	statistics	statistic	NOUN
ejpam-5716	1	56	,	,	PUNCT
ejpam-5716	1	57	college	college	NOUN
ejpam-5716	1	58	of	of	ADP
ejpam-5716	1	59	science	science	NOUN
ejpam-5716	1	60	and	and	CCONJ
ejpam-5716	1	61	mathematics	mathematic	NOUN
ejpam-5716	1	62	,	,	PUNCT
ejpam-5716	1	63	msu	msu	PROPN
ejpam-5716	1	64	-	-	PUNCT
ejpam-5716	1	65	iligan	iligan	PROPN
ejpam-5716	1	66	institute	institute	PROPN
ejpam-5716	1	67	of	of	ADP
ejpam-5716	1	68	technology	technology	PROPN
ejpam-5716	1	69	,	,	PUNCT
ejpam-5716	1	70	9200	9200	NUM
ejpam-5716	1	71	iligan	iligan	ADJ
ejpam-5716	1	72	city	city	NOUN
ejpam-5716	1	73	,	,	PUNCT
ejpam-5716	1	74	philippines	philippine	NOUN
ejpam-5716	1	75	2	2	NUM
ejpam-5716	1	76	center	center	NOUN
ejpam-5716	1	77	of	of	ADP
ejpam-5716	1	78	mathematical	mathematical	ADJ
ejpam-5716	1	79	and	and	CCONJ
ejpam-5716	1	80	theoretical	theoretical	ADJ
ejpam-5716	1	81	physical	physical	ADJ
ejpam-5716	1	82	sciences	science	NOUN
ejpam-5716	1	83	-	-	PUNCT
ejpam-5716	1	84	prism	prism	NOUN
ejpam-5716	1	85	,	,	PUNCT
ejpam-5716	1	86	msu	msu	PROPN
ejpam-5716	1	87	-	-	PUNCT
ejpam-5716	1	88	iligan	iligan	PROPN
ejpam-5716	1	89	institute	institute	PROPN
ejpam-5716	1	90	of	of	ADP
ejpam-5716	1	91	technology	technology	PROPN
ejpam-5716	1	92	,	,	PUNCT
ejpam-5716	1	93	9200	9200	NUM
ejpam-5716	1	94	iligan	iligan	ADJ
ejpam-5716	1	95	city	city	NOUN
ejpam-5716	1	96	,	,	PUNCT
ejpam-5716	1	97	philippines	philippine	NOUN
ejpam-5716	1	98	abstract	abstract	ADJ
ejpam-5716	1	99	.	.	PUNCT
ejpam-5716	2	1	in	in	ADP
ejpam-5716	2	2	this	this	DET
ejpam-5716	2	3	paper	paper	NOUN
ejpam-5716	2	4	,	,	PUNCT
ejpam-5716	2	5	we	we	PRON
ejpam-5716	2	6	introduce	introduce	VERB
ejpam-5716	2	7	a	a	DET
ejpam-5716	2	8	new	new	ADJ
ejpam-5716	2	9	graph	graph	NOUN
ejpam-5716	2	10	parameter	parameter	NOUN
ejpam-5716	2	11	called	call	VERB
ejpam-5716	2	12	the	the	DET
ejpam-5716	2	13	hop	hop	NOUN
ejpam-5716	2	14	domination	domination	NOUN
ejpam-5716	2	15	defect	defect	VERB
ejpam-5716	2	16	and	and	CCONJ
ejpam-5716	2	17	investigate	investigate	VERB
ejpam-5716	2	18	it	it	PRON
ejpam-5716	2	19	for	for	ADP
ejpam-5716	2	20	some	some	DET
ejpam-5716	2	21	classes	class	NOUN
ejpam-5716	2	22	of	of	ADP
ejpam-5716	2	23	graphs	graph	NOUN
ejpam-5716	2	24	.	.	PUNCT
ejpam-5716	3	1	the	the	DET
ejpam-5716	3	2	hop	hop	NOUN
ejpam-5716	3	3	domination	domination	NOUN
ejpam-5716	3	4	number	number	NOUN
ejpam-5716	3	5	γh(g	γh(g	PUNCT
ejpam-5716	3	6	)	)	PUNCT
ejpam-5716	3	7	of	of	ADP
ejpam-5716	3	8	a	a	DET
ejpam-5716	3	9	graph	graph	NOUN
ejpam-5716	3	10	g	g	NOUN
ejpam-5716	3	11	is	be	AUX
ejpam-5716	3	12	the	the	DET
ejpam-5716	3	13	minimum	minimum	ADJ
ejpam-5716	3	14	number	number	NOUN
ejpam-5716	3	15	of	of	ADP
ejpam-5716	3	16	vertices	vertex	NOUN
ejpam-5716	3	17	required	require	VERB
ejpam-5716	3	18	to	to	PART
ejpam-5716	3	19	hop	hop	VERB
ejpam-5716	3	20	dominate	dominate	VERB
ejpam-5716	3	21	all	all	DET
ejpam-5716	3	22	the	the	DET
ejpam-5716	3	23	vertices	vertex	NOUN
ejpam-5716	3	24	of	of	ADP
ejpam-5716	3	25	g.	g.	PROPN
ejpam-5716	3	26	the	the	DET
ejpam-5716	3	27	minimality	minimality	NOUN
ejpam-5716	3	28	of	of	ADP
ejpam-5716	3	29	γh(g	γh(g	NOUN
ejpam-5716	3	30	)	)	PUNCT
ejpam-5716	3	31	implies	imply	VERB
ejpam-5716	3	32	that	that	SCONJ
ejpam-5716	3	33	if	if	SCONJ
ejpam-5716	3	34	w	w	ADP
ejpam-5716	3	35	⊆	⊆	NUM
ejpam-5716	3	36	v	v	NOUN
ejpam-5716	3	37	(	(	PUNCT
ejpam-5716	3	38	g	g	NOUN
ejpam-5716	3	39	)	)	PUNCT
ejpam-5716	3	40	and	and	CCONJ
ejpam-5716	3	41	|w	|w	ADJ
ejpam-5716	3	42	|	|	ADV
ejpam-5716	3	43	<	<	X
ejpam-5716	3	44	γh(g	γh(g	NOUN
ejpam-5716	3	45	)	)	PUNCT
ejpam-5716	3	46	,	,	PUNCT
ejpam-5716	3	47	then	then	ADV
ejpam-5716	3	48	there	there	PRON
ejpam-5716	3	49	is	be	VERB
ejpam-5716	3	50	at	at	ADV
ejpam-5716	3	51	least	least	ADJ
ejpam-5716	3	52	one	one	NUM
ejpam-5716	3	53	vertex	vertex	NOUN
ejpam-5716	3	54	in	in	ADP
ejpam-5716	3	55	g	g	PROPN
ejpam-5716	3	56	that	that	PRON
ejpam-5716	3	57	is	be	AUX
ejpam-5716	3	58	not	not	PART
ejpam-5716	3	59	hop	hop	ADV
ejpam-5716	3	60	dominated	dominate	VERB
ejpam-5716	3	61	by	by	ADP
ejpam-5716	3	62	w	w	PROPN
ejpam-5716	3	63	.	.	PUNCT
ejpam-5716	4	1	given	give	VERB
ejpam-5716	4	2	a	a	DET
ejpam-5716	4	3	positive	positive	ADJ
ejpam-5716	4	4	integer	integer	NOUN
ejpam-5716	4	5	k	k	X
ejpam-5716	4	6	<	<	X
ejpam-5716	4	7	γh(g	γh(g	NOUN
ejpam-5716	4	8	)	)	PUNCT
ejpam-5716	4	9	,	,	PUNCT
ejpam-5716	4	10	where	where	SCONJ
ejpam-5716	4	11	γh(g	γh(g	NOUN
ejpam-5716	4	12	)	)	PUNCT
ejpam-5716	4	13	≥	≥	NOUN
ejpam-5716	4	14	2	2	NUM
ejpam-5716	4	15	,	,	PUNCT
ejpam-5716	4	16	the	the	DET
ejpam-5716	4	17	k	k	ADJ
ejpam-5716	4	18	-	-	PUNCT
ejpam-5716	4	19	hop	hop	NOUN
ejpam-5716	4	20	domination	domination	NOUN
ejpam-5716	4	21	defect	defect	NOUN
ejpam-5716	4	22	of	of	ADP
ejpam-5716	4	23	g	g	NOUN
ejpam-5716	4	24	,	,	PUNCT
ejpam-5716	4	25	denoted	denote	VERB
ejpam-5716	4	26	by	by	ADP
ejpam-5716	4	27	ζhk	ζhk	PROPN
ejpam-5716	4	28	(	(	PUNCT
ejpam-5716	4	29	g	g	NOUN
ejpam-5716	4	30	)	)	PUNCT
ejpam-5716	4	31	,	,	PUNCT
ejpam-5716	4	32	is	be	AUX
ejpam-5716	4	33	the	the	DET
ejpam-5716	4	34	minimum	minimum	ADJ
ejpam-5716	4	35	number	number	NOUN
ejpam-5716	4	36	of	of	ADP
ejpam-5716	4	37	vertices	vertex	NOUN
ejpam-5716	4	38	of	of	ADP
ejpam-5716	4	39	g	g	NOUN
ejpam-5716	4	40	that	that	PRON
ejpam-5716	4	41	is	be	AUX
ejpam-5716	4	42	not	not	PART
ejpam-5716	4	43	hop	hop	ADV
ejpam-5716	4	44	dominated	dominate	VERB
ejpam-5716	4	45	by	by	ADP
ejpam-5716	4	46	any	any	DET
ejpam-5716	4	47	subset	subset	NOUN
ejpam-5716	4	48	of	of	ADP
ejpam-5716	4	49	vertices	vertex	NOUN
ejpam-5716	4	50	of	of	ADP
ejpam-5716	4	51	g	g	NOUN
ejpam-5716	4	52	with	with	ADP
ejpam-5716	4	53	cardinality	cardinality	PROPN
ejpam-5716	4	54	γh(g)−	γh(g)−	PROPN
ejpam-5716	4	55	k.	k.	NOUN
ejpam-5716	4	56	we	we	PRON
ejpam-5716	4	57	give	give	VERB
ejpam-5716	4	58	some	some	DET
ejpam-5716	4	59	bounds	bound	NOUN
ejpam-5716	4	60	on	on	ADP
ejpam-5716	4	61	the	the	DET
ejpam-5716	4	62	k	k	ADJ
ejpam-5716	4	63	-	-	PUNCT
ejpam-5716	4	64	hop	hop	NOUN
ejpam-5716	4	65	domination	domination	NOUN
ejpam-5716	4	66	defect	defect	NOUN
ejpam-5716	4	67	of	of	ADP
ejpam-5716	4	68	a	a	DET
ejpam-5716	4	69	graph	graph	NOUN
ejpam-5716	4	70	in	in	ADP
ejpam-5716	4	71	terms	term	NOUN
ejpam-5716	4	72	of	of	ADP
ejpam-5716	4	73	its	its	PRON
ejpam-5716	4	74	order	order	NOUN
ejpam-5716	4	75	and	and	CCONJ
ejpam-5716	4	76	maximum	maximum	ADJ
ejpam-5716	4	77	hop	hop	NOUN
ejpam-5716	4	78	degree	degree	NOUN
ejpam-5716	4	79	.	.	PUNCT
ejpam-5716	5	1	furthermore	furthermore	ADV
ejpam-5716	5	2	,	,	PUNCT
ejpam-5716	5	3	we	we	PRON
ejpam-5716	5	4	determine	determine	VERB
ejpam-5716	5	5	the	the	DET
ejpam-5716	5	6	k	k	ADJ
ejpam-5716	5	7	-	-	PUNCT
ejpam-5716	5	8	hop	hop	NOUN
ejpam-5716	5	9	domination	domination	NOUN
ejpam-5716	5	10	defects	defect	NOUN
ejpam-5716	5	11	of	of	ADP
ejpam-5716	5	12	the	the	DET
ejpam-5716	5	13	join	join	NOUN
ejpam-5716	5	14	of	of	ADP
ejpam-5716	5	15	some	some	DET
ejpam-5716	5	16	graphs	graph	NOUN
ejpam-5716	5	17	.	.	PUNCT
ejpam-5716	6	1	2020	2020	NUM
ejpam-5716	6	2	mathematics	mathematic	NOUN
ejpam-5716	6	3	subject	subject	NOUN
ejpam-5716	6	4	classifications	classification	NOUN
ejpam-5716	6	5	:	:	PUNCT
ejpam-5716	6	6	05c69	05c69	X
ejpam-5716	6	7	key	key	ADJ
ejpam-5716	6	8	words	word	NOUN
ejpam-5716	6	9	and	and	CCONJ
ejpam-5716	6	10	phrases	phrase	NOUN
ejpam-5716	6	11	:	:	PUNCT
ejpam-5716	6	12	hop	hop	NOUN
ejpam-5716	6	13	domination	domination	NOUN
ejpam-5716	6	14	,	,	PUNCT
ejpam-5716	6	15	k	k	ADJ
ejpam-5716	6	16	-	-	PUNCT
ejpam-5716	6	17	hop	hop	NOUN
ejpam-5716	6	18	domination	domination	NOUN
ejpam-5716	6	19	defect	defect	NOUN
ejpam-5716	6	20	,	,	PUNCT
ejpam-5716	6	21	hop	hop	NOUN
ejpam-5716	6	22	degree	degree	NOUN
ejpam-5716	6	23	of	of	ADP
ejpam-5716	6	24	a	a	DET
ejpam-5716	6	25	graph	graph	NOUN
ejpam-5716	6	26	,	,	PUNCT
ejpam-5716	6	27	join	join	VERB
ejpam-5716	6	28	1	1	NUM
ejpam-5716	6	29	.	.	PUNCT
ejpam-5716	7	1	introduction	introduction	NOUN
ejpam-5716	7	2	natarajan	natarajan	PROPN
ejpam-5716	7	3	and	and	CCONJ
ejpam-5716	7	4	ayyaswamy	ayyaswamy	ADV
ejpam-5716	7	5	in	in	ADP
ejpam-5716	7	6	[	[	X
ejpam-5716	7	7	13	13	NUM
ejpam-5716	7	8	]	]	PUNCT
ejpam-5716	7	9	introduced	introduce	VERB
ejpam-5716	7	10	and	and	CCONJ
ejpam-5716	7	11	studied	study	VERB
ejpam-5716	7	12	hop	hop	NOUN
ejpam-5716	7	13	domination	domination	NOUN
ejpam-5716	7	14	,	,	PUNCT
ejpam-5716	7	15	which	which	PRON
ejpam-5716	7	16	,	,	PUNCT
ejpam-5716	7	17	in	in	ADP
ejpam-5716	7	18	some	some	DET
ejpam-5716	7	19	sense	sense	NOUN
ejpam-5716	7	20	,	,	PUNCT
ejpam-5716	7	21	is	be	AUX
ejpam-5716	7	22	related	relate	VERB
ejpam-5716	7	23	to	to	ADP
ejpam-5716	7	24	the	the	DET
ejpam-5716	7	25	standard	standard	ADJ
ejpam-5716	7	26	domination	domination	NOUN
ejpam-5716	7	27	.	.	PUNCT
ejpam-5716	8	1	according	accord	VERB
ejpam-5716	8	2	to	to	ADP
ejpam-5716	8	3	the	the	DET
ejpam-5716	8	4	authors	author	NOUN
ejpam-5716	8	5	,	,	PUNCT
ejpam-5716	8	6	the	the	DET
ejpam-5716	8	7	concept	concept	NOUN
ejpam-5716	8	8	has	have	VERB
ejpam-5716	8	9	its	its	PRON
ejpam-5716	8	10	origin	origin	NOUN
ejpam-5716	8	11	from	from	ADP
ejpam-5716	8	12	the	the	DET
ejpam-5716	8	13	field	field	NOUN
ejpam-5716	8	14	of	of	ADP
ejpam-5716	8	15	inorganic	inorganic	ADJ
ejpam-5716	8	16	chemistry	chemistry	NOUN
ejpam-5716	8	17	.	.	PUNCT
ejpam-5716	9	1	this	this	DET
ejpam-5716	9	2	parameter	parameter	NOUN
ejpam-5716	9	3	has	have	AUX
ejpam-5716	9	4	been	be	AUX
ejpam-5716	9	5	widely	widely	ADV
ejpam-5716	9	6	studied	study	VERB
ejpam-5716	9	7	since	since	SCONJ
ejpam-5716	9	8	its	its	PRON
ejpam-5716	9	9	appearance	appearance	NOUN
ejpam-5716	9	10	in	in	ADP
ejpam-5716	9	11	the	the	DET
ejpam-5716	9	12	literature	literature	NOUN
ejpam-5716	9	13	and	and	CCONJ
ejpam-5716	9	14	a	a	DET
ejpam-5716	9	15	significant	significant	ADJ
ejpam-5716	9	16	number	number	NOUN
ejpam-5716	9	17	of	of	ADP
ejpam-5716	9	18	variants	variant	NOUN
ejpam-5716	9	19	of	of	ADP
ejpam-5716	9	20	the	the	DET
ejpam-5716	9	21	parameter	parameter	NOUN
ejpam-5716	9	22	have	have	AUX
ejpam-5716	9	23	already	already	ADV
ejpam-5716	9	24	been	be	AUX
ejpam-5716	9	25	defined	define	VERB
ejpam-5716	9	26	and	and	CCONJ
ejpam-5716	9	27	investigated	investigate	VERB
ejpam-5716	9	28	(	(	PUNCT
ejpam-5716	9	29	see	see	VERB
ejpam-5716	9	30	for	for	ADP
ejpam-5716	9	31	example	example	NOUN
ejpam-5716	10	1	[	[	X
ejpam-5716	10	2	1	1	NUM
ejpam-5716	10	3	]	]	PUNCT
ejpam-5716	10	4	,	,	PUNCT
ejpam-5716	10	5	[	[	X
ejpam-5716	10	6	2	2	NUM
ejpam-5716	10	7	]	]	PUNCT
ejpam-5716	10	8	,	,	PUNCT
ejpam-5716	10	9	[	[	X
ejpam-5716	10	10	4	4	NUM
ejpam-5716	10	11	]	]	PUNCT
ejpam-5716	10	12	,	,	PUNCT
ejpam-5716	10	13	[	[	X
ejpam-5716	10	14	5	5	NUM
ejpam-5716	10	15	]	]	PUNCT
ejpam-5716	10	16	,	,	PUNCT
ejpam-5716	10	17	[	[	X
ejpam-5716	10	18	6	6	NUM
ejpam-5716	10	19	]	]	PUNCT
ejpam-5716	10	20	,	,	PUNCT
ejpam-5716	10	21	[	[	X
ejpam-5716	10	22	7	7	NUM
ejpam-5716	10	23	]	]	PUNCT
ejpam-5716	10	24	,	,	PUNCT
ejpam-5716	10	25	[	[	X
ejpam-5716	10	26	8	8	NUM
ejpam-5716	10	27	]	]	PUNCT
ejpam-5716	10	28	,	,	PUNCT
ejpam-5716	10	29	[	[	X
ejpam-5716	10	30	9	9	NUM
ejpam-5716	10	31	]	]	PUNCT
ejpam-5716	10	32	,	,	PUNCT
ejpam-5716	10	33	[	[	X
ejpam-5716	10	34	14	14	NUM
ejpam-5716	10	35	]	]	PUNCT
ejpam-5716	10	36	,	,	PUNCT
ejpam-5716	10	37	[	[	X
ejpam-5716	10	38	15	15	NUM
ejpam-5716	10	39	]	]	NUM
ejpam-5716	10	40	)	)	PUNCT
ejpam-5716	10	41	,	,	PUNCT
ejpam-5716	10	42	and	and	CCONJ
ejpam-5716	10	43	[	[	X
ejpam-5716	10	44	16	16	NUM
ejpam-5716	10	45	]	]	PUNCT
ejpam-5716	10	46	)	)	PUNCT
ejpam-5716	10	47	.	.	PUNCT
ejpam-5716	11	1	recently	recently	ADV
ejpam-5716	11	2	,	,	PUNCT
ejpam-5716	11	3	das	das	PROPN
ejpam-5716	11	4	et	et	PROPN
ejpam-5716	11	5	al	al	PROPN
ejpam-5716	11	6	.	.	PUNCT
ejpam-5716	12	1	[	[	X
ejpam-5716	12	2	3	3	X
ejpam-5716	12	3	]	]	PUNCT
ejpam-5716	12	4	introduced	introduce	VERB
ejpam-5716	12	5	a	a	DET
ejpam-5716	12	6	domination	domination	NOUN
ejpam-5716	12	7	parameter	parameter	NOUN
ejpam-5716	12	8	called	call	VERB
ejpam-5716	12	9	the	the	DET
ejpam-5716	12	10	domination	domination	NOUN
ejpam-5716	12	11	defect	defect	NOUN
ejpam-5716	12	12	.	.	PUNCT
ejpam-5716	13	1	as	as	SCONJ
ejpam-5716	13	2	mentioned	mention	VERB
ejpam-5716	13	3	in	in	ADP
ejpam-5716	13	4	their	their	PRON
ejpam-5716	13	5	paper	paper	NOUN
ejpam-5716	13	6	,	,	PUNCT
ejpam-5716	13	7	the	the	DET
ejpam-5716	13	8	motivation	motivation	NOUN
ejpam-5716	13	9	of	of	ADP
ejpam-5716	13	10	this	this	DET
ejpam-5716	13	11	study	study	NOUN
ejpam-5716	13	12	was	be	AUX
ejpam-5716	13	13	mainly	mainly	ADV
ejpam-5716	13	14	on	on	ADP
ejpam-5716	13	15	dealing	deal	VERB
ejpam-5716	13	16	with	with	ADP
ejpam-5716	13	17	problems	problem	NOUN
ejpam-5716	13	18	associated	associate	VERB
ejpam-5716	13	19	with	with	ADP
ejpam-5716	13	20	guarding	guard	VERB
ejpam-5716	13	21	facilities	facility	NOUN
ejpam-5716	13	22	or	or	CCONJ
ejpam-5716	13	23	placing	place	VERB
ejpam-5716	13	24	monitoring	monitoring	NOUN
ejpam-5716	13	25	devices	device	NOUN
ejpam-5716	13	26	in	in	ADP
ejpam-5716	13	27	networks	network	NOUN
ejpam-5716	13	28	when	when	SCONJ
ejpam-5716	13	29	there	there	PRON
ejpam-5716	13	30	is	be	VERB
ejpam-5716	13	31	only	only	ADV
ejpam-5716	13	32	fewer	few	ADJ
ejpam-5716	13	33	than	than	ADP
ejpam-5716	13	34	the	the	DET
ejpam-5716	13	35	minimum	minimum	ADJ
ejpam-5716	13	36	number	number	NOUN
ejpam-5716	13	37	of	of	ADP
ejpam-5716	13	38	guards	guard	NOUN
ejpam-5716	13	39	or	or	CCONJ
ejpam-5716	13	40	devices	device	NOUN
ejpam-5716	13	41	required	require	VERB
ejpam-5716	13	42	.	.	PUNCT
ejpam-5716	14	1	in	in	ADP
ejpam-5716	14	2	their	their	PRON
ejpam-5716	14	3	doi	doi	NOUN
ejpam-5716	14	4	:	:	PUNCT
ejpam-5716	14	5	https://doi.org/10.29020/nybg.ejpam.v18i1.5716	https://doi.org/10.29020/nybg.ejpam.v18i1.5716	NUM
ejpam-5716	14	6	email	email	NOUN
ejpam-5716	14	7	addresses	address	NOUN
ejpam-5716	14	8	:	:	PUNCT
ejpam-5716	14	9	jesica.anoche@g.msuiit.edu.ph	jesica.anoche@g.msuiit.edu.ph	PROPN
ejpam-5716	14	10	(	(	PUNCT
ejpam-5716	14	11	j.	j.	PROPN
ejpam-5716	14	12	anoche	anoche	PROPN
ejpam-5716	14	13	)	)	PUNCT
ejpam-5716	14	14	,	,	PUNCT
ejpam-5716	14	15	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5716	14	16	(	(	PUNCT
ejpam-5716	14	17	s.	s.	PROPN
ejpam-5716	14	18	canoy	canoy	PROPN
ejpam-5716	14	19	,	,	PUNCT
ejpam-5716	14	20	jr	jr	PROPN
ejpam-5716	14	21	.	.	PUNCT
ejpam-5716	14	22	)	)	PUNCT
ejpam-5716	14	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5716	15	1	1	1	NUM
ejpam-5716	15	2	copyright	copyright	NOUN
ejpam-5716	15	3	:	:	PUNCT
ejpam-5716	15	4	©	©	PROPN
ejpam-5716	15	5	2025	2025	NUM
ejpam-5716	15	6	the	the	DET
ejpam-5716	15	7	author(s	author(s	NOUN
ejpam-5716	15	8	)	)	PUNCT
ejpam-5716	15	9	.	.	PUNCT
ejpam-5716	16	1	(	(	PUNCT
ejpam-5716	16	2	cc	cc	NOUN
ejpam-5716	16	3	by	by	ADP
ejpam-5716	16	4	-	-	PUNCT
ejpam-5716	16	5	nc	nc	PROPN
ejpam-5716	16	6	4.0	4.0	NUM
ejpam-5716	16	7	)	)	PUNCT
ejpam-5716	16	8	j.	j.	PROPN
ejpam-5716	16	9	anoche	anoche	PROPN
ejpam-5716	16	10	,	,	PUNCT
ejpam-5716	16	11	s.r	s.r	PROPN
ejpam-5716	16	12	.	.	PROPN
ejpam-5716	16	13	canoy	canoy	PROPN
ejpam-5716	16	14	jr	jr	PROPN
ejpam-5716	16	15	.	.	PUNCT
ejpam-5716	16	16	/	/	SYM
ejpam-5716	16	17	eur	eur	PROPN
ejpam-5716	16	18	.	.	PUNCT
ejpam-5716	17	1	j.	j.	PROPN
ejpam-5716	17	2	pure	pure	PROPN
ejpam-5716	17	3	appl	appl	PROPN
ejpam-5716	17	4	.	.	PROPN
ejpam-5716	17	5	math	math	PROPN
ejpam-5716	17	6	,	,	PUNCT
ejpam-5716	17	7	18	18	NUM
ejpam-5716	17	8	(	(	PUNCT
ejpam-5716	17	9	1	1	NUM
ejpam-5716	17	10	)	)	PUNCT
ejpam-5716	17	11	(	(	PUNCT
ejpam-5716	17	12	2025	2025	NUM
ejpam-5716	17	13	)	)	PUNCT
ejpam-5716	17	14	,	,	PUNCT
ejpam-5716	17	15	5716	5716	NUM
ejpam-5716	17	16	2	2	NUM
ejpam-5716	17	17	of	of	ADP
ejpam-5716	17	18	13	13	NUM
ejpam-5716	17	19	study	study	NOUN
ejpam-5716	17	20	,	,	PUNCT
ejpam-5716	17	21	the	the	DET
ejpam-5716	17	22	authors	author	NOUN
ejpam-5716	17	23	were	be	AUX
ejpam-5716	17	24	able	able	ADJ
ejpam-5716	17	25	to	to	PART
ejpam-5716	17	26	establish	establish	VERB
ejpam-5716	17	27	various	various	ADJ
ejpam-5716	17	28	bounds	bound	NOUN
ejpam-5716	17	29	on	on	ADP
ejpam-5716	17	30	the	the	DET
ejpam-5716	17	31	domination	domination	NOUN
ejpam-5716	17	32	defect	defect	NOUN
ejpam-5716	17	33	of	of	ADP
ejpam-5716	17	34	a	a	DET
ejpam-5716	17	35	graph	graph	NOUN
ejpam-5716	17	36	in	in	ADP
ejpam-5716	17	37	terms	term	NOUN
ejpam-5716	17	38	of	of	ADP
ejpam-5716	17	39	,	,	PUNCT
ejpam-5716	17	40	among	among	ADP
ejpam-5716	17	41	others	other	NOUN
ejpam-5716	17	42	,	,	PUNCT
ejpam-5716	17	43	the	the	DET
ejpam-5716	17	44	domination	domination	NOUN
ejpam-5716	17	45	number	number	NOUN
ejpam-5716	17	46	,	,	PUNCT
ejpam-5716	17	47	order	order	NOUN
ejpam-5716	17	48	,	,	PUNCT
ejpam-5716	17	49	degree	degree	NOUN
ejpam-5716	17	50	sequence	sequence	NOUN
ejpam-5716	17	51	,	,	PUNCT
ejpam-5716	17	52	graph	graph	NOUN
ejpam-5716	17	53	homomorphisms	homomorphism	NOUN
ejpam-5716	17	54	,	,	PUNCT
ejpam-5716	17	55	and	and	CCONJ
ejpam-5716	17	56	efficient	efficient	ADJ
ejpam-5716	17	57	dominating	dominating	NOUN
ejpam-5716	17	58	set	set	NOUN
ejpam-5716	17	59	.	.	PUNCT
ejpam-5716	18	1	other	other	ADJ
ejpam-5716	18	2	studies	study	NOUN
ejpam-5716	18	3	on	on	ADP
ejpam-5716	18	4	the	the	DET
ejpam-5716	18	5	topic	topic	NOUN
ejpam-5716	18	6	(	(	PUNCT
ejpam-5716	18	7	see	see	VERB
ejpam-5716	18	8	[	[	X
ejpam-5716	18	9	10–12	10–12	NUM
ejpam-5716	18	10	]	]	PUNCT
ejpam-5716	18	11	)	)	PUNCT
ejpam-5716	18	12	focused	focus	VERB
ejpam-5716	18	13	on	on	ADP
ejpam-5716	18	14	characterizing	characterize	VERB
ejpam-5716	18	15	the	the	DET
ejpam-5716	18	16	k	k	ADJ
ejpam-5716	18	17	-	-	PUNCT
ejpam-5716	18	18	domination	domination	NOUN
ejpam-5716	18	19	defect	defect	NOUN
ejpam-5716	18	20	sets	set	NOUN
ejpam-5716	18	21	and	and	CCONJ
ejpam-5716	18	22	determining	determine	VERB
ejpam-5716	18	23	the	the	DET
ejpam-5716	18	24	k	k	ADJ
ejpam-5716	18	25	-	-	PUNCT
ejpam-5716	18	26	domination	domination	NOUN
ejpam-5716	18	27	defect	defect	NOUN
ejpam-5716	18	28	in	in	ADP
ejpam-5716	18	29	the	the	DET
ejpam-5716	18	30	join	join	NOUN
ejpam-5716	18	31	,	,	PUNCT
ejpam-5716	18	32	corona	corona	PROPN
ejpam-5716	18	33	,	,	PUNCT
ejpam-5716	18	34	edge	edge	NOUN
ejpam-5716	18	35	corona	corona	NOUN
ejpam-5716	18	36	,	,	PUNCT
ejpam-5716	18	37	and	and	CCONJ
ejpam-5716	18	38	composition	composition	NOUN
ejpam-5716	18	39	of	of	ADP
ejpam-5716	18	40	two	two	NUM
ejpam-5716	18	41	graphs	graph	NOUN
ejpam-5716	18	42	.	.	PUNCT
ejpam-5716	19	1	since	since	SCONJ
ejpam-5716	19	2	hop	hop	NOUN
ejpam-5716	19	3	domination	domination	NOUN
ejpam-5716	19	4	has	have	VERB
ejpam-5716	19	5	similar	similar	ADJ
ejpam-5716	19	6	applications	application	NOUN
ejpam-5716	19	7	(	(	PUNCT
ejpam-5716	19	8	e.g.	e.g.	ADV
ejpam-5716	19	9	in	in	ADP
ejpam-5716	19	10	facility	facility	NOUN
ejpam-5716	19	11	location	location	NOUN
ejpam-5716	19	12	,	,	PUNCT
ejpam-5716	19	13	protection	protection	NOUN
ejpam-5716	19	14	strategy	strategy	NOUN
ejpam-5716	19	15	,	,	PUNCT
ejpam-5716	19	16	management	management	NOUN
ejpam-5716	19	17	in	in	ADP
ejpam-5716	19	18	social	social	ADJ
ejpam-5716	19	19	networks	network	NOUN
ejpam-5716	19	20	)	)	PUNCT
ejpam-5716	19	21	as	as	ADP
ejpam-5716	19	22	domination	domination	NOUN
ejpam-5716	19	23	,	,	PUNCT
ejpam-5716	19	24	it	it	PRON
ejpam-5716	19	25	is	be	AUX
ejpam-5716	19	26	also	also	ADV
ejpam-5716	19	27	a	a	DET
ejpam-5716	19	28	bit	bit	NOUN
ejpam-5716	19	29	interesting	interesting	ADJ
ejpam-5716	19	30	to	to	PART
ejpam-5716	19	31	study	study	VERB
ejpam-5716	19	32	the	the	DET
ejpam-5716	19	33	effect	effect	NOUN
ejpam-5716	19	34	of	of	ADP
ejpam-5716	19	35	having	have	VERB
ejpam-5716	19	36	fewer	few	ADJ
ejpam-5716	19	37	than	than	ADP
ejpam-5716	19	38	the	the	DET
ejpam-5716	19	39	required	require	VERB
ejpam-5716	19	40	minimum	minimum	ADJ
ejpam-5716	19	41	number	number	NOUN
ejpam-5716	19	42	of	of	ADP
ejpam-5716	19	43	nodes	node	NOUN
ejpam-5716	19	44	in	in	ADP
ejpam-5716	19	45	a	a	DET
ejpam-5716	19	46	hop	hop	NOUN
ejpam-5716	19	47	dominating	dominating	NOUN
ejpam-5716	19	48	set	set	NOUN
ejpam-5716	19	49	.	.	PUNCT
ejpam-5716	20	1	in	in	ADP
ejpam-5716	20	2	this	this	DET
ejpam-5716	20	3	study	study	NOUN
ejpam-5716	20	4	,	,	PUNCT
ejpam-5716	20	5	we	we	PRON
ejpam-5716	20	6	define	define	VERB
ejpam-5716	20	7	the	the	DET
ejpam-5716	20	8	parameter	parameter	NOUN
ejpam-5716	20	9	k	k	PROPN
ejpam-5716	20	10	-	-	PUNCT
ejpam-5716	20	11	hop	hop	NOUN
ejpam-5716	20	12	domination	domination	NOUN
ejpam-5716	20	13	defect	defect	NOUN
ejpam-5716	20	14	and	and	CCONJ
ejpam-5716	20	15	study	study	VERB
ejpam-5716	20	16	it	it	PRON
ejpam-5716	20	17	for	for	ADP
ejpam-5716	20	18	some	some	DET
ejpam-5716	20	19	known	know	VERB
ejpam-5716	20	20	graphs	graph	NOUN
ejpam-5716	20	21	.	.	PUNCT
ejpam-5716	21	1	the	the	DET
ejpam-5716	21	2	study	study	NOUN
ejpam-5716	21	3	hopes	hope	VERB
ejpam-5716	21	4	to	to	PART
ejpam-5716	21	5	give	give	VERB
ejpam-5716	21	6	bounds	bound	NOUN
ejpam-5716	21	7	of	of	ADP
ejpam-5716	21	8	the	the	DET
ejpam-5716	21	9	newly	newly	ADV
ejpam-5716	21	10	defined	define	VERB
ejpam-5716	21	11	parameter	parameter	NOUN
ejpam-5716	21	12	in	in	ADP
ejpam-5716	21	13	terms	term	NOUN
ejpam-5716	21	14	of	of	ADP
ejpam-5716	21	15	the	the	DET
ejpam-5716	21	16	order	order	NOUN
ejpam-5716	21	17	,	,	PUNCT
ejpam-5716	21	18	hop	hop	NOUN
ejpam-5716	21	19	degree	degree	NOUN
ejpam-5716	21	20	of	of	ADP
ejpam-5716	21	21	the	the	DET
ejpam-5716	21	22	graph	graph	NOUN
ejpam-5716	21	23	,	,	PUNCT
ejpam-5716	21	24	and	and	CCONJ
ejpam-5716	21	25	other	other	ADJ
ejpam-5716	21	26	parameters	parameter	NOUN
ejpam-5716	21	27	.	.	PUNCT
ejpam-5716	22	1	in	in	ADP
ejpam-5716	22	2	particular	particular	ADJ
ejpam-5716	22	3	,	,	PUNCT
ejpam-5716	22	4	the	the	DET
ejpam-5716	22	5	authors	author	NOUN
ejpam-5716	22	6	would	would	AUX
ejpam-5716	22	7	like	like	VERB
ejpam-5716	22	8	to	to	PART
ejpam-5716	22	9	find	find	VERB
ejpam-5716	22	10	what	what	PRON
ejpam-5716	22	11	specific	specific	ADJ
ejpam-5716	22	12	conditions	condition	NOUN
ejpam-5716	22	13	to	to	PART
ejpam-5716	22	14	impose	impose	VERB
ejpam-5716	22	15	so	so	SCONJ
ejpam-5716	22	16	that	that	SCONJ
ejpam-5716	22	17	these	these	DET
ejpam-5716	22	18	bounds	bound	NOUN
ejpam-5716	22	19	and	and	CCONJ
ejpam-5716	22	20	some	some	DET
ejpam-5716	22	21	results	result	NOUN
ejpam-5716	22	22	which	which	PRON
ejpam-5716	22	23	seemingly	seemingly	ADV
ejpam-5716	22	24	run	run	VERB
ejpam-5716	22	25	parallel	parallel	ADJ
ejpam-5716	22	26	to	to	ADP
ejpam-5716	22	27	the	the	DET
ejpam-5716	22	28	ones	one	NOUN
ejpam-5716	22	29	found	find	VERB
ejpam-5716	22	30	in	in	ADP
ejpam-5716	22	31	[	[	X
ejpam-5716	22	32	3	3	NUM
ejpam-5716	22	33	]	]	PUNCT
ejpam-5716	22	34	,	,	PUNCT
ejpam-5716	22	35	hold	hold	VERB
ejpam-5716	22	36	in	in	ADP
ejpam-5716	22	37	the	the	DET
ejpam-5716	22	38	sense	sense	NOUN
ejpam-5716	22	39	of	of	ADP
ejpam-5716	22	40	hop	hop	NOUN
ejpam-5716	22	41	domination	domination	NOUN
ejpam-5716	22	42	.	.	PUNCT
ejpam-5716	23	1	the	the	DET
ejpam-5716	23	2	k	k	ADJ
ejpam-5716	23	3	-	-	PUNCT
ejpam-5716	23	4	hop	hop	NOUN
ejpam-5716	23	5	domination	domination	NOUN
ejpam-5716	23	6	defects	defect	NOUN
ejpam-5716	23	7	of	of	ADP
ejpam-5716	23	8	some	some	DET
ejpam-5716	23	9	join	join	NOUN
ejpam-5716	23	10	of	of	ADP
ejpam-5716	23	11	graphs	graph	NOUN
ejpam-5716	23	12	are	be	AUX
ejpam-5716	23	13	also	also	ADV
ejpam-5716	23	14	obtained	obtain	VERB
ejpam-5716	23	15	.	.	PUNCT
ejpam-5716	24	1	2	2	X
ejpam-5716	24	2	.	.	X
ejpam-5716	24	3	terminology	terminology	NOUN
ejpam-5716	24	4	and	and	CCONJ
ejpam-5716	24	5	notation	notation	NOUN
ejpam-5716	24	6	for	for	ADP
ejpam-5716	24	7	any	any	DET
ejpam-5716	24	8	two	two	NUM
ejpam-5716	24	9	vertices	vertex	NOUN
ejpam-5716	24	10	u	u	NOUN
ejpam-5716	24	11	and	and	CCONJ
ejpam-5716	24	12	v	v	NOUN
ejpam-5716	24	13	in	in	ADP
ejpam-5716	24	14	an	an	DET
ejpam-5716	24	15	undirected	undirected	ADJ
ejpam-5716	24	16	connected	connected	ADJ
ejpam-5716	24	17	graph	graph	NOUN
ejpam-5716	24	18	g	g	PROPN
ejpam-5716	24	19	,	,	PUNCT
ejpam-5716	24	20	the	the	DET
ejpam-5716	24	21	distance	distance	NOUN
ejpam-5716	24	22	dg(u	dg(u	X
ejpam-5716	24	23	,	,	PUNCT
ejpam-5716	24	24	v	v	NOUN
ejpam-5716	24	25	)	)	PUNCT
ejpam-5716	24	26	is	be	AUX
ejpam-5716	24	27	the	the	DET
ejpam-5716	24	28	length	length	NOUN
ejpam-5716	24	29	of	of	ADP
ejpam-5716	24	30	a	a	DET
ejpam-5716	24	31	shortest	short	ADJ
ejpam-5716	24	32	path	path	NOUN
ejpam-5716	24	33	joining	join	VERB
ejpam-5716	24	34	u	u	NOUN
ejpam-5716	24	35	and	and	CCONJ
ejpam-5716	24	36	v.	v.	ADP
ejpam-5716	24	37	any	any	DET
ejpam-5716	24	38	u	u	NOUN
ejpam-5716	24	39	-	-	NOUN
ejpam-5716	24	40	v	v	ADJ
ejpam-5716	24	41	path	path	NOUN
ejpam-5716	24	42	of	of	ADP
ejpam-5716	24	43	length	length	NOUN
ejpam-5716	24	44	dg(u	dg(u	PROPN
ejpam-5716	24	45	,	,	PUNCT
ejpam-5716	24	46	v	v	NOUN
ejpam-5716	24	47	)	)	PUNCT
ejpam-5716	24	48	is	be	AUX
ejpam-5716	24	49	called	call	VERB
ejpam-5716	24	50	a	a	DET
ejpam-5716	24	51	u	u	NOUN
ejpam-5716	24	52	-	-	NOUN
ejpam-5716	24	53	v	v	ADJ
ejpam-5716	24	54	geodesic	geodesic	NOUN
ejpam-5716	24	55	.	.	PUNCT
ejpam-5716	25	1	the	the	DET
ejpam-5716	25	2	distance	distance	NOUN
ejpam-5716	25	3	between	between	ADP
ejpam-5716	25	4	two	two	NUM
ejpam-5716	25	5	subsets	subset	NOUN
ejpam-5716	25	6	a	a	PRON
ejpam-5716	25	7	and	and	CCONJ
ejpam-5716	25	8	b	b	NOUN
ejpam-5716	25	9	of	of	ADP
ejpam-5716	25	10	v	v	NOUN
ejpam-5716	25	11	(	(	PUNCT
ejpam-5716	25	12	g	g	NOUN
ejpam-5716	25	13	)	)	PUNCT
ejpam-5716	25	14	is	be	AUX
ejpam-5716	25	15	given	give	VERB
ejpam-5716	25	16	by	by	ADP
ejpam-5716	25	17	dg(a	dg(a	PROPN
ejpam-5716	25	18	,	,	PUNCT
ejpam-5716	25	19	b	b	NOUN
ejpam-5716	25	20	)	)	PUNCT
ejpam-5716	25	21	=	=	SYM
ejpam-5716	25	22	min{dg(a	min{dg(a	PROPN
ejpam-5716	25	23	,	,	PUNCT
ejpam-5716	25	24	b	b	NOUN
ejpam-5716	25	25	)	)	PUNCT
ejpam-5716	25	26	:	:	PUNCT
ejpam-5716	25	27	a	a	DET
ejpam-5716	25	28	∈	∈	PROPN
ejpam-5716	25	29	a	a	PRON
ejpam-5716	25	30	and	and	CCONJ
ejpam-5716	25	31	b	b	NOUN
ejpam-5716	25	32	∈	∈	PROPN
ejpam-5716	25	33	b	b	NOUN
ejpam-5716	25	34	}	}	PUNCT
ejpam-5716	25	35	.	.	PUNCT
ejpam-5716	26	1	the	the	DET
ejpam-5716	26	2	open	open	ADJ
ejpam-5716	26	3	neighborhood	neighborhood	NOUN
ejpam-5716	26	4	of	of	ADP
ejpam-5716	26	5	a	a	DET
ejpam-5716	26	6	point	point	NOUN
ejpam-5716	26	7	u	u	NOUN
ejpam-5716	26	8	is	be	AUX
ejpam-5716	26	9	the	the	DET
ejpam-5716	26	10	set	set	NOUN
ejpam-5716	26	11	ng(u	ng(u	NOUN
ejpam-5716	26	12	)	)	PUNCT
ejpam-5716	26	13	consisting	consist	VERB
ejpam-5716	26	14	of	of	ADP
ejpam-5716	26	15	all	all	DET
ejpam-5716	26	16	points	point	NOUN
ejpam-5716	26	17	v	v	NUM
ejpam-5716	26	18	which	which	PRON
ejpam-5716	26	19	are	be	AUX
ejpam-5716	26	20	adjacent	adjacent	ADJ
ejpam-5716	26	21	to	to	PART
ejpam-5716	26	22	u.	u.	VERB
ejpam-5716	26	23	the	the	DET
ejpam-5716	26	24	closed	closed	ADJ
ejpam-5716	26	25	neighborhood	neighborhood	NOUN
ejpam-5716	26	26	of	of	ADP
ejpam-5716	26	27	u	u	NOUN
ejpam-5716	26	28	is	be	AUX
ejpam-5716	26	29	ng[u	ng[u	PROPN
ejpam-5716	26	30	]	]	X
ejpam-5716	26	31	=	=	SYM
ejpam-5716	26	32	ng(u	ng(u	PROPN
ejpam-5716	26	33	)	)	PUNCT
ejpam-5716	26	34	∪	∪	NOUN
ejpam-5716	26	35	{	{	PUNCT
ejpam-5716	26	36	u	u	NOUN
ejpam-5716	26	37	}	}	PUNCT
ejpam-5716	26	38	.	.	PUNCT
ejpam-5716	27	1	for	for	ADP
ejpam-5716	27	2	any	any	DET
ejpam-5716	27	3	a	a	DET
ejpam-5716	27	4	⊆	⊆	NUM
ejpam-5716	27	5	v	v	NOUN
ejpam-5716	27	6	(	(	PUNCT
ejpam-5716	27	7	g	g	NOUN
ejpam-5716	27	8	)	)	PUNCT
ejpam-5716	27	9	,	,	PUNCT
ejpam-5716	27	10	ng(a	ng(a	X
ejpam-5716	27	11	)	)	PUNCT
ejpam-5716	27	12	=	=	PUNCT
ejpam-5716	27	13	⋃	⋃	NOUN
ejpam-5716	27	14	v∈a	v∈a	NOUN
ejpam-5716	27	15	ng(v	ng(v	PUNCT
ejpam-5716	27	16	)	)	PUNCT
ejpam-5716	27	17	is	be	AUX
ejpam-5716	27	18	called	call	VERB
ejpam-5716	27	19	the	the	DET
ejpam-5716	27	20	open	open	ADJ
ejpam-5716	27	21	neighborhood	neighborhood	NOUN
ejpam-5716	27	22	of	of	ADP
ejpam-5716	27	23	a	a	PRON
ejpam-5716	27	24	and	and	CCONJ
ejpam-5716	27	25	ng[a	ng[a	NOUN
ejpam-5716	27	26	]	]	X
ejpam-5716	27	27	=	=	PUNCT
ejpam-5716	27	28	ng(a	ng(a	X
ejpam-5716	27	29	)	)	PUNCT
ejpam-5716	27	30	∪	∪	ADP
ejpam-5716	27	31	a	a	PRON
ejpam-5716	27	32	is	be	AUX
ejpam-5716	27	33	called	call	VERB
ejpam-5716	27	34	the	the	DET
ejpam-5716	27	35	closed	closed	ADJ
ejpam-5716	27	36	neighborhood	neighborhood	NOUN
ejpam-5716	27	37	of	of	ADP
ejpam-5716	27	38	a.	a.	NOUN
ejpam-5716	27	39	the	the	DET
ejpam-5716	27	40	degree	degree	NOUN
ejpam-5716	27	41	of	of	ADP
ejpam-5716	27	42	vertex	vertex	NOUN
ejpam-5716	27	43	v	v	NOUN
ejpam-5716	27	44	is	be	AUX
ejpam-5716	27	45	degg(v	degg(v	PROPN
ejpam-5716	27	46	)	)	PUNCT
ejpam-5716	27	47	=	=	SYM
ejpam-5716	27	48	|ng(v)|	|ng(v)|	NOUN
ejpam-5716	27	49	.	.	PUNCT
ejpam-5716	28	1	a	a	DET
ejpam-5716	28	2	vertex	vertex	NOUN
ejpam-5716	28	3	v	v	NOUN
ejpam-5716	28	4	of	of	ADP
ejpam-5716	28	5	g	g	PROPN
ejpam-5716	28	6	is	be	AUX
ejpam-5716	28	7	isolated	isolate	VERB
ejpam-5716	28	8	if	if	SCONJ
ejpam-5716	28	9	|ng(v)|	|ng(v)|	NOUN
ejpam-5716	28	10	=	=	SYM
ejpam-5716	28	11	0	0	NUM
ejpam-5716	28	12	.	.	PUNCT
ejpam-5716	29	1	the	the	DET
ejpam-5716	29	2	maximum	maximum	PROPN
ejpam-5716	29	3	degree	degree	NOUN
ejpam-5716	29	4	∆(g	∆(g	NOUN
ejpam-5716	29	5	)	)	PUNCT
ejpam-5716	29	6	of	of	ADP
ejpam-5716	29	7	g	g	PROPN
ejpam-5716	29	8	is	be	AUX
ejpam-5716	29	9	given	give	VERB
ejpam-5716	29	10	by	by	ADP
ejpam-5716	29	11	∆(g	∆(g	NOUN
ejpam-5716	29	12	)	)	PUNCT
ejpam-5716	29	13	=	=	SYM
ejpam-5716	30	1	max{|ng(v)|	max{|ng(v)|	NOUN
ejpam-5716	30	2	:	:	PUNCT
ejpam-5716	30	3	v	v	NUM
ejpam-5716	30	4	∈	∈	PROPN
ejpam-5716	30	5	v	v	NOUN
ejpam-5716	30	6	(	(	PUNCT
ejpam-5716	30	7	g	g	NOUN
ejpam-5716	30	8	)	)	PUNCT
ejpam-5716	30	9	}	}	PUNCT
ejpam-5716	30	10	and	and	CCONJ
ejpam-5716	30	11	the	the	DET
ejpam-5716	30	12	minimum	minimum	NOUN
ejpam-5716	30	13	degree	degree	NOUN
ejpam-5716	30	14	δ(g	δ(g	ADV
ejpam-5716	30	15	)	)	PUNCT
ejpam-5716	30	16	of	of	ADP
ejpam-5716	30	17	g	g	PROPN
ejpam-5716	30	18	is	be	AUX
ejpam-5716	30	19	given	give	VERB
ejpam-5716	30	20	by	by	ADP
ejpam-5716	30	21	δ(g	δ(g	NOUN
ejpam-5716	30	22	)	)	PUNCT
ejpam-5716	30	23	=	=	PUNCT
ejpam-5716	31	1	min{|ng(v)|	min{|ng(v)|	ADP
ejpam-5716	31	2	:	:	PUNCT
ejpam-5716	31	3	v	v	NUM
ejpam-5716	31	4	∈	∈	PROPN
ejpam-5716	31	5	v	v	NOUN
ejpam-5716	31	6	(	(	PUNCT
ejpam-5716	31	7	g	g	NOUN
ejpam-5716	31	8	)	)	PUNCT
ejpam-5716	31	9	}	}	PUNCT
ejpam-5716	31	10	.	.	PUNCT
ejpam-5716	32	1	a	a	DET
ejpam-5716	32	2	vertex	vertex	NOUN
ejpam-5716	32	3	is	be	AUX
ejpam-5716	32	4	called	call	VERB
ejpam-5716	32	5	an	an	DET
ejpam-5716	32	6	endvertex	endvertex	NOUN
ejpam-5716	32	7	if	if	SCONJ
ejpam-5716	32	8	its	its	PRON
ejpam-5716	32	9	degree	degree	NOUN
ejpam-5716	32	10	is	be	AUX
ejpam-5716	32	11	1	1	NUM
ejpam-5716	32	12	.	.	PUNCT
ejpam-5716	33	1	a	a	DET
ejpam-5716	33	2	vertex	vertex	NOUN
ejpam-5716	33	3	is	be	AUX
ejpam-5716	33	4	called	call	VERB
ejpam-5716	33	5	a	a	DET
ejpam-5716	33	6	support	support	NOUN
ejpam-5716	33	7	vertex	vertex	NOUN
ejpam-5716	33	8	if	if	SCONJ
ejpam-5716	33	9	it	it	PRON
ejpam-5716	33	10	is	be	AUX
ejpam-5716	33	11	adjacent	adjacent	ADJ
ejpam-5716	33	12	to	to	ADP
ejpam-5716	33	13	an	an	DET
ejpam-5716	33	14	end	end	NOUN
ejpam-5716	33	15	-	-	PUNCT
ejpam-5716	33	16	vertex	vertex	NOUN
ejpam-5716	33	17	.	.	PUNCT
ejpam-5716	34	1	the	the	DET
ejpam-5716	34	2	i(g	i(g	NOUN
ejpam-5716	34	3	)	)	PUNCT
ejpam-5716	34	4	is	be	AUX
ejpam-5716	34	5	the	the	DET
ejpam-5716	34	6	set	set	NOUN
ejpam-5716	34	7	containing	contain	VERB
ejpam-5716	34	8	all	all	DET
ejpam-5716	34	9	the	the	DET
ejpam-5716	34	10	isolated	isolated	ADJ
ejpam-5716	34	11	vertices	vertex	NOUN
ejpam-5716	34	12	of	of	ADP
ejpam-5716	34	13	g.	g.	PROPN
ejpam-5716	34	14	the	the	DET
ejpam-5716	34	15	open	open	ADJ
ejpam-5716	34	16	hop	hop	NOUN
ejpam-5716	34	17	neighborhood	neighborhood	NOUN
ejpam-5716	34	18	of	of	ADP
ejpam-5716	34	19	a	a	DET
ejpam-5716	34	20	point	point	NOUN
ejpam-5716	34	21	u	u	NOUN
ejpam-5716	34	22	is	be	AUX
ejpam-5716	34	23	the	the	DET
ejpam-5716	34	24	set	set	ADJ
ejpam-5716	34	25	n2	n2	ADJ
ejpam-5716	34	26	g(u	g(u	PROPN
ejpam-5716	34	27	)	)	PUNCT
ejpam-5716	34	28	=	=	PRON
ejpam-5716	34	29	{	{	PUNCT
ejpam-5716	34	30	v	v	NUM
ejpam-5716	34	31	∈	∈	NOUN
ejpam-5716	34	32	v	v	NOUN
ejpam-5716	34	33	(	(	PUNCT
ejpam-5716	34	34	g	g	NOUN
ejpam-5716	34	35	)	)	PUNCT
ejpam-5716	34	36	:	:	PUNCT
ejpam-5716	34	37	dg(v	dg(v	X
ejpam-5716	34	38	,	,	PUNCT
ejpam-5716	34	39	u	u	NOUN
ejpam-5716	34	40	)	)	PUNCT
ejpam-5716	34	41	=	=	SYM
ejpam-5716	34	42	2	2	NUM
ejpam-5716	34	43	}	}	PUNCT
ejpam-5716	34	44	.	.	PUNCT
ejpam-5716	35	1	the	the	DET
ejpam-5716	35	2	closed	closed	ADJ
ejpam-5716	35	3	hop	hop	NOUN
ejpam-5716	35	4	neighborhood	neighborhood	NOUN
ejpam-5716	35	5	of	of	ADP
ejpam-5716	35	6	u	u	NOUN
ejpam-5716	35	7	is	be	AUX
ejpam-5716	35	8	n2	n2	ADJ
ejpam-5716	35	9	g[u	g[u	X
ejpam-5716	35	10	]	]	X
ejpam-5716	35	11	=	=	SYM
ejpam-5716	35	12	n2	n2	ADJ
ejpam-5716	35	13	g(u	g(u	PROPN
ejpam-5716	35	14	)	)	PUNCT
ejpam-5716	35	15	∪	∪	NOUN
ejpam-5716	35	16	{	{	PUNCT
ejpam-5716	35	17	u	u	NOUN
ejpam-5716	35	18	}	}	PUNCT
ejpam-5716	35	19	.	.	PUNCT
ejpam-5716	36	1	for	for	ADP
ejpam-5716	36	2	any	any	DET
ejpam-5716	36	3	a	a	DET
ejpam-5716	36	4	⊆	⊆	NUM
ejpam-5716	36	5	v	v	NOUN
ejpam-5716	36	6	(	(	PUNCT
ejpam-5716	36	7	g	g	NOUN
ejpam-5716	36	8	)	)	PUNCT
ejpam-5716	36	9	,	,	PUNCT
ejpam-5716	36	10	n2	n2	PROPN
ejpam-5716	36	11	g(a	g(a	PROPN
ejpam-5716	36	12	)	)	PUNCT
ejpam-5716	36	13	=	=	NOUN
ejpam-5716	36	14	⋃	⋃	PROPN
ejpam-5716	36	15	v∈a	v∈a	NOUN
ejpam-5716	36	16	n2	n2	ADJ
ejpam-5716	36	17	g(v	g(v	PROPN
ejpam-5716	36	18	)	)	PUNCT
ejpam-5716	36	19	is	be	AUX
ejpam-5716	36	20	called	call	VERB
ejpam-5716	36	21	the	the	DET
ejpam-5716	36	22	open	open	ADJ
ejpam-5716	36	23	hop	hop	NOUN
ejpam-5716	36	24	neighborhood	neighborhood	NOUN
ejpam-5716	36	25	of	of	ADP
ejpam-5716	36	26	a	a	DET
ejpam-5716	36	27	and	and	CCONJ
ejpam-5716	36	28	n2	n2	ADJ
ejpam-5716	36	29	g[a	g[a	NOUN
ejpam-5716	36	30	]	]	X
ejpam-5716	36	31	=	=	SYM
ejpam-5716	36	32	n2	n2	PROPN
ejpam-5716	36	33	g(a)∪a	g(a)∪a	PROPN
ejpam-5716	36	34	is	be	AUX
ejpam-5716	36	35	called	call	VERB
ejpam-5716	36	36	the	the	DET
ejpam-5716	36	37	closed	closed	ADJ
ejpam-5716	36	38	hop	hop	NOUN
ejpam-5716	36	39	neighborhood	neighborhood	NOUN
ejpam-5716	36	40	of	of	ADP
ejpam-5716	36	41	a.	a.	NOUN
ejpam-5716	36	42	the	the	DET
ejpam-5716	36	43	maximum	maximum	ADJ
ejpam-5716	36	44	hop	hop	NOUN
ejpam-5716	36	45	degree	degree	NOUN
ejpam-5716	36	46	and	and	CCONJ
ejpam-5716	36	47	minimum	minimum	ADJ
ejpam-5716	36	48	hop	hop	NOUN
ejpam-5716	36	49	degree	degree	NOUN
ejpam-5716	36	50	of	of	ADP
ejpam-5716	36	51	g	g	NOUN
ejpam-5716	36	52	,	,	PUNCT
ejpam-5716	36	53	denoted	denote	VERB
ejpam-5716	36	54	by	by	ADP
ejpam-5716	36	55	∆h(g	∆h(g	NOUN
ejpam-5716	36	56	)	)	PUNCT
ejpam-5716	36	57	and	and	CCONJ
ejpam-5716	36	58	δh(g	δh(g	NOUN
ejpam-5716	36	59	)	)	PUNCT
ejpam-5716	36	60	,	,	PUNCT
ejpam-5716	36	61	respectively	respectively	ADV
ejpam-5716	36	62	,	,	PUNCT
ejpam-5716	36	63	is	be	AUX
ejpam-5716	36	64	given	give	VERB
ejpam-5716	36	65	by	by	ADP
ejpam-5716	36	66	∆h(g	∆h(g	NOUN
ejpam-5716	36	67	)	)	PUNCT
ejpam-5716	36	68	=	=	SYM
ejpam-5716	36	69	max{|n2	max{|n2	PROPN
ejpam-5716	36	70	g(v)|	g(v)|	NOUN
ejpam-5716	36	71	:	:	PUNCT
ejpam-5716	36	72	v	v	NUM
ejpam-5716	36	73	∈	∈	PROPN
ejpam-5716	36	74	v	v	NOUN
ejpam-5716	36	75	(	(	PUNCT
ejpam-5716	36	76	g	g	NOUN
ejpam-5716	36	77	)	)	PUNCT
ejpam-5716	36	78	}	}	PUNCT
ejpam-5716	36	79	and	and	CCONJ
ejpam-5716	36	80	δh(g	δh(g	NOUN
ejpam-5716	36	81	)	)	PUNCT
ejpam-5716	36	82	=	=	SYM
ejpam-5716	36	83	min{|n2	min{|n2	NOUN
ejpam-5716	36	84	g(v)|	g(v)|	VERB
ejpam-5716	36	85	:	:	PUNCT
ejpam-5716	36	86	v	v	NUM
ejpam-5716	36	87	∈	∈	PROPN
ejpam-5716	36	88	v	v	NOUN
ejpam-5716	36	89	(	(	PUNCT
ejpam-5716	36	90	g	g	NOUN
ejpam-5716	36	91	)	)	PUNCT
ejpam-5716	36	92	}	}	PUNCT
ejpam-5716	36	93	.	.	PUNCT
ejpam-5716	37	1	a	a	DET
ejpam-5716	37	2	set	set	NOUN
ejpam-5716	37	3	s	s	NOUN
ejpam-5716	37	4	⊆	⊆	NUM
ejpam-5716	37	5	v	v	NOUN
ejpam-5716	37	6	(	(	PUNCT
ejpam-5716	37	7	g	g	NOUN
ejpam-5716	37	8	)	)	PUNCT
ejpam-5716	37	9	is	be	AUX
ejpam-5716	37	10	a	a	DET
ejpam-5716	37	11	hop	hop	NOUN
ejpam-5716	37	12	dominating	dominating	NOUN
ejpam-5716	37	13	set	set	NOUN
ejpam-5716	37	14	if	if	SCONJ
ejpam-5716	37	15	n2	n2	ADJ
ejpam-5716	37	16	g[s	g[s	PROPN
ejpam-5716	37	17	]	]	X
ejpam-5716	37	18	=	=	SYM
ejpam-5716	37	19	v	v	NOUN
ejpam-5716	37	20	(	(	PUNCT
ejpam-5716	37	21	g	g	NOUN
ejpam-5716	37	22	)	)	PUNCT
ejpam-5716	37	23	.	.	PUNCT
ejpam-5716	38	1	the	the	DET
ejpam-5716	38	2	minimum	minimum	ADJ
ejpam-5716	38	3	cardinality	cardinality	NOUN
ejpam-5716	38	4	of	of	ADP
ejpam-5716	38	5	a	a	DET
ejpam-5716	38	6	hop	hop	NOUN
ejpam-5716	38	7	dominating	dominating	NOUN
ejpam-5716	38	8	set	set	NOUN
ejpam-5716	38	9	of	of	ADP
ejpam-5716	38	10	a	a	DET
ejpam-5716	38	11	graph	graph	NOUN
ejpam-5716	38	12	g	g	NOUN
ejpam-5716	38	13	,	,	PUNCT
ejpam-5716	38	14	denoted	denote	VERB
ejpam-5716	38	15	by	by	ADP
ejpam-5716	38	16	γh(g	γh(g	NOUN
ejpam-5716	38	17	)	)	PUNCT
ejpam-5716	38	18	,	,	PUNCT
ejpam-5716	38	19	is	be	AUX
ejpam-5716	38	20	called	call	VERB
ejpam-5716	38	21	the	the	DET
ejpam-5716	38	22	hop	hop	NOUN
ejpam-5716	38	23	domination	domination	NOUN
ejpam-5716	38	24	number	number	NOUN
ejpam-5716	38	25	of	of	ADP
ejpam-5716	38	26	g.	g.	PROPN
ejpam-5716	38	27	any	any	DET
ejpam-5716	38	28	hop	hop	NOUN
ejpam-5716	38	29	dominating	dominating	NOUN
ejpam-5716	38	30	set	set	VERB
ejpam-5716	38	31	with	with	ADP
ejpam-5716	38	32	cardinality	cardinality	NOUN
ejpam-5716	38	33	equal	equal	ADJ
ejpam-5716	38	34	to	to	ADP
ejpam-5716	38	35	γh(g	γh(g	NOUN
ejpam-5716	38	36	)	)	PUNCT
ejpam-5716	38	37	is	be	AUX
ejpam-5716	38	38	called	call	VERB
ejpam-5716	38	39	a	a	DET
ejpam-5716	38	40	γh	γh	ADV
ejpam-5716	38	41	-	-	PUNCT
ejpam-5716	38	42	set	set	NOUN
ejpam-5716	38	43	.	.	PUNCT
ejpam-5716	39	1	a	a	DET
ejpam-5716	39	2	set	set	NOUN
ejpam-5716	39	3	s	s	NOUN
ejpam-5716	39	4	⊆	⊆	NUM
ejpam-5716	39	5	v	v	NOUN
ejpam-5716	39	6	(	(	PUNCT
ejpam-5716	39	7	g	g	NOUN
ejpam-5716	39	8	)	)	PUNCT
ejpam-5716	39	9	is	be	AUX
ejpam-5716	39	10	a	a	DET
ejpam-5716	39	11	point	point	NOUN
ejpam-5716	39	12	-	-	PUNCT
ejpam-5716	39	13	wise	wise	ADJ
ejpam-5716	39	14	non	non	ADJ
ejpam-5716	39	15	-	-	ADJ
ejpam-5716	39	16	dominating	dominating	ADJ
ejpam-5716	39	17	set	set	NOUN
ejpam-5716	39	18	of	of	ADP
ejpam-5716	39	19	g	g	PROPN
ejpam-5716	39	20	if	if	SCONJ
ejpam-5716	39	21	for	for	ADP
ejpam-5716	39	22	each	each	PRON
ejpam-5716	39	23	v	v	NUM
ejpam-5716	39	24	∈	∈	PROPN
ejpam-5716	39	25	v	v	NOUN
ejpam-5716	39	26	(	(	PUNCT
ejpam-5716	39	27	g	g	NOUN
ejpam-5716	39	28	)	)	PUNCT
ejpam-5716	39	29	\	\	PROPN
ejpam-5716	40	1	s	s	X
ejpam-5716	40	2	,	,	PUNCT
ejpam-5716	40	3	there	there	PRON
ejpam-5716	40	4	exists	exist	VERB
ejpam-5716	40	5	u	u	PROPN
ejpam-5716	40	6	∈	∈	PROPN
ejpam-5716	40	7	s	s	VERB
ejpam-5716	40	8	such	such	ADJ
ejpam-5716	40	9	that	that	DET
ejpam-5716	40	10	v	v	NOUN
ejpam-5716	40	11	/∈	/∈	PUNCT
ejpam-5716	40	12	ng(u	ng(u	NOUN
ejpam-5716	40	13	)	)	PUNCT
ejpam-5716	40	14	.	.	PUNCT
ejpam-5716	41	1	the	the	DET
ejpam-5716	41	2	smallest	small	ADJ
ejpam-5716	41	3	cardinality	cardinality	NOUN
ejpam-5716	41	4	of	of	ADP
ejpam-5716	41	5	a	a	DET
ejpam-5716	41	6	point	point	NOUN
ejpam-5716	41	7	-	-	PUNCT
ejpam-5716	41	8	wise	wise	ADJ
ejpam-5716	41	9	nondominating	nondominate	VERB
ejpam-5716	41	10	set	set	NOUN
ejpam-5716	41	11	of	of	ADP
ejpam-5716	41	12	g	g	PROPN
ejpam-5716	41	13	is	be	AUX
ejpam-5716	41	14	denoted	denote	VERB
ejpam-5716	41	15	by	by	ADP
ejpam-5716	41	16	pnd(g	pnd(g	PROPN
ejpam-5716	41	17	)	)	PUNCT
ejpam-5716	41	18	.	.	PUNCT
ejpam-5716	42	1	j.	j.	PROPN
ejpam-5716	42	2	anoche	anoche	PROPN
ejpam-5716	42	3	,	,	PUNCT
ejpam-5716	42	4	s.r	s.r	PROPN
ejpam-5716	42	5	.	.	PROPN
ejpam-5716	42	6	canoy	canoy	PROPN
ejpam-5716	42	7	jr	jr	PROPN
ejpam-5716	42	8	.	.	PUNCT
ejpam-5716	42	9	/	/	SYM
ejpam-5716	42	10	eur	eur	PROPN
ejpam-5716	42	11	.	.	PUNCT
ejpam-5716	43	1	j.	j.	PROPN
ejpam-5716	43	2	pure	pure	PROPN
ejpam-5716	43	3	appl	appl	PROPN
ejpam-5716	43	4	.	.	PROPN
ejpam-5716	43	5	math	math	PROPN
ejpam-5716	43	6	,	,	PUNCT
ejpam-5716	43	7	18	18	NUM
ejpam-5716	43	8	(	(	PUNCT
ejpam-5716	43	9	1	1	NUM
ejpam-5716	43	10	)	)	PUNCT
ejpam-5716	43	11	(	(	PUNCT
ejpam-5716	43	12	2025	2025	NUM
ejpam-5716	43	13	)	)	PUNCT
ejpam-5716	43	14	,	,	PUNCT
ejpam-5716	43	15	5716	5716	NUM
ejpam-5716	43	16	3	3	NUM
ejpam-5716	43	17	of	of	ADP
ejpam-5716	43	18	13	13	NUM
ejpam-5716	43	19	let	let	VERB
ejpam-5716	43	20	g	g	NOUN
ejpam-5716	43	21	be	be	AUX
ejpam-5716	43	22	a	a	DET
ejpam-5716	43	23	non	non	ADJ
ejpam-5716	43	24	-	-	ADJ
ejpam-5716	43	25	trivial	trivial	ADJ
ejpam-5716	43	26	graph	graph	NOUN
ejpam-5716	43	27	of	of	ADP
ejpam-5716	43	28	order	order	NOUN
ejpam-5716	43	29	n	n	NOUN
ejpam-5716	43	30	and	and	CCONJ
ejpam-5716	43	31	let	let	VERB
ejpam-5716	43	32	1	1	NUM
ejpam-5716	43	33	≤	≤	NOUN
ejpam-5716	44	1	k	k	X
ejpam-5716	44	2	<	<	X
ejpam-5716	44	3	γh(g	γh(g	NOUN
ejpam-5716	44	4	)	)	PUNCT
ejpam-5716	44	5	.	.	PUNCT
ejpam-5716	45	1	let	let	VERB
ejpam-5716	45	2	s	s	PRON
ejpam-5716	45	3	⊆	⊆	NUM
ejpam-5716	45	4	v	v	NOUN
ejpam-5716	45	5	(	(	PUNCT
ejpam-5716	45	6	g	g	NOUN
ejpam-5716	45	7	)	)	PUNCT
ejpam-5716	45	8	with	with	ADP
ejpam-5716	45	9	cardinality	cardinality	NOUN
ejpam-5716	45	10	|s|	|s|	PROPN
ejpam-5716	45	11	=	=	PROPN
ejpam-5716	45	12	γh(g)−	γh(g)−	PROPN
ejpam-5716	45	13	k.	k.	NOUN
ejpam-5716	46	1	the	the	DET
ejpam-5716	46	2	set	set	PROPN
ejpam-5716	46	3	v	v	NOUN
ejpam-5716	46	4	(	(	PUNCT
ejpam-5716	46	5	g	g	NOUN
ejpam-5716	46	6	)	)	PUNCT
ejpam-5716	46	7	\n2	\n2	VERB
ejpam-5716	46	8	g[s	g[s	PROPN
ejpam-5716	46	9	]	]	PUNCT
ejpam-5716	46	10	is	be	AUX
ejpam-5716	46	11	called	call	VERB
ejpam-5716	46	12	the	the	DET
ejpam-5716	46	13	k	k	ADJ
ejpam-5716	46	14	-	-	PUNCT
ejpam-5716	46	15	hop	hop	ADJ
ejpam-5716	46	16	defect	defect	NOUN
ejpam-5716	46	17	set	set	NOUN
ejpam-5716	46	18	of	of	ADP
ejpam-5716	46	19	s	s	PRON
ejpam-5716	46	20	and	and	CCONJ
ejpam-5716	46	21	the	the	DET
ejpam-5716	46	22	k	k	ADJ
ejpam-5716	46	23	-	-	PUNCT
ejpam-5716	46	24	hop	hop	ADJ
ejpam-5716	46	25	defect	defect	NOUN
ejpam-5716	46	26	of	of	ADP
ejpam-5716	46	27	s	s	PROPN
ejpam-5716	46	28	is	be	AUX
ejpam-5716	46	29	ζhk	ζhk	NOUN
ejpam-5716	46	30	(	(	PUNCT
ejpam-5716	46	31	s	s	X
ejpam-5716	46	32	)	)	PUNCT
ejpam-5716	47	1	=	=	SYM
ejpam-5716	47	2	|v	|v	X
ejpam-5716	47	3	(	(	PUNCT
ejpam-5716	47	4	g	g	NOUN
ejpam-5716	47	5	)	)	PUNCT
ejpam-5716	47	6	\n2	\n2	ADJ
ejpam-5716	47	7	g[s]|	g[s]|	X
ejpam-5716	48	1	=	=	SYM
ejpam-5716	49	1	n−	n−	PROPN
ejpam-5716	49	2	|n2	|n2	PROPN
ejpam-5716	49	3	g[s]|	g[s]|	PROPN
ejpam-5716	49	4	.	.	PUNCT
ejpam-5716	50	1	the	the	DET
ejpam-5716	50	2	minimum	minimum	ADJ
ejpam-5716	50	3	cardinality	cardinality	NOUN
ejpam-5716	50	4	of	of	ADP
ejpam-5716	50	5	a	a	DET
ejpam-5716	50	6	k	k	ADJ
ejpam-5716	50	7	-	-	PUNCT
ejpam-5716	50	8	hop	hop	ADJ
ejpam-5716	50	9	defect	defect	NOUN
ejpam-5716	50	10	set	set	NOUN
ejpam-5716	50	11	in	in	ADP
ejpam-5716	50	12	g	g	NOUN
ejpam-5716	50	13	,	,	PUNCT
ejpam-5716	50	14	denoted	denote	VERB
ejpam-5716	50	15	by	by	ADP
ejpam-5716	50	16	ζhk	ζhk	PROPN
ejpam-5716	50	17	(	(	PUNCT
ejpam-5716	50	18	g	g	NOUN
ejpam-5716	50	19	)	)	PUNCT
ejpam-5716	50	20	,	,	PUNCT
ejpam-5716	50	21	is	be	AUX
ejpam-5716	50	22	called	call	VERB
ejpam-5716	50	23	the	the	DET
ejpam-5716	50	24	k	k	ADJ
ejpam-5716	50	25	-	-	PUNCT
ejpam-5716	50	26	hop	hop	NOUN
ejpam-5716	50	27	domination	domination	NOUN
ejpam-5716	50	28	defect	defect	NOUN
ejpam-5716	50	29	of	of	ADP
ejpam-5716	50	30	g	g	NOUN
ejpam-5716	50	31	,	,	PUNCT
ejpam-5716	51	1	i.e.	i.e.	X
ejpam-5716	51	2	,	,	PUNCT
ejpam-5716	51	3	ζhk	ζhk	NOUN
ejpam-5716	51	4	(	(	PUNCT
ejpam-5716	51	5	g	g	NOUN
ejpam-5716	51	6	)	)	PUNCT
ejpam-5716	51	7	=	=	VERB
ejpam-5716	51	8	min{ζhk	min{ζhk	NOUN
ejpam-5716	51	9	(	(	PUNCT
ejpam-5716	51	10	s	s	NOUN
ejpam-5716	51	11	)	)	PUNCT
ejpam-5716	51	12	:	:	PUNCT
ejpam-5716	51	13	s	s	VERB
ejpam-5716	51	14	⊆	⊆	NUM
ejpam-5716	51	15	v	v	NOUN
ejpam-5716	51	16	(	(	PUNCT
ejpam-5716	51	17	g	g	NOUN
ejpam-5716	51	18	)	)	PUNCT
ejpam-5716	51	19	with	with	ADP
ejpam-5716	51	20	|s|	|s|	PROPN
ejpam-5716	51	21	=	=	SYM
ejpam-5716	51	22	γh(g)−	γh(g)−	PROPN
ejpam-5716	51	23	k	k	NOUN
ejpam-5716	51	24	}	}	PUNCT
ejpam-5716	51	25	.	.	PUNCT
ejpam-5716	52	1	a	a	DET
ejpam-5716	52	2	set	set	NOUN
ejpam-5716	52	3	s	s	NOUN
ejpam-5716	52	4	⊆	⊆	NUM
ejpam-5716	52	5	v	v	NOUN
ejpam-5716	52	6	(	(	PUNCT
ejpam-5716	52	7	g	g	NOUN
ejpam-5716	52	8	)	)	PUNCT
ejpam-5716	52	9	of	of	ADP
ejpam-5716	52	10	cardinality	cardinality	NOUN
ejpam-5716	52	11	γh(g	γh(g	NOUN
ejpam-5716	52	12	)	)	PUNCT
ejpam-5716	52	13	−	−	PROPN
ejpam-5716	52	14	k	k	NOUN
ejpam-5716	52	15	for	for	ADP
ejpam-5716	52	16	which	which	PRON
ejpam-5716	52	17	|v	|v	PROPN
ejpam-5716	52	18	(	(	PUNCT
ejpam-5716	52	19	g	g	NOUN
ejpam-5716	52	20	)	)	PUNCT
ejpam-5716	52	21	\	\	NOUN
ejpam-5716	52	22	n2	n2	ADJ
ejpam-5716	52	23	g[s]|	g[s]|	X
ejpam-5716	52	24	=	=	NOUN
ejpam-5716	52	25	ζhk	ζhk	NOUN
ejpam-5716	52	26	(	(	PUNCT
ejpam-5716	52	27	g	g	NOUN
ejpam-5716	52	28	)	)	PUNCT
ejpam-5716	52	29	is	be	AUX
ejpam-5716	52	30	called	call	VERB
ejpam-5716	52	31	a	a	DET
ejpam-5716	52	32	ζhk	ζhk	NOUN
ejpam-5716	52	33	-set	-set	PUNCT
ejpam-5716	52	34	of	of	ADP
ejpam-5716	52	35	g.	g.	PROPN
ejpam-5716	52	36	thus	thus	ADV
ejpam-5716	52	37	,	,	PUNCT
ejpam-5716	52	38	〈	〈	PROPN
ejpam-5716	52	39	n2	n2	NOUN
ejpam-5716	52	40	g[s	g[s	PROPN
ejpam-5716	52	41	]	]	PUNCT
ejpam-5716	52	42	〉	〉	NOUN
ejpam-5716	52	43	is	be	AUX
ejpam-5716	52	44	an	an	DET
ejpam-5716	52	45	induced	induced	ADJ
ejpam-5716	52	46	subgraph	subgraph	NOUN
ejpam-5716	52	47	of	of	ADP
ejpam-5716	52	48	g	g	PROPN
ejpam-5716	52	49	with	with	ADP
ejpam-5716	52	50	n−	n−	NOUN
ejpam-5716	52	51	ζhk	ζhk	VERB
ejpam-5716	52	52	(	(	PUNCT
ejpam-5716	52	53	g	g	NOUN
ejpam-5716	52	54	)	)	PUNCT
ejpam-5716	52	55	vertices	vertex	NOUN
ejpam-5716	52	56	and	and	CCONJ
ejpam-5716	52	57	hop	hop	NOUN
ejpam-5716	52	58	domination	domination	NOUN
ejpam-5716	52	59	number	number	NOUN
ejpam-5716	52	60	γh(g)−	γh(g)−	PROPN
ejpam-5716	52	61	k.	k.	NOUN
ejpam-5716	52	62	let	let	VERB
ejpam-5716	52	63	g	g	NOUN
ejpam-5716	52	64	and	and	CCONJ
ejpam-5716	52	65	h	h	NOUN
ejpam-5716	52	66	be	be	AUX
ejpam-5716	52	67	undirected	undirected	ADJ
ejpam-5716	52	68	graphs	graph	NOUN
ejpam-5716	52	69	.	.	PUNCT
ejpam-5716	53	1	the	the	DET
ejpam-5716	53	2	join	join	NOUN
ejpam-5716	53	3	g	g	PROPN
ejpam-5716	53	4	+	+	CCONJ
ejpam-5716	53	5	h	h	NOUN
ejpam-5716	53	6	of	of	ADP
ejpam-5716	53	7	g	g	PROPN
ejpam-5716	53	8	and	and	CCONJ
ejpam-5716	53	9	h	h	NOUN
ejpam-5716	53	10	is	be	AUX
ejpam-5716	53	11	the	the	DET
ejpam-5716	53	12	graph	graph	NOUN
ejpam-5716	53	13	with	with	ADP
ejpam-5716	53	14	vertex	vertex	NOUN
ejpam-5716	53	15	-	-	PUNCT
ejpam-5716	53	16	set	set	VERB
ejpam-5716	53	17	v	v	NOUN
ejpam-5716	53	18	(	(	PUNCT
ejpam-5716	53	19	g	g	PROPN
ejpam-5716	53	20	+	+	NOUN
ejpam-5716	53	21	h	h	NOUN
ejpam-5716	53	22	)	)	PUNCT
ejpam-5716	53	23	=	=	NOUN
ejpam-5716	53	24	v	v	X
ejpam-5716	53	25	(	(	PUNCT
ejpam-5716	53	26	g)∪̇v	g)∪̇v	X
ejpam-5716	53	27	(	(	PUNCT
ejpam-5716	53	28	h	h	NOUN
ejpam-5716	53	29	)	)	PUNCT
ejpam-5716	53	30	and	and	CCONJ
ejpam-5716	53	31	edge	edge	NOUN
ejpam-5716	53	32	-	-	PUNCT
ejpam-5716	53	33	set	set	VERB
ejpam-5716	53	34	e(g	e(g	NOUN
ejpam-5716	53	35	+	+	NOUN
ejpam-5716	53	36	h	h	NOUN
ejpam-5716	53	37	)	)	PUNCT
ejpam-5716	53	38	=	=	SYM
ejpam-5716	53	39	e(g)∪̇e(h	e(g)∪̇e(h	PROPN
ejpam-5716	53	40	)	)	PUNCT
ejpam-5716	53	41	∪	∪	NOUN
ejpam-5716	53	42	{	{	PUNCT
ejpam-5716	53	43	uv	uv	NOUN
ejpam-5716	53	44	:	:	PUNCT
ejpam-5716	53	45	u	u	PROPN
ejpam-5716	53	46	∈	∈	PROPN
ejpam-5716	53	47	v	v	ADP
ejpam-5716	53	48	(	(	PUNCT
ejpam-5716	53	49	g	g	NOUN
ejpam-5716	53	50	)	)	PUNCT
ejpam-5716	53	51	,	,	PUNCT
ejpam-5716	53	52	v	v	X
ejpam-5716	53	53	∈	∈	PROPN
ejpam-5716	53	54	v	v	NOUN
ejpam-5716	53	55	(	(	PUNCT
ejpam-5716	53	56	h	h	NOUN
ejpam-5716	53	57	)	)	PUNCT
ejpam-5716	53	58	}	}	PUNCT
ejpam-5716	53	59	.	.	PUNCT
ejpam-5716	54	1	the	the	DET
ejpam-5716	54	2	graph	graph	NOUN
ejpam-5716	54	3	g−	g−	PROPN
ejpam-5716	54	4	v	v	NOUN
ejpam-5716	54	5	is	be	AUX
ejpam-5716	54	6	the	the	DET
ejpam-5716	54	7	graph	graph	NOUN
ejpam-5716	54	8	⟨v	⟨v	PUNCT
ejpam-5716	54	9	(	(	PUNCT
ejpam-5716	54	10	g	g	NOUN
ejpam-5716	54	11	)	)	PUNCT
ejpam-5716	54	12	\	\	NOUN
ejpam-5716	55	1	{	{	PUNCT
ejpam-5716	55	2	v}⟩	v}⟩	NOUN
ejpam-5716	55	3	induced	induce	VERB
ejpam-5716	55	4	by	by	ADP
ejpam-5716	55	5	v	v	NOUN
ejpam-5716	55	6	(	(	PUNCT
ejpam-5716	55	7	g	g	NOUN
ejpam-5716	55	8	)	)	PUNCT
ejpam-5716	55	9	\	\	NOUN
ejpam-5716	55	10	{	{	PUNCT
ejpam-5716	55	11	v	v	NOUN
ejpam-5716	55	12	}	}	PUNCT
ejpam-5716	55	13	and	and	CCONJ
ejpam-5716	55	14	g−	g−	ADJ
ejpam-5716	55	15	{	{	PUNCT
ejpam-5716	55	16	u	u	NOUN
ejpam-5716	55	17	,	,	PUNCT
ejpam-5716	55	18	v	v	NOUN
ejpam-5716	55	19	}	}	PUNCT
ejpam-5716	55	20	=	=	SYM
ejpam-5716	55	21	⟨v	⟨v	X
ejpam-5716	55	22	(	(	PUNCT
ejpam-5716	55	23	g	g	NOUN
ejpam-5716	55	24	)	)	PUNCT
ejpam-5716	55	25	\	\	NOUN
ejpam-5716	55	26	{	{	PUNCT
ejpam-5716	55	27	u	u	NOUN
ejpam-5716	55	28	,	,	PUNCT
ejpam-5716	55	29	v}⟩.	v}⟩.	VERB
ejpam-5716	55	30	3	3	NUM
ejpam-5716	55	31	.	.	PUNCT
ejpam-5716	55	32	results	result	NOUN
ejpam-5716	55	33	theorem	theorem	VERB
ejpam-5716	55	34	1	1	NUM
ejpam-5716	55	35	(	(	PUNCT
ejpam-5716	55	36	[	[	X
ejpam-5716	55	37	16	16	NUM
ejpam-5716	55	38	]	]	PUNCT
ejpam-5716	55	39	)	)	PUNCT
ejpam-5716	55	40	.	.	PUNCT
ejpam-5716	56	1	let	let	VERB
ejpam-5716	56	2	m	m	PRON
ejpam-5716	56	3	and	and	CCONJ
ejpam-5716	56	4	n	n	ADV
ejpam-5716	56	5	be	be	AUX
ejpam-5716	56	6	positive	positive	ADJ
ejpam-5716	56	7	integers	integer	NOUN
ejpam-5716	56	8	.	.	PUNCT
ejpam-5716	57	1	then	then	ADV
ejpam-5716	57	2	each	each	PRON
ejpam-5716	57	3	of	of	ADP
ejpam-5716	57	4	the	the	DET
ejpam-5716	57	5	following	follow	VERB
ejpam-5716	57	6	holds	hold	NOUN
ejpam-5716	57	7	.	.	PUNCT
ejpam-5716	58	1	(	(	PUNCT
ejpam-5716	58	2	i	i	NOUN
ejpam-5716	58	3	)	)	PUNCT
ejpam-5716	58	4	for	for	ADP
ejpam-5716	58	5	a	a	DET
ejpam-5716	58	6	complete	complete	ADJ
ejpam-5716	58	7	graph	graph	NOUN
ejpam-5716	58	8	kn	kn	PROPN
ejpam-5716	58	9	,	,	PUNCT
ejpam-5716	58	10	γh(kn	γh(kn	PROPN
ejpam-5716	58	11	)	)	PUNCT
ejpam-5716	59	1	=	=	PUNCT
ejpam-5716	59	2	n.	n.	NOUN
ejpam-5716	59	3	(	(	PUNCT
ejpam-5716	59	4	ii	ii	PROPN
ejpam-5716	59	5	)	)	PUNCT
ejpam-5716	59	6	for	for	ADP
ejpam-5716	59	7	a	a	DET
ejpam-5716	59	8	complete	complete	ADJ
ejpam-5716	59	9	bipartite	bipartite	NOUN
ejpam-5716	59	10	graph	graph	NOUN
ejpam-5716	59	11	km	km	PROPN
ejpam-5716	59	12	,	,	PUNCT
ejpam-5716	59	13	n	n	CCONJ
ejpam-5716	59	14	,	,	PUNCT
ejpam-5716	59	15	γh(km	γh(km	NOUN
ejpam-5716	59	16	,	,	PUNCT
ejpam-5716	59	17	n	n	CCONJ
ejpam-5716	59	18	)	)	PUNCT
ejpam-5716	59	19	=	=	SYM
ejpam-5716	59	20	2	2	X
ejpam-5716	59	21	.	.	PUNCT
ejpam-5716	59	22	(	(	PUNCT
ejpam-5716	59	23	iii	iii	NOUN
ejpam-5716	59	24	)	)	PUNCT
ejpam-5716	59	25	for	for	ADP
ejpam-5716	59	26	a	a	DET
ejpam-5716	59	27	path	path	NOUN
ejpam-5716	59	28	pn	pn	NOUN
ejpam-5716	59	29	on	on	ADP
ejpam-5716	59	30	n	n	PRON
ejpam-5716	59	31	vertices	vertex	NOUN
ejpam-5716	59	32	,	,	PUNCT
ejpam-5716	59	33	we	we	PRON
ejpam-5716	59	34	have	have	VERB
ejpam-5716	59	35	γh(pn	γh(pn	PRON
ejpam-5716	59	36	)	)	PUNCT
ejpam-5716	59	37	=	=	PUNCT
ejpam-5716	60	1			NOUN
ejpam-5716	60	2	2r	2r	NUM
ejpam-5716	60	3	if	if	SCONJ
ejpam-5716	60	4	n	n	NOUN
ejpam-5716	60	5	=	=	SYM
ejpam-5716	60	6	6r	6r	NUM
ejpam-5716	60	7	2r	2r	NUM
ejpam-5716	61	1	+	+	CCONJ
ejpam-5716	61	2	1	1	NUM
ejpam-5716	61	3	if	if	SCONJ
ejpam-5716	61	4	n	n	ADV
ejpam-5716	61	5	=	=	SYM
ejpam-5716	62	1	6r	6r	NUM
ejpam-5716	62	2	+	+	CCONJ
ejpam-5716	62	3	1	1	NUM
ejpam-5716	62	4	2r	2r	NUM
ejpam-5716	62	5	+	+	CCONJ
ejpam-5716	62	6	2	2	NUM
ejpam-5716	62	7	if	if	SCONJ
ejpam-5716	62	8	n	n	NOUN
ejpam-5716	62	9	=	=	SYM
ejpam-5716	62	10	6r	6r	NUM
ejpam-5716	63	1	+	+	SYM
ejpam-5716	63	2	s	s	X
ejpam-5716	63	3	;	;	PUNCT
ejpam-5716	63	4	2	2	NUM
ejpam-5716	63	5	≤	≤	NOUN
ejpam-5716	63	6	s	s	PART
ejpam-5716	63	7	≤	≤	NUM
ejpam-5716	63	8	5	5	NUM
ejpam-5716	63	9	.	.	PUNCT
ejpam-5716	64	1	(	(	PUNCT
ejpam-5716	64	2	iv	iv	X
ejpam-5716	64	3	)	)	PUNCT
ejpam-5716	64	4	for	for	ADP
ejpam-5716	64	5	a	a	DET
ejpam-5716	64	6	cycle	cycle	NOUN
ejpam-5716	64	7	cn	cn	NOUN
ejpam-5716	64	8	on	on	ADP
ejpam-5716	64	9	n	n	PRON
ejpam-5716	64	10	vertices	vertex	NOUN
ejpam-5716	64	11	,	,	PUNCT
ejpam-5716	64	12	we	we	PRON
ejpam-5716	64	13	have	have	VERB
ejpam-5716	64	14	γh(cn	γh(cn	NUM
ejpam-5716	64	15	)	)	PUNCT
ejpam-5716	65	1	=	=	PUNCT
ejpam-5716	66	1			NOUN
ejpam-5716	66	2	2r	2r	NUM
ejpam-5716	66	3	if	if	SCONJ
ejpam-5716	66	4	n	n	NOUN
ejpam-5716	66	5	=	=	SYM
ejpam-5716	66	6	6r	6r	NUM
ejpam-5716	66	7	2r	2r	NUM
ejpam-5716	67	1	+	+	CCONJ
ejpam-5716	67	2	1	1	NUM
ejpam-5716	67	3	if	if	SCONJ
ejpam-5716	67	4	n	n	ADV
ejpam-5716	67	5	=	=	SYM
ejpam-5716	68	1	6r	6r	NUM
ejpam-5716	68	2	+	+	CCONJ
ejpam-5716	68	3	1	1	NUM
ejpam-5716	68	4	2r	2r	NUM
ejpam-5716	68	5	+	+	CCONJ
ejpam-5716	68	6	2	2	NUM
ejpam-5716	68	7	if	if	SCONJ
ejpam-5716	68	8	n	n	NOUN
ejpam-5716	68	9	=	=	SYM
ejpam-5716	68	10	6r	6r	NUM
ejpam-5716	69	1	+	+	SYM
ejpam-5716	69	2	s	s	X
ejpam-5716	69	3	;	;	PUNCT
ejpam-5716	69	4	2	2	NUM
ejpam-5716	69	5	≤	≤	NOUN
ejpam-5716	69	6	s	s	PART
ejpam-5716	69	7	≤	≤	NUM
ejpam-5716	69	8	5	5	NUM
ejpam-5716	69	9	.	.	PUNCT
ejpam-5716	70	1	(	(	PUNCT
ejpam-5716	70	2	v	v	NOUN
ejpam-5716	70	3	)	)	PUNCT
ejpam-5716	70	4	γh(wn	γh(wn	PROPN
ejpam-5716	70	5	)	)	PUNCT
ejpam-5716	71	1	=	=	SYM
ejpam-5716	71	2	3	3	NUM
ejpam-5716	71	3	where	where	SCONJ
ejpam-5716	71	4	wn	wn	PROPN
ejpam-5716	71	5	is	be	AUX
ejpam-5716	71	6	a	a	DET
ejpam-5716	71	7	wheel	wheel	NOUN
ejpam-5716	71	8	with	with	ADP
ejpam-5716	71	9	n	n	NOUN
ejpam-5716	71	10	spokes	spoke	NOUN
ejpam-5716	71	11	.	.	PUNCT
ejpam-5716	72	1	(	(	PUNCT
ejpam-5716	72	2	vi	vi	NOUN
ejpam-5716	72	3	)	)	PUNCT
ejpam-5716	72	4	γh(p	γh(p	PUNCT
ejpam-5716	72	5	)	)	PUNCT
ejpam-5716	73	1	=	=	SYM
ejpam-5716	73	2	2	2	NUM
ejpam-5716	73	3	where	where	SCONJ
ejpam-5716	73	4	p	p	NOUN
ejpam-5716	73	5	denotes	denote	VERB
ejpam-5716	73	6	the	the	DET
ejpam-5716	73	7	petersen	petersen	PROPN
ejpam-5716	73	8	graph	graph	NOUN
ejpam-5716	73	9	.	.	PUNCT
ejpam-5716	73	10	theorem	theorem	NOUN
ejpam-5716	73	11	2	2	NUM
ejpam-5716	73	12	.	.	PUNCT
ejpam-5716	74	1	[	[	X
ejpam-5716	74	2	8	8	NUM
ejpam-5716	74	3	]	]	PUNCT
ejpam-5716	74	4	let	let	VERB
ejpam-5716	74	5	g	g	NOUN
ejpam-5716	74	6	and	and	CCONJ
ejpam-5716	74	7	h	h	NOUN
ejpam-5716	74	8	be	be	VERB
ejpam-5716	74	9	any	any	DET
ejpam-5716	74	10	two	two	NUM
ejpam-5716	74	11	graphs	graph	NOUN
ejpam-5716	74	12	of	of	ADP
ejpam-5716	74	13	orders	order	NOUN
ejpam-5716	74	14	m	m	VERB
ejpam-5716	74	15	and	and	CCONJ
ejpam-5716	74	16	n	n	CCONJ
ejpam-5716	74	17	,	,	PUNCT
ejpam-5716	74	18	respectively	respectively	ADV
ejpam-5716	74	19	.	.	PUNCT
ejpam-5716	75	1	then	then	ADV
ejpam-5716	75	2	γh(g+h	γh(g+h	NUM
ejpam-5716	75	3	)	)	PUNCT
ejpam-5716	75	4	=	=	SYM
ejpam-5716	75	5	pnd(g	pnd(g	PROPN
ejpam-5716	75	6	)	)	PUNCT
ejpam-5716	75	7	+	+	NUM
ejpam-5716	75	8	pnd(h	pnd(h	PROPN
ejpam-5716	75	9	)	)	PUNCT
ejpam-5716	75	10	.	.	PUNCT
ejpam-5716	76	1	in	in	ADP
ejpam-5716	76	2	particular	particular	ADJ
ejpam-5716	76	3	,	,	PUNCT
ejpam-5716	76	4	(	(	PUNCT
ejpam-5716	76	5	i	i	NOUN
ejpam-5716	76	6	)	)	PUNCT
ejpam-5716	76	7	γh(g+h	γh(g+h	PROPN
ejpam-5716	76	8	)	)	PUNCT
ejpam-5716	76	9	=	=	PUNCT
ejpam-5716	77	1	m+	m+	NUM
ejpam-5716	77	2	n	n	NOUN
ejpam-5716	77	3	if	if	SCONJ
ejpam-5716	77	4	g	g	PROPN
ejpam-5716	77	5	and	and	CCONJ
ejpam-5716	77	6	h	h	NOUN
ejpam-5716	77	7	are	be	AUX
ejpam-5716	77	8	complete	complete	ADJ
ejpam-5716	77	9	;	;	PUNCT
ejpam-5716	77	10	(	(	PUNCT
ejpam-5716	77	11	ii	ii	NOUN
ejpam-5716	77	12	)	)	PUNCT
ejpam-5716	77	13	γh(g+h	γh(g+h	PROPN
ejpam-5716	77	14	)	)	PUNCT
ejpam-5716	77	15	=	=	SYM
ejpam-5716	77	16	2	2	NUM
ejpam-5716	77	17	if	if	SCONJ
ejpam-5716	77	18	g	g	PROPN
ejpam-5716	77	19	and	and	CCONJ
ejpam-5716	77	20	h	h	NOUN
ejpam-5716	77	21	have	have	VERB
ejpam-5716	77	22	isolated	isolate	VERB
ejpam-5716	77	23	vertices	vertex	NOUN
ejpam-5716	77	24	;	;	PUNCT
ejpam-5716	77	25	j.	j.	PROPN
ejpam-5716	77	26	anoche	anoche	PROPN
ejpam-5716	77	27	,	,	PUNCT
ejpam-5716	77	28	s.r	s.r	PROPN
ejpam-5716	77	29	.	.	PROPN
ejpam-5716	77	30	canoy	canoy	PROPN
ejpam-5716	77	31	jr	jr	PROPN
ejpam-5716	77	32	.	.	PUNCT
ejpam-5716	77	33	/	/	SYM
ejpam-5716	77	34	eur	eur	PROPN
ejpam-5716	77	35	.	.	PUNCT
ejpam-5716	78	1	j.	j.	PROPN
ejpam-5716	78	2	pure	pure	PROPN
ejpam-5716	78	3	appl	appl	PROPN
ejpam-5716	78	4	.	.	PROPN
ejpam-5716	78	5	math	math	PROPN
ejpam-5716	78	6	,	,	PUNCT
ejpam-5716	78	7	18	18	NUM
ejpam-5716	78	8	(	(	PUNCT
ejpam-5716	78	9	1	1	NUM
ejpam-5716	78	10	)	)	PUNCT
ejpam-5716	78	11	(	(	PUNCT
ejpam-5716	78	12	2025	2025	NUM
ejpam-5716	78	13	)	)	PUNCT
ejpam-5716	78	14	,	,	PUNCT
ejpam-5716	78	15	5716	5716	NUM
ejpam-5716	78	16	4	4	NUM
ejpam-5716	78	17	of	of	ADP
ejpam-5716	78	18	13	13	NUM
ejpam-5716	78	19	(	(	PUNCT
ejpam-5716	78	20	iii	iii	NOUN
ejpam-5716	78	21	)	)	PUNCT
ejpam-5716	78	22	γh(g+h	γh(g+h	PROPN
ejpam-5716	78	23	)	)	PUNCT
ejpam-5716	78	24	=	=	SYM
ejpam-5716	78	25	1	1	NUM
ejpam-5716	78	26	+	+	NUM
ejpam-5716	78	27	pnd(h	pnd(h	NUM
ejpam-5716	78	28	)	)	PUNCT
ejpam-5716	79	1	if	if	SCONJ
ejpam-5716	79	2	g	g	PROPN
ejpam-5716	79	3	=	=	SYM
ejpam-5716	79	4	k1	k1	PROPN
ejpam-5716	79	5	;	;	PUNCT
ejpam-5716	79	6	(	(	PUNCT
ejpam-5716	79	7	iv	iv	X
ejpam-5716	79	8	)	)	PUNCT
ejpam-5716	79	9	γh(g+h	γh(g+h	PROPN
ejpam-5716	79	10	)	)	PUNCT
ejpam-5716	79	11	=	=	SYM
ejpam-5716	79	12	4	4	NUM
ejpam-5716	79	13	if	if	SCONJ
ejpam-5716	79	14	g	g	NOUN
ejpam-5716	79	15	=	=	VERB
ejpam-5716	79	16	pm	pm	NOUN
ejpam-5716	79	17	and	and	CCONJ
ejpam-5716	79	18	h	h	NOUN
ejpam-5716	79	19	=	=	NOUN
ejpam-5716	79	20	pn	pn	PROPN
ejpam-5716	79	21	(	(	PUNCT
ejpam-5716	79	22	m	m	PROPN
ejpam-5716	79	23	,	,	PUNCT
ejpam-5716	79	24	n	n	PRON
ejpam-5716	79	25	≥	≥	NOUN
ejpam-5716	79	26	2	2	NUM
ejpam-5716	79	27	)	)	PUNCT
ejpam-5716	79	28	;	;	PUNCT
ejpam-5716	79	29	and	and	CCONJ
ejpam-5716	79	30	(	(	PUNCT
ejpam-5716	79	31	v	v	NOUN
ejpam-5716	79	32	)	)	PUNCT
ejpam-5716	79	33	γh(g+h	γh(g+h	PROPN
ejpam-5716	79	34	)	)	PUNCT
ejpam-5716	79	35	=	=	SYM
ejpam-5716	79	36	4	4	NUM
ejpam-5716	79	37	if	if	SCONJ
ejpam-5716	79	38	g	g	NOUN
ejpam-5716	79	39	=	=	NOUN
ejpam-5716	79	40	cm	cm	NOUN
ejpam-5716	79	41	and	and	CCONJ
ejpam-5716	79	42	h	h	NOUN
ejpam-5716	80	1	=	=	SYM
ejpam-5716	80	2	cn	cn	PROPN
ejpam-5716	80	3	(	(	PUNCT
ejpam-5716	80	4	mn	mn	PROPN
ejpam-5716	80	5	≥	≥	PROPN
ejpam-5716	80	6	4	4	NUM
ejpam-5716	80	7	)	)	PUNCT
ejpam-5716	80	8	.	.	PUNCT
ejpam-5716	81	1	theorem	theorem	NOUN
ejpam-5716	81	2	3	3	X
ejpam-5716	81	3	.	.	PUNCT
ejpam-5716	82	1	let	let	VERB
ejpam-5716	82	2	g	g	PRON
ejpam-5716	82	3	be	be	AUX
ejpam-5716	82	4	a	a	DET
ejpam-5716	82	5	graph	graph	NOUN
ejpam-5716	82	6	with	with	ADP
ejpam-5716	82	7	i(g	i(g	NOUN
ejpam-5716	82	8	)	)	PUNCT
ejpam-5716	83	1	̸=	̸=	NOUN
ejpam-5716	83	2	∅	∅	NOUN
ejpam-5716	83	3	and	and	CCONJ
ejpam-5716	83	4	suppose	suppose	VERB
ejpam-5716	83	5	|i(g)|	|i(g)|	NOUN
ejpam-5716	83	6	=	=	PROPN
ejpam-5716	83	7	r.	r.	PROPN
ejpam-5716	83	8	then	then	ADV
ejpam-5716	83	9	ζhj	ζhj	VERB
ejpam-5716	83	10	(	(	PUNCT
ejpam-5716	83	11	g	g	NOUN
ejpam-5716	83	12	)	)	PUNCT
ejpam-5716	83	13	=	=	SYM
ejpam-5716	83	14	j	j	PROPN
ejpam-5716	83	15	for	for	ADP
ejpam-5716	83	16	every	every	DET
ejpam-5716	83	17	j	j	PROPN
ejpam-5716	83	18	∈	∈	PROPN
ejpam-5716	84	1	[	[	X
ejpam-5716	84	2	r	r	X
ejpam-5716	84	3	]	]	X
ejpam-5716	84	4	=	=	PUNCT
ejpam-5716	84	5	{	{	PUNCT
ejpam-5716	84	6	1	1	NUM
ejpam-5716	84	7	,	,	PUNCT
ejpam-5716	84	8	2	2	NUM
ejpam-5716	84	9	,	,	PUNCT
ejpam-5716	84	10	·	·	PUNCT
ejpam-5716	84	11	·	·	PUNCT
ejpam-5716	84	12	·	·	PUNCT
ejpam-5716	84	13	,	,	PUNCT
ejpam-5716	84	14	r	r	NOUN
ejpam-5716	84	15	}	}	PUNCT
ejpam-5716	84	16	and	and	CCONJ
ejpam-5716	84	17	ζhk	ζhk	NOUN
ejpam-5716	84	18	(	(	PUNCT
ejpam-5716	84	19	g	g	NOUN
ejpam-5716	84	20	)	)	PUNCT
ejpam-5716	84	21	=	=	SYM
ejpam-5716	84	22	r+ζhk−r(g	r+ζhk−r(g	ADV
ejpam-5716	84	23	′	′	NUM
ejpam-5716	84	24	)	)	PUNCT
ejpam-5716	84	25	for	for	ADP
ejpam-5716	84	26	every	every	DET
ejpam-5716	84	27	k	k	PROPN
ejpam-5716	84	28	∈	∈	PROPN
ejpam-5716	84	29	{	{	PUNCT
ejpam-5716	84	30	r+1	r+1	PROPN
ejpam-5716	84	31	,	,	PUNCT
ejpam-5716	84	32	·	·	PUNCT
ejpam-5716	84	33	·	·	PUNCT
ejpam-5716	84	34	·	·	PUNCT
ejpam-5716	84	35	,	,	PUNCT
ejpam-5716	84	36	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	84	37	}	}	PUNCT
ejpam-5716	84	38	,	,	PUNCT
ejpam-5716	84	39	where	where	SCONJ
ejpam-5716	84	40	g′	g′	NOUN
ejpam-5716	84	41	=	=	SYM
ejpam-5716	84	42	⟨v	⟨v	PUNCT
ejpam-5716	84	43	(	(	PUNCT
ejpam-5716	84	44	g	g	NOUN
ejpam-5716	84	45	)	)	PUNCT
ejpam-5716	84	46	\	\	NOUN
ejpam-5716	84	47	i(g)⟩.	i(g)⟩.	VERB
ejpam-5716	84	48	proof	proof	NOUN
ejpam-5716	84	49	.	.	PUNCT
ejpam-5716	85	1	let	let	VERB
ejpam-5716	85	2	i(g	i(g	NOUN
ejpam-5716	85	3	)	)	PUNCT
ejpam-5716	86	1	=	=	PRON
ejpam-5716	86	2	{	{	PUNCT
ejpam-5716	86	3	v1	v1	PROPN
ejpam-5716	86	4	,	,	PUNCT
ejpam-5716	86	5	v2	v2	PROPN
ejpam-5716	86	6	,	,	PUNCT
ejpam-5716	86	7	·	·	PUNCT
ejpam-5716	86	8	·	·	PUNCT
ejpam-5716	86	9	·	·	PUNCT
ejpam-5716	86	10	,	,	PUNCT
ejpam-5716	86	11	vr	vr	NOUN
ejpam-5716	86	12	}	}	PUNCT
ejpam-5716	86	13	and	and	CCONJ
ejpam-5716	86	14	let	let	VERB
ejpam-5716	86	15	s	s	PRON
ejpam-5716	86	16	be	be	AUX
ejpam-5716	86	17	a	a	DET
ejpam-5716	86	18	γh	γh	ADV
ejpam-5716	86	19	-	-	PUNCT
ejpam-5716	86	20	set	set	NOUN
ejpam-5716	86	21	in	in	ADP
ejpam-5716	86	22	g.	g.	PROPN
ejpam-5716	86	23	then	then	ADV
ejpam-5716	86	24	i(g	i(g	ADV
ejpam-5716	86	25	)	)	PUNCT
ejpam-5716	87	1	⊆	⊆	NUM
ejpam-5716	87	2	s.	s.	PROPN
ejpam-5716	87	3	let	let	VERB
ejpam-5716	87	4	j	j	PROPN
ejpam-5716	87	5	∈	∈	PROPN
ejpam-5716	88	1	[	[	X
ejpam-5716	88	2	r	r	X
ejpam-5716	88	3	]	]	PUNCT
ejpam-5716	88	4	.	.	PUNCT
ejpam-5716	89	1	then	then	ADV
ejpam-5716	89	2	d	d	X
ejpam-5716	89	3	=	=	SYM
ejpam-5716	89	4	s	s	PART
ejpam-5716	89	5	\	\	X
ejpam-5716	89	6	{	{	PUNCT
ejpam-5716	89	7	v1	v1	NOUN
ejpam-5716	89	8	,	,	PUNCT
ejpam-5716	89	9	v2	v2	PROPN
ejpam-5716	89	10	,	,	PUNCT
ejpam-5716	89	11	·	·	PUNCT
ejpam-5716	89	12	·	·	PUNCT
ejpam-5716	89	13	·	·	PUNCT
ejpam-5716	89	14	,	,	PUNCT
ejpam-5716	89	15	vj	vj	INTJ
ejpam-5716	89	16	}	}	PUNCT
ejpam-5716	89	17	is	be	AUX
ejpam-5716	89	18	a	a	DET
ejpam-5716	89	19	ζhj	ζhj	NOUN
ejpam-5716	89	20	-set	-set	ADJ
ejpam-5716	89	21	in	in	ADP
ejpam-5716	89	22	g	g	PROPN
ejpam-5716	89	23	and	and	CCONJ
ejpam-5716	89	24	|n2	|n2	PROPN
ejpam-5716	89	25	g[d]|	g[d]|	PROPN
ejpam-5716	89	26	=	=	SYM
ejpam-5716	89	27	|n2	|n2	PROPN
ejpam-5716	89	28	g[s]|	g[s]|	PROPN
ejpam-5716	89	29	−	−	PROPN
ejpam-5716	89	30	|n2	|n2	PROPN
ejpam-5716	89	31	g[{v1	g[{v1	PROPN
ejpam-5716	89	32	,	,	PUNCT
ejpam-5716	89	33	v2	v2	PROPN
ejpam-5716	89	34	,	,	PUNCT
ejpam-5716	89	35	·	·	PUNCT
ejpam-5716	89	36	·	·	PUNCT
ejpam-5716	89	37	·	·	PUNCT
ejpam-5716	89	38	,	,	PUNCT
ejpam-5716	89	39	vj}]|	vj}]|	NOUN
ejpam-5716	89	40	=	=	SYM
ejpam-5716	89	41	|v	|v	PROPN
ejpam-5716	89	42	(	(	PUNCT
ejpam-5716	89	43	g)|	g)|	PROPN
ejpam-5716	89	44	−	−	PROPN
ejpam-5716	89	45	j.	j.	PROPN
ejpam-5716	89	46	hence	hence	PROPN
ejpam-5716	89	47	,	,	PUNCT
ejpam-5716	89	48	ζhj	ζhj	NOUN
ejpam-5716	89	49	(	(	PUNCT
ejpam-5716	89	50	g	g	NOUN
ejpam-5716	89	51	)	)	PUNCT
ejpam-5716	90	1	=	=	SYM
ejpam-5716	90	2	|v	|v	PROPN
ejpam-5716	90	3	(	(	PUNCT
ejpam-5716	90	4	g)|	g)|	INTJ
ejpam-5716	90	5	−	−	PROPN
ejpam-5716	90	6	(	(	PUNCT
ejpam-5716	90	7	|v	|v	PROPN
ejpam-5716	90	8	(	(	PUNCT
ejpam-5716	90	9	g)|	g)|	PROPN
ejpam-5716	90	10	−	−	PROPN
ejpam-5716	90	11	j	j	PROPN
ejpam-5716	90	12	)	)	PUNCT
ejpam-5716	90	13	=	=	PUNCT
ejpam-5716	91	1	j.	j.	PROPN
ejpam-5716	91	2	next	next	ADV
ejpam-5716	91	3	,	,	PUNCT
ejpam-5716	91	4	let	let	VERB
ejpam-5716	91	5	k	k	PROPN
ejpam-5716	91	6	∈	∈	PROPN
ejpam-5716	91	7	{	{	PUNCT
ejpam-5716	91	8	r+1	r+1	PROPN
ejpam-5716	91	9	,	,	PUNCT
ejpam-5716	91	10	·	·	PUNCT
ejpam-5716	91	11	·	·	PUNCT
ejpam-5716	91	12	·	·	PUNCT
ejpam-5716	91	13	,	,	PUNCT
ejpam-5716	91	14	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	91	15	}	}	PUNCT
ejpam-5716	91	16	.	.	PUNCT
ejpam-5716	92	1	then	then	ADV
ejpam-5716	92	2	s0	s0	PROPN
ejpam-5716	92	3	=	=	PUNCT
ejpam-5716	92	4	s\i(g	s\i(g	PROPN
ejpam-5716	92	5	)	)	PUNCT
ejpam-5716	92	6	is	be	AUX
ejpam-5716	92	7	γh	γh	ADV
ejpam-5716	92	8	-	-	PUNCT
ejpam-5716	92	9	set	set	VERB
ejpam-5716	92	10	ing′	ing′	VERB
ejpam-5716	92	11	=	=	SYM
ejpam-5716	92	12	⟨v	⟨v	PUNCT
ejpam-5716	92	13	(	(	PUNCT
ejpam-5716	92	14	g	g	NOUN
ejpam-5716	92	15	)	)	PUNCT
ejpam-5716	92	16	\	\	PUNCT
ejpam-5716	92	17	i(g)⟩.	i(g)⟩.	VERB
ejpam-5716	92	18	hence	hence	ADV
ejpam-5716	92	19	,	,	PUNCT
ejpam-5716	92	20	γh(g	γh(g	PUNCT
ejpam-5716	92	21	′	′	NUM
ejpam-5716	92	22	)	)	PUNCT
ejpam-5716	92	23	=	=	SYM
ejpam-5716	92	24	γh(g)−r	γh(g)−r	NOUN
ejpam-5716	92	25	.	.	PUNCT
ejpam-5716	93	1	since	since	SCONJ
ejpam-5716	93	2	k	k	PROPN
ejpam-5716	93	3	≤	≤	PROPN
ejpam-5716	93	4	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	93	5	,	,	PUNCT
ejpam-5716	93	6	k−r	k−r	PROPN
ejpam-5716	93	7	≤	≤	PUNCT
ejpam-5716	93	8	γh(g)−(r+1	γh(g)−(r+1	NOUN
ejpam-5716	93	9	)	)	PUNCT
ejpam-5716	94	1	<	<	X
ejpam-5716	94	2	γh(g)−r	γh(g)−r	NOUN
ejpam-5716	94	3	.	.	PUNCT
ejpam-5716	95	1	let	let	VERB
ejpam-5716	95	2	s′	s′	PROPN
ejpam-5716	95	3	be	be	AUX
ejpam-5716	95	4	a	a	DET
ejpam-5716	95	5	ζhk−r	ζhk−r	NOUN
ejpam-5716	95	6	-	-	PUNCT
ejpam-5716	95	7	set	set	VERB
ejpam-5716	95	8	in	in	ADP
ejpam-5716	95	9	g′.	g′.	PROPN
ejpam-5716	95	10	then	then	ADV
ejpam-5716	95	11	|s′|	|s′|	NOUN
ejpam-5716	95	12	=	=	SYM
ejpam-5716	95	13	(	(	PUNCT
ejpam-5716	95	14	γh(g)−r)−(k−r	γh(g)−r)−(k−r	NOUN
ejpam-5716	95	15	)	)	PUNCT
ejpam-5716	96	1	=	=	PUNCT
ejpam-5716	96	2	γh(g)−k	γh(g)−k	NOUN
ejpam-5716	96	3	and	and	CCONJ
ejpam-5716	96	4	ζhk−r(g	ζhk−r(g	PROPN
ejpam-5716	96	5	′	′	NUM
ejpam-5716	96	6	)	)	PUNCT
ejpam-5716	97	1	=	=	SYM
ejpam-5716	97	2	|v	|v	PROPN
ejpam-5716	97	3	(	(	PUNCT
ejpam-5716	97	4	g′)|−	g′)|−	PROPN
ejpam-5716	97	5	|n2	|n2	PROPN
ejpam-5716	97	6	g′	g′	PROPN
ejpam-5716	98	1	[	[	X
ejpam-5716	98	2	s′]|	s′]|	X
ejpam-5716	98	3	=	=	SYM
ejpam-5716	98	4	(	(	PUNCT
ejpam-5716	98	5	|v	|v	X
ejpam-5716	98	6	(	(	PUNCT
ejpam-5716	98	7	g)|	g)|	INTJ
ejpam-5716	98	8	−	−	NOUN
ejpam-5716	98	9	r	r	NOUN
ejpam-5716	98	10	)	)	PUNCT
ejpam-5716	98	11	−	−	PROPN
ejpam-5716	98	12	|n2	|n2	PROPN
ejpam-5716	98	13	g[s	g[s	PROPN
ejpam-5716	98	14	′]|	′]|	NOUN
ejpam-5716	98	15	.	.	PUNCT
ejpam-5716	99	1	this	this	PRON
ejpam-5716	99	2	implies	imply	VERB
ejpam-5716	99	3	that	that	SCONJ
ejpam-5716	99	4	|v	|v	PROPN
ejpam-5716	99	5	(	(	PUNCT
ejpam-5716	99	6	g)|	g)|	PROPN
ejpam-5716	99	7	−	−	PROPN
ejpam-5716	99	8	|n2	|n2	PROPN
ejpam-5716	99	9	g[s	g[s	PROPN
ejpam-5716	99	10	′]|	′]|	NOUN
ejpam-5716	100	1	=	=	SYM
ejpam-5716	100	2	r	r	NOUN
ejpam-5716	100	3	+	+	NUM
ejpam-5716	100	4	ζhk−r(g	ζhk−r(g	PROPN
ejpam-5716	100	5	′	′	NUM
ejpam-5716	100	6	)	)	PUNCT
ejpam-5716	100	7	.	.	PUNCT
ejpam-5716	101	1	therefore	therefore	ADV
ejpam-5716	101	2	,	,	PUNCT
ejpam-5716	101	3	since	since	SCONJ
ejpam-5716	101	4	s′	s′	ADJ
ejpam-5716	101	5	is	be	AUX
ejpam-5716	101	6	also	also	ADV
ejpam-5716	101	7	a	a	DET
ejpam-5716	101	8	ζhk	ζhk	NOUN
ejpam-5716	101	9	-set	-set	VERB
ejpam-5716	101	10	in	in	ADP
ejpam-5716	101	11	g	g	PROPN
ejpam-5716	101	12	,	,	PUNCT
ejpam-5716	101	13	ζhj	ζhj	NOUN
ejpam-5716	101	14	(	(	PUNCT
ejpam-5716	101	15	g	g	NOUN
ejpam-5716	101	16	)	)	PUNCT
ejpam-5716	101	17	=	=	SYM
ejpam-5716	102	1	r	r	NOUN
ejpam-5716	102	2	+	+	NUM
ejpam-5716	102	3	ζhk−r(g	ζhk−r(g	PROPN
ejpam-5716	102	4	′	′	NUM
ejpam-5716	102	5	)	)	PUNCT
ejpam-5716	102	6	.	.	PUNCT
ejpam-5716	103	1	remark	remark	PROPN
ejpam-5716	103	2	1	1	NUM
ejpam-5716	103	3	.	.	PUNCT
ejpam-5716	104	1	a	a	DET
ejpam-5716	104	2	ζhk	ζhk	NOUN
ejpam-5716	104	3	-set	-set	PUNCT
ejpam-5716	104	4	of	of	ADP
ejpam-5716	104	5	a	a	DET
ejpam-5716	104	6	graph	graph	NOUN
ejpam-5716	104	7	g	g	NOUN
ejpam-5716	104	8	need	need	AUX
ejpam-5716	104	9	not	not	PART
ejpam-5716	104	10	be	be	AUX
ejpam-5716	104	11	contained	contain	VERB
ejpam-5716	104	12	in	in	ADP
ejpam-5716	104	13	any	any	DET
ejpam-5716	104	14	γh	γh	ADV
ejpam-5716	104	15	-	-	PUNCT
ejpam-5716	104	16	set	set	NOUN
ejpam-5716	104	17	of	of	ADP
ejpam-5716	104	18	g.	g.	PROPN
ejpam-5716	104	19	to	to	PART
ejpam-5716	104	20	see	see	VERB
ejpam-5716	104	21	this	this	PRON
ejpam-5716	104	22	,	,	PUNCT
ejpam-5716	104	23	consider	consider	VERB
ejpam-5716	104	24	the	the	DET
ejpam-5716	104	25	graph	graph	NOUN
ejpam-5716	104	26	in	in	ADP
ejpam-5716	104	27	figure	figure	NOUN
ejpam-5716	104	28	1	1	NUM
ejpam-5716	104	29	with	with	ADP
ejpam-5716	104	30	γh(g	γh(g	NOUN
ejpam-5716	104	31	)	)	PUNCT
ejpam-5716	104	32	=	=	SYM
ejpam-5716	105	1	2	2	X
ejpam-5716	105	2	.	.	X
ejpam-5716	105	3	the	the	DET
ejpam-5716	105	4	set	set	NOUN
ejpam-5716	105	5	{	{	PUNCT
ejpam-5716	105	6	1	1	NUM
ejpam-5716	105	7	,	,	PUNCT
ejpam-5716	105	8	4	4	NUM
ejpam-5716	105	9	}	}	PUNCT
ejpam-5716	105	10	is	be	AUX
ejpam-5716	105	11	the	the	DET
ejpam-5716	105	12	only	only	ADJ
ejpam-5716	105	13	γh	γh	ADV
ejpam-5716	105	14	-	-	PUNCT
ejpam-5716	105	15	set	set	VERB
ejpam-5716	105	16	and	and	CCONJ
ejpam-5716	105	17	{	{	PUNCT
ejpam-5716	105	18	7	7	NUM
ejpam-5716	105	19	}	}	PUNCT
ejpam-5716	105	20	is	be	AUX
ejpam-5716	105	21	the	the	DET
ejpam-5716	105	22	only	only	ADJ
ejpam-5716	105	23	ζh1	ζh1	NOUN
ejpam-5716	105	24	-set	-set	PUNCT
ejpam-5716	105	25	in	in	ADP
ejpam-5716	105	26	g	g	NOUN
ejpam-5716	105	27	and	and	CCONJ
ejpam-5716	105	28	hence	hence	ADV
ejpam-5716	105	29	,	,	PUNCT
ejpam-5716	105	30	ζh1	ζh1	ADV
ejpam-5716	105	31	(	(	PUNCT
ejpam-5716	105	32	g	g	NOUN
ejpam-5716	105	33	)	)	PUNCT
ejpam-5716	105	34	=	=	SYM
ejpam-5716	105	35	5	5	X
ejpam-5716	105	36	.	.	X
ejpam-5716	105	37	observe	observe	VERB
ejpam-5716	105	38	that	that	SCONJ
ejpam-5716	105	39	{	{	PUNCT
ejpam-5716	105	40	7	7	NUM
ejpam-5716	105	41	}	}	PUNCT
ejpam-5716	105	42	⊈	⊈	PROPN
ejpam-5716	105	43	{	{	PUNCT
ejpam-5716	105	44	1	1	NUM
ejpam-5716	105	45	,	,	PUNCT
ejpam-5716	105	46	4	4	NUM
ejpam-5716	105	47	}	}	PUNCT
ejpam-5716	105	48	.	.	PUNCT
ejpam-5716	105	49	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-5716	105	50	.........	.........	PUNCT
ejpam-5716	105	51	........	........	PUNCT
ejpam-5716	105	52	........	........	PUNCT
ejpam-5716	105	53	........	........	PUNCT
ejpam-5716	105	54	........	........	PUNCT
ejpam-5716	105	55	........	........	PUNCT
ejpam-5716	105	56	........	........	PUNCT
ejpam-5716	105	57	........	........	PUNCT
ejpam-5716	105	58	........	........	PUNCT
ejpam-5716	105	59	...	...	PUNCT
ejpam-5716	106	1	.................	.................	PUNCT
ejpam-5716	106	2	................	................	PUNCT
ejpam-5716	107	1	................	................	PUNCT
ejpam-5716	107	2	................	................	PUNCT
ejpam-5716	108	1	................	................	PUNCT
ejpam-5716	108	2	................	................	PUNCT
ejpam-5716	109	1	................	................	PUNCT
ejpam-5716	109	2	................	................	PUNCT
ejpam-5716	110	1	................	................	PUNCT
ejpam-5716	110	2	................	................	PUNCT
ejpam-5716	111	1	................	................	PUNCT
ejpam-5716	111	2	................	................	PUNCT
ejpam-5716	112	1	................	................	PUNCT
ejpam-5716	112	2	................	................	PUNCT
ejpam-5716	112	3	................	................	PUNCT
ejpam-5716	113	1	.................	.................	PUNCT
ejpam-5716	113	2	................	................	PUNCT
ejpam-5716	114	1	................	................	PUNCT
ejpam-5716	114	2	................	................	PUNCT
ejpam-5716	115	1	................	................	PUNCT
ejpam-5716	115	2	................	................	PUNCT
ejpam-5716	116	1	................	................	PUNCT
ejpam-5716	116	2	................	................	PUNCT
ejpam-5716	117	1	................	................	PUNCT
ejpam-5716	117	2	................	................	PUNCT
ejpam-5716	118	1	................	................	PUNCT
ejpam-5716	118	2	................	................	PUNCT
ejpam-5716	119	1	................	................	PUNCT
ejpam-5716	119	2	................	................	PUNCT
ejpam-5716	120	1	................	................	PUNCT
ejpam-5716	120	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-5716	121	1	.................................................................................................................................................	.................................................................................................................................................	PROPN
ejpam-5716	121	2	...................................................................................................................................	...................................................................................................................................	PROPN
ejpam-5716	122	1	..............................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................	PUNCT
ejpam-5716	122	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-5716	123	1	...........	...........	PUNCT
ejpam-5716	123	2	..........	..........	PUNCT
ejpam-5716	124	1	..........	..........	PUNCT
ejpam-5716	124	2	..........	..........	PUNCT
ejpam-5716	125	1	..........	..........	PUNCT
ejpam-5716	125	2	..........	..........	PUNCT
ejpam-5716	126	1	..........	..........	PUNCT
ejpam-5716	126	2	..........	..........	PUNCT
ejpam-5716	127	1	..........	..........	PUNCT
ejpam-5716	127	2	..........	..........	PUNCT
ejpam-5716	128	1	..........	..........	PUNCT
ejpam-5716	128	2	..........	..........	PUNCT
ejpam-5716	129	1	..........	..........	PUNCT
ejpam-5716	129	2	..........	..........	PUNCT
ejpam-5716	130	1	....	....	PUNCT
ejpam-5716	130	2	.........	.........	PUNCT
ejpam-5716	130	3	........	........	PUNCT
ejpam-5716	130	4	........	........	PUNCT
ejpam-5716	130	5	........	........	PUNCT
ejpam-5716	130	6	........	........	PUNCT
ejpam-5716	130	7	........	........	PUNCT
ejpam-5716	130	8	........	........	PUNCT
ejpam-5716	130	9	........	........	PUNCT
ejpam-5716	130	10	........	........	PUNCT
ejpam-5716	130	11	........	........	PUNCT
ejpam-5716	130	12	........	........	PUNCT
ejpam-5716	130	13	........	........	PUNCT
ejpam-5716	130	14	........	........	PUNCT
ejpam-5716	130	15	........	........	PUNCT
ejpam-5716	130	16	........	........	PUNCT
ejpam-5716	130	17	........	........	PUNCT
ejpam-5716	130	18	........	........	PUNCT
ejpam-5716	130	19	........	........	PUNCT
ejpam-5716	130	20	...	...	PUNCT
ejpam-5716	131	1	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-5716	131	2	...........................................................................................	...........................................................................................	PUNCT
ejpam-5716	132	1	.................................................................................................................................................	.................................................................................................................................................	PUNCT
ejpam-5716	132	2	...........	...........	PUNCT
ejpam-5716	133	1	..........	..........	PUNCT
ejpam-5716	133	2	..........	..........	PUNCT
ejpam-5716	134	1	..........	..........	PUNCT
ejpam-5716	134	2	..........	..........	PUNCT
ejpam-5716	135	1	..........	..........	PUNCT
ejpam-5716	135	2	..........	..........	PUNCT
ejpam-5716	136	1	..........	..........	PUNCT
ejpam-5716	136	2	..........	..........	PUNCT
ejpam-5716	137	1	..........	..........	PUNCT
ejpam-5716	137	2	..........	..........	PUNCT
ejpam-5716	138	1	..........	..........	PUNCT
ejpam-5716	138	2	..........	..........	PUNCT
ejpam-5716	139	1	..........	..........	PUNCT
ejpam-5716	139	2	....	....	PUNCT
ejpam-5716	140	1	..........	..........	PUNCT
ejpam-5716	140	2	.........	.........	PUNCT
ejpam-5716	141	1	.........	.........	PUNCT
ejpam-5716	141	2	.........	.........	PUNCT
ejpam-5716	142	1	.........	.........	PUNCT
ejpam-5716	142	2	.........	.........	PUNCT
ejpam-5716	143	1	.........	.........	PUNCT
ejpam-5716	143	2	.........	.........	PUNCT
ejpam-5716	144	1	.........	.........	PUNCT
ejpam-5716	144	2	.........	.........	PUNCT
ejpam-5716	145	1	.........	.........	PUNCT
ejpam-5716	145	2	.........	.........	PUNCT
ejpam-5716	146	1	.........	.........	PUNCT
ejpam-5716	146	2	.........	.........	PUNCT
ejpam-5716	146	3	.........	.........	PUNCT
ejpam-5716	146	4	.	.	PUNCT
ejpam-5716	147	1	.........	.........	PUNCT
ejpam-5716	147	2	........	........	PUNCT
ejpam-5716	147	3	........	........	PUNCT
ejpam-5716	147	4	........	........	PUNCT
ejpam-5716	147	5	........	........	PUNCT
ejpam-5716	147	6	........	........	PUNCT
ejpam-5716	147	7	........	........	PUNCT
ejpam-5716	147	8	........	........	PUNCT
ejpam-5716	148	1	........	........	PUNCT
ejpam-5716	148	2	...	...	PUNCT
ejpam-5716	149	1	................	................	PUNCT
ejpam-5716	149	2	...............	...............	PUNCT
ejpam-5716	149	3	...............	...............	PUNCT
ejpam-5716	149	4	...............	...............	PUNCT
ejpam-5716	149	5	...............	...............	PUNCT
ejpam-5716	149	6	...............	...............	PUNCT
ejpam-5716	149	7	...............	...............	PUNCT
ejpam-5716	149	8	...............	...............	PUNCT
ejpam-5716	149	9	...............	...............	PUNCT
ejpam-5716	149	10	...............	...............	PUNCT
ejpam-5716	149	11	...............	...............	PUNCT
ejpam-5716	149	12	...............	...............	PUNCT
ejpam-5716	149	13	...............	...............	PUNCT
ejpam-5716	149	14	...............	...............	PUNCT
ejpam-5716	149	15	...............	...............	PUNCT
ejpam-5716	149	16	...	...	PUNCT
ejpam-5716	149	17	...........	...........	PUNCT
ejpam-5716	149	18	..........	..........	PUNCT
ejpam-5716	150	1	..........	..........	PUNCT
ejpam-5716	150	2	..........	..........	PUNCT
ejpam-5716	151	1	..........	..........	PUNCT
ejpam-5716	151	2	..........	..........	PUNCT
ejpam-5716	152	1	..........	..........	PUNCT
ejpam-5716	152	2	..........	..........	PUNCT
ejpam-5716	153	1	..........	..........	PUNCT
ejpam-5716	153	2	..........	..........	PUNCT
ejpam-5716	154	1	..........	..........	PUNCT
ejpam-5716	154	2	..........	..........	PUNCT
ejpam-5716	155	1	..........	..........	PUNCT
ejpam-5716	155	2	..........	..........	PUNCT
ejpam-5716	156	1	....	....	PUNCT
ejpam-5716	156	2	.	.	PUNCT
ejpam-5716	156	3	...................................	...................................	PUNCT
ejpam-5716	157	1	....................................	....................................	PUNCT
ejpam-5716	157	2	....................................	....................................	PUNCT
ejpam-5716	158	1	....................................	....................................	PUNCT
ejpam-5716	158	2	....................................	....................................	PUNCT
ejpam-5716	159	1	....................................	....................................	PUNCT
ejpam-5716	159	2	....................................	....................................	PUNCT
ejpam-5716	160	1	....................................	....................................	PUNCT
ejpam-5716	160	2	....................................	....................................	PUNCT
ejpam-5716	161	1	....................................	....................................	PUNCT
ejpam-5716	161	2	........................................................................	........................................................................	PUNCT
ejpam-5716	162	1	....................................	....................................	PUNCT
ejpam-5716	162	2	....................................	....................................	PUNCT
ejpam-5716	163	1	1	1	NUM
ejpam-5716	163	2	2	2	NUM
ejpam-5716	163	3	3	3	NUM
ejpam-5716	163	4	4	4	NUM
ejpam-5716	163	5	5	5	NUM
ejpam-5716	163	6	6	6	NUM
ejpam-5716	163	7	7	7	NUM
ejpam-5716	163	8	8	8	NUM
ejpam-5716	163	9	9	9	NUM
ejpam-5716	163	10	10	10	NUM
ejpam-5716	163	11	11	11	NUM
ejpam-5716	163	12	12	12	NUM
ejpam-5716	163	13	13	13	NUM
ejpam-5716	163	14	14	14	NUM
ejpam-5716	163	15	•	•	NUM
ejpam-5716	163	16	•	•	NUM
ejpam-5716	163	17	figure	figure	NOUN
ejpam-5716	163	18	1	1	NUM
ejpam-5716	163	19	:	:	PUNCT
ejpam-5716	163	20	a	a	DET
ejpam-5716	163	21	graph	graph	NOUN
ejpam-5716	163	22	g	g	NOUN
ejpam-5716	163	23	with	with	ADP
ejpam-5716	163	24	γh(g	γh(g	NOUN
ejpam-5716	163	25	)	)	PUNCT
ejpam-5716	163	26	=	=	SYM
ejpam-5716	163	27	2	2	X
ejpam-5716	163	28	.	.	X
ejpam-5716	164	1	in	in	ADP
ejpam-5716	164	2	view	view	NOUN
ejpam-5716	164	3	of	of	ADP
ejpam-5716	164	4	theorem	theorem	NOUN
ejpam-5716	164	5	3	3	NUM
ejpam-5716	164	6	,	,	PUNCT
ejpam-5716	164	7	all	all	DET
ejpam-5716	164	8	graphs	graph	NOUN
ejpam-5716	164	9	considered	consider	VERB
ejpam-5716	164	10	henceforth	henceforth	ADV
ejpam-5716	164	11	,	,	PUNCT
ejpam-5716	164	12	unless	unless	SCONJ
ejpam-5716	164	13	specified	specify	VERB
ejpam-5716	164	14	,	,	PUNCT
ejpam-5716	164	15	do	do	AUX
ejpam-5716	164	16	not	not	PART
ejpam-5716	164	17	have	have	VERB
ejpam-5716	164	18	isolated	isolate	VERB
ejpam-5716	164	19	vertices	vertex	NOUN
ejpam-5716	164	20	.	.	PUNCT
ejpam-5716	165	1	furthermore	furthermore	ADV
ejpam-5716	165	2	,	,	PUNCT
ejpam-5716	165	3	given	give	VERB
ejpam-5716	165	4	a	a	DET
ejpam-5716	165	5	graph	graph	NOUN
ejpam-5716	165	6	g	g	NOUN
ejpam-5716	165	7	,	,	PUNCT
ejpam-5716	165	8	the	the	DET
ejpam-5716	165	9	positive	positive	ADJ
ejpam-5716	165	10	integer	integer	NOUN
ejpam-5716	165	11	k	k	NOUN
ejpam-5716	165	12	,	,	PUNCT
ejpam-5716	165	13	when	when	SCONJ
ejpam-5716	165	14	not	not	PART
ejpam-5716	165	15	specified	specify	VERB
ejpam-5716	165	16	,	,	PUNCT
ejpam-5716	165	17	always	always	ADV
ejpam-5716	165	18	satisfies	satisfy	VERB
ejpam-5716	165	19	the	the	DET
ejpam-5716	165	20	condition	condition	NOUN
ejpam-5716	165	21	k	k	PROPN
ejpam-5716	165	22	≤	≤	ADJ
ejpam-5716	165	23	γh(g)−	γh(g)−	PROPN
ejpam-5716	165	24	1	1	NUM
ejpam-5716	165	25	.	.	PUNCT
ejpam-5716	165	26	theorem	theorem	VERB
ejpam-5716	165	27	4	4	NUM
ejpam-5716	165	28	.	.	PUNCT
ejpam-5716	166	1	if	if	SCONJ
ejpam-5716	166	2	g	g	PROPN
ejpam-5716	166	3	is	be	AUX
ejpam-5716	166	4	a	a	DET
ejpam-5716	166	5	graph	graph	NOUN
ejpam-5716	166	6	of	of	ADP
ejpam-5716	166	7	order	order	NOUN
ejpam-5716	166	8	n	n	PRON
ejpam-5716	166	9	≥	≥	NOUN
ejpam-5716	166	10	2	2	NUM
ejpam-5716	166	11	,	,	PUNCT
ejpam-5716	166	12	then	then	ADV
ejpam-5716	166	13	1	1	NUM
ejpam-5716	166	14	≤	≤	NOUN
ejpam-5716	166	15	ζhk	ζhk	NOUN
ejpam-5716	166	16	(	(	PUNCT
ejpam-5716	166	17	g	g	NOUN
ejpam-5716	166	18	)	)	PUNCT
ejpam-5716	166	19	≤	≤	NUM
ejpam-5716	166	20	n−	n−	NOUN
ejpam-5716	166	21	1	1	NUM
ejpam-5716	166	22	.	.	PUNCT
ejpam-5716	167	1	proof	proof	NOUN
ejpam-5716	167	2	.	.	PUNCT
ejpam-5716	168	1	let	let	VERB
ejpam-5716	168	2	s	s	PRON
ejpam-5716	168	3	be	be	AUX
ejpam-5716	168	4	a	a	DET
ejpam-5716	168	5	ζhk	ζhk	NOUN
ejpam-5716	168	6	-set	-set	VERB
ejpam-5716	168	7	in	in	ADP
ejpam-5716	168	8	g.	g.	PROPN
ejpam-5716	168	9	then	then	ADV
ejpam-5716	168	10	|s|	|s|	PROPN
ejpam-5716	168	11	=	=	SYM
ejpam-5716	168	12	γh(g	γh(g	NOUN
ejpam-5716	168	13	)	)	PUNCT
ejpam-5716	168	14	−	−	PROPN
ejpam-5716	169	1	1	1	X
ejpam-5716	169	2	.	.	PUNCT
ejpam-5716	170	1	hence	hence	ADV
ejpam-5716	170	2	,	,	PUNCT
ejpam-5716	170	3	v	v	X
ejpam-5716	170	4	(	(	PUNCT
ejpam-5716	170	5	g	g	NOUN
ejpam-5716	170	6	)	)	PUNCT
ejpam-5716	170	7	\	\	NOUN
ejpam-5716	170	8	n2	n2	ADJ
ejpam-5716	170	9	g[s	g[s	PROPN
ejpam-5716	170	10	]	]	PUNCT
ejpam-5716	170	11	̸=	̸=	PROPN
ejpam-5716	170	12	∅.	∅.	ADP
ejpam-5716	170	13	this	this	PRON
ejpam-5716	170	14	implies	imply	VERB
ejpam-5716	170	15	that	that	SCONJ
ejpam-5716	170	16	ζhk	ζhk	NOUN
ejpam-5716	170	17	(	(	PUNCT
ejpam-5716	170	18	g	g	NOUN
ejpam-5716	170	19	)	)	PUNCT
ejpam-5716	170	20	=	=	SYM
ejpam-5716	170	21	|v	|v	PROPN
ejpam-5716	170	22	(	(	PUNCT
ejpam-5716	170	23	g)|	g)|	PROPN
ejpam-5716	170	24	−	−	PROPN
ejpam-5716	170	25	|n2	|n2	PROPN
ejpam-5716	170	26	g[s]|	g[s]|	PROPN
ejpam-5716	170	27	≥	≥	NUM
ejpam-5716	170	28	1	1	NUM
ejpam-5716	170	29	.	.	PUNCT
ejpam-5716	171	1	moreover	moreover	ADV
ejpam-5716	171	2	,	,	PUNCT
ejpam-5716	171	3	since	since	SCONJ
ejpam-5716	171	4	|n2	|n2	PROPN
ejpam-5716	171	5	g[s]|	g[s]|	PROPN
ejpam-5716	171	6	≥	≥	NOUN
ejpam-5716	171	7	1	1	NUM
ejpam-5716	171	8	,	,	PUNCT
ejpam-5716	171	9	ζhk	ζhk	NOUN
ejpam-5716	171	10	(	(	PUNCT
ejpam-5716	171	11	g	g	NOUN
ejpam-5716	171	12	)	)	PUNCT
ejpam-5716	171	13	=	=	SYM
ejpam-5716	171	14	|v	|v	PROPN
ejpam-5716	171	15	(	(	PUNCT
ejpam-5716	171	16	g)|	g)|	PROPN
ejpam-5716	171	17	−	−	PROPN
ejpam-5716	171	18	|n2	|n2	PROPN
ejpam-5716	171	19	g[s]|	g[s]|	PROPN
ejpam-5716	171	20	≤	≤	NUM
ejpam-5716	171	21	n−	n−	NOUN
ejpam-5716	171	22	1	1	NUM
ejpam-5716	171	23	.	.	PUNCT
ejpam-5716	172	1	this	this	PRON
ejpam-5716	172	2	proves	prove	VERB
ejpam-5716	172	3	the	the	DET
ejpam-5716	172	4	assertion	assertion	NOUN
ejpam-5716	172	5	.	.	PUNCT
ejpam-5716	173	1	j.	j.	PROPN
ejpam-5716	173	2	anoche	anoche	PROPN
ejpam-5716	173	3	,	,	PUNCT
ejpam-5716	173	4	s.r	s.r	PROPN
ejpam-5716	173	5	.	.	PROPN
ejpam-5716	173	6	canoy	canoy	PROPN
ejpam-5716	173	7	jr	jr	PROPN
ejpam-5716	173	8	.	.	PUNCT
ejpam-5716	173	9	/	/	SYM
ejpam-5716	173	10	eur	eur	PROPN
ejpam-5716	173	11	.	.	PUNCT
ejpam-5716	174	1	j.	j.	PROPN
ejpam-5716	174	2	pure	pure	PROPN
ejpam-5716	174	3	appl	appl	PROPN
ejpam-5716	174	4	.	.	PROPN
ejpam-5716	174	5	math	math	PROPN
ejpam-5716	174	6	,	,	PUNCT
ejpam-5716	174	7	18	18	NUM
ejpam-5716	174	8	(	(	PUNCT
ejpam-5716	174	9	1	1	NUM
ejpam-5716	174	10	)	)	PUNCT
ejpam-5716	174	11	(	(	PUNCT
ejpam-5716	174	12	2025	2025	NUM
ejpam-5716	174	13	)	)	PUNCT
ejpam-5716	174	14	,	,	PUNCT
ejpam-5716	174	15	5716	5716	NUM
ejpam-5716	174	16	5	5	NUM
ejpam-5716	174	17	of	of	ADP
ejpam-5716	174	18	13	13	NUM
ejpam-5716	174	19	theorem	theorem	NOUN
ejpam-5716	174	20	5	5	NUM
ejpam-5716	174	21	.	.	PUNCT
ejpam-5716	175	1	let	let	VERB
ejpam-5716	175	2	g	g	PRON
ejpam-5716	175	3	be	be	AUX
ejpam-5716	175	4	a	a	DET
ejpam-5716	175	5	non	non	ADJ
ejpam-5716	175	6	-	-	ADJ
ejpam-5716	175	7	trivial	trivial	ADJ
ejpam-5716	175	8	graph	graph	NOUN
ejpam-5716	175	9	of	of	ADP
ejpam-5716	175	10	order	order	NOUN
ejpam-5716	176	1	n.	n.	NOUN
ejpam-5716	176	2	then	then	ADV
ejpam-5716	176	3	ζh1	ζh1	ADV
ejpam-5716	176	4	(	(	PUNCT
ejpam-5716	176	5	g	g	NOUN
ejpam-5716	176	6	)	)	PUNCT
ejpam-5716	176	7	=	=	SYM
ejpam-5716	176	8	1	1	NUM
ejpam-5716	176	9	if	if	SCONJ
ejpam-5716	176	10	and	and	CCONJ
ejpam-5716	176	11	only	only	ADV
ejpam-5716	176	12	if	if	SCONJ
ejpam-5716	176	13	there	there	PRON
ejpam-5716	176	14	exists	exist	VERB
ejpam-5716	176	15	v	v	ADP
ejpam-5716	176	16	∈	∈	PROPN
ejpam-5716	176	17	v	v	NOUN
ejpam-5716	176	18	(	(	PUNCT
ejpam-5716	176	19	g	g	NOUN
ejpam-5716	176	20	)	)	PUNCT
ejpam-5716	176	21	such	such	ADJ
ejpam-5716	176	22	that	that	SCONJ
ejpam-5716	176	23	γh(g−	γh(g−	PROPN
ejpam-5716	176	24	v	v	NOUN
ejpam-5716	176	25	)	)	PUNCT
ejpam-5716	176	26	=	=	PUNCT
ejpam-5716	176	27	γh(g)−	γh(g)−	PROPN
ejpam-5716	176	28	1	1	NUM
ejpam-5716	176	29	.	.	PUNCT
ejpam-5716	177	1	proof	proof	NOUN
ejpam-5716	177	2	.	.	PUNCT
ejpam-5716	178	1	suppose	suppose	VERB
ejpam-5716	178	2	ζh1	ζh1	ADJ
ejpam-5716	178	3	(	(	PUNCT
ejpam-5716	178	4	g	g	NOUN
ejpam-5716	178	5	)	)	PUNCT
ejpam-5716	178	6	=	=	SYM
ejpam-5716	178	7	1	1	NUM
ejpam-5716	178	8	and	and	CCONJ
ejpam-5716	178	9	let	let	VERB
ejpam-5716	178	10	s	s	PRON
ejpam-5716	178	11	be	be	AUX
ejpam-5716	178	12	a	a	DET
ejpam-5716	178	13	ζh1	ζh1	NOUN
ejpam-5716	178	14	-set	-set	PUNCT
ejpam-5716	178	15	in	in	ADP
ejpam-5716	178	16	g.	g.	PROPN
ejpam-5716	178	17	then	then	ADV
ejpam-5716	178	18	|s|	|s|	PROPN
ejpam-5716	178	19	=	=	SYM
ejpam-5716	178	20	γh(g	γh(g	NOUN
ejpam-5716	178	21	)	)	PUNCT
ejpam-5716	179	1	−	−	PROPN
ejpam-5716	179	2	1	1	NUM
ejpam-5716	179	3	and	and	CCONJ
ejpam-5716	179	4	|v	|v	PROPN
ejpam-5716	179	5	(	(	PUNCT
ejpam-5716	179	6	g	g	NOUN
ejpam-5716	179	7	)	)	PUNCT
ejpam-5716	180	1	\	\	NOUN
ejpam-5716	180	2	n2	n2	ADJ
ejpam-5716	180	3	g[s]|	g[s]|	PROPN
ejpam-5716	180	4	=	=	PUNCT
ejpam-5716	181	1	1	1	X
ejpam-5716	181	2	.	.	PUNCT
ejpam-5716	181	3	let	let	VERB
ejpam-5716	181	4	v	v	NUM
ejpam-5716	181	5	∈	∈	PROPN
ejpam-5716	181	6	v	v	NOUN
ejpam-5716	181	7	(	(	PUNCT
ejpam-5716	181	8	g	g	NOUN
ejpam-5716	181	9	)	)	PUNCT
ejpam-5716	181	10	\	\	NOUN
ejpam-5716	181	11	n2	n2	ADJ
ejpam-5716	181	12	g[s	g[s	PROPN
ejpam-5716	181	13	]	]	PUNCT
ejpam-5716	181	14	.	.	PUNCT
ejpam-5716	182	1	then	then	ADV
ejpam-5716	182	2	n2	n2	PROPN
ejpam-5716	182	3	g[s	g[s	PROPN
ejpam-5716	182	4	]	]	X
ejpam-5716	182	5	=	=	SYM
ejpam-5716	182	6	v	v	X
ejpam-5716	182	7	(	(	PUNCT
ejpam-5716	182	8	g	g	NOUN
ejpam-5716	182	9	)	)	PUNCT
ejpam-5716	182	10	\	\	NOUN
ejpam-5716	182	11	{	{	PUNCT
ejpam-5716	182	12	v	v	NOUN
ejpam-5716	182	13	}	}	PUNCT
ejpam-5716	182	14	.	.	PUNCT
ejpam-5716	183	1	therefore	therefore	ADV
ejpam-5716	183	2	,	,	PUNCT
ejpam-5716	183	3	γh(g−	γh(g−	PROPN
ejpam-5716	183	4	v	v	NOUN
ejpam-5716	183	5	)	)	PUNCT
ejpam-5716	183	6	=	=	PUNCT
ejpam-5716	183	7	γh	γh	X
ejpam-5716	183	8	(	(	PUNCT
ejpam-5716	183	9	〈	〈	PROPN
ejpam-5716	183	10	n2	n2	ADJ
ejpam-5716	183	11	g[s	g[s	PROPN
ejpam-5716	183	12	]	]	PUNCT
ejpam-5716	183	13	〉	〉	NOUN
ejpam-5716	183	14	)	)	PUNCT
ejpam-5716	183	15	=	=	PUNCT
ejpam-5716	183	16	γh(g)−	γh(g)−	PROPN
ejpam-5716	183	17	1	1	NUM
ejpam-5716	183	18	.	.	PUNCT
ejpam-5716	184	1	conversely	conversely	ADV
ejpam-5716	184	2	,	,	PUNCT
ejpam-5716	184	3	let	let	VERB
ejpam-5716	184	4	v	v	NUM
ejpam-5716	184	5	∈	∈	PROPN
ejpam-5716	184	6	v	v	NOUN
ejpam-5716	184	7	(	(	PUNCT
ejpam-5716	184	8	g	g	NOUN
ejpam-5716	184	9	)	)	PUNCT
ejpam-5716	184	10	such	such	ADJ
ejpam-5716	184	11	that	that	SCONJ
ejpam-5716	184	12	γh(g−v	γh(g−v	NOUN
ejpam-5716	184	13	)	)	PUNCT
ejpam-5716	184	14	=	=	SYM
ejpam-5716	184	15	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	184	16	.	.	PUNCT
ejpam-5716	185	1	then	then	ADV
ejpam-5716	185	2	,	,	PUNCT
ejpam-5716	185	3	there	there	PRON
ejpam-5716	185	4	exists	exist	VERB
ejpam-5716	185	5	s	s	PART
ejpam-5716	185	6	′	′	NUM
ejpam-5716	185	7	⊆	⊆	NUM
ejpam-5716	185	8	v	v	NOUN
ejpam-5716	185	9	(	(	PUNCT
ejpam-5716	185	10	g	g	NOUN
ejpam-5716	185	11	)	)	PUNCT
ejpam-5716	185	12	with	with	ADP
ejpam-5716	185	13	|s′	|s′	NOUN
ejpam-5716	185	14	|	|	NOUN
ejpam-5716	185	15	=	=	PUNCT
ejpam-5716	185	16	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	185	17	and	and	CCONJ
ejpam-5716	185	18	n2	n2	ADJ
ejpam-5716	185	19	g[s	g[s	PROPN
ejpam-5716	185	20	′	′	NUM
ejpam-5716	185	21	]	]	PUNCT
ejpam-5716	186	1	=	=	SYM
ejpam-5716	186	2	v	v	X
ejpam-5716	186	3	(	(	PUNCT
ejpam-5716	186	4	g)\{v	g)\{v	PROPN
ejpam-5716	186	5	}	}	PUNCT
ejpam-5716	186	6	.	.	PUNCT
ejpam-5716	187	1	it	it	PRON
ejpam-5716	187	2	follows	follow	VERB
ejpam-5716	187	3	that	that	DET
ejpam-5716	187	4	ζh1	ζh1	NOUN
ejpam-5716	187	5	(	(	PUNCT
ejpam-5716	187	6	g	g	NOUN
ejpam-5716	187	7	)	)	PUNCT
ejpam-5716	187	8	=	=	SYM
ejpam-5716	188	1	|v	|v	PROPN
ejpam-5716	188	2	(	(	PUNCT
ejpam-5716	188	3	g)\n2	g)\n2	NOUN
ejpam-5716	188	4	g[s	g[s	PROPN
ejpam-5716	188	5	′	′	NUM
ejpam-5716	188	6	]	]	PUNCT
ejpam-5716	188	7	|	|	NOUN
ejpam-5716	188	8	=	=	PUNCT
ejpam-5716	188	9	|{v}|	|{v}|	PUNCT
ejpam-5716	188	10	=	=	SYM
ejpam-5716	188	11	1	1	X
ejpam-5716	188	12	.	.	PUNCT
ejpam-5716	188	13	therefore	therefore	ADV
ejpam-5716	188	14	,	,	PUNCT
ejpam-5716	188	15	ζh1	ζh1	ADV
ejpam-5716	188	16	(	(	PUNCT
ejpam-5716	188	17	g	g	NOUN
ejpam-5716	188	18	)	)	PUNCT
ejpam-5716	188	19	=	=	SYM
ejpam-5716	188	20	1	1	X
ejpam-5716	188	21	.	.	X
ejpam-5716	188	22	theorem	theorem	VERB
ejpam-5716	188	23	6	6	NUM
ejpam-5716	188	24	.	.	PUNCT
ejpam-5716	189	1	if	if	SCONJ
ejpam-5716	189	2	g	g	PROPN
ejpam-5716	189	3	is	be	AUX
ejpam-5716	189	4	a	a	DET
ejpam-5716	189	5	graph	graph	NOUN
ejpam-5716	189	6	on	on	ADP
ejpam-5716	189	7	n	n	DET
ejpam-5716	189	8	vertices	vertex	NOUN
ejpam-5716	189	9	,	,	PUNCT
ejpam-5716	189	10	then	then	ADV
ejpam-5716	189	11	ζhk	ζhk	NOUN
ejpam-5716	189	12	(	(	PUNCT
ejpam-5716	189	13	g	g	NOUN
ejpam-5716	189	14	)	)	PUNCT
ejpam-5716	189	15	≤	≤	NOUN
ejpam-5716	189	16	k(1	k(1	NOUN
ejpam-5716	189	17	+	+	CCONJ
ejpam-5716	189	18	∆h(g	∆h(g	NOUN
ejpam-5716	189	19	)	)	PUNCT
ejpam-5716	189	20	)	)	PUNCT
ejpam-5716	189	21	.	.	PUNCT
ejpam-5716	190	1	proof	proof	NOUN
ejpam-5716	190	2	.	.	PUNCT
ejpam-5716	191	1	let	let	VERB
ejpam-5716	191	2	s	s	PRON
ejpam-5716	191	3	be	be	AUX
ejpam-5716	191	4	a	a	DET
ejpam-5716	191	5	γh	γh	ADV
ejpam-5716	191	6	-	-	PUNCT
ejpam-5716	191	7	set	set	NOUN
ejpam-5716	191	8	in	in	ADP
ejpam-5716	191	9	g.	g.	PROPN
ejpam-5716	191	10	for	for	ADP
ejpam-5716	191	11	each	each	DET
ejpam-5716	191	12	v	v	NUM
ejpam-5716	191	13	∈	∈	PROPN
ejpam-5716	191	14	v	v	NOUN
ejpam-5716	191	15	(	(	PUNCT
ejpam-5716	191	16	g	g	NOUN
ejpam-5716	191	17	)	)	PUNCT
ejpam-5716	191	18	,	,	PUNCT
ejpam-5716	191	19	we	we	PRON
ejpam-5716	191	20	have	have	VERB
ejpam-5716	191	21	|n2	|n2	PROPN
ejpam-5716	191	22	g[v]|	g[v]|	PROPN
ejpam-5716	191	23	≤	≤	NUM
ejpam-5716	191	24	1	1	NUM
ejpam-5716	191	25	+	+	NUM
ejpam-5716	191	26	∆h(g	∆h(g	NOUN
ejpam-5716	191	27	)	)	PUNCT
ejpam-5716	191	28	.	.	PUNCT
ejpam-5716	192	1	let	let	VERB
ejpam-5716	192	2	s′	s′	ADJ
ejpam-5716	192	3	⊂	⊂	PROPN
ejpam-5716	192	4	s	s	X
ejpam-5716	192	5	with	with	ADP
ejpam-5716	192	6	|s′|	|s′|	NOUN
ejpam-5716	192	7	=	=	PUNCT
ejpam-5716	192	8	k	k	PROPN
ejpam-5716	192	9	and	and	CCONJ
ejpam-5716	192	10	set	set	VERB
ejpam-5716	192	11	s∗	s∗	PROPN
ejpam-5716	192	12	=	=	SYM
ejpam-5716	192	13	s	s	PART
ejpam-5716	192	14	\	\	PROPN
ejpam-5716	192	15	s′.	s′.	PROPN
ejpam-5716	192	16	then	then	ADV
ejpam-5716	192	17	ζhk	ζhk	PROPN
ejpam-5716	192	18	(	(	PUNCT
ejpam-5716	192	19	s	s	NOUN
ejpam-5716	192	20	∗	∗	NOUN
ejpam-5716	192	21	)	)	PUNCT
ejpam-5716	192	22	=	=	SYM
ejpam-5716	192	23	|v	|v	PROPN
ejpam-5716	192	24	(	(	PUNCT
ejpam-5716	192	25	g)−n2	g)−n2	PROPN
ejpam-5716	192	26	g[s	g[s	PROPN
ejpam-5716	192	27	∗]|	∗]|	NUM
ejpam-5716	192	28	=	=	SYM
ejpam-5716	192	29	|n2	|n2	PROPN
ejpam-5716	192	30	g[s]|	g[s]|	PROPN
ejpam-5716	192	31	−	−	NOUN
ejpam-5716	192	32	|n2	|n2	PROPN
ejpam-5716	192	33	g[s	g[s	PROPN
ejpam-5716	192	34	∗]|	∗]|	NUM
ejpam-5716	192	35	≤	≤	NUM
ejpam-5716	192	36	|n2	|n2	PROPN
ejpam-5716	192	37	g[s	g[s	PROPN
ejpam-5716	192	38	′]|+	′]|+	VERB
ejpam-5716	192	39	|n2	|n2	PROPN
ejpam-5716	192	40	g[s	g[s	PROPN
ejpam-5716	192	41	∗]|	∗]|	NUM
ejpam-5716	192	42	−	−	PROPN
ejpam-5716	192	43	|n2	|n2	PROPN
ejpam-5716	192	44	g[s	g[s	PROPN
ejpam-5716	192	45	∗]|	∗]|	NUM
ejpam-5716	192	46	=	=	SYM
ejpam-5716	192	47	|n2	|n2	PROPN
ejpam-5716	192	48	g[s	g[s	PROPN
ejpam-5716	192	49	′]|	′]|	NOUN
ejpam-5716	193	1	=	=	SYM
ejpam-5716	193	2	∑	∑	PUNCT
ejpam-5716	193	3	v∈s′	v∈s′	NUM
ejpam-5716	193	4	|n2	|n2	PROPN
ejpam-5716	193	5	g[v]|	g[v]|	PROPN
ejpam-5716	193	6	≤	≤	PROPN
ejpam-5716	193	7	k(1	k(1	PROPN
ejpam-5716	193	8	+	+	CCONJ
ejpam-5716	193	9	∆h(g	∆h(g	NOUN
ejpam-5716	193	10	)	)	PUNCT
ejpam-5716	193	11	)	)	PUNCT
ejpam-5716	193	12	.	.	PUNCT
ejpam-5716	194	1	therefore	therefore	ADV
ejpam-5716	194	2	,	,	PUNCT
ejpam-5716	194	3	ζhk	ζhk	NOUN
ejpam-5716	194	4	(	(	PUNCT
ejpam-5716	194	5	g	g	NOUN
ejpam-5716	194	6	)	)	PUNCT
ejpam-5716	194	7	≤	≤	NOUN
ejpam-5716	194	8	k(1	k(1	NOUN
ejpam-5716	194	9	+	+	CCONJ
ejpam-5716	194	10	∆h(g	∆h(g	NOUN
ejpam-5716	194	11	)	)	PUNCT
ejpam-5716	194	12	)	)	PUNCT
ejpam-5716	194	13	.	.	PUNCT
ejpam-5716	195	1	remark	remark	NOUN
ejpam-5716	195	2	2	2	NUM
ejpam-5716	195	3	.	.	PUNCT
ejpam-5716	196	1	let	let	VERB
ejpam-5716	196	2	g1	g1	PROPN
ejpam-5716	196	3	,	,	PUNCT
ejpam-5716	196	4	g2	g2	PROPN
ejpam-5716	196	5	,	,	PUNCT
ejpam-5716	196	6	·	·	PUNCT
ejpam-5716	196	7	·	·	PUNCT
ejpam-5716	196	8	·	·	PUNCT
ejpam-5716	196	9	,	,	PUNCT
ejpam-5716	196	10	gr	gr	INTJ
ejpam-5716	196	11	be	be	AUX
ejpam-5716	196	12	the	the	DET
ejpam-5716	196	13	components	component	NOUN
ejpam-5716	196	14	of	of	ADP
ejpam-5716	196	15	a	a	DET
ejpam-5716	196	16	graph	graph	NOUN
ejpam-5716	196	17	g.	g.	NOUN
ejpam-5716	197	1	then	then	ADV
ejpam-5716	197	2	each	each	PRON
ejpam-5716	197	3	of	of	ADP
ejpam-5716	197	4	the	the	DET
ejpam-5716	197	5	following	follow	VERB
ejpam-5716	197	6	holds	hold	VERB
ejpam-5716	197	7	:	:	PUNCT
ejpam-5716	197	8	(	(	PUNCT
ejpam-5716	197	9	i	i	NOUN
ejpam-5716	197	10	)	)	PUNCT
ejpam-5716	197	11	γh(g	γh(g	PUNCT
ejpam-5716	197	12	)	)	PUNCT
ejpam-5716	198	1	=	=	PUNCT
ejpam-5716	198	2	∑r	∑r	PROPN
ejpam-5716	198	3	j=1	j=1	PROPN
ejpam-5716	198	4	γh(gj	γh(gj	PROPN
ejpam-5716	198	5	)	)	PUNCT
ejpam-5716	198	6	.	.	PUNCT
ejpam-5716	199	1	(	(	PUNCT
ejpam-5716	199	2	ii	ii	NOUN
ejpam-5716	199	3	)	)	PUNCT
ejpam-5716	199	4	if	if	SCONJ
ejpam-5716	199	5	aj	aj	PROPN
ejpam-5716	199	6	⊆	⊆	NUM
ejpam-5716	199	7	v	v	PROPN
ejpam-5716	199	8	(	(	PUNCT
ejpam-5716	199	9	gi	gi	INTJ
ejpam-5716	199	10	)	)	PUNCT
ejpam-5716	199	11	for	for	ADP
ejpam-5716	199	12	each	each	DET
ejpam-5716	199	13	j	j	PROPN
ejpam-5716	199	14	∈	∈	PROPN
ejpam-5716	200	1	[	[	X
ejpam-5716	200	2	r	r	X
ejpam-5716	200	3	]	]	X
ejpam-5716	200	4	=	=	PUNCT
ejpam-5716	200	5	{	{	PUNCT
ejpam-5716	200	6	1	1	NUM
ejpam-5716	200	7	,	,	PUNCT
ejpam-5716	200	8	2	2	NUM
ejpam-5716	200	9	,	,	PUNCT
ejpam-5716	200	10	·	·	PUNCT
ejpam-5716	200	11	·	·	PUNCT
ejpam-5716	200	12	·	·	PUNCT
ejpam-5716	200	13	,	,	PUNCT
ejpam-5716	200	14	r	r	X
ejpam-5716	200	15	}	}	PUNCT
ejpam-5716	200	16	and	and	CCONJ
ejpam-5716	200	17	a	a	DET
ejpam-5716	200	18	=	=	X
ejpam-5716	200	19	∪r	∪r	NUM
ejpam-5716	200	20	j=1aj	j=1aj	PROPN
ejpam-5716	200	21	,	,	PUNCT
ejpam-5716	200	22	then	then	ADV
ejpam-5716	200	23	n2	n2	PROPN
ejpam-5716	200	24	g[a	g[a	PROPN
ejpam-5716	200	25	]	]	X
ejpam-5716	200	26	=	=	SYM
ejpam-5716	200	27	∪r	∪r	PUNCT
ejpam-5716	200	28	j=1n	j=1n	VERB
ejpam-5716	200	29	2	2	NUM
ejpam-5716	200	30	g[aj	g[aj	PROPN
ejpam-5716	200	31	]	]	X
ejpam-5716	200	32	(	(	PUNCT
ejpam-5716	200	33	a	a	DET
ejpam-5716	200	34	disjoint	disjoint	NOUN
ejpam-5716	200	35	union	union	NOUN
ejpam-5716	200	36	)	)	PUNCT
ejpam-5716	200	37	.	.	PUNCT
ejpam-5716	201	1	theorem	theorem	ADJ
ejpam-5716	201	2	7	7	NUM
ejpam-5716	201	3	.	.	PUNCT
ejpam-5716	201	4	let	let	VERB
ejpam-5716	201	5	g1	g1	PROPN
ejpam-5716	201	6	,	,	PUNCT
ejpam-5716	201	7	g2	g2	PROPN
ejpam-5716	201	8	,	,	PUNCT
ejpam-5716	201	9	·	·	PUNCT
ejpam-5716	201	10	·	·	PUNCT
ejpam-5716	201	11	·	·	PUNCT
ejpam-5716	201	12	,	,	PUNCT
ejpam-5716	201	13	gr	gr	INTJ
ejpam-5716	201	14	be	be	AUX
ejpam-5716	201	15	the	the	DET
ejpam-5716	201	16	components	component	NOUN
ejpam-5716	201	17	of	of	ADP
ejpam-5716	201	18	graph	graph	NOUN
ejpam-5716	201	19	g	g	PROPN
ejpam-5716	201	20	and	and	CCONJ
ejpam-5716	201	21	let	let	VERB
ejpam-5716	201	22	ζh1	ζh1	NOUN
ejpam-5716	201	23	(	(	PUNCT
ejpam-5716	201	24	gi	gi	AUX
ejpam-5716	201	25	)	)	PUNCT
ejpam-5716	201	26	be	be	AUX
ejpam-5716	201	27	the	the	DET
ejpam-5716	201	28	hop	hop	NOUN
ejpam-5716	201	29	domination	domination	NOUN
ejpam-5716	201	30	defect	defect	NOUN
ejpam-5716	201	31	of	of	ADP
ejpam-5716	201	32	gi	gi	NOUN
ejpam-5716	201	33	for	for	ADP
ejpam-5716	201	34	each	each	DET
ejpam-5716	201	35	i	i	PRON
ejpam-5716	201	36	∈	∈	PROPN
ejpam-5716	202	1	[	[	X
ejpam-5716	202	2	r	r	X
ejpam-5716	202	3	]	]	X
ejpam-5716	202	4	=	=	PUNCT
ejpam-5716	202	5	{	{	PUNCT
ejpam-5716	202	6	1	1	NUM
ejpam-5716	202	7	,	,	PUNCT
ejpam-5716	202	8	2	2	NUM
ejpam-5716	202	9	,	,	PUNCT
ejpam-5716	202	10	·	·	PUNCT
ejpam-5716	202	11	·	·	PUNCT
ejpam-5716	202	12	·	·	PUNCT
ejpam-5716	202	13	,	,	PUNCT
ejpam-5716	202	14	r	r	NOUN
ejpam-5716	202	15	}	}	PUNCT
ejpam-5716	202	16	.	.	PUNCT
ejpam-5716	203	1	then	then	ADV
ejpam-5716	203	2	ζh1	ζh1	ADV
ejpam-5716	203	3	(	(	PUNCT
ejpam-5716	203	4	g	g	NOUN
ejpam-5716	203	5	)	)	PUNCT
ejpam-5716	203	6	=	=	SYM
ejpam-5716	204	1	min{ζh1	min{ζh1	PROPN
ejpam-5716	204	2	(	(	PUNCT
ejpam-5716	204	3	gi	gi	NOUN
ejpam-5716	204	4	)	)	PUNCT
ejpam-5716	204	5	:	:	PUNCT
ejpam-5716	205	1	i	i	PRON
ejpam-5716	205	2	∈	∈	VERB
ejpam-5716	206	1	[	[	X
ejpam-5716	206	2	r	r	X
ejpam-5716	206	3	]	]	PUNCT
ejpam-5716	206	4	}	}	PUNCT
ejpam-5716	206	5	.	.	PUNCT
ejpam-5716	207	1	proof	proof	NOUN
ejpam-5716	207	2	.	.	PUNCT
ejpam-5716	208	1	let	let	VERB
ejpam-5716	208	2	γh(gi	γh(gi	PROPN
ejpam-5716	208	3	)	)	PUNCT
ejpam-5716	208	4	and	and	CCONJ
ejpam-5716	208	5	γh(g	γh(g	NOUN
ejpam-5716	208	6	)	)	PUNCT
ejpam-5716	208	7	be	be	AUX
ejpam-5716	208	8	the	the	DET
ejpam-5716	208	9	hop	hop	NOUN
ejpam-5716	208	10	domination	domination	NOUN
ejpam-5716	208	11	numbers	number	NOUN
ejpam-5716	208	12	of	of	ADP
ejpam-5716	208	13	gi	gi	NOUN
ejpam-5716	208	14	and	and	CCONJ
ejpam-5716	208	15	g	g	NOUN
ejpam-5716	208	16	,	,	PUNCT
ejpam-5716	208	17	respectively	respectively	ADV
ejpam-5716	208	18	.	.	PUNCT
ejpam-5716	209	1	by	by	ADP
ejpam-5716	209	2	remark	remark	NOUN
ejpam-5716	209	3	2(i	2(i	NUM
ejpam-5716	209	4	)	)	PUNCT
ejpam-5716	209	5	,	,	PUNCT
ejpam-5716	209	6	γh(g	γh(g	PUNCT
ejpam-5716	209	7	)	)	PUNCT
ejpam-5716	209	8	=	=	PUNCT
ejpam-5716	209	9	∑r	∑r	PROPN
ejpam-5716	209	10	j=1	j=1	PROPN
ejpam-5716	209	11	γh(gj	γh(gj	PROPN
ejpam-5716	209	12	)	)	PUNCT
ejpam-5716	209	13	.	.	PUNCT
ejpam-5716	210	1	for	for	ADP
ejpam-5716	210	2	each	each	DET
ejpam-5716	210	3	i	i	PRON
ejpam-5716	210	4	∈	∈	PROPN
ejpam-5716	211	1	[	[	X
ejpam-5716	211	2	r	r	X
ejpam-5716	211	3	]	]	PUNCT
ejpam-5716	211	4	,	,	PUNCT
ejpam-5716	211	5	let	let	VERB
ejpam-5716	211	6	di	di	PART
ejpam-5716	211	7	be	be	AUX
ejpam-5716	211	8	a	a	DET
ejpam-5716	211	9	ζh1	ζh1	NOUN
ejpam-5716	211	10	-set	-set	PUNCT
ejpam-5716	211	11	of	of	ADP
ejpam-5716	211	12	gi	gi	INTJ
ejpam-5716	211	13	.	.	PUNCT
ejpam-5716	212	1	then	then	ADV
ejpam-5716	212	2	|di|	|di|	PROPN
ejpam-5716	212	3	=	=	SYM
ejpam-5716	212	4	γh(gi	γh(gi	PROPN
ejpam-5716	212	5	)	)	PUNCT
ejpam-5716	213	1	−	−	PROPN
ejpam-5716	213	2	1	1	NUM
ejpam-5716	213	3	and	and	CCONJ
ejpam-5716	213	4	ζh1	ζh1	NOUN
ejpam-5716	213	5	(	(	PUNCT
ejpam-5716	213	6	gi	gi	INTJ
ejpam-5716	213	7	)	)	PUNCT
ejpam-5716	213	8	=	=	SYM
ejpam-5716	214	1	|v	|v	PROPN
ejpam-5716	214	2	(	(	PUNCT
ejpam-5716	214	3	gi	gi	INTJ
ejpam-5716	214	4	)	)	PUNCT
ejpam-5716	214	5	−	−	PROPN
ejpam-5716	214	6	n2	n2	ADJ
ejpam-5716	214	7	g[di]|	g[di]|	PROPN
ejpam-5716	214	8	.	.	PUNCT
ejpam-5716	215	1	let	let	VERB
ejpam-5716	215	2	j	j	PROPN
ejpam-5716	215	3	∈	∈	PROPN
ejpam-5716	216	1	[	[	X
ejpam-5716	216	2	r	r	X
ejpam-5716	216	3	]	]	PUNCT
ejpam-5716	216	4	be	be	AUX
ejpam-5716	216	5	such	such	ADJ
ejpam-5716	216	6	that	that	DET
ejpam-5716	216	7	ζh1	ζh1	NOUN
ejpam-5716	216	8	(	(	PUNCT
ejpam-5716	216	9	gj	gj	NOUN
ejpam-5716	216	10	)	)	PUNCT
ejpam-5716	216	11	=	=	SYM
ejpam-5716	216	12	min{ζh1	min{ζh1	PROPN
ejpam-5716	216	13	(	(	PUNCT
ejpam-5716	216	14	gi	gi	NOUN
ejpam-5716	216	15	)	)	PUNCT
ejpam-5716	216	16	:	:	PUNCT
ejpam-5716	217	1	i	i	PRON
ejpam-5716	217	2	∈	∈	VERB
ejpam-5716	218	1	[	[	X
ejpam-5716	218	2	r	r	X
ejpam-5716	218	3	]	]	PUNCT
ejpam-5716	218	4	}	}	PUNCT
ejpam-5716	218	5	.	.	PUNCT
ejpam-5716	219	1	let	let	VERB
ejpam-5716	219	2	si	si	PRON
ejpam-5716	219	3	be	be	AUX
ejpam-5716	219	4	a	a	DET
ejpam-5716	219	5	γh	γh	ADV
ejpam-5716	219	6	-	-	PUNCT
ejpam-5716	219	7	set	set	NOUN
ejpam-5716	219	8	in	in	ADP
ejpam-5716	219	9	gi	gi	NOUN
ejpam-5716	219	10	for	for	ADP
ejpam-5716	219	11	each	each	DET
ejpam-5716	219	12	i	i	PRON
ejpam-5716	219	13	∈	∈	PROPN
ejpam-5716	220	1	[	[	X
ejpam-5716	220	2	r	r	X
ejpam-5716	220	3	]	]	PUNCT
ejpam-5716	220	4	and	and	CCONJ
ejpam-5716	220	5	let	let	VERB
ejpam-5716	220	6	s	s	PRON
ejpam-5716	220	7	=	=	PUNCT
ejpam-5716	220	8	(	(	PUNCT
ejpam-5716	220	9	∪i∈[r]\{j}si	∪i∈[r]\{j}si	NOUN
ejpam-5716	220	10	)	)	PUNCT
ejpam-5716	220	11	∪dj	∪dj	NOUN
ejpam-5716	220	12	.	.	PUNCT
ejpam-5716	221	1	then	then	ADV
ejpam-5716	221	2	|s|	|s|	PROPN
ejpam-5716	221	3	=	=	SYM
ejpam-5716	221	4	∑	∑	SYM
ejpam-5716	221	5	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5716	221	6	}	}	PUNCT
ejpam-5716	221	7	|si|+	|si|+	NOUN
ejpam-5716	221	8	|dj	|dj	PUNCT
ejpam-5716	221	9	|	|	NOUN
ejpam-5716	221	10	=	=	PUNCT
ejpam-5716	221	11	γh(g)−	γh(g)−	PROPN
ejpam-5716	221	12	1	1	NUM
ejpam-5716	221	13	j.	j.	PROPN
ejpam-5716	221	14	anoche	anoche	PROPN
ejpam-5716	221	15	,	,	PUNCT
ejpam-5716	221	16	s.r	s.r	PROPN
ejpam-5716	221	17	.	.	PROPN
ejpam-5716	221	18	canoy	canoy	PROPN
ejpam-5716	221	19	jr	jr	PROPN
ejpam-5716	221	20	.	.	PUNCT
ejpam-5716	221	21	/	/	SYM
ejpam-5716	221	22	eur	eur	PROPN
ejpam-5716	221	23	.	.	PUNCT
ejpam-5716	222	1	j.	j.	PROPN
ejpam-5716	222	2	pure	pure	PROPN
ejpam-5716	222	3	appl	appl	PROPN
ejpam-5716	222	4	.	.	PROPN
ejpam-5716	222	5	math	math	PROPN
ejpam-5716	222	6	,	,	PUNCT
ejpam-5716	222	7	18	18	NUM
ejpam-5716	222	8	(	(	PUNCT
ejpam-5716	222	9	1	1	NUM
ejpam-5716	222	10	)	)	PUNCT
ejpam-5716	222	11	(	(	PUNCT
ejpam-5716	222	12	2025	2025	NUM
ejpam-5716	222	13	)	)	PUNCT
ejpam-5716	222	14	,	,	PUNCT
ejpam-5716	222	15	5716	5716	NUM
ejpam-5716	222	16	6	6	NUM
ejpam-5716	222	17	of	of	ADP
ejpam-5716	222	18	13	13	NUM
ejpam-5716	222	19	and	and	CCONJ
ejpam-5716	222	20	,	,	PUNCT
ejpam-5716	222	21	by	by	ADP
ejpam-5716	222	22	remark	remark	NOUN
ejpam-5716	222	23	2(ii	2(ii	NUM
ejpam-5716	222	24	)	)	PUNCT
ejpam-5716	222	25	,	,	PUNCT
ejpam-5716	222	26	|n2	|n2	PROPN
ejpam-5716	222	27	g[s]|	g[s]|	PROPN
ejpam-5716	223	1	=	=	PUNCT
ejpam-5716	223	2	|n2	|n2	PROPN
ejpam-5716	223	3	gj	gj	NOUN
ejpam-5716	224	1	[	[	X
ejpam-5716	224	2	dj	dj	X
ejpam-5716	224	3	]	]	X
ejpam-5716	224	4	|+	|+	NOUN
ejpam-5716	224	5	∑	∑	ADV
ejpam-5716	224	6	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5716	224	7	}	}	PUNCT
ejpam-5716	224	8	|n2	|n2	X
ejpam-5716	224	9	gi	gi	X
ejpam-5716	225	1	[	[	X
ejpam-5716	225	2	si]|	si]|	ADV
ejpam-5716	225	3	=	=	SYM
ejpam-5716	225	4	|v	|v	X
ejpam-5716	225	5	(	(	PUNCT
ejpam-5716	225	6	gj)|	gj)|	NOUN
ejpam-5716	225	7	−	−	PROPN
ejpam-5716	225	8	ζh1	ζh1	NOUN
ejpam-5716	225	9	(	(	PUNCT
ejpam-5716	225	10	gj	gj	NOUN
ejpam-5716	225	11	)	)	PUNCT
ejpam-5716	225	12	+	+	CCONJ
ejpam-5716	225	13	∑	∑	PUNCT
ejpam-5716	225	14	i∈[r]\{j	i∈[r]\{j	PROPN
ejpam-5716	225	15	}	}	PUNCT
ejpam-5716	225	16	|v	|v	NOUN
ejpam-5716	225	17	(	(	PUNCT
ejpam-5716	225	18	gi)|	gi)|	X
ejpam-5716	225	19	=	=	PUNCT
ejpam-5716	225	20	r∑	r∑	NOUN
ejpam-5716	225	21	i=1	i=1	PROPN
ejpam-5716	225	22	|v	|v	X
ejpam-5716	225	23	(	(	PUNCT
ejpam-5716	225	24	gi)|	gi)|	INTJ
ejpam-5716	225	25	−	−	PROPN
ejpam-5716	225	26	ζh1	ζh1	NOUN
ejpam-5716	225	27	(	(	PUNCT
ejpam-5716	225	28	gj	gj	NOUN
ejpam-5716	225	29	)	)	PUNCT
ejpam-5716	225	30	.	.	PUNCT
ejpam-5716	226	1	thus	thus	ADV
ejpam-5716	226	2	,	,	PUNCT
ejpam-5716	226	3	in	in	ADP
ejpam-5716	226	4	g	g	NOUN
ejpam-5716	226	5	,	,	PUNCT
ejpam-5716	226	6	ζh1	ζh1	NOUN
ejpam-5716	226	7	(	(	PUNCT
ejpam-5716	226	8	s	s	X
ejpam-5716	226	9	)	)	PUNCT
ejpam-5716	226	10	=	=	SYM
ejpam-5716	226	11	|v	|v	PROPN
ejpam-5716	226	12	(	(	PUNCT
ejpam-5716	226	13	g)|	g)|	PROPN
ejpam-5716	226	14	−	−	PROPN
ejpam-5716	226	15	|n2	|n2	PROPN
ejpam-5716	226	16	g[s]|	g[s]|	PROPN
ejpam-5716	226	17	=	=	PUNCT
ejpam-5716	227	1	ζh1	ζh1	NOUN
ejpam-5716	227	2	(	(	PUNCT
ejpam-5716	227	3	gj	gj	NOUN
ejpam-5716	227	4	)	)	PUNCT
ejpam-5716	227	5	.	.	PUNCT
ejpam-5716	228	1	it	it	PRON
ejpam-5716	228	2	now	now	ADV
ejpam-5716	228	3	remains	remain	VERB
ejpam-5716	228	4	to	to	PART
ejpam-5716	228	5	show	show	VERB
ejpam-5716	228	6	that	that	DET
ejpam-5716	228	7	ζh1	ζh1	NOUN
ejpam-5716	228	8	(	(	PUNCT
ejpam-5716	228	9	s	s	X
ejpam-5716	228	10	)	)	PUNCT
ejpam-5716	228	11	is	be	AUX
ejpam-5716	228	12	the	the	DET
ejpam-5716	228	13	minimum	minimum	NOUN
ejpam-5716	228	14	among	among	ADP
ejpam-5716	228	15	all	all	DET
ejpam-5716	228	16	subsets	subset	NOUN
ejpam-5716	228	17	of	of	ADP
ejpam-5716	228	18	v	v	NOUN
ejpam-5716	228	19	(	(	PUNCT
ejpam-5716	228	20	g	g	NOUN
ejpam-5716	228	21	)	)	PUNCT
ejpam-5716	228	22	with	with	ADP
ejpam-5716	228	23	cardinality	cardinality	NOUN
ejpam-5716	228	24	γh(g	γh(g	NOUN
ejpam-5716	228	25	)	)	PUNCT
ejpam-5716	228	26	−	−	PROPN
ejpam-5716	229	1	1	1	X
ejpam-5716	229	2	.	.	PUNCT
ejpam-5716	230	1	so	so	ADV
ejpam-5716	230	2	assume	assume	VERB
ejpam-5716	230	3	there	there	PRON
ejpam-5716	230	4	exists	exist	VERB
ejpam-5716	230	5	s	s	PART
ejpam-5716	230	6	′	′	NUM
ejpam-5716	230	7	⊆	⊆	NUM
ejpam-5716	230	8	v	v	NOUN
ejpam-5716	230	9	(	(	PUNCT
ejpam-5716	230	10	g	g	NOUN
ejpam-5716	230	11	)	)	PUNCT
ejpam-5716	230	12	such	such	ADJ
ejpam-5716	230	13	that	that	DET
ejpam-5716	230	14	|s′	|s′	NOUN
ejpam-5716	230	15	|	|	NOUN
ejpam-5716	230	16	=	=	SYM
ejpam-5716	230	17	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	230	18	and	and	CCONJ
ejpam-5716	230	19	ζh1	ζh1	NOUN
ejpam-5716	230	20	(	(	PUNCT
ejpam-5716	230	21	s	s	NOUN
ejpam-5716	230	22	′	′	NOUN
ejpam-5716	230	23	)	)	PUNCT
ejpam-5716	230	24	<	<	X
ejpam-5716	231	1	ζh1	ζh1	X
ejpam-5716	231	2	(	(	PUNCT
ejpam-5716	231	3	s	s	NOUN
ejpam-5716	231	4	)	)	PUNCT
ejpam-5716	231	5	.	.	PUNCT
ejpam-5716	232	1	let	let	VERB
ejpam-5716	232	2	s	s	PRON
ejpam-5716	232	3	′	′	VERB
ejpam-5716	232	4	=	=	PUNCT
ejpam-5716	232	5	s	s	PART
ejpam-5716	232	6	′	′	NUM
ejpam-5716	232	7	1∪s	1∪s	NUM
ejpam-5716	232	8	′	′	NUM
ejpam-5716	232	9	2∪	2∪	NUM
ejpam-5716	232	10	·	·	PUNCT
ejpam-5716	232	11	·	·	PUNCT
ejpam-5716	232	12	·	·	PUNCT
ejpam-5716	232	13	∪s	∪s	NUM
ejpam-5716	233	1	′	′	NUM
ejpam-5716	234	1	r	r	NOUN
ejpam-5716	234	2	where	where	SCONJ
ejpam-5716	234	3	s	s	VERB
ejpam-5716	235	1	′	′	NUM
ejpam-5716	235	2	i	i	NOUN
ejpam-5716	236	1	⊆	⊆	NUM
ejpam-5716	236	2	v	v	NOUN
ejpam-5716	236	3	(	(	PUNCT
ejpam-5716	236	4	gi	gi	INTJ
ejpam-5716	236	5	)	)	PUNCT
ejpam-5716	236	6	for	for	ADP
ejpam-5716	236	7	each	each	DET
ejpam-5716	236	8	i	i	PRON
ejpam-5716	236	9	∈	∈	PROPN
ejpam-5716	237	1	[	[	X
ejpam-5716	237	2	r	r	X
ejpam-5716	237	3	]	]	X
ejpam-5716	237	4	.	.	PUNCT
ejpam-5716	238	1	since	since	SCONJ
ejpam-5716	238	2	|s′	|s′	PROPN
ejpam-5716	238	3	|	|	NOUN
ejpam-5716	238	4	=	=	SYM
ejpam-5716	238	5	γh(g)−1	γh(g)−1	NOUN
ejpam-5716	238	6	,	,	PUNCT
ejpam-5716	238	7	at	at	ADP
ejpam-5716	238	8	least	least	ADJ
ejpam-5716	238	9	one	one	NUM
ejpam-5716	238	10	s	s	NOUN
ejpam-5716	238	11	′	′	NOUN
ejpam-5716	238	12	l	l	NOUN
ejpam-5716	238	13	is	be	AUX
ejpam-5716	238	14	not	not	PART
ejpam-5716	238	15	a	a	DET
ejpam-5716	238	16	hop	hop	NOUN
ejpam-5716	238	17	dominating	dominating	NOUN
ejpam-5716	238	18	set	set	NOUN
ejpam-5716	238	19	of	of	ADP
ejpam-5716	238	20	gl	gl	INTJ
ejpam-5716	238	21	by	by	ADP
ejpam-5716	238	22	remark	remark	NOUN
ejpam-5716	238	23	2(i	2(i	NUM
ejpam-5716	238	24	)	)	PUNCT
ejpam-5716	238	25	.	.	PUNCT
ejpam-5716	239	1	thus	thus	ADV
ejpam-5716	239	2	,	,	PUNCT
ejpam-5716	239	3	|s′	|s′	ADJ
ejpam-5716	239	4	l|	l|	ADJ
ejpam-5716	239	5	=	=	PUNCT
ejpam-5716	239	6	γh(gl)−	γh(gl)−	PROPN
ejpam-5716	239	7	1	1	NUM
ejpam-5716	239	8	and	and	CCONJ
ejpam-5716	239	9	ζh1	ζh1	NOUN
ejpam-5716	239	10	(	(	PUNCT
ejpam-5716	239	11	s	s	NOUN
ejpam-5716	239	12	′	′	NUM
ejpam-5716	239	13	l	l	NOUN
ejpam-5716	239	14	)	)	PUNCT
ejpam-5716	239	15	≥	≥	NOUN
ejpam-5716	239	16	ζh1	ζh1	NOUN
ejpam-5716	239	17	(	(	PUNCT
ejpam-5716	239	18	gl	gl	PROPN
ejpam-5716	239	19	)	)	PUNCT
ejpam-5716	239	20	≥	≥	NOUN
ejpam-5716	239	21	ζh1	ζh1	NOUN
ejpam-5716	239	22	(	(	PUNCT
ejpam-5716	239	23	gj	gj	NOUN
ejpam-5716	239	24	)	)	PUNCT
ejpam-5716	239	25	.	.	PUNCT
ejpam-5716	240	1	hence	hence	ADV
ejpam-5716	240	2	,	,	PUNCT
ejpam-5716	240	3	ζh1	ζh1	X
ejpam-5716	240	4	(	(	PUNCT
ejpam-5716	240	5	s	s	NOUN
ejpam-5716	240	6	′	′	NOUN
ejpam-5716	240	7	)	)	PUNCT
ejpam-5716	241	1	=	=	SYM
ejpam-5716	241	2	|v	|v	PROPN
ejpam-5716	241	3	(	(	PUNCT
ejpam-5716	241	4	g)|	g)|	PROPN
ejpam-5716	241	5	−	−	PROPN
ejpam-5716	241	6	|n2	|n2	PROPN
ejpam-5716	241	7	g[s	g[s	PROPN
ejpam-5716	241	8	′	′	NUM
ejpam-5716	242	1	]	]	PUNCT
ejpam-5716	243	1	|	|	NOUN
ejpam-5716	244	1	=	=	SYM
ejpam-5716	245	1	r∑	r∑	NOUN
ejpam-5716	246	1	i=1	i=1	PROPN
ejpam-5716	247	1	(	(	PUNCT
ejpam-5716	247	2	|v	|v	X
ejpam-5716	247	3	(	(	PUNCT
ejpam-5716	247	4	gi)|	gi)|	PROPN
ejpam-5716	247	5	−	−	PROPN
ejpam-5716	247	6	|n2	|n2	X
ejpam-5716	247	7	gi	gi	VERB
ejpam-5716	248	1	[	[	X
ejpam-5716	248	2	s	s	X
ejpam-5716	248	3	′	′	NUM
ejpam-5716	249	1	i	i	PRON
ejpam-5716	249	2	]	]	X
ejpam-5716	249	3	|	|	X
ejpam-5716	249	4	)	)	PUNCT
ejpam-5716	249	5	≥	≥	NOUN
ejpam-5716	249	6	|v	|v	PROPN
ejpam-5716	249	7	(	(	PUNCT
ejpam-5716	249	8	gl)|	gl)|	PROPN
ejpam-5716	249	9	−	−	PROPN
ejpam-5716	249	10	|n2	|n2	PROPN
ejpam-5716	249	11	gl	gl	PROPN
ejpam-5716	250	1	[	[	X
ejpam-5716	250	2	s	s	X
ejpam-5716	250	3	′	′	NUM
ejpam-5716	250	4	l	l	NOUN
ejpam-5716	250	5	]	]	X
ejpam-5716	250	6	|	|	NOUN
ejpam-5716	250	7	=	=	SYM
ejpam-5716	250	8	ζh1	ζh1	NOUN
ejpam-5716	250	9	(	(	PUNCT
ejpam-5716	250	10	s	s	NOUN
ejpam-5716	250	11	′	′	NUM
ejpam-5716	250	12	l	l	NOUN
ejpam-5716	250	13	)	)	PUNCT
ejpam-5716	250	14	≥	≥	NOUN
ejpam-5716	250	15	ζh1	ζh1	NOUN
ejpam-5716	250	16	(	(	PUNCT
ejpam-5716	250	17	gj	gj	NOUN
ejpam-5716	250	18	)	)	PUNCT
ejpam-5716	250	19	=	=	PUNCT
ejpam-5716	251	1	ζh1	ζh1	NOUN
ejpam-5716	251	2	(	(	PUNCT
ejpam-5716	251	3	s	s	NOUN
ejpam-5716	251	4	)	)	PUNCT
ejpam-5716	251	5	,	,	PUNCT
ejpam-5716	251	6	contrary	contrary	ADV
ejpam-5716	251	7	to	to	ADP
ejpam-5716	251	8	the	the	DET
ejpam-5716	251	9	assumption	assumption	NOUN
ejpam-5716	251	10	that	that	SCONJ
ejpam-5716	251	11	ζh1	ζh1	NOUN
ejpam-5716	251	12	(	(	PUNCT
ejpam-5716	251	13	s	s	NOUN
ejpam-5716	251	14	′	′	NOUN
ejpam-5716	251	15	)	)	PUNCT
ejpam-5716	251	16	<	<	X
ejpam-5716	252	1	ζh1	ζh1	X
ejpam-5716	252	2	(	(	PUNCT
ejpam-5716	252	3	s	s	NOUN
ejpam-5716	252	4	)	)	PUNCT
ejpam-5716	252	5	.	.	PUNCT
ejpam-5716	253	1	therefore	therefore	ADV
ejpam-5716	253	2	,	,	PUNCT
ejpam-5716	253	3	ζ	ζ	NOUN
ejpam-5716	253	4	h	h	NOUN
ejpam-5716	253	5	1	1	NUM
ejpam-5716	253	6	(	(	PUNCT
ejpam-5716	253	7	g	g	NOUN
ejpam-5716	253	8	)	)	PUNCT
ejpam-5716	253	9	=	=	SYM
ejpam-5716	253	10	ζh1	ζh1	NOUN
ejpam-5716	253	11	(	(	PUNCT
ejpam-5716	253	12	s	s	X
ejpam-5716	253	13	)	)	PUNCT
ejpam-5716	253	14	=	=	SYM
ejpam-5716	253	15	ζh1	ζh1	NOUN
ejpam-5716	253	16	(	(	PUNCT
ejpam-5716	253	17	gj	gj	NOUN
ejpam-5716	253	18	)	)	PUNCT
ejpam-5716	253	19	.	.	PUNCT
ejpam-5716	254	1	theorem	theorem	ADJ
ejpam-5716	254	2	8	8	NUM
ejpam-5716	254	3	.	.	PUNCT
ejpam-5716	255	1	ζhk	ζhk	PROPN
ejpam-5716	255	2	(	(	PUNCT
ejpam-5716	255	3	kn	kn	PROPN
ejpam-5716	255	4	)	)	PUNCT
ejpam-5716	255	5	=	=	PROPN
ejpam-5716	255	6	k	k	PROPN
ejpam-5716	255	7	for	for	ADP
ejpam-5716	255	8	all	all	DET
ejpam-5716	255	9	n	n	PRON
ejpam-5716	255	10	≥	≥	NOUN
ejpam-5716	255	11	2	2	NUM
ejpam-5716	255	12	and	and	CCONJ
ejpam-5716	255	13	1	1	NUM
ejpam-5716	255	14	≤	≤	NUM
ejpam-5716	255	15	k	k	X
ejpam-5716	255	16	<	<	X
ejpam-5716	255	17	n.	n.	NOUN
ejpam-5716	255	18	proof	proof	NOUN
ejpam-5716	255	19	.	.	PUNCT
ejpam-5716	256	1	by	by	ADP
ejpam-5716	256	2	theorem	theorem	NOUN
ejpam-5716	256	3	1(i	1(i	NUM
ejpam-5716	256	4	)	)	PUNCT
ejpam-5716	256	5	,	,	PUNCT
ejpam-5716	256	6	γh(kn	γh(kn	PROPN
ejpam-5716	256	7	)	)	PUNCT
ejpam-5716	257	1	=	=	VERB
ejpam-5716	257	2	n.	n.	NOUN
ejpam-5716	257	3	let	let	VERB
ejpam-5716	257	4	k	k	PRON
ejpam-5716	257	5	be	be	AUX
ejpam-5716	257	6	a	a	DET
ejpam-5716	257	7	positive	positive	ADJ
ejpam-5716	257	8	integer	integer	NOUN
ejpam-5716	257	9	such	such	ADJ
ejpam-5716	257	10	that	that	SCONJ
ejpam-5716	257	11	1	1	NUM
ejpam-5716	257	12	≤	≤	NUM
ejpam-5716	257	13	k	k	NOUN
ejpam-5716	257	14	≤	≤	PROPN
ejpam-5716	257	15	n	n	CCONJ
ejpam-5716	257	16	−	−	PROPN
ejpam-5716	257	17	1	1	NUM
ejpam-5716	257	18	and	and	CCONJ
ejpam-5716	257	19	let	let	VERB
ejpam-5716	257	20	s	s	PRON
ejpam-5716	257	21	be	be	AUX
ejpam-5716	257	22	any	any	DET
ejpam-5716	257	23	subset	subset	NOUN
ejpam-5716	257	24	of	of	ADP
ejpam-5716	257	25	v	v	PROPN
ejpam-5716	257	26	(	(	PUNCT
ejpam-5716	257	27	kn	kn	PROPN
ejpam-5716	257	28	)	)	PUNCT
ejpam-5716	257	29	with	with	ADP
ejpam-5716	257	30	|s|	|s|	PROPN
ejpam-5716	257	31	=	=	PUNCT
ejpam-5716	257	32	γh(kn	γh(kn	PROPN
ejpam-5716	257	33	)	)	PUNCT
ejpam-5716	257	34	−	−	PROPN
ejpam-5716	258	1	k	k	NOUN
ejpam-5716	258	2	=	=	PUNCT
ejpam-5716	258	3	n	n	PROPN
ejpam-5716	258	4	−	−	PROPN
ejpam-5716	258	5	k.	k.	NOUN
ejpam-5716	258	6	since	since	SCONJ
ejpam-5716	258	7	⟨s⟩	⟨s⟩	PROPN
ejpam-5716	258	8	is	be	AUX
ejpam-5716	258	9	a	a	DET
ejpam-5716	258	10	complete	complete	ADJ
ejpam-5716	258	11	graph	graph	NOUN
ejpam-5716	258	12	,	,	PUNCT
ejpam-5716	258	13	n2	n2	ADJ
ejpam-5716	258	14	kn	kn	PROPN
ejpam-5716	259	1	[	[	X
ejpam-5716	259	2	s	s	X
ejpam-5716	259	3	]	]	X
ejpam-5716	259	4	=	=	PUNCT
ejpam-5716	259	5	s.	s.	PROPN
ejpam-5716	259	6	this	this	PRON
ejpam-5716	259	7	implies	imply	VERB
ejpam-5716	259	8	that	that	SCONJ
ejpam-5716	259	9	ζhk	ζhk	NOUN
ejpam-5716	259	10	(	(	PUNCT
ejpam-5716	259	11	s	s	X
ejpam-5716	259	12	)	)	PUNCT
ejpam-5716	259	13	=	=	SYM
ejpam-5716	259	14	|v	|v	PROPN
ejpam-5716	259	15	(	(	PUNCT
ejpam-5716	259	16	kn	kn	PROPN
ejpam-5716	259	17	)	)	PUNCT
ejpam-5716	259	18	\	\	PROPN
ejpam-5716	259	19	n2	n2	PROPN
ejpam-5716	259	20	kn	kn	PROPN
ejpam-5716	260	1	[	[	X
ejpam-5716	260	2	s]|	s]|	X
ejpam-5716	260	3	=	=	SYM
ejpam-5716	260	4	n	n	CCONJ
ejpam-5716	260	5	−	−	PROPN
ejpam-5716	260	6	|s|	|s|	PROPN
ejpam-5716	260	7	=	=	SYM
ejpam-5716	260	8	n−	n−	PROPN
ejpam-5716	260	9	(	(	PUNCT
ejpam-5716	260	10	n−	n−	NOUN
ejpam-5716	260	11	k	k	NOUN
ejpam-5716	260	12	)	)	PUNCT
ejpam-5716	260	13	=	=	VERB
ejpam-5716	260	14	k.	k.	PROPN
ejpam-5716	260	15	since	since	SCONJ
ejpam-5716	260	16	s	s	NOUN
ejpam-5716	260	17	was	be	AUX
ejpam-5716	260	18	arbitrarily	arbitrarily	ADV
ejpam-5716	260	19	chosen	choose	VERB
ejpam-5716	260	20	,	,	PUNCT
ejpam-5716	260	21	it	it	PRON
ejpam-5716	260	22	follows	follow	VERB
ejpam-5716	260	23	that	that	DET
ejpam-5716	260	24	ζhk	ζhk	NOUN
ejpam-5716	260	25	(	(	PUNCT
ejpam-5716	260	26	kn	kn	PROPN
ejpam-5716	260	27	)	)	PUNCT
ejpam-5716	260	28	=	=	SYM
ejpam-5716	260	29	k.	k.	PROPN
ejpam-5716	260	30	note	note	VERB
ejpam-5716	260	31	that	that	SCONJ
ejpam-5716	260	32	γh(p3	γh(p3	NOUN
ejpam-5716	260	33	)	)	PUNCT
ejpam-5716	261	1	=	=	PUNCT
ejpam-5716	261	2	γh(p4	γh(p4	X
ejpam-5716	261	3	)	)	PUNCT
ejpam-5716	261	4	=	=	SYM
ejpam-5716	261	5	γh(p5	γh(p5	NOUN
ejpam-5716	261	6	)	)	PUNCT
ejpam-5716	261	7	=	=	SYM
ejpam-5716	261	8	2	2	X
ejpam-5716	261	9	.	.	X
ejpam-5716	261	10	therefore	therefore	ADV
ejpam-5716	261	11	,	,	PUNCT
ejpam-5716	261	12	k	k	PROPN
ejpam-5716	261	13	=	=	SYM
ejpam-5716	261	14	1	1	X
ejpam-5716	261	15	.	.	X
ejpam-5716	261	16	consider	consider	VERB
ejpam-5716	261	17	p3	p3	PROPN
ejpam-5716	261	18	=	=	PUNCT
ejpam-5716	262	1	[	[	X
ejpam-5716	262	2	a	a	PRON
ejpam-5716	262	3	,	,	PUNCT
ejpam-5716	262	4	b	b	NOUN
ejpam-5716	262	5	,	,	PUNCT
ejpam-5716	262	6	c	c	NOUN
ejpam-5716	262	7	]	]	X
ejpam-5716	262	8	,	,	PUNCT
ejpam-5716	262	9	p4	p4	NOUN
ejpam-5716	262	10	=	=	PUNCT
ejpam-5716	263	1	[	[	X
ejpam-5716	263	2	p	p	X
ejpam-5716	263	3	,	,	PUNCT
ejpam-5716	263	4	q	q	ADJ
ejpam-5716	263	5	,	,	PUNCT
ejpam-5716	263	6	r	r	NOUN
ejpam-5716	263	7	,	,	PUNCT
ejpam-5716	263	8	s	s	PART
ejpam-5716	263	9	]	]	X
ejpam-5716	263	10	,	,	PUNCT
ejpam-5716	263	11	and	and	CCONJ
ejpam-5716	263	12	p5	p5	ADJ
ejpam-5716	263	13	=	=	PUNCT
ejpam-5716	264	1	[	[	X
ejpam-5716	264	2	v	v	NOUN
ejpam-5716	264	3	,	,	PUNCT
ejpam-5716	264	4	w	w	PROPN
ejpam-5716	264	5	,	,	PUNCT
ejpam-5716	264	6	x	x	NOUN
ejpam-5716	264	7	,	,	PUNCT
ejpam-5716	264	8	y	y	PROPN
ejpam-5716	264	9	,	,	PUNCT
ejpam-5716	264	10	z	z	X
ejpam-5716	264	11	]	]	X
ejpam-5716	264	12	below	below	ADV
ejpam-5716	264	13	.	.	PUNCT
ejpam-5716	265	1	then	then	ADV
ejpam-5716	265	2	s1	s1	PROPN
ejpam-5716	265	3	=	=	PUNCT
ejpam-5716	265	4	{	{	PUNCT
ejpam-5716	265	5	a	a	NOUN
ejpam-5716	265	6	}	}	PUNCT
ejpam-5716	265	7	,	,	PUNCT
ejpam-5716	265	8	s2	s2	NOUN
ejpam-5716	265	9	=	=	PUNCT
ejpam-5716	265	10	{	{	PUNCT
ejpam-5716	265	11	p	p	X
ejpam-5716	265	12	}	}	PUNCT
ejpam-5716	265	13	,	,	PUNCT
ejpam-5716	265	14	and	and	CCONJ
ejpam-5716	265	15	s3	s3	PROPN
ejpam-5716	265	16	=	=	SYM
ejpam-5716	265	17	{	{	PUNCT
ejpam-5716	265	18	x	x	NOUN
ejpam-5716	265	19	}	}	PUNCT
ejpam-5716	265	20	are	be	AUX
ejpam-5716	265	21	ζh1	ζh1	ADJ
ejpam-5716	265	22	-sets	-set	NOUN
ejpam-5716	265	23	in	in	ADP
ejpam-5716	265	24	p3	p3	PROPN
ejpam-5716	265	25	,	,	PUNCT
ejpam-5716	265	26	p4	p4	ADJ
ejpam-5716	265	27	,	,	PUNCT
ejpam-5716	265	28	and	and	CCONJ
ejpam-5716	265	29	p5	p5	ADJ
ejpam-5716	265	30	,	,	PUNCT
ejpam-5716	265	31	respectively	respectively	ADV
ejpam-5716	265	32	.	.	PUNCT
ejpam-5716	266	1	since	since	SCONJ
ejpam-5716	266	2	|n2	|n2	PROPN
ejpam-5716	266	3	p3	p3	PROPN
ejpam-5716	266	4	[	[	X
ejpam-5716	266	5	s1]|	s1]|	X
ejpam-5716	266	6	=	=	SYM
ejpam-5716	266	7	2	2	NUM
ejpam-5716	266	8	,	,	PUNCT
ejpam-5716	266	9	|n2	|n2	PROPN
ejpam-5716	266	10	p4	p4	NOUN
ejpam-5716	266	11	[	[	X
ejpam-5716	266	12	s2]|	s2]|	NOUN
ejpam-5716	266	13	=	=	SYM
ejpam-5716	266	14	2	2	NUM
ejpam-5716	266	15	,	,	PUNCT
ejpam-5716	266	16	and	and	CCONJ
ejpam-5716	266	17	|n2	|n2	PROPN
ejpam-5716	266	18	p5	p5	PROPN
ejpam-5716	267	1	[	[	X
ejpam-5716	267	2	s3]|	s3]|	ADP
ejpam-5716	267	3	=	=	SYM
ejpam-5716	267	4	3	3	NUM
ejpam-5716	267	5	,	,	PUNCT
ejpam-5716	267	6	it	it	PRON
ejpam-5716	267	7	follows	follow	VERB
ejpam-5716	267	8	that	that	PRON
ejpam-5716	267	9	ζh1	ζh1	NOUN
ejpam-5716	267	10	(	(	PUNCT
ejpam-5716	267	11	p3	p3	PROPN
ejpam-5716	267	12	)	)	PUNCT
ejpam-5716	267	13	=	=	SYM
ejpam-5716	267	14	1	1	NUM
ejpam-5716	267	15	,	,	PUNCT
ejpam-5716	267	16	and	and	CCONJ
ejpam-5716	267	17	ζh1	ζh1	NOUN
ejpam-5716	267	18	(	(	PUNCT
ejpam-5716	267	19	p4	p4	ADJ
ejpam-5716	267	20	)	)	PUNCT
ejpam-5716	267	21	=	=	SYM
ejpam-5716	268	1	ζh1	ζh1	NOUN
ejpam-5716	268	2	(	(	PUNCT
ejpam-5716	268	3	p5	p5	ADJ
ejpam-5716	268	4	)	)	PUNCT
ejpam-5716	268	5	=	=	SYM
ejpam-5716	269	1	2	2	X
ejpam-5716	269	2	.	.	PUNCT
ejpam-5716	269	3	................................................................................................................	................................................................................................................	PROPN
ejpam-5716	269	4	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-5716	269	5	....................................	....................................	PUNCT
ejpam-5716	269	6	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	269	7	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	269	8	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	269	9	....................................	....................................	PUNCT
ejpam-5716	269	10	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	269	11	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	269	12	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	270	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-5716	270	2	....................................	....................................	PUNCT
ejpam-5716	271	1	a	a	DET
ejpam-5716	271	2	b	b	X
ejpam-5716	271	3	c	c	NOUN
ejpam-5716	271	4	p	p	NOUN
ejpam-5716	271	5	q	q	NOUN
ejpam-5716	271	6	r	r	NOUN
ejpam-5716	271	7	s	s	PROPN
ejpam-5716	271	8	v	v	NOUN
ejpam-5716	271	9	w	w	NOUN
ejpam-5716	271	10	x	x	PUNCT
ejpam-5716	271	11	y	y	PROPN
ejpam-5716	271	12	z	z	PROPN
ejpam-5716	271	13	•	•	NUM
ejpam-5716	271	14	•	•	NUM
ejpam-5716	271	15	•	•	ADP
ejpam-5716	271	16	j.	j.	PROPN
ejpam-5716	271	17	anoche	anoche	PROPN
ejpam-5716	271	18	,	,	PUNCT
ejpam-5716	271	19	s.r	s.r	PROPN
ejpam-5716	271	20	.	.	PROPN
ejpam-5716	271	21	canoy	canoy	PROPN
ejpam-5716	271	22	jr	jr	PROPN
ejpam-5716	271	23	.	.	PUNCT
ejpam-5716	271	24	/	/	SYM
ejpam-5716	271	25	eur	eur	PROPN
ejpam-5716	271	26	.	.	PUNCT
ejpam-5716	272	1	j.	j.	PROPN
ejpam-5716	272	2	pure	pure	PROPN
ejpam-5716	272	3	appl	appl	PROPN
ejpam-5716	272	4	.	.	PROPN
ejpam-5716	272	5	math	math	PROPN
ejpam-5716	272	6	,	,	PUNCT
ejpam-5716	272	7	18	18	NUM
ejpam-5716	272	8	(	(	PUNCT
ejpam-5716	272	9	1	1	NUM
ejpam-5716	272	10	)	)	PUNCT
ejpam-5716	272	11	(	(	PUNCT
ejpam-5716	272	12	2025	2025	NUM
ejpam-5716	272	13	)	)	PUNCT
ejpam-5716	272	14	,	,	PUNCT
ejpam-5716	272	15	5716	5716	NUM
ejpam-5716	272	16	7	7	NUM
ejpam-5716	272	17	of	of	ADP
ejpam-5716	272	18	13	13	NUM
ejpam-5716	272	19	theorem	theorem	NOUN
ejpam-5716	272	20	9	9	NUM
ejpam-5716	272	21	.	.	PUNCT
ejpam-5716	273	1	if	if	SCONJ
ejpam-5716	273	2	pn	pn	PROPN
ejpam-5716	273	3	is	be	AUX
ejpam-5716	273	4	a	a	DET
ejpam-5716	273	5	path	path	NOUN
ejpam-5716	273	6	on	on	ADP
ejpam-5716	273	7	n	n	PRON
ejpam-5716	273	8	≥	≥	NUM
ejpam-5716	273	9	6	6	NUM
ejpam-5716	273	10	vertices	vertex	NOUN
ejpam-5716	273	11	,	,	PUNCT
ejpam-5716	273	12	then	then	ADV
ejpam-5716	273	13	ζhk	ζhk	PROPN
ejpam-5716	273	14	(	(	PUNCT
ejpam-5716	273	15	pn	pn	NOUN
ejpam-5716	273	16	)	)	PUNCT
ejpam-5716	273	17	=	=	PUNCT
ejpam-5716	274	1			PRON
ejpam-5716	274	2	3k	3k	X
ejpam-5716	274	3	if	if	SCONJ
ejpam-5716	274	4	n	n	NOUN
ejpam-5716	274	5	=	=	SYM
ejpam-5716	274	6	6r	6r	NUM
ejpam-5716	275	1	3k	3k	NUM
ejpam-5716	276	1	−	−	NOUN
ejpam-5716	277	1	2	2	NUM
ejpam-5716	278	1	if	if	SCONJ
ejpam-5716	278	2	n	n	ADV
ejpam-5716	278	3	=	=	SYM
ejpam-5716	278	4	6r	6r	NUM
ejpam-5716	278	5	+	+	CCONJ
ejpam-5716	278	6	1	1	NUM
ejpam-5716	278	7	3k	3k	NOUN
ejpam-5716	278	8	+	+	CCONJ
ejpam-5716	278	9	s−	s−	PROPN
ejpam-5716	278	10	6	6	NUM
ejpam-5716	278	11	if	if	SCONJ
ejpam-5716	278	12	n	n	NOUN
ejpam-5716	278	13	=	=	SYM
ejpam-5716	278	14	6r	6r	NUM
ejpam-5716	279	1	+	+	SYM
ejpam-5716	279	2	s	s	X
ejpam-5716	279	3	;	;	PUNCT
ejpam-5716	279	4	2	2	NUM
ejpam-5716	279	5	≤	≤	NOUN
ejpam-5716	279	6	s	s	PART
ejpam-5716	279	7	≤	≤	NOUN
ejpam-5716	279	8	5	5	NUM
ejpam-5716	279	9	and	and	CCONJ
ejpam-5716	279	10	2	2	NUM
ejpam-5716	279	11	≤	≤	NOUN
ejpam-5716	279	12	k	k	NOUN
ejpam-5716	279	13	≤	≤	PUNCT
ejpam-5716	280	1	γh(pn)−	γh(pn)−	ADP
ejpam-5716	280	2	1	1	NUM
ejpam-5716	280	3	proof	proof	NOUN
ejpam-5716	280	4	.	.	PUNCT
ejpam-5716	281	1	we	we	PRON
ejpam-5716	281	2	denote	denote	VERB
ejpam-5716	281	3	the	the	DET
ejpam-5716	281	4	vertices	vertex	NOUN
ejpam-5716	281	5	of	of	ADP
ejpam-5716	281	6	pn	pn	PROPN
ejpam-5716	281	7	as	as	ADP
ejpam-5716	281	8	{	{	PUNCT
ejpam-5716	281	9	1	1	NUM
ejpam-5716	281	10	,	,	PUNCT
ejpam-5716	281	11	2	2	NUM
ejpam-5716	281	12	,	,	PUNCT
ejpam-5716	281	13	·	·	PUNCT
ejpam-5716	281	14	·	·	PUNCT
ejpam-5716	281	15	·	·	PUNCT
ejpam-5716	281	16	,	,	PUNCT
ejpam-5716	281	17	n	n	CCONJ
ejpam-5716	281	18	}	}	PUNCT
ejpam-5716	281	19	.	.	PUNCT
ejpam-5716	282	1	now	now	ADV
ejpam-5716	282	2	,	,	PUNCT
ejpam-5716	282	3	consider	consider	VERB
ejpam-5716	282	4	the	the	DET
ejpam-5716	282	5	following	follow	VERB
ejpam-5716	282	6	cases	case	NOUN
ejpam-5716	282	7	:	:	PUNCT
ejpam-5716	282	8	case	case	NOUN
ejpam-5716	282	9	1	1	NUM
ejpam-5716	282	10	:	:	PUNCT
ejpam-5716	282	11	suppose	suppose	VERB
ejpam-5716	282	12	n	n	X
ejpam-5716	282	13	=	=	SYM
ejpam-5716	282	14	6r	6r	NUM
ejpam-5716	282	15	.	.	PUNCT
ejpam-5716	283	1	by	by	ADP
ejpam-5716	283	2	theorem	theorem	NOUN
ejpam-5716	283	3	1	1	NUM
ejpam-5716	283	4	(	(	PUNCT
ejpam-5716	283	5	iii	iii	NOUN
ejpam-5716	283	6	)	)	PUNCT
ejpam-5716	283	7	,	,	PUNCT
ejpam-5716	283	8	γh(pn	γh(pn	NUM
ejpam-5716	283	9	)	)	PUNCT
ejpam-5716	283	10	=	=	SYM
ejpam-5716	283	11	2r	2r	NUM
ejpam-5716	283	12	.	.	PUNCT
ejpam-5716	284	1	choose	choose	VERB
ejpam-5716	284	2	a	a	DET
ejpam-5716	284	3	(	(	PUNCT
ejpam-5716	284	4	2r−k)-element	2r−k)-element	NUM
ejpam-5716	284	5	set	set	NOUN
ejpam-5716	284	6	s	s	PART
ejpam-5716	284	7	=	=	PUNCT
ejpam-5716	284	8	{	{	PUNCT
ejpam-5716	284	9	3	3	NUM
ejpam-5716	284	10	,	,	PUNCT
ejpam-5716	284	11	6	6	NUM
ejpam-5716	284	12	,	,	PUNCT
ejpam-5716	284	13	·	·	PUNCT
ejpam-5716	284	14	·	·	PUNCT
ejpam-5716	284	15	·	·	PUNCT
ejpam-5716	284	16	,	,	PUNCT
ejpam-5716	284	17	6r	6r	NUM
ejpam-5716	284	18	−	−	NUM
ejpam-5716	284	19	3k	3k	NUM
ejpam-5716	284	20	}	}	PUNCT
ejpam-5716	284	21	.	.	PUNCT
ejpam-5716	285	1	this	this	PRON
ejpam-5716	285	2	implies	imply	VERB
ejpam-5716	285	3	that	that	DET
ejpam-5716	285	4	ζhk	ζhk	NOUN
ejpam-5716	285	5	(	(	PUNCT
ejpam-5716	285	6	s	s	NOUN
ejpam-5716	285	7	)	)	PUNCT
ejpam-5716	285	8	=	=	SYM
ejpam-5716	285	9	n−	n−	VERB
ejpam-5716	285	10	|n2	|n2	PROPN
ejpam-5716	285	11	pn	pn	PROPN
ejpam-5716	285	12	[	[	X
ejpam-5716	285	13	s]|	s]|	X
ejpam-5716	285	14	=	=	SYM
ejpam-5716	285	15	n−	n−	PROPN
ejpam-5716	285	16	[	[	X
ejpam-5716	285	17	(	(	PUNCT
ejpam-5716	285	18	2r	2r	NUM
ejpam-5716	285	19	−	−	PROPN
ejpam-5716	285	20	k	k	NOUN
ejpam-5716	285	21	)	)	PUNCT
ejpam-5716	286	1	+	+	CCONJ
ejpam-5716	286	2	2(2r	2(2r	NUM
ejpam-5716	286	3	−	−	NUM
ejpam-5716	286	4	k	k	NOUN
ejpam-5716	286	5	)	)	PUNCT
ejpam-5716	286	6	]	]	PUNCT
ejpam-5716	287	1	=	=	PUNCT
ejpam-5716	288	1	6r	6r	NUM
ejpam-5716	288	2	−	−	NOUN
ejpam-5716	289	1	[	[	X
ejpam-5716	289	2	6r	6r	NUM
ejpam-5716	289	3	−	−	NUM
ejpam-5716	289	4	3k	3k	NOUN
ejpam-5716	289	5	]	]	X
ejpam-5716	289	6	=	=	SYM
ejpam-5716	289	7	3k	3k	NUM
ejpam-5716	289	8	.	.	PUNCT
ejpam-5716	290	1	thus	thus	ADV
ejpam-5716	290	2	,	,	PUNCT
ejpam-5716	290	3	it	it	PRON
ejpam-5716	290	4	is	be	AUX
ejpam-5716	290	5	the	the	DET
ejpam-5716	290	6	minimum	minimum	ADJ
ejpam-5716	290	7	value	value	NOUN
ejpam-5716	290	8	for	for	ADP
ejpam-5716	290	9	any	any	DET
ejpam-5716	290	10	set	set	NOUN
ejpam-5716	290	11	s	s	NOUN
ejpam-5716	290	12	with	with	ADP
ejpam-5716	290	13	2r	2r	NUM
ejpam-5716	290	14	−	−	PROPN
ejpam-5716	290	15	k	k	NOUN
ejpam-5716	290	16	vertices	vertice	VERB
ejpam-5716	290	17	.	.	PUNCT
ejpam-5716	291	1	hence	hence	ADV
ejpam-5716	291	2	,	,	PUNCT
ejpam-5716	291	3	ζhk	ζhk	NOUN
ejpam-5716	291	4	(	(	PUNCT
ejpam-5716	291	5	pn	pn	NOUN
ejpam-5716	291	6	)	)	PUNCT
ejpam-5716	291	7	=	=	SYM
ejpam-5716	291	8	3k	3k	X
ejpam-5716	291	9	.	.	PUNCT
ejpam-5716	292	1	case	case	NOUN
ejpam-5716	292	2	2	2	NUM
ejpam-5716	292	3	:	:	PUNCT
ejpam-5716	292	4	suppose	suppose	VERB
ejpam-5716	292	5	n	n	X
ejpam-5716	292	6	=	=	SYM
ejpam-5716	292	7	6r	6r	NUM
ejpam-5716	292	8	+	+	CCONJ
ejpam-5716	292	9	1	1	X
ejpam-5716	292	10	.	.	PUNCT
ejpam-5716	292	11	by	by	ADP
ejpam-5716	292	12	theorem	theorem	ADJ
ejpam-5716	292	13	1	1	NUM
ejpam-5716	292	14	(	(	PUNCT
ejpam-5716	292	15	iii	iii	NOUN
ejpam-5716	292	16	)	)	PUNCT
ejpam-5716	292	17	,	,	PUNCT
ejpam-5716	292	18	γh(pn	γh(pn	NUM
ejpam-5716	292	19	)	)	PUNCT
ejpam-5716	292	20	=	=	SYM
ejpam-5716	293	1	2r	2r	NUM
ejpam-5716	294	1	+	+	CCONJ
ejpam-5716	294	2	1	1	X
ejpam-5716	294	3	.	.	X
ejpam-5716	294	4	choose	choose	VERB
ejpam-5716	294	5	a	a	DET
ejpam-5716	294	6	(	(	PUNCT
ejpam-5716	294	7	2r−k+1)-element	2r−k+1)-element	NUM
ejpam-5716	294	8	set	set	NOUN
ejpam-5716	294	9	s	s	PART
ejpam-5716	294	10	=	=	PUNCT
ejpam-5716	294	11	{	{	PUNCT
ejpam-5716	294	12	3	3	NUM
ejpam-5716	294	13	,	,	PUNCT
ejpam-5716	294	14	6	6	NUM
ejpam-5716	294	15	,	,	PUNCT
ejpam-5716	294	16	·	·	PUNCT
ejpam-5716	294	17	·	·	PUNCT
ejpam-5716	294	18	·	·	PUNCT
ejpam-5716	294	19	,	,	PUNCT
ejpam-5716	294	20	6r−3k+3	6r−3k+3	NUM
ejpam-5716	294	21	}	}	PUNCT
ejpam-5716	294	22	.	.	PUNCT
ejpam-5716	295	1	this	this	PRON
ejpam-5716	295	2	implies	imply	VERB
ejpam-5716	295	3	that	that	DET
ejpam-5716	295	4	ζhk	ζhk	NOUN
ejpam-5716	295	5	(	(	PUNCT
ejpam-5716	295	6	s	s	X
ejpam-5716	295	7	)	)	PUNCT
ejpam-5716	295	8	=	=	SYM
ejpam-5716	296	1	n−|n2	n−|n2	PROPN
ejpam-5716	296	2	pn	pn	NOUN
ejpam-5716	297	1	[	[	X
ejpam-5716	297	2	s]|	s]|	X
ejpam-5716	297	3	=	=	SYM
ejpam-5716	297	4	n−	n−	PROPN
ejpam-5716	297	5	[	[	X
ejpam-5716	297	6	(	(	PUNCT
ejpam-5716	297	7	2r−k+1)+2(2r−k+1	2r−k+1)+2(2r−k+1	NUM
ejpam-5716	297	8	)	)	PUNCT
ejpam-5716	297	9	]	]	PUNCT
ejpam-5716	298	1	=	=	PUNCT
ejpam-5716	299	1	6r−	6r−	NUM
ejpam-5716	299	2	[	[	PUNCT
ejpam-5716	299	3	6r−3k+3]+1	6r−3k+3]+1	NUM
ejpam-5716	299	4	=	=	SYM
ejpam-5716	299	5	3k−2	3k−2	PROPN
ejpam-5716	299	6	.	.	PUNCT
ejpam-5716	300	1	thus	thus	ADV
ejpam-5716	300	2	,	,	PUNCT
ejpam-5716	300	3	it	it	PRON
ejpam-5716	300	4	is	be	AUX
ejpam-5716	300	5	the	the	DET
ejpam-5716	300	6	minimum	minimum	ADJ
ejpam-5716	300	7	value	value	NOUN
ejpam-5716	300	8	for	for	ADP
ejpam-5716	300	9	any	any	DET
ejpam-5716	300	10	set	set	NOUN
ejpam-5716	300	11	s	s	NOUN
ejpam-5716	300	12	with	with	ADP
ejpam-5716	300	13	2r	2r	NUM
ejpam-5716	300	14	−	−	PROPN
ejpam-5716	301	1	k	k	NOUN
ejpam-5716	301	2	+	+	CCONJ
ejpam-5716	301	3	1	1	NUM
ejpam-5716	301	4	vertices	vertex	NOUN
ejpam-5716	301	5	.	.	PUNCT
ejpam-5716	302	1	hence	hence	ADV
ejpam-5716	302	2	,	,	PUNCT
ejpam-5716	302	3	ζhk	ζhk	NOUN
ejpam-5716	302	4	(	(	PUNCT
ejpam-5716	302	5	pn	pn	NOUN
ejpam-5716	302	6	)	)	PUNCT
ejpam-5716	302	7	=	=	PUNCT
ejpam-5716	302	8	3k	3k	X
ejpam-5716	302	9	−	−	NOUN
ejpam-5716	302	10	2	2	X
ejpam-5716	302	11	.	.	PUNCT
ejpam-5716	302	12	case	case	NOUN
ejpam-5716	302	13	3	3	NUM
ejpam-5716	302	14	:	:	PUNCT
ejpam-5716	302	15	suppose	suppose	VERB
ejpam-5716	302	16	n	n	X
ejpam-5716	302	17	=	=	SYM
ejpam-5716	302	18	6r	6r	NUM
ejpam-5716	303	1	+	+	CCONJ
ejpam-5716	303	2	s	s	VERB
ejpam-5716	303	3	where	where	SCONJ
ejpam-5716	303	4	2	2	NUM
ejpam-5716	303	5	≤	≤	NOUN
ejpam-5716	303	6	s	s	PART
ejpam-5716	303	7	≤	≤	NUM
ejpam-5716	303	8	5	5	NUM
ejpam-5716	303	9	.	.	PUNCT
ejpam-5716	303	10	by	by	ADP
ejpam-5716	303	11	theorem	theorem	ADJ
ejpam-5716	303	12	1	1	NUM
ejpam-5716	303	13	(	(	PUNCT
ejpam-5716	303	14	iii	iii	NOUN
ejpam-5716	303	15	)	)	PUNCT
ejpam-5716	303	16	,	,	PUNCT
ejpam-5716	303	17	γh(pn	γh(pn	NUM
ejpam-5716	303	18	)	)	PUNCT
ejpam-5716	303	19	=	=	SYM
ejpam-5716	304	1	2r	2r	NUM
ejpam-5716	305	1	+	+	CCONJ
ejpam-5716	305	2	2	2	X
ejpam-5716	305	3	.	.	X
ejpam-5716	305	4	choose	choose	VERB
ejpam-5716	305	5	a	a	DET
ejpam-5716	305	6	(	(	PUNCT
ejpam-5716	305	7	2r−k+2)-element	2r−k+2)-element	NUM
ejpam-5716	305	8	set	set	NOUN
ejpam-5716	305	9	s	s	PART
ejpam-5716	305	10	=	=	PUNCT
ejpam-5716	305	11	{	{	PUNCT
ejpam-5716	305	12	3	3	NUM
ejpam-5716	305	13	,	,	PUNCT
ejpam-5716	305	14	6	6	NUM
ejpam-5716	305	15	,	,	PUNCT
ejpam-5716	305	16	·	·	PUNCT
ejpam-5716	305	17	·	·	PUNCT
ejpam-5716	305	18	·	·	PUNCT
ejpam-5716	305	19	,	,	PUNCT
ejpam-5716	305	20	6r−	6r−	NUM
ejpam-5716	305	21	3k+6	3k+6	NUM
ejpam-5716	305	22	}	}	PUNCT
ejpam-5716	305	23	for	for	ADP
ejpam-5716	305	24	2	2	NUM
ejpam-5716	305	25	≤	≤	NOUN
ejpam-5716	305	26	k	k	NOUN
ejpam-5716	305	27	≤	≤	NUM
ejpam-5716	306	1	γh(pn)−	γh(pn)−	ADP
ejpam-5716	307	1	1	1	X
ejpam-5716	307	2	.	.	PUNCT
ejpam-5716	308	1	this	this	PRON
ejpam-5716	308	2	implies	imply	VERB
ejpam-5716	308	3	that	that	DET
ejpam-5716	308	4	ζhk	ζhk	NOUN
ejpam-5716	308	5	(	(	PUNCT
ejpam-5716	308	6	s	s	X
ejpam-5716	308	7	)	)	PUNCT
ejpam-5716	308	8	=	=	SYM
ejpam-5716	309	1	n−|n2	n−|n2	PROPN
ejpam-5716	309	2	pn	pn	NOUN
ejpam-5716	310	1	[	[	X
ejpam-5716	310	2	s]|	s]|	X
ejpam-5716	310	3	=	=	SYM
ejpam-5716	310	4	n−[(2r−k+2)+2(2r−k+2	n−[(2r−k+2)+2(2r−k+2	NUM
ejpam-5716	310	5	)	)	PUNCT
ejpam-5716	310	6	]	]	PUNCT
ejpam-5716	311	1	=	=	PUNCT
ejpam-5716	311	2	6r−[6r−3k+6]+s	6r−[6r−3k+6]+s	X
ejpam-5716	311	3	=	=	PUNCT
ejpam-5716	311	4	3k	3k	NOUN
ejpam-5716	311	5	+	+	CCONJ
ejpam-5716	311	6	s−	s−	PROPN
ejpam-5716	311	7	6	6	NUM
ejpam-5716	311	8	.	.	PUNCT
ejpam-5716	312	1	thus	thus	ADV
ejpam-5716	312	2	,	,	PUNCT
ejpam-5716	312	3	it	it	PRON
ejpam-5716	312	4	is	be	AUX
ejpam-5716	312	5	the	the	DET
ejpam-5716	312	6	minimum	minimum	ADJ
ejpam-5716	312	7	value	value	NOUN
ejpam-5716	312	8	for	for	ADP
ejpam-5716	312	9	any	any	DET
ejpam-5716	312	10	set	set	NOUN
ejpam-5716	312	11	s	s	NOUN
ejpam-5716	312	12	with	with	ADP
ejpam-5716	312	13	2r	2r	NUM
ejpam-5716	312	14	−	−	PROPN
ejpam-5716	313	1	k	k	NOUN
ejpam-5716	313	2	+	+	CCONJ
ejpam-5716	313	3	2	2	NUM
ejpam-5716	313	4	vertices	vertex	NOUN
ejpam-5716	313	5	.	.	PUNCT
ejpam-5716	314	1	hence	hence	ADV
ejpam-5716	314	2	,	,	PUNCT
ejpam-5716	314	3	ζhk	ζhk	NOUN
ejpam-5716	314	4	(	(	PUNCT
ejpam-5716	314	5	pn	pn	NOUN
ejpam-5716	314	6	)	)	PUNCT
ejpam-5716	314	7	=	=	SYM
ejpam-5716	314	8	3k	3k	NOUN
ejpam-5716	314	9	+	+	CCONJ
ejpam-5716	314	10	s−	s−	PROPN
ejpam-5716	314	11	6	6	NUM
ejpam-5716	314	12	.	.	PUNCT
ejpam-5716	314	13	from	from	ADP
ejpam-5716	314	14	theorem	theorem	ADJ
ejpam-5716	314	15	8	8	NUM
ejpam-5716	314	16	,	,	PUNCT
ejpam-5716	314	17	we	we	PRON
ejpam-5716	314	18	have	have	VERB
ejpam-5716	314	19	ζhk	ζhk	NOUN
ejpam-5716	314	20	(	(	PUNCT
ejpam-5716	314	21	c3	c3	PROPN
ejpam-5716	314	22	)	)	PUNCT
ejpam-5716	315	1	=	=	SYM
ejpam-5716	315	2	k	k	PROPN
ejpam-5716	315	3	for	for	ADP
ejpam-5716	315	4	k	k	PROPN
ejpam-5716	315	5	∈	∈	PROPN
ejpam-5716	315	6	{	{	PUNCT
ejpam-5716	315	7	1	1	NUM
ejpam-5716	315	8	,	,	PUNCT
ejpam-5716	315	9	2	2	NUM
ejpam-5716	315	10	}	}	PUNCT
ejpam-5716	315	11	.	.	PUNCT
ejpam-5716	316	1	now	now	ADV
ejpam-5716	316	2	,	,	PUNCT
ejpam-5716	316	3	since	since	SCONJ
ejpam-5716	316	4	γh(c4	γh(c4	NOUN
ejpam-5716	316	5	)	)	PUNCT
ejpam-5716	316	6	=	=	SYM
ejpam-5716	316	7	γh(c5	γh(c5	NOUN
ejpam-5716	316	8	)	)	PUNCT
ejpam-5716	316	9	=	=	SYM
ejpam-5716	316	10	2	2	NUM
ejpam-5716	316	11	,	,	PUNCT
ejpam-5716	316	12	k	k	NOUN
ejpam-5716	316	13	=	=	NOUN
ejpam-5716	316	14	1	1	X
ejpam-5716	316	15	.	.	PUNCT
ejpam-5716	316	16	it	it	PRON
ejpam-5716	316	17	can	can	AUX
ejpam-5716	316	18	easily	easily	ADV
ejpam-5716	316	19	be	be	AUX
ejpam-5716	316	20	verified	verify	VERB
ejpam-5716	316	21	that	that	SCONJ
ejpam-5716	316	22	|n2	|n2	PROPN
ejpam-5716	316	23	c4	c4	NOUN
ejpam-5716	316	24	[	[	X
ejpam-5716	316	25	s]|	s]|	X
ejpam-5716	316	26	=	=	SYM
ejpam-5716	316	27	2	2	NUM
ejpam-5716	316	28	and	and	CCONJ
ejpam-5716	316	29	|n2	|n2	PROPN
ejpam-5716	316	30	c5	c5	PROPN
ejpam-5716	317	1	[	[	X
ejpam-5716	317	2	s′]|	s′]|	X
ejpam-5716	317	3	=	=	SYM
ejpam-5716	317	4	3	3	NUM
ejpam-5716	317	5	for	for	ADP
ejpam-5716	317	6	any	any	DET
ejpam-5716	317	7	singleton	singleton	NOUN
ejpam-5716	317	8	subsets	subset	NOUN
ejpam-5716	317	9	s	s	PART
ejpam-5716	317	10	and	and	CCONJ
ejpam-5716	317	11	s′	s′	NUM
ejpam-5716	317	12	of	of	ADP
ejpam-5716	317	13	v	v	NOUN
ejpam-5716	317	14	(	(	PUNCT
ejpam-5716	317	15	c4	c4	NOUN
ejpam-5716	317	16	)	)	PUNCT
ejpam-5716	317	17	and	and	CCONJ
ejpam-5716	317	18	v	v	NOUN
ejpam-5716	317	19	(	(	PUNCT
ejpam-5716	317	20	c5	c5	PROPN
ejpam-5716	317	21	)	)	PUNCT
ejpam-5716	317	22	,	,	PUNCT
ejpam-5716	317	23	respectively	respectively	ADV
ejpam-5716	317	24	.	.	PUNCT
ejpam-5716	318	1	hence	hence	ADV
ejpam-5716	318	2	,	,	PUNCT
ejpam-5716	318	3	ζ	ζ	NOUN
ejpam-5716	318	4	h	h	NOUN
ejpam-5716	318	5	k	k	PROPN
ejpam-5716	318	6	(	(	PUNCT
ejpam-5716	318	7	c4	c4	NOUN
ejpam-5716	318	8	)	)	PUNCT
ejpam-5716	318	9	=	=	SYM
ejpam-5716	318	10	ζhk	ζhk	NOUN
ejpam-5716	318	11	(	(	PUNCT
ejpam-5716	318	12	c5	c5	PROPN
ejpam-5716	318	13	)	)	PUNCT
ejpam-5716	318	14	=	=	SYM
ejpam-5716	319	1	2	2	X
ejpam-5716	319	2	.	.	PUNCT
ejpam-5716	319	3	the	the	DET
ejpam-5716	319	4	proof	proof	NOUN
ejpam-5716	319	5	of	of	ADP
ejpam-5716	319	6	the	the	DET
ejpam-5716	319	7	next	next	ADJ
ejpam-5716	319	8	result	result	NOUN
ejpam-5716	319	9	uses	use	VERB
ejpam-5716	319	10	theorem	theorem	VERB
ejpam-5716	319	11	1(iv	1(iv	NUM
ejpam-5716	319	12	)	)	PUNCT
ejpam-5716	319	13	and	and	CCONJ
ejpam-5716	319	14	follows	follow	VERB
ejpam-5716	319	15	along	along	ADP
ejpam-5716	319	16	the	the	DET
ejpam-5716	319	17	same	same	ADJ
ejpam-5716	319	18	lines	line	NOUN
ejpam-5716	319	19	as	as	ADP
ejpam-5716	319	20	that	that	PRON
ejpam-5716	319	21	of	of	ADP
ejpam-5716	319	22	theorem	theorem	ADJ
ejpam-5716	319	23	9	9	NUM
ejpam-5716	319	24	.	.	PUNCT
ejpam-5716	319	25	theorem	theorem	NOUN
ejpam-5716	319	26	10	10	NUM
ejpam-5716	319	27	.	.	PUNCT
ejpam-5716	320	1	if	if	SCONJ
ejpam-5716	320	2	cn	cn	PROPN
ejpam-5716	320	3	is	be	AUX
ejpam-5716	320	4	a	a	DET
ejpam-5716	320	5	cycle	cycle	NOUN
ejpam-5716	320	6	on	on	ADP
ejpam-5716	320	7	n	n	PRON
ejpam-5716	320	8	≥	≥	NUM
ejpam-5716	320	9	6	6	NUM
ejpam-5716	320	10	vertices	vertex	NOUN
ejpam-5716	320	11	,	,	PUNCT
ejpam-5716	320	12	then	then	ADV
ejpam-5716	320	13	ζhk	ζhk	PROPN
ejpam-5716	320	14	(	(	PUNCT
ejpam-5716	320	15	cn	cn	PROPN
ejpam-5716	320	16	)	)	PUNCT
ejpam-5716	321	1	=	=	PUNCT
ejpam-5716	322	1			PRON
ejpam-5716	322	2	3k	3k	X
ejpam-5716	322	3	if	if	SCONJ
ejpam-5716	322	4	n	n	NOUN
ejpam-5716	322	5	=	=	SYM
ejpam-5716	322	6	6r	6r	NUM
ejpam-5716	323	1	3k	3k	NUM
ejpam-5716	324	1	−	−	NOUN
ejpam-5716	325	1	2	2	NUM
ejpam-5716	326	1	if	if	SCONJ
ejpam-5716	326	2	n	n	ADV
ejpam-5716	326	3	=	=	SYM
ejpam-5716	326	4	6r	6r	NUM
ejpam-5716	326	5	+	+	CCONJ
ejpam-5716	326	6	1	1	NUM
ejpam-5716	326	7	3k	3k	NOUN
ejpam-5716	326	8	+	+	CCONJ
ejpam-5716	326	9	s−	s−	PROPN
ejpam-5716	326	10	6	6	NUM
ejpam-5716	326	11	if	if	SCONJ
ejpam-5716	326	12	n	n	NOUN
ejpam-5716	326	13	=	=	SYM
ejpam-5716	326	14	6r	6r	NUM
ejpam-5716	327	1	+	+	SYM
ejpam-5716	327	2	s	s	X
ejpam-5716	327	3	;	;	PUNCT
ejpam-5716	327	4	2	2	NUM
ejpam-5716	327	5	≤	≤	NOUN
ejpam-5716	327	6	s	s	PART
ejpam-5716	327	7	≤	≤	NOUN
ejpam-5716	327	8	5	5	NUM
ejpam-5716	327	9	and	and	CCONJ
ejpam-5716	327	10	2	2	NUM
ejpam-5716	327	11	≤	≤	NOUN
ejpam-5716	327	12	k	k	X
ejpam-5716	327	13	≤	≤	NUM
ejpam-5716	328	1	γh(cn)−	γh(cn)−	ADP
ejpam-5716	328	2	1	1	X
ejpam-5716	328	3	.	.	PUNCT
ejpam-5716	329	1	lemma	lemma	PROPN
ejpam-5716	329	2	1	1	X
ejpam-5716	329	3	.	.	PUNCT
ejpam-5716	330	1	let	let	VERB
ejpam-5716	330	2	g	g	PRON
ejpam-5716	330	3	be	be	AUX
ejpam-5716	330	4	a	a	DET
ejpam-5716	330	5	nontrivial	nontrivial	ADJ
ejpam-5716	330	6	connected	connect	VERB
ejpam-5716	330	7	graph	graph	NOUN
ejpam-5716	330	8	with	with	ADP
ejpam-5716	330	9	γh(g	γh(g	NOUN
ejpam-5716	330	10	)	)	PUNCT
ejpam-5716	330	11	≥	≥	NOUN
ejpam-5716	330	12	2	2	NUM
ejpam-5716	330	13	and	and	CCONJ
ejpam-5716	330	14	let	let	VERB
ejpam-5716	330	15	k	k	PROPN
ejpam-5716	330	16	=	=	SYM
ejpam-5716	330	17	γh(g)−	γh(g)−	PROPN
ejpam-5716	331	1	1	1	NUM
ejpam-5716	331	2	.	.	PUNCT
ejpam-5716	331	3	then	then	ADV
ejpam-5716	331	4	s	s	VERB
ejpam-5716	331	5	⊆	⊆	NUM
ejpam-5716	331	6	v	v	NOUN
ejpam-5716	331	7	(	(	PUNCT
ejpam-5716	331	8	g	g	NOUN
ejpam-5716	331	9	)	)	PUNCT
ejpam-5716	331	10	is	be	AUX
ejpam-5716	331	11	a	a	DET
ejpam-5716	331	12	ζhk	ζhk	NOUN
ejpam-5716	331	13	-set	-set	PUNCT
ejpam-5716	331	14	of	of	ADP
ejpam-5716	331	15	g	g	PROPN
ejpam-5716	331	16	if	if	SCONJ
ejpam-5716	332	1	and	and	CCONJ
ejpam-5716	332	2	only	only	ADV
ejpam-5716	332	3	if	if	SCONJ
ejpam-5716	332	4	s	s	VERB
ejpam-5716	332	5	=	=	PRON
ejpam-5716	332	6	{	{	PUNCT
ejpam-5716	332	7	x	x	NOUN
ejpam-5716	332	8	}	}	PUNCT
ejpam-5716	332	9	for	for	ADP
ejpam-5716	332	10	some	some	PRON
ejpam-5716	332	11	x	x	SYM
ejpam-5716	332	12	∈	∈	PROPN
ejpam-5716	332	13	v	v	ADP
ejpam-5716	332	14	(	(	PUNCT
ejpam-5716	332	15	g	g	NOUN
ejpam-5716	332	16	)	)	PUNCT
ejpam-5716	332	17	with	with	ADP
ejpam-5716	332	18	n2	n2	ADJ
ejpam-5716	332	19	g(x	g(x	NOUN
ejpam-5716	332	20	)	)	PUNCT
ejpam-5716	332	21	=	=	SYM
ejpam-5716	332	22	△	△	NOUN
ejpam-5716	332	23	h(g	h(g	NOUN
ejpam-5716	332	24	)	)	PUNCT
ejpam-5716	332	25	.	.	PUNCT
ejpam-5716	333	1	proof	proof	NOUN
ejpam-5716	333	2	.	.	PUNCT
ejpam-5716	334	1	let	let	VERB
ejpam-5716	334	2	k	k	PROPN
ejpam-5716	334	3	=	=	PRON
ejpam-5716	334	4	γh(g	γh(g	NOUN
ejpam-5716	334	5	)	)	PUNCT
ejpam-5716	334	6	−	−	PROPN
ejpam-5716	334	7	1	1	NUM
ejpam-5716	334	8	and	and	CCONJ
ejpam-5716	334	9	let	let	VERB
ejpam-5716	334	10	s	s	PRON
ejpam-5716	334	11	⊆	⊆	NUM
ejpam-5716	334	12	v	v	NOUN
ejpam-5716	334	13	(	(	PUNCT
ejpam-5716	334	14	g	g	NOUN
ejpam-5716	334	15	)	)	PUNCT
ejpam-5716	334	16	be	be	AUX
ejpam-5716	334	17	a	a	DET
ejpam-5716	334	18	ζhk	ζhk	NOUN
ejpam-5716	334	19	-set	-set	PUNCT
ejpam-5716	334	20	of	of	ADP
ejpam-5716	334	21	g.	g.	PROPN
ejpam-5716	334	22	then	then	ADV
ejpam-5716	334	23	|s|	|s|	PROPN
ejpam-5716	334	24	=	=	SYM
ejpam-5716	334	25	1	1	NUM
ejpam-5716	334	26	,	,	PUNCT
ejpam-5716	334	27	say	say	INTJ
ejpam-5716	334	28	,	,	PUNCT
ejpam-5716	334	29	j.	j.	PROPN
ejpam-5716	334	30	anoche	anoche	PROPN
ejpam-5716	334	31	,	,	PUNCT
ejpam-5716	334	32	s.r	s.r	PROPN
ejpam-5716	334	33	.	.	PROPN
ejpam-5716	334	34	canoy	canoy	PROPN
ejpam-5716	334	35	jr	jr	PROPN
ejpam-5716	334	36	.	.	PUNCT
ejpam-5716	334	37	/	/	SYM
ejpam-5716	334	38	eur	eur	PROPN
ejpam-5716	334	39	.	.	PUNCT
ejpam-5716	335	1	j.	j.	PROPN
ejpam-5716	335	2	pure	pure	PROPN
ejpam-5716	335	3	appl	appl	PROPN
ejpam-5716	335	4	.	.	PROPN
ejpam-5716	335	5	math	math	PROPN
ejpam-5716	335	6	,	,	PUNCT
ejpam-5716	335	7	18	18	NUM
ejpam-5716	335	8	(	(	PUNCT
ejpam-5716	335	9	1	1	NUM
ejpam-5716	335	10	)	)	PUNCT
ejpam-5716	335	11	(	(	PUNCT
ejpam-5716	335	12	2025	2025	NUM
ejpam-5716	335	13	)	)	PUNCT
ejpam-5716	335	14	,	,	PUNCT
ejpam-5716	335	15	5716	5716	NUM
ejpam-5716	335	16	8	8	NUM
ejpam-5716	335	17	of	of	ADP
ejpam-5716	335	18	13	13	NUM
ejpam-5716	335	19	s	s	NOUN
ejpam-5716	335	20	=	=	PUNCT
ejpam-5716	335	21	{	{	PUNCT
ejpam-5716	335	22	x	x	NOUN
ejpam-5716	335	23	}	}	PUNCT
ejpam-5716	335	24	and	and	CCONJ
ejpam-5716	335	25	ζhk	ζhk	NOUN
ejpam-5716	335	26	(	(	PUNCT
ejpam-5716	335	27	s	s	NOUN
ejpam-5716	335	28	)	)	PUNCT
ejpam-5716	335	29	=	=	SYM
ejpam-5716	335	30	n	n	NUM
ejpam-5716	335	31	−	−	PROPN
ejpam-5716	335	32	|n2	|n2	PROPN
ejpam-5716	335	33	g[x]|	g[x]|	PROPN
ejpam-5716	335	34	=	=	PUNCT
ejpam-5716	335	35	ζhk	ζhk	PROPN
ejpam-5716	335	36	(	(	PUNCT
ejpam-5716	335	37	g	g	NOUN
ejpam-5716	335	38	)	)	PUNCT
ejpam-5716	335	39	.	.	PUNCT
ejpam-5716	336	1	this	this	PRON
ejpam-5716	336	2	implies	imply	VERB
ejpam-5716	336	3	that	that	SCONJ
ejpam-5716	336	4	|n2	|n2	PROPN
ejpam-5716	336	5	g[x]|	g[x]|	PROPN
ejpam-5716	336	6	is	be	AUX
ejpam-5716	336	7	maximum	maximum	ADJ
ejpam-5716	336	8	in	in	ADP
ejpam-5716	336	9	g.	g.	PROPN
ejpam-5716	336	10	thus	thus	ADV
ejpam-5716	336	11	,	,	PUNCT
ejpam-5716	336	12	n2	n2	ADJ
ejpam-5716	336	13	g(x	g(x	NOUN
ejpam-5716	336	14	)	)	PUNCT
ejpam-5716	336	15	=	=	SYM
ejpam-5716	336	16	△	△	NOUN
ejpam-5716	336	17	h(g	h(g	NOUN
ejpam-5716	336	18	)	)	PUNCT
ejpam-5716	336	19	.	.	PUNCT
ejpam-5716	337	1	conversely	conversely	ADV
ejpam-5716	337	2	,	,	PUNCT
ejpam-5716	337	3	suppose	suppose	VERB
ejpam-5716	337	4	s	s	VERB
ejpam-5716	337	5	=	=	PUNCT
ejpam-5716	337	6	{	{	PUNCT
ejpam-5716	337	7	x	x	NOUN
ejpam-5716	337	8	}	}	PUNCT
ejpam-5716	337	9	with	with	ADP
ejpam-5716	337	10	n2	n2	ADJ
ejpam-5716	337	11	g(x	g(x	NOUN
ejpam-5716	337	12	)	)	PUNCT
ejpam-5716	337	13	=	=	SYM
ejpam-5716	337	14	△	△	NOUN
ejpam-5716	337	15	h(g	h(g	NOUN
ejpam-5716	337	16	)	)	PUNCT
ejpam-5716	337	17	.	.	PUNCT
ejpam-5716	338	1	since	since	SCONJ
ejpam-5716	338	2	n−|n2	n−|n2	PROPN
ejpam-5716	338	3	g[s]|	g[s]|	X
ejpam-5716	338	4	=	=	SYM
ejpam-5716	338	5	n−|n2	n−|n2	PROPN
ejpam-5716	338	6	g[x]|	g[x]|	PROPN
ejpam-5716	338	7	=	=	SYM
ejpam-5716	338	8	n−	n−	PROPN
ejpam-5716	338	9	△	△	X
ejpam-5716	338	10	h(g	h(g	NOUN
ejpam-5716	338	11	)	)	PUNCT
ejpam-5716	338	12	is	be	AUX
ejpam-5716	338	13	the	the	DET
ejpam-5716	338	14	minimum	minimum	ADJ
ejpam-5716	338	15	possible	possible	ADJ
ejpam-5716	338	16	value	value	NOUN
ejpam-5716	338	17	for	for	ADP
ejpam-5716	338	18	any	any	DET
ejpam-5716	338	19	singleton	singleton	NOUN
ejpam-5716	338	20	subset	subset	NOUN
ejpam-5716	338	21	of	of	ADP
ejpam-5716	338	22	v	v	NOUN
ejpam-5716	338	23	(	(	PUNCT
ejpam-5716	338	24	g	g	NOUN
ejpam-5716	338	25	)	)	PUNCT
ejpam-5716	338	26	,	,	PUNCT
ejpam-5716	338	27	it	it	PRON
ejpam-5716	338	28	follows	follow	VERB
ejpam-5716	338	29	that	that	SCONJ
ejpam-5716	338	30	s	s	VERB
ejpam-5716	338	31	is	be	AUX
ejpam-5716	338	32	a	a	DET
ejpam-5716	338	33	ζhk	ζhk	NOUN
ejpam-5716	338	34	-set	-set	PUNCT
ejpam-5716	338	35	of	of	ADP
ejpam-5716	338	36	g.	g.	PROPN
ejpam-5716	338	37	theorem	theorem	VERB
ejpam-5716	338	38	11	11	NUM
ejpam-5716	338	39	.	.	PUNCT
ejpam-5716	339	1	if	if	SCONJ
ejpam-5716	339	2	g	g	PROPN
ejpam-5716	339	3	=	=	SYM
ejpam-5716	339	4	km1,m2	km1,m2	PROPN
ejpam-5716	339	5	,	,	PUNCT
ejpam-5716	339	6	·	·	PUNCT
ejpam-5716	339	7	·	·	PUNCT
ejpam-5716	339	8	·	·	PUNCT
ejpam-5716	339	9	,	,	PUNCT
ejpam-5716	339	10	mt	mt	PROPN
ejpam-5716	339	11	is	be	AUX
ejpam-5716	339	12	a	a	DET
ejpam-5716	339	13	complete	complete	ADJ
ejpam-5716	339	14	multipartite	multipartite	ADJ
ejpam-5716	339	15	graph	graph	NOUN
ejpam-5716	339	16	with	with	ADP
ejpam-5716	339	17	1	1	NUM
ejpam-5716	339	18	≤	≤	NOUN
ejpam-5716	339	19	m1	m1	NOUN
ejpam-5716	339	20	≤	≤	NUM
ejpam-5716	339	21	m2	m2	PROPN
ejpam-5716	339	22	≤	≤	NOUN
ejpam-5716	339	23	·	·	PUNCT
ejpam-5716	339	24	·	·	PUNCT
ejpam-5716	339	25	·	·	PUNCT
ejpam-5716	340	1	≤	≤	NUM
ejpam-5716	340	2	mt	mt	PROPN
ejpam-5716	340	3	,	,	PUNCT
ejpam-5716	340	4	then	then	ADV
ejpam-5716	340	5	γh(g	γh(g	PUNCT
ejpam-5716	340	6	)	)	PUNCT
ejpam-5716	340	7	=	=	SYM
ejpam-5716	340	8	t.	t.	NOUN
ejpam-5716	340	9	proof	proof	NOUN
ejpam-5716	340	10	.	.	PUNCT
ejpam-5716	341	1	let	let	VERB
ejpam-5716	341	2	q1	q1	PROPN
ejpam-5716	341	3	,	,	PUNCT
ejpam-5716	341	4	q2	q2	NOUN
ejpam-5716	341	5	,	,	PUNCT
ejpam-5716	341	6	·	·	PUNCT
ejpam-5716	341	7	·	·	PUNCT
ejpam-5716	341	8	·	·	PUNCT
ejpam-5716	341	9	,	,	PUNCT
ejpam-5716	341	10	qt	qt	INTJ
ejpam-5716	341	11	be	be	AUX
ejpam-5716	341	12	the	the	DET
ejpam-5716	341	13	partite	partite	ADJ
ejpam-5716	341	14	sets	set	NOUN
ejpam-5716	341	15	of	of	ADP
ejpam-5716	341	16	g	g	NOUN
ejpam-5716	341	17	and	and	CCONJ
ejpam-5716	341	18	let	let	VERB
ejpam-5716	341	19	s	s	PRON
ejpam-5716	341	20	be	be	AUX
ejpam-5716	341	21	a	a	DET
ejpam-5716	341	22	γh	γh	ADV
ejpam-5716	341	23	-	-	PUNCT
ejpam-5716	341	24	set	set	NOUN
ejpam-5716	341	25	of	of	ADP
ejpam-5716	341	26	g.	g.	PROPN
ejpam-5716	341	27	suppose	suppose	VERB
ejpam-5716	341	28	there	there	PRON
ejpam-5716	341	29	exists	exist	VERB
ejpam-5716	341	30	j	j	PROPN
ejpam-5716	341	31	∈	∈	PROPN
ejpam-5716	342	1	[	[	X
ejpam-5716	342	2	t	t	X
ejpam-5716	342	3	]	]	X
ejpam-5716	342	4	=	=	PUNCT
ejpam-5716	342	5	{	{	PUNCT
ejpam-5716	342	6	1	1	NUM
ejpam-5716	342	7	,	,	PUNCT
ejpam-5716	342	8	2	2	NUM
ejpam-5716	342	9	,	,	PUNCT
ejpam-5716	342	10	·	·	PUNCT
ejpam-5716	342	11	·	·	PUNCT
ejpam-5716	342	12	·	·	PUNCT
ejpam-5716	342	13	,	,	PUNCT
ejpam-5716	342	14	t	t	X
ejpam-5716	342	15	}	}	PUNCT
ejpam-5716	342	16	such	such	ADJ
ejpam-5716	342	17	that	that	PRON
ejpam-5716	342	18	s	s	VERB
ejpam-5716	342	19	∩qj	∩qj	NOUN
ejpam-5716	342	20	=	=	VERB
ejpam-5716	342	21	∅.	∅.	NOUN
ejpam-5716	342	22	then	then	ADV
ejpam-5716	342	23	qj	qj	PROPN
ejpam-5716	342	24	⊆	⊆	NUM
ejpam-5716	342	25	ng(s	ng(s	NUM
ejpam-5716	342	26	)	)	PUNCT
ejpam-5716	342	27	.	.	PUNCT
ejpam-5716	343	1	hence	hence	ADV
ejpam-5716	343	2	,	,	PUNCT
ejpam-5716	343	3	the	the	DET
ejpam-5716	343	4	vertices	vertex	NOUN
ejpam-5716	343	5	in	in	ADP
ejpam-5716	343	6	qj	qj	PROPN
ejpam-5716	343	7	are	be	AUX
ejpam-5716	343	8	not	not	PART
ejpam-5716	343	9	hop	hop	ADV
ejpam-5716	343	10	dominated	dominate	VERB
ejpam-5716	343	11	by	by	ADP
ejpam-5716	343	12	any	any	DET
ejpam-5716	343	13	element	element	NOUN
ejpam-5716	343	14	of	of	ADP
ejpam-5716	343	15	s.	s.	PROPN
ejpam-5716	343	16	this	this	PRON
ejpam-5716	343	17	implies	imply	VERB
ejpam-5716	343	18	that	that	SCONJ
ejpam-5716	343	19	s	s	VERB
ejpam-5716	343	20	is	be	AUX
ejpam-5716	343	21	not	not	PART
ejpam-5716	343	22	a	a	DET
ejpam-5716	343	23	hop	hop	NOUN
ejpam-5716	343	24	dominating	dominating	NOUN
ejpam-5716	343	25	set	set	NOUN
ejpam-5716	343	26	in	in	ADP
ejpam-5716	343	27	g	g	PROPN
ejpam-5716	343	28	,	,	PUNCT
ejpam-5716	343	29	a	a	DET
ejpam-5716	343	30	contradiction	contradiction	NOUN
ejpam-5716	343	31	.	.	PUNCT
ejpam-5716	344	1	therefore	therefore	ADV
ejpam-5716	344	2	,	,	PUNCT
ejpam-5716	344	3	s	s	VERB
ejpam-5716	344	4	∩qj	∩qj	NOUN
ejpam-5716	344	5	̸=	̸=	PROPN
ejpam-5716	344	6	∅	∅	NOUN
ejpam-5716	344	7	for	for	ADP
ejpam-5716	344	8	every	every	DET
ejpam-5716	344	9	j	j	PROPN
ejpam-5716	344	10	∈	∈	PROPN
ejpam-5716	345	1	[	[	X
ejpam-5716	345	2	t	t	X
ejpam-5716	345	3	]	]	PUNCT
ejpam-5716	345	4	.	.	PUNCT
ejpam-5716	346	1	since	since	SCONJ
ejpam-5716	346	2	s	s	PROPN
ejpam-5716	346	3	is	be	AUX
ejpam-5716	346	4	a	a	DET
ejpam-5716	346	5	γh	γh	ADV
ejpam-5716	346	6	-	-	PUNCT
ejpam-5716	346	7	set	set	NOUN
ejpam-5716	346	8	of	of	ADP
ejpam-5716	346	9	g	g	PROPN
ejpam-5716	346	10	,	,	PUNCT
ejpam-5716	346	11	|s	|s	PROPN
ejpam-5716	346	12	∩qj	∩qj	NOUN
ejpam-5716	346	13	|	|	NOUN
ejpam-5716	346	14	=	=	NOUN
ejpam-5716	346	15	1	1	NUM
ejpam-5716	346	16	for	for	ADP
ejpam-5716	346	17	every	every	DET
ejpam-5716	346	18	j	j	PROPN
ejpam-5716	346	19	∈	∈	PROPN
ejpam-5716	346	20	[	[	X
ejpam-5716	346	21	t	t	X
ejpam-5716	346	22	]	]	PUNCT
ejpam-5716	346	23	.	.	PUNCT
ejpam-5716	347	1	accordingly	accordingly	ADV
ejpam-5716	347	2	,	,	PUNCT
ejpam-5716	347	3	γh(g	γh(g	NOUN
ejpam-5716	347	4	)	)	PUNCT
ejpam-5716	348	1	=	=	SYM
ejpam-5716	348	2	|s|	|s|	NOUN
ejpam-5716	348	3	=	=	SYM
ejpam-5716	348	4	t.	t.	PROPN
ejpam-5716	348	5	theorem	theorem	NOUN
ejpam-5716	348	6	12	12	NUM
ejpam-5716	348	7	.	.	PUNCT
ejpam-5716	349	1	for	for	ADP
ejpam-5716	349	2	a	a	DET
ejpam-5716	349	3	complete	complete	ADJ
ejpam-5716	349	4	multipartite	multipartite	ADJ
ejpam-5716	349	5	graph	graph	NOUN
ejpam-5716	349	6	g	g	PROPN
ejpam-5716	349	7	=	=	PUNCT
ejpam-5716	349	8	km1,m2	km1,m2	PROPN
ejpam-5716	349	9	,	,	PUNCT
ejpam-5716	349	10	·	·	PUNCT
ejpam-5716	349	11	·	·	PUNCT
ejpam-5716	349	12	·	·	PUNCT
ejpam-5716	349	13	,	,	PUNCT
ejpam-5716	349	14	mt	mt	PROPN
ejpam-5716	349	15	where	where	SCONJ
ejpam-5716	349	16	m1	m1	PROPN
ejpam-5716	349	17	≤	≤	PROPN
ejpam-5716	349	18	m2	m2	PROPN
ejpam-5716	349	19	≤	≤	NOUN
ejpam-5716	349	20	·	·	PUNCT
ejpam-5716	349	21	·	·	PUNCT
ejpam-5716	349	22	·	·	PUNCT
ejpam-5716	349	23	≤	≤	NUM
ejpam-5716	349	24	mt	mt	PROPN
ejpam-5716	349	25	,	,	PUNCT
ejpam-5716	349	26	ζ	ζ	PROPN
ejpam-5716	349	27	h	h	NOUN
ejpam-5716	349	28	k	k	NOUN
ejpam-5716	349	29	(	(	PUNCT
ejpam-5716	349	30	g	g	NOUN
ejpam-5716	349	31	)	)	PUNCT
ejpam-5716	349	32	=	=	SYM
ejpam-5716	350	1	∑k	∑k	PROPN
ejpam-5716	350	2	j=1mj	j=1mj	PROPN
ejpam-5716	350	3	.	.	PUNCT
ejpam-5716	351	1	proof	proof	NOUN
ejpam-5716	351	2	.	.	PUNCT
ejpam-5716	352	1	let	let	VERB
ejpam-5716	352	2	q1	q1	PROPN
ejpam-5716	352	3	,	,	PUNCT
ejpam-5716	352	4	q2	q2	NOUN
ejpam-5716	352	5	,	,	PUNCT
ejpam-5716	352	6	·	·	PUNCT
ejpam-5716	352	7	·	·	PUNCT
ejpam-5716	352	8	·	·	PUNCT
ejpam-5716	352	9	,	,	PUNCT
ejpam-5716	352	10	qt	qt	INTJ
ejpam-5716	352	11	be	be	AUX
ejpam-5716	352	12	the	the	DET
ejpam-5716	352	13	partite	partite	ADJ
ejpam-5716	352	14	sets	set	NOUN
ejpam-5716	352	15	of	of	ADP
ejpam-5716	352	16	g	g	NOUN
ejpam-5716	352	17	with	with	ADP
ejpam-5716	352	18	cardinalities	cardinality	NOUN
ejpam-5716	352	19	m1	m1	PROPN
ejpam-5716	352	20	≤	≤	NUM
ejpam-5716	352	21	m2	m2	PROPN
ejpam-5716	352	22	≤	≤	NOUN
ejpam-5716	352	23	·	·	PUNCT
ejpam-5716	352	24	·	·	PUNCT
ejpam-5716	352	25	·	·	PUNCT
ejpam-5716	353	1	≤	≤	NUM
ejpam-5716	353	2	mt	mt	PROPN
ejpam-5716	353	3	.	.	PUNCT
ejpam-5716	353	4	by	by	ADP
ejpam-5716	353	5	theorem	theorem	NOUN
ejpam-5716	353	6	11	11	NUM
ejpam-5716	353	7	,	,	PUNCT
ejpam-5716	353	8	γh(g	γh(g	NOUN
ejpam-5716	353	9	)	)	PUNCT
ejpam-5716	353	10	=	=	SYM
ejpam-5716	354	1	t.	t.	NOUN
ejpam-5716	354	2	choose	choose	VERB
ejpam-5716	354	3	a	a	DET
ejpam-5716	354	4	(	(	PUNCT
ejpam-5716	354	5	t	t	PROPN
ejpam-5716	354	6	−	−	PROPN
ejpam-5716	354	7	k)-element	k)-element	PUNCT
ejpam-5716	354	8	set	set	VERB
ejpam-5716	354	9	s	s	PART
ejpam-5716	354	10	=	=	PUNCT
ejpam-5716	354	11	{	{	PUNCT
ejpam-5716	354	12	qk+1	qk+1	NOUN
ejpam-5716	354	13	,	,	PUNCT
ejpam-5716	354	14	qk+2	qk+2	NOUN
ejpam-5716	354	15	,	,	PUNCT
ejpam-5716	354	16	·	·	PUNCT
ejpam-5716	354	17	·	·	PUNCT
ejpam-5716	354	18	·	·	PUNCT
ejpam-5716	354	19	,	,	PUNCT
ejpam-5716	354	20	qt	qt	ADP
ejpam-5716	354	21	}	}	PUNCT
ejpam-5716	354	22	where	where	SCONJ
ejpam-5716	354	23	qj	qj	PROPN
ejpam-5716	354	24	∈	∈	PROPN
ejpam-5716	354	25	qj	qj	PROPN
ejpam-5716	354	26	for	for	ADP
ejpam-5716	354	27	each	each	DET
ejpam-5716	354	28	j	j	PROPN
ejpam-5716	354	29	∈	∈	PROPN
ejpam-5716	354	30	{	{	PUNCT
ejpam-5716	354	31	k+1	k+1	NOUN
ejpam-5716	354	32	,	,	PUNCT
ejpam-5716	354	33	k+2	k+2	NOUN
ejpam-5716	354	34	,	,	PUNCT
ejpam-5716	354	35	·	·	PUNCT
ejpam-5716	354	36	·	·	PUNCT
ejpam-5716	354	37	·	·	PUNCT
ejpam-5716	354	38	,	,	PUNCT
ejpam-5716	354	39	t	t	PROPN
ejpam-5716	354	40	}	}	PUNCT
ejpam-5716	354	41	.	.	PUNCT
ejpam-5716	355	1	then	then	ADV
ejpam-5716	355	2	n2	n2	ADJ
ejpam-5716	355	3	g[s	g[s	PROPN
ejpam-5716	355	4	]	]	X
ejpam-5716	355	5	=	=	SYM
ejpam-5716	355	6	∪t	∪t	NUM
ejpam-5716	355	7	j	j	X
ejpam-5716	355	8	=	=	NOUN
ejpam-5716	355	9	k+1n	k+1n	PROPN
ejpam-5716	355	10	2	2	NUM
ejpam-5716	355	11	g[qj	g[qj	NOUN
ejpam-5716	355	12	]	]	PUNCT
ejpam-5716	355	13	=	=	SYM
ejpam-5716	355	14	∪t	∪t	NUM
ejpam-5716	355	15	j	j	X
ejpam-5716	355	16	=	=	NOUN
ejpam-5716	355	17	k+1qj	k+1qj	X
ejpam-5716	355	18	.	.	PUNCT
ejpam-5716	356	1	it	it	PRON
ejpam-5716	356	2	follows	follow	VERB
ejpam-5716	356	3	that	that	SCONJ
ejpam-5716	356	4	|n2	|n2	PROPN
ejpam-5716	356	5	g[s]|	g[s]|	PROPN
ejpam-5716	356	6	=	=	PROPN
ejpam-5716	357	1	∑t	∑t	PROPN
ejpam-5716	357	2	j	j	PROPN
ejpam-5716	357	3	=	=	PRON
ejpam-5716	357	4	k+1	k+1	X
ejpam-5716	357	5	|qj	|qj	NUM
ejpam-5716	357	6	|	|	NOUN
ejpam-5716	357	7	=	=	SYM
ejpam-5716	357	8	∑t	∑t	PROPN
ejpam-5716	357	9	j	j	PROPN
ejpam-5716	357	10	=	=	PROPN
ejpam-5716	357	11	k+1mj	k+1mj	PROPN
ejpam-5716	357	12	.	.	PUNCT
ejpam-5716	358	1	this	this	PRON
ejpam-5716	358	2	is	be	AUX
ejpam-5716	358	3	the	the	DET
ejpam-5716	358	4	maximum	maximum	ADJ
ejpam-5716	358	5	value	value	NOUN
ejpam-5716	358	6	that	that	PRON
ejpam-5716	358	7	can	can	AUX
ejpam-5716	358	8	be	be	AUX
ejpam-5716	358	9	obtained	obtain	VERB
ejpam-5716	358	10	for	for	ADP
ejpam-5716	358	11	any	any	DET
ejpam-5716	358	12	set	set	NOUN
ejpam-5716	358	13	s	s	NOUN
ejpam-5716	358	14	with	with	ADP
ejpam-5716	358	15	t−	t−	PROPN
ejpam-5716	358	16	k	k	PROPN
ejpam-5716	358	17	vertices	vertex	NOUN
ejpam-5716	358	18	because	because	SCONJ
ejpam-5716	358	19	m1	m1	PROPN
ejpam-5716	358	20	≤	≤	NUM
ejpam-5716	358	21	m2	m2	PROPN
ejpam-5716	358	22	≤	≤	NOUN
ejpam-5716	358	23	·	·	PUNCT
ejpam-5716	358	24	·	·	PUNCT
ejpam-5716	358	25	·	·	PUNCT
ejpam-5716	359	1	≤	≤	NUM
ejpam-5716	359	2	mt	mt	PROPN
ejpam-5716	359	3	.	.	PUNCT
ejpam-5716	360	1	thus	thus	ADV
ejpam-5716	360	2	,	,	PUNCT
ejpam-5716	360	3	ζhk	ζhk	NOUN
ejpam-5716	360	4	(	(	PUNCT
ejpam-5716	360	5	g	g	NOUN
ejpam-5716	360	6	)	)	PUNCT
ejpam-5716	360	7	=	=	SYM
ejpam-5716	360	8	ζhk	ζhk	NOUN
ejpam-5716	360	9	(	(	PUNCT
ejpam-5716	360	10	s	s	X
ejpam-5716	360	11	)	)	PUNCT
ejpam-5716	360	12	=	=	SYM
ejpam-5716	360	13	|v	|v	PROPN
ejpam-5716	360	14	(	(	PUNCT
ejpam-5716	360	15	g)|	g)|	PROPN
ejpam-5716	360	16	−	−	PROPN
ejpam-5716	360	17	|n2	|n2	PROPN
ejpam-5716	360	18	g[s]|	g[s]|	PROPN
ejpam-5716	360	19	=	=	PUNCT
ejpam-5716	361	1	t∑	t∑	PROPN
ejpam-5716	361	2	j=1	j=1	PROPN
ejpam-5716	361	3	mj	mj	PROPN
ejpam-5716	361	4	−	−	PROPN
ejpam-5716	361	5	t∑	t∑	PROPN
ejpam-5716	361	6	j	j	X
ejpam-5716	362	1	=	=	NOUN
ejpam-5716	362	2	k+1	k+1	X
ejpam-5716	362	3	mj	mj	PROPN
ejpam-5716	362	4	=	=	PUNCT
ejpam-5716	362	5	k∑	k∑	PROPN
ejpam-5716	363	1	j=1	j=1	PROPN
ejpam-5716	363	2	mj	mj	PROPN
ejpam-5716	363	3	.	.	PUNCT
ejpam-5716	364	1	the	the	DET
ejpam-5716	364	2	next	next	ADJ
ejpam-5716	364	3	result	result	NOUN
ejpam-5716	364	4	is	be	AUX
ejpam-5716	364	5	a	a	DET
ejpam-5716	364	6	consequence	consequence	NOUN
ejpam-5716	364	7	of	of	ADP
ejpam-5716	364	8	theorem	theorem	NOUN
ejpam-5716	364	9	12	12	NUM
ejpam-5716	364	10	.	.	PUNCT
ejpam-5716	365	1	corollary	corollary	ADJ
ejpam-5716	365	2	1	1	NUM
ejpam-5716	365	3	.	.	PUNCT
ejpam-5716	366	1	for	for	ADP
ejpam-5716	366	2	a	a	DET
ejpam-5716	366	3	complete	complete	ADJ
ejpam-5716	366	4	bipartite	bipartite	NOUN
ejpam-5716	366	5	graph	graph	NOUN
ejpam-5716	366	6	km	km	PROPN
ejpam-5716	366	7	,	,	PUNCT
ejpam-5716	366	8	n	n	CCONJ
ejpam-5716	366	9	where	where	SCONJ
ejpam-5716	366	10	2	2	NUM
ejpam-5716	366	11	≤	≤	NUM
ejpam-5716	366	12	m	m	VERB
ejpam-5716	366	13	≤	≤	NOUN
ejpam-5716	366	14	n	n	CCONJ
ejpam-5716	366	15	,	,	PUNCT
ejpam-5716	366	16	ζhk	ζhk	NOUN
ejpam-5716	366	17	(	(	PUNCT
ejpam-5716	366	18	km	km	PROPN
ejpam-5716	366	19	,	,	PUNCT
ejpam-5716	366	20	n	n	CCONJ
ejpam-5716	366	21	)	)	PUNCT
ejpam-5716	366	22	=	=	SYM
ejpam-5716	366	23	m.	m.	NOUN
ejpam-5716	366	24	theorem	theorem	VERB
ejpam-5716	366	25	13	13	NUM
ejpam-5716	366	26	.	.	PUNCT
ejpam-5716	367	1	for	for	ADP
ejpam-5716	367	2	a	a	DET
ejpam-5716	367	3	petersen	petersen	NOUN
ejpam-5716	367	4	graph	graph	NOUN
ejpam-5716	367	5	p	p	NOUN
ejpam-5716	367	6	,	,	PUNCT
ejpam-5716	367	7	ζhk	ζhk	NOUN
ejpam-5716	367	8	(	(	PUNCT
ejpam-5716	367	9	p	p	NOUN
ejpam-5716	367	10	)	)	PUNCT
ejpam-5716	367	11	=	=	SYM
ejpam-5716	367	12	3	3	X
ejpam-5716	367	13	.	.	X
ejpam-5716	367	14	proof	proof	NOUN
ejpam-5716	367	15	.	.	PUNCT
ejpam-5716	368	1	by	by	ADP
ejpam-5716	368	2	theorem	theorem	ADJ
ejpam-5716	368	3	1(vi	1(vi	NUM
ejpam-5716	368	4	)	)	PUNCT
ejpam-5716	368	5	,	,	PUNCT
ejpam-5716	368	6	γh(p	γh(p	NUM
ejpam-5716	368	7	)	)	PUNCT
ejpam-5716	368	8	=	=	SYM
ejpam-5716	369	1	2	2	X
ejpam-5716	369	2	.	.	PUNCT
ejpam-5716	369	3	it	it	PRON
ejpam-5716	369	4	follows	follow	VERB
ejpam-5716	369	5	that	that	SCONJ
ejpam-5716	369	6	k	k	PROPN
ejpam-5716	370	1	=	=	PUNCT
ejpam-5716	370	2	1	1	X
ejpam-5716	370	3	.	.	PUNCT
ejpam-5716	371	1	let	let	VERB
ejpam-5716	371	2	s	s	PRON
ejpam-5716	371	3	be	be	AUX
ejpam-5716	371	4	a	a	DET
ejpam-5716	371	5	ζhk	ζhk	NOUN
ejpam-5716	371	6	-set	-set	PUNCT
ejpam-5716	371	7	of	of	ADP
ejpam-5716	371	8	p	p	PROPN
ejpam-5716	371	9	.	.	PUNCT
ejpam-5716	372	1	then	then	ADV
ejpam-5716	372	2	|s|	|s|	PROPN
ejpam-5716	372	3	=	=	SYM
ejpam-5716	372	4	1	1	NUM
ejpam-5716	372	5	,	,	PUNCT
ejpam-5716	372	6	say	say	VERB
ejpam-5716	372	7	s	s	X
ejpam-5716	372	8	=	=	PUNCT
ejpam-5716	372	9	{	{	PUNCT
ejpam-5716	372	10	v	v	NOUN
ejpam-5716	372	11	}	}	PUNCT
ejpam-5716	372	12	.	.	PUNCT
ejpam-5716	373	1	since	since	SCONJ
ejpam-5716	373	2	|n2	|n2	PROPN
ejpam-5716	373	3	p	p	PROPN
ejpam-5716	374	1	[	[	X
ejpam-5716	374	2	x]|	x]|	PROPN
ejpam-5716	374	3	=	=	SYM
ejpam-5716	374	4	7	7	NUM
ejpam-5716	374	5	for	for	ADP
ejpam-5716	374	6	every	every	DET
ejpam-5716	374	7	x	x	SYM
ejpam-5716	374	8	∈	∈	PROPN
ejpam-5716	374	9	v	v	NOUN
ejpam-5716	374	10	(	(	PUNCT
ejpam-5716	374	11	p	p	NOUN
ejpam-5716	374	12	)	)	PUNCT
ejpam-5716	374	13	,	,	PUNCT
ejpam-5716	374	14	it	it	PRON
ejpam-5716	374	15	follows	follow	VERB
ejpam-5716	374	16	that	that	SCONJ
ejpam-5716	374	17	|n2	|n2	PROPN
ejpam-5716	374	18	p	p	X
ejpam-5716	375	1	[	[	X
ejpam-5716	375	2	s]|	s]|	X
ejpam-5716	375	3	=	=	SYM
ejpam-5716	375	4	7	7	X
ejpam-5716	375	5	.	.	PUNCT
ejpam-5716	376	1	therefore	therefore	ADV
ejpam-5716	376	2	,	,	PUNCT
ejpam-5716	376	3	ζhk	ζhk	X
ejpam-5716	376	4	(	(	PUNCT
ejpam-5716	376	5	p	p	NOUN
ejpam-5716	376	6	)	)	PUNCT
ejpam-5716	376	7	=	=	SYM
ejpam-5716	376	8	ζhk	ζhk	NOUN
ejpam-5716	376	9	(	(	PUNCT
ejpam-5716	376	10	s	s	X
ejpam-5716	376	11	)	)	PUNCT
ejpam-5716	376	12	=	=	SYM
ejpam-5716	376	13	|v	|v	X
ejpam-5716	376	14	(	(	PUNCT
ejpam-5716	376	15	p	p	NOUN
ejpam-5716	376	16	)	)	PUNCT
ejpam-5716	376	17	|	|	ADV
ejpam-5716	376	18	−	−	PROPN
ejpam-5716	376	19	|n2	|n2	PROPN
ejpam-5716	376	20	p	p	X
ejpam-5716	377	1	[	[	X
ejpam-5716	377	2	s]|	s]|	X
ejpam-5716	377	3	=	=	SYM
ejpam-5716	377	4	10−	10−	NOUN
ejpam-5716	377	5	7	7	NUM
ejpam-5716	377	6	=	=	SYM
ejpam-5716	377	7	3	3	NUM
ejpam-5716	377	8	.	.	PUNCT
ejpam-5716	377	9	theorem	theorem	NOUN
ejpam-5716	377	10	14	14	NUM
ejpam-5716	377	11	.	.	PUNCT
ejpam-5716	378	1	let	let	VERB
ejpam-5716	378	2	g	g	PRON
ejpam-5716	378	3	be	be	AUX
ejpam-5716	378	4	a	a	DET
ejpam-5716	378	5	graph	graph	NOUN
ejpam-5716	378	6	with	with	ADP
ejpam-5716	378	7	diam(g	diam(g	NOUN
ejpam-5716	378	8	)	)	PUNCT
ejpam-5716	378	9	≥	≥	NOUN
ejpam-5716	378	10	3	3	NUM
ejpam-5716	378	11	and	and	CCONJ
ejpam-5716	378	12	let	let	VERB
ejpam-5716	378	13	g′	g′	NOUN
ejpam-5716	378	14	be	be	AUX
ejpam-5716	378	15	a	a	DET
ejpam-5716	378	16	graph	graph	NOUN
ejpam-5716	378	17	obtained	obtain	VERB
ejpam-5716	378	18	by	by	ADP
ejpam-5716	378	19	adding	add	VERB
ejpam-5716	378	20	any	any	DET
ejpam-5716	378	21	number	number	NOUN
ejpam-5716	378	22	of	of	ADP
ejpam-5716	378	23	edges	edge	NOUN
ejpam-5716	378	24	xy	xy	PROPN
ejpam-5716	378	25	to	to	ADP
ejpam-5716	378	26	e(g	e(g	PROPN
ejpam-5716	378	27	)	)	PUNCT
ejpam-5716	378	28	with	with	ADP
ejpam-5716	378	29	dg(x	dg(x	PROPN
ejpam-5716	378	30	,	,	PUNCT
ejpam-5716	378	31	y	y	PROPN
ejpam-5716	378	32	)	)	PUNCT
ejpam-5716	378	33	≥	≥	NOUN
ejpam-5716	378	34	3	3	NUM
ejpam-5716	378	35	such	such	ADJ
ejpam-5716	378	36	that	that	PRON
ejpam-5716	378	37	γh(g	γh(g	NOUN
ejpam-5716	378	38	)	)	PUNCT
ejpam-5716	378	39	=	=	NOUN
ejpam-5716	378	40	γh(g	γh(g	NOUN
ejpam-5716	378	41	′	′	NOUN
ejpam-5716	378	42	)	)	PUNCT
ejpam-5716	378	43	.	.	PUNCT
ejpam-5716	379	1	then	then	ADV
ejpam-5716	379	2	ζhk	ζhk	PROPN
ejpam-5716	379	3	(	(	PUNCT
ejpam-5716	379	4	g	g	NOUN
ejpam-5716	379	5	′	′	NUM
ejpam-5716	379	6	)	)	PUNCT
ejpam-5716	379	7	≤	≤	NUM
ejpam-5716	379	8	ζhk	ζhk	NOUN
ejpam-5716	379	9	(	(	PUNCT
ejpam-5716	379	10	g	g	NOUN
ejpam-5716	379	11	)	)	PUNCT
ejpam-5716	379	12	where	where	SCONJ
ejpam-5716	379	13	1	1	NUM
ejpam-5716	379	14	≤	≤	NUM
ejpam-5716	379	15	k	k	PROPN
ejpam-5716	379	16	≤	≤	PROPN
ejpam-5716	379	17	γh(g)−	γh(g)−	PROPN
ejpam-5716	379	18	1	1	NUM
ejpam-5716	379	19	.	.	PUNCT
ejpam-5716	379	20	j.	j.	PROPN
ejpam-5716	379	21	anoche	anoche	PROPN
ejpam-5716	379	22	,	,	PUNCT
ejpam-5716	379	23	s.r	s.r	PROPN
ejpam-5716	379	24	.	.	PROPN
ejpam-5716	379	25	canoy	canoy	PROPN
ejpam-5716	379	26	jr	jr	PROPN
ejpam-5716	379	27	.	.	PUNCT
ejpam-5716	379	28	/	/	SYM
ejpam-5716	379	29	eur	eur	PROPN
ejpam-5716	379	30	.	.	PUNCT
ejpam-5716	380	1	j.	j.	PROPN
ejpam-5716	380	2	pure	pure	PROPN
ejpam-5716	380	3	appl	appl	PROPN
ejpam-5716	380	4	.	.	PROPN
ejpam-5716	380	5	math	math	PROPN
ejpam-5716	380	6	,	,	PUNCT
ejpam-5716	380	7	18	18	NUM
ejpam-5716	380	8	(	(	PUNCT
ejpam-5716	380	9	1	1	NUM
ejpam-5716	380	10	)	)	PUNCT
ejpam-5716	380	11	(	(	PUNCT
ejpam-5716	380	12	2025	2025	NUM
ejpam-5716	380	13	)	)	PUNCT
ejpam-5716	380	14	,	,	PUNCT
ejpam-5716	380	15	5716	5716	NUM
ejpam-5716	380	16	9	9	NUM
ejpam-5716	380	17	of	of	ADP
ejpam-5716	380	18	13	13	NUM
ejpam-5716	380	19	proof	proof	NOUN
ejpam-5716	380	20	.	.	PUNCT
ejpam-5716	381	1	let	let	VERB
ejpam-5716	381	2	1	1	NUM
ejpam-5716	381	3	≤	≤	NOUN
ejpam-5716	381	4	k	k	NOUN
ejpam-5716	381	5	≤	≤	NOUN
ejpam-5716	381	6	γh(g	γh(g	NOUN
ejpam-5716	381	7	)	)	PUNCT
ejpam-5716	381	8	−	−	PROPN
ejpam-5716	381	9	1	1	NUM
ejpam-5716	381	10	and	and	CCONJ
ejpam-5716	381	11	let	let	VERB
ejpam-5716	381	12	s	s	PRON
ejpam-5716	381	13	be	be	AUX
ejpam-5716	381	14	a	a	DET
ejpam-5716	381	15	ζhk	ζhk	NOUN
ejpam-5716	381	16	-set	-set	PUNCT
ejpam-5716	381	17	of	of	ADP
ejpam-5716	381	18	g.	g.	PROPN
ejpam-5716	381	19	since	since	SCONJ
ejpam-5716	381	20	γh(g	γh(g	NOUN
ejpam-5716	381	21	)	)	PUNCT
ejpam-5716	381	22	=	=	NOUN
ejpam-5716	381	23	γh(g	γh(g	NOUN
ejpam-5716	381	24	′	′	NOUN
ejpam-5716	381	25	)	)	PUNCT
ejpam-5716	381	26	,	,	PUNCT
ejpam-5716	381	27	|s|	|s|	PROPN
ejpam-5716	381	28	=	=	SYM
ejpam-5716	381	29	γh(g)−k	γh(g)−k	NOUN
ejpam-5716	381	30	=	=	PUNCT
ejpam-5716	381	31	γh(g	γh(g	PRON
ejpam-5716	381	32	′)−k	′)−k	PROPN
ejpam-5716	381	33	.	.	PUNCT
ejpam-5716	382	1	let	let	VERB
ejpam-5716	382	2	x	x	SYM
ejpam-5716	382	3	∈	∈	PROPN
ejpam-5716	382	4	n2	n2	NOUN
ejpam-5716	382	5	g[s	g[s	PROPN
ejpam-5716	382	6	]	]	PUNCT
ejpam-5716	382	7	.	.	PUNCT
ejpam-5716	383	1	if	if	SCONJ
ejpam-5716	383	2	x	x	SYM
ejpam-5716	383	3	∈	∈	PROPN
ejpam-5716	383	4	s	s	NOUN
ejpam-5716	383	5	,	,	PUNCT
ejpam-5716	383	6	then	then	ADV
ejpam-5716	383	7	x	x	SYM
ejpam-5716	383	8	∈	∈	PROPN
ejpam-5716	383	9	n2	n2	NOUN
ejpam-5716	383	10	g′	g′	NOUN
ejpam-5716	384	1	[	[	X
ejpam-5716	384	2	s	s	X
ejpam-5716	384	3	]	]	X
ejpam-5716	384	4	.	.	PUNCT
ejpam-5716	385	1	if	if	SCONJ
ejpam-5716	385	2	x	x	SYM
ejpam-5716	385	3	∈	∈	PROPN
ejpam-5716	385	4	n2	n2	NOUN
ejpam-5716	385	5	g(s)\s	g(s)\s	NOUN
ejpam-5716	385	6	,	,	PUNCT
ejpam-5716	385	7	then	then	ADV
ejpam-5716	385	8	there	there	PRON
ejpam-5716	385	9	exists	exist	VERB
ejpam-5716	385	10	z	z	PROPN
ejpam-5716	385	11	∈	∈	PROPN
ejpam-5716	385	12	s	s	VERB
ejpam-5716	385	13	such	such	ADJ
ejpam-5716	385	14	that	that	PRON
ejpam-5716	385	15	dg(x	dg(x	NOUN
ejpam-5716	385	16	,	,	PUNCT
ejpam-5716	385	17	z	z	NOUN
ejpam-5716	385	18	)	)	PUNCT
ejpam-5716	385	19	=	=	SYM
ejpam-5716	385	20	2	2	X
ejpam-5716	385	21	.	.	PUNCT
ejpam-5716	386	1	it	it	PRON
ejpam-5716	386	2	follows	follow	VERB
ejpam-5716	386	3	that	that	SCONJ
ejpam-5716	386	4	xz	xz	PROPN
ejpam-5716	386	5	/∈	/∈	PUNCT
ejpam-5716	386	6	e(g′	e(g′	PROPN
ejpam-5716	386	7	)	)	PUNCT
ejpam-5716	386	8	.	.	PUNCT
ejpam-5716	387	1	hence	hence	ADV
ejpam-5716	387	2	,	,	PUNCT
ejpam-5716	387	3	dg′(x	dg′(x	PROPN
ejpam-5716	387	4	,	,	PUNCT
ejpam-5716	387	5	z	z	NOUN
ejpam-5716	387	6	)	)	PUNCT
ejpam-5716	387	7	=	=	SYM
ejpam-5716	388	1	2	2	X
ejpam-5716	388	2	.	.	PUNCT
ejpam-5716	388	3	this	this	PRON
ejpam-5716	388	4	implies	imply	VERB
ejpam-5716	388	5	that	that	SCONJ
ejpam-5716	388	6	x	x	SYM
ejpam-5716	388	7	∈	∈	PROPN
ejpam-5716	388	8	n2	n2	PROPN
ejpam-5716	388	9	g′(s	g′(s	PROPN
ejpam-5716	388	10	)	)	PUNCT
ejpam-5716	388	11	.	.	PUNCT
ejpam-5716	389	1	thus	thus	ADV
ejpam-5716	389	2	,	,	PUNCT
ejpam-5716	389	3	n2	n2	ADJ
ejpam-5716	389	4	g[s	g[s	PROPN
ejpam-5716	389	5	]	]	PUNCT
ejpam-5716	389	6	⊆	⊆	NUM
ejpam-5716	389	7	n2	n2	ADJ
ejpam-5716	389	8	g′	g′	NOUN
ejpam-5716	390	1	[	[	X
ejpam-5716	390	2	s	s	X
ejpam-5716	390	3	]	]	X
ejpam-5716	390	4	.	.	PUNCT
ejpam-5716	391	1	therefore	therefore	ADV
ejpam-5716	391	2	,	,	PUNCT
ejpam-5716	391	3	ζhk	ζhk	NOUN
ejpam-5716	391	4	(	(	PUNCT
ejpam-5716	391	5	g	g	NOUN
ejpam-5716	391	6	′	′	NUM
ejpam-5716	391	7	)	)	PUNCT
ejpam-5716	391	8	≤	≤	NUM
ejpam-5716	391	9	n−	n−	NOUN
ejpam-5716	391	10	|n2	|n2	PROPN
ejpam-5716	391	11	g′	g′	NOUN
ejpam-5716	392	1	[	[	X
ejpam-5716	392	2	s]|	s]|	PROPN
ejpam-5716	392	3	≤	≤	NUM
ejpam-5716	392	4	n−	n−	PROPN
ejpam-5716	392	5	|n2	|n2	PROPN
ejpam-5716	392	6	g[s]|	g[s]|	X
ejpam-5716	392	7	=	=	NOUN
ejpam-5716	392	8	ζhk	ζhk	NOUN
ejpam-5716	392	9	(	(	PUNCT
ejpam-5716	392	10	g	g	NOUN
ejpam-5716	392	11	)	)	PUNCT
ejpam-5716	392	12	.	.	PUNCT
ejpam-5716	393	1	theorem	theorem	NOUN
ejpam-5716	393	2	15	15	NUM
ejpam-5716	393	3	.	.	PUNCT
ejpam-5716	394	1	let	let	VERB
ejpam-5716	394	2	g	g	PRON
ejpam-5716	394	3	be	be	AUX
ejpam-5716	394	4	a	a	DET
ejpam-5716	394	5	graph	graph	NOUN
ejpam-5716	394	6	of	of	ADP
ejpam-5716	394	7	order	order	NOUN
ejpam-5716	394	8	n	n	NOUN
ejpam-5716	394	9	and	and	CCONJ
ejpam-5716	394	10	let	let	VERB
ejpam-5716	394	11	v	v	PART
ejpam-5716	394	12	be	be	AUX
ejpam-5716	394	13	a	a	DET
ejpam-5716	394	14	vertex	vertex	NOUN
ejpam-5716	394	15	with	with	ADP
ejpam-5716	394	16	the	the	DET
ejpam-5716	394	17	property	property	NOUN
ejpam-5716	394	18	that	that	PRON
ejpam-5716	394	19	for	for	ADP
ejpam-5716	394	20	every	every	DET
ejpam-5716	394	21	pair	pair	NOUN
ejpam-5716	394	22	of	of	ADP
ejpam-5716	394	23	vertices	vertex	NOUN
ejpam-5716	394	24	x	x	PUNCT
ejpam-5716	394	25	and	and	CCONJ
ejpam-5716	394	26	y	y	PROPN
ejpam-5716	394	27	with	with	ADP
ejpam-5716	394	28	dg(x	dg(x	PROPN
ejpam-5716	394	29	,	,	PUNCT
ejpam-5716	394	30	y	y	NOUN
ejpam-5716	394	31	)	)	PUNCT
ejpam-5716	394	32	=	=	SYM
ejpam-5716	394	33	2	2	NUM
ejpam-5716	394	34	and	and	CCONJ
ejpam-5716	394	35	v	v	ADP
ejpam-5716	394	36	∈	∈	PROPN
ejpam-5716	394	37	ng(x	ng(x	NUM
ejpam-5716	394	38	)	)	PUNCT
ejpam-5716	394	39	∩ng(y	∩ng(y	PROPN
ejpam-5716	394	40	)	)	PUNCT
ejpam-5716	394	41	,	,	PUNCT
ejpam-5716	394	42	it	it	PRON
ejpam-5716	394	43	holds	hold	VERB
ejpam-5716	394	44	that	that	SCONJ
ejpam-5716	394	45	|ng(x	|ng(x	VERB
ejpam-5716	394	46	)	)	PUNCT
ejpam-5716	394	47	∩	∩	NOUN
ejpam-5716	394	48	ng(y)|	ng(y)|	PRON
ejpam-5716	394	49	≥	≥	PROPN
ejpam-5716	394	50	2	2	NUM
ejpam-5716	394	51	.	.	PUNCT
ejpam-5716	395	1	if	if	SCONJ
ejpam-5716	395	2	g′	g′	NOUN
ejpam-5716	395	3	=	=	SYM
ejpam-5716	395	4	⟨v	⟨v	PUNCT
ejpam-5716	395	5	(	(	PUNCT
ejpam-5716	395	6	g	g	NOUN
ejpam-5716	395	7	)	)	PUNCT
ejpam-5716	395	8	\	\	NOUN
ejpam-5716	395	9	{	{	PUNCT
ejpam-5716	395	10	v}⟩	v}⟩	NOUN
ejpam-5716	395	11	and	and	CCONJ
ejpam-5716	395	12	γh(g	γh(g	NOUN
ejpam-5716	395	13	)	)	PUNCT
ejpam-5716	395	14	>	>	X
ejpam-5716	395	15	γh(g	γh(g	X
ejpam-5716	395	16	′	′	NUM
ejpam-5716	395	17	)	)	PUNCT
ejpam-5716	395	18	≥	≥	NOUN
ejpam-5716	395	19	2	2	NUM
ejpam-5716	395	20	,	,	PUNCT
ejpam-5716	395	21	then	then	ADV
ejpam-5716	395	22	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	395	23	)	)	PUNCT
ejpam-5716	395	24	≤	≤	NUM
ejpam-5716	395	25	ζhk	ζhk	NOUN
ejpam-5716	395	26	(	(	PUNCT
ejpam-5716	395	27	g	g	NOUN
ejpam-5716	395	28	′	′	NUM
ejpam-5716	395	29	)	)	PUNCT
ejpam-5716	396	1	+	+	CCONJ
ejpam-5716	396	2	1	1	NUM
ejpam-5716	396	3	where	where	SCONJ
ejpam-5716	396	4	1	1	NUM
ejpam-5716	396	5	≤	≤	NUM
ejpam-5716	396	6	k	k	PROPN
ejpam-5716	396	7	≤	≤	PROPN
ejpam-5716	396	8	γh(g)−	γh(g)−	PROPN
ejpam-5716	396	9	2	2	NUM
ejpam-5716	396	10	.	.	PUNCT
ejpam-5716	397	1	proof	proof	NOUN
ejpam-5716	397	2	.	.	PUNCT
ejpam-5716	398	1	let	let	VERB
ejpam-5716	398	2	s	s	PRON
ejpam-5716	398	3	be	be	AUX
ejpam-5716	398	4	a	a	DET
ejpam-5716	398	5	γh	γh	ADV
ejpam-5716	398	6	-	-	PUNCT
ejpam-5716	398	7	set	set	NOUN
ejpam-5716	398	8	in	in	ADP
ejpam-5716	398	9	g′.	g′.	NOUN
ejpam-5716	398	10	then	then	ADV
ejpam-5716	398	11	v	v	ADP
ejpam-5716	398	12	/∈	/∈	PUNCT
ejpam-5716	398	13	s.	s.	PROPN
ejpam-5716	398	14	let	let	VERB
ejpam-5716	398	15	s′	s′	ADJ
ejpam-5716	398	16	=	=	PUNCT
ejpam-5716	398	17	s	s	NOUN
ejpam-5716	398	18	∪	∪	X
ejpam-5716	398	19	{	{	PUNCT
ejpam-5716	398	20	v	v	NOUN
ejpam-5716	398	21	}	}	PUNCT
ejpam-5716	398	22	and	and	CCONJ
ejpam-5716	398	23	let	let	VERB
ejpam-5716	398	24	x	x	SYM
ejpam-5716	398	25	∈	∈	PROPN
ejpam-5716	398	26	v	v	X
ejpam-5716	398	27	(	(	PUNCT
ejpam-5716	398	28	g	g	NOUN
ejpam-5716	398	29	)	)	PUNCT
ejpam-5716	398	30	\	\	PUNCT
ejpam-5716	399	1	s′.	s′.	PROPN
ejpam-5716	399	2	since	since	SCONJ
ejpam-5716	399	3	x	x	PROPN
ejpam-5716	399	4	/∈	/∈	PROPN
ejpam-5716	399	5	s′	s′	NOUN
ejpam-5716	399	6	,	,	PUNCT
ejpam-5716	399	7	x	x	X
ejpam-5716	399	8	/∈	/∈	NOUN
ejpam-5716	399	9	s	s	PART
ejpam-5716	399	10	and	and	CCONJ
ejpam-5716	399	11	x	x	PUNCT
ejpam-5716	399	12	̸=	̸=	PROPN
ejpam-5716	399	13	v.	v.	ADP
ejpam-5716	399	14	hence	hence	ADV
ejpam-5716	399	15	,	,	PUNCT
ejpam-5716	399	16	x	x	PUNCT
ejpam-5716	399	17	∈	∈	NOUN
ejpam-5716	399	18	v	v	X
ejpam-5716	399	19	(	(	PUNCT
ejpam-5716	399	20	g′)\s	g′)\s	PROPN
ejpam-5716	399	21	.	.	PUNCT
ejpam-5716	400	1	since	since	SCONJ
ejpam-5716	400	2	s	s	PROPN
ejpam-5716	400	3	is	be	AUX
ejpam-5716	400	4	a	a	DET
ejpam-5716	400	5	hop	hop	NOUN
ejpam-5716	400	6	dominating	dominating	NOUN
ejpam-5716	400	7	set	set	VERB
ejpam-5716	400	8	in	in	ADP
ejpam-5716	400	9	g′	g′	NOUN
ejpam-5716	400	10	,	,	PUNCT
ejpam-5716	400	11	there	there	PRON
ejpam-5716	400	12	exists	exist	VERB
ejpam-5716	400	13	z	z	PROPN
ejpam-5716	400	14	∈	∈	PROPN
ejpam-5716	400	15	s	s	VERB
ejpam-5716	400	16	such	such	ADJ
ejpam-5716	400	17	that	that	DET
ejpam-5716	400	18	dg′(z	dg′(z	PROPN
ejpam-5716	400	19	,	,	PUNCT
ejpam-5716	400	20	x	x	NOUN
ejpam-5716	400	21	)	)	PUNCT
ejpam-5716	400	22	=	=	SYM
ejpam-5716	401	1	2	2	X
ejpam-5716	401	2	.	.	PUNCT
ejpam-5716	402	1	this	this	PRON
ejpam-5716	402	2	implies	imply	VERB
ejpam-5716	402	3	that	that	SCONJ
ejpam-5716	402	4	there	there	PRON
ejpam-5716	402	5	exists	exist	VERB
ejpam-5716	402	6	z	z	PROPN
ejpam-5716	402	7	∈	∈	PROPN
ejpam-5716	402	8	s′	s′	NOUN
ejpam-5716	402	9	such	such	ADJ
ejpam-5716	402	10	that	that	SCONJ
ejpam-5716	402	11	dg(z	dg(z	NOUN
ejpam-5716	402	12	,	,	PUNCT
ejpam-5716	402	13	x	x	X
ejpam-5716	402	14	)	)	PUNCT
ejpam-5716	402	15	=	=	SYM
ejpam-5716	402	16	2	2	X
ejpam-5716	402	17	.	.	X
ejpam-5716	402	18	therefore	therefore	ADV
ejpam-5716	402	19	,	,	PUNCT
ejpam-5716	402	20	s′	s′	PROPN
ejpam-5716	402	21	is	be	AUX
ejpam-5716	402	22	a	a	DET
ejpam-5716	402	23	hop	hop	NOUN
ejpam-5716	402	24	dominating	dominating	NOUN
ejpam-5716	402	25	set	set	VERB
ejpam-5716	402	26	in	in	ADP
ejpam-5716	402	27	g	g	NOUN
ejpam-5716	402	28	and	and	CCONJ
ejpam-5716	402	29	γh(g	γh(g	NOUN
ejpam-5716	402	30	)	)	PUNCT
ejpam-5716	402	31	≤	≤	NUM
ejpam-5716	402	32	|s′|	|s′|	NOUN
ejpam-5716	402	33	=	=	SYM
ejpam-5716	402	34	γh(g	γh(g	X
ejpam-5716	402	35	′	′	NUM
ejpam-5716	402	36	)	)	PUNCT
ejpam-5716	403	1	+	+	CCONJ
ejpam-5716	403	2	1	1	X
ejpam-5716	403	3	.	.	PUNCT
ejpam-5716	403	4	since	since	SCONJ
ejpam-5716	403	5	γh(g	γh(g	NOUN
ejpam-5716	403	6	′	′	NUM
ejpam-5716	403	7	)	)	PUNCT
ejpam-5716	403	8	<	<	X
ejpam-5716	403	9	γh(g	γh(g	NOUN
ejpam-5716	403	10	)	)	PUNCT
ejpam-5716	403	11	,	,	PUNCT
ejpam-5716	403	12	γh(g	γh(g	PUNCT
ejpam-5716	403	13	′	′	NUM
ejpam-5716	403	14	)	)	PUNCT
ejpam-5716	403	15	+	+	CCONJ
ejpam-5716	403	16	1	1	NUM
ejpam-5716	403	17	≤	≤	NOUN
ejpam-5716	403	18	γh(g	γh(g	NOUN
ejpam-5716	403	19	)	)	PUNCT
ejpam-5716	403	20	.	.	PUNCT
ejpam-5716	404	1	thus	thus	ADV
ejpam-5716	404	2	,	,	PUNCT
ejpam-5716	404	3	γh(g	γh(g	NOUN
ejpam-5716	404	4	)	)	PUNCT
ejpam-5716	404	5	=	=	NOUN
ejpam-5716	404	6	γh(g	γh(g	NOUN
ejpam-5716	404	7	′	′	NOUN
ejpam-5716	404	8	)	)	PUNCT
ejpam-5716	405	1	+	+	CCONJ
ejpam-5716	405	2	1	1	X
ejpam-5716	405	3	.	.	PUNCT
ejpam-5716	405	4	now	now	ADV
ejpam-5716	405	5	let	let	VERB
ejpam-5716	405	6	d	d	PRON
ejpam-5716	405	7	be	be	AUX
ejpam-5716	405	8	a	a	DET
ejpam-5716	405	9	ζhk	ζhk	NOUN
ejpam-5716	405	10	-set	-set	PUNCT
ejpam-5716	405	11	of	of	ADP
ejpam-5716	405	12	g′	g′	NOUN
ejpam-5716	405	13	where	where	SCONJ
ejpam-5716	405	14	1	1	NUM
ejpam-5716	405	15	≤	≤	NUM
ejpam-5716	405	16	k	k	X
ejpam-5716	405	17	≤	≤	NOUN
ejpam-5716	405	18	γh(g	γh(g	NOUN
ejpam-5716	405	19	)	)	PUNCT
ejpam-5716	405	20	−	−	PROPN
ejpam-5716	406	1	2	2	X
ejpam-5716	406	2	.	.	PUNCT
ejpam-5716	406	3	then	then	ADV
ejpam-5716	406	4	|d|	|d|	PROPN
ejpam-5716	406	5	=	=	SYM
ejpam-5716	406	6	γh(g	γh(g	NOUN
ejpam-5716	406	7	′	′	NUM
ejpam-5716	406	8	)	)	PUNCT
ejpam-5716	406	9	−	−	PROPN
ejpam-5716	406	10	k	k	PROPN
ejpam-5716	406	11	and	and	CCONJ
ejpam-5716	406	12	ζhk	ζhk	PROPN
ejpam-5716	406	13	(	(	PUNCT
ejpam-5716	406	14	g	g	NOUN
ejpam-5716	406	15	′	′	NUM
ejpam-5716	406	16	)	)	PUNCT
ejpam-5716	406	17	=	=	PUNCT
ejpam-5716	406	18	(	(	PUNCT
ejpam-5716	406	19	n	n	CCONJ
ejpam-5716	406	20	−	−	PROPN
ejpam-5716	406	21	1	1	NUM
ejpam-5716	406	22	)	)	PUNCT
ejpam-5716	406	23	−	−	PROPN
ejpam-5716	406	24	|n2	|n2	PROPN
ejpam-5716	406	25	g′	g′	PROPN
ejpam-5716	407	1	[	[	X
ejpam-5716	407	2	d]|	d]|	PROPN
ejpam-5716	407	3	.	.	PUNCT
ejpam-5716	408	1	this	this	PRON
ejpam-5716	408	2	implies	imply	VERB
ejpam-5716	408	3	that	that	SCONJ
ejpam-5716	408	4	|n2	|n2	PROPN
ejpam-5716	408	5	g′	g′	NOUN
ejpam-5716	409	1	[	[	X
ejpam-5716	409	2	d]|	d]|	X
ejpam-5716	409	3	=	=	SYM
ejpam-5716	409	4	(	(	PUNCT
ejpam-5716	409	5	n	n	CCONJ
ejpam-5716	409	6	−	−	PROPN
ejpam-5716	409	7	1	1	NUM
ejpam-5716	409	8	)	)	PUNCT
ejpam-5716	409	9	−	−	PROPN
ejpam-5716	409	10	ζhk	ζhk	NOUN
ejpam-5716	409	11	(	(	PUNCT
ejpam-5716	409	12	g	g	PROPN
ejpam-5716	409	13	′	′	NUM
ejpam-5716	409	14	)	)	PUNCT
ejpam-5716	409	15	.	.	PUNCT
ejpam-5716	410	1	since	since	SCONJ
ejpam-5716	410	2	|d|	|d|	PROPN
ejpam-5716	410	3	=	=	X
ejpam-5716	410	4	γh(g	γh(g	X
ejpam-5716	410	5	′)−	′)−	PROPN
ejpam-5716	410	6	k	k	NOUN
ejpam-5716	410	7	=	=	PUNCT
ejpam-5716	410	8	γh(g)−	γh(g)−	PROPN
ejpam-5716	410	9	(	(	PUNCT
ejpam-5716	410	10	k	k	NOUN
ejpam-5716	410	11	+	+	PROPN
ejpam-5716	410	12	1	1	NUM
ejpam-5716	410	13	)	)	PUNCT
ejpam-5716	410	14	,	,	PUNCT
ejpam-5716	410	15	it	it	PRON
ejpam-5716	410	16	follows	follow	VERB
ejpam-5716	410	17	that	that	DET
ejpam-5716	410	18	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	410	19	)	)	PUNCT
ejpam-5716	410	20	≤	≤	NUM
ejpam-5716	410	21	n−	n−	PROPN
ejpam-5716	410	22	|n2	|n2	PROPN
ejpam-5716	410	23	g[d]|	g[d]|	PROPN
ejpam-5716	410	24	.	.	PUNCT
ejpam-5716	411	1	consider	consider	VERB
ejpam-5716	411	2	the	the	DET
ejpam-5716	411	3	following	follow	VERB
ejpam-5716	411	4	cases	case	NOUN
ejpam-5716	411	5	:	:	PUNCT
ejpam-5716	411	6	case	case	NOUN
ejpam-5716	411	7	1	1	NUM
ejpam-5716	411	8	:	:	PUNCT
ejpam-5716	411	9	|n2	|n2	PROPN
ejpam-5716	411	10	g[d]|	g[d]|	PROPN
ejpam-5716	411	11	=	=	SYM
ejpam-5716	411	12	|n2	|n2	PROPN
ejpam-5716	411	13	g′	g′	NOUN
ejpam-5716	412	1	[	[	X
ejpam-5716	412	2	d]|	d]|	PROPN
ejpam-5716	412	3	.	.	PUNCT
ejpam-5716	413	1	then	then	ADV
ejpam-5716	413	2	(	(	PUNCT
ejpam-5716	413	3	n	n	CCONJ
ejpam-5716	413	4	−	−	PROPN
ejpam-5716	413	5	1	1	NUM
ejpam-5716	413	6	)	)	PUNCT
ejpam-5716	413	7	−	−	PROPN
ejpam-5716	414	1	ζhk	ζhk	NOUN
ejpam-5716	415	1	(	(	PUNCT
ejpam-5716	415	2	g	g	NOUN
ejpam-5716	415	3	′	′	NUM
ejpam-5716	415	4	)	)	PUNCT
ejpam-5716	416	1	=	=	PUNCT
ejpam-5716	416	2	|n2	|n2	PROPN
ejpam-5716	416	3	g′	g′	NOUN
ejpam-5716	417	1	[	[	X
ejpam-5716	417	2	d]|	d]|	X
ejpam-5716	417	3	=	=	SYM
ejpam-5716	417	4	|n2	|n2	PROPN
ejpam-5716	417	5	g[d]|	g[d]|	PROPN
ejpam-5716	417	6	≤	≤	PUNCT
ejpam-5716	417	7	n	n	CCONJ
ejpam-5716	417	8	−	−	PROPN
ejpam-5716	417	9	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	417	10	)	)	PUNCT
ejpam-5716	417	11	.	.	PUNCT
ejpam-5716	418	1	thus	thus	ADV
ejpam-5716	418	2	,	,	PUNCT
ejpam-5716	418	3	we	we	PRON
ejpam-5716	418	4	have	have	VERB
ejpam-5716	418	5	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	418	6	)	)	PUNCT
ejpam-5716	418	7	≤	≤	NUM
ejpam-5716	418	8	ζhk	ζhk	NOUN
ejpam-5716	418	9	(	(	PUNCT
ejpam-5716	418	10	g	g	NOUN
ejpam-5716	418	11	′	′	NUM
ejpam-5716	418	12	)	)	PUNCT
ejpam-5716	419	1	+	+	CCONJ
ejpam-5716	419	2	1	1	X
ejpam-5716	419	3	.	.	X
ejpam-5716	419	4	case	case	NOUN
ejpam-5716	419	5	2	2	NUM
ejpam-5716	419	6	:	:	PUNCT
ejpam-5716	419	7	|n2	|n2	PROPN
ejpam-5716	419	8	g[d]|	g[d]|	PROPN
ejpam-5716	419	9	=	=	SYM
ejpam-5716	419	10	̸	̸	NUM
ejpam-5716	419	11	|n2	|n2	NOUN
ejpam-5716	419	12	g′	g′	NOUN
ejpam-5716	420	1	[	[	X
ejpam-5716	420	2	d]|	d]|	PROPN
ejpam-5716	420	3	.	.	PROPN
ejpam-5716	420	4	since	since	SCONJ
ejpam-5716	420	5	n2	n2	PROPN
ejpam-5716	420	6	g′	g′	PROPN
ejpam-5716	420	7	[	[	X
ejpam-5716	420	8	d	d	X
ejpam-5716	420	9	]	]	X
ejpam-5716	420	10	⊆	⊆	NUM
ejpam-5716	420	11	n2	n2	PROPN
ejpam-5716	420	12	g[d	g[d	PROPN
ejpam-5716	420	13	]	]	PUNCT
ejpam-5716	420	14	,	,	PUNCT
ejpam-5716	420	15	the	the	DET
ejpam-5716	420	16	assumption	assumption	NOUN
ejpam-5716	420	17	implies	imply	VERB
ejpam-5716	420	18	that	that	SCONJ
ejpam-5716	420	19	there	there	PRON
ejpam-5716	420	20	exists	exist	VERB
ejpam-5716	420	21	w	w	PROPN
ejpam-5716	420	22	∈	∈	PROPN
ejpam-5716	420	23	n2	n2	NOUN
ejpam-5716	420	24	g(d	g(d	PROPN
ejpam-5716	420	25	)	)	PUNCT
ejpam-5716	420	26	\	\	PROPN
ejpam-5716	420	27	n2	n2	ADJ
ejpam-5716	420	28	g′(d	g′(d	PROPN
ejpam-5716	420	29	)	)	PUNCT
ejpam-5716	420	30	.	.	PUNCT
ejpam-5716	421	1	suppose	suppose	VERB
ejpam-5716	421	2	w	w	ADP
ejpam-5716	421	3	̸=	̸=	PROPN
ejpam-5716	421	4	v.	v.	CCONJ
ejpam-5716	421	5	since	since	SCONJ
ejpam-5716	421	6	w	w	PROPN
ejpam-5716	421	7	∈	∈	PROPN
ejpam-5716	421	8	n2	n2	NOUN
ejpam-5716	421	9	g(d	g(d	PROPN
ejpam-5716	421	10	)	)	PUNCT
ejpam-5716	421	11	,	,	PUNCT
ejpam-5716	421	12	there	there	PRON
ejpam-5716	421	13	exists	exist	VERB
ejpam-5716	421	14	u	u	NOUN
ejpam-5716	421	15	∈	∈	PROPN
ejpam-5716	421	16	d	d	ADP
ejpam-5716	422	1	such	such	ADJ
ejpam-5716	422	2	that	that	PRON
ejpam-5716	422	3	dg(w	dg(w	NUM
ejpam-5716	422	4	,	,	PUNCT
ejpam-5716	422	5	u	u	NOUN
ejpam-5716	422	6	)	)	PUNCT
ejpam-5716	422	7	=	=	SYM
ejpam-5716	422	8	2	2	X
ejpam-5716	422	9	.	.	PUNCT
ejpam-5716	422	10	since	since	SCONJ
ejpam-5716	422	11	u	u	PROPN
ejpam-5716	422	12	∈	∈	PROPN
ejpam-5716	422	13	d	d	PROPN
ejpam-5716	422	14	,	,	PUNCT
ejpam-5716	422	15	u	u	PROPN
ejpam-5716	422	16	̸=	̸=	PROPN
ejpam-5716	422	17	v.	v.	ADP
ejpam-5716	422	18	the	the	DET
ejpam-5716	422	19	assumption	assumption	NOUN
ejpam-5716	422	20	that	that	SCONJ
ejpam-5716	422	21	w	w	PROPN
ejpam-5716	422	22	/∈	/∈	PUNCT
ejpam-5716	422	23	n2	n2	ADJ
ejpam-5716	422	24	g′(d	g′(d	NOUN
ejpam-5716	422	25	)	)	PUNCT
ejpam-5716	422	26	would	would	AUX
ejpam-5716	422	27	imply	imply	VERB
ejpam-5716	422	28	that	that	DET
ejpam-5716	422	29	v	v	NUM
ejpam-5716	422	30	∈	∈	PROPN
ejpam-5716	422	31	ng(w)∩ng(u	ng(w)∩ng(u	PROPN
ejpam-5716	422	32	)	)	PUNCT
ejpam-5716	422	33	and	and	CCONJ
ejpam-5716	422	34	the	the	DET
ejpam-5716	422	35	path	path	NOUN
ejpam-5716	422	36	[	[	X
ejpam-5716	422	37	w	w	PROPN
ejpam-5716	422	38	,	,	PUNCT
ejpam-5716	422	39	v	v	NOUN
ejpam-5716	422	40	,	,	PUNCT
ejpam-5716	422	41	u	u	NOUN
ejpam-5716	422	42	]	]	X
ejpam-5716	422	43	is	be	AUX
ejpam-5716	422	44	the	the	DET
ejpam-5716	422	45	only	only	ADJ
ejpam-5716	422	46	w	w	NOUN
ejpam-5716	422	47	-	-	PUNCT
ejpam-5716	422	48	u	u	NOUN
ejpam-5716	422	49	geodesic	geodesic	NOUN
ejpam-5716	422	50	in	in	ADP
ejpam-5716	422	51	g	g	PROPN
ejpam-5716	422	52	,	,	PUNCT
ejpam-5716	422	53	contradicting	contradict	VERB
ejpam-5716	422	54	the	the	DET
ejpam-5716	422	55	property	property	NOUN
ejpam-5716	422	56	of	of	ADP
ejpam-5716	422	57	v.	v.	ADP
ejpam-5716	422	58	hence	hence	ADV
ejpam-5716	422	59	,	,	PUNCT
ejpam-5716	422	60	w	w	PROPN
ejpam-5716	422	61	=	=	PUNCT
ejpam-5716	422	62	v.	v.	CCONJ
ejpam-5716	422	63	therefore	therefore	ADV
ejpam-5716	422	64	,	,	PUNCT
ejpam-5716	422	65	|n2	|n2	PROPN
ejpam-5716	422	66	g[d]|	g[d]|	PROPN
ejpam-5716	422	67	=	=	SYM
ejpam-5716	422	68	|n2	|n2	PROPN
ejpam-5716	422	69	g′	g′	NOUN
ejpam-5716	423	1	[	[	X
ejpam-5716	423	2	d]|+	d]|+	NOUN
ejpam-5716	423	3	1	1	NUM
ejpam-5716	423	4	and	and	CCONJ
ejpam-5716	423	5	(	(	PUNCT
ejpam-5716	423	6	n−	n−	NOUN
ejpam-5716	423	7	1)−	1)−	PROPN
ejpam-5716	423	8	ζhk	ζhk	NOUN
ejpam-5716	423	9	(	(	PUNCT
ejpam-5716	423	10	g	g	NOUN
ejpam-5716	423	11	′	′	NUM
ejpam-5716	423	12	)	)	PUNCT
ejpam-5716	424	1	=	=	PUNCT
ejpam-5716	424	2	|n2	|n2	PROPN
ejpam-5716	424	3	g′	g′	NOUN
ejpam-5716	425	1	[	[	X
ejpam-5716	425	2	d]|	d]|	X
ejpam-5716	425	3	=	=	SYM
ejpam-5716	425	4	|n2	|n2	PROPN
ejpam-5716	425	5	g[d]|	g[d]|	VERB
ejpam-5716	425	6	−	−	NUM
ejpam-5716	425	7	1	1	NUM
ejpam-5716	425	8	≤	≤	NOUN
ejpam-5716	425	9	n−	n−	NOUN
ejpam-5716	425	10	ζhk+1(g)−	ζhk+1(g)−	NOUN
ejpam-5716	425	11	1	1	NUM
ejpam-5716	425	12	.	.	PUNCT
ejpam-5716	425	13	thus	thus	ADV
ejpam-5716	425	14	,	,	PUNCT
ejpam-5716	425	15	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	425	16	)	)	PUNCT
ejpam-5716	425	17	≤	≤	NUM
ejpam-5716	425	18	ζhk	ζhk	NOUN
ejpam-5716	425	19	(	(	PUNCT
ejpam-5716	425	20	g	g	NOUN
ejpam-5716	425	21	′	′	NUM
ejpam-5716	425	22	)	)	PUNCT
ejpam-5716	425	23	≤	≤	NUM
ejpam-5716	425	24	ζhk	ζhk	NOUN
ejpam-5716	425	25	(	(	PUNCT
ejpam-5716	425	26	g	g	NOUN
ejpam-5716	425	27	′	′	NUM
ejpam-5716	425	28	)	)	PUNCT
ejpam-5716	426	1	+	+	CCONJ
ejpam-5716	426	2	1	1	X
ejpam-5716	426	3	.	.	X
ejpam-5716	426	4	therefore	therefore	ADV
ejpam-5716	426	5	,	,	PUNCT
ejpam-5716	426	6	the	the	DET
ejpam-5716	426	7	assertion	assertion	NOUN
ejpam-5716	426	8	holds	hold	VERB
ejpam-5716	426	9	.	.	PUNCT
ejpam-5716	427	1	remark	remark	PROPN
ejpam-5716	427	2	3	3	NUM
ejpam-5716	427	3	.	.	PUNCT
ejpam-5716	428	1	equality	equality	NOUN
ejpam-5716	428	2	of	of	ADP
ejpam-5716	428	3	the	the	DET
ejpam-5716	428	4	two	two	NUM
ejpam-5716	428	5	expressions	expression	NOUN
ejpam-5716	428	6	(	(	PUNCT
ejpam-5716	428	7	defects	defect	NOUN
ejpam-5716	428	8	)	)	PUNCT
ejpam-5716	428	9	given	give	VERB
ejpam-5716	428	10	in	in	ADP
ejpam-5716	428	11	theorem	theorem	ADJ
ejpam-5716	428	12	15	15	NUM
ejpam-5716	428	13	is	be	AUX
ejpam-5716	428	14	attainable	attainable	ADJ
ejpam-5716	428	15	.	.	PUNCT
ejpam-5716	429	1	j.	j.	PROPN
ejpam-5716	429	2	anoche	anoche	PROPN
ejpam-5716	429	3	,	,	PUNCT
ejpam-5716	429	4	s.r	s.r	PROPN
ejpam-5716	429	5	.	.	PROPN
ejpam-5716	429	6	canoy	canoy	PROPN
ejpam-5716	429	7	jr	jr	PROPN
ejpam-5716	429	8	.	.	PUNCT
ejpam-5716	429	9	/	/	SYM
ejpam-5716	429	10	eur	eur	PROPN
ejpam-5716	429	11	.	.	PUNCT
ejpam-5716	430	1	j.	j.	PROPN
ejpam-5716	430	2	pure	pure	PROPN
ejpam-5716	430	3	appl	appl	PROPN
ejpam-5716	430	4	.	.	PROPN
ejpam-5716	430	5	math	math	PROPN
ejpam-5716	430	6	,	,	PUNCT
ejpam-5716	430	7	18	18	NUM
ejpam-5716	430	8	(	(	PUNCT
ejpam-5716	430	9	1	1	NUM
ejpam-5716	430	10	)	)	PUNCT
ejpam-5716	430	11	(	(	PUNCT
ejpam-5716	430	12	2025	2025	NUM
ejpam-5716	430	13	)	)	PUNCT
ejpam-5716	430	14	,	,	PUNCT
ejpam-5716	430	15	5716	5716	NUM
ejpam-5716	430	16	10	10	NUM
ejpam-5716	430	17	of	of	ADP
ejpam-5716	430	18	13	13	NUM
ejpam-5716	430	19	consider	consider	VERB
ejpam-5716	430	20	g	g	NOUN
ejpam-5716	430	21	=	=	NOUN
ejpam-5716	430	22	w4	w4	NOUN
ejpam-5716	430	23	=	=	SYM
ejpam-5716	430	24	⟨{v}⟩+	⟨{v}⟩+	PROPN
ejpam-5716	431	1	[	[	X
ejpam-5716	431	2	a	a	X
ejpam-5716	431	3	,	,	PUNCT
ejpam-5716	431	4	b	b	NOUN
ejpam-5716	431	5	,	,	PUNCT
ejpam-5716	431	6	c	c	NOUN
ejpam-5716	431	7	,	,	PUNCT
ejpam-5716	431	8	d	d	NOUN
ejpam-5716	431	9	,	,	PUNCT
ejpam-5716	431	10	a	a	PRON
ejpam-5716	431	11	]	]	X
ejpam-5716	431	12	.	.	PUNCT
ejpam-5716	432	1	let	let	VERB
ejpam-5716	432	2	g′	g′	NOUN
ejpam-5716	432	3	=	=	SYM
ejpam-5716	432	4	g−	g−	PROPN
ejpam-5716	432	5	v	v	NOUN
ejpam-5716	432	6	=	=	SYM
ejpam-5716	432	7	c4	c4	NOUN
ejpam-5716	432	8	=	=	PUNCT
ejpam-5716	433	1	[	[	X
ejpam-5716	433	2	a	a	PRON
ejpam-5716	433	3	,	,	PUNCT
ejpam-5716	433	4	b	b	NOUN
ejpam-5716	433	5	,	,	PUNCT
ejpam-5716	433	6	c	c	NOUN
ejpam-5716	433	7	,	,	PUNCT
ejpam-5716	433	8	d	d	NOUN
ejpam-5716	433	9	,	,	PUNCT
ejpam-5716	433	10	a	a	PRON
ejpam-5716	433	11	]	]	X
ejpam-5716	433	12	.	.	PUNCT
ejpam-5716	434	1	observe	observe	VERB
ejpam-5716	434	2	that	that	SCONJ
ejpam-5716	434	3	v	v	ADJ
ejpam-5716	434	4	satisfies	satisfy	VERB
ejpam-5716	434	5	the	the	DET
ejpam-5716	434	6	property	property	NOUN
ejpam-5716	434	7	given	give	VERB
ejpam-5716	434	8	in	in	ADP
ejpam-5716	434	9	theorem	theorem	ADJ
ejpam-5716	434	10	15	15	NUM
ejpam-5716	434	11	,	,	PUNCT
ejpam-5716	434	12	and	and	CCONJ
ejpam-5716	434	13	γh(g	γh(g	NOUN
ejpam-5716	434	14	)	)	PUNCT
ejpam-5716	434	15	=	=	SYM
ejpam-5716	434	16	3	3	X
ejpam-5716	434	17	>	>	SYM
ejpam-5716	434	18	2	2	NUM
ejpam-5716	434	19	=	=	NOUN
ejpam-5716	434	20	γh(g	γh(g	NOUN
ejpam-5716	434	21	′	′	NOUN
ejpam-5716	434	22	)	)	PUNCT
ejpam-5716	434	23	.	.	PUNCT
ejpam-5716	435	1	then	then	ADV
ejpam-5716	435	2	k	k	PROPN
ejpam-5716	435	3	=	=	PUNCT
ejpam-5716	435	4	γh(g)−	γh(g)−	PROPN
ejpam-5716	435	5	2	2	NUM
ejpam-5716	435	6	=	=	SYM
ejpam-5716	435	7	1	1	NUM
ejpam-5716	435	8	.	.	PUNCT
ejpam-5716	436	1	if	if	SCONJ
ejpam-5716	436	2	d	d	PROPN
ejpam-5716	436	3	is	be	AUX
ejpam-5716	436	4	ζhk	ζhk	NOUN
ejpam-5716	436	5	-set	-set	VERB
ejpam-5716	436	6	in	in	ADP
ejpam-5716	436	7	g′	g′	PROPN
ejpam-5716	436	8	,	,	PUNCT
ejpam-5716	436	9	then	then	ADV
ejpam-5716	436	10	|d|	|d|	PROPN
ejpam-5716	436	11	=	=	PUNCT
ejpam-5716	436	12	γh(g	γh(g	X
ejpam-5716	436	13	′)−	′)−	PROPN
ejpam-5716	436	14	1	1	NUM
ejpam-5716	436	15	=	=	SYM
ejpam-5716	436	16	1	1	X
ejpam-5716	436	17	.	.	PUNCT
ejpam-5716	437	1	in	in	ADP
ejpam-5716	437	2	this	this	DET
ejpam-5716	437	3	case	case	NOUN
ejpam-5716	437	4	,	,	PUNCT
ejpam-5716	437	5	we	we	PRON
ejpam-5716	437	6	may	may	AUX
ejpam-5716	437	7	take	take	VERB
ejpam-5716	437	8	any	any	PRON
ejpam-5716	437	9	of	of	ADP
ejpam-5716	437	10	the	the	DET
ejpam-5716	437	11	four	four	NUM
ejpam-5716	437	12	vertices	vertex	NOUN
ejpam-5716	437	13	of	of	ADP
ejpam-5716	437	14	c4	c4	NOUN
ejpam-5716	437	15	as	as	ADP
ejpam-5716	437	16	the	the	DET
ejpam-5716	437	17	element	element	NOUN
ejpam-5716	437	18	of	of	ADP
ejpam-5716	437	19	d	d	PROPN
ejpam-5716	437	20	,	,	PUNCT
ejpam-5716	437	21	say	say	VERB
ejpam-5716	437	22	d	d	X
ejpam-5716	437	23	=	=	PRON
ejpam-5716	437	24	{	{	PUNCT
ejpam-5716	437	25	a	a	NOUN
ejpam-5716	437	26	}	}	PUNCT
ejpam-5716	437	27	.	.	PUNCT
ejpam-5716	438	1	then	then	ADV
ejpam-5716	438	2	n2	n2	PROPN
ejpam-5716	438	3	g[a	g[a	PROPN
ejpam-5716	438	4	]	]	X
ejpam-5716	438	5	=	=	X
ejpam-5716	438	6	{	{	PUNCT
ejpam-5716	438	7	a	a	X
ejpam-5716	438	8	,	,	PUNCT
ejpam-5716	438	9	c	c	NOUN
ejpam-5716	438	10	}	}	PUNCT
ejpam-5716	438	11	and	and	CCONJ
ejpam-5716	438	12	n2	n2	ADJ
ejpam-5716	438	13	g′	g′	NOUN
ejpam-5716	439	1	[	[	X
ejpam-5716	439	2	a	a	X
ejpam-5716	439	3	]	]	X
ejpam-5716	439	4	=	=	X
ejpam-5716	439	5	{	{	PUNCT
ejpam-5716	439	6	a	a	X
ejpam-5716	439	7	,	,	PUNCT
ejpam-5716	439	8	c	c	NOUN
ejpam-5716	439	9	}	}	PUNCT
ejpam-5716	439	10	.	.	PUNCT
ejpam-5716	440	1	it	it	PRON
ejpam-5716	440	2	follows	follow	VERB
ejpam-5716	440	3	that	that	DET
ejpam-5716	440	4	ζhk+1(g	ζhk+1(g	NOUN
ejpam-5716	440	5	)	)	PUNCT
ejpam-5716	441	1	=	=	SYM
ejpam-5716	441	2	|v	|v	PROPN
ejpam-5716	441	3	(	(	PUNCT
ejpam-5716	441	4	g)|	g)|	PROPN
ejpam-5716	441	5	−	−	PROPN
ejpam-5716	441	6	|n2	|n2	PROPN
ejpam-5716	441	7	g[a]|	g[a]|	NOUN
ejpam-5716	441	8	=	=	SYM
ejpam-5716	441	9	3	3	NUM
ejpam-5716	441	10	=	=	SYM
ejpam-5716	441	11	(	(	PUNCT
ejpam-5716	441	12	|v	|v	X
ejpam-5716	441	13	(	(	PUNCT
ejpam-5716	441	14	g′)|	g′)|	PROPN
ejpam-5716	441	15	−	−	PROPN
ejpam-5716	441	16	|n2	|n2	PROPN
ejpam-5716	441	17	g′	g′	NOUN
ejpam-5716	441	18	[	[	X
ejpam-5716	441	19	a]|	a]|	PROPN
ejpam-5716	441	20	)	)	PUNCT
ejpam-5716	441	21	+	+	CCONJ
ejpam-5716	441	22	1	1	NUM
ejpam-5716	441	23	=	=	SYM
ejpam-5716	441	24	ζhk	ζhk	NOUN
ejpam-5716	441	25	(	(	PUNCT
ejpam-5716	441	26	g	g	NOUN
ejpam-5716	441	27	′	′	NUM
ejpam-5716	441	28	)	)	PUNCT
ejpam-5716	442	1	+	+	CCONJ
ejpam-5716	442	2	1	1	X
ejpam-5716	442	3	.	.	X
ejpam-5716	442	4	theorem	theorem	VERB
ejpam-5716	442	5	16	16	NUM
ejpam-5716	442	6	.	.	PUNCT
ejpam-5716	443	1	let	let	VERB
ejpam-5716	443	2	g	g	PRON
ejpam-5716	443	3	be	be	AUX
ejpam-5716	443	4	a	a	DET
ejpam-5716	443	5	graph	graph	NOUN
ejpam-5716	443	6	of	of	ADP
ejpam-5716	443	7	order	order	NOUN
ejpam-5716	443	8	n	n	PRON
ejpam-5716	443	9	such	such	ADJ
ejpam-5716	443	10	that	that	SCONJ
ejpam-5716	443	11	γh(g	γh(g	PUNCT
ejpam-5716	443	12	−	−	PROPN
ejpam-5716	443	13	v	v	NOUN
ejpam-5716	443	14	)	)	PUNCT
ejpam-5716	443	15	=	=	NOUN
ejpam-5716	443	16	γh(g	γh(g	NOUN
ejpam-5716	443	17	)	)	PUNCT
ejpam-5716	443	18	for	for	ADP
ejpam-5716	443	19	every	every	DET
ejpam-5716	443	20	v	v	NUM
ejpam-5716	443	21	∈	∈	PROPN
ejpam-5716	443	22	v	v	NOUN
ejpam-5716	443	23	(	(	PUNCT
ejpam-5716	443	24	g	g	NOUN
ejpam-5716	443	25	)	)	PUNCT
ejpam-5716	443	26	.	.	PUNCT
ejpam-5716	444	1	if	if	SCONJ
ejpam-5716	444	2	there	there	PRON
ejpam-5716	444	3	exist	exist	VERB
ejpam-5716	444	4	u	u	NOUN
ejpam-5716	444	5	,	,	PUNCT
ejpam-5716	444	6	v	v	NOUN
ejpam-5716	444	7	∈	∈	PROPN
ejpam-5716	444	8	v	v	NOUN
ejpam-5716	444	9	(	(	PUNCT
ejpam-5716	444	10	g	g	NOUN
ejpam-5716	444	11	)	)	PUNCT
ejpam-5716	445	1	such	such	ADJ
ejpam-5716	445	2	that	that	DET
ejpam-5716	445	3	uv	uv	NOUN
ejpam-5716	445	4	/∈	/∈	PUNCT
ejpam-5716	445	5	e(g	e(g	PROPN
ejpam-5716	445	6	)	)	PUNCT
ejpam-5716	446	1	and	and	CCONJ
ejpam-5716	446	2	γh(g	γh(g	PUNCT
ejpam-5716	446	3	−	−	PROPN
ejpam-5716	446	4	{	{	PUNCT
ejpam-5716	446	5	u	u	NOUN
ejpam-5716	446	6	,	,	PUNCT
ejpam-5716	446	7	v	v	NOUN
ejpam-5716	446	8	}	}	PUNCT
ejpam-5716	446	9	)	)	PUNCT
ejpam-5716	446	10	<	<	X
ejpam-5716	446	11	γh(g	γh(g	NOUN
ejpam-5716	446	12	)	)	PUNCT
ejpam-5716	446	13	,	,	PUNCT
ejpam-5716	446	14	then	then	ADV
ejpam-5716	446	15	ζh1	ζh1	ADV
ejpam-5716	446	16	(	(	PUNCT
ejpam-5716	446	17	g	g	NOUN
ejpam-5716	446	18	)	)	PUNCT
ejpam-5716	446	19	=	=	SYM
ejpam-5716	446	20	2	2	X
ejpam-5716	446	21	.	.	PUNCT
ejpam-5716	446	22	proof	proof	NOUN
ejpam-5716	446	23	.	.	PUNCT
ejpam-5716	447	1	let	let	VERB
ejpam-5716	447	2	u	u	NOUN
ejpam-5716	447	3	,	,	PUNCT
ejpam-5716	447	4	v	v	PROPN
ejpam-5716	447	5	∈	∈	PROPN
ejpam-5716	447	6	v	v	NOUN
ejpam-5716	447	7	(	(	PUNCT
ejpam-5716	447	8	g	g	NOUN
ejpam-5716	447	9	)	)	PUNCT
ejpam-5716	447	10	be	be	AUX
ejpam-5716	447	11	such	such	ADJ
ejpam-5716	447	12	that	that	DET
ejpam-5716	447	13	uv	uv	NOUN
ejpam-5716	447	14	/∈	/∈	PUNCT
ejpam-5716	447	15	e(g	e(g	PROPN
ejpam-5716	447	16	)	)	PUNCT
ejpam-5716	447	17	and	and	CCONJ
ejpam-5716	447	18	γh(g	γh(g	PUNCT
ejpam-5716	447	19	−	−	PROPN
ejpam-5716	447	20	{	{	PUNCT
ejpam-5716	447	21	u	u	NOUN
ejpam-5716	447	22	,	,	PUNCT
ejpam-5716	447	23	v	v	NOUN
ejpam-5716	447	24	}	}	PUNCT
ejpam-5716	447	25	)	)	PUNCT
ejpam-5716	447	26	<	<	X
ejpam-5716	447	27	γh(g	γh(g	NOUN
ejpam-5716	447	28	)	)	PUNCT
ejpam-5716	447	29	.	.	PUNCT
ejpam-5716	448	1	for	for	ADP
ejpam-5716	448	2	convenience	convenience	NOUN
ejpam-5716	448	3	,	,	PUNCT
ejpam-5716	448	4	let	let	VERB
ejpam-5716	448	5	h	h	NOUN
ejpam-5716	448	6	=	=	SYM
ejpam-5716	448	7	g−{u	g−{u	PROPN
ejpam-5716	448	8	,	,	PUNCT
ejpam-5716	448	9	v	v	NOUN
ejpam-5716	448	10	}	}	PUNCT
ejpam-5716	448	11	.	.	PUNCT
ejpam-5716	449	1	then	then	ADV
ejpam-5716	449	2	γh(h	γh(h	PUNCT
ejpam-5716	449	3	)	)	PUNCT
ejpam-5716	449	4	+	+	CCONJ
ejpam-5716	449	5	1	1	NUM
ejpam-5716	449	6	≤	≤	NOUN
ejpam-5716	449	7	γh(g	γh(g	NOUN
ejpam-5716	449	8	)	)	PUNCT
ejpam-5716	449	9	.	.	PUNCT
ejpam-5716	450	1	let	let	VERB
ejpam-5716	450	2	s	s	PRON
ejpam-5716	450	3	be	be	AUX
ejpam-5716	450	4	a	a	DET
ejpam-5716	450	5	γh	γh	ADV
ejpam-5716	450	6	-	-	PUNCT
ejpam-5716	450	7	set	set	NOUN
ejpam-5716	450	8	of	of	ADP
ejpam-5716	450	9	h.	h.	PROPN
ejpam-5716	450	10	then	then	ADV
ejpam-5716	450	11	u	u	PROPN
ejpam-5716	450	12	/∈	/∈	PROPN
ejpam-5716	450	13	s.	s.	PROPN
ejpam-5716	450	14	set	set	VERB
ejpam-5716	450	15	s′	s′	ADJ
ejpam-5716	450	16	=	=	PUNCT
ejpam-5716	450	17	s	s	NOUN
ejpam-5716	450	18	∪	∪	X
ejpam-5716	450	19	{	{	PUNCT
ejpam-5716	450	20	u	u	NOUN
ejpam-5716	450	21	}	}	PUNCT
ejpam-5716	450	22	and	and	CCONJ
ejpam-5716	450	23	let	let	VERB
ejpam-5716	450	24	h	h	NOUN
ejpam-5716	450	25	′	′	NUM
ejpam-5716	451	1	=	=	PUNCT
ejpam-5716	451	2	g	g	ADP
ejpam-5716	451	3	−	−	PROPN
ejpam-5716	452	1	v.	v.	CCONJ
ejpam-5716	452	2	let	let	VERB
ejpam-5716	452	3	x	x	SYM
ejpam-5716	452	4	∈	∈	PROPN
ejpam-5716	452	5	h	h	NOUN
ejpam-5716	452	6	′	′	NOUN
ejpam-5716	452	7	\	\	PUNCT
ejpam-5716	453	1	s′.	s′.	PROPN
ejpam-5716	453	2	then	then	ADV
ejpam-5716	453	3	x	x	X
ejpam-5716	453	4	/∈	/∈	PUNCT
ejpam-5716	453	5	{	{	PUNCT
ejpam-5716	453	6	u	u	NOUN
ejpam-5716	453	7	,	,	PUNCT
ejpam-5716	453	8	v	v	NOUN
ejpam-5716	453	9	}	}	PUNCT
ejpam-5716	453	10	.	.	PUNCT
ejpam-5716	454	1	hence	hence	ADV
ejpam-5716	454	2	,	,	PUNCT
ejpam-5716	454	3	x	x	PUNCT
ejpam-5716	454	4	∈	∈	NOUN
ejpam-5716	454	5	h	h	NOUN
ejpam-5716	454	6	\s	\s	NOUN
ejpam-5716	454	7	.	.	PUNCT
ejpam-5716	455	1	since	since	SCONJ
ejpam-5716	455	2	s	s	PROPN
ejpam-5716	455	3	is	be	AUX
ejpam-5716	455	4	a	a	DET
ejpam-5716	455	5	hop	hop	NOUN
ejpam-5716	455	6	dominating	dominating	NOUN
ejpam-5716	455	7	set	set	NOUN
ejpam-5716	455	8	of	of	ADP
ejpam-5716	455	9	h	h	NOUN
ejpam-5716	455	10	,	,	PUNCT
ejpam-5716	455	11	there	there	PRON
ejpam-5716	455	12	exists	exist	VERB
ejpam-5716	455	13	y	y	PROPN
ejpam-5716	455	14	∈	∈	PROPN
ejpam-5716	455	15	s	s	VERB
ejpam-5716	455	16	such	such	ADJ
ejpam-5716	455	17	that	that	SCONJ
ejpam-5716	455	18	dh(x	dh(x	NOUN
ejpam-5716	455	19	,	,	PUNCT
ejpam-5716	455	20	y	y	NOUN
ejpam-5716	455	21	)	)	PUNCT
ejpam-5716	455	22	=	=	SYM
ejpam-5716	456	1	2	2	X
ejpam-5716	456	2	.	.	PUNCT
ejpam-5716	456	3	it	it	PRON
ejpam-5716	456	4	follows	follow	VERB
ejpam-5716	456	5	that	that	SCONJ
ejpam-5716	456	6	y	y	PROPN
ejpam-5716	456	7	∈	∈	PROPN
ejpam-5716	456	8	s′	s′	NUM
ejpam-5716	456	9	and	and	CCONJ
ejpam-5716	456	10	dh′(x	dh′(x	PROPN
ejpam-5716	456	11	,	,	PUNCT
ejpam-5716	456	12	y	y	NOUN
ejpam-5716	456	13	)	)	PUNCT
ejpam-5716	456	14	=	=	SYM
ejpam-5716	457	1	2	2	X
ejpam-5716	457	2	.	.	PUNCT
ejpam-5716	457	3	this	this	PRON
ejpam-5716	457	4	shows	show	VERB
ejpam-5716	457	5	that	that	SCONJ
ejpam-5716	457	6	s′	s′	ADJ
ejpam-5716	457	7	is	be	AUX
ejpam-5716	457	8	a	a	DET
ejpam-5716	457	9	hop	hop	NOUN
ejpam-5716	457	10	dominating	dominating	NOUN
ejpam-5716	457	11	set	set	VERB
ejpam-5716	457	12	in	in	ADP
ejpam-5716	457	13	h	h	NOUN
ejpam-5716	457	14	′.	′.	NOUN
ejpam-5716	457	15	since	since	SCONJ
ejpam-5716	457	16	γh(h)+1	γh(h)+1	PROPN
ejpam-5716	457	17	≤	≤	NOUN
ejpam-5716	457	18	γh(g	γh(g	NOUN
ejpam-5716	457	19	)	)	PUNCT
ejpam-5716	457	20	=	=	SYM
ejpam-5716	457	21	γh(h	γh(h	NUM
ejpam-5716	457	22	′	′	NOUN
ejpam-5716	457	23	)	)	PUNCT
ejpam-5716	457	24	≤	≤	NOUN
ejpam-5716	457	25	|s′|	|s′|	NOUN
ejpam-5716	457	26	=	=	SYM
ejpam-5716	457	27	γh(h)+1	γh(h)+1	NOUN
ejpam-5716	457	28	,	,	PUNCT
ejpam-5716	457	29	γh(g	γh(g	NOUN
ejpam-5716	457	30	)	)	PUNCT
ejpam-5716	457	31	=	=	SYM
ejpam-5716	457	32	γh(h	γh(h	NUM
ejpam-5716	457	33	′	′	NUM
ejpam-5716	457	34	)	)	PUNCT
ejpam-5716	457	35	=	=	PRON
ejpam-5716	457	36	|s′|	|s′|	NOUN
ejpam-5716	457	37	=	=	SYM
ejpam-5716	457	38	γh(h)+1	γh(h)+1	PROPN
ejpam-5716	457	39	,	,	PUNCT
ejpam-5716	457	40	that	that	ADV
ejpam-5716	457	41	is	be	AUX
ejpam-5716	457	42	,	,	PUNCT
ejpam-5716	457	43	γh(h	γh(h	PUNCT
ejpam-5716	457	44	)	)	PUNCT
ejpam-5716	457	45	=	=	NOUN
ejpam-5716	457	46	γh(g	γh(g	NOUN
ejpam-5716	457	47	)	)	PUNCT
ejpam-5716	457	48	−	−	PROPN
ejpam-5716	458	1	1	1	X
ejpam-5716	458	2	.	.	PUNCT
ejpam-5716	459	1	hence	hence	ADV
ejpam-5716	459	2	,	,	PUNCT
ejpam-5716	459	3	|s|	|s|	PROPN
ejpam-5716	459	4	=	=	NOUN
ejpam-5716	459	5	γh(g	γh(g	NOUN
ejpam-5716	459	6	)	)	PUNCT
ejpam-5716	459	7	−	−	PROPN
ejpam-5716	460	1	1	1	X
ejpam-5716	460	2	.	.	PUNCT
ejpam-5716	460	3	clearly	clearly	ADV
ejpam-5716	460	4	,	,	PUNCT
ejpam-5716	460	5	v	v	INTJ
ejpam-5716	460	6	(	(	PUNCT
ejpam-5716	460	7	h	h	NOUN
ejpam-5716	460	8	)	)	PUNCT
ejpam-5716	460	9	⊆	⊆	NUM
ejpam-5716	460	10	n2	n2	ADJ
ejpam-5716	460	11	g[s	g[s	PROPN
ejpam-5716	460	12	]	]	PUNCT
ejpam-5716	460	13	.	.	PUNCT
ejpam-5716	460	14	suppose	suppose	VERB
ejpam-5716	460	15	n2	n2	ADJ
ejpam-5716	460	16	g[s	g[s	PROPN
ejpam-5716	460	17	]	]	PUNCT
ejpam-5716	460	18	̸=	̸=	PROPN
ejpam-5716	460	19	v	v	NOUN
ejpam-5716	460	20	(	(	PUNCT
ejpam-5716	460	21	h	h	NOUN
ejpam-5716	460	22	)	)	PUNCT
ejpam-5716	460	23	.	.	PUNCT
ejpam-5716	461	1	then	then	ADV
ejpam-5716	461	2	u	u	PROPN
ejpam-5716	461	3	∈	∈	PROPN
ejpam-5716	461	4	n2	n2	ADJ
ejpam-5716	461	5	g(s	g(s	PROPN
ejpam-5716	461	6	)	)	PUNCT
ejpam-5716	461	7	or	or	CCONJ
ejpam-5716	461	8	v	v	ADP
ejpam-5716	461	9	∈	∈	PROPN
ejpam-5716	461	10	n2	n2	ADJ
ejpam-5716	461	11	g(s	g(s	PROPN
ejpam-5716	461	12	)	)	PUNCT
ejpam-5716	461	13	,	,	PUNCT
ejpam-5716	461	14	say	say	VERB
ejpam-5716	461	15	v	v	ADP
ejpam-5716	461	16	∈	∈	PROPN
ejpam-5716	461	17	n2	n2	ADJ
ejpam-5716	461	18	g(s	g(s	PROPN
ejpam-5716	461	19	)	)	PUNCT
ejpam-5716	461	20	.	.	PUNCT
ejpam-5716	462	1	then	then	ADV
ejpam-5716	462	2	there	there	PRON
ejpam-5716	462	3	exists	exist	VERB
ejpam-5716	462	4	w	w	PROPN
ejpam-5716	462	5	∈	∈	PROPN
ejpam-5716	462	6	s	s	VERB
ejpam-5716	462	7	such	such	ADJ
ejpam-5716	462	8	that	that	PRON
ejpam-5716	462	9	dg(v	dg(v	ADJ
ejpam-5716	462	10	,	,	PUNCT
ejpam-5716	462	11	w	w	NOUN
ejpam-5716	462	12	)	)	PUNCT
ejpam-5716	462	13	=	=	SYM
ejpam-5716	462	14	2	2	X
ejpam-5716	462	15	.	.	X
ejpam-5716	462	16	let	let	VERB
ejpam-5716	462	17	[	[	X
ejpam-5716	462	18	v	v	ADP
ejpam-5716	462	19	,	,	PUNCT
ejpam-5716	462	20	p	p	X
ejpam-5716	462	21	,	,	PUNCT
ejpam-5716	462	22	w	w	PROPN
ejpam-5716	462	23	]	]	PUNCT
ejpam-5716	462	24	be	be	AUX
ejpam-5716	462	25	a	a	DET
ejpam-5716	462	26	v	v	NOUN
ejpam-5716	462	27	-	-	PUNCT
ejpam-5716	462	28	w	w	NOUN
ejpam-5716	462	29	geodesic	geodesic	NOUN
ejpam-5716	462	30	in	in	ADP
ejpam-5716	462	31	g.	g.	PROPN
ejpam-5716	462	32	since	since	SCONJ
ejpam-5716	462	33	uv	uv	PROPN
ejpam-5716	462	34	/∈	/∈	PROPN
ejpam-5716	462	35	e(g	e(g	PROPN
ejpam-5716	462	36	)	)	PUNCT
ejpam-5716	462	37	,	,	PUNCT
ejpam-5716	462	38	p	p	PROPN
ejpam-5716	462	39	̸=	̸=	PROPN
ejpam-5716	462	40	u.	u.	VERB
ejpam-5716	462	41	this	this	PRON
ejpam-5716	462	42	implies	imply	VERB
ejpam-5716	462	43	that	that	SCONJ
ejpam-5716	462	44	[	[	X
ejpam-5716	462	45	v	v	NOUN
ejpam-5716	462	46	,	,	PUNCT
ejpam-5716	462	47	p	p	X
ejpam-5716	462	48	,	,	PUNCT
ejpam-5716	462	49	w	w	PROPN
ejpam-5716	462	50	]	]	X
ejpam-5716	462	51	is	be	AUX
ejpam-5716	462	52	a	a	DET
ejpam-5716	462	53	v	v	NOUN
ejpam-5716	462	54	-	-	PUNCT
ejpam-5716	462	55	w	w	NOUN
ejpam-5716	462	56	geodesic	geodesic	NOUN
ejpam-5716	462	57	in	in	ADP
ejpam-5716	462	58	h∗	h∗	PROPN
ejpam-5716	462	59	=	=	PROPN
ejpam-5716	463	1	g	g	PROPN
ejpam-5716	463	2	\	\	PROPN
ejpam-5716	463	3	u.	u.	PROPN
ejpam-5716	463	4	hence	hence	ADV
ejpam-5716	463	5	,	,	PUNCT
ejpam-5716	463	6	dh∗(v	dh∗(v	NOUN
ejpam-5716	463	7	,	,	PUNCT
ejpam-5716	463	8	w	w	NOUN
ejpam-5716	463	9	)	)	PUNCT
ejpam-5716	463	10	=	=	SYM
ejpam-5716	463	11	2	2	X
ejpam-5716	463	12	.	.	PUNCT
ejpam-5716	464	1	it	it	PRON
ejpam-5716	464	2	follows	follow	VERB
ejpam-5716	464	3	that	that	SCONJ
ejpam-5716	464	4	s	s	VERB
ejpam-5716	464	5	is	be	AUX
ejpam-5716	464	6	a	a	DET
ejpam-5716	464	7	hop	hop	NOUN
ejpam-5716	464	8	dominating	dominating	NOUN
ejpam-5716	464	9	set	set	NOUN
ejpam-5716	464	10	h∗.	h∗.	VERB
ejpam-5716	464	11	this	this	PRON
ejpam-5716	464	12	,	,	PUNCT
ejpam-5716	464	13	however	however	ADV
ejpam-5716	464	14	,	,	PUNCT
ejpam-5716	464	15	is	be	AUX
ejpam-5716	464	16	not	not	PART
ejpam-5716	464	17	possible	possible	ADJ
ejpam-5716	464	18	because	because	SCONJ
ejpam-5716	464	19	γh(h	γh(h	NUM
ejpam-5716	464	20	)	)	PUNCT
ejpam-5716	464	21	=	=	PUNCT
ejpam-5716	465	1	|s|	|s|	PROPN
ejpam-5716	465	2	<	<	X
ejpam-5716	465	3	γh(g	γh(g	NOUN
ejpam-5716	465	4	)	)	PUNCT
ejpam-5716	465	5	=	=	SYM
ejpam-5716	465	6	γh(h	γh(h	NOUN
ejpam-5716	465	7	∗	∗	NOUN
ejpam-5716	465	8	)	)	PUNCT
ejpam-5716	465	9	by	by	ADP
ejpam-5716	465	10	assumption	assumption	NOUN
ejpam-5716	465	11	.	.	PUNCT
ejpam-5716	466	1	therefore	therefore	ADV
ejpam-5716	466	2	,	,	PUNCT
ejpam-5716	466	3	n2	n2	ADJ
ejpam-5716	466	4	g[s	g[s	PROPN
ejpam-5716	466	5	]	]	X
ejpam-5716	466	6	=	=	SYM
ejpam-5716	466	7	v	v	X
ejpam-5716	466	8	(	(	PUNCT
ejpam-5716	466	9	h	h	NOUN
ejpam-5716	466	10	)	)	PUNCT
ejpam-5716	466	11	.	.	PUNCT
ejpam-5716	467	1	it	it	PRON
ejpam-5716	467	2	follows	follow	VERB
ejpam-5716	467	3	that	that	DET
ejpam-5716	467	4	ζh1	ζh1	NOUN
ejpam-5716	467	5	(	(	PUNCT
ejpam-5716	467	6	s	s	X
ejpam-5716	467	7	)	)	PUNCT
ejpam-5716	467	8	=	=	SYM
ejpam-5716	468	1	n	n	NUM
ejpam-5716	468	2	−	−	PROPN
ejpam-5716	468	3	|v	|v	PROPN
ejpam-5716	468	4	(	(	PUNCT
ejpam-5716	468	5	h)|	h)|	NOUN
ejpam-5716	468	6	=	=	SYM
ejpam-5716	468	7	n	n	CCONJ
ejpam-5716	468	8	−	−	PROPN
ejpam-5716	469	1	(	(	PUNCT
ejpam-5716	469	2	n	n	CCONJ
ejpam-5716	469	3	−	−	PROPN
ejpam-5716	469	4	2	2	NUM
ejpam-5716	469	5	)	)	PUNCT
ejpam-5716	469	6	=	=	SYM
ejpam-5716	469	7	2	2	X
ejpam-5716	469	8	.	.	PUNCT
ejpam-5716	469	9	since	since	SCONJ
ejpam-5716	469	10	γh(g	γh(g	NOUN
ejpam-5716	469	11	−	−	PROPN
ejpam-5716	469	12	{	{	PUNCT
ejpam-5716	469	13	v	v	NOUN
ejpam-5716	469	14	}	}	PUNCT
ejpam-5716	469	15	)	)	PUNCT
ejpam-5716	469	16	=	=	NOUN
ejpam-5716	469	17	γh(g	γh(g	NOUN
ejpam-5716	469	18	)	)	PUNCT
ejpam-5716	469	19	for	for	ADP
ejpam-5716	469	20	every	every	PRON
ejpam-5716	469	21	v	v	NUM
ejpam-5716	469	22	∈	∈	PROPN
ejpam-5716	469	23	v	v	NOUN
ejpam-5716	469	24	(	(	PUNCT
ejpam-5716	469	25	g	g	NOUN
ejpam-5716	469	26	)	)	PUNCT
ejpam-5716	469	27	,	,	PUNCT
ejpam-5716	469	28	ζh1	ζh1	NOUN
ejpam-5716	469	29	(	(	PUNCT
ejpam-5716	469	30	g	g	NOUN
ejpam-5716	469	31	)	)	PUNCT
ejpam-5716	469	32	̸=	̸=	PROPN
ejpam-5716	469	33	1	1	NUM
ejpam-5716	469	34	by	by	ADP
ejpam-5716	469	35	theorem	theorem	NOUN
ejpam-5716	469	36	5	5	NUM
ejpam-5716	469	37	.	.	PUNCT
ejpam-5716	469	38	therefore	therefore	ADV
ejpam-5716	469	39	,	,	PUNCT
ejpam-5716	469	40	ζh1	ζh1	ADV
ejpam-5716	469	41	(	(	PUNCT
ejpam-5716	469	42	g	g	NOUN
ejpam-5716	469	43	)	)	PUNCT
ejpam-5716	469	44	=	=	SYM
ejpam-5716	469	45	ζh1	ζh1	NOUN
ejpam-5716	469	46	(	(	PUNCT
ejpam-5716	469	47	s	s	X
ejpam-5716	469	48	)	)	PUNCT
ejpam-5716	469	49	=	=	SYM
ejpam-5716	469	50	2	2	X
ejpam-5716	469	51	.	.	NOUN
ejpam-5716	469	52	example	example	NOUN
ejpam-5716	469	53	1	1	NUM
ejpam-5716	469	54	.	.	PUNCT
ejpam-5716	470	1	let	let	VERB
ejpam-5716	470	2	g	g	PRON
ejpam-5716	470	3	be	be	AUX
ejpam-5716	470	4	a	a	DET
ejpam-5716	470	5	graph	graph	NOUN
ejpam-5716	470	6	obtained	obtain	VERB
ejpam-5716	470	7	from	from	ADP
ejpam-5716	470	8	c7	c7	PROPN
ejpam-5716	470	9	=	=	PUNCT
ejpam-5716	471	1	[	[	X
ejpam-5716	471	2	v1	v1	NOUN
ejpam-5716	471	3	,	,	PUNCT
ejpam-5716	471	4	v2	v2	PROPN
ejpam-5716	471	5	,	,	PUNCT
ejpam-5716	471	6	·	·	PUNCT
ejpam-5716	471	7	·	·	PUNCT
ejpam-5716	471	8	·	·	PUNCT
ejpam-5716	471	9	,	,	PUNCT
ejpam-5716	471	10	v7	v7	VERB
ejpam-5716	471	11	,	,	PUNCT
ejpam-5716	471	12	v1	v1	NOUN
ejpam-5716	471	13	]	]	PUNCT
ejpam-5716	471	14	by	by	ADP
ejpam-5716	471	15	adding	add	VERB
ejpam-5716	471	16	the	the	DET
ejpam-5716	471	17	pendant	pendant	ADJ
ejpam-5716	471	18	edge	edge	NOUN
ejpam-5716	471	19	pv1	pv1	VERB
ejpam-5716	471	20	.	.	PUNCT
ejpam-5716	471	21	then	then	ADV
ejpam-5716	471	22	γh(g	γh(g	NOUN
ejpam-5716	471	23	)	)	PUNCT
ejpam-5716	471	24	=	=	SYM
ejpam-5716	471	25	7	7	NUM
ejpam-5716	471	26	(	(	PUNCT
ejpam-5716	471	27	s	s	NOUN
ejpam-5716	471	28	=	=	NOUN
ejpam-5716	471	29	{	{	PUNCT
ejpam-5716	471	30	v1	v1	PROPN
ejpam-5716	471	31	,	,	PUNCT
ejpam-5716	471	32	v2	v2	PROPN
ejpam-5716	471	33	,	,	PUNCT
ejpam-5716	471	34	v5	v5	PROPN
ejpam-5716	471	35	}	}	PUNCT
ejpam-5716	471	36	is	be	AUX
ejpam-5716	471	37	a	a	DET
ejpam-5716	471	38	γh	γh	ADV
ejpam-5716	471	39	-	-	PUNCT
ejpam-5716	471	40	set	set	NOUN
ejpam-5716	471	41	in	in	ADP
ejpam-5716	471	42	g	g	NOUN
ejpam-5716	471	43	)	)	PUNCT
ejpam-5716	471	44	.	.	PUNCT
ejpam-5716	472	1	one	one	PRON
ejpam-5716	472	2	can	can	AUX
ejpam-5716	472	3	easily	easily	ADV
ejpam-5716	472	4	verify	verify	VERB
ejpam-5716	472	5	that	that	SCONJ
ejpam-5716	472	6	γh(g	γh(g	NOUN
ejpam-5716	472	7	\	\	PROPN
ejpam-5716	472	8	v	v	NOUN
ejpam-5716	472	9	)	)	PUNCT
ejpam-5716	472	10	=	=	NOUN
ejpam-5716	472	11	γh(g	γh(g	NOUN
ejpam-5716	472	12	)	)	PUNCT
ejpam-5716	472	13	for	for	ADP
ejpam-5716	472	14	every	every	DET
ejpam-5716	472	15	v	v	NUM
ejpam-5716	472	16	∈	∈	PROPN
ejpam-5716	472	17	v	v	NOUN
ejpam-5716	472	18	(	(	PUNCT
ejpam-5716	472	19	g	g	NOUN
ejpam-5716	472	20	)	)	PUNCT
ejpam-5716	472	21	.	.	PUNCT
ejpam-5716	473	1	consider	consider	VERB
ejpam-5716	473	2	the	the	DET
ejpam-5716	473	3	non	non	ADJ
ejpam-5716	473	4	-	-	ADJ
ejpam-5716	473	5	adjacent	adjacent	ADJ
ejpam-5716	473	6	vertices	vertex	NOUN
ejpam-5716	473	7	p	p	NOUN
ejpam-5716	473	8	and	and	CCONJ
ejpam-5716	473	9	v2	v2	PROPN
ejpam-5716	473	10	of	of	ADP
ejpam-5716	473	11	g.	g.	PROPN
ejpam-5716	473	12	then	then	ADV
ejpam-5716	473	13	g	g	PROPN
ejpam-5716	473	14	\	\	PROPN
ejpam-5716	473	15	{	{	PUNCT
ejpam-5716	473	16	p	p	X
ejpam-5716	473	17	,	,	PUNCT
ejpam-5716	473	18	v2	v2	NOUN
ejpam-5716	473	19	}	}	PUNCT
ejpam-5716	473	20	=	=	SYM
ejpam-5716	473	21	p6	p6	PROPN
ejpam-5716	473	22	.	.	PUNCT
ejpam-5716	474	1	hence	hence	ADV
ejpam-5716	474	2	,	,	PUNCT
ejpam-5716	474	3	γh(g	γh(g	PUNCT
ejpam-5716	474	4	\	\	PUNCT
ejpam-5716	474	5	{	{	PUNCT
ejpam-5716	474	6	p	p	X
ejpam-5716	474	7	,	,	PUNCT
ejpam-5716	474	8	v2	v2	PROPN
ejpam-5716	474	9	}	}	PUNCT
ejpam-5716	474	10	)	)	PUNCT
ejpam-5716	474	11	=	=	SYM
ejpam-5716	474	12	2	2	NUM
ejpam-5716	474	13	<	<	X
ejpam-5716	474	14	γh(g	γh(g	NOUN
ejpam-5716	474	15	)	)	PUNCT
ejpam-5716	474	16	.	.	PUNCT
ejpam-5716	475	1	by	by	ADP
ejpam-5716	475	2	theorem	theorem	NOUN
ejpam-5716	475	3	16	16	NUM
ejpam-5716	475	4	,	,	PUNCT
ejpam-5716	475	5	ζh1	ζh1	NOUN
ejpam-5716	475	6	(	(	PUNCT
ejpam-5716	475	7	g	g	NOUN
ejpam-5716	475	8	)	)	PUNCT
ejpam-5716	475	9	=	=	SYM
ejpam-5716	475	10	2	2	X
ejpam-5716	475	11	.	.	X
ejpam-5716	475	12	it	it	PRON
ejpam-5716	475	13	should	should	AUX
ejpam-5716	475	14	be	be	AUX
ejpam-5716	475	15	noted	note	VERB
ejpam-5716	475	16	that	that	SCONJ
ejpam-5716	475	17	the	the	DET
ejpam-5716	475	18	converse	converse	NOUN
ejpam-5716	475	19	of	of	ADP
ejpam-5716	475	20	theorem	theorem	NOUN
ejpam-5716	475	21	16	16	NUM
ejpam-5716	475	22	is	be	AUX
ejpam-5716	475	23	not	not	PART
ejpam-5716	475	24	true	true	ADJ
ejpam-5716	475	25	.	.	PUNCT
ejpam-5716	476	1	to	to	PART
ejpam-5716	476	2	see	see	VERB
ejpam-5716	476	3	this	this	PRON
ejpam-5716	476	4	,	,	PUNCT
ejpam-5716	476	5	consider	consider	VERB
ejpam-5716	476	6	g	g	NOUN
ejpam-5716	476	7	=	=	NOUN
ejpam-5716	476	8	c4	c4	NOUN
ejpam-5716	476	9	.	.	PUNCT
ejpam-5716	477	1	then	then	ADV
ejpam-5716	477	2	γh(g	γh(g	NOUN
ejpam-5716	477	3	)	)	PUNCT
ejpam-5716	477	4	=	=	SYM
ejpam-5716	477	5	2	2	NUM
ejpam-5716	477	6	and	and	CCONJ
ejpam-5716	477	7	γh(g	γh(g	NOUN
ejpam-5716	477	8	\	\	PROPN
ejpam-5716	477	9	v	v	NOUN
ejpam-5716	477	10	)	)	PUNCT
ejpam-5716	477	11	=	=	SYM
ejpam-5716	477	12	γh(p3	γh(p3	NOUN
ejpam-5716	477	13	)	)	PUNCT
ejpam-5716	477	14	=	=	SYM
ejpam-5716	477	15	2	2	NUM
ejpam-5716	477	16	=	=	PUNCT
ejpam-5716	477	17	γh(g	γh(g	NOUN
ejpam-5716	477	18	)	)	PUNCT
ejpam-5716	477	19	for	for	ADP
ejpam-5716	477	20	every	every	DET
ejpam-5716	477	21	v	v	NUM
ejpam-5716	477	22	∈	∈	PROPN
ejpam-5716	477	23	v	v	NOUN
ejpam-5716	477	24	(	(	PUNCT
ejpam-5716	477	25	c4	c4	NOUN
ejpam-5716	477	26	)	)	PUNCT
ejpam-5716	477	27	.	.	PUNCT
ejpam-5716	478	1	moreover	moreover	ADV
ejpam-5716	478	2	,	,	PUNCT
ejpam-5716	478	3	ζh1	ζh1	ADV
ejpam-5716	478	4	(	(	PUNCT
ejpam-5716	478	5	g	g	NOUN
ejpam-5716	478	6	)	)	PUNCT
ejpam-5716	478	7	=	=	SYM
ejpam-5716	478	8	2	2	X
ejpam-5716	478	9	.	.	PUNCT
ejpam-5716	478	10	however	however	ADV
ejpam-5716	478	11	,	,	PUNCT
ejpam-5716	478	12	one	one	PRON
ejpam-5716	478	13	can	can	AUX
ejpam-5716	478	14	not	not	PART
ejpam-5716	478	15	find	find	VERB
ejpam-5716	478	16	non	non	ADJ
ejpam-5716	478	17	-	-	ADJ
ejpam-5716	478	18	adjacent	adjacent	ADJ
ejpam-5716	478	19	vertices	vertex	NOUN
ejpam-5716	478	20	p	p	NOUN
ejpam-5716	478	21	,	,	PUNCT
ejpam-5716	478	22	q	q	PROPN
ejpam-5716	478	23	∈	∈	PROPN
ejpam-5716	478	24	v	v	ADP
ejpam-5716	478	25	(	(	PUNCT
ejpam-5716	478	26	g	g	NOUN
ejpam-5716	478	27	)	)	PUNCT
ejpam-5716	478	28	such	such	ADJ
ejpam-5716	478	29	that	that	SCONJ
ejpam-5716	478	30	γh(g	γh(g	PUNCT
ejpam-5716	478	31	\	\	PROPN
ejpam-5716	478	32	{	{	PUNCT
ejpam-5716	478	33	p	p	X
ejpam-5716	478	34	,	,	PUNCT
ejpam-5716	478	35	q	q	NOUN
ejpam-5716	478	36	}	}	PUNCT
ejpam-5716	478	37	=	=	SYM
ejpam-5716	478	38	1	1	X
ejpam-5716	478	39	.	.	PUNCT
ejpam-5716	479	1	lemma	lemma	PROPN
ejpam-5716	479	2	2	2	X
ejpam-5716	479	3	.	.	PUNCT
ejpam-5716	480	1	let	let	VERB
ejpam-5716	480	2	g	g	NOUN
ejpam-5716	480	3	and	and	CCONJ
ejpam-5716	480	4	h	h	NOUN
ejpam-5716	480	5	be	be	VERB
ejpam-5716	480	6	any	any	DET
ejpam-5716	480	7	two	two	NUM
ejpam-5716	480	8	graphs	graph	NOUN
ejpam-5716	480	9	of	of	ADP
ejpam-5716	480	10	orders	order	NOUN
ejpam-5716	480	11	m	m	VERB
ejpam-5716	480	12	and	and	CCONJ
ejpam-5716	480	13	n	n	CCONJ
ejpam-5716	480	14	,	,	PUNCT
ejpam-5716	480	15	respectively	respectively	ADV
ejpam-5716	480	16	.	.	PUNCT
ejpam-5716	481	1	if	if	SCONJ
ejpam-5716	481	2	x	x	SYM
ejpam-5716	481	3	∈	∈	PROPN
ejpam-5716	481	4	v	v	NOUN
ejpam-5716	481	5	(	(	PUNCT
ejpam-5716	481	6	g+h	g+h	PROPN
ejpam-5716	481	7	)	)	PUNCT
ejpam-5716	481	8	and	and	CCONJ
ejpam-5716	481	9	|n2	|n2	PROPN
ejpam-5716	481	10	g+h(x)|	g+h(x)|	NOUN
ejpam-5716	481	11	=	=	SYM
ejpam-5716	481	12	∆h(g+h	∆h(g+h	NOUN
ejpam-5716	481	13	)	)	PUNCT
ejpam-5716	481	14	,	,	PUNCT
ejpam-5716	481	15	then	then	ADV
ejpam-5716	481	16	|n2	|n2	PROPN
ejpam-5716	481	17	g+h	g+h	PUNCT
ejpam-5716	482	1	[	[	X
ejpam-5716	482	2	x]|	x]|	PUNCT
ejpam-5716	482	3	=	=	SYM
ejpam-5716	482	4	max{m−	max{m−	PROPN
ejpam-5716	482	5	δ(g	δ(g	X
ejpam-5716	482	6	)	)	PUNCT
ejpam-5716	482	7	,	,	PUNCT
ejpam-5716	482	8	n−	n−	PROPN
ejpam-5716	482	9	δ(h	δ(h	PROPN
ejpam-5716	482	10	)	)	PUNCT
ejpam-5716	482	11	}	}	PUNCT
ejpam-5716	482	12	.	.	PUNCT
ejpam-5716	483	1	proof	proof	NOUN
ejpam-5716	483	2	.	.	PUNCT
ejpam-5716	484	1	let	let	VERB
ejpam-5716	484	2	x	x	SYM
ejpam-5716	484	3	∈	∈	PROPN
ejpam-5716	484	4	v	v	X
ejpam-5716	484	5	(	(	PUNCT
ejpam-5716	484	6	g	g	NOUN
ejpam-5716	484	7	)	)	PUNCT
ejpam-5716	484	8	.	.	PUNCT
ejpam-5716	485	1	since	since	SCONJ
ejpam-5716	485	2	v	v	NOUN
ejpam-5716	485	3	(	(	PUNCT
ejpam-5716	485	4	h	h	NOUN
ejpam-5716	485	5	)	)	PUNCT
ejpam-5716	485	6	⊆	⊆	NUM
ejpam-5716	485	7	ng(x	ng(x	NUM
ejpam-5716	485	8	)	)	PUNCT
ejpam-5716	485	9	,	,	PUNCT
ejpam-5716	485	10	it	it	PRON
ejpam-5716	485	11	follows	follow	VERB
ejpam-5716	485	12	that	that	DET
ejpam-5716	485	13	n2	n2	NOUN
ejpam-5716	485	14	g+h	g+h	PROPN
ejpam-5716	486	1	[	[	X
ejpam-5716	486	2	x	x	X
ejpam-5716	486	3	]	]	X
ejpam-5716	486	4	∩	∩	ADJ
ejpam-5716	486	5	v	v	X
ejpam-5716	486	6	(	(	PUNCT
ejpam-5716	486	7	h	h	NOUN
ejpam-5716	486	8	)	)	PUNCT
ejpam-5716	486	9	=	=	PUNCT
ejpam-5716	486	10	∅.	∅.	VERB
ejpam-5716	486	11	hence	hence	ADV
ejpam-5716	486	12	,	,	PUNCT
ejpam-5716	486	13	n2	n2	PROPN
ejpam-5716	486	14	g+h	g+h	PROPN
ejpam-5716	487	1	[	[	X
ejpam-5716	487	2	x	x	X
ejpam-5716	487	3	]	]	X
ejpam-5716	487	4	⊆	⊆	NUM
ejpam-5716	487	5	v	v	NOUN
ejpam-5716	487	6	(	(	PUNCT
ejpam-5716	487	7	g	g	NOUN
ejpam-5716	487	8	)	)	PUNCT
ejpam-5716	487	9	.	.	PUNCT
ejpam-5716	488	1	now	now	ADV
ejpam-5716	488	2	p	p	X
ejpam-5716	488	3	∈	∈	PROPN
ejpam-5716	488	4	n2	n2	NOUN
ejpam-5716	488	5	g+h	g+h	PUNCT
ejpam-5716	489	1	[	[	X
ejpam-5716	489	2	x	x	X
ejpam-5716	489	3	]	]	X
ejpam-5716	489	4	if	if	SCONJ
ejpam-5716	489	5	and	and	CCONJ
ejpam-5716	489	6	only	only	ADV
ejpam-5716	489	7	if	if	SCONJ
ejpam-5716	489	8	p	p	X
ejpam-5716	489	9	=	=	PUNCT
ejpam-5716	489	10	x	x	X
ejpam-5716	489	11	or	or	CCONJ
ejpam-5716	489	12	dg+h(x	dg+h(x	PROPN
ejpam-5716	489	13	,	,	PUNCT
ejpam-5716	489	14	p	p	NOUN
ejpam-5716	489	15	)	)	PUNCT
ejpam-5716	489	16	=	=	SYM
ejpam-5716	489	17	2	2	X
ejpam-5716	489	18	.	.	PUNCT
ejpam-5716	489	19	this	this	DET
ejpam-5716	489	20	j.	j.	PROPN
ejpam-5716	489	21	anoche	anoche	PROPN
ejpam-5716	489	22	,	,	PUNCT
ejpam-5716	489	23	s.r	s.r	PROPN
ejpam-5716	489	24	.	.	PROPN
ejpam-5716	489	25	canoy	canoy	PROPN
ejpam-5716	489	26	jr	jr	PROPN
ejpam-5716	489	27	.	.	PUNCT
ejpam-5716	489	28	/	/	SYM
ejpam-5716	489	29	eur	eur	PROPN
ejpam-5716	489	30	.	.	PUNCT
ejpam-5716	490	1	j.	j.	PROPN
ejpam-5716	490	2	pure	pure	PROPN
ejpam-5716	490	3	appl	appl	PROPN
ejpam-5716	490	4	.	.	PROPN
ejpam-5716	490	5	math	math	PROPN
ejpam-5716	490	6	,	,	PUNCT
ejpam-5716	490	7	18	18	NUM
ejpam-5716	490	8	(	(	PUNCT
ejpam-5716	490	9	1	1	NUM
ejpam-5716	490	10	)	)	PUNCT
ejpam-5716	490	11	(	(	PUNCT
ejpam-5716	490	12	2025	2025	NUM
ejpam-5716	490	13	)	)	PUNCT
ejpam-5716	490	14	,	,	PUNCT
ejpam-5716	490	15	5716	5716	NUM
ejpam-5716	490	16	11	11	NUM
ejpam-5716	490	17	of	of	ADP
ejpam-5716	490	18	13	13	NUM
ejpam-5716	490	19	implies	imply	VERB
ejpam-5716	490	20	that	that	SCONJ
ejpam-5716	490	21	p	p	PROPN
ejpam-5716	490	22	∈	∈	PROPN
ejpam-5716	490	23	n2	n2	NOUN
ejpam-5716	490	24	g+h	g+h	PUNCT
ejpam-5716	491	1	[	[	X
ejpam-5716	491	2	x	x	X
ejpam-5716	491	3	]	]	X
ejpam-5716	491	4	if	if	SCONJ
ejpam-5716	491	5	and	and	CCONJ
ejpam-5716	491	6	only	only	ADV
ejpam-5716	491	7	if	if	SCONJ
ejpam-5716	491	8	p	p	PROPN
ejpam-5716	491	9	∈	∈	PROPN
ejpam-5716	491	10	v	v	ADP
ejpam-5716	491	11	(	(	PUNCT
ejpam-5716	491	12	g)\ng(x	g)\ng(x	NOUN
ejpam-5716	491	13	)	)	PUNCT
ejpam-5716	491	14	.	.	PUNCT
ejpam-5716	492	1	thus	thus	ADV
ejpam-5716	492	2	,	,	PUNCT
ejpam-5716	492	3	n	n	PROPN
ejpam-5716	492	4	2	2	NUM
ejpam-5716	492	5	g+h	g+h	NOUN
ejpam-5716	493	1	[	[	X
ejpam-5716	493	2	x	x	X
ejpam-5716	493	3	]	]	X
ejpam-5716	493	4	=	=	SYM
ejpam-5716	493	5	v	v	X
ejpam-5716	493	6	(	(	PUNCT
ejpam-5716	493	7	g)\ng(x	g)\ng(x	NOUN
ejpam-5716	493	8	)	)	PUNCT
ejpam-5716	493	9	.	.	PUNCT
ejpam-5716	494	1	consequently	consequently	ADV
ejpam-5716	494	2	,	,	PUNCT
ejpam-5716	494	3	|n2	|n2	PROPN
ejpam-5716	494	4	g+h	g+h	PROPN
ejpam-5716	495	1	[	[	X
ejpam-5716	495	2	x]|	x]|	PROPN
ejpam-5716	495	3	=	=	SYM
ejpam-5716	495	4	m−	m−	PROPN
ejpam-5716	495	5	|ng(x)|	|ng(x)|	VERB
ejpam-5716	495	6	=	=	SYM
ejpam-5716	495	7	m−	m−	PROPN
ejpam-5716	495	8	degg(x	degg(x	NOUN
ejpam-5716	495	9	)	)	PUNCT
ejpam-5716	495	10	.	.	PUNCT
ejpam-5716	496	1	clearly	clearly	ADV
ejpam-5716	496	2	,	,	PUNCT
ejpam-5716	496	3	max{|n2	max{|n2	PROPN
ejpam-5716	496	4	g+h	g+h	PROPN
ejpam-5716	497	1	[	[	X
ejpam-5716	497	2	x]|	x]|	PROPN
ejpam-5716	497	3	:	:	PUNCT
ejpam-5716	497	4	x	x	X
ejpam-5716	497	5	∈	∈	NOUN
ejpam-5716	497	6	v	v	ADP
ejpam-5716	497	7	(	(	PUNCT
ejpam-5716	497	8	g	g	NOUN
ejpam-5716	497	9	)	)	PUNCT
ejpam-5716	497	10	}	}	PUNCT
ejpam-5716	497	11	=	=	SYM
ejpam-5716	497	12	max{m−	max{m−	NOUN
ejpam-5716	497	13	degg(x	degg(x	NOUN
ejpam-5716	497	14	)	)	PUNCT
ejpam-5716	497	15	:	:	PUNCT
ejpam-5716	498	1	x	x	X
ejpam-5716	498	2	∈	∈	NOUN
ejpam-5716	498	3	v	v	ADP
ejpam-5716	498	4	(	(	PUNCT
ejpam-5716	498	5	g	g	NOUN
ejpam-5716	498	6	)	)	PUNCT
ejpam-5716	498	7	}	}	PUNCT
ejpam-5716	498	8	=	=	SYM
ejpam-5716	498	9	m−	m−	PROPN
ejpam-5716	498	10	δ(g	δ(g	PROPN
ejpam-5716	498	11	)	)	PUNCT
ejpam-5716	498	12	.	.	PUNCT
ejpam-5716	499	1	similarly	similarly	ADV
ejpam-5716	499	2	,	,	PUNCT
ejpam-5716	499	3	max{|n2	max{|n2	PROPN
ejpam-5716	499	4	g+h	g+h	PROPN
ejpam-5716	500	1	[	[	X
ejpam-5716	500	2	x]|	x]|	PROPN
ejpam-5716	500	3	:	:	PUNCT
ejpam-5716	500	4	x	x	X
ejpam-5716	501	1	∈	∈	NOUN
ejpam-5716	501	2	v	v	ADP
ejpam-5716	501	3	(	(	PUNCT
ejpam-5716	501	4	h	h	NOUN
ejpam-5716	501	5	)	)	PUNCT
ejpam-5716	501	6	}	}	PUNCT
ejpam-5716	501	7	=	=	SYM
ejpam-5716	501	8	max{n−	max{n−	PROPN
ejpam-5716	501	9	degh(x	degh(x	NOUN
ejpam-5716	501	10	)	)	PUNCT
ejpam-5716	501	11	:	:	PUNCT
ejpam-5716	502	1	x	x	X
ejpam-5716	502	2	∈	∈	NOUN
ejpam-5716	502	3	v	v	ADP
ejpam-5716	502	4	(	(	PUNCT
ejpam-5716	502	5	h	h	NOUN
ejpam-5716	502	6	)	)	PUNCT
ejpam-5716	502	7	}	}	PUNCT
ejpam-5716	502	8	=	=	PUNCT
ejpam-5716	502	9	n−	n−	PROPN
ejpam-5716	502	10	δ(h	δ(h	PROPN
ejpam-5716	502	11	)	)	PUNCT
ejpam-5716	502	12	.	.	PUNCT
ejpam-5716	503	1	therefore	therefore	ADV
ejpam-5716	503	2	,	,	PUNCT
ejpam-5716	503	3	if	if	SCONJ
ejpam-5716	503	4	x	x	PROPN
ejpam-5716	503	5	∈	∈	PROPN
ejpam-5716	503	6	v	v	NOUN
ejpam-5716	503	7	(	(	PUNCT
ejpam-5716	503	8	g+h	g+h	NOUN
ejpam-5716	503	9	)	)	PUNCT
ejpam-5716	503	10	such	such	ADJ
ejpam-5716	503	11	that	that	DET
ejpam-5716	503	12	∆h(g+h	∆h(g+h	NOUN
ejpam-5716	503	13	)	)	PUNCT
ejpam-5716	504	1	=	=	PUNCT
ejpam-5716	504	2	|n2	|n2	PROPN
ejpam-5716	504	3	g+h(x)|	g+h(x)|	PROPN
ejpam-5716	504	4	,	,	PUNCT
ejpam-5716	504	5	then	then	ADV
ejpam-5716	504	6	|n2	|n2	PROPN
ejpam-5716	504	7	g+h	g+h	PUNCT
ejpam-5716	505	1	[	[	X
ejpam-5716	505	2	x]|	x]|	PUNCT
ejpam-5716	505	3	=	=	SYM
ejpam-5716	505	4	max{m−	max{m−	PROPN
ejpam-5716	505	5	δ(g	δ(g	X
ejpam-5716	505	6	)	)	PUNCT
ejpam-5716	505	7	,	,	PUNCT
ejpam-5716	505	8	n−	n−	PROPN
ejpam-5716	505	9	δ(h	δ(h	PROPN
ejpam-5716	505	10	)	)	PUNCT
ejpam-5716	505	11	}	}	PUNCT
ejpam-5716	505	12	.	.	PUNCT
ejpam-5716	506	1	this	this	PRON
ejpam-5716	506	2	proves	prove	VERB
ejpam-5716	506	3	the	the	DET
ejpam-5716	506	4	assertion	assertion	NOUN
ejpam-5716	506	5	.	.	PUNCT
ejpam-5716	507	1	theorem	theorem	ADJ
ejpam-5716	507	2	17	17	NUM
ejpam-5716	507	3	.	.	PUNCT
ejpam-5716	508	1	let	let	VERB
ejpam-5716	508	2	g	g	NOUN
ejpam-5716	509	1	and	and	CCONJ
ejpam-5716	509	2	h	h	NOUN
ejpam-5716	509	3	be	be	AUX
ejpam-5716	509	4	graphs	graph	NOUN
ejpam-5716	509	5	of	of	ADP
ejpam-5716	509	6	orders	order	NOUN
ejpam-5716	509	7	m	m	VERB
ejpam-5716	509	8	and	and	CCONJ
ejpam-5716	509	9	n	n	CCONJ
ejpam-5716	509	10	,	,	PUNCT
ejpam-5716	509	11	respectively	respectively	ADV
ejpam-5716	509	12	.	.	PUNCT
ejpam-5716	510	1	then	then	ADV
ejpam-5716	510	2	each	each	PRON
ejpam-5716	510	3	of	of	ADP
ejpam-5716	510	4	the	the	DET
ejpam-5716	510	5	following	follow	VERB
ejpam-5716	510	6	holds	hold	VERB
ejpam-5716	510	7	:	:	PUNCT
ejpam-5716	510	8	(	(	PUNCT
ejpam-5716	510	9	i	i	NOUN
ejpam-5716	510	10	)	)	PUNCT
ejpam-5716	510	11	ζhk	ζhk	NOUN
ejpam-5716	510	12	(	(	PUNCT
ejpam-5716	510	13	g+h	g+h	NOUN
ejpam-5716	510	14	)	)	PUNCT
ejpam-5716	510	15	=	=	PROPN
ejpam-5716	510	16	min{m+	min{m+	PROPN
ejpam-5716	510	17	δ(h	δ(h	PROPN
ejpam-5716	510	18	)	)	PUNCT
ejpam-5716	510	19	,	,	PUNCT
ejpam-5716	510	20	n+	n+	NUM
ejpam-5716	510	21	δ(g	δ(g	SCONJ
ejpam-5716	510	22	)	)	PUNCT
ejpam-5716	510	23	}	}	PUNCT
ejpam-5716	510	24	where	where	SCONJ
ejpam-5716	510	25	k	k	PROPN
ejpam-5716	510	26	=	=	SYM
ejpam-5716	510	27	γh(g+h)−	γh(g+h)−	PROPN
ejpam-5716	510	28	1	1	NUM
ejpam-5716	510	29	.	.	PUNCT
ejpam-5716	510	30	(	(	PUNCT
ejpam-5716	510	31	ii	ii	NOUN
ejpam-5716	510	32	)	)	PUNCT
ejpam-5716	510	33	ζh1	ζh1	NOUN
ejpam-5716	510	34	(	(	PUNCT
ejpam-5716	510	35	g	g	NOUN
ejpam-5716	510	36	+	+	NOUN
ejpam-5716	510	37	h	h	NOUN
ejpam-5716	510	38	)	)	PUNCT
ejpam-5716	510	39	=	=	SYM
ejpam-5716	510	40	1	1	NUM
ejpam-5716	510	41	if	if	SCONJ
ejpam-5716	510	42	and	and	CCONJ
ejpam-5716	510	43	only	only	ADV
ejpam-5716	510	44	if	if	SCONJ
ejpam-5716	510	45	there	there	PRON
ejpam-5716	510	46	exists	exist	VERB
ejpam-5716	510	47	v	v	ADP
ejpam-5716	510	48	∈	∈	PROPN
ejpam-5716	510	49	v	v	NOUN
ejpam-5716	510	50	(	(	PUNCT
ejpam-5716	510	51	g	g	PROPN
ejpam-5716	510	52	+	+	NOUN
ejpam-5716	510	53	h	h	NOUN
ejpam-5716	510	54	)	)	PUNCT
ejpam-5716	510	55	such	such	ADJ
ejpam-5716	511	1	that	that	DET
ejpam-5716	511	2	v	v	NUM
ejpam-5716	511	3	∈	∈	PROPN
ejpam-5716	511	4	v	v	NOUN
ejpam-5716	511	5	(	(	PUNCT
ejpam-5716	511	6	g	g	NOUN
ejpam-5716	511	7	)	)	PUNCT
ejpam-5716	511	8	and	and	CCONJ
ejpam-5716	511	9	pnd(g−	pnd(g−	NOUN
ejpam-5716	511	10	v	v	X
ejpam-5716	511	11	)	)	PUNCT
ejpam-5716	511	12	=	=	PUNCT
ejpam-5716	511	13	pnd(g)−	pnd(g)−	NOUN
ejpam-5716	511	14	1	1	NUM
ejpam-5716	511	15	or	or	CCONJ
ejpam-5716	511	16	v	v	ADP
ejpam-5716	511	17	∈	∈	PROPN
ejpam-5716	511	18	v	v	NOUN
ejpam-5716	511	19	(	(	PUNCT
ejpam-5716	511	20	h	h	NOUN
ejpam-5716	511	21	)	)	PUNCT
ejpam-5716	511	22	and	and	CCONJ
ejpam-5716	511	23	pnd(h	pnd(h	PROPN
ejpam-5716	511	24	−	−	NOUN
ejpam-5716	511	25	v	v	NOUN
ejpam-5716	511	26	)	)	PUNCT
ejpam-5716	511	27	=	=	SYM
ejpam-5716	511	28	pnd(h)−	pnd(h)−	PROPN
ejpam-5716	511	29	1	1	NUM
ejpam-5716	511	30	.	.	PUNCT
ejpam-5716	511	31	(	(	PUNCT
ejpam-5716	511	32	iii	iii	X
ejpam-5716	511	33	)	)	PUNCT
ejpam-5716	511	34	if	if	SCONJ
ejpam-5716	511	35	i(g	i(g	NOUN
ejpam-5716	511	36	)	)	PUNCT
ejpam-5716	511	37	̸=	̸=	PROPN
ejpam-5716	511	38	∅	∅	NOUN
ejpam-5716	511	39	and	and	CCONJ
ejpam-5716	511	40	i(h	i(h	NOUN
ejpam-5716	511	41	)	)	PUNCT
ejpam-5716	511	42	̸=	̸=	NOUN
ejpam-5716	511	43	∅	∅	NOUN
ejpam-5716	511	44	,	,	PUNCT
ejpam-5716	511	45	then	then	ADV
ejpam-5716	511	46	ζh1	ζh1	ADV
ejpam-5716	511	47	(	(	PUNCT
ejpam-5716	511	48	g+h	g+h	NOUN
ejpam-5716	511	49	)	)	PUNCT
ejpam-5716	511	50	=	=	PUNCT
ejpam-5716	511	51	min{m	min{m	PROPN
ejpam-5716	511	52	,	,	PUNCT
ejpam-5716	511	53	n	n	CCONJ
ejpam-5716	511	54	}	}	PUNCT
ejpam-5716	511	55	.	.	PUNCT
ejpam-5716	512	1	(	(	PUNCT
ejpam-5716	512	2	iv	iv	X
ejpam-5716	512	3	)	)	PUNCT
ejpam-5716	512	4	if	if	SCONJ
ejpam-5716	512	5	i(g	i(g	NOUN
ejpam-5716	512	6	)	)	PUNCT
ejpam-5716	512	7	̸=	̸=	PROPN
ejpam-5716	512	8	∅	∅	NOUN
ejpam-5716	512	9	and	and	CCONJ
ejpam-5716	512	10	h	h	NOUN
ejpam-5716	512	11	=	=	SYM
ejpam-5716	512	12	kn	kn	PROPN
ejpam-5716	512	13	,	,	PUNCT
ejpam-5716	512	14	then	then	ADV
ejpam-5716	512	15	ζhk	ζhk	PROPN
ejpam-5716	512	16	(	(	PUNCT
ejpam-5716	512	17	g+h	g+h	PROPN
ejpam-5716	512	18	)	)	PUNCT
ejpam-5716	513	1	=	=	SYM
ejpam-5716	513	2	k	k	NOUN
ejpam-5716	513	3	,	,	PUNCT
ejpam-5716	513	4	where	where	SCONJ
ejpam-5716	513	5	1	1	NUM
ejpam-5716	513	6	≤	≤	NUM
ejpam-5716	513	7	k	k	PROPN
ejpam-5716	513	8	≤	≤	ADJ
ejpam-5716	513	9	n.	n.	NOUN
ejpam-5716	513	10	proof	proof	NOUN
ejpam-5716	513	11	.	.	PUNCT
ejpam-5716	514	1	(	(	PUNCT
ejpam-5716	514	2	i	i	NOUN
ejpam-5716	514	3	)	)	PUNCT
ejpam-5716	514	4	let	let	VERB
ejpam-5716	514	5	s	s	PRON
ejpam-5716	514	6	be	be	AUX
ejpam-5716	514	7	a	a	DET
ejpam-5716	514	8	ζhk	ζhk	NOUN
ejpam-5716	514	9	-set	-set	ADJ
ejpam-5716	514	10	in	in	ADP
ejpam-5716	514	11	g	g	PROPN
ejpam-5716	514	12	+	+	CCONJ
ejpam-5716	514	13	h.	h.	PROPN
ejpam-5716	514	14	by	by	ADP
ejpam-5716	514	15	lemma	lemma	PROPN
ejpam-5716	514	16	1	1	NUM
ejpam-5716	514	17	,	,	PUNCT
ejpam-5716	514	18	s	s	PART
ejpam-5716	514	19	=	=	PUNCT
ejpam-5716	514	20	{	{	PUNCT
ejpam-5716	514	21	x	x	NOUN
ejpam-5716	514	22	}	}	PUNCT
ejpam-5716	514	23	where	where	SCONJ
ejpam-5716	514	24	|n2	|n2	PROPN
ejpam-5716	514	25	g+h(x)|	g+h(x)|	NOUN
ejpam-5716	514	26	=	=	SYM
ejpam-5716	514	27	∆h(g	∆h(g	NOUN
ejpam-5716	514	28	+	+	CCONJ
ejpam-5716	514	29	h	h	NOUN
ejpam-5716	514	30	)	)	PUNCT
ejpam-5716	514	31	.	.	PUNCT
ejpam-5716	515	1	by	by	ADP
ejpam-5716	515	2	lemma	lemma	PROPN
ejpam-5716	515	3	2	2	NUM
ejpam-5716	515	4	,	,	PUNCT
ejpam-5716	515	5	we	we	PRON
ejpam-5716	515	6	may	may	AUX
ejpam-5716	515	7	assume	assume	VERB
ejpam-5716	515	8	without	without	ADP
ejpam-5716	515	9	loss	loss	NOUN
ejpam-5716	515	10	of	of	ADP
ejpam-5716	515	11	generality	generality	NOUN
ejpam-5716	515	12	that	that	PRON
ejpam-5716	515	13	|n2	|n2	PROPN
ejpam-5716	515	14	g+h	g+h	PUNCT
ejpam-5716	516	1	[	[	X
ejpam-5716	516	2	x	x	X
ejpam-5716	516	3	]	]	X
ejpam-5716	516	4	=	=	PUNCT
ejpam-5716	516	5	m−	m−	PROPN
ejpam-5716	516	6	δ(g	δ(g	PROPN
ejpam-5716	516	7	)	)	PUNCT
ejpam-5716	516	8	≥	≥	NOUN
ejpam-5716	516	9	n−	n−	PROPN
ejpam-5716	516	10	δ(h	δ(h	PROPN
ejpam-5716	516	11	)	)	PUNCT
ejpam-5716	516	12	for	for	ADP
ejpam-5716	516	13	x	x	PROPN
ejpam-5716	516	14	∈	∈	PROPN
ejpam-5716	516	15	v	v	ADP
ejpam-5716	516	16	(	(	PUNCT
ejpam-5716	516	17	g	g	NOUN
ejpam-5716	516	18	)	)	PUNCT
ejpam-5716	516	19	.	.	PUNCT
ejpam-5716	517	1	then	then	ADV
ejpam-5716	517	2	ζhk	ζhk	PROPN
ejpam-5716	517	3	(	(	PUNCT
ejpam-5716	517	4	g+h	g+h	PROPN
ejpam-5716	517	5	)	)	PUNCT
ejpam-5716	517	6	=	=	PRON
ejpam-5716	518	1	(	(	PUNCT
ejpam-5716	518	2	m+	m+	NUM
ejpam-5716	518	3	n)−	n)−	PROPN
ejpam-5716	518	4	(	(	PUNCT
ejpam-5716	518	5	m−	m−	PROPN
ejpam-5716	518	6	δ(g	δ(g	PROPN
ejpam-5716	518	7	)	)	PUNCT
ejpam-5716	518	8	)	)	PUNCT
ejpam-5716	518	9	=	=	SYM
ejpam-5716	518	10	n+	n+	X
ejpam-5716	518	11	δ(g	δ(g	ADJ
ejpam-5716	518	12	)	)	PUNCT
ejpam-5716	518	13	≤	≤	NUM
ejpam-5716	518	14	m+	m+	NUM
ejpam-5716	518	15	δ(h	δ(h	NOUN
ejpam-5716	518	16	)	)	PUNCT
ejpam-5716	518	17	=	=	PUNCT
ejpam-5716	518	18	(	(	PUNCT
ejpam-5716	518	19	m+	m+	NUM
ejpam-5716	518	20	n)−	n)−	PROPN
ejpam-5716	518	21	(	(	PUNCT
ejpam-5716	518	22	n−	n−	NOUN
ejpam-5716	518	23	δ(h	δ(h	PROPN
ejpam-5716	518	24	)	)	PUNCT
ejpam-5716	518	25	)	)	PUNCT
ejpam-5716	518	26	.	.	PUNCT
ejpam-5716	519	1	(	(	PUNCT
ejpam-5716	519	2	ii	ii	NOUN
ejpam-5716	519	3	)	)	PUNCT
ejpam-5716	519	4	by	by	ADP
ejpam-5716	519	5	theorem	theorem	ADJ
ejpam-5716	519	6	5	5	NUM
ejpam-5716	519	7	and	and	CCONJ
ejpam-5716	519	8	theorem	theorem	VERB
ejpam-5716	519	9	2	2	NUM
ejpam-5716	519	10	,	,	PUNCT
ejpam-5716	519	11	ζh1	ζh1	NOUN
ejpam-5716	519	12	(	(	PUNCT
ejpam-5716	519	13	g	g	NOUN
ejpam-5716	519	14	+	+	NOUN
ejpam-5716	519	15	h	h	NOUN
ejpam-5716	519	16	)	)	PUNCT
ejpam-5716	519	17	=	=	SYM
ejpam-5716	519	18	1	1	NUM
ejpam-5716	519	19	if	if	SCONJ
ejpam-5716	519	20	and	and	CCONJ
ejpam-5716	519	21	only	only	ADV
ejpam-5716	519	22	if	if	SCONJ
ejpam-5716	519	23	there	there	PRON
ejpam-5716	519	24	exists	exist	VERB
ejpam-5716	519	25	a	a	DET
ejpam-5716	519	26	vertex	vertex	NOUN
ejpam-5716	519	27	v	v	ADP
ejpam-5716	519	28	∈	∈	NOUN
ejpam-5716	519	29	v	v	NOUN
ejpam-5716	519	30	(	(	PUNCT
ejpam-5716	519	31	g	g	PROPN
ejpam-5716	519	32	+	+	NOUN
ejpam-5716	519	33	h	h	NOUN
ejpam-5716	519	34	)	)	PUNCT
ejpam-5716	519	35	such	such	ADJ
ejpam-5716	519	36	that	that	SCONJ
ejpam-5716	519	37	γh((g	γh((g	DET
ejpam-5716	519	38	+	+	PROPN
ejpam-5716	519	39	h	h	NOUN
ejpam-5716	519	40	)	)	PUNCT
ejpam-5716	519	41	−	−	PROPN
ejpam-5716	519	42	v	v	NOUN
ejpam-5716	519	43	)	)	PUNCT
ejpam-5716	519	44	=	=	SYM
ejpam-5716	520	1	γh((g	γh((g	PRON
ejpam-5716	520	2	+	+	NUM
ejpam-5716	520	3	h	h	NOUN
ejpam-5716	520	4	)	)	PUNCT
ejpam-5716	520	5	)	)	PUNCT
ejpam-5716	521	1	−	−	PROPN
ejpam-5716	521	2	1	1	NUM
ejpam-5716	521	3	=	=	SYM
ejpam-5716	521	4	pnd(g	pnd(g	PROPN
ejpam-5716	521	5	)	)	PUNCT
ejpam-5716	521	6	+	+	NUM
ejpam-5716	522	1	pnd(h	pnd(h	NUM
ejpam-5716	522	2	)	)	PUNCT
ejpam-5716	523	1	−	−	PROPN
ejpam-5716	524	1	1	1	X
ejpam-5716	524	2	.	.	PUNCT
ejpam-5716	525	1	if	if	SCONJ
ejpam-5716	525	2	v	v	NUM
ejpam-5716	525	3	∈	∈	PROPN
ejpam-5716	525	4	v	v	NOUN
ejpam-5716	525	5	(	(	PUNCT
ejpam-5716	525	6	g	g	NOUN
ejpam-5716	525	7	)	)	PUNCT
ejpam-5716	525	8	,	,	PUNCT
ejpam-5716	525	9	then	then	ADV
ejpam-5716	525	10	(	(	PUNCT
ejpam-5716	525	11	g	g	PROPN
ejpam-5716	525	12	+	+	NOUN
ejpam-5716	525	13	h	h	NOUN
ejpam-5716	525	14	)	)	PUNCT
ejpam-5716	525	15	−	−	PROPN
ejpam-5716	525	16	v	v	NOUN
ejpam-5716	525	17	=	=	SYM
ejpam-5716	525	18	(	(	PUNCT
ejpam-5716	525	19	g	g	NOUN
ejpam-5716	525	20	−	−	PROPN
ejpam-5716	525	21	v	v	NOUN
ejpam-5716	525	22	)	)	PUNCT
ejpam-5716	526	1	+	+	NOUN
ejpam-5716	526	2	h.	h.	PROPN
ejpam-5716	526	3	otherwise	otherwise	ADV
ejpam-5716	526	4	,	,	PUNCT
ejpam-5716	526	5	(	(	PUNCT
ejpam-5716	526	6	g	g	PROPN
ejpam-5716	526	7	+	+	NOUN
ejpam-5716	526	8	h	h	NOUN
ejpam-5716	526	9	)	)	PUNCT
ejpam-5716	526	10	−	−	PROPN
ejpam-5716	526	11	v	v	NOUN
ejpam-5716	526	12	=	=	SYM
ejpam-5716	526	13	g	g	PROPN
ejpam-5716	526	14	+	+	CCONJ
ejpam-5716	526	15	(	(	PUNCT
ejpam-5716	526	16	h	h	NOUN
ejpam-5716	526	17	−	−	PROPN
ejpam-5716	526	18	v	v	NOUN
ejpam-5716	526	19	)	)	PUNCT
ejpam-5716	526	20	.	.	PUNCT
ejpam-5716	527	1	by	by	ADP
ejpam-5716	527	2	theorem	theorem	NOUN
ejpam-5716	527	3	2	2	NUM
ejpam-5716	527	4	,	,	PUNCT
ejpam-5716	527	5	γh((g+h)−	γh((g+h)−	NOUN
ejpam-5716	527	6	v	v	NOUN
ejpam-5716	527	7	)	)	PUNCT
ejpam-5716	527	8	=	=	SYM
ejpam-5716	527	9	pnd(g−	pnd(g−	NOUN
ejpam-5716	527	10	v	v	NOUN
ejpam-5716	527	11	)	)	PUNCT
ejpam-5716	527	12	+	+	NUM
ejpam-5716	527	13	pnd(h	pnd(h	NUM
ejpam-5716	527	14	)	)	PUNCT
ejpam-5716	527	15	or	or	CCONJ
ejpam-5716	527	16	γh((g+h)−	γh((g+h)−	NOUN
ejpam-5716	527	17	v	v	NOUN
ejpam-5716	527	18	)	)	PUNCT
ejpam-5716	527	19	=	=	SYM
ejpam-5716	527	20	pnd(g	pnd(g	PROPN
ejpam-5716	527	21	)	)	PUNCT
ejpam-5716	527	22	+	+	NUM
ejpam-5716	528	1	pnd(h	pnd(h	NUM
ejpam-5716	528	2	−	−	NOUN
ejpam-5716	528	3	v	v	NOUN
ejpam-5716	528	4	)	)	PUNCT
ejpam-5716	528	5	.	.	PUNCT
ejpam-5716	529	1	therefore	therefore	ADV
ejpam-5716	529	2	,	,	PUNCT
ejpam-5716	529	3	ζh1	ζh1	ADV
ejpam-5716	529	4	(	(	PUNCT
ejpam-5716	529	5	g+h	g+h	NOUN
ejpam-5716	529	6	)	)	PUNCT
ejpam-5716	529	7	=	=	SYM
ejpam-5716	529	8	1	1	NUM
ejpam-5716	529	9	if	if	SCONJ
ejpam-5716	529	10	and	and	CCONJ
ejpam-5716	529	11	only	only	ADV
ejpam-5716	529	12	if	if	SCONJ
ejpam-5716	529	13	there	there	PRON
ejpam-5716	529	14	exists	exist	VERB
ejpam-5716	529	15	a	a	DET
ejpam-5716	529	16	vertex	vertex	NOUN
ejpam-5716	529	17	v	v	ADP
ejpam-5716	529	18	∈	∈	PROPN
ejpam-5716	529	19	v	v	NOUN
ejpam-5716	529	20	(	(	PUNCT
ejpam-5716	529	21	g	g	NOUN
ejpam-5716	529	22	)	)	PUNCT
ejpam-5716	529	23	such	such	ADJ
ejpam-5716	529	24	that	that	PRON
ejpam-5716	529	25	pnd(g−	pnd(g−	NOUN
ejpam-5716	529	26	v	v	NOUN
ejpam-5716	529	27	)	)	PUNCT
ejpam-5716	530	1	=	=	PUNCT
ejpam-5716	530	2	pnd(g)−	pnd(g)−	NOUN
ejpam-5716	530	3	1	1	NUM
ejpam-5716	530	4	or	or	CCONJ
ejpam-5716	530	5	v	v	ADP
ejpam-5716	530	6	∈	∈	PROPN
ejpam-5716	530	7	v	v	NOUN
ejpam-5716	530	8	(	(	PUNCT
ejpam-5716	530	9	h	h	NOUN
ejpam-5716	530	10	)	)	PUNCT
ejpam-5716	530	11	with	with	ADP
ejpam-5716	530	12	pnd(h	pnd(h	PROPN
ejpam-5716	530	13	−	−	PROPN
ejpam-5716	530	14	v	v	NOUN
ejpam-5716	530	15	)	)	PUNCT
ejpam-5716	530	16	=	=	SYM
ejpam-5716	530	17	pnd(h)−	pnd(h)−	PROPN
ejpam-5716	530	18	1	1	NUM
ejpam-5716	530	19	.	.	PUNCT
ejpam-5716	530	20	(	(	PUNCT
ejpam-5716	530	21	iii	iii	X
ejpam-5716	530	22	)	)	PUNCT
ejpam-5716	530	23	if	if	SCONJ
ejpam-5716	530	24	i(g	i(g	NOUN
ejpam-5716	530	25	)	)	PUNCT
ejpam-5716	530	26	̸=	̸=	PROPN
ejpam-5716	530	27	∅	∅	NOUN
ejpam-5716	530	28	and	and	CCONJ
ejpam-5716	530	29	i(h	i(h	NOUN
ejpam-5716	530	30	)	)	PUNCT
ejpam-5716	530	31	̸=	̸=	NOUN
ejpam-5716	530	32	∅	∅	NOUN
ejpam-5716	530	33	,	,	PUNCT
ejpam-5716	530	34	then	then	ADV
ejpam-5716	530	35	γh(g	γh(g	PUNCT
ejpam-5716	530	36	+	+	CCONJ
ejpam-5716	530	37	h	h	X
ejpam-5716	530	38	)	)	PUNCT
ejpam-5716	530	39	=	=	SYM
ejpam-5716	530	40	2	2	NUM
ejpam-5716	530	41	,	,	PUNCT
ejpam-5716	530	42	by	by	ADP
ejpam-5716	530	43	theorem	theorem	NOUN
ejpam-5716	530	44	2	2	NUM
ejpam-5716	530	45	.	.	PUNCT
ejpam-5716	531	1	thus	thus	ADV
ejpam-5716	531	2	,	,	PUNCT
ejpam-5716	531	3	k	k	PROPN
ejpam-5716	531	4	=	=	SYM
ejpam-5716	531	5	1	1	X
ejpam-5716	531	6	.	.	PUNCT
ejpam-5716	531	7	let	let	VERB
ejpam-5716	531	8	p	p	PRON
ejpam-5716	531	9	∈	∈	PROPN
ejpam-5716	531	10	i(g	i(g	NOUN
ejpam-5716	531	11	)	)	PUNCT
ejpam-5716	531	12	and	and	CCONJ
ejpam-5716	531	13	q	q	PROPN
ejpam-5716	531	14	∈	∈	PROPN
ejpam-5716	531	15	i(h	i(h	NOUN
ejpam-5716	531	16	)	)	PUNCT
ejpam-5716	531	17	.	.	PUNCT
ejpam-5716	532	1	since	since	SCONJ
ejpam-5716	532	2	n2	n2	ADJ
ejpam-5716	532	3	g(p	g(p	PROPN
ejpam-5716	532	4	)	)	PUNCT
ejpam-5716	532	5	=	=	SYM
ejpam-5716	532	6	v	v	X
ejpam-5716	532	7	(	(	PUNCT
ejpam-5716	532	8	g	g	NOUN
ejpam-5716	532	9	)	)	PUNCT
ejpam-5716	532	10	\	\	NOUN
ejpam-5716	532	11	{	{	PUNCT
ejpam-5716	532	12	p	p	NOUN
ejpam-5716	532	13	}	}	PUNCT
ejpam-5716	532	14	and	and	CCONJ
ejpam-5716	532	15	n2	n2	ADJ
ejpam-5716	532	16	h(q	h(q	ADV
ejpam-5716	532	17	)	)	PUNCT
ejpam-5716	533	1	=	=	SYM
ejpam-5716	533	2	v	v	X
ejpam-5716	533	3	(	(	PUNCT
ejpam-5716	533	4	h	h	NOUN
ejpam-5716	533	5	)	)	PUNCT
ejpam-5716	533	6	\	\	NOUN
ejpam-5716	533	7	{	{	PUNCT
ejpam-5716	533	8	q	q	NOUN
ejpam-5716	533	9	}	}	PUNCT
ejpam-5716	533	10	,	,	PUNCT
ejpam-5716	533	11	it	it	PRON
ejpam-5716	533	12	follows	follow	VERB
ejpam-5716	533	13	that	that	SCONJ
ejpam-5716	533	14	∆h(g	∆h(g	VERB
ejpam-5716	533	15	+	+	NOUN
ejpam-5716	533	16	h	h	NOUN
ejpam-5716	533	17	)	)	PUNCT
ejpam-5716	533	18	=	=	SYM
ejpam-5716	533	19	max{|n2	max{|n2	PROPN
ejpam-5716	533	20	g(p)|	g(p)|	PROPN
ejpam-5716	533	21	,	,	PUNCT
ejpam-5716	533	22	|n2	|n2	PROPN
ejpam-5716	533	23	h(q)|	h(q)|	PROPN
ejpam-5716	533	24	}	}	PUNCT
ejpam-5716	533	25	.	.	PUNCT
ejpam-5716	534	1	therefore	therefore	ADV
ejpam-5716	534	2	,	,	PUNCT
ejpam-5716	534	3	since	since	SCONJ
ejpam-5716	534	4	δ(g	δ(g	PROPN
ejpam-5716	534	5	)	)	PUNCT
ejpam-5716	534	6	=	=	SYM
ejpam-5716	534	7	|ng(p)|	|ng(p)|	NOUN
ejpam-5716	534	8	=	=	SYM
ejpam-5716	534	9	0	0	NUM
ejpam-5716	534	10	and	and	CCONJ
ejpam-5716	534	11	δ(h	δ(h	PROPN
ejpam-5716	534	12	)	)	PUNCT
ejpam-5716	534	13	=	=	PUNCT
ejpam-5716	534	14	|nh(q)|	|nh(q)|	X
ejpam-5716	534	15	=	=	SYM
ejpam-5716	534	16	0	0	NUM
ejpam-5716	534	17	,	,	PUNCT
ejpam-5716	534	18	it	it	PRON
ejpam-5716	534	19	follows	follow	VERB
ejpam-5716	534	20	from	from	ADP
ejpam-5716	534	21	(	(	PUNCT
ejpam-5716	534	22	i	i	NOUN
ejpam-5716	534	23	)	)	PUNCT
ejpam-5716	534	24	that	that	ADV
ejpam-5716	534	25	ζh1	ζh1	ADV
ejpam-5716	534	26	(	(	PUNCT
ejpam-5716	534	27	g+h	g+h	NOUN
ejpam-5716	534	28	)	)	PUNCT
ejpam-5716	534	29	=	=	PUNCT
ejpam-5716	534	30	min{m	min{m	PROPN
ejpam-5716	534	31	,	,	PUNCT
ejpam-5716	534	32	n	n	CCONJ
ejpam-5716	534	33	}	}	PUNCT
ejpam-5716	534	34	.	.	PUNCT
ejpam-5716	535	1	(	(	PUNCT
ejpam-5716	535	2	iv	iv	X
ejpam-5716	535	3	)	)	PUNCT
ejpam-5716	535	4	since	since	SCONJ
ejpam-5716	535	5	pnd(g	pnd(g	ADP
ejpam-5716	535	6	)	)	PUNCT
ejpam-5716	535	7	=	=	SYM
ejpam-5716	535	8	1	1	NUM
ejpam-5716	535	9	and	and	CCONJ
ejpam-5716	535	10	pnd(kn	pnd(kn	NUM
ejpam-5716	535	11	)	)	PUNCT
ejpam-5716	536	1	=	=	SYM
ejpam-5716	537	1	n	n	CCONJ
ejpam-5716	537	2	,	,	PUNCT
ejpam-5716	537	3	γh(g	γh(g	PUNCT
ejpam-5716	537	4	+	+	X
ejpam-5716	537	5	kn	kn	NOUN
ejpam-5716	537	6	)	)	PUNCT
ejpam-5716	537	7	=	=	SYM
ejpam-5716	537	8	n	n	PROPN
ejpam-5716	537	9	+	+	CCONJ
ejpam-5716	537	10	1	1	NUM
ejpam-5716	537	11	by	by	ADP
ejpam-5716	537	12	theorem	theorem	NOUN
ejpam-5716	537	13	2	2	NUM
ejpam-5716	537	14	.	.	PUNCT
ejpam-5716	538	1	let	let	VERB
ejpam-5716	538	2	k	k	PRON
ejpam-5716	538	3	be	be	AUX
ejpam-5716	538	4	such	such	ADJ
ejpam-5716	538	5	that	that	SCONJ
ejpam-5716	538	6	1	1	NUM
ejpam-5716	538	7	≤	≤	NUM
ejpam-5716	538	8	k	k	NOUN
ejpam-5716	538	9	≤	≤	NOUN
ejpam-5716	538	10	n	n	CCONJ
ejpam-5716	538	11	and	and	CCONJ
ejpam-5716	538	12	let	let	VERB
ejpam-5716	538	13	s	s	PRON
ejpam-5716	538	14	=	=	VERB
ejpam-5716	538	15	sg	sg	PROPN
ejpam-5716	538	16	∪	∪	PROPN
ejpam-5716	538	17	sn	sn	PROPN
ejpam-5716	538	18	be	be	AUX
ejpam-5716	538	19	a	a	DET
ejpam-5716	538	20	ζhk	ζhk	NOUN
ejpam-5716	538	21	-set	-set	ADJ
ejpam-5716	538	22	in	in	ADP
ejpam-5716	538	23	g	g	PROPN
ejpam-5716	538	24	+	+	PROPN
ejpam-5716	538	25	kn	kn	PROPN
ejpam-5716	538	26	,	,	PUNCT
ejpam-5716	538	27	where	where	SCONJ
ejpam-5716	538	28	sg	sg	PROPN
ejpam-5716	538	29	⊆	⊆	NUM
ejpam-5716	538	30	v	v	NOUN
ejpam-5716	538	31	(	(	PUNCT
ejpam-5716	538	32	g	g	NOUN
ejpam-5716	538	33	)	)	PUNCT
ejpam-5716	538	34	and	and	CCONJ
ejpam-5716	538	35	j.	j.	PROPN
ejpam-5716	538	36	anoche	anoche	PROPN
ejpam-5716	538	37	,	,	PUNCT
ejpam-5716	538	38	s.r	s.r	PROPN
ejpam-5716	538	39	.	.	PROPN
ejpam-5716	538	40	canoy	canoy	PROPN
ejpam-5716	538	41	jr	jr	PROPN
ejpam-5716	538	42	.	.	PUNCT
ejpam-5716	538	43	/	/	SYM
ejpam-5716	538	44	eur	eur	PROPN
ejpam-5716	538	45	.	.	PUNCT
ejpam-5716	539	1	j.	j.	PROPN
ejpam-5716	539	2	pure	pure	PROPN
ejpam-5716	539	3	appl	appl	PROPN
ejpam-5716	539	4	.	.	PROPN
ejpam-5716	539	5	math	math	PROPN
ejpam-5716	539	6	,	,	PUNCT
ejpam-5716	539	7	18	18	NUM
ejpam-5716	539	8	(	(	PUNCT
ejpam-5716	539	9	1	1	NUM
ejpam-5716	539	10	)	)	PUNCT
ejpam-5716	539	11	(	(	PUNCT
ejpam-5716	539	12	2025	2025	NUM
ejpam-5716	539	13	)	)	PUNCT
ejpam-5716	539	14	,	,	PUNCT
ejpam-5716	539	15	5716	5716	NUM
ejpam-5716	539	16	12	12	NUM
ejpam-5716	539	17	of	of	ADP
ejpam-5716	539	18	13	13	NUM
ejpam-5716	539	19	sn	sn	NOUN
ejpam-5716	539	20	⊆	⊆	NUM
ejpam-5716	539	21	v	v	NOUN
ejpam-5716	539	22	(	(	PUNCT
ejpam-5716	539	23	kn	kn	PROPN
ejpam-5716	539	24	)	)	PUNCT
ejpam-5716	539	25	.	.	PUNCT
ejpam-5716	540	1	then	then	ADV
ejpam-5716	540	2	|s|	|s|	PROPN
ejpam-5716	540	3	=	=	SYM
ejpam-5716	540	4	|sg|+	|sg|+	NOUN
ejpam-5716	540	5	|sn|	|sn|	PROPN
ejpam-5716	540	6	=	=	SYM
ejpam-5716	540	7	(	(	PUNCT
ejpam-5716	540	8	n+	n+	NUM
ejpam-5716	540	9	1)−	1)−	PROPN
ejpam-5716	540	10	k	k	PROPN
ejpam-5716	540	11	and	and	CCONJ
ejpam-5716	540	12	|n2	|n2	PROPN
ejpam-5716	540	13	g+kn	g+kn	NOUN
ejpam-5716	540	14	[	[	X
ejpam-5716	540	15	s]|	s]|	X
ejpam-5716	540	16	=	=	SYM
ejpam-5716	540	17	|n2	|n2	PROPN
ejpam-5716	540	18	g+kn	g+kn	NOUN
ejpam-5716	541	1	[	[	X
ejpam-5716	541	2	sg]|+	sg]|+	X
ejpam-5716	541	3	|n2	|n2	PRON
ejpam-5716	541	4	g+kn	g+kn	NOUN
ejpam-5716	542	1	[	[	X
ejpam-5716	542	2	sn]|	sn]|	ADP
ejpam-5716	542	3	=	=	PUNCT
ejpam-5716	542	4	|n2	|n2	X
ejpam-5716	542	5	g+kn	g+kn	NOUN
ejpam-5716	542	6	[	[	X
ejpam-5716	542	7	sg]|+	sg]|+	X
ejpam-5716	542	8	|sn|	|sn|	PROPN
ejpam-5716	542	9	.	.	PUNCT
ejpam-5716	543	1	since	since	SCONJ
ejpam-5716	543	2	n2	n2	ADJ
ejpam-5716	543	3	g+kn	g+kn	NOUN
ejpam-5716	543	4	[	[	X
ejpam-5716	543	5	t	t	X
ejpam-5716	543	6	]	]	X
ejpam-5716	543	7	=	=	SYM
ejpam-5716	543	8	v	v	X
ejpam-5716	543	9	(	(	PUNCT
ejpam-5716	543	10	g	g	NOUN
ejpam-5716	543	11	)	)	PUNCT
ejpam-5716	543	12	for	for	ADP
ejpam-5716	543	13	any	any	DET
ejpam-5716	543	14	t	t	NOUN
ejpam-5716	543	15	∈	∈	PROPN
ejpam-5716	543	16	i(g	i(g	PROPN
ejpam-5716	543	17	)	)	PUNCT
ejpam-5716	543	18	and	and	CCONJ
ejpam-5716	543	19	the	the	DET
ejpam-5716	543	20	value	value	NOUN
ejpam-5716	543	21	|n2	|n2	PROPN
ejpam-5716	543	22	g+kn	g+kn	NOUN
ejpam-5716	543	23	[	[	X
ejpam-5716	543	24	s]|	s]|	PROPN
ejpam-5716	543	25	is	be	AUX
ejpam-5716	543	26	maximum	maximum	ADJ
ejpam-5716	543	27	,	,	PUNCT
ejpam-5716	543	28	it	it	PRON
ejpam-5716	543	29	follows	follow	VERB
ejpam-5716	543	30	that	that	SCONJ
ejpam-5716	543	31	sg	sg	ADV
ejpam-5716	543	32	=	=	SYM
ejpam-5716	543	33	{	{	PUNCT
ejpam-5716	543	34	w	w	NOUN
ejpam-5716	543	35	}	}	PUNCT
ejpam-5716	543	36	for	for	ADP
ejpam-5716	543	37	some	some	DET
ejpam-5716	543	38	w	w	NOUN
ejpam-5716	543	39	∈	∈	NOUN
ejpam-5716	543	40	i(g	i(g	NOUN
ejpam-5716	543	41	)	)	PUNCT
ejpam-5716	543	42	.	.	PUNCT
ejpam-5716	544	1	this	this	PRON
ejpam-5716	544	2	implies	imply	VERB
ejpam-5716	544	3	that	that	SCONJ
ejpam-5716	544	4	|sn|	|sn|	X
ejpam-5716	544	5	=	=	SYM
ejpam-5716	544	6	(	(	PUNCT
ejpam-5716	544	7	n	n	NOUN
ejpam-5716	544	8	+	+	NUM
ejpam-5716	544	9	1	1	NUM
ejpam-5716	544	10	)	)	PUNCT
ejpam-5716	544	11	−	−	PROPN
ejpam-5716	545	1	k	k	NOUN
ejpam-5716	546	1	−	−	PROPN
ejpam-5716	546	2	1	1	NUM
ejpam-5716	546	3	=	=	SYM
ejpam-5716	546	4	n	n	PROPN
ejpam-5716	546	5	−	−	PROPN
ejpam-5716	546	6	k.	k.	PROPN
ejpam-5716	547	1	therefore	therefore	ADV
ejpam-5716	547	2	,	,	PUNCT
ejpam-5716	547	3	ζhk	ζhk	X
ejpam-5716	547	4	(	(	PUNCT
ejpam-5716	547	5	g+h	g+h	NOUN
ejpam-5716	547	6	)	)	PUNCT
ejpam-5716	547	7	=	=	PRON
ejpam-5716	548	1	(	(	PUNCT
ejpam-5716	548	2	m+	m+	NUM
ejpam-5716	548	3	n)−	n)−	PROPN
ejpam-5716	548	4	|n2	|n2	PROPN
ejpam-5716	548	5	g+kn	g+kn	NOUN
ejpam-5716	549	1	[	[	X
ejpam-5716	549	2	s]|	s]|	X
ejpam-5716	549	3	=	=	SYM
ejpam-5716	549	4	(	(	PUNCT
ejpam-5716	549	5	m+	m+	NUM
ejpam-5716	549	6	n)−	n)−	PROPN
ejpam-5716	549	7	(	(	PUNCT
ejpam-5716	549	8	m+	m+	NUM
ejpam-5716	549	9	n−	n−	NOUN
ejpam-5716	549	10	k	k	NOUN
ejpam-5716	549	11	)	)	PUNCT
ejpam-5716	549	12	=	=	SYM
ejpam-5716	549	13	k.	k.	PROPN
ejpam-5716	549	14	4	4	X
ejpam-5716	549	15	.	.	PUNCT
ejpam-5716	549	16	conclusion	conclusion	NOUN
ejpam-5716	549	17	in	in	ADP
ejpam-5716	549	18	this	this	DET
ejpam-5716	549	19	paper	paper	NOUN
ejpam-5716	549	20	,	,	PUNCT
ejpam-5716	549	21	we	we	PRON
ejpam-5716	549	22	introduced	introduce	VERB
ejpam-5716	549	23	and	and	CCONJ
ejpam-5716	549	24	studied	study	VERB
ejpam-5716	549	25	a	a	DET
ejpam-5716	549	26	new	new	ADJ
ejpam-5716	549	27	graph	graph	NOUN
ejpam-5716	549	28	invariant	invariant	NOUN
ejpam-5716	549	29	called	call	VERB
ejpam-5716	549	30	the	the	DET
ejpam-5716	549	31	k	k	ADJ
ejpam-5716	549	32	-	-	PUNCT
ejpam-5716	549	33	hop	hop	NOUN
ejpam-5716	549	34	domination	domination	NOUN
ejpam-5716	549	35	defect	defect	NOUN
ejpam-5716	549	36	of	of	ADP
ejpam-5716	549	37	a	a	DET
ejpam-5716	549	38	graph	graph	NOUN
ejpam-5716	549	39	.	.	PUNCT
ejpam-5716	550	1	we	we	PRON
ejpam-5716	550	2	obtained	obtain	VERB
ejpam-5716	550	3	the	the	DET
ejpam-5716	550	4	k	k	ADJ
ejpam-5716	550	5	-	-	PUNCT
ejpam-5716	550	6	hop	hop	NOUN
ejpam-5716	550	7	domination	domination	NOUN
ejpam-5716	550	8	defects	defect	NOUN
ejpam-5716	550	9	of	of	ADP
ejpam-5716	550	10	some	some	DET
ejpam-5716	550	11	known	know	VERB
ejpam-5716	550	12	graphs	graph	NOUN
ejpam-5716	550	13	including	include	VERB
ejpam-5716	550	14	the	the	DET
ejpam-5716	550	15	join	join	NOUN
ejpam-5716	550	16	of	of	ADP
ejpam-5716	550	17	some	some	DET
ejpam-5716	550	18	graphs	graph	NOUN
ejpam-5716	550	19	.	.	PUNCT
ejpam-5716	551	1	also	also	ADV
ejpam-5716	551	2	,	,	PUNCT
ejpam-5716	551	3	we	we	PRON
ejpam-5716	551	4	provided	provide	VERB
ejpam-5716	551	5	some	some	DET
ejpam-5716	551	6	bounds	bound	NOUN
ejpam-5716	551	7	on	on	ADP
ejpam-5716	551	8	the	the	DET
ejpam-5716	551	9	k	k	ADJ
ejpam-5716	551	10	-	-	PUNCT
ejpam-5716	551	11	hop	hop	NOUN
ejpam-5716	551	12	domination	domination	NOUN
ejpam-5716	551	13	defect	defect	NOUN
ejpam-5716	551	14	of	of	ADP
ejpam-5716	551	15	a	a	DET
ejpam-5716	551	16	graph	graph	NOUN
ejpam-5716	551	17	g	g	NOUN
ejpam-5716	551	18	in	in	ADP
ejpam-5716	551	19	terms	term	NOUN
ejpam-5716	551	20	of	of	ADP
ejpam-5716	551	21	its	its	PRON
ejpam-5716	551	22	order	order	NOUN
ejpam-5716	551	23	and	and	CCONJ
ejpam-5716	551	24	maximum	maximum	ADJ
ejpam-5716	551	25	hop	hop	NOUN
ejpam-5716	551	26	degree	degree	NOUN
ejpam-5716	551	27	and	and	CCONJ
ejpam-5716	551	28	characterized	characterize	VERB
ejpam-5716	551	29	the	the	DET
ejpam-5716	551	30	graphs	graph	NOUN
ejpam-5716	551	31	that	that	PRON
ejpam-5716	551	32	yield	yield	VERB
ejpam-5716	551	33	a	a	DET
ejpam-5716	551	34	k	k	ADJ
ejpam-5716	551	35	-	-	PUNCT
ejpam-5716	551	36	domination	domination	NOUN
ejpam-5716	551	37	defect	defect	NOUN
ejpam-5716	551	38	equal	equal	ADJ
ejpam-5716	551	39	to	to	ADP
ejpam-5716	551	40	1	1	NUM
ejpam-5716	551	41	.	.	PUNCT
ejpam-5716	552	1	it	it	PRON
ejpam-5716	552	2	is	be	AUX
ejpam-5716	552	3	recommended	recommend	VERB
ejpam-5716	552	4	that	that	SCONJ
ejpam-5716	552	5	the	the	DET
ejpam-5716	552	6	newly	newly	ADV
ejpam-5716	552	7	defined	define	VERB
ejpam-5716	552	8	parameter	parameter	NOUN
ejpam-5716	552	9	be	be	AUX
ejpam-5716	552	10	studied	study	VERB
ejpam-5716	552	11	further	far	ADV
ejpam-5716	552	12	for	for	ADP
ejpam-5716	552	13	other	other	ADJ
ejpam-5716	552	14	classes	class	NOUN
ejpam-5716	552	15	of	of	ADP
ejpam-5716	552	16	graphs	graph	NOUN
ejpam-5716	552	17	.	.	PUNCT
ejpam-5716	553	1	acknowledgements	acknowledgement	NOUN
ejpam-5716	553	2	the	the	DET
ejpam-5716	553	3	authors	author	NOUN
ejpam-5716	553	4	would	would	AUX
ejpam-5716	553	5	like	like	VERB
ejpam-5716	553	6	to	to	PART
ejpam-5716	553	7	thank	thank	VERB
ejpam-5716	553	8	the	the	DET
ejpam-5716	553	9	department	department	NOUN
ejpam-5716	553	10	of	of	ADP
ejpam-5716	553	11	science	science	NOUN
ejpam-5716	553	12	and	and	CCONJ
ejpam-5716	553	13	technology	technology	NOUN
ejpam-5716	553	14	accelerated	accelerate	VERB
ejpam-5716	553	15	science	science	NOUN
ejpam-5716	553	16	and	and	CCONJ
ejpam-5716	553	17	technology	technology	NOUN
ejpam-5716	553	18	human	human	ADJ
ejpam-5716	553	19	resource	resource	NOUN
ejpam-5716	553	20	development	development	NOUN
ejpam-5716	553	21	program	program	NOUN
ejpam-5716	553	22	(	(	PUNCT
ejpam-5716	553	23	dost	dost	NOUN
ejpam-5716	553	24	-	-	PUNCT
ejpam-5716	553	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5716	553	26	,	,	PUNCT
ejpam-5716	553	27	and	and	CCONJ
ejpam-5716	553	28	msu	msu	PROPN
ejpam-5716	553	29	-	-	PUNCT
ejpam-5716	553	30	iligan	iligan	PROPN
ejpam-5716	553	31	institute	institute	PROPN
ejpam-5716	553	32	of	of	ADP
ejpam-5716	553	33	technology	technology	PROPN
ejpam-5716	553	34	,	,	PUNCT
ejpam-5716	553	35	philippines	philippine	NOUN
ejpam-5716	553	36	for	for	ADP
ejpam-5716	553	37	funding	fund	VERB
ejpam-5716	553	38	this	this	DET
ejpam-5716	553	39	research	research	NOUN
ejpam-5716	553	40	.	.	PUNCT
ejpam-5716	554	1	references	reference	NOUN
ejpam-5716	554	2	[	[	X
ejpam-5716	554	3	1	1	NUM
ejpam-5716	554	4	]	]	X
ejpam-5716	554	5	n.j	n.j	PROPN
ejpam-5716	554	6	.	.	PROPN
ejpam-5716	554	7	adolfo	adolfo	PROPN
ejpam-5716	554	8	,	,	PUNCT
ejpam-5716	554	9	i.	i.	PROPN
ejpam-5716	554	10	aniversario	aniversario	PROPN
ejpam-5716	554	11	,	,	PUNCT
ejpam-5716	554	12	and	and	CCONJ
ejpam-5716	554	13	f.	f.	PROPN
ejpam-5716	554	14	jamil	jamil	PROPN
ejpam-5716	554	15	.	.	PUNCT
ejpam-5716	555	1	closed	close	VERB
ejpam-5716	555	2	geodetic	geodetic	ADJ
ejpam-5716	555	3	hop	hop	NOUN
ejpam-5716	555	4	domination	domination	NOUN
ejpam-5716	555	5	in	in	ADP
ejpam-5716	555	6	graphs	graph	NOUN
ejpam-5716	555	7	.	.	PUNCT
ejpam-5716	556	1	european	european	ADJ
ejpam-5716	556	2	journal	journal	PROPN
ejpam-5716	556	3	of	of	ADP
ejpam-5716	556	4	pure	pure	ADJ
ejpam-5716	556	5	and	and	CCONJ
ejpam-5716	556	6	applied	applied	ADJ
ejpam-5716	556	7	mathematics	mathematic	NOUN
ejpam-5716	556	8	,	,	PUNCT
ejpam-5716	556	9	17(3):1618–1636	17(3):1618–1636	NUM
ejpam-5716	556	10	,	,	PUNCT
ejpam-5716	556	11	2024	2024	NUM
ejpam-5716	556	12	.	.	PUNCT
ejpam-5716	557	1	[	[	X
ejpam-5716	557	2	2	2	NUM
ejpam-5716	557	3	]	]	SYM
ejpam-5716	557	4	d.b	d.b	PROPN
ejpam-5716	557	5	.	.	PROPN
ejpam-5716	557	6	catian	catian	PROPN
ejpam-5716	557	7	,	,	PUNCT
ejpam-5716	557	8	i.	i.	PROPN
ejpam-5716	557	9	aniversario	aniversario	PROPN
ejpam-5716	557	10	,	,	PUNCT
ejpam-5716	557	11	and	and	CCONJ
ejpam-5716	557	12	f.	f.	PROPN
ejpam-5716	557	13	jamil	jamil	PROPN
ejpam-5716	557	14	.	.	PUNCT
ejpam-5716	558	1	on	on	ADP
ejpam-5716	558	2	minimal	minimal	ADJ
ejpam-5716	558	3	geodetic	geodetic	ADJ
ejpam-5716	558	4	hop	hop	NOUN
ejpam-5716	558	5	domination	domination	NOUN
ejpam-5716	558	6	in	in	ADP
ejpam-5716	558	7	graphs	graph	NOUN
ejpam-5716	558	8	.	.	PUNCT
ejpam-5716	559	1	european	european	ADJ
ejpam-5716	559	2	journal	journal	PROPN
ejpam-5716	559	3	of	of	ADP
ejpam-5716	559	4	pure	pure	ADJ
ejpam-5716	559	5	and	and	CCONJ
ejpam-5716	559	6	applied	applied	ADJ
ejpam-5716	559	7	mathematics	mathematic	NOUN
ejpam-5716	559	8	,	,	PUNCT
ejpam-5716	559	9	17(3):1737–1750	17(3):1737–1750	NUM
ejpam-5716	559	10	,	,	PUNCT
ejpam-5716	559	11	2024	2024	NUM
ejpam-5716	559	12	.	.	PUNCT
ejpam-5716	560	1	[	[	X
ejpam-5716	560	2	3	3	NUM
ejpam-5716	560	3	]	]	PUNCT
ejpam-5716	560	4	a.	a.	NOUN
ejpam-5716	560	5	das	das	PROPN
ejpam-5716	560	6	and	and	CCONJ
ejpam-5716	560	7	w.	w.	PROPN
ejpam-5716	560	8	j.	j.	PROPN
ejpam-5716	560	9	desormeaux	desormeaux	PROPN
ejpam-5716	560	10	.	.	PUNCT
ejpam-5716	561	1	domination	domination	NOUN
ejpam-5716	561	2	defect	defect	NOUN
ejpam-5716	561	3	in	in	ADP
ejpam-5716	561	4	graphs	graph	NOUN
ejpam-5716	561	5	:	:	PUNCT
ejpam-5716	561	6	guarding	guard	VERB
ejpam-5716	561	7	with	with	ADP
ejpam-5716	561	8	fewer	few	ADJ
ejpam-5716	561	9	guards	guard	NOUN
ejpam-5716	561	10	.	.	PUNCT
ejpam-5716	562	1	indian	indian	PROPN
ejpam-5716	562	2	j.	j.	PROPN
ejpam-5716	562	3	pure	pure	PROPN
ejpam-5716	562	4	appl	appl	PROPN
ejpam-5716	562	5	.	.	PUNCT
ejpam-5716	562	6	math	math	PROPN
ejpam-5716	562	7	.	.	PUNCT
ejpam-5716	562	8	,	,	PUNCT
ejpam-5716	563	1	49(2):349–364	49(2):349–364	NOUN
ejpam-5716	563	2	,	,	PUNCT
ejpam-5716	563	3	2018	2018	NUM
ejpam-5716	563	4	.	.	PUNCT
ejpam-5716	564	1	[	[	X
ejpam-5716	564	2	4	4	X
ejpam-5716	564	3	]	]	PUNCT
ejpam-5716	564	4	j.	j.	PROPN
ejpam-5716	564	5	hassan	hassan	PROPN
ejpam-5716	564	6	and	and	CCONJ
ejpam-5716	564	7	s.	s.	PROPN
ejpam-5716	564	8	canoy	canoy	PROPN
ejpam-5716	564	9	jr	jr	PROPN
ejpam-5716	564	10	.	.	PROPN
ejpam-5716	564	11	hop	hop	PROPN
ejpam-5716	564	12	independent	independent	ADJ
ejpam-5716	564	13	hop	hop	NOUN
ejpam-5716	564	14	domination	domination	NOUN
ejpam-5716	564	15	in	in	ADP
ejpam-5716	564	16	graphs	graph	NOUN
ejpam-5716	564	17	.	.	PUNCT
ejpam-5716	565	1	eur	eur	PROPN
ejpam-5716	565	2	.	.	PUNCT
ejpam-5716	566	1	j.	j.	PROPN
ejpam-5716	566	2	pure	pure	PROPN
ejpam-5716	566	3	appl	appl	PROPN
ejpam-5716	566	4	.	.	PUNCT
ejpam-5716	566	5	math	math	PROPN
ejpam-5716	566	6	.	.	PUNCT
ejpam-5716	566	7	,	,	PUNCT
ejpam-5716	566	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5716	566	9	,	,	PUNCT
ejpam-5716	566	10	2022	2022	NUM
ejpam-5716	566	11	.	.	PUNCT
ejpam-5716	567	1	[	[	X
ejpam-5716	567	2	5	5	X
ejpam-5716	567	3	]	]	PUNCT
ejpam-5716	567	4	j.	j.	PROPN
ejpam-5716	567	5	hassan	hassan	PROPN
ejpam-5716	567	6	,	,	PUNCT
ejpam-5716	567	7	s.	s.	PROPN
ejpam-5716	567	8	canoy	canoy	PROPN
ejpam-5716	567	9	jr	jr	PROPN
ejpam-5716	567	10	,	,	PUNCT
ejpam-5716	567	11	and	and	CCONJ
ejpam-5716	567	12	c.j	c.j	PROPN
ejpam-5716	567	13	.	.	PROPN
ejpam-5716	567	14	saromines	saromine	NOUN
ejpam-5716	567	15	.	.	PUNCT
ejpam-5716	568	1	convex	convex	VERB
ejpam-5716	568	2	hop	hop	NOUN
ejpam-5716	568	3	domination	domination	NOUN
ejpam-5716	568	4	in	in	ADP
ejpam-5716	568	5	graphs	graph	NOUN
ejpam-5716	568	6	.	.	PUNCT
ejpam-5716	569	1	european	european	ADJ
ejpam-5716	569	2	journal	journal	PROPN
ejpam-5716	569	3	of	of	ADP
ejpam-5716	569	4	pure	pure	ADJ
ejpam-5716	569	5	and	and	CCONJ
ejpam-5716	569	6	applied	applied	ADJ
ejpam-5716	569	7	mathematics	mathematic	NOUN
ejpam-5716	569	8	,	,	PUNCT
ejpam-5716	569	9	16(1):319–335	16(1):319–335	NUM
ejpam-5716	569	10	,	,	PUNCT
ejpam-5716	569	11	2023	2023	NUM
ejpam-5716	569	12	.	.	PUNCT
ejpam-5716	570	1	[	[	X
ejpam-5716	570	2	6	6	NUM
ejpam-5716	570	3	]	]	PUNCT
ejpam-5716	570	4	m.	m.	NOUN
ejpam-5716	570	5	henning	henning	PROPN
ejpam-5716	570	6	and	and	CCONJ
ejpam-5716	570	7	n.	n.	PROPN
ejpam-5716	570	8	rad	rad	PROPN
ejpam-5716	570	9	.	.	PROPN
ejpam-5716	571	1	on	on	ADP
ejpam-5716	571	2	2	2	NUM
ejpam-5716	571	3	-	-	PUNCT
ejpam-5716	571	4	step	step	NOUN
ejpam-5716	571	5	and	and	CCONJ
ejpam-5716	571	6	hop	hop	NOUN
ejpam-5716	571	7	dominating	dominating	NOUN
ejpam-5716	571	8	sets	set	NOUN
ejpam-5716	571	9	in	in	ADP
ejpam-5716	571	10	graphs	graph	NOUN
ejpam-5716	571	11	.	.	PUNCT
ejpam-5716	572	1	graphs	graph	NOUN
ejpam-5716	572	2	and	and	CCONJ
ejpam-5716	572	3	combinatorics	combinatoric	NOUN
ejpam-5716	572	4	.	.	PUNCT
ejpam-5716	572	5	,	,	PUNCT
ejpam-5716	572	6	33(4):913–927	33(4):913–927	PROPN
ejpam-5716	572	7	,	,	PUNCT
ejpam-5716	572	8	2017	2017	NUM
ejpam-5716	572	9	.	.	PUNCT
ejpam-5716	573	1	[	[	X
ejpam-5716	573	2	7	7	X
ejpam-5716	573	3	]	]	X
ejpam-5716	573	4	s.	s.	PROPN
ejpam-5716	573	5	canoy	canoy	PROPN
ejpam-5716	573	6	jr	jr	PROPN
ejpam-5716	573	7	and	and	CCONJ
ejpam-5716	573	8	j.	j.	PROPN
ejpam-5716	573	9	hassan	hassan	PROPN
ejpam-5716	573	10	.	.	PUNCT
ejpam-5716	574	1	weakly	weakly	ADJ
ejpam-5716	574	2	convex	convex	VERB
ejpam-5716	574	3	hop	hop	NOUN
ejpam-5716	574	4	dominating	dominating	NOUN
ejpam-5716	574	5	sets	set	NOUN
ejpam-5716	574	6	in	in	ADP
ejpam-5716	574	7	graphs	graph	NOUN
ejpam-5716	574	8	.	.	PUNCT
ejpam-5716	575	1	european	european	ADJ
ejpam-5716	575	2	journal	journal	PROPN
ejpam-5716	575	3	of	of	ADP
ejpam-5716	575	4	pure	pure	ADJ
ejpam-5716	575	5	and	and	CCONJ
ejpam-5716	575	6	applied	applied	ADJ
ejpam-5716	575	7	mathematics	mathematic	NOUN
ejpam-5716	575	8	,	,	PUNCT
ejpam-5716	575	9	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-5716	575	10	,	,	PUNCT
ejpam-5716	575	11	2023	2023	NUM
ejpam-5716	575	12	.	.	PUNCT
ejpam-5716	576	1	j.	j.	PROPN
ejpam-5716	576	2	anoche	anoche	PROPN
ejpam-5716	576	3	,	,	PUNCT
ejpam-5716	576	4	s.r	s.r	PROPN
ejpam-5716	576	5	.	.	PROPN
ejpam-5716	576	6	canoy	canoy	PROPN
ejpam-5716	576	7	jr	jr	PROPN
ejpam-5716	576	8	.	.	PUNCT
ejpam-5716	576	9	/	/	SYM
ejpam-5716	576	10	eur	eur	PROPN
ejpam-5716	576	11	.	.	PUNCT
ejpam-5716	577	1	j.	j.	PROPN
ejpam-5716	577	2	pure	pure	PROPN
ejpam-5716	577	3	appl	appl	PROPN
ejpam-5716	577	4	.	.	PROPN
ejpam-5716	577	5	math	math	PROPN
ejpam-5716	577	6	,	,	PUNCT
ejpam-5716	577	7	18	18	NUM
ejpam-5716	577	8	(	(	PUNCT
ejpam-5716	577	9	1	1	NUM
ejpam-5716	577	10	)	)	PUNCT
ejpam-5716	577	11	(	(	PUNCT
ejpam-5716	577	12	2025	2025	NUM
ejpam-5716	577	13	)	)	PUNCT
ejpam-5716	577	14	,	,	PUNCT
ejpam-5716	577	15	5716	5716	NUM
ejpam-5716	577	16	13	13	NUM
ejpam-5716	577	17	of	of	ADP
ejpam-5716	577	18	13	13	NUM
ejpam-5716	578	1	[	[	SYM
ejpam-5716	578	2	8	8	NUM
ejpam-5716	578	3	]	]	PUNCT
ejpam-5716	578	4	s.	s.	PROPN
ejpam-5716	578	5	canoy	canoy	PROPN
ejpam-5716	578	6	jr	jr	PROPN
ejpam-5716	578	7	,	,	PUNCT
ejpam-5716	578	8	r.	r.	PROPN
ejpam-5716	578	9	mollejon	mollejon	NOUN
ejpam-5716	578	10	,	,	PUNCT
ejpam-5716	578	11	and	and	CCONJ
ejpam-5716	578	12	j.g	j.g	PROPN
ejpam-5716	578	13	.	.	PROPN
ejpam-5716	578	14	canoy	canoy	PROPN
ejpam-5716	578	15	.	.	PUNCT
ejpam-5716	579	1	hop	hop	PROPN
ejpam-5716	579	2	dominating	dominating	NOUN
ejpam-5716	579	3	sets	set	NOUN
ejpam-5716	579	4	in	in	ADP
ejpam-5716	579	5	graphs	graph	NOUN
ejpam-5716	579	6	under	under	ADP
ejpam-5716	579	7	binary	binary	ADJ
ejpam-5716	579	8	operations	operation	NOUN
ejpam-5716	579	9	.	.	PUNCT
ejpam-5716	580	1	eur	eur	PROPN
ejpam-5716	580	2	.	.	PUNCT
ejpam-5716	581	1	j.	j.	PROPN
ejpam-5716	581	2	pure	pure	PROPN
ejpam-5716	581	3	appl	appl	PROPN
ejpam-5716	581	4	.	.	PUNCT
ejpam-5716	581	5	math	math	PROPN
ejpam-5716	581	6	.	.	PUNCT
ejpam-5716	581	7	,	,	PUNCT
ejpam-5716	582	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-5716	582	2	,	,	PUNCT
ejpam-5716	582	3	2019	2019	NUM
ejpam-5716	582	4	.	.	PUNCT
ejpam-5716	583	1	[	[	X
ejpam-5716	583	2	9	9	NUM
ejpam-5716	583	3	]	]	PUNCT
ejpam-5716	583	4	s.	s.	PROPN
ejpam-5716	583	5	canoy	canoy	PROPN
ejpam-5716	583	6	jr	jr	PROPN
ejpam-5716	583	7	and	and	CCONJ
ejpam-5716	583	8	g.	g.	PROPN
ejpam-5716	583	9	salasalan	salasalan	NOUN
ejpam-5716	583	10	.	.	PUNCT
ejpam-5716	584	1	locating	locate	VERB
ejpam-5716	584	2	-	-	PUNCT
ejpam-5716	584	3	hop	hop	NOUN
ejpam-5716	584	4	domination	domination	NOUN
ejpam-5716	584	5	in	in	ADP
ejpam-5716	584	6	graphs	graph	NOUN
ejpam-5716	584	7	.	.	PUNCT
ejpam-5716	585	1	kyungpook	kyungpook	PROPN
ejpam-5716	585	2	mathematical	mathematical	PROPN
ejpam-5716	585	3	journal	journal	PROPN
ejpam-5716	585	4	,	,	PUNCT
ejpam-5716	585	5	62:193–204	62:193–204	PROPN
ejpam-5716	585	6	,	,	PUNCT
ejpam-5716	585	7	2022	2022	NUM
ejpam-5716	585	8	.	.	PUNCT
ejpam-5716	586	1	[	[	X
ejpam-5716	586	2	10	10	NUM
ejpam-5716	586	3	]	]	PUNCT
ejpam-5716	586	4	a.	a.	NOUN
ejpam-5716	586	5	miranda	miranda	PROPN
ejpam-5716	586	6	and	and	CCONJ
ejpam-5716	586	7	r.	r.	PROPN
ejpam-5716	586	8	eballe	eballe	PROPN
ejpam-5716	586	9	.	.	PUNCT
ejpam-5716	587	1	domination	domination	NOUN
ejpam-5716	587	2	defect	defect	NOUN
ejpam-5716	587	3	for	for	ADP
ejpam-5716	587	4	the	the	DET
ejpam-5716	587	5	join	join	NOUN
ejpam-5716	587	6	and	and	CCONJ
ejpam-5716	587	7	corona	corona	NOUN
ejpam-5716	587	8	of	of	ADP
ejpam-5716	587	9	graphs	graph	NOUN
ejpam-5716	587	10	.	.	PUNCT
ejpam-5716	588	1	applied	apply	VERB
ejpam-5716	588	2	mathematical	mathematical	ADJ
ejpam-5716	588	3	sciences	science	NOUN
ejpam-5716	588	4	,	,	PUNCT
ejpam-5716	588	5	15(12):615	15(12):615	NUM
ejpam-5716	588	6	–	–	PUNCT
ejpam-5716	588	7	623	623	NUM
ejpam-5716	588	8	,	,	PUNCT
ejpam-5716	588	9	2021	2021	NUM
ejpam-5716	588	10	.	.	PUNCT
ejpam-5716	589	1	[	[	X
ejpam-5716	589	2	11	11	NUM
ejpam-5716	589	3	]	]	PUNCT
ejpam-5716	589	4	a.	a.	NOUN
ejpam-5716	589	5	miranda	miranda	PROPN
ejpam-5716	589	6	and	and	CCONJ
ejpam-5716	589	7	r.	r.	PROPN
ejpam-5716	589	8	eballe	eballe	PROPN
ejpam-5716	589	9	.	.	PUNCT
ejpam-5716	590	1	domination	domination	NOUN
ejpam-5716	590	2	defect	defect	NOUN
ejpam-5716	590	3	in	in	ADP
ejpam-5716	590	4	the	the	DET
ejpam-5716	590	5	edge	edge	NOUN
ejpam-5716	590	6	corona	corona	NOUN
ejpam-5716	590	7	of	of	ADP
ejpam-5716	590	8	graphs	graph	NOUN
ejpam-5716	590	9	.	.	PUNCT
ejpam-5716	591	1	asian	asian	ADJ
ejpam-5716	591	2	research	research	PROPN
ejpam-5716	591	3	journal	journal	NOUN
ejpam-5716	591	4	of	of	ADP
ejpam-5716	591	5	mathematics	mathematic	NOUN
ejpam-5716	591	6	,	,	PUNCT
ejpam-5716	591	7	18(12):95–101	18(12):95–101	PROPN
ejpam-5716	591	8	,	,	PUNCT
ejpam-5716	591	9	2022	2022	NUM
ejpam-5716	591	10	.	.	PUNCT
ejpam-5716	592	1	[	[	X
ejpam-5716	592	2	12	12	NUM
ejpam-5716	592	3	]	]	PUNCT
ejpam-5716	592	4	a.	a.	NOUN
ejpam-5716	592	5	miranda	miranda	PROPN
ejpam-5716	592	6	and	and	CCONJ
ejpam-5716	592	7	r.	r.	PROPN
ejpam-5716	592	8	eballe	eballe	PROPN
ejpam-5716	592	9	.	.	PUNCT
ejpam-5716	593	1	domination	domination	NOUN
ejpam-5716	593	2	defect	defect	NOUN
ejpam-5716	593	3	in	in	ADP
ejpam-5716	593	4	the	the	DET
ejpam-5716	593	5	composition	composition	NOUN
ejpam-5716	593	6	of	of	ADP
ejpam-5716	593	7	graphs	graph	NOUN
ejpam-5716	593	8	.	.	PUNCT
ejpam-5716	594	1	advances	advance	NOUN
ejpam-5716	594	2	and	and	CCONJ
ejpam-5716	594	3	applications	application	NOUN
ejpam-5716	594	4	in	in	ADP
ejpam-5716	594	5	discrete	discrete	ADJ
ejpam-5716	594	6	mathematics	mathematic	NOUN
ejpam-5716	594	7	,	,	PUNCT
ejpam-5716	594	8	39(2):209–219	39(2):209–219	PROPN
ejpam-5716	594	9	,	,	PUNCT
ejpam-5716	594	10	2023	2023	NUM
ejpam-5716	594	11	.	.	PUNCT
ejpam-5716	595	1	[	[	X
ejpam-5716	595	2	13	13	NUM
ejpam-5716	595	3	]	]	X
ejpam-5716	595	4	c.	c.	PROPN
ejpam-5716	595	5	natarajan	natarajan	PROPN
ejpam-5716	595	6	and	and	CCONJ
ejpam-5716	595	7	s.	s.	PROPN
ejpam-5716	595	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5716	595	9	.	.	PUNCT
ejpam-5716	596	1	hop	hop	PROPN
ejpam-5716	596	2	domination	domination	NOUN
ejpam-5716	596	3	in	in	ADP
ejpam-5716	596	4	graphs	graphs	PROPN
ejpam-5716	596	5	ii	ii	PROPN
ejpam-5716	596	6	.	.	PUNCT
ejpam-5716	596	7	versita	versita	PROPN
ejpam-5716	596	8	,	,	PUNCT
ejpam-5716	596	9	23(2):187	23(2):187	NUM
ejpam-5716	596	10	–	–	PUNCT
ejpam-5716	596	11	199	199	NUM
ejpam-5716	596	12	,	,	PUNCT
ejpam-5716	596	13	2015	2015	NUM
ejpam-5716	596	14	.	.	PUNCT
ejpam-5716	597	1	[	[	X
ejpam-5716	597	2	14	14	NUM
ejpam-5716	597	3	]	]	X
ejpam-5716	597	4	g.	g.	NOUN
ejpam-5716	597	5	salasalan	salasalan	NOUN
ejpam-5716	597	6	and	and	CCONJ
ejpam-5716	597	7	jr	jr	PROPN
ejpam-5716	597	8	.	.	PROPN
ejpam-5716	597	9	s.	s.	PROPN
ejpam-5716	597	10	canoy	canoy	PROPN
ejpam-5716	597	11	.	.	PUNCT
ejpam-5716	598	1	global	global	ADJ
ejpam-5716	598	2	hop	hop	PROPN
ejpam-5716	598	3	domination	domination	PROPN
ejpam-5716	598	4	numbers	number	NOUN
ejpam-5716	598	5	of	of	ADP
ejpam-5716	598	6	graphs	graph	NOUN
ejpam-5716	598	7	.	.	PUNCT
ejpam-5716	599	1	eur	eur	PROPN
ejpam-5716	599	2	.	.	PUNCT
ejpam-5716	600	1	j.	j.	PROPN
ejpam-5716	600	2	pure	pure	PROPN
ejpam-5716	600	3	appl	appl	PROPN
ejpam-5716	600	4	.	.	PUNCT
ejpam-5716	600	5	math	math	PROPN
ejpam-5716	600	6	.	.	PUNCT
ejpam-5716	600	7	,	,	PUNCT
ejpam-5716	600	8	14(1):112–125	14(1):112–125	NUM
ejpam-5716	600	9	,	,	PUNCT
ejpam-5716	600	10	2021	2021	NUM
ejpam-5716	600	11	.	.	PUNCT
ejpam-5716	601	1	[	[	X
ejpam-5716	601	2	15	15	NUM
ejpam-5716	601	3	]	]	X
ejpam-5716	601	4	c.j	c.j	PROPN
ejpam-5716	601	5	.	.	PROPN
ejpam-5716	601	6	saromines	saromine	NOUN
ejpam-5716	601	7	and	and	CCONJ
ejpam-5716	601	8	s.	s.	PROPN
ejpam-5716	601	9	canoy	canoy	PROPN
ejpam-5716	601	10	jr	jr	PROPN
ejpam-5716	601	11	.	.	PROPN
ejpam-5716	601	12	geodetic	geodetic	ADJ
ejpam-5716	601	13	hop	hop	NOUN
ejpam-5716	601	14	dominating	dominating	NOUN
ejpam-5716	601	15	sets	set	NOUN
ejpam-5716	601	16	in	in	ADP
ejpam-5716	601	17	a	a	DET
ejpam-5716	601	18	graph	graph	NOUN
ejpam-5716	601	19	.	.	PUNCT
ejpam-5716	602	1	european	european	ADJ
ejpam-5716	602	2	journal	journal	PROPN
ejpam-5716	602	3	of	of	ADP
ejpam-5716	602	4	pure	pure	ADJ
ejpam-5716	602	5	and	and	CCONJ
ejpam-5716	602	6	applied	applied	ADJ
ejpam-5716	602	7	mathematics	mathematic	NOUN
ejpam-5716	602	8	,	,	PUNCT
ejpam-5716	602	9	16(1):5–17	16(1):5–17	NUM
ejpam-5716	602	10	,	,	PUNCT
ejpam-5716	602	11	2023	2023	NUM
ejpam-5716	602	12	.	.	PUNCT
ejpam-5716	603	1	[	[	X
ejpam-5716	603	2	16	16	NUM
ejpam-5716	603	3	]	]	X
ejpam-5716	603	4	c.	c.	PROPN
ejpam-5716	603	5	natarajan	natarajan	PROPN
ejpam-5716	603	6	s.k	s.k	PROPN
ejpam-5716	603	7	.	.	PROPN
ejpam-5716	603	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5716	603	9	and	and	CCONJ
ejpam-5716	603	10	y.b	y.b	PROPN
ejpam-5716	603	11	.	.	PROPN
ejpam-5716	603	12	venkatakrishnan	venkatakrishnan	PROPN
ejpam-5716	603	13	.	.	PUNCT
ejpam-5716	604	1	hop	hop	PROPN
ejpam-5716	604	2	domination	domination	NOUN
ejpam-5716	604	3	in	in	ADP
ejpam-5716	604	4	graphs	graph	NOUN
ejpam-5716	604	5	.	.	PUNCT
ejpam-5716	605	1	ams	ams	PROPN
ejpam-5716	605	2	msc	msc	PROPN
ejpam-5716	605	3	,	,	PUNCT
ejpam-5716	605	4	2010	2010	NUM
ejpam-5716	605	5	.	.	PUNCT