id	sid	tid	token	lemma	pos
ejpam-6536	1	1	european	european	PROPN
ejpam-6536	1	2	journal	journal	PROPN
ejpam-6536	1	3	of	of	ADP
ejpam-6536	1	4	pure	pure	ADJ
ejpam-6536	1	5	and	and	CCONJ
ejpam-6536	1	6	applied	applied	ADJ
ejpam-6536	1	7	mathematics	mathematic	NOUN
ejpam-6536	1	8	2025	2025	NUM
ejpam-6536	1	9	,	,	PUNCT
ejpam-6536	1	10	vol	vol	NOUN
ejpam-6536	1	11	.	.	PROPN
ejpam-6536	1	12	18	18	NUM
ejpam-6536	1	13	,	,	PUNCT
ejpam-6536	1	14	issue	issue	NOUN
ejpam-6536	1	15	3	3	NUM
ejpam-6536	1	16	,	,	PUNCT
ejpam-6536	1	17	article	article	NOUN
ejpam-6536	1	18	number	number	NOUN
ejpam-6536	1	19	6536	6536	NUM
ejpam-6536	1	20	issn	issn	PROPN
ejpam-6536	1	21	1307	1307	NUM
ejpam-6536	1	22	-	-	SYM
ejpam-6536	1	23	5543	5543	NUM
ejpam-6536	1	24	–	–	PUNCT
ejpam-6536	1	25	ejpam.com	ejpam.com	X
ejpam-6536	1	26	published	publish	VERB
ejpam-6536	1	27	by	by	ADP
ejpam-6536	1	28	new	new	PROPN
ejpam-6536	1	29	york	york	PROPN
ejpam-6536	1	30	business	business	PROPN
ejpam-6536	1	31	global	global	ADJ
ejpam-6536	1	32	on	on	ADP
ejpam-6536	1	33	pairs	pair	NOUN
ejpam-6536	1	34	of	of	ADP
ejpam-6536	1	35	disjoint	disjoint	NOUN
ejpam-6536	1	36	hop	hop	NOUN
ejpam-6536	1	37	dominating	dominating	NOUN
ejpam-6536	1	38	sets	set	NOUN
ejpam-6536	1	39	in	in	ADP
ejpam-6536	1	40	graphs	graph	NOUN
ejpam-6536	1	41	viralou	viralou	ADP
ejpam-6536	1	42	abrille	abrille	PROPN
ejpam-6536	1	43	b.	b.	PROPN
ejpam-6536	1	44	besana1,2,∗	besana1,2,∗	PROPN
ejpam-6536	1	45	,	,	PUNCT
ejpam-6536	2	1	ferdinand	ferdinand	PROPN
ejpam-6536	2	2	p.	p.	PROPN
ejpam-6536	2	3	jamil1,2	jamil1,2	PROPN
ejpam-6536	2	4	,	,	PUNCT
ejpam-6536	2	5	sergio	sergio	PROPN
ejpam-6536	2	6	r.	r.	PROPN
ejpam-6536	2	7	canoy	canoy	PROPN
ejpam-6536	2	8	,	,	PUNCT
ejpam-6536	2	9	jr.1,2	jr.1,2	ADJ
ejpam-6536	2	10	1	1	NUM
ejpam-6536	2	11	department	department	NOUN
ejpam-6536	2	12	of	of	ADP
ejpam-6536	2	13	mathematics	mathematic	NOUN
ejpam-6536	2	14	and	and	CCONJ
ejpam-6536	2	15	statistics	statistic	NOUN
ejpam-6536	2	16	,	,	PUNCT
ejpam-6536	2	17	college	college	NOUN
ejpam-6536	2	18	of	of	ADP
ejpam-6536	2	19	science	science	NOUN
ejpam-6536	2	20	and	and	CCONJ
ejpam-6536	2	21	mathematics	mathematic	NOUN
ejpam-6536	2	22	,	,	PUNCT
ejpam-6536	2	23	mindanao	mindanao	PROPN
ejpam-6536	2	24	state	state	PROPN
ejpam-6536	2	25	university	university	PROPN
ejpam-6536	2	26	iligan	iligan	PROPN
ejpam-6536	2	27	institute	institute	PROPN
ejpam-6536	2	28	of	of	ADP
ejpam-6536	2	29	technology	technology	PROPN
ejpam-6536	2	30	,	,	PUNCT
ejpam-6536	2	31	9200	9200	NUM
ejpam-6536	2	32	iligan	iligan	ADJ
ejpam-6536	2	33	city	city	NOUN
ejpam-6536	2	34	,	,	PUNCT
ejpam-6536	2	35	philippines	philippine	NOUN
ejpam-6536	2	36	2	2	NUM
ejpam-6536	2	37	center	center	NOUN
ejpam-6536	2	38	for	for	ADP
ejpam-6536	2	39	mathematical	mathematical	ADJ
ejpam-6536	2	40	and	and	CCONJ
ejpam-6536	2	41	theoretical	theoretical	ADJ
ejpam-6536	2	42	physical	physical	ADJ
ejpam-6536	2	43	sciences	science	NOUN
ejpam-6536	2	44	,	,	PUNCT
ejpam-6536	2	45	premier	premier	PROPN
ejpam-6536	2	46	research	research	PROPN
ejpam-6536	2	47	institute	institute	PROPN
ejpam-6536	2	48	of	of	ADP
ejpam-6536	2	49	science	science	NOUN
ejpam-6536	2	50	and	and	CCONJ
ejpam-6536	2	51	mathematics	mathematic	NOUN
ejpam-6536	2	52	,	,	PUNCT
ejpam-6536	2	53	mindanao	mindanao	PROPN
ejpam-6536	2	54	state	state	PROPN
ejpam-6536	2	55	university	university	PROPN
ejpam-6536	2	56	iligan	iligan	PROPN
ejpam-6536	2	57	institute	institute	PROPN
ejpam-6536	2	58	of	of	ADP
ejpam-6536	2	59	technology	technology	PROPN
ejpam-6536	2	60	,	,	PUNCT
ejpam-6536	2	61	9200	9200	NUM
ejpam-6536	2	62	iligan	iligan	ADJ
ejpam-6536	2	63	city	city	NOUN
ejpam-6536	2	64	,	,	PUNCT
ejpam-6536	2	65	philippines	philippine	NOUN
ejpam-6536	2	66	abstract	abstract	ADJ
ejpam-6536	2	67	.	.	PUNCT
ejpam-6536	3	1	a	a	DET
ejpam-6536	3	2	set	set	NOUN
ejpam-6536	3	3	s	s	NOUN
ejpam-6536	3	4	of	of	ADP
ejpam-6536	3	5	vertices	vertex	NOUN
ejpam-6536	3	6	of	of	ADP
ejpam-6536	3	7	a	a	DET
ejpam-6536	3	8	graph	graph	NOUN
ejpam-6536	3	9	g	g	NOUN
ejpam-6536	3	10	is	be	AUX
ejpam-6536	3	11	a	a	DET
ejpam-6536	3	12	hop	hop	NOUN
ejpam-6536	3	13	dominating	dominating	NOUN
ejpam-6536	3	14	set	set	NOUN
ejpam-6536	3	15	of	of	ADP
ejpam-6536	3	16	g	g	PROPN
ejpam-6536	3	17	if	if	SCONJ
ejpam-6536	3	18	for	for	ADP
ejpam-6536	3	19	every	every	PRON
ejpam-6536	3	20	v	v	NUM
ejpam-6536	3	21	∈	∈	NOUN
ejpam-6536	3	22	v	v	NOUN
ejpam-6536	3	23	(	(	PUNCT
ejpam-6536	3	24	g	g	NOUN
ejpam-6536	3	25	)	)	PUNCT
ejpam-6536	3	26	\	\	PROPN
ejpam-6536	4	1	s	s	X
ejpam-6536	4	2	,	,	PUNCT
ejpam-6536	4	3	v	v	NOUN
ejpam-6536	4	4	is	be	AUX
ejpam-6536	4	5	at	at	ADP
ejpam-6536	4	6	distance	distance	NOUN
ejpam-6536	4	7	2	2	NUM
ejpam-6536	4	8	from	from	ADP
ejpam-6536	4	9	a	a	DET
ejpam-6536	4	10	vertex	vertex	NOUN
ejpam-6536	4	11	in	in	ADP
ejpam-6536	4	12	s.	s.	PROPN
ejpam-6536	4	13	the	the	DET
ejpam-6536	4	14	minimum	minimum	PROPN
ejpam-6536	4	15	cardinality	cardinality	NOUN
ejpam-6536	4	16	γh(g	γh(g	NOUN
ejpam-6536	4	17	)	)	PUNCT
ejpam-6536	4	18	of	of	ADP
ejpam-6536	4	19	a	a	DET
ejpam-6536	4	20	hop	hop	NOUN
ejpam-6536	4	21	dominating	dominating	NOUN
ejpam-6536	4	22	set	set	NOUN
ejpam-6536	4	23	is	be	AUX
ejpam-6536	4	24	the	the	DET
ejpam-6536	4	25	hop	hop	NOUN
ejpam-6536	4	26	domination	domination	NOUN
ejpam-6536	4	27	number	number	NOUN
ejpam-6536	4	28	of	of	ADP
ejpam-6536	4	29	g.	g.	PROPN
ejpam-6536	4	30	any	any	DET
ejpam-6536	4	31	hop	hop	NOUN
ejpam-6536	4	32	dominating	dominating	NOUN
ejpam-6536	4	33	set	set	NOUN
ejpam-6536	4	34	of	of	ADP
ejpam-6536	4	35	cardinality	cardinality	NOUN
ejpam-6536	4	36	γh(g	γh(g	PUNCT
ejpam-6536	4	37	)	)	PUNCT
ejpam-6536	4	38	is	be	AUX
ejpam-6536	4	39	a	a	DET
ejpam-6536	4	40	γh	γh	ADV
ejpam-6536	4	41	-	-	PUNCT
ejpam-6536	4	42	set	set	NOUN
ejpam-6536	4	43	.	.	PUNCT
ejpam-6536	5	1	a	a	DET
ejpam-6536	5	2	pair	pair	NOUN
ejpam-6536	5	3	(	(	PUNCT
ejpam-6536	5	4	s	s	PROPN
ejpam-6536	5	5	,	,	PUNCT
ejpam-6536	5	6	t	t	PROPN
ejpam-6536	5	7	)	)	PUNCT
ejpam-6536	5	8	of	of	ADP
ejpam-6536	5	9	sets	set	NOUN
ejpam-6536	5	10	of	of	ADP
ejpam-6536	5	11	vertices	vertex	NOUN
ejpam-6536	5	12	of	of	ADP
ejpam-6536	5	13	g	g	PROPN
ejpam-6536	5	14	is	be	AUX
ejpam-6536	5	15	a	a	DET
ejpam-6536	5	16	disjoint	disjoint	ADJ
ejpam-6536	5	17	hop	hop	NOUN
ejpam-6536	5	18	dominating	dominating	NOUN
ejpam-6536	5	19	pair	pair	NOUN
ejpam-6536	5	20	if	if	SCONJ
ejpam-6536	5	21	s	s	VERB
ejpam-6536	5	22	∩	∩	ADJ
ejpam-6536	5	23	t	t	NOUN
ejpam-6536	5	24	=	=	SYM
ejpam-6536	5	25	∅	∅	NOUN
ejpam-6536	5	26	and	and	CCONJ
ejpam-6536	5	27	both	both	DET
ejpam-6536	5	28	s	s	NOUN
ejpam-6536	5	29	and	and	CCONJ
ejpam-6536	5	30	t	t	PROPN
ejpam-6536	5	31	are	be	AUX
ejpam-6536	5	32	hop	hop	NOUN
ejpam-6536	5	33	dominating	dominating	NOUN
ejpam-6536	5	34	sets	set	NOUN
ejpam-6536	5	35	of	of	ADP
ejpam-6536	5	36	g.	g.	PROPN
ejpam-6536	5	37	in	in	ADP
ejpam-6536	5	38	particular	particular	ADJ
ejpam-6536	5	39	,	,	PUNCT
ejpam-6536	5	40	if	if	SCONJ
ejpam-6536	5	41	s	s	VERB
ejpam-6536	5	42	is	be	AUX
ejpam-6536	5	43	a	a	DET
ejpam-6536	5	44	γh	γh	ADV
ejpam-6536	5	45	-	-	PUNCT
ejpam-6536	5	46	set	set	NOUN
ejpam-6536	5	47	,	,	PUNCT
ejpam-6536	5	48	then	then	ADV
ejpam-6536	5	49	t	t	PROPN
ejpam-6536	5	50	is	be	AUX
ejpam-6536	5	51	an	an	DET
ejpam-6536	5	52	inverse	inverse	NOUN
ejpam-6536	5	53	hop	hop	NOUN
ejpam-6536	5	54	dominating	dominating	NOUN
ejpam-6536	5	55	set	set	NOUN
ejpam-6536	5	56	of	of	ADP
ejpam-6536	5	57	g.	g.	PROPN
ejpam-6536	5	58	the	the	DET
ejpam-6536	5	59	minimum	minimum	ADJ
ejpam-6536	5	60	sum	sum	NOUN
ejpam-6536	5	61	|s|	|s|	PROPN
ejpam-6536	5	62	+	+	CCONJ
ejpam-6536	5	63	|t	|t	VERB
ejpam-6536	5	64	|	|	ADV
ejpam-6536	5	65	among	among	ADP
ejpam-6536	5	66	all	all	DET
ejpam-6536	5	67	pairs	pair	NOUN
ejpam-6536	5	68	(	(	PUNCT
ejpam-6536	5	69	s	s	X
ejpam-6536	5	70	,	,	PUNCT
ejpam-6536	5	71	t	t	PROPN
ejpam-6536	5	72	)	)	PUNCT
ejpam-6536	5	73	of	of	ADP
ejpam-6536	5	74	disjoint	disjoint	NOUN
ejpam-6536	5	75	hop	hop	NOUN
ejpam-6536	5	76	dominating	dominating	NOUN
ejpam-6536	5	77	sets	set	NOUN
ejpam-6536	5	78	of	of	ADP
ejpam-6536	5	79	g	g	PROPN
ejpam-6536	5	80	is	be	AUX
ejpam-6536	5	81	the	the	DET
ejpam-6536	5	82	disjoint	disjoint	ADJ
ejpam-6536	5	83	hop	hop	NOUN
ejpam-6536	5	84	domination	domination	NOUN
ejpam-6536	5	85	number	number	NOUN
ejpam-6536	5	86	,	,	PUNCT
ejpam-6536	5	87	denoted	denote	VERB
ejpam-6536	5	88	by	by	ADP
ejpam-6536	5	89	γhh(g	γhh(g	NOUN
ejpam-6536	5	90	)	)	PUNCT
ejpam-6536	5	91	.	.	PUNCT
ejpam-6536	6	1	the	the	DET
ejpam-6536	6	2	minimum	minimum	ADJ
ejpam-6536	6	3	cardinality	cardinality	NOUN
ejpam-6536	6	4	of	of	ADP
ejpam-6536	6	5	an	an	DET
ejpam-6536	6	6	inverse	inverse	NOUN
ejpam-6536	6	7	hop	hop	NOUN
ejpam-6536	6	8	dominating	dominating	NOUN
ejpam-6536	6	9	set	set	NOUN
ejpam-6536	6	10	of	of	ADP
ejpam-6536	6	11	g	g	PROPN
ejpam-6536	6	12	is	be	AUX
ejpam-6536	6	13	the	the	DET
ejpam-6536	6	14	inverse	inverse	ADJ
ejpam-6536	6	15	hop	hop	NOUN
ejpam-6536	6	16	domination	domination	NOUN
ejpam-6536	6	17	number	number	NOUN
ejpam-6536	6	18	of	of	ADP
ejpam-6536	6	19	g	g	NOUN
ejpam-6536	6	20	,	,	PUNCT
ejpam-6536	6	21	denoted	denote	VERB
ejpam-6536	6	22	by	by	ADP
ejpam-6536	6	23	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	6	24	)	)	PUNCT
ejpam-6536	6	25	.	.	PUNCT
ejpam-6536	7	1	in	in	ADP
ejpam-6536	7	2	this	this	DET
ejpam-6536	7	3	paper	paper	NOUN
ejpam-6536	7	4	,	,	PUNCT
ejpam-6536	7	5	we	we	PRON
ejpam-6536	7	6	initiate	initiate	VERB
ejpam-6536	7	7	the	the	DET
ejpam-6536	7	8	study	study	NOUN
ejpam-6536	7	9	of	of	ADP
ejpam-6536	7	10	inverse	inverse	NOUN
ejpam-6536	7	11	hop	hop	NOUN
ejpam-6536	7	12	domination	domination	NOUN
ejpam-6536	7	13	and	and	CCONJ
ejpam-6536	7	14	disjoint	disjoint	VERB
ejpam-6536	7	15	hop	hop	PROPN
ejpam-6536	7	16	domination	domination	NOUN
ejpam-6536	7	17	.	.	PUNCT
ejpam-6536	8	1	interestingly	interestingly	ADV
ejpam-6536	8	2	,	,	PUNCT
ejpam-6536	8	3	for	for	SCONJ
ejpam-6536	8	4	every	every	DET
ejpam-6536	8	5	pair	pair	NOUN
ejpam-6536	8	6	of	of	ADP
ejpam-6536	8	7	positive	positive	ADJ
ejpam-6536	8	8	integers	integer	NOUN
ejpam-6536	8	9	m	m	VERB
ejpam-6536	8	10	and	and	CCONJ
ejpam-6536	8	11	n	n	ADV
ejpam-6536	8	12	with	with	ADP
ejpam-6536	8	13	2	2	NUM
ejpam-6536	8	14	≤	≤	NUM
ejpam-6536	8	15	m	m	VERB
ejpam-6536	8	16	≤	≤	NOUN
ejpam-6536	8	17	n	n	CCONJ
ejpam-6536	8	18	,	,	PUNCT
ejpam-6536	8	19	there	there	PRON
ejpam-6536	8	20	exists	exist	VERB
ejpam-6536	8	21	a	a	DET
ejpam-6536	8	22	connected	connected	ADJ
ejpam-6536	8	23	graph	graph	NOUN
ejpam-6536	8	24	g	g	NOUN
ejpam-6536	8	25	for	for	ADP
ejpam-6536	8	26	which	which	PRON
ejpam-6536	8	27	γh(g	γh(g	NOUN
ejpam-6536	8	28	)	)	PUNCT
ejpam-6536	8	29	=	=	PUNCT
ejpam-6536	8	30	m	m	NOUN
ejpam-6536	8	31	and	and	CCONJ
ejpam-6536	8	32	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	8	33	)	)	PUNCT
ejpam-6536	9	1	=	=	SYM
ejpam-6536	9	2	n.	n.	PROPN
ejpam-6536	9	3	also	also	ADV
ejpam-6536	9	4	,	,	PUNCT
ejpam-6536	9	5	for	for	ADP
ejpam-6536	9	6	each	each	DET
ejpam-6536	9	7	positive	positive	ADJ
ejpam-6536	9	8	integer	integer	NOUN
ejpam-6536	9	9	n	n	PRON
ejpam-6536	9	10	≥	≥	NOUN
ejpam-6536	9	11	4	4	NUM
ejpam-6536	9	12	,	,	PUNCT
ejpam-6536	9	13	there	there	PRON
ejpam-6536	9	14	exists	exist	VERB
ejpam-6536	9	15	a	a	DET
ejpam-6536	9	16	connected	connected	ADJ
ejpam-6536	9	17	graph	graph	NOUN
ejpam-6536	9	18	g	g	NOUN
ejpam-6536	9	19	for	for	ADP
ejpam-6536	9	20	which	which	PRON
ejpam-6536	9	21	γh(g	γh(g	NOUN
ejpam-6536	9	22	)	)	PUNCT
ejpam-6536	10	1	+	+	CCONJ
ejpam-6536	10	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	10	3	)	)	PUNCT
ejpam-6536	10	4	−	−	NUM
ejpam-6536	10	5	γhh(g	γhh(g	NOUN
ejpam-6536	10	6	)	)	PUNCT
ejpam-6536	10	7	=	=	VERB
ejpam-6536	11	1	n.	n.	NOUN
ejpam-6536	11	2	here	here	ADV
ejpam-6536	11	3	we	we	PRON
ejpam-6536	11	4	investigate	investigate	VERB
ejpam-6536	11	5	these	these	DET
ejpam-6536	11	6	new	new	ADJ
ejpam-6536	11	7	concepts	concept	NOUN
ejpam-6536	11	8	for	for	ADP
ejpam-6536	11	9	some	some	DET
ejpam-6536	11	10	specific	specific	ADJ
ejpam-6536	11	11	graphs	graph	NOUN
ejpam-6536	11	12	including	include	VERB
ejpam-6536	11	13	the	the	DET
ejpam-6536	11	14	join	join	NOUN
ejpam-6536	11	15	,	,	PUNCT
ejpam-6536	11	16	corona	corona	NOUN
ejpam-6536	11	17	and	and	CCONJ
ejpam-6536	11	18	lexicographic	lexicographic	ADJ
ejpam-6536	11	19	product	product	NOUN
ejpam-6536	11	20	of	of	ADP
ejpam-6536	11	21	graphs	graph	NOUN
ejpam-6536	11	22	.	.	PUNCT
ejpam-6536	12	1	2020	2020	NUM
ejpam-6536	12	2	mathematics	mathematic	NOUN
ejpam-6536	12	3	subject	subject	NOUN
ejpam-6536	12	4	classifications	classification	NOUN
ejpam-6536	12	5	:	:	PUNCT
ejpam-6536	12	6	05c69	05c69	X
ejpam-6536	12	7	key	key	ADJ
ejpam-6536	12	8	words	word	NOUN
ejpam-6536	12	9	and	and	CCONJ
ejpam-6536	12	10	phrases	phrase	NOUN
ejpam-6536	12	11	:	:	PUNCT
ejpam-6536	12	12	hop	hop	NOUN
ejpam-6536	12	13	domination	domination	NOUN
ejpam-6536	12	14	,	,	PUNCT
ejpam-6536	12	15	inverse	inverse	NOUN
ejpam-6536	12	16	hop	hop	NOUN
ejpam-6536	12	17	domination	domination	NOUN
ejpam-6536	12	18	,	,	PUNCT
ejpam-6536	12	19	disjoint	disjoint	VERB
ejpam-6536	12	20	hop	hop	NOUN
ejpam-6536	12	21	domination	domination	PROPN
ejpam-6536	12	22	1	1	NUM
ejpam-6536	12	23	.	.	PUNCT
ejpam-6536	13	1	introduction	introduction	NOUN
ejpam-6536	13	2	all	all	ADV
ejpam-6536	13	3	throughout	throughout	ADP
ejpam-6536	13	4	this	this	DET
ejpam-6536	13	5	paper	paper	NOUN
ejpam-6536	13	6	,	,	PUNCT
ejpam-6536	13	7	we	we	PRON
ejpam-6536	13	8	consider	consider	VERB
ejpam-6536	13	9	only	only	ADV
ejpam-6536	13	10	graphs	graph	NOUN
ejpam-6536	13	11	which	which	PRON
ejpam-6536	13	12	are	be	AUX
ejpam-6536	13	13	simple	simple	ADJ
ejpam-6536	13	14	,	,	PUNCT
ejpam-6536	13	15	finite	finite	ADJ
ejpam-6536	13	16	and	and	CCONJ
ejpam-6536	13	17	undirected	undirected	ADJ
ejpam-6536	13	18	.	.	PUNCT
ejpam-6536	14	1	given	give	VERB
ejpam-6536	14	2	a	a	DET
ejpam-6536	14	3	graph	graph	NOUN
ejpam-6536	14	4	g	g	NOUN
ejpam-6536	14	5	=	=	PUNCT
ejpam-6536	14	6	(	(	PUNCT
ejpam-6536	14	7	v	v	NOUN
ejpam-6536	14	8	(	(	PUNCT
ejpam-6536	14	9	g	g	NOUN
ejpam-6536	14	10	)	)	PUNCT
ejpam-6536	14	11	,	,	PUNCT
ejpam-6536	14	12	e(g	e(g	PROPN
ejpam-6536	14	13	)	)	PUNCT
ejpam-6536	14	14	)	)	PUNCT
ejpam-6536	14	15	,	,	PUNCT
ejpam-6536	14	16	we	we	PRON
ejpam-6536	14	17	call	call	VERB
ejpam-6536	14	18	v	v	ADP
ejpam-6536	14	19	(	(	PUNCT
ejpam-6536	14	20	g	g	NOUN
ejpam-6536	14	21	)	)	PUNCT
ejpam-6536	14	22	the	the	DET
ejpam-6536	14	23	vertex	vertex	NOUN
ejpam-6536	14	24	set	set	NOUN
ejpam-6536	14	25	of	of	ADP
ejpam-6536	14	26	g	g	PROPN
ejpam-6536	14	27	and	and	CCONJ
ejpam-6536	14	28	e(g	e(g	PROPN
ejpam-6536	14	29	)	)	PUNCT
ejpam-6536	14	30	its	its	PRON
ejpam-6536	14	31	edge	edge	NOUN
ejpam-6536	14	32	set	set	NOUN
ejpam-6536	14	33	.	.	PUNCT
ejpam-6536	15	1	the	the	DET
ejpam-6536	15	2	cardinality	cardinality	PROPN
ejpam-6536	15	3	|v	|v	PROPN
ejpam-6536	15	4	(	(	PUNCT
ejpam-6536	15	5	g)|	g)|	NOUN
ejpam-6536	15	6	of	of	ADP
ejpam-6536	15	7	v	v	NOUN
ejpam-6536	15	8	(	(	PUNCT
ejpam-6536	15	9	g	g	NOUN
ejpam-6536	15	10	)	)	PUNCT
ejpam-6536	15	11	is	be	AUX
ejpam-6536	15	12	the	the	DET
ejpam-6536	15	13	order	order	NOUN
ejpam-6536	15	14	of	of	ADP
ejpam-6536	15	15	g.	g.	PROPN
ejpam-6536	15	16	all	all	DET
ejpam-6536	15	17	terminologies	terminology	NOUN
ejpam-6536	15	18	used	use	VERB
ejpam-6536	15	19	here	here	ADV
ejpam-6536	15	20	which	which	PRON
ejpam-6536	15	21	are	be	AUX
ejpam-6536	15	22	not	not	PART
ejpam-6536	15	23	defined	define	VERB
ejpam-6536	15	24	are	be	AUX
ejpam-6536	15	25	adapted	adapt	VERB
ejpam-6536	15	26	from	from	ADP
ejpam-6536	15	27	[	[	X
ejpam-6536	15	28	1	1	NUM
ejpam-6536	15	29	]	]	PUNCT
ejpam-6536	15	30	.	.	PUNCT
ejpam-6536	16	1	let	let	VERB
ejpam-6536	16	2	g	g	NOUN
ejpam-6536	16	3	and	and	CCONJ
ejpam-6536	16	4	h	h	NOUN
ejpam-6536	16	5	be	be	AUX
ejpam-6536	16	6	disjoint	disjoint	NOUN
ejpam-6536	16	7	graphs	graph	NOUN
ejpam-6536	16	8	.	.	PUNCT
ejpam-6536	17	1	the	the	DET
ejpam-6536	17	2	join	join	NOUN
ejpam-6536	17	3	g	g	PROPN
ejpam-6536	17	4	+	+	CCONJ
ejpam-6536	17	5	h	h	NOUN
ejpam-6536	17	6	of	of	ADP
ejpam-6536	17	7	g	g	PROPN
ejpam-6536	17	8	and	and	CCONJ
ejpam-6536	17	9	h	h	NOUN
ejpam-6536	17	10	is	be	AUX
ejpam-6536	17	11	the	the	DET
ejpam-6536	17	12	graph	graph	NOUN
ejpam-6536	17	13	with	with	ADP
ejpam-6536	17	14	vertex	vertex	NOUN
ejpam-6536	17	15	set	set	VERB
ejpam-6536	17	16	v	v	NOUN
ejpam-6536	17	17	(	(	PUNCT
ejpam-6536	17	18	g	g	NOUN
ejpam-6536	17	19	)	)	PUNCT
ejpam-6536	17	20	∪	∪	NOUN
ejpam-6536	17	21	v	v	NOUN
ejpam-6536	17	22	(	(	PUNCT
ejpam-6536	17	23	h	h	NOUN
ejpam-6536	17	24	)	)	PUNCT
ejpam-6536	17	25	and	and	CCONJ
ejpam-6536	17	26	edge	edge	VERB
ejpam-6536	17	27	set	set	VERB
ejpam-6536	17	28	e(g	e(g	NOUN
ejpam-6536	17	29	)	)	PUNCT
ejpam-6536	17	30	∪	∪	ADP
ejpam-6536	17	31	e(h	e(h	PROPN
ejpam-6536	17	32	)	)	PUNCT
ejpam-6536	17	33	∪	∪	NOUN
ejpam-6536	17	34	{	{	PUNCT
ejpam-6536	17	35	uv	uv	NOUN
ejpam-6536	17	36	:	:	PUNCT
ejpam-6536	17	37	u	u	PROPN
ejpam-6536	17	38	∈	∈	PROPN
ejpam-6536	17	39	v	v	ADP
ejpam-6536	17	40	(	(	PUNCT
ejpam-6536	17	41	g	g	NOUN
ejpam-6536	17	42	)	)	PUNCT
ejpam-6536	17	43	,	,	PUNCT
ejpam-6536	17	44	v	v	X
ejpam-6536	17	45	∈	∈	PROPN
ejpam-6536	17	46	v	v	NOUN
ejpam-6536	17	47	(	(	PUNCT
ejpam-6536	17	48	h	h	NOUN
ejpam-6536	17	49	)	)	PUNCT
ejpam-6536	17	50	}	}	PUNCT
ejpam-6536	17	51	.	.	PUNCT
ejpam-6536	18	1	the	the	DET
ejpam-6536	18	2	corona	corona	NOUN
ejpam-6536	18	3	g	g	PROPN
ejpam-6536	18	4	◦	◦	NOUN
ejpam-6536	18	5	h	h	NOUN
ejpam-6536	18	6	of	of	ADP
ejpam-6536	18	7	g	g	PROPN
ejpam-6536	18	8	and	and	CCONJ
ejpam-6536	18	9	h	h	NOUN
ejpam-6536	18	10	is	be	AUX
ejpam-6536	18	11	the	the	DET
ejpam-6536	18	12	graph	graph	NOUN
ejpam-6536	18	13	obtained	obtain	VERB
ejpam-6536	18	14	by	by	ADP
ejpam-6536	18	15	taking	take	VERB
ejpam-6536	18	16	one	one	NUM
ejpam-6536	18	17	copy	copy	NOUN
ejpam-6536	18	18	of	of	ADP
ejpam-6536	18	19	g	g	PROPN
ejpam-6536	18	20	and	and	CCONJ
ejpam-6536	18	21	|v	|v	PROPN
ejpam-6536	18	22	(	(	PUNCT
ejpam-6536	18	23	g)|	g)|	NOUN
ejpam-6536	18	24	copies	copy	NOUN
ejpam-6536	18	25	of	of	ADP
ejpam-6536	18	26	h	h	NOUN
ejpam-6536	18	27	,	,	PUNCT
ejpam-6536	18	28	∗corresponding	∗corresponde	VERB
ejpam-6536	18	29	author	author	NOUN
ejpam-6536	18	30	.	.	PUNCT
ejpam-6536	19	1	doi	doi	NOUN
ejpam-6536	19	2	:	:	PUNCT
ejpam-6536	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6536	https://doi.org/10.29020/nybg.ejpam.v18i3.6536	VERB
ejpam-6536	19	4	email	email	NOUN
ejpam-6536	19	5	addresses	address	NOUN
ejpam-6536	19	6	:	:	PUNCT
ejpam-6536	19	7	viralouabrille.besana@g.msuiit.edu.ph	viralouabrille.besana@g.msuiit.edu.ph	PROPN
ejpam-6536	19	8	(	(	PUNCT
ejpam-6536	19	9	v.a	v.a	PROPN
ejpam-6536	19	10	besana	besana	PROPN
ejpam-6536	19	11	)	)	PUNCT
ejpam-6536	19	12	,	,	PUNCT
ejpam-6536	19	13	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-6536	19	14	(	(	PUNCT
ejpam-6536	19	15	f.	f.	PROPN
ejpam-6536	19	16	jamil),sergio.canoy@g.msuiit.edu.ph	jamil),sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6536	19	17	(	(	PUNCT
ejpam-6536	19	18	s.	s.	PROPN
ejpam-6536	19	19	canoy	canoy	PROPN
ejpam-6536	19	20	jr	jr	PROPN
ejpam-6536	19	21	.	.	PUNCT
ejpam-6536	19	22	)	)	PUNCT
ejpam-6536	19	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6536	20	1	1	1	NUM
ejpam-6536	20	2	copyright	copyright	NOUN
ejpam-6536	20	3	:	:	PUNCT
ejpam-6536	20	4	©	©	PROPN
ejpam-6536	20	5	2025	2025	NUM
ejpam-6536	20	6	the	the	DET
ejpam-6536	20	7	author(s	author(s	NOUN
ejpam-6536	20	8	)	)	PUNCT
ejpam-6536	20	9	.	.	PUNCT
ejpam-6536	21	1	(	(	PUNCT
ejpam-6536	21	2	cc	cc	NOUN
ejpam-6536	21	3	by	by	ADP
ejpam-6536	21	4	-	-	PUNCT
ejpam-6536	21	5	nc	nc	PROPN
ejpam-6536	21	6	4.0	4.0	NUM
ejpam-6536	21	7	)	)	PUNCT
ejpam-6536	21	8	v.	v.	ADP
ejpam-6536	21	9	a	a	DET
ejpam-6536	21	10	besana	besana	PROPN
ejpam-6536	21	11	,	,	PUNCT
ejpam-6536	21	12	f.	f.	PROPN
ejpam-6536	21	13	jamil	jamil	PROPN
ejpam-6536	21	14	,	,	PUNCT
ejpam-6536	21	15	s.	s.	PROPN
ejpam-6536	21	16	canoy	canoy	PROPN
ejpam-6536	21	17	jr	jr	PROPN
ejpam-6536	21	18	.	.	PROPN
ejpam-6536	21	19	/	/	SYM
ejpam-6536	21	20	eur	eur	PROPN
ejpam-6536	21	21	.	.	PUNCT
ejpam-6536	22	1	j.	j.	PROPN
ejpam-6536	22	2	pure	pure	PROPN
ejpam-6536	22	3	appl	appl	PROPN
ejpam-6536	22	4	.	.	PROPN
ejpam-6536	22	5	math	math	PROPN
ejpam-6536	22	6	,	,	PUNCT
ejpam-6536	22	7	18	18	NUM
ejpam-6536	22	8	(	(	PUNCT
ejpam-6536	22	9	3	3	NUM
ejpam-6536	22	10	)	)	PUNCT
ejpam-6536	22	11	(	(	PUNCT
ejpam-6536	22	12	2025	2025	NUM
ejpam-6536	22	13	)	)	PUNCT
ejpam-6536	22	14	,	,	PUNCT
ejpam-6536	22	15	6536	6536	NUM
ejpam-6536	22	16	2	2	NUM
ejpam-6536	22	17	of	of	ADP
ejpam-6536	22	18	17	17	NUM
ejpam-6536	22	19	and	and	CCONJ
ejpam-6536	22	20	then	then	ADV
ejpam-6536	22	21	joining	join	VERB
ejpam-6536	22	22	each	each	DET
ejpam-6536	22	23	ith	ith	PROPN
ejpam-6536	22	24	vertex	vertex	NOUN
ejpam-6536	22	25	of	of	ADP
ejpam-6536	22	26	g	g	NOUN
ejpam-6536	22	27	to	to	ADP
ejpam-6536	22	28	every	every	DET
ejpam-6536	22	29	vertex	vertex	NOUN
ejpam-6536	22	30	in	in	ADP
ejpam-6536	22	31	the	the	DET
ejpam-6536	22	32	ith	ith	PROPN
ejpam-6536	22	33	copy	copy	NOUN
ejpam-6536	22	34	of	of	ADP
ejpam-6536	22	35	h.	h.	PROPN
ejpam-6536	22	36	in	in	ADP
ejpam-6536	22	37	particular	particular	ADJ
ejpam-6536	22	38	,	,	PUNCT
ejpam-6536	22	39	we	we	PRON
ejpam-6536	22	40	call	call	VERB
ejpam-6536	22	41	g	g	PROPN
ejpam-6536	22	42	◦	◦	NOUN
ejpam-6536	22	43	k1	k1	X
ejpam-6536	22	44	the	the	DET
ejpam-6536	22	45	corona	corona	NOUN
ejpam-6536	22	46	of	of	ADP
ejpam-6536	22	47	g	g	PROPN
ejpam-6536	22	48	,	,	PUNCT
ejpam-6536	22	49	and	and	CCONJ
ejpam-6536	22	50	write	write	VERB
ejpam-6536	22	51	cor(g	cor(g	PROPN
ejpam-6536	22	52	)	)	PUNCT
ejpam-6536	22	53	=	=	SYM
ejpam-6536	22	54	g	g	PROPN
ejpam-6536	22	55	◦	◦	NOUN
ejpam-6536	22	56	k1	k1	NOUN
ejpam-6536	22	57	.	.	PUNCT
ejpam-6536	23	1	the	the	DET
ejpam-6536	23	2	lexicographic	lexicographic	ADJ
ejpam-6536	23	3	product	product	NOUN
ejpam-6536	23	4	g[h	g[h	PROPN
ejpam-6536	23	5	]	]	PUNCT
ejpam-6536	23	6	of	of	ADP
ejpam-6536	23	7	g	g	PROPN
ejpam-6536	23	8	and	and	CCONJ
ejpam-6536	23	9	h	h	NOUN
ejpam-6536	23	10	is	be	AUX
ejpam-6536	23	11	the	the	DET
ejpam-6536	23	12	graph	graph	NOUN
ejpam-6536	23	13	with	with	ADP
ejpam-6536	23	14	v	v	NOUN
ejpam-6536	23	15	(	(	PUNCT
ejpam-6536	23	16	g[h	g[h	PROPN
ejpam-6536	23	17	]	]	PUNCT
ejpam-6536	23	18	)	)	PUNCT
ejpam-6536	24	1	=	=	SYM
ejpam-6536	24	2	v	v	X
ejpam-6536	24	3	(	(	PUNCT
ejpam-6536	24	4	g	g	NOUN
ejpam-6536	24	5	)	)	PUNCT
ejpam-6536	24	6	×	×	NOUN
ejpam-6536	24	7	v	v	NOUN
ejpam-6536	24	8	(	(	PUNCT
ejpam-6536	24	9	h	h	NOUN
ejpam-6536	24	10	)	)	PUNCT
ejpam-6536	24	11	and	and	CCONJ
ejpam-6536	24	12	(	(	PUNCT
ejpam-6536	24	13	u	u	NOUN
ejpam-6536	24	14	,	,	PUNCT
ejpam-6536	24	15	v)(u′	v)(u′	NOUN
ejpam-6536	24	16	,	,	PUNCT
ejpam-6536	24	17	v′	v′	NOUN
ejpam-6536	24	18	)	)	PUNCT
ejpam-6536	24	19	∈	∈	NOUN
ejpam-6536	24	20	e(g[h	e(g[h	NOUN
ejpam-6536	24	21	]	]	PUNCT
ejpam-6536	24	22	)	)	PUNCT
ejpam-6536	24	23	if	if	SCONJ
ejpam-6536	24	24	and	and	CCONJ
ejpam-6536	24	25	only	only	ADV
ejpam-6536	24	26	if	if	SCONJ
ejpam-6536	24	27	either	either	CCONJ
ejpam-6536	24	28	uu′	uu′	PROPN
ejpam-6536	24	29	∈	∈	PROPN
ejpam-6536	24	30	e(g	e(g	PROPN
ejpam-6536	24	31	)	)	PUNCT
ejpam-6536	24	32	or	or	CCONJ
ejpam-6536	24	33	u	u	X
ejpam-6536	24	34	=	=	PUNCT
ejpam-6536	24	35	u′	u′	PROPN
ejpam-6536	24	36	and	and	CCONJ
ejpam-6536	24	37	vv′	vv′	NOUN
ejpam-6536	24	38	∈	∈	PROPN
ejpam-6536	24	39	e(h	e(h	PROPN
ejpam-6536	24	40	)	)	PUNCT
ejpam-6536	24	41	.	.	PUNCT
ejpam-6536	25	1	in	in	ADP
ejpam-6536	25	2	any	any	PRON
ejpam-6536	25	3	of	of	ADP
ejpam-6536	25	4	these	these	DET
ejpam-6536	25	5	graphs	graph	NOUN
ejpam-6536	25	6	,	,	PUNCT
ejpam-6536	25	7	g	g	PROPN
ejpam-6536	25	8	and	and	CCONJ
ejpam-6536	25	9	h	h	NOUN
ejpam-6536	25	10	are	be	AUX
ejpam-6536	25	11	referred	refer	VERB
ejpam-6536	25	12	to	to	ADP
ejpam-6536	25	13	as	as	ADP
ejpam-6536	25	14	their	their	PRON
ejpam-6536	25	15	basic	basic	ADJ
ejpam-6536	25	16	component	component	NOUN
ejpam-6536	25	17	graphs	graph	NOUN
ejpam-6536	25	18	.	.	PUNCT
ejpam-6536	26	1	vertices	vertice	VERB
ejpam-6536	26	2	u	u	NOUN
ejpam-6536	26	3	and	and	CCONJ
ejpam-6536	26	4	v	v	NOUN
ejpam-6536	26	5	of	of	ADP
ejpam-6536	26	6	a	a	DET
ejpam-6536	26	7	graph	graph	NOUN
ejpam-6536	26	8	g	g	NOUN
ejpam-6536	26	9	are	be	AUX
ejpam-6536	26	10	neighbors	neighbor	NOUN
ejpam-6536	26	11	if	if	SCONJ
ejpam-6536	26	12	uv	uv	PROPN
ejpam-6536	26	13	∈	∈	PROPN
ejpam-6536	26	14	e(g	e(g	PROPN
ejpam-6536	26	15	)	)	PUNCT
ejpam-6536	26	16	.	.	PUNCT
ejpam-6536	27	1	the	the	DET
ejpam-6536	27	2	open	open	ADJ
ejpam-6536	27	3	neighborhood	neighborhood	NOUN
ejpam-6536	27	4	of	of	ADP
ejpam-6536	27	5	v	v	NOUN
ejpam-6536	27	6	refers	refer	VERB
ejpam-6536	27	7	to	to	ADP
ejpam-6536	27	8	the	the	DET
ejpam-6536	27	9	set	set	NOUN
ejpam-6536	27	10	ng(v	ng(v	PUNCT
ejpam-6536	27	11	)	)	PUNCT
ejpam-6536	27	12	consisting	consist	VERB
ejpam-6536	27	13	of	of	ADP
ejpam-6536	27	14	all	all	DET
ejpam-6536	27	15	neighbors	neighbor	NOUN
ejpam-6536	27	16	of	of	ADP
ejpam-6536	27	17	v.	v.	ADP
ejpam-6536	27	18	the	the	DET
ejpam-6536	27	19	degree	degree	NOUN
ejpam-6536	27	20	of	of	ADP
ejpam-6536	27	21	v	v	NOUN
ejpam-6536	27	22	refers	refer	VERB
ejpam-6536	27	23	to	to	ADP
ejpam-6536	27	24	the	the	DET
ejpam-6536	27	25	cardinality	cardinality	NOUN
ejpam-6536	27	26	|ng(v)|	|ng(v)|	NOUN
ejpam-6536	27	27	of	of	ADP
ejpam-6536	27	28	the	the	DET
ejpam-6536	27	29	open	open	ADJ
ejpam-6536	27	30	neighborhood	neighborhood	NOUN
ejpam-6536	27	31	of	of	ADP
ejpam-6536	27	32	v.	v.	ADP
ejpam-6536	27	33	vertex	vertex	NOUN
ejpam-6536	27	34	v	v	NOUN
ejpam-6536	27	35	is	be	AUX
ejpam-6536	27	36	isolated	isolate	VERB
ejpam-6536	27	37	if	if	SCONJ
ejpam-6536	27	38	the	the	DET
ejpam-6536	27	39	degree	degree	NOUN
ejpam-6536	27	40	of	of	ADP
ejpam-6536	27	41	v	v	NOUN
ejpam-6536	27	42	is	be	AUX
ejpam-6536	27	43	0	0	NUM
ejpam-6536	27	44	.	.	PUNCT
ejpam-6536	28	1	the	the	DET
ejpam-6536	28	2	closed	closed	ADJ
ejpam-6536	28	3	neighborhood	neighborhood	NOUN
ejpam-6536	28	4	of	of	ADP
ejpam-6536	28	5	v	v	NOUN
ejpam-6536	28	6	is	be	AUX
ejpam-6536	28	7	the	the	DET
ejpam-6536	28	8	set	set	NOUN
ejpam-6536	28	9	ng[v	ng[v	NOUN
ejpam-6536	28	10	]	]	X
ejpam-6536	28	11	=	=	SYM
ejpam-6536	28	12	ng(v	ng(v	X
ejpam-6536	28	13	)	)	PUNCT
ejpam-6536	28	14	∪	∪	ADP
ejpam-6536	28	15	{	{	PUNCT
ejpam-6536	28	16	v	v	NOUN
ejpam-6536	28	17	}	}	PUNCT
ejpam-6536	28	18	.	.	PUNCT
ejpam-6536	29	1	customarily	customarily	ADV
ejpam-6536	29	2	,	,	PUNCT
ejpam-6536	29	3	for	for	ADP
ejpam-6536	29	4	s	s	PROPN
ejpam-6536	29	5	⊆	⊆	NUM
ejpam-6536	29	6	v	v	NOUN
ejpam-6536	29	7	(	(	PUNCT
ejpam-6536	29	8	g	g	NOUN
ejpam-6536	29	9	)	)	PUNCT
ejpam-6536	29	10	,	,	PUNCT
ejpam-6536	29	11	ng(s	ng(s	NUM
ejpam-6536	29	12	)	)	PUNCT
ejpam-6536	29	13	=	=	SYM
ejpam-6536	29	14	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-6536	29	15	)	)	PUNCT
ejpam-6536	29	16	and	and	CCONJ
ejpam-6536	29	17	ng[s	ng[s	PROPN
ejpam-6536	29	18	]	]	PUNCT
ejpam-6536	29	19	=	=	SYM
ejpam-6536	29	20	∪v∈sng[v	∪v∈sng[v	X
ejpam-6536	29	21	]	]	PUNCT
ejpam-6536	29	22	.	.	PUNCT
ejpam-6536	30	1	a	a	DET
ejpam-6536	30	2	subset	subset	NOUN
ejpam-6536	30	3	s	s	VERB
ejpam-6536	30	4	⊆	⊆	NUM
ejpam-6536	30	5	v	v	NOUN
ejpam-6536	30	6	(	(	PUNCT
ejpam-6536	30	7	g	g	NOUN
ejpam-6536	30	8	)	)	PUNCT
ejpam-6536	30	9	is	be	AUX
ejpam-6536	30	10	a	a	DET
ejpam-6536	30	11	dominating	dominating	NOUN
ejpam-6536	30	12	set	set	NOUN
ejpam-6536	30	13	of	of	ADP
ejpam-6536	30	14	g	g	PROPN
ejpam-6536	30	15	if	if	SCONJ
ejpam-6536	30	16	ng[s	ng[	NOUN
ejpam-6536	30	17	]	]	PUNCT
ejpam-6536	30	18	=	=	SYM
ejpam-6536	30	19	v	v	NOUN
ejpam-6536	30	20	(	(	PUNCT
ejpam-6536	30	21	g	g	NOUN
ejpam-6536	30	22	)	)	PUNCT
ejpam-6536	30	23	.	.	PUNCT
ejpam-6536	31	1	in	in	ADP
ejpam-6536	31	2	case	case	NOUN
ejpam-6536	31	3	ng(s	ng(s	NUM
ejpam-6536	31	4	)	)	PUNCT
ejpam-6536	31	5	=	=	SYM
ejpam-6536	31	6	v	v	X
ejpam-6536	31	7	(	(	PUNCT
ejpam-6536	31	8	g	g	NOUN
ejpam-6536	31	9	)	)	PUNCT
ejpam-6536	31	10	,	,	PUNCT
ejpam-6536	31	11	then	then	ADV
ejpam-6536	31	12	s	s	VERB
ejpam-6536	31	13	is	be	AUX
ejpam-6536	31	14	a	a	DET
ejpam-6536	31	15	total	total	ADJ
ejpam-6536	31	16	dominating	dominating	NOUN
ejpam-6536	31	17	set	set	NOUN
ejpam-6536	31	18	of	of	ADP
ejpam-6536	31	19	g.	g.	PROPN
ejpam-6536	31	20	the	the	DET
ejpam-6536	31	21	minimum	minimum	PROPN
ejpam-6536	31	22	cardinality	cardinality	PROPN
ejpam-6536	31	23	γ(g	γ(g	PROPN
ejpam-6536	31	24	)	)	PUNCT
ejpam-6536	31	25	of	of	ADP
ejpam-6536	31	26	a	a	DET
ejpam-6536	31	27	dominating	dominating	NOUN
ejpam-6536	31	28	set	set	NOUN
ejpam-6536	31	29	of	of	ADP
ejpam-6536	31	30	g	g	PROPN
ejpam-6536	31	31	is	be	AUX
ejpam-6536	31	32	the	the	DET
ejpam-6536	31	33	domination	domination	NOUN
ejpam-6536	31	34	number	number	NOUN
ejpam-6536	31	35	of	of	ADP
ejpam-6536	31	36	g	g	NOUN
ejpam-6536	31	37	,	,	PUNCT
ejpam-6536	31	38	and	and	CCONJ
ejpam-6536	31	39	the	the	DET
ejpam-6536	31	40	minimum	minimum	ADJ
ejpam-6536	31	41	cardinality	cardinality	NOUN
ejpam-6536	31	42	γt(g	γt(g	PUNCT
ejpam-6536	31	43	)	)	PUNCT
ejpam-6536	31	44	of	of	ADP
ejpam-6536	31	45	a	a	DET
ejpam-6536	31	46	total	total	ADJ
ejpam-6536	31	47	dominating	dominating	NOUN
ejpam-6536	31	48	set	set	NOUN
ejpam-6536	31	49	is	be	AUX
ejpam-6536	31	50	the	the	DET
ejpam-6536	31	51	total	total	ADJ
ejpam-6536	31	52	domination	domination	NOUN
ejpam-6536	31	53	number	number	NOUN
ejpam-6536	31	54	of	of	ADP
ejpam-6536	31	55	g.	g.	PROPN
ejpam-6536	31	56	a	a	DET
ejpam-6536	31	57	dominating	dominating	NOUN
ejpam-6536	31	58	set	set	NOUN
ejpam-6536	31	59	of	of	ADP
ejpam-6536	31	60	cardinality	cardinality	PROPN
ejpam-6536	31	61	γ(g	γ(g	PROPN
ejpam-6536	31	62	)	)	PUNCT
ejpam-6536	31	63	is	be	AUX
ejpam-6536	31	64	called	call	VERB
ejpam-6536	31	65	a	a	DET
ejpam-6536	31	66	γ	γ	NOUN
ejpam-6536	31	67	-	-	PUNCT
ejpam-6536	31	68	set	set	NOUN
ejpam-6536	31	69	of	of	ADP
ejpam-6536	31	70	g.	g.	PROPN
ejpam-6536	31	71	similarly	similarly	ADV
ejpam-6536	31	72	,	,	PUNCT
ejpam-6536	31	73	a	a	DET
ejpam-6536	31	74	γt	γt	NOUN
ejpam-6536	31	75	-	-	ADJ
ejpam-6536	31	76	set	set	ADJ
ejpam-6536	31	77	is	be	AUX
ejpam-6536	31	78	a	a	DET
ejpam-6536	31	79	total	total	ADJ
ejpam-6536	31	80	dominating	dominating	NOUN
ejpam-6536	31	81	set	set	NOUN
ejpam-6536	31	82	of	of	ADP
ejpam-6536	31	83	cardinality	cardinality	NOUN
ejpam-6536	31	84	γt(g	γt(g	NUM
ejpam-6536	31	85	)	)	PUNCT
ejpam-6536	31	86	.	.	PUNCT
ejpam-6536	32	1	the	the	DET
ejpam-6536	32	2	reader	reader	NOUN
ejpam-6536	32	3	is	be	AUX
ejpam-6536	32	4	referred	refer	VERB
ejpam-6536	32	5	to	to	ADP
ejpam-6536	32	6	[	[	X
ejpam-6536	32	7	2–6	2–6	X
ejpam-6536	32	8	]	]	X
ejpam-6536	32	9	for	for	ADP
ejpam-6536	32	10	the	the	DET
ejpam-6536	32	11	history	history	NOUN
ejpam-6536	32	12	,	,	PUNCT
ejpam-6536	32	13	fundamental	fundamental	ADJ
ejpam-6536	32	14	concepts	concept	NOUN
ejpam-6536	32	15	and	and	CCONJ
ejpam-6536	32	16	some	some	PRON
ejpam-6536	32	17	of	of	ADP
ejpam-6536	32	18	the	the	DET
ejpam-6536	32	19	recent	recent	ADJ
ejpam-6536	32	20	developments	development	NOUN
ejpam-6536	32	21	in	in	ADP
ejpam-6536	32	22	domination	domination	NOUN
ejpam-6536	32	23	in	in	ADP
ejpam-6536	32	24	graphs	graph	NOUN
ejpam-6536	32	25	as	as	ADV
ejpam-6536	32	26	well	well	ADV
ejpam-6536	32	27	as	as	ADP
ejpam-6536	32	28	its	its	PRON
ejpam-6536	32	29	various	various	ADJ
ejpam-6536	32	30	applications	application	NOUN
ejpam-6536	32	31	.	.	PUNCT
ejpam-6536	33	1	a	a	DET
ejpam-6536	33	2	set	set	NOUN
ejpam-6536	33	3	s	s	NOUN
ejpam-6536	33	4	⊆	⊆	NUM
ejpam-6536	33	5	v	v	NOUN
ejpam-6536	33	6	(	(	PUNCT
ejpam-6536	33	7	g	g	NOUN
ejpam-6536	33	8	)	)	PUNCT
ejpam-6536	33	9	is	be	AUX
ejpam-6536	33	10	a	a	DET
ejpam-6536	33	11	(	(	PUNCT
ejpam-6536	33	12	1	1	NUM
ejpam-6536	33	13	,	,	PUNCT
ejpam-6536	33	14	2)∗-dominating	2)∗-dominate	VERB
ejpam-6536	33	15	set	set	NOUN
ejpam-6536	33	16	(	(	PUNCT
ejpam-6536	33	17	resp	resp	NOUN
ejpam-6536	33	18	.	.	PUNCT
ejpam-6536	34	1	(	(	PUNCT
ejpam-6536	34	2	1	1	NUM
ejpam-6536	34	3	,	,	PUNCT
ejpam-6536	34	4	2)∗-total	2)∗-total	ADJ
ejpam-6536	34	5	dominating	dominating	NOUN
ejpam-6536	34	6	set	set	NOUN
ejpam-6536	34	7	)	)	PUNCT
ejpam-6536	34	8	of	of	ADP
ejpam-6536	34	9	g	g	PROPN
ejpam-6536	34	10	if	if	SCONJ
ejpam-6536	34	11	it	it	PRON
ejpam-6536	34	12	is	be	AUX
ejpam-6536	34	13	a	a	DET
ejpam-6536	34	14	dominating	dominating	NOUN
ejpam-6536	34	15	(	(	PUNCT
ejpam-6536	34	16	resp	resp	NOUN
ejpam-6536	34	17	.	.	PUNCT
ejpam-6536	35	1	total	total	ADJ
ejpam-6536	35	2	dominating	dominating	NOUN
ejpam-6536	35	3	)	)	PUNCT
ejpam-6536	35	4	set	set	NOUN
ejpam-6536	35	5	of	of	ADP
ejpam-6536	35	6	g	g	PROPN
ejpam-6536	35	7	and	and	CCONJ
ejpam-6536	35	8	for	for	ADP
ejpam-6536	35	9	each	each	DET
ejpam-6536	35	10	x	x	SYM
ejpam-6536	35	11	∈	∈	PROPN
ejpam-6536	35	12	v	v	X
ejpam-6536	35	13	(	(	PUNCT
ejpam-6536	35	14	g)\s	g)\s	NOUN
ejpam-6536	35	15	there	there	PRON
ejpam-6536	35	16	exists	exist	VERB
ejpam-6536	35	17	z	z	PROPN
ejpam-6536	35	18	∈	∈	PROPN
ejpam-6536	35	19	s	s	VERB
ejpam-6536	35	20	such	such	ADJ
ejpam-6536	35	21	that	that	PRON
ejpam-6536	35	22	dg(x	dg(x	NOUN
ejpam-6536	35	23	,	,	PUNCT
ejpam-6536	35	24	z	z	NOUN
ejpam-6536	35	25	)	)	PUNCT
ejpam-6536	35	26	=	=	SYM
ejpam-6536	35	27	2	2	X
ejpam-6536	35	28	.	.	X
ejpam-6536	35	29	the	the	DET
ejpam-6536	35	30	smallest	small	ADJ
ejpam-6536	35	31	cardinality	cardinality	NOUN
ejpam-6536	35	32	of	of	ADP
ejpam-6536	35	33	a	a	DET
ejpam-6536	35	34	(	(	PUNCT
ejpam-6536	35	35	1	1	NUM
ejpam-6536	35	36	,	,	PUNCT
ejpam-6536	35	37	2)∗-dominating	2)∗-dominating	NUM
ejpam-6536	35	38	(	(	PUNCT
ejpam-6536	35	39	resp	resp	NOUN
ejpam-6536	35	40	.	.	PUNCT
ejpam-6536	36	1	(	(	PUNCT
ejpam-6536	36	2	1	1	NUM
ejpam-6536	36	3	,	,	PUNCT
ejpam-6536	36	4	2)∗-total	2)∗-total	ADJ
ejpam-6536	36	5	dominating	dominating	NOUN
ejpam-6536	36	6	)	)	PUNCT
ejpam-6536	36	7	set	set	NOUN
ejpam-6536	36	8	of	of	ADP
ejpam-6536	36	9	g	g	NOUN
ejpam-6536	36	10	,	,	PUNCT
ejpam-6536	36	11	denoted	denote	VERB
ejpam-6536	36	12	by	by	ADP
ejpam-6536	36	13	γ∗	γ∗	NOUN
ejpam-6536	36	14	1,2(g	1,2(g	NUM
ejpam-6536	36	15	)	)	PUNCT
ejpam-6536	36	16	(	(	PUNCT
ejpam-6536	36	17	resp	resp	NOUN
ejpam-6536	36	18	.	.	PUNCT
ejpam-6536	36	19	γ∗t	γ∗t	PROPN
ejpam-6536	36	20	1,2(g	1,2(g	NUM
ejpam-6536	36	21	)	)	PUNCT
ejpam-6536	36	22	)	)	PUNCT
ejpam-6536	36	23	,	,	PUNCT
ejpam-6536	36	24	is	be	AUX
ejpam-6536	36	25	the	the	DET
ejpam-6536	36	26	(	(	PUNCT
ejpam-6536	36	27	1	1	NUM
ejpam-6536	36	28	,	,	PUNCT
ejpam-6536	36	29	2)∗-domination	2)∗-domination	NOUN
ejpam-6536	36	30	number	number	NOUN
ejpam-6536	36	31	(	(	PUNCT
ejpam-6536	36	32	resp	resp	NOUN
ejpam-6536	36	33	.	.	PUNCT
ejpam-6536	37	1	(	(	PUNCT
ejpam-6536	37	2	1	1	NUM
ejpam-6536	37	3	,	,	PUNCT
ejpam-6536	37	4	2)∗-total	2)∗-total	ADJ
ejpam-6536	37	5	domination	domination	NOUN
ejpam-6536	37	6	number	number	NOUN
ejpam-6536	37	7	)	)	PUNCT
ejpam-6536	37	8	of	of	ADP
ejpam-6536	37	9	g.	g.	PROPN
ejpam-6536	37	10	any	any	DET
ejpam-6536	37	11	(	(	PUNCT
ejpam-6536	37	12	1	1	NUM
ejpam-6536	37	13	,	,	PUNCT
ejpam-6536	37	14	2)∗-dominating	2)∗-dominating	NUM
ejpam-6536	37	15	(	(	PUNCT
ejpam-6536	37	16	resp	resp	NOUN
ejpam-6536	37	17	.	.	PUNCT
ejpam-6536	38	1	(	(	PUNCT
ejpam-6536	38	2	1	1	NUM
ejpam-6536	38	3	,	,	PUNCT
ejpam-6536	38	4	2)∗-total	2)∗-total	ADJ
ejpam-6536	38	5	dominating	dominating	NOUN
ejpam-6536	38	6	)	)	PUNCT
ejpam-6536	38	7	set	set	NOUN
ejpam-6536	38	8	of	of	ADP
ejpam-6536	38	9	g	g	PROPN
ejpam-6536	38	10	of	of	ADP
ejpam-6536	38	11	cardinality	cardinality	PROPN
ejpam-6536	38	12	γ∗	γ∗	PROPN
ejpam-6536	38	13	1,2(g	1,2(g	NUM
ejpam-6536	38	14	)	)	PUNCT
ejpam-6536	38	15	(	(	PUNCT
ejpam-6536	38	16	resp	resp	NOUN
ejpam-6536	38	17	.	.	PUNCT
ejpam-6536	38	18	γ∗t	γ∗t	PROPN
ejpam-6536	39	1	1,2(g	1,2(g	NUM
ejpam-6536	39	2	)	)	PUNCT
ejpam-6536	39	3	)	)	PUNCT
ejpam-6536	39	4	is	be	AUX
ejpam-6536	39	5	a	a	DET
ejpam-6536	39	6	γ∗	γ∗	NOUN
ejpam-6536	39	7	1,2	1,2	NUM
ejpam-6536	39	8	-	-	PUNCT
ejpam-6536	39	9	set	set	VERB
ejpam-6536	39	10	(	(	PUNCT
ejpam-6536	39	11	resp	resp	NOUN
ejpam-6536	39	12	.	.	PUNCT
ejpam-6536	40	1	γ∗t	γ∗t	NUM
ejpam-6536	40	2	1,2	1,2	NUM
ejpam-6536	40	3	-	-	PUNCT
ejpam-6536	40	4	set	set	NOUN
ejpam-6536	40	5	)	)	PUNCT
ejpam-6536	40	6	of	of	ADP
ejpam-6536	40	7	g.	g.	PROPN
ejpam-6536	40	8	both	both	PRON
ejpam-6536	40	9	(	(	PUNCT
ejpam-6536	40	10	1	1	NUM
ejpam-6536	40	11	,	,	PUNCT
ejpam-6536	40	12	2)∗-domination	2)∗-domination	NOUN
ejpam-6536	40	13	and	and	CCONJ
ejpam-6536	40	14	(	(	PUNCT
ejpam-6536	40	15	1	1	NUM
ejpam-6536	40	16	,	,	PUNCT
ejpam-6536	40	17	2)∗-total	2)∗-total	ADJ
ejpam-6536	40	18	domination	domination	NOUN
ejpam-6536	40	19	are	be	AUX
ejpam-6536	40	20	introduced	introduce	VERB
ejpam-6536	40	21	and	and	CCONJ
ejpam-6536	40	22	studied	study	VERB
ejpam-6536	40	23	in	in	ADP
ejpam-6536	40	24	[	[	X
ejpam-6536	40	25	7	7	NUM
ejpam-6536	40	26	]	]	PUNCT
ejpam-6536	40	27	.	.	PUNCT
ejpam-6536	41	1	a	a	DET
ejpam-6536	41	2	set	set	NOUN
ejpam-6536	41	3	s	s	NOUN
ejpam-6536	41	4	⊆	⊆	NUM
ejpam-6536	41	5	v	v	NOUN
ejpam-6536	41	6	(	(	PUNCT
ejpam-6536	41	7	g	g	NOUN
ejpam-6536	41	8	)	)	PUNCT
ejpam-6536	41	9	is	be	AUX
ejpam-6536	41	10	a	a	DET
ejpam-6536	41	11	point	point	NOUN
ejpam-6536	41	12	-	-	PUNCT
ejpam-6536	41	13	wise	wise	ADJ
ejpam-6536	41	14	non	non	ADJ
ejpam-6536	41	15	-	-	ADJ
ejpam-6536	41	16	dominating	dominating	ADJ
ejpam-6536	41	17	set	set	NOUN
ejpam-6536	41	18	of	of	ADP
ejpam-6536	41	19	g	g	PROPN
ejpam-6536	41	20	if	if	SCONJ
ejpam-6536	41	21	for	for	ADP
ejpam-6536	41	22	each	each	PRON
ejpam-6536	41	23	v	v	NUM
ejpam-6536	41	24	∈	∈	PROPN
ejpam-6536	41	25	v	v	NOUN
ejpam-6536	41	26	(	(	PUNCT
ejpam-6536	41	27	g	g	NOUN
ejpam-6536	41	28	)	)	PUNCT
ejpam-6536	41	29	\	\	PROPN
ejpam-6536	42	1	s	s	X
ejpam-6536	42	2	,	,	PUNCT
ejpam-6536	42	3	there	there	PRON
ejpam-6536	42	4	exists	exist	VERB
ejpam-6536	42	5	u	u	PROPN
ejpam-6536	42	6	∈	∈	PROPN
ejpam-6536	42	7	s	s	VERB
ejpam-6536	42	8	such	such	ADJ
ejpam-6536	42	9	that	that	DET
ejpam-6536	42	10	v	v	NOUN
ejpam-6536	42	11	/∈	/∈	PUNCT
ejpam-6536	42	12	ng(u	ng(u	NOUN
ejpam-6536	42	13	)	)	PUNCT
ejpam-6536	42	14	.	.	PUNCT
ejpam-6536	43	1	the	the	DET
ejpam-6536	43	2	smallest	small	ADJ
ejpam-6536	43	3	cardinality	cardinality	NOUN
ejpam-6536	43	4	of	of	ADP
ejpam-6536	43	5	a	a	DET
ejpam-6536	43	6	point	point	NOUN
ejpam-6536	43	7	-	-	PUNCT
ejpam-6536	43	8	wise	wise	ADJ
ejpam-6536	43	9	non	non	ADJ
ejpam-6536	43	10	-	-	ADJ
ejpam-6536	43	11	dominating	dominating	ADJ
ejpam-6536	43	12	set	set	NOUN
ejpam-6536	43	13	of	of	ADP
ejpam-6536	43	14	g	g	NOUN
ejpam-6536	43	15	,	,	PUNCT
ejpam-6536	43	16	denoted	denote	VERB
ejpam-6536	43	17	by	by	ADP
ejpam-6536	43	18	pnd(g	pnd(g	PROPN
ejpam-6536	43	19	)	)	PUNCT
ejpam-6536	43	20	,	,	PUNCT
ejpam-6536	43	21	is	be	AUX
ejpam-6536	43	22	called	call	VERB
ejpam-6536	43	23	the	the	DET
ejpam-6536	43	24	point	point	NOUN
ejpam-6536	43	25	-	-	PUNCT
ejpam-6536	43	26	wise	wise	ADJ
ejpam-6536	43	27	non	non	ADJ
ejpam-6536	43	28	-	-	ADJ
ejpam-6536	43	29	domination	domination	ADJ
ejpam-6536	43	30	number	number	NOUN
ejpam-6536	43	31	of	of	ADP
ejpam-6536	43	32	g.	g.	PROPN
ejpam-6536	43	33	a	a	DET
ejpam-6536	43	34	dominating	dominating	NOUN
ejpam-6536	43	35	set	set	NOUN
ejpam-6536	43	36	s	s	PRON
ejpam-6536	43	37	which	which	PRON
ejpam-6536	43	38	is	be	AUX
ejpam-6536	43	39	also	also	ADV
ejpam-6536	43	40	a	a	DET
ejpam-6536	43	41	point	point	NOUN
ejpam-6536	43	42	-	-	PUNCT
ejpam-6536	43	43	wise	wise	ADJ
ejpam-6536	43	44	non	non	ADJ
ejpam-6536	43	45	-	-	ADJ
ejpam-6536	43	46	dominating	dominating	ADJ
ejpam-6536	43	47	set	set	NOUN
ejpam-6536	43	48	of	of	ADP
ejpam-6536	43	49	g	g	PROPN
ejpam-6536	43	50	is	be	AUX
ejpam-6536	43	51	called	call	VERB
ejpam-6536	43	52	a	a	DET
ejpam-6536	43	53	dominating	dominating	NOUN
ejpam-6536	43	54	point	point	NOUN
ejpam-6536	43	55	-	-	PUNCT
ejpam-6536	43	56	wise	wise	ADJ
ejpam-6536	43	57	non	non	ADJ
ejpam-6536	43	58	-	-	ADJ
ejpam-6536	43	59	dominating	dominating	ADJ
ejpam-6536	43	60	set	set	NOUN
ejpam-6536	43	61	of	of	ADP
ejpam-6536	43	62	g.	g.	PROPN
ejpam-6536	43	63	the	the	DET
ejpam-6536	43	64	smallest	small	ADJ
ejpam-6536	43	65	cardinality	cardinality	NOUN
ejpam-6536	43	66	of	of	ADP
ejpam-6536	43	67	a	a	DET
ejpam-6536	43	68	dominating	dominating	NOUN
ejpam-6536	43	69	point	point	NOUN
ejpam-6536	43	70	-	-	PUNCT
ejpam-6536	43	71	wise	wise	ADJ
ejpam-6536	43	72	non	non	ADJ
ejpam-6536	43	73	-	-	ADJ
ejpam-6536	43	74	dominating	dominating	ADJ
ejpam-6536	43	75	set	set	NOUN
ejpam-6536	43	76	of	of	ADP
ejpam-6536	43	77	g	g	NOUN
ejpam-6536	43	78	will	will	AUX
ejpam-6536	43	79	be	be	AUX
ejpam-6536	43	80	denoted	denote	VERB
ejpam-6536	43	81	by	by	ADP
ejpam-6536	43	82	γpnd(g	γpnd(g	PROPN
ejpam-6536	43	83	)	)	PUNCT
ejpam-6536	43	84	.	.	PUNCT
ejpam-6536	44	1	any	any	DET
ejpam-6536	44	2	point	point	NOUN
ejpam-6536	44	3	-	-	PUNCT
ejpam-6536	44	4	wise	wise	ADV
ejpam-6536	44	5	nondominating	nondominate	VERB
ejpam-6536	44	6	(	(	PUNCT
ejpam-6536	44	7	resp	resp	NOUN
ejpam-6536	44	8	.	.	PUNCT
ejpam-6536	45	1	dominating	dominating	NOUN
ejpam-6536	45	2	point	point	NOUN
ejpam-6536	45	3	-	-	PUNCT
ejpam-6536	45	4	wise	wise	ADJ
ejpam-6536	45	5	non	non	ADJ
ejpam-6536	45	6	-	-	ADJ
ejpam-6536	45	7	dominating	dominating	ADJ
ejpam-6536	45	8	)	)	PUNCT
ejpam-6536	45	9	set	set	NOUN
ejpam-6536	45	10	s	s	PRON
ejpam-6536	45	11	of	of	ADP
ejpam-6536	45	12	g	g	NOUN
ejpam-6536	45	13	of	of	ADP
ejpam-6536	45	14	cardinality	cardinality	PROPN
ejpam-6536	45	15	|s|	|s|	PROPN
ejpam-6536	45	16	=	=	SYM
ejpam-6536	45	17	pnd(g	pnd(g	PROPN
ejpam-6536	45	18	)	)	PUNCT
ejpam-6536	45	19	(	(	PUNCT
ejpam-6536	45	20	resp	resp	NOUN
ejpam-6536	45	21	.	.	PUNCT
ejpam-6536	46	1	|s|	|s|	PROPN
ejpam-6536	46	2	=	=	SYM
ejpam-6536	46	3	γpnd(g	γpnd(g	PROPN
ejpam-6536	46	4	)	)	PUNCT
ejpam-6536	46	5	)	)	PUNCT
ejpam-6536	47	1	,	,	PUNCT
ejpam-6536	47	2	is	be	AUX
ejpam-6536	47	3	called	call	VERB
ejpam-6536	47	4	a	a	DET
ejpam-6536	47	5	pnd	pnd	NOUN
ejpam-6536	47	6	-	-	PUNCT
ejpam-6536	47	7	set	set	VERB
ejpam-6536	47	8	(	(	PUNCT
ejpam-6536	47	9	resp	resp	NOUN
ejpam-6536	47	10	.	.	PUNCT
ejpam-6536	48	1	γpnd	γpnd	NOUN
ejpam-6536	48	2	-	-	PUNCT
ejpam-6536	48	3	set	set	NOUN
ejpam-6536	48	4	)	)	PUNCT
ejpam-6536	48	5	of	of	ADP
ejpam-6536	48	6	g.	g.	PROPN
ejpam-6536	48	7	point	point	PROPN
ejpam-6536	48	8	-	-	PUNCT
ejpam-6536	48	9	wise	wise	ADJ
ejpam-6536	48	10	non	non	ADJ
ejpam-6536	48	11	-	-	ADJ
ejpam-6536	48	12	dominating	dominating	ADJ
ejpam-6536	48	13	sets	set	NOUN
ejpam-6536	48	14	and	and	CCONJ
ejpam-6536	48	15	dominating	dominating	NOUN
ejpam-6536	48	16	point	point	NOUN
ejpam-6536	48	17	-	-	PUNCT
ejpam-6536	48	18	wise	wise	ADJ
ejpam-6536	48	19	non	non	ADJ
ejpam-6536	48	20	-	-	ADJ
ejpam-6536	48	21	dominating	dominating	ADJ
ejpam-6536	48	22	sets	set	NOUN
ejpam-6536	48	23	are	be	AUX
ejpam-6536	48	24	discussed	discuss	VERB
ejpam-6536	48	25	in	in	ADP
ejpam-6536	48	26	[	[	X
ejpam-6536	48	27	7	7	NUM
ejpam-6536	48	28	]	]	PUNCT
ejpam-6536	48	29	.	.	PUNCT
ejpam-6536	49	1	let	let	VERB
ejpam-6536	49	2	g	g	PRON
ejpam-6536	49	3	be	be	AUX
ejpam-6536	49	4	a	a	DET
ejpam-6536	49	5	graph	graph	NOUN
ejpam-6536	49	6	without	without	ADP
ejpam-6536	49	7	isolated	isolated	ADJ
ejpam-6536	49	8	vertices	vertex	NOUN
ejpam-6536	49	9	.	.	PUNCT
ejpam-6536	50	1	a	a	DET
ejpam-6536	50	2	subset	subset	NOUN
ejpam-6536	50	3	s	s	VERB
ejpam-6536	50	4	⊆	⊆	NUM
ejpam-6536	50	5	v	v	NOUN
ejpam-6536	50	6	(	(	PUNCT
ejpam-6536	50	7	g	g	NOUN
ejpam-6536	50	8	)	)	PUNCT
ejpam-6536	50	9	is	be	AUX
ejpam-6536	50	10	an	an	DET
ejpam-6536	50	11	inverse	inverse	NOUN
ejpam-6536	50	12	dominating	dominating	NOUN
ejpam-6536	50	13	set	set	NOUN
ejpam-6536	50	14	of	of	ADP
ejpam-6536	50	15	g	g	PROPN
ejpam-6536	50	16	if	if	SCONJ
ejpam-6536	50	17	v	v	X
ejpam-6536	50	18	(	(	PUNCT
ejpam-6536	50	19	g	g	NOUN
ejpam-6536	50	20	)	)	PUNCT
ejpam-6536	50	21	\	\	PUNCT
ejpam-6536	51	1	s	s	PART
ejpam-6536	51	2	contains	contain	VERB
ejpam-6536	51	3	a	a	DET
ejpam-6536	51	4	γ	γ	NOUN
ejpam-6536	51	5	-	-	PUNCT
ejpam-6536	51	6	set	set	NOUN
ejpam-6536	51	7	of	of	ADP
ejpam-6536	51	8	g.	g.	PROPN
ejpam-6536	51	9	a	a	DET
ejpam-6536	51	10	minimum	minimum	ADJ
ejpam-6536	51	11	cardinality	cardinality	NOUN
ejpam-6536	51	12	of	of	ADP
ejpam-6536	51	13	an	an	DET
ejpam-6536	51	14	inverse	inverse	NOUN
ejpam-6536	51	15	dominating	dominating	NOUN
ejpam-6536	51	16	set	set	NOUN
ejpam-6536	51	17	of	of	ADP
ejpam-6536	51	18	g	g	PROPN
ejpam-6536	51	19	is	be	AUX
ejpam-6536	51	20	the	the	DET
ejpam-6536	51	21	inverse	inverse	ADJ
ejpam-6536	51	22	domination	domination	NOUN
ejpam-6536	51	23	number	number	NOUN
ejpam-6536	51	24	of	of	ADP
ejpam-6536	51	25	g	g	NOUN
ejpam-6536	51	26	,	,	PUNCT
ejpam-6536	51	27	and	and	CCONJ
ejpam-6536	51	28	is	be	AUX
ejpam-6536	51	29	denoted	denote	VERB
ejpam-6536	51	30	by	by	ADP
ejpam-6536	51	31	γ̃(g	γ̃(g	PROPN
ejpam-6536	51	32	)	)	PUNCT
ejpam-6536	51	33	.	.	PUNCT
ejpam-6536	52	1	motivated	motivate	VERB
ejpam-6536	52	2	by	by	ADP
ejpam-6536	52	3	c.	c.	PROPN
ejpam-6536	52	4	berge[2	berge[2	PROPN
ejpam-6536	52	5	]	]	PUNCT
ejpam-6536	52	6	,	,	PUNCT
ejpam-6536	52	7	inverse	inverse	ADJ
ejpam-6536	52	8	domination	domination	NOUN
ejpam-6536	52	9	of	of	ADP
ejpam-6536	52	10	a	a	DET
ejpam-6536	52	11	graph	graph	NOUN
ejpam-6536	52	12	was	be	AUX
ejpam-6536	52	13	introduced	introduce	VERB
ejpam-6536	52	14	by	by	ADP
ejpam-6536	52	15	v.r	v.r	PROPN
ejpam-6536	52	16	.	.	PROPN
ejpam-6536	52	17	kulli	kulli	PROPN
ejpam-6536	52	18	and	and	CCONJ
ejpam-6536	52	19	s.c	s.c	PROPN
ejpam-6536	52	20	.	.	PROPN
ejpam-6536	52	21	sigarkanti	sigarkanti	NOUN
ejpam-6536	53	1	[	[	X
ejpam-6536	53	2	8	8	NUM
ejpam-6536	53	3	]	]	PUNCT
ejpam-6536	53	4	in	in	ADP
ejpam-6536	53	5	1991	1991	NUM
ejpam-6536	53	6	,	,	PUNCT
ejpam-6536	54	1	and	and	CCONJ
ejpam-6536	55	1	studied	study	VERB
ejpam-6536	55	2	further	far	ADV
ejpam-6536	55	3	in	in	ADP
ejpam-6536	55	4	[	[	X
ejpam-6536	55	5	9–12	9–12	NOUN
ejpam-6536	55	6	]	]	PUNCT
ejpam-6536	55	7	.	.	PUNCT
ejpam-6536	56	1	it	it	PRON
ejpam-6536	56	2	may	may	AUX
ejpam-6536	56	3	be	be	AUX
ejpam-6536	56	4	noted	note	VERB
ejpam-6536	56	5	that	that	SCONJ
ejpam-6536	56	6	p.g	p.g	PROPN
ejpam-6536	56	7	.	.	PROPN
ejpam-6536	56	8	bhat	bhat	PROPN
ejpam-6536	56	9	and	and	CCONJ
ejpam-6536	56	10	s.r	s.r	PROPN
ejpam-6536	56	11	.	.	PROPN
ejpam-6536	56	12	bhat	bhat	PROPN
ejpam-6536	56	13	in	in	ADP
ejpam-6536	56	14	[	[	X
ejpam-6536	56	15	9	9	NUM
ejpam-6536	56	16	]	]	PUNCT
ejpam-6536	56	17	made	make	VERB
ejpam-6536	56	18	mention	mention	NOUN
ejpam-6536	56	19	of	of	ADP
ejpam-6536	56	20	its	its	PRON
ejpam-6536	56	21	application	application	NOUN
ejpam-6536	56	22	in	in	ADP
ejpam-6536	56	23	an	an	DET
ejpam-6536	56	24	information	information	NOUN
ejpam-6536	56	25	retrieval	retrieval	NOUN
ejpam-6536	56	26	system	system	NOUN
ejpam-6536	56	27	.	.	PUNCT
ejpam-6536	57	1	for	for	ADP
ejpam-6536	57	2	a	a	DET
ejpam-6536	57	3	graph	graph	NOUN
ejpam-6536	57	4	g	g	NOUN
ejpam-6536	57	5	with	with	ADP
ejpam-6536	57	6	no	no	DET
ejpam-6536	57	7	isolated	isolated	ADJ
ejpam-6536	57	8	vertex	vertex	NOUN
ejpam-6536	57	9	,	,	PUNCT
ejpam-6536	57	10	any	any	DET
ejpam-6536	57	11	pair	pair	NOUN
ejpam-6536	57	12	of	of	ADP
ejpam-6536	57	13	subsets	subset	NOUN
ejpam-6536	57	14	s	s	PROPN
ejpam-6536	57	15	and	and	CCONJ
ejpam-6536	57	16	d	d	PROPN
ejpam-6536	57	17	of	of	ADP
ejpam-6536	57	18	v	v	NOUN
ejpam-6536	57	19	(	(	PUNCT
ejpam-6536	57	20	g	g	NOUN
ejpam-6536	57	21	)	)	PUNCT
ejpam-6536	57	22	is	be	AUX
ejpam-6536	57	23	called	call	VERB
ejpam-6536	57	24	dd	dd	NOUN
ejpam-6536	57	25	-	-	PUNCT
ejpam-6536	57	26	pair	pair	NOUN
ejpam-6536	57	27	if	if	SCONJ
ejpam-6536	57	28	s	s	PRON
ejpam-6536	57	29	and	and	CCONJ
ejpam-6536	57	30	d	d	NOUN
ejpam-6536	57	31	are	be	AUX
ejpam-6536	57	32	disjoint	disjoint	ADJ
ejpam-6536	57	33	dominating	dominating	NOUN
ejpam-6536	57	34	sets	set	NOUN
ejpam-6536	57	35	of	of	ADP
ejpam-6536	57	36	g.	g.	PROPN
ejpam-6536	57	37	the	the	DET
ejpam-6536	57	38	symbol	symbol	NOUN
ejpam-6536	57	39	γγ(g	γγ(g	NOUN
ejpam-6536	57	40	)	)	PUNCT
ejpam-6536	57	41	is	be	AUX
ejpam-6536	57	42	the	the	DET
ejpam-6536	57	43	smallest	small	ADJ
ejpam-6536	57	44	sum	sum	NOUN
ejpam-6536	57	45	|s|	|s|	NOUN
ejpam-6536	57	46	+	+	CCONJ
ejpam-6536	57	47	|d|	|d|	PROPN
ejpam-6536	57	48	for	for	ADP
ejpam-6536	57	49	all	all	DET
ejpam-6536	57	50	dd	dd	NOUN
ejpam-6536	57	51	-	-	PUNCT
ejpam-6536	57	52	pairs	pair	NOUN
ejpam-6536	57	53	(	(	PUNCT
ejpam-6536	57	54	s	s	X
ejpam-6536	57	55	,	,	PUNCT
ejpam-6536	57	56	d	d	NOUN
ejpam-6536	57	57	)	)	PUNCT
ejpam-6536	57	58	of	of	ADP
ejpam-6536	57	59	g.	g.	PROPN
ejpam-6536	57	60	since	since	SCONJ
ejpam-6536	57	61	an	an	DET
ejpam-6536	57	62	inverse	inverse	NOUN
ejpam-6536	57	63	dominating	dominating	NOUN
ejpam-6536	57	64	set	set	VERB
ejpam-6536	57	65	together	together	ADV
ejpam-6536	57	66	with	with	ADP
ejpam-6536	57	67	its	its	PRON
ejpam-6536	57	68	associated	associated	ADJ
ejpam-6536	57	69	γ	γ	X
ejpam-6536	57	70	-	-	PUNCT
ejpam-6536	57	71	set	set	ADJ
ejpam-6536	57	72	constitute	constitute	VERB
ejpam-6536	57	73	a	a	DET
ejpam-6536	57	74	dd	dd	NOUN
ejpam-6536	57	75	-	-	PUNCT
ejpam-6536	57	76	pair	pair	NOUN
ejpam-6536	57	77	,	,	PUNCT
ejpam-6536	57	78	γγ(g	γγ(g	NOUN
ejpam-6536	57	79	)	)	PUNCT
ejpam-6536	57	80	≤	≤	PROPN
ejpam-6536	57	81	γ(g	γ(g	PROPN
ejpam-6536	57	82	)	)	PUNCT
ejpam-6536	58	1	+	+	PUNCT
ejpam-6536	58	2	γ̃(g	γ̃(g	NOUN
ejpam-6536	58	3	)	)	PUNCT
ejpam-6536	58	4	.	.	PUNCT
ejpam-6536	59	1	disjoint	disjoint	NOUN
ejpam-6536	59	2	dominating	dominating	NOUN
ejpam-6536	59	3	sets	set	NOUN
ejpam-6536	59	4	v.	v.	ADP
ejpam-6536	59	5	a	a	DET
ejpam-6536	59	6	besana	besana	PROPN
ejpam-6536	59	7	,	,	PUNCT
ejpam-6536	59	8	f.	f.	PROPN
ejpam-6536	59	9	jamil	jamil	PROPN
ejpam-6536	59	10	,	,	PUNCT
ejpam-6536	59	11	s.	s.	PROPN
ejpam-6536	59	12	canoy	canoy	PROPN
ejpam-6536	59	13	jr	jr	PROPN
ejpam-6536	59	14	.	.	PROPN
ejpam-6536	59	15	/	/	SYM
ejpam-6536	59	16	eur	eur	PROPN
ejpam-6536	59	17	.	.	PUNCT
ejpam-6536	60	1	j.	j.	PROPN
ejpam-6536	60	2	pure	pure	PROPN
ejpam-6536	60	3	appl	appl	PROPN
ejpam-6536	60	4	.	.	PROPN
ejpam-6536	60	5	math	math	PROPN
ejpam-6536	60	6	,	,	PUNCT
ejpam-6536	60	7	18	18	NUM
ejpam-6536	60	8	(	(	PUNCT
ejpam-6536	60	9	3	3	NUM
ejpam-6536	60	10	)	)	PUNCT
ejpam-6536	60	11	(	(	PUNCT
ejpam-6536	60	12	2025	2025	NUM
ejpam-6536	60	13	)	)	PUNCT
ejpam-6536	60	14	,	,	PUNCT
ejpam-6536	60	15	6536	6536	NUM
ejpam-6536	60	16	3	3	NUM
ejpam-6536	60	17	of	of	ADP
ejpam-6536	60	18	17	17	NUM
ejpam-6536	60	19	are	be	AUX
ejpam-6536	60	20	studied	study	VERB
ejpam-6536	60	21	extensively	extensively	ADV
ejpam-6536	60	22	in	in	ADP
ejpam-6536	60	23	[	[	X
ejpam-6536	60	24	11–13	11–13	NUM
ejpam-6536	60	25	]	]	X
ejpam-6536	60	26	.	.	PUNCT
ejpam-6536	61	1	a	a	DET
ejpam-6536	61	2	subset	subset	NOUN
ejpam-6536	61	3	s	s	VERB
ejpam-6536	61	4	⊆	⊆	NUM
ejpam-6536	61	5	v	v	NOUN
ejpam-6536	61	6	(	(	PUNCT
ejpam-6536	61	7	g	g	NOUN
ejpam-6536	61	8	)	)	PUNCT
ejpam-6536	61	9	of	of	ADP
ejpam-6536	61	10	a	a	DET
ejpam-6536	61	11	connected	connected	ADJ
ejpam-6536	61	12	graph	graph	NOUN
ejpam-6536	61	13	g	g	PROPN
ejpam-6536	61	14	is	be	AUX
ejpam-6536	61	15	a	a	DET
ejpam-6536	61	16	hop	hop	NOUN
ejpam-6536	61	17	dominating	dominating	NOUN
ejpam-6536	61	18	set	set	NOUN
ejpam-6536	61	19	(	(	PUNCT
ejpam-6536	61	20	resp	resp	NOUN
ejpam-6536	61	21	.	.	PUNCT
ejpam-6536	62	1	total	total	ADJ
ejpam-6536	62	2	hop	hop	NOUN
ejpam-6536	62	3	dominating	dominating	NOUN
ejpam-6536	62	4	set	set	NOUN
ejpam-6536	62	5	)	)	PUNCT
ejpam-6536	62	6	of	of	ADP
ejpam-6536	62	7	g	g	PROPN
ejpam-6536	62	8	if	if	SCONJ
ejpam-6536	62	9	for	for	ADP
ejpam-6536	62	10	each	each	PRON
ejpam-6536	62	11	v	v	NUM
ejpam-6536	62	12	∈	∈	PROPN
ejpam-6536	62	13	v	v	NOUN
ejpam-6536	62	14	(	(	PUNCT
ejpam-6536	62	15	g	g	NOUN
ejpam-6536	62	16	)	)	PUNCT
ejpam-6536	62	17	\	\	PROPN
ejpam-6536	63	1	s	s	PART
ejpam-6536	63	2	(	(	PUNCT
ejpam-6536	63	3	resp	resp	NOUN
ejpam-6536	63	4	.	.	PUNCT
ejpam-6536	64	1	v	v	ADP
ejpam-6536	64	2	∈	∈	PROPN
ejpam-6536	64	3	v	v	NOUN
ejpam-6536	64	4	(	(	PUNCT
ejpam-6536	64	5	g	g	NOUN
ejpam-6536	64	6	)	)	PUNCT
ejpam-6536	64	7	)	)	PUNCT
ejpam-6536	65	1	,	,	PUNCT
ejpam-6536	65	2	there	there	PRON
ejpam-6536	65	3	exists	exist	VERB
ejpam-6536	65	4	u	u	PROPN
ejpam-6536	65	5	∈	∈	PROPN
ejpam-6536	65	6	s	s	X
ejpam-6536	65	7	for	for	ADP
ejpam-6536	65	8	which	which	PRON
ejpam-6536	65	9	dg(u	dg(u	ADJ
ejpam-6536	65	10	,	,	PUNCT
ejpam-6536	65	11	v	v	NOUN
ejpam-6536	65	12	)	)	PUNCT
ejpam-6536	65	13	=	=	SYM
ejpam-6536	65	14	2	2	X
ejpam-6536	65	15	.	.	PUNCT
ejpam-6536	65	16	the	the	DET
ejpam-6536	65	17	minimum	minimum	ADJ
ejpam-6536	65	18	cardinality	cardinality	NOUN
ejpam-6536	65	19	of	of	ADP
ejpam-6536	65	20	a	a	DET
ejpam-6536	65	21	hop	hop	NOUN
ejpam-6536	65	22	dominating	dominating	NOUN
ejpam-6536	65	23	set	set	NOUN
ejpam-6536	65	24	(	(	PUNCT
ejpam-6536	65	25	resp	resp	NOUN
ejpam-6536	65	26	.	.	PUNCT
ejpam-6536	66	1	total	total	ADJ
ejpam-6536	66	2	hop	hop	NOUN
ejpam-6536	66	3	dominating	dominating	NOUN
ejpam-6536	66	4	set	set	NOUN
ejpam-6536	66	5	)	)	PUNCT
ejpam-6536	66	6	is	be	AUX
ejpam-6536	66	7	called	call	VERB
ejpam-6536	66	8	the	the	DET
ejpam-6536	66	9	hop	hop	NOUN
ejpam-6536	66	10	domination	domination	NOUN
ejpam-6536	66	11	number	number	NOUN
ejpam-6536	66	12	(	(	PUNCT
ejpam-6536	66	13	resp	resp	NOUN
ejpam-6536	66	14	.	.	PUNCT
ejpam-6536	67	1	total	total	ADJ
ejpam-6536	67	2	hop	hop	PROPN
ejpam-6536	67	3	domination	domination	NOUN
ejpam-6536	67	4	number	number	NOUN
ejpam-6536	67	5	)	)	PUNCT
ejpam-6536	67	6	of	of	ADP
ejpam-6536	67	7	g	g	NOUN
ejpam-6536	67	8	,	,	PUNCT
ejpam-6536	67	9	and	and	CCONJ
ejpam-6536	67	10	is	be	AUX
ejpam-6536	67	11	denoted	denote	VERB
ejpam-6536	67	12	by	by	ADP
ejpam-6536	67	13	γh(g	γh(g	NOUN
ejpam-6536	67	14	)	)	PUNCT
ejpam-6536	67	15	(	(	PUNCT
ejpam-6536	67	16	resp	resp	NOUN
ejpam-6536	67	17	.	.	PUNCT
ejpam-6536	67	18	γth(g	γth(g	NOUN
ejpam-6536	67	19	)	)	PUNCT
ejpam-6536	67	20	)	)	PUNCT
ejpam-6536	67	21	.	.	PUNCT
ejpam-6536	68	1	any	any	DET
ejpam-6536	68	2	hop	hop	NOUN
ejpam-6536	68	3	dominating	dominating	NOUN
ejpam-6536	68	4	set	set	NOUN
ejpam-6536	68	5	(	(	PUNCT
ejpam-6536	68	6	resp	resp	NOUN
ejpam-6536	68	7	.	.	PUNCT
ejpam-6536	69	1	total	total	ADJ
ejpam-6536	69	2	hop	hop	NOUN
ejpam-6536	69	3	dominating	dominating	NOUN
ejpam-6536	69	4	set	set	NOUN
ejpam-6536	69	5	)	)	PUNCT
ejpam-6536	69	6	of	of	ADP
ejpam-6536	69	7	cardinality	cardinality	NOUN
ejpam-6536	69	8	γh(g	γh(g	NOUN
ejpam-6536	69	9	)	)	PUNCT
ejpam-6536	69	10	(	(	PUNCT
ejpam-6536	69	11	resp	resp	NOUN
ejpam-6536	69	12	.	.	PUNCT
ejpam-6536	69	13	γth(g	γth(g	NOUN
ejpam-6536	69	14	)	)	PUNCT
ejpam-6536	69	15	)	)	PUNCT
ejpam-6536	69	16	is	be	AUX
ejpam-6536	69	17	called	call	VERB
ejpam-6536	69	18	γh	γh	ADV
ejpam-6536	69	19	-	-	PUNCT
ejpam-6536	69	20	set	set	VERB
ejpam-6536	69	21	(	(	PUNCT
ejpam-6536	69	22	resp	resp	NOUN
ejpam-6536	69	23	.	.	PUNCT
ejpam-6536	70	1	γth	γth	ADJ
ejpam-6536	70	2	-	-	PUNCT
ejpam-6536	70	3	set	set	NOUN
ejpam-6536	70	4	)	)	PUNCT
ejpam-6536	70	5	of	of	ADP
ejpam-6536	70	6	g.	g.	PROPN
ejpam-6536	70	7	using	use	VERB
ejpam-6536	70	8	the	the	DET
ejpam-6536	70	9	symbol	symbol	NOUN
ejpam-6536	70	10	hd(g	hd(g	NOUN
ejpam-6536	70	11	)	)	PUNCT
ejpam-6536	71	1	to	to	PART
ejpam-6536	71	2	denote	denote	VERB
ejpam-6536	71	3	the	the	DET
ejpam-6536	71	4	family	family	NOUN
ejpam-6536	71	5	of	of	ADP
ejpam-6536	71	6	all	all	DET
ejpam-6536	71	7	hop	hop	NOUN
ejpam-6536	71	8	dominating	dominating	NOUN
ejpam-6536	71	9	sets	set	NOUN
ejpam-6536	71	10	of	of	ADP
ejpam-6536	71	11	g	g	NOUN
ejpam-6536	71	12	,	,	PUNCT
ejpam-6536	71	13	more	more	ADV
ejpam-6536	71	14	precisely	precisely	ADV
ejpam-6536	71	15	,	,	PUNCT
ejpam-6536	71	16	γh(g	γh(g	NOUN
ejpam-6536	71	17	)	)	PUNCT
ejpam-6536	71	18	=	=	NOUN
ejpam-6536	71	19	min{|s|	min{|s|	NOUN
ejpam-6536	71	20	:	:	PUNCT
ejpam-6536	72	1	s	s	VERB
ejpam-6536	72	2	∈	∈	NOUN
ejpam-6536	72	3	hd(g	hd(g	NOUN
ejpam-6536	72	4	)	)	PUNCT
ejpam-6536	72	5	}	}	PUNCT
ejpam-6536	72	6	.	.	PUNCT
ejpam-6536	73	1	hop	hop	PROPN
ejpam-6536	73	2	domination	domination	NOUN
ejpam-6536	73	3	was	be	AUX
ejpam-6536	73	4	introduced	introduce	VERB
ejpam-6536	73	5	by	by	ADP
ejpam-6536	73	6	c.	c.	PROPN
ejpam-6536	73	7	natarajan	natarajan	PROPN
ejpam-6536	73	8	c	c	PROPN
ejpam-6536	73	9	and	and	CCONJ
ejpam-6536	73	10	s.k	s.k	PROPN
ejpam-6536	73	11	.	.	PROPN
ejpam-6536	73	12	ayyaswamy	ayyaswamy	PROPN
ejpam-6536	74	1	[	[	X
ejpam-6536	74	2	14	14	NUM
ejpam-6536	74	3	]	]	PUNCT
ejpam-6536	74	4	in	in	ADP
ejpam-6536	74	5	2015	2015	NUM
ejpam-6536	74	6	,	,	PUNCT
ejpam-6536	74	7	and	and	CCONJ
ejpam-6536	74	8	is	be	AUX
ejpam-6536	74	9	investigated	investigate	VERB
ejpam-6536	74	10	further	far	ADV
ejpam-6536	74	11	in	in	ADP
ejpam-6536	74	12	[	[	X
ejpam-6536	74	13	7	7	NUM
ejpam-6536	74	14	,	,	PUNCT
ejpam-6536	74	15	15–19	15–19	PROPN
ejpam-6536	74	16	]	]	PUNCT
ejpam-6536	74	17	.	.	PUNCT
ejpam-6536	75	1	for	for	ADP
ejpam-6536	75	2	a	a	DET
ejpam-6536	75	3	vertex	vertex	NOUN
ejpam-6536	75	4	v	v	NOUN
ejpam-6536	75	5	of	of	ADP
ejpam-6536	75	6	a	a	DET
ejpam-6536	75	7	connected	connected	ADJ
ejpam-6536	75	8	graph	graph	NOUN
ejpam-6536	75	9	g	g	NOUN
ejpam-6536	75	10	,	,	PUNCT
ejpam-6536	75	11	ng(v	ng(v	PUNCT
ejpam-6536	75	12	,	,	PUNCT
ejpam-6536	75	13	2	2	X
ejpam-6536	75	14	)	)	PUNCT
ejpam-6536	75	15	=	=	PRON
ejpam-6536	75	16	{	{	PUNCT
ejpam-6536	75	17	u	u	NOUN
ejpam-6536	75	18	∈	∈	PROPN
ejpam-6536	75	19	v	v	NOUN
ejpam-6536	75	20	(	(	PUNCT
ejpam-6536	75	21	g	g	NOUN
ejpam-6536	75	22	)	)	PUNCT
ejpam-6536	75	23	:	:	PUNCT
ejpam-6536	75	24	dg(u	dg(u	X
ejpam-6536	75	25	,	,	PUNCT
ejpam-6536	75	26	v	v	NOUN
ejpam-6536	75	27	)	)	PUNCT
ejpam-6536	75	28	=	=	SYM
ejpam-6536	75	29	2	2	NUM
ejpam-6536	75	30	}	}	PUNCT
ejpam-6536	75	31	,	,	PUNCT
ejpam-6536	75	32	and	and	CCONJ
ejpam-6536	75	33	for	for	ADP
ejpam-6536	75	34	s	s	PROPN
ejpam-6536	75	35	⊆	⊆	NUM
ejpam-6536	75	36	v	v	NOUN
ejpam-6536	75	37	(	(	PUNCT
ejpam-6536	75	38	g	g	NOUN
ejpam-6536	75	39	)	)	PUNCT
ejpam-6536	75	40	,	,	PUNCT
ejpam-6536	75	41	ng(s	ng(s	CCONJ
ejpam-6536	75	42	,	,	PUNCT
ejpam-6536	75	43	2	2	X
ejpam-6536	75	44	)	)	PUNCT
ejpam-6536	75	45	=	=	SYM
ejpam-6536	75	46	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-6536	75	47	,	,	PUNCT
ejpam-6536	75	48	2	2	NUM
ejpam-6536	75	49	)	)	PUNCT
ejpam-6536	75	50	and	and	CCONJ
ejpam-6536	75	51	ng[s	ng[s	PROPN
ejpam-6536	75	52	,	,	PUNCT
ejpam-6536	75	53	2	2	NUM
ejpam-6536	75	54	]	]	PUNCT
ejpam-6536	75	55	=	=	PUNCT
ejpam-6536	75	56	ng(s	ng(s	NOUN
ejpam-6536	75	57	,	,	PUNCT
ejpam-6536	75	58	2	2	X
ejpam-6536	75	59	)	)	PUNCT
ejpam-6536	75	60	∪	∪	ADP
ejpam-6536	75	61	s.	s.	PROPN
ejpam-6536	75	62	precisely	precisely	ADV
ejpam-6536	75	63	,	,	PUNCT
ejpam-6536	75	64	s	s	VERB
ejpam-6536	75	65	is	be	AUX
ejpam-6536	75	66	a	a	DET
ejpam-6536	75	67	hop	hop	NOUN
ejpam-6536	75	68	dominating	dominating	NOUN
ejpam-6536	75	69	set	set	NOUN
ejpam-6536	75	70	(	(	PUNCT
ejpam-6536	75	71	resp	resp	NOUN
ejpam-6536	75	72	.	.	PUNCT
ejpam-6536	76	1	total	total	ADJ
ejpam-6536	76	2	hop	hop	NOUN
ejpam-6536	76	3	dominating	dominating	NOUN
ejpam-6536	76	4	set	set	NOUN
ejpam-6536	76	5	)	)	PUNCT
ejpam-6536	77	1	if	if	SCONJ
ejpam-6536	77	2	and	and	CCONJ
ejpam-6536	77	3	only	only	ADV
ejpam-6536	77	4	if	if	SCONJ
ejpam-6536	77	5	ng[s	ng[	NOUN
ejpam-6536	77	6	,	,	PUNCT
ejpam-6536	77	7	2	2	NUM
ejpam-6536	77	8	]	]	PUNCT
ejpam-6536	77	9	=	=	SYM
ejpam-6536	77	10	v	v	X
ejpam-6536	77	11	(	(	PUNCT
ejpam-6536	77	12	g	g	NOUN
ejpam-6536	77	13	)	)	PUNCT
ejpam-6536	77	14	(	(	PUNCT
ejpam-6536	77	15	resp	resp	NOUN
ejpam-6536	77	16	.	.	PUNCT
ejpam-6536	77	17	ng(s	ng(s	PROPN
ejpam-6536	77	18	,	,	PUNCT
ejpam-6536	77	19	2	2	X
ejpam-6536	77	20	)	)	PUNCT
ejpam-6536	77	21	=	=	NOUN
ejpam-6536	77	22	v	v	NOUN
ejpam-6536	77	23	(	(	PUNCT
ejpam-6536	77	24	g	g	NOUN
ejpam-6536	77	25	)	)	PUNCT
ejpam-6536	77	26	)	)	PUNCT
ejpam-6536	77	27	.	.	PUNCT
ejpam-6536	78	1	the	the	DET
ejpam-6536	78	2	relevance	relevance	NOUN
ejpam-6536	78	3	of	of	ADP
ejpam-6536	78	4	hop	hop	NOUN
ejpam-6536	78	5	domination	domination	NOUN
ejpam-6536	78	6	is	be	AUX
ejpam-6536	78	7	very	very	ADV
ejpam-6536	78	8	well	well	ADV
ejpam-6536	78	9	illustrated	illustrate	VERB
ejpam-6536	78	10	by	by	ADP
ejpam-6536	78	11	the	the	DET
ejpam-6536	78	12	relatively	relatively	ADV
ejpam-6536	78	13	well	well	ADV
ejpam-6536	78	14	-	-	PUNCT
ejpam-6536	78	15	known	know	VERB
ejpam-6536	78	16	application	application	NOUN
ejpam-6536	78	17	cited	cite	VERB
ejpam-6536	78	18	in	in	ADP
ejpam-6536	78	19	[	[	X
ejpam-6536	78	20	20	20	NUM
ejpam-6536	78	21	]	]	PUNCT
ejpam-6536	78	22	which	which	PRON
ejpam-6536	78	23	,	,	PUNCT
ejpam-6536	78	24	for	for	ADP
ejpam-6536	78	25	our	our	PRON
ejpam-6536	78	26	purpose	purpose	NOUN
ejpam-6536	78	27	,	,	PUNCT
ejpam-6536	78	28	can	can	AUX
ejpam-6536	78	29	be	be	AUX
ejpam-6536	78	30	rephrased	rephrase	VERB
ejpam-6536	78	31	as	as	SCONJ
ejpam-6536	78	32	follows	follow	VERB
ejpam-6536	78	33	:	:	PUNCT
ejpam-6536	78	34	a	a	DET
ejpam-6536	78	35	factory	factory	NOUN
ejpam-6536	78	36	wants	want	VERB
ejpam-6536	78	37	to	to	PART
ejpam-6536	78	38	set	set	VERB
ejpam-6536	78	39	up	up	ADP
ejpam-6536	78	40	a	a	DET
ejpam-6536	78	41	quality	quality	NOUN
ejpam-6536	78	42	assurance	assurance	NOUN
ejpam-6536	78	43	team	team	NOUN
ejpam-6536	78	44	where	where	SCONJ
ejpam-6536	78	45	some	some	DET
ejpam-6536	78	46	employees	employee	NOUN
ejpam-6536	78	47	evaluate	evaluate	VERB
ejpam-6536	78	48	their	their	PRON
ejpam-6536	78	49	co	co	NOUN
ejpam-6536	78	50	-	-	NOUN
ejpam-6536	78	51	workers	worker	NOUN
ejpam-6536	78	52	.	.	PUNCT
ejpam-6536	79	1	to	to	PART
ejpam-6536	79	2	keep	keep	VERB
ejpam-6536	79	3	costs	cost	NOUN
ejpam-6536	79	4	low	low	ADJ
ejpam-6536	79	5	and	and	CCONJ
ejpam-6536	79	6	evaluators	evaluator	NOUN
ejpam-6536	79	7	anonymous	anonymous	ADJ
ejpam-6536	79	8	,	,	PUNCT
ejpam-6536	79	9	the	the	DET
ejpam-6536	79	10	number	number	NOUN
ejpam-6536	79	11	of	of	ADP
ejpam-6536	79	12	evaluators	evaluator	NOUN
ejpam-6536	79	13	is	be	AUX
ejpam-6536	79	14	kept	keep	VERB
ejpam-6536	79	15	as	as	ADV
ejpam-6536	79	16	small	small	ADJ
ejpam-6536	79	17	as	as	ADP
ejpam-6536	79	18	possible	possible	ADJ
ejpam-6536	79	19	and	and	CCONJ
ejpam-6536	79	20	evaluators	evaluator	NOUN
ejpam-6536	79	21	should	should	AUX
ejpam-6536	79	22	not	not	PART
ejpam-6536	79	23	be	be	AUX
ejpam-6536	79	24	direct	direct	ADJ
ejpam-6536	79	25	friends	friend	NOUN
ejpam-6536	79	26	or	or	CCONJ
ejpam-6536	79	27	enemies	enemy	NOUN
ejpam-6536	79	28	of	of	ADP
ejpam-6536	79	29	the	the	DET
ejpam-6536	79	30	workers	worker	NOUN
ejpam-6536	79	31	they	they	PRON
ejpam-6536	79	32	assess	assess	VERB
ejpam-6536	79	33	to	to	PART
ejpam-6536	79	34	avoid	avoid	VERB
ejpam-6536	79	35	bias	bias	NOUN
ejpam-6536	79	36	.	.	PUNCT
ejpam-6536	80	1	a	a	DET
ejpam-6536	80	2	social	social	ADJ
ejpam-6536	80	3	network	network	NOUN
ejpam-6536	80	4	can	can	AUX
ejpam-6536	80	5	be	be	AUX
ejpam-6536	80	6	modelled	model	VERB
ejpam-6536	80	7	by	by	ADP
ejpam-6536	80	8	a	a	DET
ejpam-6536	80	9	graph	graph	NOUN
ejpam-6536	80	10	g	g	NOUN
ejpam-6536	80	11	with	with	ADP
ejpam-6536	80	12	vertices	vertex	NOUN
ejpam-6536	80	13	representing	represent	VERB
ejpam-6536	80	14	the	the	DET
ejpam-6536	80	15	workers	worker	NOUN
ejpam-6536	80	16	where	where	SCONJ
ejpam-6536	80	17	two	two	NUM
ejpam-6536	80	18	workers	worker	NOUN
ejpam-6536	80	19	are	be	AUX
ejpam-6536	80	20	adjacent	adjacent	ADJ
ejpam-6536	80	21	in	in	ADP
ejpam-6536	80	22	g	g	PROPN
ejpam-6536	80	23	whenever	whenever	SCONJ
ejpam-6536	80	24	they	they	PRON
ejpam-6536	80	25	are	be	AUX
ejpam-6536	80	26	either	either	CCONJ
ejpam-6536	80	27	friends	friend	NOUN
ejpam-6536	80	28	or	or	CCONJ
ejpam-6536	80	29	enemies	enemy	NOUN
ejpam-6536	80	30	of	of	ADP
ejpam-6536	80	31	each	each	DET
ejpam-6536	80	32	other	other	ADJ
ejpam-6536	80	33	.	.	PUNCT
ejpam-6536	81	1	in	in	ADP
ejpam-6536	81	2	this	this	DET
ejpam-6536	81	3	graph	graph	NOUN
ejpam-6536	81	4	,	,	PUNCT
ejpam-6536	81	5	evaluators	evaluator	NOUN
ejpam-6536	81	6	are	be	AUX
ejpam-6536	81	7	not	not	PART
ejpam-6536	81	8	connected	connect	VERB
ejpam-6536	81	9	to	to	ADP
ejpam-6536	81	10	the	the	DET
ejpam-6536	81	11	people	people	NOUN
ejpam-6536	81	12	they	they	PRON
ejpam-6536	81	13	evaluate	evaluate	VERB
ejpam-6536	81	14	,	,	PUNCT
ejpam-6536	81	15	but	but	CCONJ
ejpam-6536	81	16	instead	instead	ADV
ejpam-6536	81	17	are	be	AUX
ejpam-6536	81	18	connected	connect	VERB
ejpam-6536	81	19	to	to	ADP
ejpam-6536	81	20	the	the	DET
ejpam-6536	81	21	friends	friend	NOUN
ejpam-6536	81	22	or	or	CCONJ
ejpam-6536	81	23	enemies	enemy	NOUN
ejpam-6536	81	24	of	of	ADP
ejpam-6536	81	25	those	those	DET
ejpam-6536	81	26	people	people	NOUN
ejpam-6536	81	27	.	.	PUNCT
ejpam-6536	82	1	in	in	ADP
ejpam-6536	82	2	hop	hop	PROPN
ejpam-6536	82	3	domination	domination	NOUN
ejpam-6536	82	4	,	,	PUNCT
ejpam-6536	82	5	every	every	DET
ejpam-6536	82	6	worker	worker	NOUN
ejpam-6536	82	7	is	be	AUX
ejpam-6536	82	8	evaluated	evaluate	VERB
ejpam-6536	82	9	by	by	ADP
ejpam-6536	82	10	someone	someone	PRON
ejpam-6536	82	11	who	who	PRON
ejpam-6536	82	12	is	be	AUX
ejpam-6536	82	13	two	two	NUM
ejpam-6536	82	14	steps	step	NOUN
ejpam-6536	82	15	away	away	ADV
ejpam-6536	82	16	in	in	ADP
ejpam-6536	82	17	the	the	DET
ejpam-6536	82	18	social	social	ADJ
ejpam-6536	82	19	network	network	NOUN
ejpam-6536	82	20	.	.	PUNCT
ejpam-6536	83	1	this	this	DET
ejpam-6536	83	2	method	method	NOUN
ejpam-6536	83	3	ensures	ensure	VERB
ejpam-6536	83	4	privacy	privacy	NOUN
ejpam-6536	83	5	,	,	PUNCT
ejpam-6536	83	6	fairness	fairness	NOUN
ejpam-6536	83	7	and	and	CCONJ
ejpam-6536	83	8	efficient	efficient	ADJ
ejpam-6536	83	9	evaluation	evaluation	NOUN
ejpam-6536	83	10	.	.	PUNCT
ejpam-6536	84	1	the	the	DET
ejpam-6536	84	2	present	present	ADJ
ejpam-6536	84	3	study	study	NOUN
ejpam-6536	84	4	is	be	AUX
ejpam-6536	84	5	motivated	motivate	VERB
ejpam-6536	84	6	by	by	ADP
ejpam-6536	84	7	the	the	DET
ejpam-6536	84	8	situation	situation	NOUN
ejpam-6536	84	9	where	where	SCONJ
ejpam-6536	84	10	the	the	DET
ejpam-6536	84	11	management	management	NOUN
ejpam-6536	84	12	considers	consider	VERB
ejpam-6536	84	13	the	the	DET
ejpam-6536	84	14	possibility	possibility	NOUN
ejpam-6536	84	15	that	that	SCONJ
ejpam-6536	84	16	the	the	DET
ejpam-6536	84	17	quality	quality	NOUN
ejpam-6536	84	18	assurance	assurance	NOUN
ejpam-6536	84	19	team	team	NOUN
ejpam-6536	84	20	might	might	AUX
ejpam-6536	84	21	fail	fail	VERB
ejpam-6536	84	22	to	to	PART
ejpam-6536	84	23	deliver	deliver	VERB
ejpam-6536	84	24	the	the	DET
ejpam-6536	84	25	desired	desire	VERB
ejpam-6536	84	26	output	output	NOUN
ejpam-6536	84	27	,	,	PUNCT
ejpam-6536	84	28	and	and	CCONJ
ejpam-6536	84	29	reserves	reserve	NOUN
ejpam-6536	84	30	another	another	DET
ejpam-6536	84	31	separate	separate	ADJ
ejpam-6536	84	32	team	team	NOUN
ejpam-6536	84	33	(	(	PUNCT
ejpam-6536	84	34	composed	compose	VERB
ejpam-6536	84	35	of	of	ADP
ejpam-6536	84	36	evaluators	evaluator	NOUN
ejpam-6536	84	37	who	who	PRON
ejpam-6536	84	38	are	be	AUX
ejpam-6536	84	39	not	not	PART
ejpam-6536	84	40	members	member	NOUN
ejpam-6536	84	41	of	of	ADP
ejpam-6536	84	42	the	the	DET
ejpam-6536	84	43	first	first	ADJ
ejpam-6536	84	44	team	team	NOUN
ejpam-6536	84	45	)	)	PUNCT
ejpam-6536	84	46	that	that	PRON
ejpam-6536	84	47	can	can	AUX
ejpam-6536	84	48	perform	perform	VERB
ejpam-6536	84	49	the	the	DET
ejpam-6536	84	50	same	same	ADJ
ejpam-6536	84	51	evaluation	evaluation	NOUN
ejpam-6536	84	52	job	job	NOUN
ejpam-6536	84	53	.	.	PUNCT
ejpam-6536	85	1	it	it	PRON
ejpam-6536	85	2	deals	deal	VERB
ejpam-6536	85	3	mainly	mainly	ADV
ejpam-6536	85	4	with	with	ADP
ejpam-6536	85	5	the	the	DET
ejpam-6536	85	6	following	follow	VERB
ejpam-6536	85	7	two	two	NUM
ejpam-6536	85	8	more	more	ADV
ejpam-6536	85	9	likely	likely	ADJ
ejpam-6536	85	10	approaches	approach	NOUN
ejpam-6536	85	11	:	:	PUNCT
ejpam-6536	85	12	•	•	SCONJ
ejpam-6536	85	13	the	the	DET
ejpam-6536	85	14	second	second	ADJ
ejpam-6536	85	15	team	team	NOUN
ejpam-6536	85	16	will	will	AUX
ejpam-6536	85	17	proceed	proceed	VERB
ejpam-6536	85	18	only	only	ADV
ejpam-6536	85	19	after	after	SCONJ
ejpam-6536	85	20	the	the	DET
ejpam-6536	85	21	management	management	NOUN
ejpam-6536	85	22	found	find	VERB
ejpam-6536	85	23	that	that	SCONJ
ejpam-6536	85	24	the	the	DET
ejpam-6536	85	25	first	first	ADJ
ejpam-6536	85	26	team	team	NOUN
ejpam-6536	85	27	’s	’s	PART
ejpam-6536	85	28	evaluation	evaluation	NOUN
ejpam-6536	85	29	result	result	NOUN
ejpam-6536	85	30	is	be	AUX
ejpam-6536	85	31	a	a	DET
ejpam-6536	85	32	failure	failure	NOUN
ejpam-6536	85	33	;	;	PUNCT
ejpam-6536	85	34	or	or	CCONJ
ejpam-6536	85	35	•	•	NOUN
ejpam-6536	85	36	the	the	DET
ejpam-6536	85	37	second	second	ADJ
ejpam-6536	85	38	team	team	NOUN
ejpam-6536	85	39	will	will	AUX
ejpam-6536	85	40	perform	perform	VERB
ejpam-6536	85	41	its	its	PRON
ejpam-6536	85	42	task	task	NOUN
ejpam-6536	85	43	simultaneously	simultaneously	ADV
ejpam-6536	85	44	with	with	ADP
ejpam-6536	85	45	the	the	DET
ejpam-6536	85	46	first	first	ADJ
ejpam-6536	85	47	team	team	NOUN
ejpam-6536	85	48	.	.	PUNCT
ejpam-6536	86	1	2	2	X
ejpam-6536	86	2	.	.	X
ejpam-6536	86	3	some	some	DET
ejpam-6536	86	4	existing	exist	VERB
ejpam-6536	86	5	results	result	NOUN
ejpam-6536	86	6	in	in	ADP
ejpam-6536	86	7	hop	hop	NOUN
ejpam-6536	86	8	domination	domination	NOUN
ejpam-6536	86	9	the	the	DET
ejpam-6536	86	10	following	follow	VERB
ejpam-6536	86	11	existing	exist	VERB
ejpam-6536	86	12	results	result	NOUN
ejpam-6536	86	13	are	be	AUX
ejpam-6536	86	14	useful	useful	ADJ
ejpam-6536	86	15	in	in	ADP
ejpam-6536	86	16	the	the	DET
ejpam-6536	86	17	present	present	ADJ
ejpam-6536	86	18	study	study	NOUN
ejpam-6536	86	19	.	.	PUNCT
ejpam-6536	87	1	proposition	proposition	NOUN
ejpam-6536	87	2	1	1	NUM
ejpam-6536	87	3	.	.	PUNCT
ejpam-6536	88	1	[	[	X
ejpam-6536	88	2	14	14	NUM
ejpam-6536	88	3	]	]	PUNCT
ejpam-6536	88	4	(	(	PUNCT
ejpam-6536	88	5	i	i	NOUN
ejpam-6536	88	6	)	)	PUNCT
ejpam-6536	88	7	for	for	ADP
ejpam-6536	88	8	a	a	DET
ejpam-6536	88	9	complete	complete	ADJ
ejpam-6536	88	10	graph	graph	NOUN
ejpam-6536	88	11	kn	kn	PROPN
ejpam-6536	88	12	,	,	PUNCT
ejpam-6536	88	13	γh(kn	γh(kn	PROPN
ejpam-6536	88	14	)	)	PUNCT
ejpam-6536	89	1	=	=	PUNCT
ejpam-6536	89	2	n.	n.	NOUN
ejpam-6536	89	3	(	(	PUNCT
ejpam-6536	89	4	ii	ii	PROPN
ejpam-6536	89	5	)	)	PUNCT
ejpam-6536	89	6	for	for	ADP
ejpam-6536	89	7	a	a	DET
ejpam-6536	89	8	complete	complete	ADJ
ejpam-6536	89	9	bipartite	bipartite	NOUN
ejpam-6536	89	10	graph	graph	NOUN
ejpam-6536	89	11	km	km	PROPN
ejpam-6536	89	12	,	,	PUNCT
ejpam-6536	89	13	n	n	CCONJ
ejpam-6536	89	14	,	,	PUNCT
ejpam-6536	89	15	γh(km	γh(km	NOUN
ejpam-6536	89	16	,	,	PUNCT
ejpam-6536	89	17	n	n	CCONJ
ejpam-6536	89	18	)	)	PUNCT
ejpam-6536	89	19	=	=	SYM
ejpam-6536	89	20	2	2	X
ejpam-6536	89	21	.	.	X
ejpam-6536	90	1	v.	v.	ADP
ejpam-6536	90	2	a	a	DET
ejpam-6536	90	3	besana	besana	PROPN
ejpam-6536	90	4	,	,	PUNCT
ejpam-6536	90	5	f.	f.	PROPN
ejpam-6536	90	6	jamil	jamil	PROPN
ejpam-6536	90	7	,	,	PUNCT
ejpam-6536	90	8	s.	s.	PROPN
ejpam-6536	90	9	canoy	canoy	PROPN
ejpam-6536	90	10	jr	jr	PROPN
ejpam-6536	90	11	.	.	PROPN
ejpam-6536	90	12	/	/	SYM
ejpam-6536	90	13	eur	eur	PROPN
ejpam-6536	90	14	.	.	PUNCT
ejpam-6536	91	1	j.	j.	PROPN
ejpam-6536	91	2	pure	pure	PROPN
ejpam-6536	91	3	appl	appl	PROPN
ejpam-6536	91	4	.	.	PROPN
ejpam-6536	91	5	math	math	PROPN
ejpam-6536	91	6	,	,	PUNCT
ejpam-6536	91	7	18	18	NUM
ejpam-6536	91	8	(	(	PUNCT
ejpam-6536	91	9	3	3	NUM
ejpam-6536	91	10	)	)	PUNCT
ejpam-6536	91	11	(	(	PUNCT
ejpam-6536	91	12	2025	2025	NUM
ejpam-6536	91	13	)	)	PUNCT
ejpam-6536	91	14	,	,	PUNCT
ejpam-6536	91	15	6536	6536	NUM
ejpam-6536	91	16	4	4	NUM
ejpam-6536	91	17	of	of	ADP
ejpam-6536	91	18	17	17	NUM
ejpam-6536	91	19	(	(	PUNCT
ejpam-6536	91	20	iii	iii	NOUN
ejpam-6536	91	21	)	)	PUNCT
ejpam-6536	91	22	for	for	ADP
ejpam-6536	91	23	a	a	DET
ejpam-6536	91	24	path	path	NOUN
ejpam-6536	91	25	pn	pn	NOUN
ejpam-6536	91	26	on	on	ADP
ejpam-6536	91	27	n	n	PRON
ejpam-6536	91	28	vertices	vertex	NOUN
ejpam-6536	91	29	,	,	PUNCT
ejpam-6536	91	30	γh(pn	γh(pn	NUM
ejpam-6536	91	31	)	)	PUNCT
ejpam-6536	91	32	=	=	SYM
ejpam-6536	91	33			NUM
ejpam-6536	91	34	2r	2r	NUM
ejpam-6536	91	35	,	,	PUNCT
ejpam-6536	91	36	if	if	SCONJ
ejpam-6536	91	37	n	n	NOUN
ejpam-6536	91	38	=	=	SYM
ejpam-6536	91	39	6r	6r	NUM
ejpam-6536	91	40	;	;	PUNCT
ejpam-6536	92	1	2r	2r	NUM
ejpam-6536	92	2	+	+	CCONJ
ejpam-6536	92	3	1	1	NUM
ejpam-6536	92	4	,	,	PUNCT
ejpam-6536	92	5	if	if	SCONJ
ejpam-6536	92	6	n	n	NOUN
ejpam-6536	92	7	=	=	SYM
ejpam-6536	92	8	6r	6r	NUM
ejpam-6536	92	9	+	+	CCONJ
ejpam-6536	92	10	1	1	NUM
ejpam-6536	92	11	;	;	PUNCT
ejpam-6536	92	12	2r	2r	NUM
ejpam-6536	92	13	+	+	CCONJ
ejpam-6536	92	14	2	2	NUM
ejpam-6536	92	15	,	,	PUNCT
ejpam-6536	92	16	if	if	SCONJ
ejpam-6536	92	17	n	n	NOUN
ejpam-6536	92	18	=	=	SYM
ejpam-6536	92	19	6r	6r	NUM
ejpam-6536	92	20	+	+	SYM
ejpam-6536	92	21	s	s	X
ejpam-6536	92	22	;	;	PUNCT
ejpam-6536	92	23	2	2	NUM
ejpam-6536	92	24	≤	≤	NOUN
ejpam-6536	92	25	s	s	PART
ejpam-6536	92	26	≤	≤	NUM
ejpam-6536	92	27	5	5	NUM
ejpam-6536	92	28	.	.	PUNCT
ejpam-6536	92	29	(	(	PUNCT
ejpam-6536	92	30	iv	iv	X
ejpam-6536	92	31	)	)	PUNCT
ejpam-6536	92	32	for	for	ADP
ejpam-6536	92	33	a	a	DET
ejpam-6536	92	34	cycle	cycle	NOUN
ejpam-6536	92	35	cn	cn	NOUN
ejpam-6536	92	36	of	of	ADP
ejpam-6536	92	37	length	length	NOUN
ejpam-6536	92	38	n	n	CCONJ
ejpam-6536	92	39	,	,	PUNCT
ejpam-6536	92	40	γh(cn	γh(cn	PROPN
ejpam-6536	92	41	)	)	PUNCT
ejpam-6536	92	42	=	=	PUNCT
ejpam-6536	93	1			NUM
ejpam-6536	93	2	2r	2r	NUM
ejpam-6536	93	3	,	,	PUNCT
ejpam-6536	93	4	if	if	SCONJ
ejpam-6536	93	5	n	n	NOUN
ejpam-6536	93	6	=	=	SYM
ejpam-6536	93	7	6r	6r	NUM
ejpam-6536	93	8	;	;	PUNCT
ejpam-6536	93	9	2r	2r	NUM
ejpam-6536	93	10	+	+	CCONJ
ejpam-6536	93	11	1	1	NUM
ejpam-6536	93	12	,	,	PUNCT
ejpam-6536	93	13	if	if	SCONJ
ejpam-6536	93	14	n	n	NOUN
ejpam-6536	93	15	=	=	SYM
ejpam-6536	93	16	6r	6r	NUM
ejpam-6536	93	17	+	+	CCONJ
ejpam-6536	93	18	1	1	NUM
ejpam-6536	93	19	;	;	PUNCT
ejpam-6536	93	20	2r	2r	NUM
ejpam-6536	93	21	+	+	CCONJ
ejpam-6536	93	22	2	2	NUM
ejpam-6536	93	23	,	,	PUNCT
ejpam-6536	93	24	if	if	SCONJ
ejpam-6536	93	25	n	n	NOUN
ejpam-6536	93	26	=	=	SYM
ejpam-6536	93	27	6r	6r	NUM
ejpam-6536	93	28	+	+	SYM
ejpam-6536	93	29	s	s	X
ejpam-6536	93	30	;	;	PUNCT
ejpam-6536	93	31	2	2	NUM
ejpam-6536	93	32	≤	≤	NOUN
ejpam-6536	93	33	s	s	PART
ejpam-6536	93	34	≤	≤	NUM
ejpam-6536	93	35	5	5	NUM
ejpam-6536	93	36	.	.	PUNCT
ejpam-6536	94	1	(	(	PUNCT
ejpam-6536	94	2	v	v	NOUN
ejpam-6536	94	3	)	)	PUNCT
ejpam-6536	94	4	for	for	ADP
ejpam-6536	94	5	the	the	DET
ejpam-6536	94	6	petersen	petersen	PROPN
ejpam-6536	94	7	graph	graph	NOUN
ejpam-6536	94	8	p	p	NOUN
ejpam-6536	94	9	,	,	PUNCT
ejpam-6536	94	10	γh(p	γh(p	NUM
ejpam-6536	94	11	)	)	PUNCT
ejpam-6536	95	1	=	=	SYM
ejpam-6536	95	2	2	2	X
ejpam-6536	95	3	.	.	X
ejpam-6536	95	4	proposition	proposition	NOUN
ejpam-6536	95	5	2	2	NUM
ejpam-6536	95	6	.	.	PUNCT
ejpam-6536	96	1	[	[	X
ejpam-6536	96	2	7	7	X
ejpam-6536	96	3	]	]	PUNCT
ejpam-6536	96	4	let	let	VERB
ejpam-6536	96	5	g	g	PRON
ejpam-6536	96	6	be	be	AUX
ejpam-6536	96	7	a	a	DET
ejpam-6536	96	8	graph	graph	NOUN
ejpam-6536	96	9	of	of	ADP
ejpam-6536	96	10	order	order	NOUN
ejpam-6536	96	11	n.	n.	NOUN
ejpam-6536	96	12	then	then	ADV
ejpam-6536	96	13	1	1	NUM
ejpam-6536	96	14	≤	≤	NUM
ejpam-6536	96	15	pnd(g	pnd(g	ADP
ejpam-6536	96	16	)	)	PUNCT
ejpam-6536	96	17	≤	≤	NOUN
ejpam-6536	96	18	n.	n.	NOUN
ejpam-6536	96	19	moreover	moreover	ADV
ejpam-6536	96	20	,	,	PUNCT
ejpam-6536	96	21	(	(	PUNCT
ejpam-6536	96	22	i	i	NOUN
ejpam-6536	96	23	)	)	PUNCT
ejpam-6536	97	1	pnd(g	pnd(g	ADP
ejpam-6536	97	2	)	)	PUNCT
ejpam-6536	97	3	=	=	SYM
ejpam-6536	98	1	n	n	NOUN
ejpam-6536	98	2	if	if	SCONJ
ejpam-6536	98	3	and	and	CCONJ
ejpam-6536	98	4	only	only	ADV
ejpam-6536	98	5	if	if	SCONJ
ejpam-6536	98	6	g	g	PROPN
ejpam-6536	98	7	=	=	PROPN
ejpam-6536	98	8	kn	kn	PROPN
ejpam-6536	98	9	.	.	PUNCT
ejpam-6536	98	10	(	(	PUNCT
ejpam-6536	98	11	ii	ii	NOUN
ejpam-6536	98	12	)	)	PUNCT
ejpam-6536	98	13	pnd(g	pnd(g	PROPN
ejpam-6536	98	14	)	)	PUNCT
ejpam-6536	98	15	=	=	SYM
ejpam-6536	98	16	1	1	NUM
ejpam-6536	98	17	if	if	SCONJ
ejpam-6536	98	18	and	and	CCONJ
ejpam-6536	98	19	only	only	ADV
ejpam-6536	98	20	if	if	SCONJ
ejpam-6536	98	21	g	g	PROPN
ejpam-6536	98	22	has	have	VERB
ejpam-6536	98	23	an	an	DET
ejpam-6536	98	24	isolated	isolated	ADJ
ejpam-6536	98	25	vertex	vertex	NOUN
ejpam-6536	98	26	.	.	PUNCT
ejpam-6536	99	1	(	(	PUNCT
ejpam-6536	99	2	iii	iii	NOUN
ejpam-6536	99	3	)	)	PUNCT
ejpam-6536	99	4	pnd(g	pnd(g	PROPN
ejpam-6536	99	5	)	)	PUNCT
ejpam-6536	99	6	=	=	SYM
ejpam-6536	99	7	2	2	NUM
ejpam-6536	99	8	if	if	SCONJ
ejpam-6536	99	9	and	and	CCONJ
ejpam-6536	99	10	only	only	ADV
ejpam-6536	99	11	if	if	SCONJ
ejpam-6536	99	12	g	g	PROPN
ejpam-6536	99	13	has	have	VERB
ejpam-6536	99	14	no	no	DET
ejpam-6536	99	15	isolated	isolated	ADJ
ejpam-6536	99	16	vertex	vertex	NOUN
ejpam-6536	99	17	and	and	CCONJ
ejpam-6536	99	18	there	there	PRON
ejpam-6536	99	19	exist	exist	VERB
ejpam-6536	99	20	distinct	distinct	ADJ
ejpam-6536	99	21	vertices	vertex	NOUN
ejpam-6536	99	22	a	a	PRON
ejpam-6536	99	23	and	and	CCONJ
ejpam-6536	99	24	b	b	NOUN
ejpam-6536	99	25	of	of	ADP
ejpam-6536	99	26	g	g	NOUN
ejpam-6536	100	1	such	such	ADJ
ejpam-6536	100	2	that	that	DET
ejpam-6536	100	3	ng(a	ng(a	NOUN
ejpam-6536	100	4	)	)	PUNCT
ejpam-6536	100	5	∩	∩	NOUN
ejpam-6536	100	6	ng(b	ng(b	CCONJ
ejpam-6536	100	7	)	)	PUNCT
ejpam-6536	100	8	=	=	PUNCT
ejpam-6536	100	9	∅.	∅.	NOUN
ejpam-6536	100	10	theorem	theorem	VERB
ejpam-6536	100	11	1	1	NUM
ejpam-6536	100	12	.	.	PUNCT
ejpam-6536	101	1	[	[	X
ejpam-6536	101	2	7	7	X
ejpam-6536	101	3	]	]	X
ejpam-6536	101	4	let	let	VERB
ejpam-6536	101	5	g	g	NOUN
ejpam-6536	101	6	and	and	CCONJ
ejpam-6536	101	7	h	h	NOUN
ejpam-6536	101	8	be	be	VERB
ejpam-6536	101	9	any	any	DET
ejpam-6536	101	10	two	two	NUM
ejpam-6536	101	11	graphs	graph	NOUN
ejpam-6536	101	12	.	.	PUNCT
ejpam-6536	102	1	a	a	DET
ejpam-6536	102	2	set	set	NOUN
ejpam-6536	102	3	s	s	NOUN
ejpam-6536	102	4	⊆	⊆	NUM
ejpam-6536	102	5	v	v	NOUN
ejpam-6536	102	6	(	(	PUNCT
ejpam-6536	102	7	g+h	g+h	PROPN
ejpam-6536	102	8	)	)	PUNCT
ejpam-6536	102	9	is	be	AUX
ejpam-6536	102	10	a	a	DET
ejpam-6536	102	11	hop	hop	NOUN
ejpam-6536	102	12	dominating	dominating	NOUN
ejpam-6536	102	13	set	set	NOUN
ejpam-6536	102	14	of	of	ADP
ejpam-6536	102	15	g	g	PROPN
ejpam-6536	103	1	+	+	CCONJ
ejpam-6536	103	2	h	h	NOUN
ejpam-6536	103	3	if	if	SCONJ
ejpam-6536	103	4	and	and	CCONJ
ejpam-6536	103	5	only	only	ADV
ejpam-6536	103	6	if	if	SCONJ
ejpam-6536	103	7	s	s	VERB
ejpam-6536	103	8	=	=	PUNCT
ejpam-6536	103	9	sg	sg	X
ejpam-6536	103	10	∪	∪	ADJ
ejpam-6536	103	11	sh	sh	PROPN
ejpam-6536	103	12	,	,	PUNCT
ejpam-6536	103	13	where	where	SCONJ
ejpam-6536	103	14	sg	sg	PROPN
ejpam-6536	103	15	and	and	CCONJ
ejpam-6536	103	16	sh	sh	PROPN
ejpam-6536	103	17	are	be	AUX
ejpam-6536	103	18	point	point	ADV
ejpam-6536	103	19	-	-	PUNCT
ejpam-6536	103	20	wise	wise	ADJ
ejpam-6536	103	21	non	non	ADJ
ejpam-6536	103	22	-	-	ADJ
ejpam-6536	103	23	dominating	dominating	ADJ
ejpam-6536	103	24	sets	set	NOUN
ejpam-6536	103	25	of	of	ADP
ejpam-6536	103	26	g	g	PROPN
ejpam-6536	103	27	and	and	CCONJ
ejpam-6536	103	28	h	h	NOUN
ejpam-6536	103	29	,	,	PUNCT
ejpam-6536	103	30	respectively	respectively	ADV
ejpam-6536	103	31	.	.	PUNCT
ejpam-6536	104	1	theorem	theorem	NOUN
ejpam-6536	104	2	2	2	NUM
ejpam-6536	104	3	.	.	PUNCT
ejpam-6536	105	1	[	[	X
ejpam-6536	105	2	7	7	X
ejpam-6536	105	3	]	]	X
ejpam-6536	105	4	let	let	VERB
ejpam-6536	105	5	g	g	NOUN
ejpam-6536	105	6	and	and	CCONJ
ejpam-6536	105	7	h	h	NOUN
ejpam-6536	105	8	be	be	VERB
ejpam-6536	105	9	any	any	DET
ejpam-6536	105	10	two	two	NUM
ejpam-6536	105	11	graphs	graph	NOUN
ejpam-6536	105	12	.	.	PUNCT
ejpam-6536	106	1	a	a	DET
ejpam-6536	106	2	set	set	NOUN
ejpam-6536	106	3	c	c	NOUN
ejpam-6536	106	4	⊆	⊆	NUM
ejpam-6536	106	5	v	v	NOUN
ejpam-6536	106	6	(	(	PUNCT
ejpam-6536	106	7	g	g	PROPN
ejpam-6536	106	8	◦	◦	NOUN
ejpam-6536	106	9	h	h	NOUN
ejpam-6536	106	10	)	)	PUNCT
ejpam-6536	106	11	is	be	AUX
ejpam-6536	106	12	a	a	DET
ejpam-6536	106	13	hop	hop	NOUN
ejpam-6536	106	14	dominating	dominating	NOUN
ejpam-6536	106	15	set	set	NOUN
ejpam-6536	106	16	of	of	ADP
ejpam-6536	106	17	g	g	PROPN
ejpam-6536	106	18	◦	◦	NOUN
ejpam-6536	106	19	h	h	NOUN
ejpam-6536	107	1	if	if	SCONJ
ejpam-6536	108	1	and	and	CCONJ
ejpam-6536	108	2	only	only	ADV
ejpam-6536	108	3	if	if	SCONJ
ejpam-6536	108	4	c	c	X
ejpam-6536	108	5	=	=	PUNCT
ejpam-6536	108	6	a	a	DET
ejpam-6536	108	7	∪	∪	X
ejpam-6536	108	8	(	(	PUNCT
ejpam-6536	108	9	∪v∈v	∪v∈v	X
ejpam-6536	108	10	(	(	PUNCT
ejpam-6536	108	11	g)∩ng(a)sv	g)∩ng(a)sv	PROPN
ejpam-6536	108	12	)	)	PUNCT
ejpam-6536	108	13	∪	∪	PROPN
ejpam-6536	108	14	(	(	PUNCT
ejpam-6536	108	15	∪w∈v	∪w∈v	PROPN
ejpam-6536	108	16	(	(	PUNCT
ejpam-6536	108	17	g)\ng(a)ew	g)\ng(a)ew	PROPN
ejpam-6536	108	18	)	)	PUNCT
ejpam-6536	108	19	,	,	PUNCT
ejpam-6536	108	20	where	where	SCONJ
ejpam-6536	108	21	(	(	PUNCT
ejpam-6536	108	22	i	i	NOUN
ejpam-6536	108	23	)	)	PUNCT
ejpam-6536	108	24	a	a	DET
ejpam-6536	108	25	⊆	⊆	NUM
ejpam-6536	108	26	v	v	NOUN
ejpam-6536	108	27	(	(	PUNCT
ejpam-6536	108	28	g	g	NOUN
ejpam-6536	108	29	)	)	PUNCT
ejpam-6536	108	30	such	such	ADJ
ejpam-6536	108	31	that	that	PRON
ejpam-6536	108	32	for	for	ADP
ejpam-6536	108	33	each	each	DET
ejpam-6536	108	34	w	w	PROPN
ejpam-6536	108	35	∈	∈	PROPN
ejpam-6536	108	36	v	v	ADP
ejpam-6536	108	37	(	(	PUNCT
ejpam-6536	108	38	g	g	NOUN
ejpam-6536	108	39	)	)	PUNCT
ejpam-6536	108	40	\	\	PROPN
ejpam-6536	109	1	a	a	PRON
ejpam-6536	109	2	,	,	PUNCT
ejpam-6536	109	3	there	there	PRON
ejpam-6536	109	4	exists	exist	VERB
ejpam-6536	109	5	x	x	X
ejpam-6536	109	6	∈	∈	PROPN
ejpam-6536	109	7	a	a	PRON
ejpam-6536	109	8	with	with	ADP
ejpam-6536	109	9	dg(x	dg(x	NUM
ejpam-6536	109	10	,	,	PUNCT
ejpam-6536	109	11	w	w	NOUN
ejpam-6536	109	12	)	)	PUNCT
ejpam-6536	109	13	=	=	SYM
ejpam-6536	109	14	2	2	NUM
ejpam-6536	109	15	or	or	CCONJ
ejpam-6536	109	16	there	there	PRON
ejpam-6536	109	17	exists	exist	VERB
ejpam-6536	109	18	y	y	PROPN
ejpam-6536	109	19	∈	∈	PROPN
ejpam-6536	109	20	v	v	ADP
ejpam-6536	109	21	(	(	PUNCT
ejpam-6536	109	22	g	g	NOUN
ejpam-6536	109	23	)	)	PUNCT
ejpam-6536	109	24	∩	∩	NOUN
ejpam-6536	109	25	ng(w	ng(w	NOUN
ejpam-6536	109	26	)	)	PUNCT
ejpam-6536	109	27	with	with	ADP
ejpam-6536	109	28	v	v	PROPN
ejpam-6536	109	29	(	(	PUNCT
ejpam-6536	109	30	hy	hy	NOUN
ejpam-6536	109	31	)	)	PUNCT
ejpam-6536	109	32	∩	∩	NOUN
ejpam-6536	109	33	c	c	PROPN
ejpam-6536	109	34	̸=	̸=	PROPN
ejpam-6536	109	35	∅	∅	NOUN
ejpam-6536	109	36	;	;	PUNCT
ejpam-6536	109	37	(	(	PUNCT
ejpam-6536	109	38	ii	ii	NOUN
ejpam-6536	109	39	)	)	PUNCT
ejpam-6536	109	40	sv	sv	VERB
ejpam-6536	110	1	⊆	⊆	NUM
ejpam-6536	110	2	v	v	X
ejpam-6536	110	3	(	(	PUNCT
ejpam-6536	110	4	hv	hv	PROPN
ejpam-6536	110	5	)	)	PUNCT
ejpam-6536	110	6	for	for	ADP
ejpam-6536	110	7	each	each	DET
ejpam-6536	110	8	v	v	NUM
ejpam-6536	110	9	∈	∈	PROPN
ejpam-6536	110	10	v	v	NOUN
ejpam-6536	110	11	(	(	PUNCT
ejpam-6536	110	12	g	g	NOUN
ejpam-6536	110	13	)	)	PUNCT
ejpam-6536	110	14	∩	∩	NOUN
ejpam-6536	110	15	ng(a	ng(a	NOUN
ejpam-6536	110	16	)	)	PUNCT
ejpam-6536	110	17	;	;	PUNCT
ejpam-6536	110	18	and	and	CCONJ
ejpam-6536	110	19	(	(	PUNCT
ejpam-6536	110	20	iii	iii	X
ejpam-6536	110	21	)	)	PUNCT
ejpam-6536	110	22	ew	ew	NOUN
ejpam-6536	110	23	⊆	⊆	NUM
ejpam-6536	110	24	v	v	NOUN
ejpam-6536	110	25	(	(	PUNCT
ejpam-6536	110	26	hw	hw	NOUN
ejpam-6536	110	27	)	)	PUNCT
ejpam-6536	110	28	is	be	AUX
ejpam-6536	110	29	a	a	DET
ejpam-6536	110	30	point	point	NOUN
ejpam-6536	110	31	-	-	PUNCT
ejpam-6536	110	32	wise	wise	ADJ
ejpam-6536	110	33	non	non	ADJ
ejpam-6536	110	34	-	-	ADJ
ejpam-6536	110	35	dominating	dominating	ADJ
ejpam-6536	110	36	set	set	NOUN
ejpam-6536	110	37	of	of	ADP
ejpam-6536	110	38	hw	hw	PRON
ejpam-6536	110	39	for	for	ADP
ejpam-6536	110	40	each	each	DET
ejpam-6536	110	41	w	w	PROPN
ejpam-6536	110	42	∈	∈	PROPN
ejpam-6536	110	43	v	v	ADP
ejpam-6536	110	44	(	(	PUNCT
ejpam-6536	110	45	g	g	NOUN
ejpam-6536	110	46	)	)	PUNCT
ejpam-6536	110	47	\	\	NOUN
ejpam-6536	110	48	ng(a	ng(a	NOUN
ejpam-6536	110	49	)	)	PUNCT
ejpam-6536	110	50	.	.	PUNCT
ejpam-6536	111	1	theorem	theorem	NOUN
ejpam-6536	111	2	3	3	NUM
ejpam-6536	111	3	.	.	PUNCT
ejpam-6536	112	1	[	[	X
ejpam-6536	112	2	7]let	7]let	NOUN
ejpam-6536	112	3	g	g	NOUN
ejpam-6536	112	4	be	be	VERB
ejpam-6536	112	5	a	a	DET
ejpam-6536	112	6	nontrivial	nontrivial	ADJ
ejpam-6536	112	7	connected	connect	VERB
ejpam-6536	112	8	graph	graph	NOUN
ejpam-6536	112	9	and	and	CCONJ
ejpam-6536	112	10	let	let	VERB
ejpam-6536	112	11	h	h	NOUN
ejpam-6536	112	12	be	be	AUX
ejpam-6536	112	13	any	any	DET
ejpam-6536	112	14	graph	graph	NOUN
ejpam-6536	112	15	.	.	PUNCT
ejpam-6536	113	1	then	then	ADV
ejpam-6536	113	2	(	(	PUNCT
ejpam-6536	113	3	i	i	NOUN
ejpam-6536	113	4	)	)	PUNCT
ejpam-6536	113	5	γh(g	γh(g	PUNCT
ejpam-6536	113	6	◦	◦	NOUN
ejpam-6536	113	7	h	h	NOUN
ejpam-6536	113	8	)	)	PUNCT
ejpam-6536	113	9	≤	≤	NOUN
ejpam-6536	113	10	min{γ∗t	min{γ∗t	PROPN
ejpam-6536	113	11	1,2(g	1,2(g	NUM
ejpam-6536	113	12	)	)	PUNCT
ejpam-6536	113	13	,	,	PUNCT
ejpam-6536	113	14	[	[	X
ejpam-6536	113	15	1	1	NUM
ejpam-6536	113	16	+	+	NUM
ejpam-6536	113	17	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-6536	113	18	)	)	PUNCT
ejpam-6536	113	19	}	}	PUNCT
ejpam-6536	113	20	.	.	PUNCT
ejpam-6536	114	1	(	(	PUNCT
ejpam-6536	114	2	ii	ii	NOUN
ejpam-6536	114	3	)	)	PUNCT
ejpam-6536	114	4	γh(g	γh(g	PUNCT
ejpam-6536	114	5	◦	◦	NOUN
ejpam-6536	114	6	h	h	NOUN
ejpam-6536	114	7	)	)	PUNCT
ejpam-6536	114	8	=	=	SYM
ejpam-6536	114	9	2	2	NUM
ejpam-6536	114	10	if	if	SCONJ
ejpam-6536	114	11	γ∗t	γ∗t	ADP
ejpam-6536	114	12	1,2(g	1,2(g	NUM
ejpam-6536	114	13	)	)	PUNCT
ejpam-6536	114	14	=	=	SYM
ejpam-6536	114	15	2	2	X
ejpam-6536	114	16	.	.	X
ejpam-6536	115	1	v.	v.	ADP
ejpam-6536	115	2	a	a	DET
ejpam-6536	115	3	besana	besana	PROPN
ejpam-6536	115	4	,	,	PUNCT
ejpam-6536	115	5	f.	f.	PROPN
ejpam-6536	115	6	jamil	jamil	PROPN
ejpam-6536	115	7	,	,	PUNCT
ejpam-6536	115	8	s.	s.	PROPN
ejpam-6536	115	9	canoy	canoy	PROPN
ejpam-6536	115	10	jr	jr	PROPN
ejpam-6536	115	11	.	.	PROPN
ejpam-6536	115	12	/	/	SYM
ejpam-6536	115	13	eur	eur	PROPN
ejpam-6536	115	14	.	.	PUNCT
ejpam-6536	116	1	j.	j.	PROPN
ejpam-6536	116	2	pure	pure	PROPN
ejpam-6536	116	3	appl	appl	PROPN
ejpam-6536	116	4	.	.	PROPN
ejpam-6536	116	5	math	math	PROPN
ejpam-6536	116	6	,	,	PUNCT
ejpam-6536	116	7	18	18	NUM
ejpam-6536	116	8	(	(	PUNCT
ejpam-6536	116	9	3	3	NUM
ejpam-6536	116	10	)	)	PUNCT
ejpam-6536	116	11	(	(	PUNCT
ejpam-6536	116	12	2025	2025	NUM
ejpam-6536	116	13	)	)	PUNCT
ejpam-6536	116	14	,	,	PUNCT
ejpam-6536	116	15	6536	6536	NUM
ejpam-6536	116	16	5	5	NUM
ejpam-6536	116	17	of	of	ADP
ejpam-6536	116	18	17	17	NUM
ejpam-6536	116	19	(	(	PUNCT
ejpam-6536	116	20	iii	iii	NOUN
ejpam-6536	116	21	)	)	PUNCT
ejpam-6536	116	22	γh(g	γh(g	PUNCT
ejpam-6536	116	23	◦	◦	NOUN
ejpam-6536	116	24	h	h	NOUN
ejpam-6536	116	25	)	)	PUNCT
ejpam-6536	116	26	=	=	SYM
ejpam-6536	116	27	2	2	NUM
ejpam-6536	116	28	if	if	SCONJ
ejpam-6536	116	29	γ(g	γ(g	NOUN
ejpam-6536	116	30	)	)	PUNCT
ejpam-6536	116	31	=	=	SYM
ejpam-6536	117	1	1	1	NUM
ejpam-6536	117	2	and	and	CCONJ
ejpam-6536	117	3	h	h	NOUN
ejpam-6536	117	4	has	have	VERB
ejpam-6536	117	5	an	an	DET
ejpam-6536	117	6	isolated	isolated	ADJ
ejpam-6536	117	7	vertex	vertex	NOUN
ejpam-6536	117	8	.	.	PUNCT
ejpam-6536	118	1	theorem	theorem	VERB
ejpam-6536	118	2	4	4	NUM
ejpam-6536	118	3	.	.	PUNCT
ejpam-6536	119	1	[	[	X
ejpam-6536	119	2	7	7	X
ejpam-6536	119	3	]	]	X
ejpam-6536	119	4	let	let	VERB
ejpam-6536	119	5	g	g	NOUN
ejpam-6536	119	6	and	and	CCONJ
ejpam-6536	119	7	h	h	PROPN
ejpam-6536	119	8	be	be	VERB
ejpam-6536	119	9	non	non	ADJ
ejpam-6536	119	10	-	-	ADJ
ejpam-6536	119	11	trivial	trivial	ADJ
ejpam-6536	119	12	connected	connected	ADJ
ejpam-6536	119	13	graphs	graph	NOUN
ejpam-6536	119	14	.	.	PUNCT
ejpam-6536	120	1	a	a	DET
ejpam-6536	120	2	subset	subset	NOUN
ejpam-6536	120	3	c	c	NOUN
ejpam-6536	120	4	=	=	SYM
ejpam-6536	120	5	∪x∈s	∪x∈s	PROPN
ejpam-6536	120	6	(	(	PUNCT
ejpam-6536	120	7	{	{	PUNCT
ejpam-6536	120	8	x	x	NOUN
ejpam-6536	120	9	}	}	PUNCT
ejpam-6536	120	10	×	×	PROPN
ejpam-6536	120	11	tx	tx	PROPN
ejpam-6536	120	12	)	)	PUNCT
ejpam-6536	120	13	of	of	ADP
ejpam-6536	120	14	v	v	NOUN
ejpam-6536	120	15	(	(	PUNCT
ejpam-6536	120	16	g[h	g[h	PROPN
ejpam-6536	120	17	]	]	PUNCT
ejpam-6536	120	18	)	)	PUNCT
ejpam-6536	120	19	is	be	AUX
ejpam-6536	120	20	a	a	DET
ejpam-6536	120	21	hop	hop	NOUN
ejpam-6536	120	22	dominating	dominating	NOUN
ejpam-6536	120	23	set	set	NOUN
ejpam-6536	120	24	of	of	ADP
ejpam-6536	120	25	g[h	g[h	PROPN
ejpam-6536	120	26	]	]	PUNCT
ejpam-6536	120	27	if	if	SCONJ
ejpam-6536	121	1	and	and	CCONJ
ejpam-6536	121	2	only	only	ADV
ejpam-6536	121	3	if	if	SCONJ
ejpam-6536	121	4	the	the	DET
ejpam-6536	121	5	following	follow	VERB
ejpam-6536	121	6	conditions	condition	NOUN
ejpam-6536	121	7	hold	hold	VERB
ejpam-6536	121	8	:	:	PUNCT
ejpam-6536	121	9	(	(	PUNCT
ejpam-6536	121	10	i	i	NOUN
ejpam-6536	121	11	)	)	PUNCT
ejpam-6536	121	12	s	s	AUX
ejpam-6536	121	13	is	be	AUX
ejpam-6536	121	14	a	a	DET
ejpam-6536	121	15	hop	hop	NOUN
ejpam-6536	121	16	dominating	dominating	NOUN
ejpam-6536	121	17	set	set	NOUN
ejpam-6536	121	18	of	of	ADP
ejpam-6536	121	19	g	g	NOUN
ejpam-6536	121	20	;	;	PUNCT
ejpam-6536	121	21	(	(	PUNCT
ejpam-6536	121	22	ii	ii	NOUN
ejpam-6536	121	23	)	)	PUNCT
ejpam-6536	121	24	tx	tx	PROPN
ejpam-6536	121	25	is	be	AUX
ejpam-6536	121	26	a	a	DET
ejpam-6536	121	27	point	point	NOUN
ejpam-6536	121	28	-	-	PUNCT
ejpam-6536	121	29	wise	wise	ADJ
ejpam-6536	121	30	non	non	ADJ
ejpam-6536	121	31	-	-	ADJ
ejpam-6536	121	32	dominating	dominating	ADJ
ejpam-6536	121	33	set	set	NOUN
ejpam-6536	121	34	of	of	ADP
ejpam-6536	121	35	h	h	NOUN
ejpam-6536	121	36	for	for	ADP
ejpam-6536	121	37	each	each	DET
ejpam-6536	121	38	x	x	SYM
ejpam-6536	121	39	∈	∈	PROPN
ejpam-6536	121	40	s	s	VERB
ejpam-6536	121	41	with	with	ADP
ejpam-6536	121	42	|ng(x	|ng(x	ADP
ejpam-6536	121	43	,	,	PUNCT
ejpam-6536	121	44	2	2	X
ejpam-6536	121	45	)	)	PUNCT
ejpam-6536	122	1	∩	∩	NOUN
ejpam-6536	122	2	s|	s|	VERB
ejpam-6536	122	3	=	=	SYM
ejpam-6536	122	4	0	0	X
ejpam-6536	122	5	.	.	PUNCT
ejpam-6536	123	1	corollary	corollary	ADJ
ejpam-6536	123	2	1	1	NUM
ejpam-6536	123	3	.	.	PUNCT
ejpam-6536	124	1	[	[	X
ejpam-6536	124	2	7	7	X
ejpam-6536	124	3	]	]	X
ejpam-6536	124	4	let	let	VERB
ejpam-6536	124	5	g	g	NOUN
ejpam-6536	124	6	and	and	CCONJ
ejpam-6536	124	7	h	h	PROPN
ejpam-6536	124	8	be	be	VERB
ejpam-6536	124	9	non	non	ADJ
ejpam-6536	124	10	-	-	ADJ
ejpam-6536	124	11	trivial	trivial	ADJ
ejpam-6536	124	12	connected	connected	ADJ
ejpam-6536	124	13	graphs	graph	NOUN
ejpam-6536	124	14	of	of	ADP
ejpam-6536	124	15	orders	order	NOUN
ejpam-6536	124	16	m	m	VERB
ejpam-6536	124	17	and	and	CCONJ
ejpam-6536	124	18	n	n	CCONJ
ejpam-6536	124	19	,	,	PUNCT
ejpam-6536	124	20	respectively	respectively	ADV
ejpam-6536	124	21	.	.	PUNCT
ejpam-6536	125	1	then	then	ADV
ejpam-6536	125	2	(	(	PUNCT
ejpam-6536	125	3	i	i	NOUN
ejpam-6536	125	4	)	)	PUNCT
ejpam-6536	125	5	γh(g[h	γh(g[h	NOUN
ejpam-6536	125	6	]	]	X
ejpam-6536	125	7	)	)	PUNCT
ejpam-6536	125	8	=	=	SYM
ejpam-6536	125	9	ρh(g	ρh(g	NOUN
ejpam-6536	125	10	)	)	PUNCT
ejpam-6536	125	11	if	if	SCONJ
ejpam-6536	125	12	γ(g	γ(g	PROPN
ejpam-6536	125	13	)	)	PUNCT
ejpam-6536	125	14	=	=	SYM
ejpam-6536	126	1	1	1	NUM
ejpam-6536	126	2	,	,	PUNCT
ejpam-6536	126	3	where	where	SCONJ
ejpam-6536	126	4	ρh(g	ρh(g	NOUN
ejpam-6536	126	5	)	)	PUNCT
ejpam-6536	126	6	=	=	SYM
ejpam-6536	126	7	min{|s	min{|s	PROPN
ejpam-6536	126	8	∩	∩	NOUN
ejpam-6536	126	9	ng(s	ng(s	CCONJ
ejpam-6536	126	10	,	,	PUNCT
ejpam-6536	126	11	2)|	2)|	NUM
ejpam-6536	126	12	+	+	CCONJ
ejpam-6536	126	13	pnd(h)|s	pnd(h)|s	NOUN
ejpam-6536	126	14	\	\	NOUN
ejpam-6536	126	15	ng(s	ng(s	PUNCT
ejpam-6536	126	16	,	,	PUNCT
ejpam-6536	126	17	2)|	2)|	NUM
ejpam-6536	126	18	:	:	PUNCT
ejpam-6536	126	19	s	s	X
ejpam-6536	126	20	is	be	AUX
ejpam-6536	126	21	a	a	DET
ejpam-6536	126	22	hop	hop	NOUN
ejpam-6536	126	23	dominating	dominating	NOUN
ejpam-6536	126	24	set	set	NOUN
ejpam-6536	126	25	of	of	ADP
ejpam-6536	126	26	g	g	PROPN
ejpam-6536	126	27	}	}	PUNCT
ejpam-6536	126	28	;	;	PUNCT
ejpam-6536	126	29	(	(	PUNCT
ejpam-6536	126	30	ii	ii	NOUN
ejpam-6536	126	31	)	)	PUNCT
ejpam-6536	126	32	γh(g[h	γh(g[h	NOUN
ejpam-6536	126	33	]	]	X
ejpam-6536	126	34	)	)	PUNCT
ejpam-6536	126	35	=	=	SYM
ejpam-6536	126	36	γth(g	γth(g	NOUN
ejpam-6536	126	37	)	)	PUNCT
ejpam-6536	126	38	if	if	SCONJ
ejpam-6536	126	39	γ(g	γ(g	PROPN
ejpam-6536	126	40	)	)	PUNCT
ejpam-6536	126	41	̸=	̸=	PROPN
ejpam-6536	126	42	1	1	NUM
ejpam-6536	126	43	;	;	PUNCT
ejpam-6536	126	44	and	and	CCONJ
ejpam-6536	126	45	(	(	PUNCT
ejpam-6536	126	46	iii	iii	NOUN
ejpam-6536	126	47	)	)	PUNCT
ejpam-6536	126	48	γh(g[h	γh(g[h	NOUN
ejpam-6536	126	49	]	]	X
ejpam-6536	126	50	)	)	PUNCT
ejpam-6536	126	51	=	=	SYM
ejpam-6536	126	52	m[pnd(h	m[pnd(h	NOUN
ejpam-6536	126	53	)	)	PUNCT
ejpam-6536	126	54	]	]	PUNCT
ejpam-6536	127	1	if	if	SCONJ
ejpam-6536	127	2	g	g	PROPN
ejpam-6536	127	3	=	=	SYM
ejpam-6536	127	4	km	km	PROPN
ejpam-6536	127	5	.	.	PUNCT
ejpam-6536	128	1	3	3	X
ejpam-6536	128	2	.	.	X
ejpam-6536	128	3	results	result	NOUN
ejpam-6536	128	4	by	by	ADP
ejpam-6536	128	5	an	an	DET
ejpam-6536	128	6	ntc	ntc	NOUN
ejpam-6536	128	7	graph	graph	NOUN
ejpam-6536	128	8	we	we	PRON
ejpam-6536	128	9	mean	mean	VERB
ejpam-6536	128	10	a	a	DET
ejpam-6536	128	11	nontrivial	nontrivial	ADJ
ejpam-6536	128	12	connected	connect	VERB
ejpam-6536	128	13	graph	graph	NOUN
ejpam-6536	128	14	.	.	PUNCT
ejpam-6536	129	1	for	for	ADP
ejpam-6536	129	2	vertices	vertex	NOUN
ejpam-6536	129	3	u	u	NOUN
ejpam-6536	129	4	and	and	CCONJ
ejpam-6536	129	5	v	v	NOUN
ejpam-6536	129	6	of	of	ADP
ejpam-6536	129	7	an	an	DET
ejpam-6536	129	8	ntc	ntc	NOUN
ejpam-6536	129	9	graph	graph	NOUN
ejpam-6536	129	10	g	g	PROPN
ejpam-6536	129	11	,	,	PUNCT
ejpam-6536	129	12	a	a	DET
ejpam-6536	129	13	u	u	NOUN
ejpam-6536	129	14	-	-	NOUN
ejpam-6536	129	15	v	v	ADJ
ejpam-6536	129	16	geodesic	geodesic	NOUN
ejpam-6536	129	17	is	be	AUX
ejpam-6536	129	18	any	any	DET
ejpam-6536	129	19	shortest	short	ADJ
ejpam-6536	129	20	path	path	NOUN
ejpam-6536	129	21	in	in	ADP
ejpam-6536	129	22	g	g	NOUN
ejpam-6536	129	23	joining	join	VERB
ejpam-6536	129	24	u	u	NOUN
ejpam-6536	129	25	and	and	CCONJ
ejpam-6536	129	26	v.	v.	ADP
ejpam-6536	129	27	the	the	DET
ejpam-6536	129	28	length	length	NOUN
ejpam-6536	129	29	of	of	ADP
ejpam-6536	129	30	a	a	DET
ejpam-6536	129	31	u	u	NOUN
ejpam-6536	129	32	-	-	NOUN
ejpam-6536	129	33	v	v	ADJ
ejpam-6536	129	34	geodesic	geodesic	NOUN
ejpam-6536	129	35	is	be	AUX
ejpam-6536	129	36	the	the	DET
ejpam-6536	129	37	distance	distance	NOUN
ejpam-6536	129	38	between	between	ADP
ejpam-6536	129	39	u	u	NOUN
ejpam-6536	129	40	and	and	CCONJ
ejpam-6536	129	41	v	v	NOUN
ejpam-6536	129	42	,	,	PUNCT
ejpam-6536	129	43	and	and	CCONJ
ejpam-6536	129	44	is	be	AUX
ejpam-6536	129	45	denoted	denote	VERB
ejpam-6536	129	46	by	by	ADP
ejpam-6536	129	47	dg(u	dg(u	NOUN
ejpam-6536	129	48	,	,	PUNCT
ejpam-6536	129	49	v	v	NOUN
ejpam-6536	129	50	)	)	PUNCT
ejpam-6536	129	51	.	.	PUNCT
ejpam-6536	130	1	the	the	DET
ejpam-6536	130	2	eccentricity	eccentricity	NOUN
ejpam-6536	130	3	of	of	ADP
ejpam-6536	130	4	v	v	NOUN
ejpam-6536	130	5	refers	refer	VERB
ejpam-6536	130	6	to	to	ADP
ejpam-6536	130	7	the	the	DET
ejpam-6536	130	8	quantity	quantity	NOUN
ejpam-6536	130	9	e(v	e(v	NOUN
ejpam-6536	130	10	)	)	PUNCT
ejpam-6536	131	1	=	=	SYM
ejpam-6536	131	2	max{dg(u	max{dg(u	X
ejpam-6536	131	3	,	,	PUNCT
ejpam-6536	131	4	v	v	NOUN
ejpam-6536	131	5	)	)	PUNCT
ejpam-6536	131	6	:	:	PUNCT
ejpam-6536	132	1	v	v	X
ejpam-6536	132	2	∈	∈	PROPN
ejpam-6536	132	3	v	v	NOUN
ejpam-6536	132	4	(	(	PUNCT
ejpam-6536	132	5	g	g	NOUN
ejpam-6536	132	6	)	)	PUNCT
ejpam-6536	132	7	}	}	PUNCT
ejpam-6536	132	8	.	.	PUNCT
ejpam-6536	133	1	the	the	DET
ejpam-6536	133	2	diameter	diameter	NOUN
ejpam-6536	133	3	and	and	CCONJ
ejpam-6536	133	4	radius	radius	NOUN
ejpam-6536	133	5	of	of	ADP
ejpam-6536	133	6	g	g	PROPN
ejpam-6536	133	7	are	be	AUX
ejpam-6536	133	8	defined	define	VERB
ejpam-6536	133	9	,	,	PUNCT
ejpam-6536	133	10	respectively	respectively	ADV
ejpam-6536	133	11	,	,	PUNCT
ejpam-6536	133	12	as	as	ADP
ejpam-6536	133	13	diam(g	diam(g	NOUN
ejpam-6536	133	14	)	)	PUNCT
ejpam-6536	134	1	=	=	SYM
ejpam-6536	134	2	max{e(v	max{e(v	PROPN
ejpam-6536	134	3	)	)	PUNCT
ejpam-6536	134	4	:	:	PUNCT
ejpam-6536	134	5	v	v	X
ejpam-6536	134	6	∈	∈	PROPN
ejpam-6536	134	7	v	v	NOUN
ejpam-6536	134	8	(	(	PUNCT
ejpam-6536	134	9	g	g	NOUN
ejpam-6536	134	10	)	)	PUNCT
ejpam-6536	134	11	}	}	PUNCT
ejpam-6536	134	12	and	and	CCONJ
ejpam-6536	134	13	r(g	r(g	NUM
ejpam-6536	134	14	)	)	PUNCT
ejpam-6536	134	15	=	=	PUNCT
ejpam-6536	134	16	min{e(v	min{e(v	PROPN
ejpam-6536	134	17	)	)	PUNCT
ejpam-6536	134	18	:	:	PUNCT
ejpam-6536	134	19	v	v	X
ejpam-6536	134	20	∈	∈	PROPN
ejpam-6536	134	21	v	v	NOUN
ejpam-6536	134	22	(	(	PUNCT
ejpam-6536	134	23	g	g	NOUN
ejpam-6536	134	24	)	)	PUNCT
ejpam-6536	134	25	}	}	PUNCT
ejpam-6536	134	26	.	.	PUNCT
ejpam-6536	135	1	proposition	proposition	NOUN
ejpam-6536	135	2	3	3	X
ejpam-6536	135	3	.	.	PUNCT
ejpam-6536	136	1	let	let	VERB
ejpam-6536	136	2	g	g	NOUN
ejpam-6536	136	3	be	be	AUX
ejpam-6536	136	4	an	an	DET
ejpam-6536	136	5	ntc	ntc	NOUN
ejpam-6536	136	6	graph	graph	NOUN
ejpam-6536	136	7	with	with	ADP
ejpam-6536	136	8	r(g	r(g	NUM
ejpam-6536	136	9	)	)	PUNCT
ejpam-6536	136	10	≥	≥	NOUN
ejpam-6536	136	11	2	2	NUM
ejpam-6536	136	12	.	.	X
ejpam-6536	137	1	for	for	ADP
ejpam-6536	137	2	each	each	DET
ejpam-6536	137	3	γh	γh	ADV
ejpam-6536	137	4	-	-	PUNCT
ejpam-6536	137	5	set	set	NOUN
ejpam-6536	137	6	s	s	NOUN
ejpam-6536	137	7	⊆	⊆	NUM
ejpam-6536	137	8	v	v	NOUN
ejpam-6536	137	9	(	(	PUNCT
ejpam-6536	137	10	g	g	NOUN
ejpam-6536	137	11	)	)	PUNCT
ejpam-6536	137	12	,	,	PUNCT
ejpam-6536	137	13	v	v	X
ejpam-6536	137	14	(	(	PUNCT
ejpam-6536	137	15	g)\s	g)\s	NOUN
ejpam-6536	137	16	is	be	AUX
ejpam-6536	137	17	a	a	DET
ejpam-6536	137	18	hop	hop	NOUN
ejpam-6536	137	19	dominating	dominating	NOUN
ejpam-6536	137	20	set	set	NOUN
ejpam-6536	137	21	of	of	ADP
ejpam-6536	137	22	g.	g.	PROPN
ejpam-6536	137	23	proof	proof	NOUN
ejpam-6536	137	24	:	:	PUNCT
ejpam-6536	137	25	let	let	VERB
ejpam-6536	137	26	s	s	PRON
ejpam-6536	137	27	⊆	⊆	NUM
ejpam-6536	137	28	v	v	NOUN
ejpam-6536	137	29	(	(	PUNCT
ejpam-6536	137	30	g	g	NOUN
ejpam-6536	137	31	)	)	PUNCT
ejpam-6536	137	32	be	be	AUX
ejpam-6536	137	33	a	a	DET
ejpam-6536	137	34	γh	γh	ADV
ejpam-6536	137	35	-	-	PUNCT
ejpam-6536	137	36	set	set	NOUN
ejpam-6536	137	37	of	of	ADP
ejpam-6536	137	38	g.	g.	PROPN
ejpam-6536	137	39	suppose	suppose	VERB
ejpam-6536	137	40	,	,	PUNCT
ejpam-6536	137	41	in	in	ADP
ejpam-6536	137	42	the	the	DET
ejpam-6536	137	43	contrary	contrary	NOUN
ejpam-6536	137	44	,	,	PUNCT
ejpam-6536	137	45	that	that	SCONJ
ejpam-6536	137	46	there	there	PRON
ejpam-6536	137	47	exists	exist	VERB
ejpam-6536	137	48	u	u	PROPN
ejpam-6536	137	49	∈	∈	PROPN
ejpam-6536	137	50	s	s	X
ejpam-6536	137	51	for	for	ADP
ejpam-6536	137	52	which	which	PRON
ejpam-6536	137	53	dg(u	dg(u	ADJ
ejpam-6536	137	54	,	,	PUNCT
ejpam-6536	137	55	v	v	NOUN
ejpam-6536	137	56	)	)	PUNCT
ejpam-6536	137	57	̸=	̸=	PROPN
ejpam-6536	137	58	2	2	NUM
ejpam-6536	137	59	for	for	ADP
ejpam-6536	137	60	all	all	PRON
ejpam-6536	137	61	v	v	ADP
ejpam-6536	137	62	∈	∈	NOUN
ejpam-6536	137	63	v	v	NOUN
ejpam-6536	137	64	(	(	PUNCT
ejpam-6536	137	65	g	g	NOUN
ejpam-6536	137	66	)	)	PUNCT
ejpam-6536	137	67	\	\	PUNCT
ejpam-6536	138	1	s.	s.	PROPN
ejpam-6536	138	2	since	since	SCONJ
ejpam-6536	138	3	r(g	r(g	NUM
ejpam-6536	138	4	)	)	PUNCT
ejpam-6536	138	5	≥	≥	NOUN
ejpam-6536	138	6	2	2	NUM
ejpam-6536	138	7	,	,	PUNCT
ejpam-6536	138	8	there	there	PRON
ejpam-6536	138	9	exists	exist	VERB
ejpam-6536	138	10	v	v	ADP
ejpam-6536	138	11	∈	∈	PROPN
ejpam-6536	138	12	v	v	NOUN
ejpam-6536	138	13	(	(	PUNCT
ejpam-6536	138	14	g	g	NOUN
ejpam-6536	138	15	)	)	PUNCT
ejpam-6536	138	16	such	such	ADJ
ejpam-6536	138	17	that	that	SCONJ
ejpam-6536	138	18	dg(u	dg(u	ADJ
ejpam-6536	138	19	,	,	PUNCT
ejpam-6536	138	20	v	v	NOUN
ejpam-6536	138	21	)	)	PUNCT
ejpam-6536	138	22	=	=	SYM
ejpam-6536	138	23	2	2	X
ejpam-6536	138	24	.	.	PUNCT
ejpam-6536	139	1	the	the	DET
ejpam-6536	139	2	previous	previous	ADJ
ejpam-6536	139	3	statement	statement	NOUN
ejpam-6536	139	4	implies	imply	VERB
ejpam-6536	139	5	that	that	SCONJ
ejpam-6536	139	6	v	v	X
ejpam-6536	139	7	∈	∈	PROPN
ejpam-6536	139	8	s.	s.	PROPN
ejpam-6536	139	9	put	put	VERB
ejpam-6536	139	10	s∗	s∗	PROPN
ejpam-6536	139	11	=	=	SYM
ejpam-6536	139	12	s	s	PART
ejpam-6536	139	13	\	\	X
ejpam-6536	139	14	{	{	PUNCT
ejpam-6536	139	15	u	u	NOUN
ejpam-6536	139	16	}	}	PUNCT
ejpam-6536	139	17	.	.	PUNCT
ejpam-6536	140	1	then	then	ADV
ejpam-6536	140	2	s∗	s∗	PROPN
ejpam-6536	140	3	is	be	AUX
ejpam-6536	140	4	a	a	DET
ejpam-6536	140	5	hop	hop	NOUN
ejpam-6536	140	6	dominating	dominating	NOUN
ejpam-6536	140	7	set	set	NOUN
ejpam-6536	140	8	of	of	ADP
ejpam-6536	140	9	g	g	PROPN
ejpam-6536	140	10	,	,	PUNCT
ejpam-6536	140	11	a	a	DET
ejpam-6536	140	12	contradiction	contradiction	NOUN
ejpam-6536	140	13	since	since	SCONJ
ejpam-6536	140	14	|s∗|	|s∗|	NUM
ejpam-6536	140	15	<	<	X
ejpam-6536	140	16	|s|	|s|	NOUN
ejpam-6536	140	17	=	=	NOUN
ejpam-6536	140	18	γh(g	γh(g	NOUN
ejpam-6536	140	19	)	)	PUNCT
ejpam-6536	140	20	.	.	PUNCT
ejpam-6536	141	1	■	■	PUNCT
ejpam-6536	141	2	in	in	ADP
ejpam-6536	141	3	what	what	PRON
ejpam-6536	141	4	follows	follow	VERB
ejpam-6536	141	5	,	,	PUNCT
ejpam-6536	141	6	g	g	PROPN
ejpam-6536	141	7	is	be	AUX
ejpam-6536	141	8	the	the	DET
ejpam-6536	141	9	family	family	NOUN
ejpam-6536	141	10	of	of	ADP
ejpam-6536	141	11	all	all	DET
ejpam-6536	141	12	ntc	ntc	NOUN
ejpam-6536	141	13	graphs	graph	NOUN
ejpam-6536	141	14	g	g	ADP
ejpam-6536	141	15	such	such	ADJ
ejpam-6536	141	16	that	that	DET
ejpam-6536	141	17	r(g	r(g	NUM
ejpam-6536	141	18	)	)	PUNCT
ejpam-6536	141	19	≥	≥	NOUN
ejpam-6536	141	20	2	2	NUM
ejpam-6536	141	21	.	.	SYM
ejpam-6536	141	22	3.1	3.1	NUM
ejpam-6536	141	23	.	.	PUNCT
ejpam-6536	141	24	inverse	inverse	PROPN
ejpam-6536	141	25	hop	hop	PROPN
ejpam-6536	141	26	domination	domination	PROPN
ejpam-6536	141	27	let	let	VERB
ejpam-6536	141	28	g	g	PROPN
ejpam-6536	141	29	∈	∈	PROPN
ejpam-6536	141	30	g	g	PROPN
ejpam-6536	141	31	.	.	PUNCT
ejpam-6536	142	1	a	a	DET
ejpam-6536	142	2	subset	subset	NOUN
ejpam-6536	142	3	s	s	VERB
ejpam-6536	142	4	⊆	⊆	NUM
ejpam-6536	142	5	v	v	NOUN
ejpam-6536	142	6	(	(	PUNCT
ejpam-6536	142	7	g	g	NOUN
ejpam-6536	142	8	)	)	PUNCT
ejpam-6536	142	9	is	be	AUX
ejpam-6536	142	10	an	an	DET
ejpam-6536	142	11	inverse	inverse	NOUN
ejpam-6536	142	12	hop	hop	NOUN
ejpam-6536	142	13	dominating	dominating	NOUN
ejpam-6536	142	14	set	set	NOUN
ejpam-6536	142	15	provided	provide	VERB
ejpam-6536	142	16	s	s	VERB
ejpam-6536	142	17	is	be	AUX
ejpam-6536	142	18	a	a	DET
ejpam-6536	142	19	hop	hop	NOUN
ejpam-6536	142	20	dominating	dominating	NOUN
ejpam-6536	142	21	set	set	NOUN
ejpam-6536	142	22	and	and	CCONJ
ejpam-6536	142	23	v	v	NOUN
ejpam-6536	142	24	(	(	PUNCT
ejpam-6536	142	25	g)\s	g)\s	NOUN
ejpam-6536	142	26	contains	contain	VERB
ejpam-6536	142	27	a	a	DET
ejpam-6536	142	28	γh	γh	ADV
ejpam-6536	142	29	-	-	PUNCT
ejpam-6536	142	30	set	set	NOUN
ejpam-6536	142	31	of	of	ADP
ejpam-6536	142	32	g.	g.	PROPN
ejpam-6536	142	33	the	the	DET
ejpam-6536	142	34	minimum	minimum	ADJ
ejpam-6536	142	35	cardinality	cardinality	NOUN
ejpam-6536	142	36	of	of	ADP
ejpam-6536	142	37	an	an	DET
ejpam-6536	142	38	inverse	inverse	NOUN
ejpam-6536	142	39	hop	hop	NOUN
ejpam-6536	142	40	dominating	dominating	NOUN
ejpam-6536	142	41	set	set	NOUN
ejpam-6536	142	42	is	be	AUX
ejpam-6536	142	43	called	call	VERB
ejpam-6536	142	44	the	the	DET
ejpam-6536	142	45	inverse	inverse	NOUN
ejpam-6536	142	46	hop	hop	NOUN
ejpam-6536	142	47	domination	domination	NOUN
ejpam-6536	142	48	number	number	NOUN
ejpam-6536	142	49	of	of	ADP
ejpam-6536	142	50	g	g	NOUN
ejpam-6536	142	51	,	,	PUNCT
ejpam-6536	142	52	and	and	CCONJ
ejpam-6536	142	53	is	be	AUX
ejpam-6536	142	54	denoted	denote	VERB
ejpam-6536	142	55	by	by	ADP
ejpam-6536	142	56	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	142	57	)	)	PUNCT
ejpam-6536	142	58	.	.	PUNCT
ejpam-6536	143	1	clearly	clearly	ADV
ejpam-6536	143	2	,	,	PUNCT
ejpam-6536	143	3	for	for	ADP
ejpam-6536	143	4	g	g	PROPN
ejpam-6536	143	5	∈	∈	PROPN
ejpam-6536	143	6	g	g	NOUN
ejpam-6536	143	7	of	of	ADP
ejpam-6536	143	8	order	order	NOUN
ejpam-6536	143	9	n	n	CCONJ
ejpam-6536	143	10	,	,	PUNCT
ejpam-6536	143	11	2	2	NUM
ejpam-6536	143	12	≤	≤	NOUN
ejpam-6536	143	13	γh(g	γh(g	NOUN
ejpam-6536	143	14	)	)	PUNCT
ejpam-6536	143	15	≤	≤	NOUN
ejpam-6536	143	16	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	143	17	)	)	PUNCT
ejpam-6536	143	18	≤	≤	NOUN
ejpam-6536	143	19	n	n	CCONJ
ejpam-6536	143	20	−	−	NOUN
ejpam-6536	143	21	γh(g	γh(g	NOUN
ejpam-6536	143	22	)	)	PUNCT
ejpam-6536	143	23	≤	≤	NOUN
ejpam-6536	144	1	n	n	CCONJ
ejpam-6536	144	2	−	−	PROPN
ejpam-6536	144	3	2	2	NUM
ejpam-6536	144	4	.	.	PUNCT
ejpam-6536	145	1	(	(	PUNCT
ejpam-6536	145	2	1	1	X
ejpam-6536	145	3	)	)	PUNCT
ejpam-6536	145	4	v.	v.	ADP
ejpam-6536	145	5	a	a	DET
ejpam-6536	145	6	besana	besana	PROPN
ejpam-6536	145	7	,	,	PUNCT
ejpam-6536	145	8	f.	f.	PROPN
ejpam-6536	145	9	jamil	jamil	PROPN
ejpam-6536	145	10	,	,	PUNCT
ejpam-6536	145	11	s.	s.	PROPN
ejpam-6536	145	12	canoy	canoy	PROPN
ejpam-6536	145	13	jr	jr	PROPN
ejpam-6536	145	14	.	.	PROPN
ejpam-6536	145	15	/	/	SYM
ejpam-6536	145	16	eur	eur	PROPN
ejpam-6536	145	17	.	.	PUNCT
ejpam-6536	146	1	j.	j.	PROPN
ejpam-6536	146	2	pure	pure	PROPN
ejpam-6536	146	3	appl	appl	PROPN
ejpam-6536	146	4	.	.	PROPN
ejpam-6536	146	5	math	math	PROPN
ejpam-6536	146	6	,	,	PUNCT
ejpam-6536	146	7	18	18	NUM
ejpam-6536	146	8	(	(	PUNCT
ejpam-6536	146	9	3	3	NUM
ejpam-6536	146	10	)	)	PUNCT
ejpam-6536	146	11	(	(	PUNCT
ejpam-6536	146	12	2025	2025	NUM
ejpam-6536	146	13	)	)	PUNCT
ejpam-6536	146	14	,	,	PUNCT
ejpam-6536	146	15	6536	6536	NUM
ejpam-6536	146	16	6	6	NUM
ejpam-6536	146	17	of	of	ADP
ejpam-6536	146	18	17	17	NUM
ejpam-6536	146	19	theorem	theorem	NOUN
ejpam-6536	146	20	5	5	NUM
ejpam-6536	146	21	.	.	PUNCT
ejpam-6536	147	1	let	let	VERB
ejpam-6536	147	2	g	g	PROPN
ejpam-6536	147	3	∈	∈	PROPN
ejpam-6536	147	4	g	g	NOUN
ejpam-6536	147	5	of	of	ADP
ejpam-6536	147	6	order	order	NOUN
ejpam-6536	147	7	n.	n.	NOUN
ejpam-6536	147	8	then	then	ADV
ejpam-6536	147	9	(	(	PUNCT
ejpam-6536	147	10	i	i	NOUN
ejpam-6536	147	11	)	)	PUNCT
ejpam-6536	147	12	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	147	13	)	)	PUNCT
ejpam-6536	147	14	=	=	SYM
ejpam-6536	147	15	2	2	NUM
ejpam-6536	147	16	if	if	SCONJ
ejpam-6536	147	17	and	and	CCONJ
ejpam-6536	147	18	only	only	ADV
ejpam-6536	147	19	if	if	SCONJ
ejpam-6536	147	20	γh(g	γh(g	NOUN
ejpam-6536	147	21	)	)	PUNCT
ejpam-6536	147	22	=	=	SYM
ejpam-6536	147	23	2	2	NUM
ejpam-6536	147	24	and	and	CCONJ
ejpam-6536	147	25	g	g	PROPN
ejpam-6536	147	26	has	have	VERB
ejpam-6536	147	27	two	two	NUM
ejpam-6536	147	28	disjoint	disjoint	ADJ
ejpam-6536	147	29	γh	γh	NOUN
ejpam-6536	147	30	-	-	PUNCT
ejpam-6536	147	31	sets	set	NOUN
ejpam-6536	147	32	.	.	PUNCT
ejpam-6536	148	1	(	(	PUNCT
ejpam-6536	148	2	ii	ii	NOUN
ejpam-6536	148	3	)	)	PUNCT
ejpam-6536	148	4	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	148	5	)	)	PUNCT
ejpam-6536	148	6	=	=	SYM
ejpam-6536	149	1	n	n	CCONJ
ejpam-6536	149	2	−	−	NUM
ejpam-6536	149	3	2	2	NUM
ejpam-6536	149	4	if	if	SCONJ
ejpam-6536	149	5	and	and	CCONJ
ejpam-6536	149	6	only	only	ADV
ejpam-6536	149	7	if	if	SCONJ
ejpam-6536	149	8	γh(g	γh(g	NOUN
ejpam-6536	149	9	)	)	PUNCT
ejpam-6536	149	10	=	=	SYM
ejpam-6536	149	11	2	2	NUM
ejpam-6536	149	12	and	and	CCONJ
ejpam-6536	149	13	for	for	ADP
ejpam-6536	149	14	every	every	DET
ejpam-6536	149	15	γh	γh	ADV
ejpam-6536	149	16	-	-	PUNCT
ejpam-6536	149	17	set	set	VERB
ejpam-6536	149	18	{	{	PUNCT
ejpam-6536	149	19	u	u	NOUN
ejpam-6536	149	20	,	,	PUNCT
ejpam-6536	149	21	v	v	NOUN
ejpam-6536	149	22	}	}	PUNCT
ejpam-6536	149	23	of	of	ADP
ejpam-6536	149	24	g	g	NOUN
ejpam-6536	149	25	,	,	PUNCT
ejpam-6536	149	26	dg(x	dg(x	NUM
ejpam-6536	149	27	,	,	PUNCT
ejpam-6536	149	28	y	y	NOUN
ejpam-6536	149	29	)	)	PUNCT
ejpam-6536	149	30	̸=	̸=	PROPN
ejpam-6536	149	31	2	2	NUM
ejpam-6536	149	32	for	for	ADP
ejpam-6536	149	33	all	all	DET
ejpam-6536	149	34	x	x	NOUN
ejpam-6536	149	35	,	,	PUNCT
ejpam-6536	149	36	y	y	PROPN
ejpam-6536	149	37	∈	∈	PROPN
ejpam-6536	149	38	v	v	ADP
ejpam-6536	149	39	(	(	PUNCT
ejpam-6536	149	40	g	g	NOUN
ejpam-6536	149	41	)	)	PUNCT
ejpam-6536	149	42	\	\	NOUN
ejpam-6536	150	1	{	{	PUNCT
ejpam-6536	150	2	u	u	NOUN
ejpam-6536	150	3	,	,	PUNCT
ejpam-6536	150	4	v	v	NOUN
ejpam-6536	150	5	}	}	PUNCT
ejpam-6536	150	6	.	.	PUNCT
ejpam-6536	151	1	proof	proof	NOUN
ejpam-6536	151	2	:	:	PUNCT
ejpam-6536	151	3	for	for	ADP
ejpam-6536	151	4	(	(	PUNCT
ejpam-6536	151	5	i	i	NOUN
ejpam-6536	151	6	)	)	PUNCT
ejpam-6536	151	7	,	,	PUNCT
ejpam-6536	151	8	from	from	ADP
ejpam-6536	151	9	inequality	inequality	NOUN
ejpam-6536	151	10	1	1	NUM
ejpam-6536	151	11	,	,	PUNCT
ejpam-6536	151	12	if	if	SCONJ
ejpam-6536	151	13	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	151	14	)	)	PUNCT
ejpam-6536	151	15	=	=	SYM
ejpam-6536	151	16	2	2	NUM
ejpam-6536	151	17	,	,	PUNCT
ejpam-6536	151	18	then	then	ADV
ejpam-6536	151	19	γh(g	γh(g	PUNCT
ejpam-6536	151	20	)	)	PUNCT
ejpam-6536	151	21	=	=	SYM
ejpam-6536	151	22	2	2	NUM
ejpam-6536	151	23	and	and	CCONJ
ejpam-6536	151	24	the	the	DET
ejpam-6536	151	25	conclusion	conclusion	NOUN
ejpam-6536	151	26	follows	follow	VERB
ejpam-6536	151	27	.	.	PUNCT
ejpam-6536	152	1	the	the	DET
ejpam-6536	152	2	converse	converse	NOUN
ejpam-6536	152	3	is	be	AUX
ejpam-6536	152	4	clear	clear	ADJ
ejpam-6536	152	5	.	.	PUNCT
ejpam-6536	153	1	suppose	suppose	VERB
ejpam-6536	153	2	that	that	SCONJ
ejpam-6536	153	3	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	153	4	)	)	PUNCT
ejpam-6536	153	5	=	=	SYM
ejpam-6536	154	1	n	n	CCONJ
ejpam-6536	154	2	−	−	PROPN
ejpam-6536	154	3	2	2	NUM
ejpam-6536	154	4	.	.	PUNCT
ejpam-6536	155	1	then	then	ADV
ejpam-6536	155	2	inequality	inequality	NOUN
ejpam-6536	155	3	1	1	NUM
ejpam-6536	155	4	implies	imply	VERB
ejpam-6536	155	5	that	that	PRON
ejpam-6536	155	6	γh(g	γh(g	NOUN
ejpam-6536	155	7	)	)	PUNCT
ejpam-6536	155	8	=	=	SYM
ejpam-6536	155	9	2	2	X
ejpam-6536	155	10	.	.	X
ejpam-6536	155	11	let	let	VERB
ejpam-6536	155	12	{	{	PUNCT
ejpam-6536	155	13	u	u	NOUN
ejpam-6536	155	14	,	,	PUNCT
ejpam-6536	155	15	v	v	NOUN
ejpam-6536	155	16	}	}	PUNCT
ejpam-6536	155	17	be	be	AUX
ejpam-6536	155	18	a	a	DET
ejpam-6536	155	19	γh	γh	ADV
ejpam-6536	155	20	-	-	PUNCT
ejpam-6536	155	21	set	set	NOUN
ejpam-6536	155	22	of	of	ADP
ejpam-6536	155	23	g.	g.	PROPN
ejpam-6536	155	24	then	then	ADV
ejpam-6536	155	25	s	s	VERB
ejpam-6536	155	26	=	=	SYM
ejpam-6536	155	27	v	v	ADJ
ejpam-6536	155	28	(	(	PUNCT
ejpam-6536	155	29	g	g	NOUN
ejpam-6536	155	30	)	)	PUNCT
ejpam-6536	155	31	\	\	NOUN
ejpam-6536	156	1	{	{	PUNCT
ejpam-6536	156	2	u	u	NOUN
ejpam-6536	156	3	,	,	PUNCT
ejpam-6536	156	4	v	v	NOUN
ejpam-6536	156	5	}	}	PUNCT
ejpam-6536	156	6	is	be	AUX
ejpam-6536	156	7	a	a	DET
ejpam-6536	156	8	γ̃h	γ̃h	NOUN
ejpam-6536	156	9	-	-	PUNCT
ejpam-6536	156	10	set	set	NOUN
ejpam-6536	156	11	of	of	ADP
ejpam-6536	156	12	g.	g.	PROPN
ejpam-6536	156	13	let	let	VERB
ejpam-6536	156	14	x	x	PRON
ejpam-6536	156	15	,	,	PUNCT
ejpam-6536	156	16	y	y	PROPN
ejpam-6536	156	17	∈	∈	PROPN
ejpam-6536	156	18	s	s	VERB
ejpam-6536	156	19	with	with	ADP
ejpam-6536	156	20	dg(x	dg(x	PROPN
ejpam-6536	156	21	,	,	PUNCT
ejpam-6536	156	22	y	y	NOUN
ejpam-6536	156	23	)	)	PUNCT
ejpam-6536	157	1	=	=	SYM
ejpam-6536	157	2	2	2	X
ejpam-6536	157	3	.	.	X
ejpam-6536	158	1	first	first	ADV
ejpam-6536	158	2	,	,	PUNCT
ejpam-6536	158	3	if	if	SCONJ
ejpam-6536	158	4	u	u	NOUN
ejpam-6536	158	5	,	,	PUNCT
ejpam-6536	158	6	v	v	NUM
ejpam-6536	158	7	/∈	/∈	PUNCT
ejpam-6536	158	8	ng(x	ng(x	NUM
ejpam-6536	158	9	,	,	PUNCT
ejpam-6536	158	10	2	2	NUM
ejpam-6536	158	11	)	)	PUNCT
ejpam-6536	158	12	,	,	PUNCT
ejpam-6536	158	13	then	then	ADV
ejpam-6536	158	14	s	s	VERB
ejpam-6536	158	15	\	\	X
ejpam-6536	158	16	{	{	PUNCT
ejpam-6536	158	17	x	x	NOUN
ejpam-6536	158	18	}	}	PUNCT
ejpam-6536	158	19	is	be	AUX
ejpam-6536	158	20	a	a	DET
ejpam-6536	158	21	hop	hop	NOUN
ejpam-6536	158	22	dominating	dominating	NOUN
ejpam-6536	158	23	set	set	NOUN
ejpam-6536	158	24	of	of	ADP
ejpam-6536	158	25	g	g	PROPN
ejpam-6536	158	26	,	,	PUNCT
ejpam-6536	158	27	a	a	DET
ejpam-6536	158	28	contradiction	contradiction	NOUN
ejpam-6536	158	29	.	.	PUNCT
ejpam-6536	159	1	next	next	ADV
ejpam-6536	159	2	,	,	PUNCT
ejpam-6536	159	3	if	if	SCONJ
ejpam-6536	159	4	u	u	NOUN
ejpam-6536	159	5	,	,	PUNCT
ejpam-6536	159	6	v	v	PROPN
ejpam-6536	159	7	∈	∈	PROPN
ejpam-6536	159	8	ng(x	ng(x	NUM
ejpam-6536	159	9	,	,	PUNCT
ejpam-6536	159	10	2	2	NUM
ejpam-6536	159	11	)	)	PUNCT
ejpam-6536	159	12	,	,	PUNCT
ejpam-6536	159	13	then	then	ADV
ejpam-6536	159	14	s	s	VERB
ejpam-6536	159	15	\	\	PROPN
ejpam-6536	159	16	{	{	PUNCT
ejpam-6536	159	17	y	y	NOUN
ejpam-6536	159	18	}	}	PUNCT
ejpam-6536	159	19	is	be	AUX
ejpam-6536	159	20	a	a	DET
ejpam-6536	159	21	hop	hop	NOUN
ejpam-6536	159	22	dominating	dominating	NOUN
ejpam-6536	159	23	set	set	NOUN
ejpam-6536	159	24	of	of	ADP
ejpam-6536	159	25	g	g	PROPN
ejpam-6536	159	26	,	,	PUNCT
ejpam-6536	159	27	a	a	DET
ejpam-6536	159	28	contradiction	contradiction	NOUN
ejpam-6536	159	29	.	.	PUNCT
ejpam-6536	160	1	now	now	ADV
ejpam-6536	160	2	assume	assume	VERB
ejpam-6536	160	3	that	that	SCONJ
ejpam-6536	160	4	u	u	PROPN
ejpam-6536	160	5	∈	∈	PROPN
ejpam-6536	160	6	ng(x	ng(x	NUM
ejpam-6536	160	7	,	,	PUNCT
ejpam-6536	160	8	2	2	NUM
ejpam-6536	160	9	)	)	PUNCT
ejpam-6536	160	10	and	and	CCONJ
ejpam-6536	160	11	v	v	NOUN
ejpam-6536	160	12	/∈	/∈	PUNCT
ejpam-6536	160	13	ng(x	ng(x	NUM
ejpam-6536	160	14	,	,	PUNCT
ejpam-6536	160	15	2	2	NUM
ejpam-6536	160	16	)	)	PUNCT
ejpam-6536	160	17	,	,	PUNCT
ejpam-6536	160	18	and	and	CCONJ
ejpam-6536	160	19	let	let	VERB
ejpam-6536	160	20	[	[	X
ejpam-6536	160	21	x	x	X
ejpam-6536	160	22	,	,	PUNCT
ejpam-6536	160	23	z	z	PROPN
ejpam-6536	160	24	,	,	PUNCT
ejpam-6536	160	25	u	u	X
ejpam-6536	160	26	]	]	X
ejpam-6536	160	27	be	be	AUX
ejpam-6536	160	28	a	a	DET
ejpam-6536	160	29	x	x	NOUN
ejpam-6536	160	30	-	-	PUNCT
ejpam-6536	160	31	u	u	NOUN
ejpam-6536	160	32	geodesic	geodesic	NOUN
ejpam-6536	160	33	in	in	ADP
ejpam-6536	160	34	g.	g.	PROPN
ejpam-6536	160	35	suppose	suppose	VERB
ejpam-6536	160	36	that	that	SCONJ
ejpam-6536	160	37	z	z	PROPN
ejpam-6536	160	38	̸=	̸=	PROPN
ejpam-6536	160	39	v.	v.	CCONJ
ejpam-6536	160	40	then	then	ADV
ejpam-6536	160	41	dg(z	dg(z	NUM
ejpam-6536	160	42	,	,	PUNCT
ejpam-6536	160	43	v	v	NOUN
ejpam-6536	160	44	)	)	PUNCT
ejpam-6536	160	45	=	=	SYM
ejpam-6536	160	46	2	2	NUM
ejpam-6536	160	47	and	and	CCONJ
ejpam-6536	160	48	s\{y	s\{y	NUM
ejpam-6536	160	49	}	}	PUNCT
ejpam-6536	160	50	is	be	AUX
ejpam-6536	160	51	a	a	DET
ejpam-6536	160	52	hop	hop	NOUN
ejpam-6536	160	53	dominating	dominating	NOUN
ejpam-6536	160	54	set	set	NOUN
ejpam-6536	160	55	of	of	ADP
ejpam-6536	160	56	g	g	PROPN
ejpam-6536	160	57	,	,	PUNCT
ejpam-6536	160	58	a	a	DET
ejpam-6536	160	59	contradiction	contradiction	NOUN
ejpam-6536	160	60	.	.	PUNCT
ejpam-6536	161	1	suppose	suppose	VERB
ejpam-6536	161	2	that	that	SCONJ
ejpam-6536	161	3	z	z	NOUN
ejpam-6536	161	4	=	=	PUNCT
ejpam-6536	161	5	v.	v.	INTJ
ejpam-6536	161	6	if	if	SCONJ
ejpam-6536	161	7	[	[	X
ejpam-6536	161	8	x	x	X
ejpam-6536	161	9	,	,	PUNCT
ejpam-6536	161	10	v	v	NOUN
ejpam-6536	161	11	,	,	PUNCT
ejpam-6536	161	12	y	y	PROPN
ejpam-6536	161	13	]	]	PUNCT
ejpam-6536	161	14	is	be	AUX
ejpam-6536	161	15	a	a	DET
ejpam-6536	161	16	x	x	NOUN
ejpam-6536	161	17	-	-	NOUN
ejpam-6536	161	18	y	y	ADJ
ejpam-6536	161	19	geodesic	geodesic	NOUN
ejpam-6536	161	20	in	in	ADP
ejpam-6536	161	21	g	g	PROPN
ejpam-6536	161	22	,	,	PUNCT
ejpam-6536	161	23	then	then	ADV
ejpam-6536	161	24	s	s	VERB
ejpam-6536	161	25	\	\	PROPN
ejpam-6536	161	26	{	{	PUNCT
ejpam-6536	161	27	y	y	NOUN
ejpam-6536	161	28	}	}	PUNCT
ejpam-6536	161	29	is	be	AUX
ejpam-6536	161	30	a	a	DET
ejpam-6536	161	31	hop	hop	NOUN
ejpam-6536	161	32	dominating	dominating	NOUN
ejpam-6536	161	33	set	set	NOUN
ejpam-6536	161	34	of	of	ADP
ejpam-6536	161	35	g	g	PROPN
ejpam-6536	161	36	,	,	PUNCT
ejpam-6536	161	37	a	a	DET
ejpam-6536	161	38	contradiction	contradiction	NOUN
ejpam-6536	161	39	.	.	PUNCT
ejpam-6536	162	1	suppose	suppose	VERB
ejpam-6536	162	2	not	not	PART
ejpam-6536	162	3	,	,	PUNCT
ejpam-6536	162	4	and	and	CCONJ
ejpam-6536	162	5	let	let	VERB
ejpam-6536	162	6	[	[	X
ejpam-6536	162	7	x	x	X
ejpam-6536	162	8	,	,	PUNCT
ejpam-6536	162	9	w	w	PROPN
ejpam-6536	162	10	,	,	PUNCT
ejpam-6536	162	11	y	y	PROPN
ejpam-6536	162	12	]	]	PUNCT
ejpam-6536	162	13	be	be	AUX
ejpam-6536	162	14	a	a	DET
ejpam-6536	162	15	geodesic	geodesic	NOUN
ejpam-6536	162	16	in	in	ADP
ejpam-6536	162	17	g.	g.	PROPN
ejpam-6536	162	18	if	if	SCONJ
ejpam-6536	162	19	wv	wv	PROPN
ejpam-6536	162	20	∈	∈	PROPN
ejpam-6536	162	21	e(g	e(g	PROPN
ejpam-6536	162	22	)	)	PUNCT
ejpam-6536	162	23	,	,	PUNCT
ejpam-6536	162	24	then	then	ADV
ejpam-6536	162	25	s	s	AUX
ejpam-6536	162	26	\{w	\{w	NOUN
ejpam-6536	162	27	}	}	PUNCT
ejpam-6536	162	28	is	be	AUX
ejpam-6536	162	29	a	a	DET
ejpam-6536	162	30	hop	hop	NOUN
ejpam-6536	162	31	dominating	dominating	NOUN
ejpam-6536	162	32	set	set	NOUN
ejpam-6536	162	33	of	of	ADP
ejpam-6536	162	34	g.	g.	PROPN
ejpam-6536	163	1	if	if	SCONJ
ejpam-6536	163	2	wv	wv	PROPN
ejpam-6536	163	3	/∈	/∈	PUNCT
ejpam-6536	163	4	e(g	e(g	PROPN
ejpam-6536	163	5	)	)	PUNCT
ejpam-6536	163	6	,	,	PUNCT
ejpam-6536	163	7	then	then	ADV
ejpam-6536	163	8	s	s	VERB
ejpam-6536	163	9	\	\	PROPN
ejpam-6536	163	10	{	{	PUNCT
ejpam-6536	163	11	y	y	NOUN
ejpam-6536	163	12	}	}	PUNCT
ejpam-6536	163	13	is	be	AUX
ejpam-6536	163	14	a	a	DET
ejpam-6536	163	15	hop	hop	NOUN
ejpam-6536	163	16	dominating	dominating	NOUN
ejpam-6536	163	17	set	set	NOUN
ejpam-6536	163	18	of	of	ADP
ejpam-6536	163	19	g	g	PROPN
ejpam-6536	163	20	,	,	PUNCT
ejpam-6536	163	21	a	a	DET
ejpam-6536	163	22	contradiction	contradiction	NOUN
ejpam-6536	163	23	.	.	PUNCT
ejpam-6536	164	1	the	the	DET
ejpam-6536	164	2	above	above	ADJ
ejpam-6536	164	3	contradictions	contradiction	NOUN
ejpam-6536	164	4	imply	imply	VERB
ejpam-6536	164	5	that	that	SCONJ
ejpam-6536	164	6	dg(x	dg(x	ADV
ejpam-6536	164	7	,	,	PUNCT
ejpam-6536	164	8	y	y	NOUN
ejpam-6536	164	9	)	)	PUNCT
ejpam-6536	164	10	̸=	̸=	PROPN
ejpam-6536	164	11	2	2	NUM
ejpam-6536	164	12	for	for	ADP
ejpam-6536	164	13	all	all	DET
ejpam-6536	164	14	x	x	NOUN
ejpam-6536	164	15	,	,	PUNCT
ejpam-6536	164	16	y	y	PROPN
ejpam-6536	164	17	∈	∈	PROPN
ejpam-6536	164	18	v	v	NOUN
ejpam-6536	164	19	(	(	PUNCT
ejpam-6536	164	20	g)\{u	g)\{u	PROPN
ejpam-6536	164	21	,	,	PUNCT
ejpam-6536	164	22	v	v	NOUN
ejpam-6536	164	23	}	}	PUNCT
ejpam-6536	164	24	.	.	PUNCT
ejpam-6536	165	1	conversely	conversely	ADV
ejpam-6536	165	2	,	,	PUNCT
ejpam-6536	165	3	suppose	suppose	VERB
ejpam-6536	165	4	that	that	SCONJ
ejpam-6536	165	5	γh(g	γh(g	NOUN
ejpam-6536	165	6	)	)	PUNCT
ejpam-6536	165	7	=	=	SYM
ejpam-6536	165	8	2	2	NUM
ejpam-6536	165	9	,	,	PUNCT
ejpam-6536	165	10	and	and	CCONJ
ejpam-6536	165	11	let	let	VERB
ejpam-6536	165	12	{	{	PUNCT
ejpam-6536	165	13	u	u	NOUN
ejpam-6536	165	14	,	,	PUNCT
ejpam-6536	165	15	v	v	NOUN
ejpam-6536	165	16	}	}	PUNCT
ejpam-6536	165	17	be	be	AUX
ejpam-6536	165	18	a	a	DET
ejpam-6536	165	19	γh	γh	ADV
ejpam-6536	165	20	-	-	PUNCT
ejpam-6536	165	21	set	set	NOUN
ejpam-6536	165	22	of	of	ADP
ejpam-6536	165	23	g.	g.	PROPN
ejpam-6536	165	24	if	if	SCONJ
ejpam-6536	165	25	s	s	VERB
ejpam-6536	165	26	=	=	SYM
ejpam-6536	165	27	v	v	PROPN
ejpam-6536	165	28	(	(	PUNCT
ejpam-6536	165	29	g)\{u	g)\{u	PROPN
ejpam-6536	165	30	,	,	PUNCT
ejpam-6536	165	31	v	v	NOUN
ejpam-6536	165	32	}	}	PUNCT
ejpam-6536	165	33	is	be	AUX
ejpam-6536	165	34	not	not	PART
ejpam-6536	165	35	a	a	DET
ejpam-6536	165	36	γ̃h	γ̃h	ADV
ejpam-6536	165	37	-	-	PUNCT
ejpam-6536	165	38	set	set	NOUN
ejpam-6536	165	39	of	of	ADP
ejpam-6536	165	40	g	g	NOUN
ejpam-6536	165	41	,	,	PUNCT
ejpam-6536	165	42	then	then	ADV
ejpam-6536	165	43	there	there	PRON
ejpam-6536	165	44	exists	exist	VERB
ejpam-6536	165	45	x	x	X
ejpam-6536	165	46	∈	∈	NOUN
ejpam-6536	165	47	s	s	VERB
ejpam-6536	165	48	such	such	ADJ
ejpam-6536	165	49	that	that	PRON
ejpam-6536	165	50	s	s	VERB
ejpam-6536	165	51	\	\	X
ejpam-6536	165	52	{	{	PUNCT
ejpam-6536	165	53	x	x	NOUN
ejpam-6536	165	54	}	}	PUNCT
ejpam-6536	165	55	is	be	AUX
ejpam-6536	165	56	a	a	DET
ejpam-6536	165	57	hop	hop	NOUN
ejpam-6536	165	58	dominating	dominating	NOUN
ejpam-6536	165	59	set	set	NOUN
ejpam-6536	165	60	of	of	ADP
ejpam-6536	165	61	g.	g.	PROPN
ejpam-6536	165	62	this	this	PRON
ejpam-6536	165	63	means	mean	VERB
ejpam-6536	165	64	that	that	SCONJ
ejpam-6536	165	65	,	,	PUNCT
ejpam-6536	165	66	in	in	ADP
ejpam-6536	165	67	particular	particular	ADJ
ejpam-6536	165	68	,	,	PUNCT
ejpam-6536	165	69	there	there	PRON
ejpam-6536	165	70	exists	exist	VERB
ejpam-6536	165	71	y	y	PROPN
ejpam-6536	165	72	∈	∈	PROPN
ejpam-6536	165	73	s	s	PART
ejpam-6536	165	74	\	\	X
ejpam-6536	165	75	{	{	PUNCT
ejpam-6536	165	76	x	x	X
ejpam-6536	165	77	}	}	PUNCT
ejpam-6536	165	78	such	such	ADJ
ejpam-6536	165	79	that	that	PRON
ejpam-6536	165	80	dg(x	dg(x	PROPN
ejpam-6536	165	81	,	,	PUNCT
ejpam-6536	165	82	y	y	NOUN
ejpam-6536	165	83	)	)	PUNCT
ejpam-6536	165	84	=	=	SYM
ejpam-6536	165	85	2	2	NUM
ejpam-6536	165	86	,	,	PUNCT
ejpam-6536	165	87	contrary	contrary	ADV
ejpam-6536	165	88	to	to	ADP
ejpam-6536	165	89	the	the	DET
ejpam-6536	165	90	hypothesis	hypothesis	NOUN
ejpam-6536	165	91	.	.	PUNCT
ejpam-6536	166	1	■	■	PUNCT
ejpam-6536	166	2	observe	observe	VERB
ejpam-6536	166	3	that	that	SCONJ
ejpam-6536	166	4	for	for	ADP
ejpam-6536	166	5	graph	graph	NOUN
ejpam-6536	166	6	g1	g1	NOUN
ejpam-6536	166	7	in	in	ADP
ejpam-6536	166	8	figure	figure	NOUN
ejpam-6536	166	9	1	1	NUM
ejpam-6536	166	10	,	,	PUNCT
ejpam-6536	166	11	{	{	PUNCT
ejpam-6536	166	12	u	u	NOUN
ejpam-6536	166	13	,	,	PUNCT
ejpam-6536	166	14	v	v	NOUN
ejpam-6536	166	15	}	}	PUNCT
ejpam-6536	166	16	in	in	ADP
ejpam-6536	166	17	particular	particular	ADJ
ejpam-6536	166	18	,	,	PUNCT
ejpam-6536	166	19	is	be	AUX
ejpam-6536	166	20	a	a	DET
ejpam-6536	166	21	γh	γh	ADV
ejpam-6536	166	22	-	-	PUNCT
ejpam-6536	166	23	set	set	VERB
ejpam-6536	166	24	and	and	CCONJ
ejpam-6536	166	25	x	x	NOUN
ejpam-6536	166	26	,	,	PUNCT
ejpam-6536	166	27	z	z	PROPN
ejpam-6536	166	28	∈	∈	PROPN
ejpam-6536	166	29	v	v	X
ejpam-6536	166	30	(	(	PUNCT
ejpam-6536	166	31	g1	g1	PROPN
ejpam-6536	166	32	)	)	PUNCT
ejpam-6536	166	33	\	\	NOUN
ejpam-6536	166	34	{	{	PUNCT
ejpam-6536	166	35	u	u	NOUN
ejpam-6536	166	36	,	,	PUNCT
ejpam-6536	166	37	v	v	NOUN
ejpam-6536	166	38	}	}	PUNCT
ejpam-6536	166	39	with	with	ADP
ejpam-6536	166	40	dg(x	dg(x	NUM
ejpam-6536	166	41	,	,	PUNCT
ejpam-6536	166	42	z	z	NOUN
ejpam-6536	166	43	)	)	PUNCT
ejpam-6536	166	44	=	=	SYM
ejpam-6536	166	45	2	2	X
ejpam-6536	166	46	.	.	PUNCT
ejpam-6536	166	47	by	by	ADP
ejpam-6536	166	48	theorem	theorem	NOUN
ejpam-6536	166	49	5(ii	5(ii	NUM
ejpam-6536	166	50	)	)	PUNCT
ejpam-6536	166	51	,	,	PUNCT
ejpam-6536	166	52	γ̃h(g1	γ̃h(g1	PROPN
ejpam-6536	166	53	)	)	PUNCT
ejpam-6536	166	54	<	<	X
ejpam-6536	166	55	3	3	X
ejpam-6536	166	56	.	.	PUNCT
ejpam-6536	166	57	since	since	SCONJ
ejpam-6536	166	58	{	{	PUNCT
ejpam-6536	166	59	x	x	NOUN
ejpam-6536	166	60	,	,	PUNCT
ejpam-6536	166	61	y	y	PRON
ejpam-6536	166	62	}	}	PUNCT
ejpam-6536	166	63	is	be	AUX
ejpam-6536	166	64	a	a	DET
ejpam-6536	166	65	γh	γh	ADV
ejpam-6536	166	66	-	-	PUNCT
ejpam-6536	166	67	set	set	VERB
ejpam-6536	166	68	,	,	PUNCT
ejpam-6536	166	69	γ̃h(g1	γ̃h(g1	ADJ
ejpam-6536	166	70	)	)	PUNCT
ejpam-6536	166	71	=	=	SYM
ejpam-6536	166	72	2	2	NUM
ejpam-6536	166	73	as	as	SCONJ
ejpam-6536	166	74	also	also	ADV
ejpam-6536	166	75	affirmed	affirm	VERB
ejpam-6536	166	76	by	by	ADP
ejpam-6536	166	77	statement	statement	NOUN
ejpam-6536	166	78	(	(	PUNCT
ejpam-6536	166	79	i	i	NOUN
ejpam-6536	166	80	)	)	PUNCT
ejpam-6536	166	81	.	.	PUNCT
ejpam-6536	167	1	for	for	ADP
ejpam-6536	167	2	g2	g2	PROPN
ejpam-6536	167	3	in	in	ADP
ejpam-6536	167	4	figure	figure	NOUN
ejpam-6536	167	5	1	1	NUM
ejpam-6536	167	6	,	,	PUNCT
ejpam-6536	167	7	{	{	PUNCT
ejpam-6536	167	8	u	u	NOUN
ejpam-6536	167	9	,	,	PUNCT
ejpam-6536	167	10	v	v	NOUN
ejpam-6536	167	11	}	}	PUNCT
ejpam-6536	167	12	and	and	CCONJ
ejpam-6536	167	13	{	{	PUNCT
ejpam-6536	167	14	v	v	NOUN
ejpam-6536	167	15	,	,	PUNCT
ejpam-6536	167	16	w	w	NOUN
ejpam-6536	167	17	}	}	PUNCT
ejpam-6536	167	18	are	be	AUX
ejpam-6536	167	19	the	the	DET
ejpam-6536	167	20	only	only	ADJ
ejpam-6536	167	21	γh	γh	NOUN
ejpam-6536	167	22	-	-	PUNCT
ejpam-6536	167	23	sets	set	NOUN
ejpam-6536	167	24	of	of	ADP
ejpam-6536	167	25	g2	g2	PROPN
ejpam-6536	167	26	.	.	PUNCT
ejpam-6536	168	1	both	both	DET
ejpam-6536	168	2	γh	γh	NOUN
ejpam-6536	168	3	-	-	PUNCT
ejpam-6536	168	4	sets	set	NOUN
ejpam-6536	168	5	satisfy	satisfy	VERB
ejpam-6536	168	6	the	the	DET
ejpam-6536	168	7	conditions	condition	NOUN
ejpam-6536	168	8	in	in	ADP
ejpam-6536	168	9	theorem	theorem	NOUN
ejpam-6536	168	10	5(ii	5(ii	NUM
ejpam-6536	168	11	)	)	PUNCT
ejpam-6536	168	12	.	.	PUNCT
ejpam-6536	169	1	thus	thus	ADV
ejpam-6536	169	2	,	,	PUNCT
ejpam-6536	169	3	γ̃h(g2	γ̃h(g2	ADJ
ejpam-6536	169	4	)	)	PUNCT
ejpam-6536	169	5	=	=	SYM
ejpam-6536	170	1	n	n	CCONJ
ejpam-6536	170	2	−	−	NUM
ejpam-6536	170	3	2	2	NUM
ejpam-6536	170	4	=	=	SYM
ejpam-6536	170	5	6	6	NUM
ejpam-6536	170	6	−	−	NOUN
ejpam-6536	170	7	2	2	NUM
ejpam-6536	170	8	=	=	SYM
ejpam-6536	170	9	4	4	NUM
ejpam-6536	170	10	.	.	PUNCT
ejpam-6536	170	11	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	171	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	171	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	172	1	....................................	....................................	PUNCT
ejpam-6536	172	2	...........	...........	PUNCT
ejpam-6536	173	1	..........	..........	PUNCT
ejpam-6536	173	2	..........	..........	PUNCT
ejpam-6536	174	1	..........	..........	PUNCT
ejpam-6536	174	2	..........	..........	PUNCT
ejpam-6536	175	1	..........	..........	PUNCT
ejpam-6536	175	2	..........	..........	PUNCT
ejpam-6536	176	1	..........	..........	PUNCT
ejpam-6536	176	2	.......	.......	PUNCT
ejpam-6536	177	1	....................................	....................................	PUNCT
ejpam-6536	177	2	........................................................................................	........................................................................................	PUNCT
ejpam-6536	178	1	....................................	....................................	PUNCT
ejpam-6536	179	1	....................................	....................................	PUNCT
ejpam-6536	180	1	•	•	NUM
ejpam-6536	181	1	•	•	NUM
ejpam-6536	181	2	•	•	NUM
ejpam-6536	181	3	•	•	NOUN
ejpam-6536	181	4	•	•	NUM
ejpam-6536	181	5	u	u	NOUN
ejpam-6536	181	6	vx	vx	PROPN
ejpam-6536	181	7	y	y	PROPN
ejpam-6536	181	8	z	z	PROPN
ejpam-6536	181	9	g1	g1	PROPN
ejpam-6536	181	10	:	:	PUNCT
ejpam-6536	182	1	.......................................................................................................................................	.......................................................................................................................................	PROPN
ejpam-6536	182	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	182	3	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	183	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6536	183	2	....................................	....................................	PUNCT
ejpam-6536	184	1	...........	...........	PUNCT
ejpam-6536	184	2	..........	..........	PUNCT
ejpam-6536	185	1	..........	..........	PUNCT
ejpam-6536	185	2	..........	..........	PUNCT
ejpam-6536	186	1	..........	..........	PUNCT
ejpam-6536	186	2	..........	..........	PUNCT
ejpam-6536	187	1	..........	..........	PUNCT
ejpam-6536	187	2	..........	..........	PUNCT
ejpam-6536	187	3	.......	.......	PUNCT
ejpam-6536	188	1	....................................	....................................	PUNCT
ejpam-6536	188	2	........................................................................................	........................................................................................	PUNCT
ejpam-6536	189	1	....................................	....................................	PUNCT
ejpam-6536	190	1	....................................	....................................	PUNCT
ejpam-6536	191	1	•	•	NUM
ejpam-6536	192	1	•	•	NUM
ejpam-6536	192	2	•	•	NUM
ejpam-6536	192	3	•	•	NUM
ejpam-6536	192	4	•	•	NOUN
ejpam-6536	192	5	•	•	NUM
ejpam-6536	192	6	u	u	PROPN
ejpam-6536	192	7	v	v	PROPN
ejpam-6536	192	8	w	w	PROPN
ejpam-6536	192	9	g2	g2	PROPN
ejpam-6536	192	10	:	:	PUNCT
ejpam-6536	192	11	figure	figure	VERB
ejpam-6536	192	12	1	1	NUM
ejpam-6536	192	13	:	:	PUNCT
ejpam-6536	192	14	examples	example	NOUN
ejpam-6536	192	15	of	of	ADP
ejpam-6536	192	16	graphs	graph	NOUN
ejpam-6536	192	17	described	describe	VERB
ejpam-6536	192	18	in	in	ADP
ejpam-6536	192	19	theorem	theorem	NOUN
ejpam-6536	192	20	5	5	NUM
ejpam-6536	192	21	in	in	ADP
ejpam-6536	192	22	view	view	NOUN
ejpam-6536	192	23	of	of	ADP
ejpam-6536	192	24	proposition	proposition	NOUN
ejpam-6536	192	25	1	1	NUM
ejpam-6536	192	26	,	,	PUNCT
ejpam-6536	192	27	the	the	DET
ejpam-6536	192	28	following	follow	VERB
ejpam-6536	192	29	observations	observation	NOUN
ejpam-6536	192	30	hold	hold	VERB
ejpam-6536	192	31	.	.	PUNCT
ejpam-6536	193	1	observation	observation	NOUN
ejpam-6536	193	2	1	1	NUM
ejpam-6536	193	3	.	.	PUNCT
ejpam-6536	194	1	(	(	PUNCT
ejpam-6536	194	2	i	i	NOUN
ejpam-6536	194	3	)	)	PUNCT
ejpam-6536	194	4	for	for	ADP
ejpam-6536	194	5	a	a	DET
ejpam-6536	194	6	complete	complete	ADJ
ejpam-6536	194	7	multipartite	multipartite	ADJ
ejpam-6536	194	8	graph	graph	NOUN
ejpam-6536	194	9	g	g	PROPN
ejpam-6536	194	10	=	=	PUNCT
ejpam-6536	194	11	kr1,r2,	kr1,r2,	PROPN
ejpam-6536	194	12	...	...	PUNCT
ejpam-6536	194	13	,rn	,rn	PUNCT
ejpam-6536	194	14	with	with	ADP
ejpam-6536	194	15	2	2	NUM
ejpam-6536	194	16	≤	≤	NOUN
ejpam-6536	194	17	r1	r1	NOUN
ejpam-6536	194	18	≤	≤	NUM
ejpam-6536	194	19	r2	r2	PROPN
ejpam-6536	194	20	≤	≤	PUNCT
ejpam-6536	194	21	·	·	PUNCT
ejpam-6536	194	22	·	·	PUNCT
ejpam-6536	194	23	·	·	PUNCT
ejpam-6536	194	24	≤	≤	NUM
ejpam-6536	194	25	rn	rn	PROPN
ejpam-6536	194	26	,	,	PUNCT
ejpam-6536	194	27	γ̃h(g	γ̃h(g	X
ejpam-6536	194	28	)	)	PUNCT
ejpam-6536	194	29	=	=	SYM
ejpam-6536	195	1	n.	n.	NOUN
ejpam-6536	195	2	(	(	PUNCT
ejpam-6536	195	3	ii	ii	PROPN
ejpam-6536	195	4	)	)	PUNCT
ejpam-6536	195	5	for	for	ADP
ejpam-6536	195	6	a	a	DET
ejpam-6536	195	7	path	path	NOUN
ejpam-6536	195	8	pn	pn	NOUN
ejpam-6536	195	9	on	on	ADP
ejpam-6536	195	10	n	n	PRON
ejpam-6536	195	11	≥	≥	NUM
ejpam-6536	195	12	4	4	NUM
ejpam-6536	195	13	vertices	vertex	NOUN
ejpam-6536	195	14	,	,	PUNCT
ejpam-6536	195	15	γ̃h(pn	γ̃h(pn	NOUN
ejpam-6536	195	16	)	)	PUNCT
ejpam-6536	195	17	=	=	SYM
ejpam-6536	195	18	{	{	PUNCT
ejpam-6536	195	19	2r	2r	NUM
ejpam-6536	196	1	+	+	CCONJ
ejpam-6536	196	2	3	3	NUM
ejpam-6536	196	3	,	,	PUNCT
ejpam-6536	196	4	if	if	SCONJ
ejpam-6536	196	5	n	n	NOUN
ejpam-6536	196	6	=	=	SYM
ejpam-6536	196	7	6r	6r	NUM
ejpam-6536	197	1	+	+	CCONJ
ejpam-6536	197	2	5	5	NUM
ejpam-6536	197	3	;	;	PUNCT
ejpam-6536	197	4	2r	2r	NUM
ejpam-6536	197	5	+	+	CCONJ
ejpam-6536	198	1	2	2	NUM
ejpam-6536	198	2	,	,	PUNCT
ejpam-6536	198	3	if	if	SCONJ
ejpam-6536	198	4	n	n	NOUN
ejpam-6536	198	5	=	=	SYM
ejpam-6536	198	6	6r	6r	NUM
ejpam-6536	198	7	+	+	SYM
ejpam-6536	198	8	s	s	X
ejpam-6536	198	9	;	;	PUNCT
ejpam-6536	198	10	0	0	NUM
ejpam-6536	198	11	≤	≤	NUM
ejpam-6536	198	12	s	s	PART
ejpam-6536	198	13	≤	≤	NOUN
ejpam-6536	198	14	4	4	NUM
ejpam-6536	198	15	.	.	PUNCT
ejpam-6536	199	1	v.	v.	ADP
ejpam-6536	199	2	a	a	DET
ejpam-6536	199	3	besana	besana	PROPN
ejpam-6536	199	4	,	,	PUNCT
ejpam-6536	199	5	f.	f.	PROPN
ejpam-6536	199	6	jamil	jamil	PROPN
ejpam-6536	199	7	,	,	PUNCT
ejpam-6536	199	8	s.	s.	PROPN
ejpam-6536	199	9	canoy	canoy	PROPN
ejpam-6536	199	10	jr	jr	PROPN
ejpam-6536	199	11	.	.	PROPN
ejpam-6536	199	12	/	/	SYM
ejpam-6536	199	13	eur	eur	PROPN
ejpam-6536	199	14	.	.	PUNCT
ejpam-6536	200	1	j.	j.	PROPN
ejpam-6536	200	2	pure	pure	PROPN
ejpam-6536	200	3	appl	appl	PROPN
ejpam-6536	200	4	.	.	PROPN
ejpam-6536	200	5	math	math	PROPN
ejpam-6536	200	6	,	,	PUNCT
ejpam-6536	200	7	18	18	NUM
ejpam-6536	200	8	(	(	PUNCT
ejpam-6536	200	9	3	3	NUM
ejpam-6536	200	10	)	)	PUNCT
ejpam-6536	200	11	(	(	PUNCT
ejpam-6536	200	12	2025	2025	NUM
ejpam-6536	200	13	)	)	PUNCT
ejpam-6536	200	14	,	,	PUNCT
ejpam-6536	200	15	6536	6536	NUM
ejpam-6536	200	16	7	7	NUM
ejpam-6536	200	17	of	of	ADP
ejpam-6536	200	18	17	17	NUM
ejpam-6536	200	19	(	(	PUNCT
ejpam-6536	200	20	iii	iii	NOUN
ejpam-6536	200	21	)	)	PUNCT
ejpam-6536	200	22	for	for	ADP
ejpam-6536	200	23	a	a	DET
ejpam-6536	200	24	cycle	cycle	NOUN
ejpam-6536	200	25	cn	cn	NOUN
ejpam-6536	200	26	of	of	ADP
ejpam-6536	200	27	length	length	NOUN
ejpam-6536	200	28	n	n	PROPN
ejpam-6536	200	29	≥	≥	NOUN
ejpam-6536	200	30	4	4	NUM
ejpam-6536	200	31	,	,	PUNCT
ejpam-6536	200	32	γ̃h(cn	γ̃h(cn	ADJ
ejpam-6536	200	33	)	)	PUNCT
ejpam-6536	200	34	=	=	SYM
ejpam-6536	200	35			PUNCT
ejpam-6536	201	1	r	r	NOUN
ejpam-6536	201	2	,	,	PUNCT
ejpam-6536	201	3	if	if	SCONJ
ejpam-6536	201	4	n	n	NOUN
ejpam-6536	201	5	=	=	NOUN
ejpam-6536	201	6	3r	3r	NUM
ejpam-6536	201	7	;	;	PUNCT
ejpam-6536	201	8	2r	2r	NUM
ejpam-6536	202	1	+	+	CCONJ
ejpam-6536	202	2	1	1	NUM
ejpam-6536	202	3	,	,	PUNCT
ejpam-6536	202	4	if	if	SCONJ
ejpam-6536	202	5	n	n	NOUN
ejpam-6536	202	6	=	=	SYM
ejpam-6536	202	7	6r	6r	NUM
ejpam-6536	202	8	+	+	CCONJ
ejpam-6536	202	9	1	1	NUM
ejpam-6536	202	10	;	;	PUNCT
ejpam-6536	202	11	2r	2r	NUM
ejpam-6536	202	12	+	+	CCONJ
ejpam-6536	203	1	2	2	NUM
ejpam-6536	203	2	,	,	PUNCT
ejpam-6536	203	3	if	if	SCONJ
ejpam-6536	203	4	n	n	NOUN
ejpam-6536	203	5	=	=	SYM
ejpam-6536	203	6	6r	6r	NUM
ejpam-6536	203	7	+	+	CCONJ
ejpam-6536	203	8	s	s	NOUN
ejpam-6536	203	9	,	,	PUNCT
ejpam-6536	203	10	s	s	PART
ejpam-6536	203	11	=	=	SYM
ejpam-6536	203	12	2	2	NUM
ejpam-6536	203	13	,	,	PUNCT
ejpam-6536	203	14	4	4	NUM
ejpam-6536	203	15	,	,	PUNCT
ejpam-6536	203	16	5	5	NUM
ejpam-6536	203	17	.	.	PUNCT
ejpam-6536	203	18	(	(	PUNCT
ejpam-6536	203	19	iv	iv	X
ejpam-6536	203	20	)	)	PUNCT
ejpam-6536	203	21	for	for	ADP
ejpam-6536	203	22	the	the	DET
ejpam-6536	203	23	petersen	petersen	PROPN
ejpam-6536	203	24	graph	graph	NOUN
ejpam-6536	203	25	p	p	NOUN
ejpam-6536	203	26	,	,	PUNCT
ejpam-6536	203	27	γ̃h(p	γ̃h(p	X
ejpam-6536	203	28	)	)	PUNCT
ejpam-6536	203	29	=	=	SYM
ejpam-6536	204	1	2	2	X
ejpam-6536	204	2	.	.	X
ejpam-6536	204	3	theorem	theorem	VERB
ejpam-6536	204	4	6	6	NUM
ejpam-6536	204	5	.	.	PUNCT
ejpam-6536	204	6	for	for	ADP
ejpam-6536	204	7	every	every	DET
ejpam-6536	204	8	pair	pair	NOUN
ejpam-6536	204	9	of	of	ADP
ejpam-6536	204	10	positive	positive	ADJ
ejpam-6536	204	11	integers	integer	NOUN
ejpam-6536	204	12	m	m	VERB
ejpam-6536	204	13	and	and	CCONJ
ejpam-6536	204	14	n	n	ADV
ejpam-6536	204	15	with	with	ADP
ejpam-6536	204	16	2	2	NUM
ejpam-6536	204	17	≤	≤	NUM
ejpam-6536	204	18	m	m	VERB
ejpam-6536	204	19	≤	≤	NOUN
ejpam-6536	204	20	n	n	CCONJ
ejpam-6536	204	21	,	,	PUNCT
ejpam-6536	204	22	there	there	PRON
ejpam-6536	204	23	exists	exist	VERB
ejpam-6536	204	24	g	g	PROPN
ejpam-6536	204	25	∈	∈	PROPN
ejpam-6536	204	26	g	g	PROPN
ejpam-6536	204	27	for	for	ADP
ejpam-6536	204	28	which	which	PRON
ejpam-6536	204	29	γh(g	γh(g	NOUN
ejpam-6536	204	30	)	)	PUNCT
ejpam-6536	204	31	=	=	PUNCT
ejpam-6536	204	32	m	m	NOUN
ejpam-6536	204	33	and	and	CCONJ
ejpam-6536	204	34	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	204	35	)	)	PUNCT
ejpam-6536	204	36	=	=	SYM
ejpam-6536	204	37	n.	n.	NOUN
ejpam-6536	204	38	proof	proof	NOUN
ejpam-6536	204	39	:	:	PUNCT
ejpam-6536	204	40	if	if	SCONJ
ejpam-6536	204	41	m	m	VERB
ejpam-6536	204	42	=	=	SYM
ejpam-6536	204	43	n	n	CCONJ
ejpam-6536	204	44	,	,	PUNCT
ejpam-6536	204	45	then	then	ADV
ejpam-6536	204	46	we	we	PRON
ejpam-6536	204	47	take	take	VERB
ejpam-6536	204	48	g	g	NOUN
ejpam-6536	204	49	=	=	SYM
ejpam-6536	204	50	kr1,r2,	kr1,r2,	PROPN
ejpam-6536	204	51	...	...	PUNCT
ejpam-6536	204	52	,rn	,rn	PUNCT
ejpam-6536	204	53	with	with	ADP
ejpam-6536	204	54	2	2	NUM
ejpam-6536	204	55	≤	≤	NOUN
ejpam-6536	204	56	r1	r1	NOUN
ejpam-6536	204	57	≤	≤	NUM
ejpam-6536	204	58	r2	r2	PROPN
ejpam-6536	204	59	≤	≤	PUNCT
ejpam-6536	204	60	·	·	PUNCT
ejpam-6536	204	61	·	·	PUNCT
ejpam-6536	204	62	·	·	PUNCT
ejpam-6536	205	1	≤	≤	NUM
ejpam-6536	205	2	rn	rn	PROPN
ejpam-6536	205	3	.	.	PROPN
ejpam-6536	205	4	assume	assume	VERB
ejpam-6536	205	5	that	that	SCONJ
ejpam-6536	205	6	m	m	VERB
ejpam-6536	205	7	<	<	X
ejpam-6536	205	8	n	n	CCONJ
ejpam-6536	205	9	,	,	PUNCT
ejpam-6536	205	10	and	and	CCONJ
ejpam-6536	205	11	write	write	VERB
ejpam-6536	205	12	n	n	PRON
ejpam-6536	205	13	=	=	SYM
ejpam-6536	205	14	m	m	PROPN
ejpam-6536	205	15	+	+	NOUN
ejpam-6536	205	16	k	k	ADJ
ejpam-6536	205	17	,	,	PUNCT
ejpam-6536	205	18	where	where	SCONJ
ejpam-6536	205	19	k	k	PROPN
ejpam-6536	205	20	≥	≥	PROPN
ejpam-6536	205	21	1	1	NUM
ejpam-6536	205	22	.	.	PUNCT
ejpam-6536	206	1	if	if	SCONJ
ejpam-6536	206	2	m	m	ADV
ejpam-6536	206	3	=	=	SYM
ejpam-6536	206	4	2	2	NUM
ejpam-6536	206	5	,	,	PUNCT
ejpam-6536	206	6	then	then	ADV
ejpam-6536	206	7	take	take	VERB
ejpam-6536	206	8	the	the	DET
ejpam-6536	206	9	graph	graph	NOUN
ejpam-6536	206	10	g	g	NOUN
ejpam-6536	206	11	=	=	PUNCT
ejpam-6536	206	12	(	(	PUNCT
ejpam-6536	206	13	k1	k1	PROPN
ejpam-6536	206	14	∪	∪	X
ejpam-6536	206	15	kk+1	kk+1	X
ejpam-6536	206	16	)	)	PUNCT
ejpam-6536	206	17	+	+	X
ejpam-6536	206	18	k2	k2	X
ejpam-6536	206	19	(	(	PUNCT
ejpam-6536	206	20	see	see	VERB
ejpam-6536	206	21	graph	graph	NOUN
ejpam-6536	206	22	g1	g1	NOUN
ejpam-6536	206	23	in	in	ADP
ejpam-6536	206	24	figure	figure	NOUN
ejpam-6536	206	25	2	2	NUM
ejpam-6536	206	26	when	when	SCONJ
ejpam-6536	206	27	k	k	PROPN
ejpam-6536	206	28	=	=	NOUN
ejpam-6536	206	29	2	2	NUM
ejpam-6536	206	30	)	)	PUNCT
ejpam-6536	206	31	.	.	PUNCT
ejpam-6536	207	1	if	if	SCONJ
ejpam-6536	207	2	v	v	X
ejpam-6536	207	3	(	(	PUNCT
ejpam-6536	207	4	k1	k1	NOUN
ejpam-6536	207	5	)	)	PUNCT
ejpam-6536	207	6	=	=	SYM
ejpam-6536	207	7	{	{	PUNCT
ejpam-6536	207	8	v	v	NOUN
ejpam-6536	207	9	}	}	PUNCT
ejpam-6536	207	10	and	and	CCONJ
ejpam-6536	207	11	v	v	NOUN
ejpam-6536	207	12	(	(	PUNCT
ejpam-6536	207	13	k2	k2	NOUN
ejpam-6536	207	14	)	)	PUNCT
ejpam-6536	207	15	=	=	SYM
ejpam-6536	207	16	{	{	PUNCT
ejpam-6536	207	17	y1	y1	NOUN
ejpam-6536	207	18	,	,	PUNCT
ejpam-6536	207	19	y2	y2	PROPN
ejpam-6536	207	20	}	}	PUNCT
ejpam-6536	207	21	,	,	PUNCT
ejpam-6536	207	22	then	then	ADV
ejpam-6536	207	23	{	{	PUNCT
ejpam-6536	207	24	v	v	NOUN
ejpam-6536	207	25	,	,	PUNCT
ejpam-6536	207	26	y1	y1	NOUN
ejpam-6536	207	27	}	}	PUNCT
ejpam-6536	207	28	and	and	CCONJ
ejpam-6536	207	29	v	v	ADP
ejpam-6536	207	30	(	(	PUNCT
ejpam-6536	207	31	kk+1	kk+1	NOUN
ejpam-6536	207	32	)	)	PUNCT
ejpam-6536	207	33	∪	∪	NOUN
ejpam-6536	207	34	{	{	PUNCT
ejpam-6536	207	35	y2	y2	NOUN
ejpam-6536	207	36	}	}	PUNCT
ejpam-6536	207	37	are	be	AUX
ejpam-6536	207	38	,	,	PUNCT
ejpam-6536	207	39	respectively	respectively	ADV
ejpam-6536	207	40	,	,	PUNCT
ejpam-6536	207	41	a	a	DET
ejpam-6536	207	42	γh	γh	ADV
ejpam-6536	207	43	-	-	PUNCT
ejpam-6536	207	44	set	set	NOUN
ejpam-6536	207	45	and	and	CCONJ
ejpam-6536	207	46	a	a	DET
ejpam-6536	207	47	γ̃h	γ̃h	NOUN
ejpam-6536	207	48	-	-	PUNCT
ejpam-6536	207	49	set	set	NOUN
ejpam-6536	207	50	of	of	ADP
ejpam-6536	207	51	g.	g.	PROPN
ejpam-6536	207	52	suppose	suppose	VERB
ejpam-6536	207	53	that	that	SCONJ
ejpam-6536	207	54	m	m	PROPN
ejpam-6536	207	55	≥	≥	NOUN
ejpam-6536	207	56	3	3	NUM
ejpam-6536	207	57	.	.	PUNCT
ejpam-6536	208	1	then	then	ADV
ejpam-6536	208	2	we	we	PRON
ejpam-6536	208	3	take	take	VERB
ejpam-6536	208	4	the	the	DET
ejpam-6536	208	5	graph	graph	NOUN
ejpam-6536	208	6	g	g	NOUN
ejpam-6536	208	7	=	=	PUNCT
ejpam-6536	208	8	(	(	PUNCT
ejpam-6536	208	9	k1	k1	PROPN
ejpam-6536	208	10	∪	∪	X
ejpam-6536	208	11	kk+1	kk+1	X
ejpam-6536	208	12	)	)	PUNCT
ejpam-6536	208	13	+	+	SYM
ejpam-6536	208	14	kr1,r2,	kr1,r2,	PROPN
ejpam-6536	208	15	...	...	PUNCT
ejpam-6536	208	16	,rm−1	,rm−1	PUNCT
ejpam-6536	208	17	,	,	PUNCT
ejpam-6536	208	18	where	where	SCONJ
ejpam-6536	208	19	r1	r1	PROPN
ejpam-6536	208	20	=	=	SYM
ejpam-6536	208	21	r2	r2	PROPN
ejpam-6536	208	22	=	=	PUNCT
ejpam-6536	208	23	·	·	PUNCT
ejpam-6536	208	24	·	·	PUNCT
ejpam-6536	208	25	·	·	PUNCT
ejpam-6536	209	1	=	=	PUNCT
ejpam-6536	209	2	rm−1	rm−1	NOUN
ejpam-6536	209	3	=	=	SYM
ejpam-6536	209	4	2	2	NUM
ejpam-6536	209	5	(	(	PUNCT
ejpam-6536	209	6	see	see	VERB
ejpam-6536	209	7	graph	graph	NOUN
ejpam-6536	209	8	g2	g2	PROPN
ejpam-6536	209	9	in	in	ADP
ejpam-6536	209	10	figure	figure	NOUN
ejpam-6536	209	11	2	2	NUM
ejpam-6536	209	12	for	for	ADP
ejpam-6536	209	13	m	m	NOUN
ejpam-6536	209	14	=	=	SYM
ejpam-6536	209	15	3	3	NUM
ejpam-6536	209	16	and	and	CCONJ
ejpam-6536	209	17	k	k	NOUN
ejpam-6536	209	18	=	=	NOUN
ejpam-6536	209	19	2	2	NUM
ejpam-6536	209	20	)	)	PUNCT
ejpam-6536	209	21	.	.	PUNCT
ejpam-6536	210	1	put	put	VERB
ejpam-6536	210	2	v	v	NOUN
ejpam-6536	210	3	(	(	PUNCT
ejpam-6536	210	4	k1	k1	NOUN
ejpam-6536	210	5	)	)	PUNCT
ejpam-6536	210	6	=	=	SYM
ejpam-6536	210	7	{	{	PUNCT
ejpam-6536	210	8	v	v	NOUN
ejpam-6536	210	9	}	}	PUNCT
ejpam-6536	210	10	and	and	CCONJ
ejpam-6536	210	11	let	let	VERB
ejpam-6536	210	12	urj	urj	VERB
ejpam-6536	210	13	=	=	PUNCT
ejpam-6536	210	14	{	{	PUNCT
ejpam-6536	210	15	y1	y1	PROPN
ejpam-6536	210	16	rj	rj	PROPN
ejpam-6536	210	17	,	,	PUNCT
ejpam-6536	210	18	y2	y2	PROPN
ejpam-6536	210	19	rj	rj	PROPN
ejpam-6536	210	20	}	}	PUNCT
ejpam-6536	210	21	(	(	PUNCT
ejpam-6536	210	22	j	j	NOUN
ejpam-6536	210	23	=	=	SYM
ejpam-6536	210	24	1	1	NUM
ejpam-6536	210	25	,	,	PUNCT
ejpam-6536	210	26	2	2	NUM
ejpam-6536	210	27	,	,	PUNCT
ejpam-6536	210	28	.	.	PUNCT
ejpam-6536	210	29	.	.	PUNCT
ejpam-6536	211	1	.	.	PUNCT
ejpam-6536	212	1	,	,	PUNCT
ejpam-6536	212	2	m−1	m−1	PROPN
ejpam-6536	212	3	)	)	PUNCT
ejpam-6536	212	4	be	be	AUX
ejpam-6536	212	5	the	the	DET
ejpam-6536	212	6	partite	partite	ADJ
ejpam-6536	212	7	sets	set	NOUN
ejpam-6536	212	8	of	of	ADP
ejpam-6536	212	9	kr1,r2,	kr1,r2,	NOUN
ejpam-6536	212	10	...	...	PUNCT
ejpam-6536	212	11	,rm−1	,rm−1	PROPN
ejpam-6536	212	12	.	.	PUNCT
ejpam-6536	213	1	then	then	ADV
ejpam-6536	213	2	{	{	PUNCT
ejpam-6536	213	3	v	v	NOUN
ejpam-6536	213	4	,	,	PUNCT
ejpam-6536	213	5	y1	y1	PROPN
ejpam-6536	213	6	rj	rj	X
ejpam-6536	213	7	:	:	PUNCT
ejpam-6536	213	8	j	j	PROPN
ejpam-6536	213	9	=	=	SYM
ejpam-6536	213	10	1	1	NUM
ejpam-6536	213	11	,	,	PUNCT
ejpam-6536	213	12	2	2	NUM
ejpam-6536	213	13	,	,	PUNCT
ejpam-6536	213	14	.	.	PUNCT
ejpam-6536	213	15	.	.	PUNCT
ejpam-6536	213	16	.	.	PUNCT
ejpam-6536	214	1	,	,	PUNCT
ejpam-6536	214	2	m−1	m−1	PROPN
ejpam-6536	214	3	}	}	PUNCT
ejpam-6536	214	4	and	and	CCONJ
ejpam-6536	214	5	v	v	X
ejpam-6536	214	6	(	(	PUNCT
ejpam-6536	214	7	kk+1)∪{y2	kk+1)∪{y2	PROPN
ejpam-6536	214	8	rj	rj	PROPN
ejpam-6536	214	9	:	:	PUNCT
ejpam-6536	214	10	j	j	PROPN
ejpam-6536	214	11	=	=	SYM
ejpam-6536	214	12	1	1	NUM
ejpam-6536	214	13	,	,	PUNCT
ejpam-6536	214	14	2	2	NUM
ejpam-6536	214	15	,	,	PUNCT
ejpam-6536	214	16	.	.	PUNCT
ejpam-6536	214	17	.	.	PUNCT
ejpam-6536	215	1	.	.	PUNCT
ejpam-6536	216	1	,	,	PUNCT
ejpam-6536	216	2	m−1	m−1	PROPN
ejpam-6536	216	3	}	}	PUNCT
ejpam-6536	216	4	are	be	AUX
ejpam-6536	216	5	,	,	PUNCT
ejpam-6536	216	6	respectively	respectively	ADV
ejpam-6536	216	7	,	,	PUNCT
ejpam-6536	216	8	a	a	DET
ejpam-6536	216	9	γh	γh	ADV
ejpam-6536	216	10	-	-	PUNCT
ejpam-6536	216	11	set	set	NOUN
ejpam-6536	216	12	and	and	CCONJ
ejpam-6536	216	13	a	a	DET
ejpam-6536	216	14	γ̃h	γ̃h	NOUN
ejpam-6536	216	15	-	-	PUNCT
ejpam-6536	216	16	set	set	NOUN
ejpam-6536	216	17	of	of	ADP
ejpam-6536	216	18	g.	g.	PROPN
ejpam-6536	216	19	in	in	ADP
ejpam-6536	216	20	any	any	DET
ejpam-6536	216	21	case	case	NOUN
ejpam-6536	216	22	,	,	PUNCT
ejpam-6536	216	23	γh(g	γh(g	NOUN
ejpam-6536	216	24	)	)	PUNCT
ejpam-6536	216	25	=	=	SYM
ejpam-6536	216	26	m	m	NOUN
ejpam-6536	216	27	and	and	CCONJ
ejpam-6536	216	28	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	216	29	)	)	PUNCT
ejpam-6536	216	30	=	=	SYM
ejpam-6536	217	1	(	(	PUNCT
ejpam-6536	217	2	m	m	VERB
ejpam-6536	217	3	−	−	NOUN
ejpam-6536	217	4	1	1	NUM
ejpam-6536	217	5	)	)	PUNCT
ejpam-6536	217	6	+	+	CCONJ
ejpam-6536	218	1	(	(	PUNCT
ejpam-6536	218	2	k	k	X
ejpam-6536	218	3	+	+	PROPN
ejpam-6536	218	4	1	1	X
ejpam-6536	218	5	)	)	PUNCT
ejpam-6536	218	6	=	=	VERB
ejpam-6536	218	7	n.	n.	NOUN
ejpam-6536	218	8	■	■	PROPN
ejpam-6536	218	9	....................................	....................................	PUNCT
ejpam-6536	218	10	....................................	....................................	PUNCT
ejpam-6536	219	1	....................................	....................................	PUNCT
ejpam-6536	219	2	....................................	....................................	PUNCT
ejpam-6536	220	1	....................................	....................................	PUNCT
ejpam-6536	221	1	....................................	....................................	PUNCT
ejpam-6536	222	1	•	•	NUM
ejpam-6536	222	2	•	•	NUM
ejpam-6536	222	3	•	•	NUM
ejpam-6536	222	4	•	•	NUM
ejpam-6536	222	5	•	•	NOUN
ejpam-6536	222	6	•	•	NOUN
ejpam-6536	222	7	.........	.........	PUNCT
ejpam-6536	222	8	........	........	PUNCT
ejpam-6536	222	9	........	........	PUNCT
ejpam-6536	222	10	........	........	PUNCT
ejpam-6536	222	11	........	........	PUNCT
ejpam-6536	222	12	........	........	PUNCT
ejpam-6536	222	13	........	........	PUNCT
ejpam-6536	222	14	........	........	PUNCT
ejpam-6536	222	15	........	........	PUNCT
ejpam-6536	222	16	...	...	PUNCT
ejpam-6536	223	1	....................................	....................................	PUNCT
ejpam-6536	223	2	...................................................	...................................................	PUNCT
ejpam-6536	224	1	....................................	....................................	PUNCT
ejpam-6536	224	2	............	............	PUNCT
ejpam-6536	224	3	...........	...........	PUNCT
ejpam-6536	224	4	...........	...........	PUNCT
ejpam-6536	224	5	...........	...........	PUNCT
ejpam-6536	224	6	......	......	PUNCT
ejpam-6536	224	7	.	.	PUNCT
ejpam-6536	224	8	...................................	...................................	PUNCT
ejpam-6536	225	1	....................................	....................................	PUNCT
ejpam-6536	225	2	.........................................	.........................................	PUNCT
ejpam-6536	225	3	........................................	........................................	PUNCT
ejpam-6536	225	4	........................................	........................................	PUNCT
ejpam-6536	225	5	........................................	........................................	PUNCT
ejpam-6536	225	6	........................................	........................................	PUNCT
ejpam-6536	226	1	........	........	PUNCT
ejpam-6536	226	2	......................	......................	PUNCT
ejpam-6536	227	1	.....................	.....................	PUNCT
ejpam-6536	227	2	.....................	.....................	PUNCT
ejpam-6536	227	3	.....................	.....................	PUNCT
ejpam-6536	227	4	.....................	.....................	PUNCT
ejpam-6536	227	5	.....................	.....................	PUNCT
ejpam-6536	227	6	.....................	.....................	PUNCT
ejpam-6536	227	7	.....................	.....................	PUNCT
ejpam-6536	227	8	.....................	.....................	PUNCT
ejpam-6536	227	9	.....................	.....................	PUNCT
ejpam-6536	228	1	..........	..........	PUNCT
ejpam-6536	228	2	..........................	..........................	PUNCT
ejpam-6536	229	1	.........................	.........................	PUNCT
ejpam-6536	229	2	.........................	.........................	PUNCT
ejpam-6536	229	3	.........................	.........................	PUNCT
ejpam-6536	229	4	.........................	.........................	PUNCT
ejpam-6536	229	5	.........................	.........................	PUNCT
ejpam-6536	229	6	.........................	.........................	PUNCT
ejpam-6536	229	7	.........................	.........................	PUNCT
ejpam-6536	229	8	.........................	.........................	PUNCT
ejpam-6536	229	9	.........................	.........................	PUNCT
ejpam-6536	229	10	...........	...........	PUNCT
ejpam-6536	229	11	...................	...................	PUNCT
ejpam-6536	229	12	..................	..................	PUNCT
ejpam-6536	230	1	..................	..................	PUNCT
ejpam-6536	230	2	..................	..................	PUNCT
ejpam-6536	231	1	..................	..................	PUNCT
ejpam-6536	231	2	..................	..................	PUNCT
ejpam-6536	232	1	..................	..................	PUNCT
ejpam-6536	232	2	..................	..................	PUNCT
ejpam-6536	233	1	..................	..................	PUNCT
ejpam-6536	233	2	..................	..................	PUNCT
ejpam-6536	234	1	..................	..................	PUNCT
ejpam-6536	234	2	..................	..................	PUNCT
ejpam-6536	235	1	..................	..................	PUNCT
ejpam-6536	235	2	..................	..................	PUNCT
ejpam-6536	236	1	..................	..................	PUNCT
ejpam-6536	236	2	........	........	PUNCT
ejpam-6536	237	1	.........................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	237	2	................................................	................................................	PUNCT
ejpam-6536	238	1	................................................	................................................	PUNCT
ejpam-6536	238	2	................................................	................................................	PUNCT
ejpam-6536	238	3	................................................	................................................	PUNCT
ejpam-6536	239	1	.......................................................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	240	1	........................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................	PROPN
ejpam-6536	241	1	g1	g1	PROPN
ejpam-6536	241	2	=	=	SYM
ejpam-6536	241	3	(	(	PUNCT
ejpam-6536	241	4	k1	k1	PROPN
ejpam-6536	241	5	∪	∪	X
ejpam-6536	241	6	k3	k3	PROPN
ejpam-6536	241	7	)	)	PUNCT
ejpam-6536	241	8	+	+	SYM
ejpam-6536	241	9	k2	k2	PROPN
ejpam-6536	241	10	v	v	ADP
ejpam-6536	241	11	x1	x1	PROPN
ejpam-6536	242	1	x2	x2	NOUN
ejpam-6536	242	2	x3	x3	ADJ
ejpam-6536	242	3	y1	y1	INTJ
ejpam-6536	242	4	y2	y2	INTJ
ejpam-6536	242	5	....................................	....................................	PUNCT
ejpam-6536	242	6	....................................	....................................	PUNCT
ejpam-6536	243	1	....................................	....................................	PUNCT
ejpam-6536	243	2	....................................	....................................	PUNCT
ejpam-6536	244	1	....................................	....................................	PUNCT
ejpam-6536	244	2	....................................	....................................	PUNCT
ejpam-6536	245	1	....................................	....................................	PUNCT
ejpam-6536	246	1	....................................	....................................	PUNCT
ejpam-6536	247	1	•	•	NUM
ejpam-6536	247	2	•	•	NUM
ejpam-6536	247	3	•	•	NUM
ejpam-6536	247	4	•	•	NUM
ejpam-6536	247	5	•	•	NUM
ejpam-6536	247	6	•	•	NUM
ejpam-6536	247	7	•	•	NOUN
ejpam-6536	247	8	•	•	NOUN
ejpam-6536	247	9	.........	.........	PUNCT
ejpam-6536	247	10	........	........	PUNCT
ejpam-6536	247	11	........	........	PUNCT
ejpam-6536	247	12	........	........	PUNCT
ejpam-6536	247	13	........	........	PUNCT
ejpam-6536	247	14	........	........	PUNCT
ejpam-6536	247	15	........	........	PUNCT
ejpam-6536	247	16	........	........	PUNCT
ejpam-6536	247	17	........	........	PUNCT
ejpam-6536	247	18	...	...	PUNCT
ejpam-6536	248	1	....................................	....................................	PUNCT
ejpam-6536	248	2	...................................................	...................................................	PUNCT
ejpam-6536	249	1	....................................	....................................	PUNCT
ejpam-6536	249	2	............	............	PUNCT
ejpam-6536	249	3	...........	...........	PUNCT
ejpam-6536	249	4	...........	...........	PUNCT
ejpam-6536	249	5	...........	...........	PUNCT
ejpam-6536	249	6	......	......	PUNCT
ejpam-6536	249	7	.	.	PUNCT
ejpam-6536	249	8	...................................	...................................	PUNCT
ejpam-6536	250	1	....................................	....................................	PUNCT
ejpam-6536	250	2	.........................................	.........................................	PUNCT
ejpam-6536	250	3	........................................	........................................	PUNCT
ejpam-6536	250	4	........................................	........................................	PUNCT
ejpam-6536	250	5	........................................	........................................	PUNCT
ejpam-6536	250	6	........................................	........................................	PUNCT
ejpam-6536	251	1	........	........	PUNCT
ejpam-6536	251	2	......................	......................	PUNCT
ejpam-6536	252	1	.....................	.....................	PUNCT
ejpam-6536	252	2	.....................	.....................	PUNCT
ejpam-6536	252	3	.....................	.....................	PUNCT
ejpam-6536	252	4	.....................	.....................	PUNCT
ejpam-6536	252	5	.....................	.....................	PUNCT
ejpam-6536	252	6	.....................	.....................	PUNCT
ejpam-6536	252	7	.....................	.....................	PUNCT
ejpam-6536	252	8	.....................	.....................	PUNCT
ejpam-6536	252	9	.....................	.....................	PUNCT
ejpam-6536	253	1	..........	..........	PUNCT
ejpam-6536	253	2	..........................	..........................	PUNCT
ejpam-6536	254	1	.........................	.........................	PUNCT
ejpam-6536	254	2	.........................	.........................	PUNCT
ejpam-6536	254	3	.........................	.........................	PUNCT
ejpam-6536	254	4	.........................	.........................	PUNCT
ejpam-6536	254	5	.........................	.........................	PUNCT
ejpam-6536	254	6	.........................	.........................	PUNCT
ejpam-6536	254	7	.........................	.........................	PUNCT
ejpam-6536	254	8	.........................	.........................	PUNCT
ejpam-6536	254	9	.........................	.........................	PUNCT
ejpam-6536	254	10	...........	...........	PUNCT
ejpam-6536	254	11	...................	...................	PUNCT
ejpam-6536	254	12	..................	..................	PUNCT
ejpam-6536	255	1	..................	..................	PUNCT
ejpam-6536	255	2	..................	..................	PUNCT
ejpam-6536	256	1	..................	..................	PUNCT
ejpam-6536	256	2	..................	..................	PUNCT
ejpam-6536	257	1	..................	..................	PUNCT
ejpam-6536	257	2	..................	..................	PUNCT
ejpam-6536	258	1	..................	..................	PUNCT
ejpam-6536	258	2	..................	..................	PUNCT
ejpam-6536	259	1	..................	..................	PUNCT
ejpam-6536	259	2	..................	..................	PUNCT
ejpam-6536	260	1	..................	..................	PUNCT
ejpam-6536	260	2	..................	..................	PUNCT
ejpam-6536	261	1	..................	..................	PUNCT
ejpam-6536	261	2	........	........	PUNCT
ejpam-6536	262	1	.........................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	262	2	................................................	................................................	PUNCT
ejpam-6536	263	1	................................................	................................................	PUNCT
ejpam-6536	263	2	................................................	................................................	PUNCT
ejpam-6536	263	3	................................................	................................................	PUNCT
ejpam-6536	264	1	.......................................................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	265	1	........................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................	PROPN
ejpam-6536	265	2	......................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	265	3	..............................................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	265	4	......................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	266	1	.......................................................................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................................................................	PROPN
ejpam-6536	266	2	........................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................	PROPN
ejpam-6536	267	1	.............................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	267	2	................................................	................................................	PUNCT
ejpam-6536	268	1	................................................	................................................	PUNCT
ejpam-6536	268	2	................................................	................................................	PUNCT
ejpam-6536	268	3	................................................	................................................	PUNCT
ejpam-6536	269	1	...................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	269	2	...............	...............	PUNCT
ejpam-6536	270	1	................	................	PUNCT
ejpam-6536	270	2	................	................	PUNCT
ejpam-6536	270	3	.................	.................	PUNCT
ejpam-6536	270	4	..................	..................	PUNCT
ejpam-6536	270	5	....................	....................	PUNCT
ejpam-6536	270	6	......................	......................	PUNCT
ejpam-6536	270	7	.........................	.........................	PUNCT
ejpam-6536	270	8	..............................	..............................	PUNCT
ejpam-6536	271	1	............................................	............................................	PUNCT
ejpam-6536	271	2	.................................................................................................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	271	3	...................	...................	PUNCT
ejpam-6536	271	4	....................	....................	PUNCT
ejpam-6536	272	1	.....................	.....................	PUNCT
ejpam-6536	272	2	.......................	.......................	PUNCT
ejpam-6536	272	3	..........................	..........................	PUNCT
ejpam-6536	272	4	...............................	...............................	PUNCT
ejpam-6536	272	5	........................................	........................................	PUNCT
ejpam-6536	273	1	............................................................................................................................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	273	2	................	................	PUNCT
ejpam-6536	273	3	.................	.................	PUNCT
ejpam-6536	273	4	..................	..................	PUNCT
ejpam-6536	273	5	....................	....................	PUNCT
ejpam-6536	273	6	......................	......................	PUNCT
ejpam-6536	273	7	.........................	.........................	PUNCT
ejpam-6536	273	8	................................	................................	PUNCT
ejpam-6536	274	1	...................................................................................................................................................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	274	2	...............	...............	PUNCT
ejpam-6536	275	1	................	................	PUNCT
ejpam-6536	275	2	................	................	PUNCT
ejpam-6536	275	3	.................	.................	PUNCT
ejpam-6536	275	4	..................	..................	PUNCT
ejpam-6536	275	5	...................	...................	PUNCT
ejpam-6536	275	6	.....................	.....................	PUNCT
ejpam-6536	276	1	.......................	.......................	PUNCT
ejpam-6536	276	2	..........................	..........................	PUNCT
ejpam-6536	276	3	.................................	.................................	PUNCT
ejpam-6536	277	1	....................................................	....................................................	PUNCT
ejpam-6536	277	2	............................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................	PUNCT
ejpam-6536	278	1	g2	g2	PROPN
ejpam-6536	278	2	=	=	PRON
ejpam-6536	279	1	(	(	PUNCT
ejpam-6536	279	2	k1	k1	PROPN
ejpam-6536	279	3	∪	∪	X
ejpam-6536	279	4	k3	k3	PROPN
ejpam-6536	279	5	)	)	PUNCT
ejpam-6536	280	1	+	+	CCONJ
ejpam-6536	280	2	k2,2	k2,2	PROPN
ejpam-6536	280	3	v	v	ADP
ejpam-6536	280	4	x1	x1	PROPN
ejpam-6536	281	1	x2	x2	PROPN
ejpam-6536	281	2	x3	x3	ADJ
ejpam-6536	281	3	y1	y1	INTJ
ejpam-6536	281	4	y2	y2	INTJ
ejpam-6536	281	5	z1	z1	ADJ
ejpam-6536	281	6	z2	z2	PROPN
ejpam-6536	281	7	figure	figure	NOUN
ejpam-6536	281	8	2	2	NUM
ejpam-6536	281	9	:	:	PUNCT
ejpam-6536	281	10	examples	example	NOUN
ejpam-6536	281	11	of	of	ADP
ejpam-6536	281	12	graphs	graph	NOUN
ejpam-6536	281	13	described	describe	VERB
ejpam-6536	281	14	in	in	ADP
ejpam-6536	281	15	the	the	DET
ejpam-6536	281	16	proof	proof	NOUN
ejpam-6536	281	17	of	of	ADP
ejpam-6536	281	18	theorem	theorem	ADJ
ejpam-6536	281	19	6	6	NUM
ejpam-6536	281	20	corollary	corollary	ADJ
ejpam-6536	281	21	2	2	NUM
ejpam-6536	281	22	.	.	PUNCT
ejpam-6536	282	1	the	the	DET
ejpam-6536	282	2	difference	difference	NOUN
ejpam-6536	282	3	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	282	4	)	)	PUNCT
ejpam-6536	282	5	−	−	NOUN
ejpam-6536	282	6	γh(g	γh(g	NOUN
ejpam-6536	282	7	)	)	PUNCT
ejpam-6536	282	8	can	can	AUX
ejpam-6536	282	9	be	be	AUX
ejpam-6536	282	10	made	make	VERB
ejpam-6536	282	11	arbitrarily	arbitrarily	ADV
ejpam-6536	282	12	large	large	ADJ
ejpam-6536	282	13	.	.	PUNCT
ejpam-6536	283	1	3.2	3.2	NUM
ejpam-6536	283	2	.	.	PUNCT
ejpam-6536	284	1	disjoint	disjoint	VERB
ejpam-6536	284	2	hop	hop	PROPN
ejpam-6536	284	3	domination	domination	NOUN
ejpam-6536	284	4	for	for	ADP
ejpam-6536	284	5	g	g	PROPN
ejpam-6536	284	6	∈	∈	PROPN
ejpam-6536	284	7	g	g	PROPN
ejpam-6536	284	8	,	,	PUNCT
ejpam-6536	284	9	proposition	proposition	NOUN
ejpam-6536	284	10	3	3	NUM
ejpam-6536	284	11	guarantees	guarantee	VERB
ejpam-6536	284	12	the	the	DET
ejpam-6536	284	13	existence	existence	NOUN
ejpam-6536	284	14	in	in	ADP
ejpam-6536	284	15	g	g	NOUN
ejpam-6536	284	16	of	of	ADP
ejpam-6536	284	17	hop	hop	NOUN
ejpam-6536	284	18	dominating	dominating	NOUN
ejpam-6536	284	19	sets	set	NOUN
ejpam-6536	284	20	a	a	PRON
ejpam-6536	284	21	and	and	CCONJ
ejpam-6536	284	22	b	b	NOUN
ejpam-6536	284	23	with	with	ADP
ejpam-6536	284	24	a	a	DET
ejpam-6536	284	25	∩	∩	ADJ
ejpam-6536	284	26	b	b	NOUN
ejpam-6536	284	27	=	=	PUNCT
ejpam-6536	284	28	∅.	∅.	NOUN
ejpam-6536	284	29	denote	denote	VERB
ejpam-6536	284	30	by	by	ADP
ejpam-6536	284	31	phd(g	phd(g	PROPN
ejpam-6536	284	32	)	)	PUNCT
ejpam-6536	284	33	the	the	DET
ejpam-6536	284	34	family	family	NOUN
ejpam-6536	284	35	of	of	ADP
ejpam-6536	284	36	all	all	DET
ejpam-6536	284	37	pairs	pair	NOUN
ejpam-6536	284	38	(	(	PUNCT
ejpam-6536	284	39	a	a	DET
ejpam-6536	284	40	,	,	PUNCT
ejpam-6536	284	41	b	b	NOUN
ejpam-6536	284	42	)	)	PUNCT
ejpam-6536	284	43	where	where	SCONJ
ejpam-6536	284	44	a	a	PRON
ejpam-6536	284	45	and	and	CCONJ
ejpam-6536	284	46	b	b	NOUN
ejpam-6536	284	47	are	be	AUX
ejpam-6536	284	48	disjoint	disjoint	ADJ
ejpam-6536	284	49	hop	hop	NOUN
ejpam-6536	284	50	dominating	dominating	NOUN
ejpam-6536	284	51	sets	set	NOUN
ejpam-6536	284	52	of	of	ADP
ejpam-6536	284	53	g.	g.	PROPN
ejpam-6536	284	54	we	we	PRON
ejpam-6536	284	55	define	define	VERB
ejpam-6536	284	56	γhh(g	γhh(g	NOUN
ejpam-6536	284	57	)	)	PUNCT
ejpam-6536	284	58	=	=	SYM
ejpam-6536	284	59	min{|a|	min{|a|	NOUN
ejpam-6536	285	1	+	+	CCONJ
ejpam-6536	285	2	|b|	|b|	PROPN
ejpam-6536	285	3	:	:	PUNCT
ejpam-6536	285	4	(	(	PUNCT
ejpam-6536	285	5	a	a	PRON
ejpam-6536	285	6	,	,	PUNCT
ejpam-6536	285	7	b	b	NOUN
ejpam-6536	285	8	)	)	PUNCT
ejpam-6536	285	9	∈	∈	PROPN
ejpam-6536	285	10	phd(g	phd(g	PROPN
ejpam-6536	285	11	)	)	PUNCT
ejpam-6536	285	12	}	}	PUNCT
ejpam-6536	285	13	.	.	PUNCT
ejpam-6536	286	1	any	any	DET
ejpam-6536	286	2	pair	pair	NOUN
ejpam-6536	286	3	(	(	PUNCT
ejpam-6536	286	4	a	a	PRON
ejpam-6536	286	5	,	,	PUNCT
ejpam-6536	286	6	b	b	NOUN
ejpam-6536	286	7	)	)	PUNCT
ejpam-6536	286	8	∈	∈	PROPN
ejpam-6536	286	9	phd(g	phd(g	PROPN
ejpam-6536	286	10	)	)	PUNCT
ejpam-6536	286	11	with	with	ADP
ejpam-6536	286	12	|a|	|a|	NOUN
ejpam-6536	286	13	+	+	CCONJ
ejpam-6536	286	14	|b|	|b|	PROPN
ejpam-6536	286	15	=	=	SYM
ejpam-6536	286	16	γhh(g	γhh(g	NOUN
ejpam-6536	286	17	)	)	PUNCT
ejpam-6536	286	18	is	be	AUX
ejpam-6536	286	19	called	call	VERB
ejpam-6536	286	20	γhh	γhh	NOUN
ejpam-6536	286	21	-	-	PUNCT
ejpam-6536	286	22	pair	pair	NOUN
ejpam-6536	286	23	of	of	ADP
ejpam-6536	286	24	g.	g.	PROPN
ejpam-6536	286	25	v.	v.	ADP
ejpam-6536	286	26	a	a	DET
ejpam-6536	286	27	besana	besana	PROPN
ejpam-6536	286	28	,	,	PUNCT
ejpam-6536	286	29	f.	f.	PROPN
ejpam-6536	286	30	jamil	jamil	PROPN
ejpam-6536	286	31	,	,	PUNCT
ejpam-6536	286	32	s.	s.	PROPN
ejpam-6536	286	33	canoy	canoy	PROPN
ejpam-6536	286	34	jr	jr	PROPN
ejpam-6536	286	35	.	.	PROPN
ejpam-6536	286	36	/	/	SYM
ejpam-6536	286	37	eur	eur	PROPN
ejpam-6536	286	38	.	.	PUNCT
ejpam-6536	287	1	j.	j.	PROPN
ejpam-6536	287	2	pure	pure	PROPN
ejpam-6536	287	3	appl	appl	PROPN
ejpam-6536	287	4	.	.	PROPN
ejpam-6536	287	5	math	math	PROPN
ejpam-6536	287	6	,	,	PUNCT
ejpam-6536	287	7	18	18	NUM
ejpam-6536	287	8	(	(	PUNCT
ejpam-6536	287	9	3	3	NUM
ejpam-6536	287	10	)	)	PUNCT
ejpam-6536	287	11	(	(	PUNCT
ejpam-6536	287	12	2025	2025	NUM
ejpam-6536	287	13	)	)	PUNCT
ejpam-6536	287	14	,	,	PUNCT
ejpam-6536	287	15	6536	6536	NUM
ejpam-6536	287	16	8	8	NUM
ejpam-6536	287	17	of	of	ADP
ejpam-6536	287	18	17	17	NUM
ejpam-6536	287	19	it	it	PRON
ejpam-6536	287	20	should	should	AUX
ejpam-6536	287	21	be	be	AUX
ejpam-6536	287	22	noted	note	VERB
ejpam-6536	287	23	that	that	SCONJ
ejpam-6536	287	24	for	for	ADP
ejpam-6536	287	25	(	(	PUNCT
ejpam-6536	287	26	a	a	PRON
ejpam-6536	287	27	,	,	PUNCT
ejpam-6536	287	28	b	b	NOUN
ejpam-6536	287	29	)	)	PUNCT
ejpam-6536	287	30	∈	∈	PROPN
ejpam-6536	287	31	phd(g	phd(g	PROPN
ejpam-6536	287	32	)	)	PUNCT
ejpam-6536	287	33	,	,	PUNCT
ejpam-6536	287	34	any	any	PRON
ejpam-6536	287	35	of	of	ADP
ejpam-6536	287	36	a	a	PRON
ejpam-6536	287	37	and	and	CCONJ
ejpam-6536	287	38	b	b	NOUN
ejpam-6536	287	39	need	need	AUX
ejpam-6536	287	40	not	not	PART
ejpam-6536	287	41	be	be	AUX
ejpam-6536	287	42	a	a	DET
ejpam-6536	287	43	γh	γh	ADV
ejpam-6536	287	44	-	-	PUNCT
ejpam-6536	287	45	set	set	NOUN
ejpam-6536	287	46	of	of	ADP
ejpam-6536	287	47	g.	g.	PROPN
ejpam-6536	287	48	for	for	ADP
ejpam-6536	287	49	all	all	PRON
ejpam-6536	287	50	g	g	PROPN
ejpam-6536	287	51	∈	∈	PROPN
ejpam-6536	287	52	g	g	NOUN
ejpam-6536	287	53	of	of	ADP
ejpam-6536	287	54	order	order	NOUN
ejpam-6536	287	55	n	n	CCONJ
ejpam-6536	287	56	,	,	PUNCT
ejpam-6536	287	57	2γh(g	2γh(g	NUM
ejpam-6536	287	58	)	)	PUNCT
ejpam-6536	287	59	≤	≤	NUM
ejpam-6536	287	60	γhh(g	γhh(g	NOUN
ejpam-6536	287	61	)	)	PUNCT
ejpam-6536	287	62	≤	≤	NOUN
ejpam-6536	287	63	γh(g	γh(g	NOUN
ejpam-6536	287	64	)	)	PUNCT
ejpam-6536	288	1	+	+	CCONJ
ejpam-6536	288	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	288	3	)	)	PUNCT
ejpam-6536	288	4	≤	≤	NOUN
ejpam-6536	288	5	n.	n.	NOUN
ejpam-6536	288	6	(	(	PUNCT
ejpam-6536	288	7	2	2	NUM
ejpam-6536	288	8	)	)	PUNCT
ejpam-6536	288	9	if	if	SCONJ
ejpam-6536	288	10	g	g	PROPN
ejpam-6536	288	11	is	be	AUX
ejpam-6536	288	12	any	any	PRON
ejpam-6536	288	13	of	of	ADP
ejpam-6536	288	14	the	the	DET
ejpam-6536	288	15	graphs	graph	NOUN
ejpam-6536	288	16	g1	g1	PROPN
ejpam-6536	288	17	and	and	CCONJ
ejpam-6536	288	18	g2	g2	PROPN
ejpam-6536	288	19	in	in	ADP
ejpam-6536	288	20	figure	figure	NOUN
ejpam-6536	288	21	2	2	NUM
ejpam-6536	288	22	,	,	PUNCT
ejpam-6536	288	23	then	then	ADV
ejpam-6536	288	24	γhh(g	γhh(g	NOUN
ejpam-6536	288	25	)	)	PUNCT
ejpam-6536	288	26	=	=	NOUN
ejpam-6536	288	27	γh(g	γh(g	NOUN
ejpam-6536	288	28	)	)	PUNCT
ejpam-6536	288	29	+	+	CCONJ
ejpam-6536	288	30	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	288	31	)	)	PUNCT
ejpam-6536	288	32	=	=	SYM
ejpam-6536	288	33	|v	|v	PROPN
ejpam-6536	288	34	(	(	PUNCT
ejpam-6536	288	35	g)|	g)|	NOUN
ejpam-6536	288	36	.	.	PUNCT
ejpam-6536	289	1	consider	consider	VERB
ejpam-6536	289	2	the	the	DET
ejpam-6536	289	3	graph	graph	NOUN
ejpam-6536	289	4	g	g	NOUN
ejpam-6536	289	5	in	in	ADP
ejpam-6536	289	6	figure	figure	NOUN
ejpam-6536	289	7	3	3	NUM
ejpam-6536	289	8	,	,	PUNCT
ejpam-6536	289	9	the	the	DET
ejpam-6536	289	10	sets	set	NOUN
ejpam-6536	289	11	{	{	PUNCT
ejpam-6536	289	12	a1	a1	NOUN
ejpam-6536	289	13	,	,	PUNCT
ejpam-6536	289	14	b1	b1	NOUN
ejpam-6536	289	15	,	,	PUNCT
ejpam-6536	289	16	c1	c1	NOUN
ejpam-6536	289	17	}	}	PUNCT
ejpam-6536	289	18	and	and	CCONJ
ejpam-6536	289	19	{	{	PUNCT
ejpam-6536	289	20	a2	a2	PROPN
ejpam-6536	289	21	,	,	PUNCT
ejpam-6536	289	22	a3	a3	NOUN
ejpam-6536	289	23	,	,	PUNCT
ejpam-6536	289	24	b2	b2	NOUN
ejpam-6536	289	25	,	,	PUNCT
ejpam-6536	289	26	b3	b3	PROPN
ejpam-6536	289	27	,	,	PUNCT
ejpam-6536	289	28	c2	c2	PROPN
ejpam-6536	289	29	,	,	PUNCT
ejpam-6536	289	30	c3	c3	PROPN
ejpam-6536	289	31	}	}	PUNCT
ejpam-6536	289	32	are	be	AUX
ejpam-6536	289	33	a	a	DET
ejpam-6536	289	34	γh	γh	ADV
ejpam-6536	289	35	-	-	PUNCT
ejpam-6536	289	36	set	set	NOUN
ejpam-6536	289	37	and	and	CCONJ
ejpam-6536	289	38	a	a	DET
ejpam-6536	289	39	γ̃h	γ̃h	NOUN
ejpam-6536	289	40	-	-	PUNCT
ejpam-6536	289	41	set	set	NOUN
ejpam-6536	289	42	,	,	PUNCT
ejpam-6536	289	43	respectively	respectively	ADV
ejpam-6536	289	44	,	,	PUNCT
ejpam-6536	289	45	of	of	ADP
ejpam-6536	289	46	g.	g.	PROPN
ejpam-6536	289	47	while	while	SCONJ
ejpam-6536	289	48	the	the	DET
ejpam-6536	289	49	sets	set	NOUN
ejpam-6536	289	50	{	{	PUNCT
ejpam-6536	289	51	a1	a1	NOUN
ejpam-6536	289	52	,	,	PUNCT
ejpam-6536	289	53	a2	a2	PROPN
ejpam-6536	289	54	,	,	PUNCT
ejpam-6536	289	55	b3	b3	PROPN
ejpam-6536	289	56	,	,	PUNCT
ejpam-6536	289	57	c3	c3	NOUN
ejpam-6536	289	58	}	}	PUNCT
ejpam-6536	289	59	and	and	CCONJ
ejpam-6536	289	60	{	{	PUNCT
ejpam-6536	289	61	b1	b1	PROPN
ejpam-6536	289	62	,	,	PUNCT
ejpam-6536	289	63	c1	c1	NOUN
ejpam-6536	289	64	,	,	PUNCT
ejpam-6536	289	65	b2	b2	NOUN
ejpam-6536	289	66	,	,	PUNCT
ejpam-6536	289	67	a3	a3	NOUN
ejpam-6536	289	68	}	}	PUNCT
ejpam-6536	289	69	constitute	constitute	VERB
ejpam-6536	289	70	a	a	DET
ejpam-6536	289	71	γhh	γhh	NOUN
ejpam-6536	289	72	-	-	PUNCT
ejpam-6536	289	73	pair	pair	NOUN
ejpam-6536	289	74	of	of	ADP
ejpam-6536	289	75	g.	g.	NOUN
ejpam-6536	289	76	for	for	ADP
ejpam-6536	289	77	this	this	DET
ejpam-6536	289	78	g	g	NOUN
ejpam-6536	289	79	,	,	PUNCT
ejpam-6536	289	80	2γh(g	2γh(g	NUM
ejpam-6536	289	81	)	)	PUNCT
ejpam-6536	289	82	<	<	X
ejpam-6536	289	83	γhh(g	γhh(g	NOUN
ejpam-6536	289	84	)	)	PUNCT
ejpam-6536	289	85	<	<	X
ejpam-6536	289	86	γh(g	γh(g	NOUN
ejpam-6536	289	87	)	)	PUNCT
ejpam-6536	290	1	+	+	CCONJ
ejpam-6536	290	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	290	3	)	)	PUNCT
ejpam-6536	290	4	.	.	PUNCT
ejpam-6536	291	1	...........	...........	PUNCT
ejpam-6536	291	2	..........	..........	PUNCT
ejpam-6536	292	1	..........	..........	PUNCT
ejpam-6536	292	2	..........	..........	PUNCT
ejpam-6536	293	1	..........	..........	PUNCT
ejpam-6536	293	2	..........	..........	PUNCT
ejpam-6536	294	1	..........	..........	PUNCT
ejpam-6536	294	2	..........	..........	PUNCT
ejpam-6536	295	1	..........	..........	PUNCT
ejpam-6536	295	2	..........	..........	PUNCT
ejpam-6536	296	1	..........	..........	PUNCT
ejpam-6536	296	2	..........	..........	PUNCT
ejpam-6536	297	1	.....	.....	PUNCT
ejpam-6536	297	2	....................................	....................................	PUNCT
ejpam-6536	298	1	.........................................................................................................................................................	.........................................................................................................................................................	PUNCT
ejpam-6536	298	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-6536	299	1	....................................	....................................	PUNCT
ejpam-6536	299	2	....................................	....................................	PUNCT
ejpam-6536	299	3	............	............	PUNCT
ejpam-6536	299	4	...........	...........	PUNCT
ejpam-6536	299	5	.........	.........	PUNCT
ejpam-6536	300	1	....................................	....................................	PUNCT
ejpam-6536	300	2	............	............	PUNCT
ejpam-6536	300	3	...........	...........	PUNCT
ejpam-6536	300	4	.........	.........	PUNCT
ejpam-6536	300	5	....................................	....................................	PUNCT
ejpam-6536	300	6	....................................	....................................	PUNCT
ejpam-6536	300	7	................................	................................	PUNCT
ejpam-6536	300	8	....................................	....................................	PUNCT
ejpam-6536	300	9	................................	................................	PUNCT
ejpam-6536	300	10	....................................	....................................	PUNCT
ejpam-6536	300	11	....................................	....................................	PUNCT
ejpam-6536	300	12	.........	.........	PUNCT
ejpam-6536	300	13	........	........	PUNCT
ejpam-6536	300	14	........	........	PUNCT
ejpam-6536	300	15	........	........	PUNCT
ejpam-6536	300	16	........	........	PUNCT
ejpam-6536	300	17	...	...	PUNCT
ejpam-6536	301	1	....................................	....................................	PUNCT
ejpam-6536	301	2	.........	.........	PUNCT
ejpam-6536	301	3	........	........	PUNCT
ejpam-6536	301	4	........	........	PUNCT
ejpam-6536	301	5	........	........	PUNCT
ejpam-6536	301	6	........	........	PUNCT
ejpam-6536	301	7	...	...	PUNCT
ejpam-6536	302	1	....................................	....................................	PUNCT
ejpam-6536	302	2	....................................	....................................	PUNCT
ejpam-6536	303	1	•	•	NUM
ejpam-6536	303	2	••	••	NOUN
ejpam-6536	303	3	•	•	NUM
ejpam-6536	303	4	•	•	NUM
ejpam-6536	303	5	•	•	NUM
ejpam-6536	303	6	•	•	NUM
ejpam-6536	303	7	•	•	NUM
ejpam-6536	303	8	•	•	NUM
ejpam-6536	303	9	•	•	NUM
ejpam-6536	303	10	•	•	NUM
ejpam-6536	303	11	•	•	NOUN
ejpam-6536	303	12	•	•	NUM
ejpam-6536	303	13	a1	a1	NOUN
ejpam-6536	303	14	a2	a2	PROPN
ejpam-6536	303	15	a3	a3	PROPN
ejpam-6536	303	16	b1	b1	PROPN
ejpam-6536	303	17	b2	b2	PROPN
ejpam-6536	303	18	b3	b3	PROPN
ejpam-6536	303	19	c1	c1	PROPN
ejpam-6536	303	20	c2	c2	PROPN
ejpam-6536	303	21	c3	c3	PROPN
ejpam-6536	303	22	g	g	PROPN
ejpam-6536	303	23	:	:	PUNCT
ejpam-6536	303	24	figure	figure	NOUN
ejpam-6536	303	25	3	3	NUM
ejpam-6536	303	26	:	:	PUNCT
ejpam-6536	303	27	graph	graph	VERB
ejpam-6536	303	28	g	g	NOUN
ejpam-6536	303	29	with	with	ADP
ejpam-6536	303	30	2γh(g	2γh(g	NOUN
ejpam-6536	303	31	)	)	PUNCT
ejpam-6536	303	32	<	<	X
ejpam-6536	303	33	γhh(g	γhh(g	NOUN
ejpam-6536	303	34	)	)	PUNCT
ejpam-6536	303	35	<	<	X
ejpam-6536	303	36	γh(g	γh(g	NOUN
ejpam-6536	303	37	)	)	PUNCT
ejpam-6536	303	38	+	+	CCONJ
ejpam-6536	303	39	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	303	40	)	)	PUNCT
ejpam-6536	303	41	proposition	proposition	NOUN
ejpam-6536	303	42	4	4	NUM
ejpam-6536	303	43	.	.	PUNCT
ejpam-6536	304	1	for	for	ADP
ejpam-6536	304	2	all	all	PRON
ejpam-6536	304	3	g	g	PROPN
ejpam-6536	304	4	∈	∈	PROPN
ejpam-6536	304	5	g	g	NOUN
ejpam-6536	304	6	,	,	PUNCT
ejpam-6536	304	7	if	if	SCONJ
ejpam-6536	304	8	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	304	9	)	)	PUNCT
ejpam-6536	304	10	≤	≤	NOUN
ejpam-6536	304	11	1	1	NUM
ejpam-6536	304	12	+	+	NUM
ejpam-6536	304	13	γh(g	γh(g	NOUN
ejpam-6536	304	14	)	)	PUNCT
ejpam-6536	304	15	,	,	PUNCT
ejpam-6536	304	16	then	then	ADV
ejpam-6536	304	17	γhh(g	γhh(g	NOUN
ejpam-6536	304	18	)	)	PUNCT
ejpam-6536	304	19	=	=	NOUN
ejpam-6536	304	20	γh(g	γh(g	NOUN
ejpam-6536	304	21	)	)	PUNCT
ejpam-6536	304	22	+	+	CCONJ
ejpam-6536	304	23	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	304	24	)	)	PUNCT
ejpam-6536	304	25	,	,	PUNCT
ejpam-6536	304	26	(	(	PUNCT
ejpam-6536	304	27	3	3	X
ejpam-6536	304	28	)	)	PUNCT
ejpam-6536	304	29	but	but	CCONJ
ejpam-6536	304	30	not	not	PART
ejpam-6536	304	31	conversely	conversely	ADV
ejpam-6536	304	32	.	.	PUNCT
ejpam-6536	305	1	in	in	ADP
ejpam-6536	305	2	particular	particular	ADJ
ejpam-6536	305	3	,	,	PUNCT
ejpam-6536	305	4	(	(	PUNCT
ejpam-6536	305	5	i	i	NOUN
ejpam-6536	305	6	)	)	PUNCT
ejpam-6536	305	7	γhh(g	γhh(g	PROPN
ejpam-6536	305	8	)	)	PUNCT
ejpam-6536	305	9	=	=	SYM
ejpam-6536	305	10	2γh(g	2γh(g	NOUN
ejpam-6536	305	11	)	)	PUNCT
ejpam-6536	305	12	for	for	ADP
ejpam-6536	305	13	any	any	PRON
ejpam-6536	305	14	of	of	ADP
ejpam-6536	305	15	the	the	DET
ejpam-6536	305	16	following	follow	VERB
ejpam-6536	305	17	graphs	graph	NOUN
ejpam-6536	305	18	g	g	NOUN
ejpam-6536	305	19	:	:	PUNCT
ejpam-6536	305	20	the	the	DET
ejpam-6536	305	21	complete	complete	ADJ
ejpam-6536	305	22	multipartite	multipartite	ADJ
ejpam-6536	305	23	graph	graph	NOUN
ejpam-6536	305	24	,	,	PUNCT
ejpam-6536	305	25	cycle	cycle	NOUN
ejpam-6536	305	26	cn	cn	PROPN
ejpam-6536	305	27	and	and	CCONJ
ejpam-6536	305	28	the	the	DET
ejpam-6536	305	29	petersen	petersen	PROPN
ejpam-6536	305	30	graph	graph	NOUN
ejpam-6536	305	31	described	describe	VERB
ejpam-6536	305	32	in	in	ADP
ejpam-6536	305	33	proposition	proposition	NOUN
ejpam-6536	305	34	1	1	NUM
ejpam-6536	305	35	.	.	PUNCT
ejpam-6536	305	36	(	(	PUNCT
ejpam-6536	305	37	ii	ii	NOUN
ejpam-6536	305	38	)	)	PUNCT
ejpam-6536	305	39	for	for	ADP
ejpam-6536	305	40	a	a	DET
ejpam-6536	305	41	path	path	NOUN
ejpam-6536	305	42	pn	pn	NOUN
ejpam-6536	305	43	on	on	ADP
ejpam-6536	305	44	n	n	PRON
ejpam-6536	305	45	≥	≥	NUM
ejpam-6536	305	46	4	4	NUM
ejpam-6536	305	47	vertices	vertex	NOUN
ejpam-6536	305	48	,	,	PUNCT
ejpam-6536	305	49	γhh(pn	γhh(pn	NOUN
ejpam-6536	305	50	)	)	PUNCT
ejpam-6536	305	51	=	=	SYM
ejpam-6536	305	52			NUM
ejpam-6536	305	53	4r	4r	NOUN
ejpam-6536	305	54	+	+	CCONJ
ejpam-6536	305	55	4	4	NUM
ejpam-6536	305	56	,	,	PUNCT
ejpam-6536	305	57	if	if	SCONJ
ejpam-6536	305	58	n	n	NOUN
ejpam-6536	305	59	=	=	SYM
ejpam-6536	305	60	6r	6r	NUM
ejpam-6536	306	1	+	+	CCONJ
ejpam-6536	306	2	s	s	NOUN
ejpam-6536	306	3	,	,	PUNCT
ejpam-6536	306	4	2	2	NUM
ejpam-6536	306	5	≤	≤	NOUN
ejpam-6536	306	6	s	s	PART
ejpam-6536	306	7	≤	≤	NOUN
ejpam-6536	306	8	4	4	NUM
ejpam-6536	306	9	;	;	PUNCT
ejpam-6536	306	10	4r	4r	NUM
ejpam-6536	306	11	+	+	CCONJ
ejpam-6536	306	12	2	2	NUM
ejpam-6536	306	13	,	,	PUNCT
ejpam-6536	306	14	if	if	SCONJ
ejpam-6536	306	15	n	n	NOUN
ejpam-6536	306	16	=	=	SYM
ejpam-6536	306	17	6r	6r	NUM
ejpam-6536	306	18	;	;	PUNCT
ejpam-6536	306	19	4r	4r	NUM
ejpam-6536	306	20	+	+	CCONJ
ejpam-6536	306	21	3	3	NUM
ejpam-6536	306	22	,	,	PUNCT
ejpam-6536	306	23	if	if	SCONJ
ejpam-6536	306	24	n	n	NOUN
ejpam-6536	306	25	=	=	SYM
ejpam-6536	306	26	6r	6r	NUM
ejpam-6536	307	1	+	+	CCONJ
ejpam-6536	307	2	1	1	NUM
ejpam-6536	307	3	;	;	PUNCT
ejpam-6536	307	4	4r	4r	NOUN
ejpam-6536	307	5	+	+	CCONJ
ejpam-6536	307	6	5	5	NUM
ejpam-6536	307	7	,	,	PUNCT
ejpam-6536	307	8	if	if	SCONJ
ejpam-6536	307	9	n	n	NOUN
ejpam-6536	307	10	=	=	SYM
ejpam-6536	307	11	6r	6r	NUM
ejpam-6536	308	1	+	+	CCONJ
ejpam-6536	308	2	5	5	NUM
ejpam-6536	308	3	.	.	X
ejpam-6536	308	4	proof	proof	NOUN
ejpam-6536	308	5	:	:	PUNCT
ejpam-6536	308	6	equation	equation	NOUN
ejpam-6536	308	7	3	3	NUM
ejpam-6536	308	8	is	be	AUX
ejpam-6536	308	9	clear	clear	ADJ
ejpam-6536	308	10	if	if	SCONJ
ejpam-6536	308	11	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	308	12	)	)	PUNCT
ejpam-6536	308	13	=	=	NOUN
ejpam-6536	308	14	γh(g	γh(g	NOUN
ejpam-6536	308	15	)	)	PUNCT
ejpam-6536	308	16	.	.	PUNCT
ejpam-6536	309	1	assume	assume	VERB
ejpam-6536	309	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	309	3	)	)	PUNCT
ejpam-6536	309	4	=	=	SYM
ejpam-6536	309	5	1	1	NUM
ejpam-6536	309	6	+	+	NUM
ejpam-6536	309	7	γh(g	γh(g	NOUN
ejpam-6536	309	8	)	)	PUNCT
ejpam-6536	309	9	,	,	PUNCT
ejpam-6536	309	10	and	and	CCONJ
ejpam-6536	309	11	let	let	VERB
ejpam-6536	309	12	(	(	PUNCT
ejpam-6536	309	13	a	a	PRON
ejpam-6536	309	14	,	,	PUNCT
ejpam-6536	309	15	b	b	NOUN
ejpam-6536	309	16	)	)	PUNCT
ejpam-6536	309	17	∈	∈	PROPN
ejpam-6536	309	18	phd(g	phd(g	PROPN
ejpam-6536	309	19	)	)	PUNCT
ejpam-6536	309	20	.	.	PUNCT
ejpam-6536	310	1	if	if	SCONJ
ejpam-6536	310	2	|a|+|b|	|a|+|b|	X
ejpam-6536	310	3	<	<	X
ejpam-6536	310	4	1	1	NUM
ejpam-6536	310	5	+	+	NUM
ejpam-6536	310	6	2γh(g	2γh(g	NOUN
ejpam-6536	310	7	)	)	PUNCT
ejpam-6536	310	8	,	,	PUNCT
ejpam-6536	310	9	then	then	ADV
ejpam-6536	310	10	|a|	|a|	PROPN
ejpam-6536	310	11	=	=	SYM
ejpam-6536	310	12	|b|	|b|	PROPN
ejpam-6536	310	13	=	=	PUNCT
ejpam-6536	310	14	γh(g	γh(g	NOUN
ejpam-6536	310	15	)	)	PUNCT
ejpam-6536	310	16	.	.	PUNCT
ejpam-6536	311	1	consequently	consequently	ADV
ejpam-6536	311	2	,	,	PUNCT
ejpam-6536	311	3	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	311	4	)	)	PUNCT
ejpam-6536	311	5	=	=	NOUN
ejpam-6536	311	6	γh(g	γh(g	NOUN
ejpam-6536	311	7	)	)	PUNCT
ejpam-6536	311	8	,	,	PUNCT
ejpam-6536	311	9	a	a	DET
ejpam-6536	311	10	contradiction	contradiction	NOUN
ejpam-6536	311	11	.	.	PUNCT
ejpam-6536	312	1	since	since	SCONJ
ejpam-6536	312	2	(	(	PUNCT
ejpam-6536	312	3	a	a	DET
ejpam-6536	312	4	,	,	PUNCT
ejpam-6536	312	5	b	b	NOUN
ejpam-6536	312	6	)	)	PUNCT
ejpam-6536	312	7	is	be	AUX
ejpam-6536	312	8	arbitrary	arbitrary	ADJ
ejpam-6536	312	9	,	,	PUNCT
ejpam-6536	312	10	γh(g)+	γh(g)+	VERB
ejpam-6536	312	11	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	312	12	)	)	PUNCT
ejpam-6536	312	13	=	=	SYM
ejpam-6536	312	14	1	1	NUM
ejpam-6536	312	15	+	+	NUM
ejpam-6536	312	16	2γh(g	2γh(g	NOUN
ejpam-6536	312	17	)	)	PUNCT
ejpam-6536	312	18	≤	≤	NUM
ejpam-6536	312	19	γhh(g	γhh(g	NOUN
ejpam-6536	312	20	)	)	PUNCT
ejpam-6536	312	21	.	.	PUNCT
ejpam-6536	313	1	equation	equation	NOUN
ejpam-6536	313	2	2	2	NUM
ejpam-6536	313	3	yields	yield	NOUN
ejpam-6536	313	4	the	the	DET
ejpam-6536	313	5	desired	desire	VERB
ejpam-6536	313	6	equality	equality	NOUN
ejpam-6536	313	7	.	.	PUNCT
ejpam-6536	314	1	v.	v.	ADP
ejpam-6536	314	2	a	a	DET
ejpam-6536	314	3	besana	besana	PROPN
ejpam-6536	314	4	,	,	PUNCT
ejpam-6536	314	5	f.	f.	PROPN
ejpam-6536	314	6	jamil	jamil	PROPN
ejpam-6536	314	7	,	,	PUNCT
ejpam-6536	314	8	s.	s.	PROPN
ejpam-6536	314	9	canoy	canoy	PROPN
ejpam-6536	314	10	jr	jr	PROPN
ejpam-6536	314	11	.	.	PROPN
ejpam-6536	314	12	/	/	SYM
ejpam-6536	314	13	eur	eur	PROPN
ejpam-6536	314	14	.	.	PUNCT
ejpam-6536	315	1	j.	j.	PROPN
ejpam-6536	315	2	pure	pure	PROPN
ejpam-6536	315	3	appl	appl	PROPN
ejpam-6536	315	4	.	.	PROPN
ejpam-6536	315	5	math	math	PROPN
ejpam-6536	315	6	,	,	PUNCT
ejpam-6536	315	7	18	18	NUM
ejpam-6536	315	8	(	(	PUNCT
ejpam-6536	315	9	3	3	NUM
ejpam-6536	315	10	)	)	PUNCT
ejpam-6536	315	11	(	(	PUNCT
ejpam-6536	315	12	2025	2025	NUM
ejpam-6536	315	13	)	)	PUNCT
ejpam-6536	315	14	,	,	PUNCT
ejpam-6536	315	15	6536	6536	NUM
ejpam-6536	315	16	9	9	NUM
ejpam-6536	315	17	of	of	ADP
ejpam-6536	315	18	17	17	NUM
ejpam-6536	315	19	revisit	revisit	NOUN
ejpam-6536	315	20	the	the	DET
ejpam-6536	315	21	graph	graph	NOUN
ejpam-6536	315	22	g	g	PROPN
ejpam-6536	315	23	=	=	PUNCT
ejpam-6536	315	24	(	(	PUNCT
ejpam-6536	315	25	k1	k1	PROPN
ejpam-6536	315	26	∪	∪	X
ejpam-6536	315	27	kk+1	kk+1	X
ejpam-6536	315	28	)	)	PUNCT
ejpam-6536	315	29	+	+	SYM
ejpam-6536	315	30	kr1,r2,	kr1,r2,	PROPN
ejpam-6536	315	31	...	...	PUNCT
ejpam-6536	315	32	,rm−1	,rm−1	PUNCT
ejpam-6536	315	33	,	,	PUNCT
ejpam-6536	315	34	where	where	SCONJ
ejpam-6536	315	35	r1	r1	PROPN
ejpam-6536	315	36	=	=	SYM
ejpam-6536	315	37	r2	r2	PROPN
ejpam-6536	315	38	=	=	PUNCT
ejpam-6536	315	39	·	·	PUNCT
ejpam-6536	315	40	·	·	PUNCT
ejpam-6536	315	41	·	·	PUNCT
ejpam-6536	316	1	=	=	PUNCT
ejpam-6536	316	2	rm−1	rm−1	NOUN
ejpam-6536	316	3	=	=	SYM
ejpam-6536	316	4	2	2	NUM
ejpam-6536	316	5	,	,	PUNCT
ejpam-6536	316	6	in	in	ADP
ejpam-6536	316	7	theorem	theorem	NOUN
ejpam-6536	316	8	6	6	NUM
ejpam-6536	316	9	.	.	PUNCT
ejpam-6536	316	10	as	as	SCONJ
ejpam-6536	316	11	shown	show	VERB
ejpam-6536	316	12	,	,	PUNCT
ejpam-6536	316	13	γhh(g	γhh(g	NOUN
ejpam-6536	316	14	)	)	PUNCT
ejpam-6536	316	15	=	=	SYM
ejpam-6536	316	16	2	2	NUM
ejpam-6536	316	17	m	m	NOUN
ejpam-6536	316	18	+	+	NOUN
ejpam-6536	316	19	k	k	X
ejpam-6536	316	20	=	=	PUNCT
ejpam-6536	316	21	γh(g	γh(g	NOUN
ejpam-6536	316	22	)	)	PUNCT
ejpam-6536	316	23	+	+	CCONJ
ejpam-6536	316	24	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	316	25	)	)	PUNCT
ejpam-6536	316	26	.	.	PUNCT
ejpam-6536	317	1	however	however	ADV
ejpam-6536	317	2	,	,	PUNCT
ejpam-6536	317	3	if	if	SCONJ
ejpam-6536	317	4	k	k	PROPN
ejpam-6536	317	5	≥	≥	NUM
ejpam-6536	317	6	2	2	NUM
ejpam-6536	317	7	,	,	PUNCT
ejpam-6536	317	8	then	then	ADV
ejpam-6536	317	9	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	317	10	)	)	PUNCT
ejpam-6536	317	11	>	>	X
ejpam-6536	317	12	1	1	NUM
ejpam-6536	317	13	+	+	NOUN
ejpam-6536	317	14	γh(g	γh(g	NOUN
ejpam-6536	317	15	)	)	PUNCT
ejpam-6536	317	16	.	.	PUNCT
ejpam-6536	318	1	the	the	DET
ejpam-6536	318	2	rest	rest	NOUN
ejpam-6536	318	3	of	of	ADP
ejpam-6536	318	4	the	the	DET
ejpam-6536	318	5	proof	proof	NOUN
ejpam-6536	318	6	follows	follow	VERB
ejpam-6536	318	7	from	from	ADP
ejpam-6536	318	8	proposition	proposition	NOUN
ejpam-6536	318	9	1	1	NUM
ejpam-6536	318	10	and	and	CCONJ
ejpam-6536	318	11	observation	observation	NOUN
ejpam-6536	318	12	1	1	NUM
ejpam-6536	318	13	.	.	PUNCT
ejpam-6536	319	1	■	■	PUNCT
ejpam-6536	319	2	proposition	proposition	NOUN
ejpam-6536	319	3	5	5	NUM
ejpam-6536	319	4	.	.	PUNCT
ejpam-6536	319	5	for	for	ADP
ejpam-6536	319	6	each	each	DET
ejpam-6536	319	7	positive	positive	ADJ
ejpam-6536	319	8	integer	integer	NOUN
ejpam-6536	319	9	n	n	PRON
ejpam-6536	319	10	≥	≥	NOUN
ejpam-6536	319	11	4	4	NUM
ejpam-6536	319	12	,	,	PUNCT
ejpam-6536	319	13	there	there	PRON
ejpam-6536	319	14	exists	exist	VERB
ejpam-6536	319	15	g	g	PROPN
ejpam-6536	319	16	∈	∈	PROPN
ejpam-6536	319	17	g	g	PROPN
ejpam-6536	319	18	for	for	ADP
ejpam-6536	319	19	which	which	PRON
ejpam-6536	319	20	γh(g	γh(g	NOUN
ejpam-6536	319	21	)	)	PUNCT
ejpam-6536	320	1	+	+	CCONJ
ejpam-6536	320	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	320	3	)	)	PUNCT
ejpam-6536	320	4	−	−	NUM
ejpam-6536	320	5	γhh(g	γhh(g	NOUN
ejpam-6536	320	6	)	)	PUNCT
ejpam-6536	320	7	=	=	SYM
ejpam-6536	320	8	n.	n.	NOUN
ejpam-6536	320	9	proof	proof	NOUN
ejpam-6536	320	10	:	:	PUNCT
ejpam-6536	320	11	let	let	VERB
ejpam-6536	320	12	g	g	NOUN
ejpam-6536	320	13	be	be	AUX
ejpam-6536	320	14	the	the	DET
ejpam-6536	320	15	graph	graph	NOUN
ejpam-6536	320	16	given	give	VERB
ejpam-6536	320	17	in	in	ADP
ejpam-6536	320	18	figure	figure	NOUN
ejpam-6536	320	19	4	4	NUM
ejpam-6536	320	20	which	which	PRON
ejpam-6536	320	21	is	be	AUX
ejpam-6536	320	22	obtained	obtain	VERB
ejpam-6536	320	23	from	from	ADP
ejpam-6536	320	24	the	the	DET
ejpam-6536	320	25	complete	complete	ADJ
ejpam-6536	320	26	graph	graph	NOUN
ejpam-6536	320	27	k4	k4	NOUN
ejpam-6536	320	28	(	(	PUNCT
ejpam-6536	320	29	with	with	ADP
ejpam-6536	320	30	vertices	vertex	NOUN
ejpam-6536	320	31	{	{	PUNCT
ejpam-6536	320	32	u	u	NOUN
ejpam-6536	320	33	,	,	PUNCT
ejpam-6536	320	34	v	v	NOUN
ejpam-6536	320	35	,	,	PUNCT
ejpam-6536	320	36	w	w	PROPN
ejpam-6536	320	37	,	,	PUNCT
ejpam-6536	320	38	z	z	NOUN
ejpam-6536	320	39	}	}	PUNCT
ejpam-6536	320	40	)	)	PUNCT
ejpam-6536	320	41	by	by	ADP
ejpam-6536	320	42	adding	add	VERB
ejpam-6536	320	43	to	to	AUX
ejpam-6536	320	44	k4	k4	VERB
ejpam-6536	320	45	three	three	NUM
ejpam-6536	320	46	copies	copy	NOUN
ejpam-6536	320	47	of	of	ADP
ejpam-6536	320	48	the	the	DET
ejpam-6536	320	49	join	join	NOUN
ejpam-6536	320	50	k1	k1	NOUN
ejpam-6536	320	51	+	+	CCONJ
ejpam-6536	320	52	c4	c4	NOUN
ejpam-6536	320	53	through	through	ADP
ejpam-6536	320	54	the	the	DET
ejpam-6536	320	55	vertices	vertex	NOUN
ejpam-6536	320	56	u	u	NOUN
ejpam-6536	320	57	,	,	PUNCT
ejpam-6536	320	58	v	v	NOUN
ejpam-6536	320	59	and	and	CCONJ
ejpam-6536	320	60	w	w	NOUN
ejpam-6536	320	61	and	and	CCONJ
ejpam-6536	320	62	then	then	ADV
ejpam-6536	320	63	adding	add	VERB
ejpam-6536	320	64	the	the	DET
ejpam-6536	320	65	join	join	NOUN
ejpam-6536	320	66	⟨z⟩+kn−2	⟨z⟩+kn−2	PROPN
ejpam-6536	320	67	.	.	PUNCT
ejpam-6536	321	1	let	let	VERB
ejpam-6536	321	2	v	v	X
ejpam-6536	321	3	(	(	PUNCT
ejpam-6536	321	4	kn−2	kn−2	PROPN
ejpam-6536	321	5	)	)	PUNCT
ejpam-6536	321	6	=	=	PUNCT
ejpam-6536	322	1	{	{	PUNCT
ejpam-6536	322	2	x1	x1	PROPN
ejpam-6536	322	3	,	,	PUNCT
ejpam-6536	322	4	x2	x2	PROPN
ejpam-6536	322	5	,	,	PUNCT
ejpam-6536	322	6	.	.	PUNCT
ejpam-6536	322	7	.	.	PUNCT
ejpam-6536	322	8	.	.	PUNCT
ejpam-6536	323	1	,	,	PUNCT
ejpam-6536	323	2	xn−2	xn−2	PROPN
ejpam-6536	323	3	}	}	PUNCT
ejpam-6536	323	4	..........................	..........................	PUNCT
ejpam-6536	323	5	.........................	.........................	PUNCT
ejpam-6536	323	6	.........................	.........................	PUNCT
ejpam-6536	323	7	.........................	.........................	PUNCT
ejpam-6536	323	8	.........................	.........................	PUNCT
ejpam-6536	323	9	.........................	.........................	PUNCT
ejpam-6536	323	10	...........	...........	PUNCT
ejpam-6536	323	11	....................................	....................................	PUNCT
ejpam-6536	323	12	.............................................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-6536	323	13	..............................................................	..............................................................	PUNCT
ejpam-6536	323	14	.........................	.........................	PUNCT
ejpam-6536	323	15	.........................	.........................	PUNCT
ejpam-6536	323	16	.........................	.........................	PUNCT
ejpam-6536	323	17	.........................	.........................	PUNCT
ejpam-6536	323	18	.........................	.........................	PUNCT
ejpam-6536	323	19	...........	...........	PUNCT
ejpam-6536	323	20	....................................	....................................	PUNCT
ejpam-6536	323	21	.........	.........	PUNCT
ejpam-6536	323	22	........	........	PUNCT
ejpam-6536	323	23	........	........	PUNCT
ejpam-6536	323	24	........	........	PUNCT
ejpam-6536	323	25	........	........	PUNCT
ejpam-6536	323	26	........	........	PUNCT
ejpam-6536	323	27	........	........	PUNCT
ejpam-6536	323	28	........	........	PUNCT
ejpam-6536	323	29	........	........	PUNCT
ejpam-6536	323	30	........	........	PUNCT
ejpam-6536	323	31	........	........	PUNCT
ejpam-6536	323	32	........	........	PUNCT
ejpam-6536	323	33	..	..	PUNCT
ejpam-6536	323	34	.	.	PUNCT
ejpam-6536	324	1	...................................	...................................	PUNCT
ejpam-6536	325	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-6536	326	1	....................................	....................................	PUNCT
ejpam-6536	327	1	....................................	....................................	PUNCT
ejpam-6536	328	1	•	•	NUM
ejpam-6536	328	2	••	••	NOUN
ejpam-6536	328	3	•	•	NUM
ejpam-6536	328	4	•	•	NUM
ejpam-6536	328	5	•	•	NUM
ejpam-6536	328	6	•	•	NOUN
ejpam-6536	328	7	•	•	NOUN
ejpam-6536	328	8	••	••	NOUN
ejpam-6536	328	9	•	•	NUM
ejpam-6536	328	10	•	•	NUM
ejpam-6536	328	11	•	•	NUM
ejpam-6536	328	12	•	•	NUM
ejpam-6536	328	13	•	•	NOUN
ejpam-6536	328	14	•	•	NOUN
ejpam-6536	328	15	..................................................................................................................................................................	..................................................................................................................................................................	PROPN
ejpam-6536	328	16	............................................................................................................	............................................................................................................	PUNCT
ejpam-6536	328	17	...................	...................	PUNCT
ejpam-6536	328	18	..................	..................	PUNCT
ejpam-6536	328	19	..............	..............	PUNCT
ejpam-6536	328	20	....................................	....................................	PUNCT
ejpam-6536	328	21	........................................................................	........................................................................	PUNCT
ejpam-6536	328	22	....................................	....................................	PUNCT
ejpam-6536	328	23	...................	...................	PUNCT
ejpam-6536	328	24	..................	..................	PUNCT
ejpam-6536	328	25	..............	..............	PUNCT
ejpam-6536	328	26	....................................	....................................	PUNCT
ejpam-6536	328	27	....................................	....................................	PUNCT
ejpam-6536	328	28	.........	.........	PUNCT
ejpam-6536	328	29	........	........	PUNCT
ejpam-6536	328	30	........	........	PUNCT
ejpam-6536	328	31	........	........	PUNCT
ejpam-6536	328	32	........	........	PUNCT
ejpam-6536	328	33	........	........	PUNCT
ejpam-6536	328	34	......	......	PUNCT
ejpam-6536	328	35	..............	..............	PUNCT
ejpam-6536	328	36	.............	.............	PUNCT
ejpam-6536	328	37	.............	.............	PUNCT
ejpam-6536	328	38	.............	.............	PUNCT
ejpam-6536	328	39	.............	.............	PUNCT
ejpam-6536	328	40	.............	.............	PUNCT
ejpam-6536	328	41	.............	.............	PUNCT
ejpam-6536	328	42	..	..	PUNCT
ejpam-6536	328	43	........................................................	........................................................	PUNCT
ejpam-6536	328	44	........................................................	........................................................	PUNCT
ejpam-6536	328	45	..........	..........	PUNCT
ejpam-6536	329	1	..........	..........	PUNCT
ejpam-6536	329	2	..........	..........	PUNCT
ejpam-6536	330	1	.......	.......	PUNCT
ejpam-6536	330	2	.........	.........	PUNCT
ejpam-6536	330	3	........	........	PUNCT
ejpam-6536	330	4	........	........	PUNCT
ejpam-6536	330	5	........	........	PUNCT
ejpam-6536	331	1	....................................	....................................	PUNCT
ejpam-6536	331	2	b	b	X
ejpam-6536	331	3	b1	b1	PROPN
ejpam-6536	331	4	b2	b2	NOUN
ejpam-6536	331	5	b3	b3	PROPN
ejpam-6536	331	6	b4	b4	PROPN
ejpam-6536	331	7	....................................	....................................	PUNCT
ejpam-6536	331	8	....................................	....................................	PUNCT
ejpam-6536	331	9	....................................	....................................	PUNCT
ejpam-6536	331	10	.....................................	.....................................	PUNCT
ejpam-6536	331	11	.	.	PUNCT
ejpam-6536	331	12	.	.	PUNCT
ejpam-6536	332	1	u	u	PRON
ejpam-6536	332	2	v	v	PROPN
ejpam-6536	332	3	w	w	NOUN
ejpam-6536	332	4	z	z	NOUN
ejpam-6536	333	1	x1	x1	NOUN
ejpam-6536	334	1	x2	x2	NOUN
ejpam-6536	334	2	x3	x3	VERB
ejpam-6536	334	3	xn−2	xn−2	PROPN
ejpam-6536	334	4	.........	.........	PUNCT
ejpam-6536	334	5	.........	.........	PUNCT
ejpam-6536	335	1	..........	..........	PUNCT
ejpam-6536	335	2	...........	...........	PUNCT
ejpam-6536	335	3	.............	.............	PUNCT
ejpam-6536	335	4	.................	.................	PUNCT
ejpam-6536	336	1	............................................................................................................................................................................................................................	............................................................................................................................................................................................................................	PUNCT
ejpam-6536	336	2	.........	.........	PUNCT
ejpam-6536	337	1	.........	.........	PUNCT
ejpam-6536	337	2	...........	...........	PUNCT
ejpam-6536	337	3	.................	.................	PUNCT
ejpam-6536	337	4	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-6536	337	5	..........	..........	PUNCT
ejpam-6536	337	6	...............	...............	PUNCT
ejpam-6536	338	1	....................................................................................................................................................................	....................................................................................................................................................................	PUNCT
ejpam-6536	338	2	............................................	............................................	PUNCT
ejpam-6536	339	1	.................	.................	PUNCT
ejpam-6536	339	2	.........................................................................................................................	.........................................................................................................................	PUNCT
ejpam-6536	339	3	...............	...............	PUNCT
ejpam-6536	339	4	............	............	PUNCT
ejpam-6536	339	5	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-6536	339	6	.............	.............	PUNCT
ejpam-6536	340	1	..	..	PUNCT
ejpam-6536	340	2	...............................................................................	...............................................................................	PUNCT
ejpam-6536	341	1	..................	..................	PUNCT
ejpam-6536	341	2	..	..	PUNCT
ejpam-6536	341	3	...........	...........	PUNCT
ejpam-6536	341	4	..........	..........	PUNCT
ejpam-6536	342	1	..........	..........	PUNCT
ejpam-6536	342	2	..........	..........	PUNCT
ejpam-6536	343	1	..........	..........	PUNCT
ejpam-6536	343	2	..........	..........	PUNCT
ejpam-6536	344	1	..........	..........	PUNCT
ejpam-6536	344	2	..........	..........	PUNCT
ejpam-6536	345	1	..........	..........	PUNCT
ejpam-6536	345	2	..........	..........	PUNCT
ejpam-6536	346	1	..........	..........	PUNCT
ejpam-6536	346	2	..........	..........	PUNCT
ejpam-6536	347	1	.....	.....	PUNCT
ejpam-6536	347	2	.........	.........	PUNCT
ejpam-6536	347	3	........	........	PUNCT
ejpam-6536	347	4	........	........	PUNCT
ejpam-6536	347	5	........	........	PUNCT
ejpam-6536	347	6	........	........	PUNCT
ejpam-6536	347	7	........	........	PUNCT
ejpam-6536	347	8	........	........	PUNCT
ejpam-6536	347	9	........	........	PUNCT
ejpam-6536	347	10	........	........	PUNCT
ejpam-6536	347	11	........	........	PUNCT
ejpam-6536	347	12	........	........	PUNCT
ejpam-6536	347	13	........	........	PUNCT
ejpam-6536	348	1	...........................................................................................................	...........................................................................................................	PUNCT
ejpam-6536	348	2	...........................................................................................................................................................................................	...........................................................................................................................................................................................	PUNCT
ejpam-6536	349	1	............................................................................................................	............................................................................................................	PUNCT
ejpam-6536	349	2	...................	...................	PUNCT
ejpam-6536	350	1	..................	..................	PUNCT
ejpam-6536	350	2	..............	..............	PUNCT
ejpam-6536	351	1	....................................	....................................	PUNCT
ejpam-6536	351	2	........................................................................	........................................................................	PUNCT
ejpam-6536	352	1	....................................	....................................	PUNCT
ejpam-6536	352	2	...................	...................	PUNCT
ejpam-6536	353	1	..................	..................	PUNCT
ejpam-6536	353	2	..............	..............	PUNCT
ejpam-6536	354	1	....................................	....................................	PUNCT
ejpam-6536	355	1	....................................	....................................	PUNCT
ejpam-6536	356	1	•	•	NUM
ejpam-6536	356	2	•	•	NUM
ejpam-6536	356	3	••	••	NOUN
ejpam-6536	356	4	•	•	NOUN
ejpam-6536	356	5	•	•	NUM
ejpam-6536	356	6	...........	...........	PUNCT
ejpam-6536	356	7	........	........	PUNCT
ejpam-6536	356	8	........	........	PUNCT
ejpam-6536	356	9	........	........	PUNCT
ejpam-6536	356	10	........	........	PUNCT
ejpam-6536	356	11	........	........	PUNCT
ejpam-6536	357	1	....	....	PUNCT
ejpam-6536	357	2	..............	..............	PUNCT
ejpam-6536	357	3	.............	.............	PUNCT
ejpam-6536	357	4	.............	.............	PUNCT
ejpam-6536	357	5	.............	.............	PUNCT
ejpam-6536	357	6	.............	.............	PUNCT
ejpam-6536	357	7	.............	.............	PUNCT
ejpam-6536	357	8	.............	.............	PUNCT
ejpam-6536	357	9	..	..	PUNCT
ejpam-6536	357	10	........................................................	........................................................	PUNCT
ejpam-6536	357	11	........................................................	........................................................	PUNCT
ejpam-6536	358	1	..........	..........	PUNCT
ejpam-6536	359	1	..........	..........	PUNCT
ejpam-6536	360	1	..........	..........	PUNCT
ejpam-6536	361	1	.......	.......	PUNCT
ejpam-6536	362	1	.........	.........	PUNCT
ejpam-6536	363	1	........	........	PUNCT
ejpam-6536	364	1	........	........	PUNCT
ejpam-6536	365	1	........	........	PUNCT
ejpam-6536	366	1	....................................	....................................	PUNCT
ejpam-6536	366	2	c	c	PROPN
ejpam-6536	366	3	c1	c1	PROPN
ejpam-6536	366	4	c2	c2	PROPN
ejpam-6536	366	5	c3	c3	PROPN
ejpam-6536	366	6	c4	c4	PROPN
ejpam-6536	366	7	............................................................................................................	............................................................................................................	PUNCT
ejpam-6536	366	8	...................	...................	PUNCT
ejpam-6536	366	9	..................	..................	PUNCT
ejpam-6536	367	1	..............	..............	PUNCT
ejpam-6536	367	2	....................................	....................................	PUNCT
ejpam-6536	368	1	........................................................................	........................................................................	PUNCT
ejpam-6536	368	2	....................................	....................................	PUNCT
ejpam-6536	369	1	...................	...................	PUNCT
ejpam-6536	369	2	..................	..................	PUNCT
ejpam-6536	370	1	..............	..............	PUNCT
ejpam-6536	370	2	....................................	....................................	PUNCT
ejpam-6536	371	1	....................................	....................................	PUNCT
ejpam-6536	372	1	•	•	NUM
ejpam-6536	372	2	•	•	NUM
ejpam-6536	372	3	••	••	NOUN
ejpam-6536	372	4	•	•	NOUN
ejpam-6536	372	5	•	•	NUM
ejpam-6536	372	6	...........	...........	PUNCT
ejpam-6536	372	7	........	........	PUNCT
ejpam-6536	372	8	........	........	PUNCT
ejpam-6536	372	9	........	........	PUNCT
ejpam-6536	372	10	........	........	PUNCT
ejpam-6536	372	11	........	........	PUNCT
ejpam-6536	373	1	....	....	PUNCT
ejpam-6536	373	2	..............	..............	PUNCT
ejpam-6536	373	3	.............	.............	PUNCT
ejpam-6536	373	4	.............	.............	PUNCT
ejpam-6536	373	5	.............	.............	PUNCT
ejpam-6536	373	6	.............	.............	PUNCT
ejpam-6536	373	7	.............	.............	PUNCT
ejpam-6536	373	8	.............	.............	PUNCT
ejpam-6536	373	9	..	..	PUNCT
ejpam-6536	373	10	........................................................	........................................................	PUNCT
ejpam-6536	373	11	........................................................	........................................................	PUNCT
ejpam-6536	374	1	..........	..........	PUNCT
ejpam-6536	375	1	..........	..........	PUNCT
ejpam-6536	376	1	..........	..........	PUNCT
ejpam-6536	377	1	.......	.......	PUNCT
ejpam-6536	378	1	.........	.........	PUNCT
ejpam-6536	379	1	........	........	PUNCT
ejpam-6536	380	1	........	........	PUNCT
ejpam-6536	381	1	........	........	PUNCT
ejpam-6536	382	1	....................................	....................................	PUNCT
ejpam-6536	383	1	a	a	DET
ejpam-6536	383	2	a1	a1	NOUN
ejpam-6536	383	3	a2	a2	PROPN
ejpam-6536	383	4	a3	a3	NOUN
ejpam-6536	383	5	a4	a4	PROPN
ejpam-6536	383	6	figure	figure	NOUN
ejpam-6536	383	7	4	4	NUM
ejpam-6536	383	8	:	:	PUNCT
ejpam-6536	383	9	a	a	DET
ejpam-6536	383	10	graph	graph	NOUN
ejpam-6536	383	11	g	g	NOUN
ejpam-6536	383	12	with	with	ADP
ejpam-6536	383	13	γhh(g	γhh(g	NOUN
ejpam-6536	383	14	)	)	PUNCT
ejpam-6536	383	15	<	<	X
ejpam-6536	383	16	γh(g	γh(g	NOUN
ejpam-6536	383	17	)	)	PUNCT
ejpam-6536	384	1	+	+	CCONJ
ejpam-6536	384	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	384	3	)	)	PUNCT
ejpam-6536	384	4	and	and	CCONJ
ejpam-6536	384	5	let	let	VERB
ejpam-6536	384	6	the	the	DET
ejpam-6536	384	7	copies	copy	NOUN
ejpam-6536	384	8	of	of	ADP
ejpam-6536	384	9	k1	k1	PROPN
ejpam-6536	384	10	+	+	NOUN
ejpam-6536	384	11	c4	c4	NOUN
ejpam-6536	384	12	be	be	AUX
ejpam-6536	384	13	given	give	VERB
ejpam-6536	384	14	by	by	ADP
ejpam-6536	384	15	the	the	DET
ejpam-6536	384	16	vertices	vertex	NOUN
ejpam-6536	384	17	{	{	PUNCT
ejpam-6536	384	18	a	a	DET
ejpam-6536	384	19	,	,	PUNCT
ejpam-6536	384	20	a1	a1	NOUN
ejpam-6536	384	21	,	,	PUNCT
ejpam-6536	384	22	a2	a2	PROPN
ejpam-6536	384	23	,	,	PUNCT
ejpam-6536	384	24	a3	a3	NOUN
ejpam-6536	384	25	,	,	PUNCT
ejpam-6536	384	26	a4	a4	PROPN
ejpam-6536	384	27	}	}	PUNCT
ejpam-6536	384	28	,	,	PUNCT
ejpam-6536	384	29	{	{	PUNCT
ejpam-6536	384	30	b	b	NOUN
ejpam-6536	384	31	,	,	PUNCT
ejpam-6536	384	32	b1	b1	NOUN
ejpam-6536	384	33	,	,	PUNCT
ejpam-6536	384	34	b2	b2	NOUN
ejpam-6536	384	35	,	,	PUNCT
ejpam-6536	384	36	b3	b3	NOUN
ejpam-6536	384	37	,	,	PUNCT
ejpam-6536	384	38	b4	b4	NOUN
ejpam-6536	384	39	}	}	PUNCT
ejpam-6536	384	40	and	and	CCONJ
ejpam-6536	384	41	{	{	PUNCT
ejpam-6536	384	42	c	c	X
ejpam-6536	384	43	,	,	PUNCT
ejpam-6536	384	44	c1	c1	PROPN
ejpam-6536	384	45	,	,	PUNCT
ejpam-6536	384	46	c2	c2	PROPN
ejpam-6536	384	47	,	,	PUNCT
ejpam-6536	384	48	c3	c3	PROPN
ejpam-6536	384	49	,	,	PUNCT
ejpam-6536	384	50	c4	c4	NOUN
ejpam-6536	384	51	}	}	PUNCT
ejpam-6536	384	52	with	with	ADP
ejpam-6536	384	53	au	au	PROPN
ejpam-6536	384	54	,	,	PUNCT
ejpam-6536	384	55	vb	vb	PROPN
ejpam-6536	384	56	,	,	PUNCT
ejpam-6536	384	57	wc	wc	PROPN
ejpam-6536	384	58	∈	∈	PROPN
ejpam-6536	384	59	e(g	e(g	PROPN
ejpam-6536	384	60	)	)	PUNCT
ejpam-6536	384	61	.	.	PUNCT
ejpam-6536	385	1	then	then	ADV
ejpam-6536	385	2	{	{	PUNCT
ejpam-6536	385	3	u	u	NOUN
ejpam-6536	385	4	,	,	PUNCT
ejpam-6536	385	5	v	v	NOUN
ejpam-6536	385	6	,	,	PUNCT
ejpam-6536	385	7	w	w	PROPN
ejpam-6536	385	8	,	,	PUNCT
ejpam-6536	385	9	z	z	NOUN
ejpam-6536	385	10	}	}	PUNCT
ejpam-6536	385	11	is	be	AUX
ejpam-6536	385	12	a	a	DET
ejpam-6536	385	13	γh	γh	ADV
ejpam-6536	385	14	-	-	PUNCT
ejpam-6536	385	15	set	set	NOUN
ejpam-6536	385	16	of	of	ADP
ejpam-6536	385	17	g	g	PROPN
ejpam-6536	385	18	and	and	CCONJ
ejpam-6536	385	19	{	{	PUNCT
ejpam-6536	385	20	a	a	PRON
ejpam-6536	385	21	,	,	PUNCT
ejpam-6536	385	22	a1	a1	NOUN
ejpam-6536	385	23	,	,	PUNCT
ejpam-6536	385	24	a2	a2	PROPN
ejpam-6536	385	25	}	}	PUNCT
ejpam-6536	385	26	∪	∪	NOUN
ejpam-6536	385	27	{	{	PUNCT
ejpam-6536	385	28	b	b	NOUN
ejpam-6536	385	29	,	,	PUNCT
ejpam-6536	385	30	b1	b1	NOUN
ejpam-6536	385	31	,	,	PUNCT
ejpam-6536	385	32	b2	b2	NOUN
ejpam-6536	385	33	}	}	PUNCT
ejpam-6536	385	34	∪	∪	X
ejpam-6536	385	35	{	{	PUNCT
ejpam-6536	385	36	c	c	NOUN
ejpam-6536	385	37	,	,	PUNCT
ejpam-6536	385	38	c1	c1	PROPN
ejpam-6536	385	39	,	,	PUNCT
ejpam-6536	385	40	c2	c2	PROPN
ejpam-6536	385	41	}	}	PUNCT
ejpam-6536	385	42	∪	∪	VERB
ejpam-6536	385	43	{	{	PUNCT
ejpam-6536	385	44	x1	x1	PROPN
ejpam-6536	385	45	,	,	PUNCT
ejpam-6536	385	46	x2	x2	PROPN
ejpam-6536	385	47	,	,	PUNCT
ejpam-6536	385	48	.	.	PUNCT
ejpam-6536	385	49	.	.	PUNCT
ejpam-6536	386	1	.	.	PUNCT
ejpam-6536	387	1	,	,	PUNCT
ejpam-6536	387	2	xn−2	xn−2	PROPN
ejpam-6536	387	3	}	}	PUNCT
ejpam-6536	387	4	is	be	AUX
ejpam-6536	387	5	a	a	DET
ejpam-6536	387	6	γ̃h	γ̃h	NOUN
ejpam-6536	387	7	-	-	PUNCT
ejpam-6536	387	8	set	set	NOUN
ejpam-6536	387	9	of	of	ADP
ejpam-6536	387	10	g.	g.	PROPN
ejpam-6536	387	11	on	on	ADP
ejpam-6536	387	12	the	the	DET
ejpam-6536	387	13	other	other	ADJ
ejpam-6536	387	14	hand	hand	NOUN
ejpam-6536	387	15	,	,	PUNCT
ejpam-6536	387	16	the	the	DET
ejpam-6536	387	17	sets	set	NOUN
ejpam-6536	387	18	{	{	PUNCT
ejpam-6536	387	19	w	w	NOUN
ejpam-6536	387	20	,	,	PUNCT
ejpam-6536	387	21	c	c	NOUN
ejpam-6536	387	22	,	,	PUNCT
ejpam-6536	387	23	b3	b3	PROPN
ejpam-6536	387	24	,	,	PUNCT
ejpam-6536	387	25	b4	b4	NOUN
ejpam-6536	387	26	,	,	PUNCT
ejpam-6536	387	27	c3	c3	PROPN
ejpam-6536	387	28	,	,	PUNCT
ejpam-6536	387	29	c4	c4	NOUN
ejpam-6536	387	30	}	}	PUNCT
ejpam-6536	387	31	and	and	CCONJ
ejpam-6536	387	32	{	{	PUNCT
ejpam-6536	387	33	u	u	NOUN
ejpam-6536	387	34	,	,	PUNCT
ejpam-6536	387	35	v	v	NOUN
ejpam-6536	387	36	,	,	PUNCT
ejpam-6536	387	37	z	z	PROPN
ejpam-6536	387	38	,	,	PUNCT
ejpam-6536	387	39	c1	c1	PROPN
ejpam-6536	387	40	,	,	PUNCT
ejpam-6536	387	41	c2	c2	PROPN
ejpam-6536	387	42	}	}	PUNCT
ejpam-6536	387	43	constitute	constitute	VERB
ejpam-6536	387	44	a	a	DET
ejpam-6536	387	45	γhh	γhh	NOUN
ejpam-6536	387	46	-	-	PUNCT
ejpam-6536	387	47	pair	pair	NOUN
ejpam-6536	387	48	of	of	ADP
ejpam-6536	387	49	g.	g.	PROPN
ejpam-6536	387	50	thus	thus	ADV
ejpam-6536	387	51	,	,	PUNCT
ejpam-6536	387	52	γh(g	γh(g	NOUN
ejpam-6536	387	53	)	)	PUNCT
ejpam-6536	388	1	+	+	CCONJ
ejpam-6536	388	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	388	3	)	)	PUNCT
ejpam-6536	388	4	−	−	NUM
ejpam-6536	388	5	γhh(g	γhh(g	NOUN
ejpam-6536	388	6	)	)	PUNCT
ejpam-6536	388	7	=	=	SYM
ejpam-6536	388	8	4	4	NUM
ejpam-6536	388	9	+	+	CCONJ
ejpam-6536	388	10	(	(	PUNCT
ejpam-6536	388	11	7	7	NUM
ejpam-6536	388	12	+	+	NUM
ejpam-6536	388	13	n	n	CCONJ
ejpam-6536	388	14	)	)	PUNCT
ejpam-6536	388	15	−	−	PROPN
ejpam-6536	389	1	11	11	NUM
ejpam-6536	389	2	=	=	SYM
ejpam-6536	389	3	n.	n.	NOUN
ejpam-6536	389	4	■	■	PUNCT
ejpam-6536	389	5	corollary	corollary	ADJ
ejpam-6536	389	6	3	3	NUM
ejpam-6536	389	7	.	.	PUNCT
ejpam-6536	390	1	the	the	DET
ejpam-6536	390	2	quantity	quantity	NOUN
ejpam-6536	390	3	γh(g	γh(g	PUNCT
ejpam-6536	390	4	)	)	PUNCT
ejpam-6536	391	1	+	+	CCONJ
ejpam-6536	391	2	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	391	3	)	)	PUNCT
ejpam-6536	391	4	−	−	NUM
ejpam-6536	391	5	γhh(g	γhh(g	NOUN
ejpam-6536	391	6	)	)	PUNCT
ejpam-6536	391	7	can	can	AUX
ejpam-6536	391	8	be	be	AUX
ejpam-6536	391	9	made	make	VERB
ejpam-6536	391	10	arbitrarily	arbitrarily	ADV
ejpam-6536	391	11	large	large	ADJ
ejpam-6536	391	12	.	.	PUNCT
ejpam-6536	392	1	3.3	3.3	NUM
ejpam-6536	392	2	.	.	PUNCT
ejpam-6536	393	1	in	in	ADP
ejpam-6536	393	2	the	the	DET
ejpam-6536	393	3	join	join	NOUN
ejpam-6536	393	4	of	of	ADP
ejpam-6536	393	5	graphs	graph	NOUN
ejpam-6536	393	6	a	a	DET
ejpam-6536	393	7	proof	proof	NOUN
ejpam-6536	393	8	similar	similar	ADJ
ejpam-6536	393	9	to	to	ADP
ejpam-6536	393	10	that	that	PRON
ejpam-6536	393	11	of	of	ADP
ejpam-6536	393	12	proposition	proposition	NOUN
ejpam-6536	393	13	3	3	NUM
ejpam-6536	393	14	establishes	establish	VERB
ejpam-6536	393	15	the	the	DET
ejpam-6536	393	16	following	follow	VERB
ejpam-6536	393	17	lemma	lemma	PROPN
ejpam-6536	393	18	.	.	PUNCT
ejpam-6536	394	1	lemma	lemma	PROPN
ejpam-6536	394	2	1	1	X
ejpam-6536	394	3	.	.	PUNCT
ejpam-6536	395	1	let	let	VERB
ejpam-6536	395	2	g	g	PROPN
ejpam-6536	395	3	∈	∈	PROPN
ejpam-6536	395	4	g	g	PROPN
ejpam-6536	395	5	.	.	PUNCT
ejpam-6536	396	1	if	if	SCONJ
ejpam-6536	396	2	s	s	VERB
ejpam-6536	396	3	⊆	⊆	NUM
ejpam-6536	396	4	v	v	NOUN
ejpam-6536	396	5	(	(	PUNCT
ejpam-6536	396	6	g	g	NOUN
ejpam-6536	396	7	)	)	PUNCT
ejpam-6536	396	8	is	be	AUX
ejpam-6536	396	9	a	a	DET
ejpam-6536	396	10	pnd	pnd	NOUN
ejpam-6536	396	11	-	-	PUNCT
ejpam-6536	396	12	set	set	NOUN
ejpam-6536	396	13	of	of	ADP
ejpam-6536	396	14	g	g	NOUN
ejpam-6536	396	15	,	,	PUNCT
ejpam-6536	396	16	then	then	ADV
ejpam-6536	396	17	v	v	X
ejpam-6536	396	18	(	(	PUNCT
ejpam-6536	396	19	g)\s	g)\s	NOUN
ejpam-6536	396	20	contains	contain	VERB
ejpam-6536	396	21	a	a	DET
ejpam-6536	396	22	point	point	NOUN
ejpam-6536	396	23	-	-	PUNCT
ejpam-6536	396	24	wise	wise	ADJ
ejpam-6536	396	25	non	non	ADJ
ejpam-6536	396	26	-	-	ADJ
ejpam-6536	396	27	dominating	dominating	ADJ
ejpam-6536	396	28	set	set	NOUN
ejpam-6536	396	29	of	of	ADP
ejpam-6536	396	30	g.	g.	PROPN
ejpam-6536	396	31	lemma	lemma	PROPN
ejpam-6536	396	32	1	1	NUM
ejpam-6536	396	33	makes	make	VERB
ejpam-6536	396	34	sense	sense	NOUN
ejpam-6536	396	35	to	to	ADP
ejpam-6536	396	36	the	the	DET
ejpam-6536	396	37	following	follow	VERB
ejpam-6536	396	38	definition	definition	NOUN
ejpam-6536	396	39	.	.	PUNCT
ejpam-6536	397	1	let	let	VERB
ejpam-6536	397	2	g	g	PROPN
ejpam-6536	397	3	∈	∈	PROPN
ejpam-6536	397	4	g	g	PROPN
ejpam-6536	397	5	.	.	PUNCT
ejpam-6536	398	1	a	a	DET
ejpam-6536	398	2	subset	subset	NOUN
ejpam-6536	398	3	s	s	VERB
ejpam-6536	398	4	⊆	⊆	NUM
ejpam-6536	398	5	v	v	NOUN
ejpam-6536	398	6	(	(	PUNCT
ejpam-6536	398	7	g	g	NOUN
ejpam-6536	398	8	)	)	PUNCT
ejpam-6536	398	9	is	be	AUX
ejpam-6536	398	10	an	an	DET
ejpam-6536	398	11	inverse	inverse	NOUN
ejpam-6536	398	12	point	point	NOUN
ejpam-6536	398	13	-	-	PUNCT
ejpam-6536	398	14	wise	wise	ADJ
ejpam-6536	398	15	non	non	ADJ
ejpam-6536	398	16	-	-	ADJ
ejpam-6536	398	17	dominating	dominating	ADJ
ejpam-6536	398	18	set	set	NOUN
ejpam-6536	398	19	of	of	ADP
ejpam-6536	398	20	g	g	PROPN
ejpam-6536	398	21	if	if	SCONJ
ejpam-6536	398	22	there	there	PRON
ejpam-6536	398	23	exists	exist	VERB
ejpam-6536	398	24	a	a	DET
ejpam-6536	398	25	pnd	pnd	NOUN
ejpam-6536	398	26	-	-	PUNCT
ejpam-6536	398	27	set	set	VERB
ejpam-6536	398	28	d	d	NOUN
ejpam-6536	398	29	of	of	ADP
ejpam-6536	398	30	g	g	NOUN
ejpam-6536	398	31	for	for	ADP
ejpam-6536	398	32	which	which	PRON
ejpam-6536	398	33	s	s	VERB
ejpam-6536	398	34	∩	∩	ADJ
ejpam-6536	398	35	d	d	NOUN
ejpam-6536	398	36	=	=	PUNCT
ejpam-6536	398	37	∅.	∅.	VERB
ejpam-6536	398	38	the	the	DET
ejpam-6536	398	39	minimum	minimum	ADJ
ejpam-6536	398	40	cardinality	cardinality	NOUN
ejpam-6536	398	41	of	of	ADP
ejpam-6536	398	42	an	an	DET
ejpam-6536	398	43	inverse	inverse	NOUN
ejpam-6536	398	44	point	point	NOUN
ejpam-6536	398	45	-	-	PUNCT
ejpam-6536	398	46	wise	wise	ADJ
ejpam-6536	398	47	non	non	ADJ
ejpam-6536	398	48	-	-	ADJ
ejpam-6536	398	49	dominating	dominating	ADJ
ejpam-6536	398	50	set	set	NOUN
ejpam-6536	398	51	of	of	ADP
ejpam-6536	398	52	g	g	PROPN
ejpam-6536	398	53	is	be	AUX
ejpam-6536	398	54	denoted	denote	VERB
ejpam-6536	398	55	by	by	ADP
ejpam-6536	398	56	ipnd(g	ipnd(g	PROPN
ejpam-6536	398	57	)	)	PUNCT
ejpam-6536	398	58	.	.	PUNCT
ejpam-6536	399	1	any	any	DET
ejpam-6536	399	2	inverse	inverse	NOUN
ejpam-6536	399	3	point	point	NOUN
ejpam-6536	399	4	-	-	PUNCT
ejpam-6536	399	5	wise	wise	ADJ
ejpam-6536	399	6	non	non	ADJ
ejpam-6536	399	7	-	-	ADJ
ejpam-6536	399	8	dominating	dominating	ADJ
ejpam-6536	399	9	set	set	NOUN
ejpam-6536	399	10	of	of	ADP
ejpam-6536	399	11	g	g	NOUN
ejpam-6536	399	12	of	of	ADP
ejpam-6536	399	13	cardinality	cardinality	PROPN
ejpam-6536	399	14	ipnd(g	ipnd(g	PROPN
ejpam-6536	399	15	)	)	PUNCT
ejpam-6536	399	16	is	be	AUX
ejpam-6536	399	17	called	call	VERB
ejpam-6536	399	18	ipnd	ipnd	NOUN
ejpam-6536	399	19	-	-	PUNCT
ejpam-6536	399	20	set	set	NOUN
ejpam-6536	399	21	of	of	ADP
ejpam-6536	399	22	g.	g.	PROPN
ejpam-6536	399	23	v.	v.	ADP
ejpam-6536	399	24	a	a	DET
ejpam-6536	399	25	besana	besana	PROPN
ejpam-6536	399	26	,	,	PUNCT
ejpam-6536	399	27	f.	f.	PROPN
ejpam-6536	399	28	jamil	jamil	PROPN
ejpam-6536	399	29	,	,	PUNCT
ejpam-6536	399	30	s.	s.	PROPN
ejpam-6536	399	31	canoy	canoy	PROPN
ejpam-6536	399	32	jr	jr	PROPN
ejpam-6536	399	33	.	.	PROPN
ejpam-6536	399	34	/	/	SYM
ejpam-6536	399	35	eur	eur	PROPN
ejpam-6536	399	36	.	.	PUNCT
ejpam-6536	400	1	j.	j.	PROPN
ejpam-6536	400	2	pure	pure	PROPN
ejpam-6536	400	3	appl	appl	PROPN
ejpam-6536	400	4	.	.	PROPN
ejpam-6536	400	5	math	math	PROPN
ejpam-6536	400	6	,	,	PUNCT
ejpam-6536	400	7	18	18	NUM
ejpam-6536	400	8	(	(	PUNCT
ejpam-6536	400	9	3	3	NUM
ejpam-6536	400	10	)	)	PUNCT
ejpam-6536	400	11	(	(	PUNCT
ejpam-6536	400	12	2025	2025	NUM
ejpam-6536	400	13	)	)	PUNCT
ejpam-6536	400	14	,	,	PUNCT
ejpam-6536	400	15	6536	6536	NUM
ejpam-6536	400	16	10	10	NUM
ejpam-6536	400	17	of	of	ADP
ejpam-6536	400	18	17	17	NUM
ejpam-6536	400	19	theorem	theorem	NOUN
ejpam-6536	400	20	7	7	NUM
ejpam-6536	400	21	.	.	PUNCT
ejpam-6536	401	1	let	let	VERB
ejpam-6536	401	2	g	g	NOUN
ejpam-6536	401	3	,	,	PUNCT
ejpam-6536	401	4	h	h	NOUN
ejpam-6536	401	5	∈	∈	PROPN
ejpam-6536	401	6	g	g	PROPN
ejpam-6536	401	7	and	and	CCONJ
ejpam-6536	401	8	s	s	VERB
ejpam-6536	401	9	⊆	⊆	NUM
ejpam-6536	401	10	v	v	NOUN
ejpam-6536	401	11	(	(	PUNCT
ejpam-6536	401	12	g+h	g+h	PROPN
ejpam-6536	401	13	)	)	PUNCT
ejpam-6536	401	14	.	.	PUNCT
ejpam-6536	402	1	then	then	ADV
ejpam-6536	402	2	s	s	VERB
ejpam-6536	402	3	is	be	AUX
ejpam-6536	402	4	an	an	DET
ejpam-6536	402	5	inverse	inverse	NOUN
ejpam-6536	402	6	hop	hop	NOUN
ejpam-6536	402	7	dominating	dominating	NOUN
ejpam-6536	402	8	set	set	NOUN
ejpam-6536	402	9	of	of	ADP
ejpam-6536	402	10	g+h	g+h	PROPN
ejpam-6536	402	11	if	if	SCONJ
ejpam-6536	402	12	and	and	CCONJ
ejpam-6536	402	13	only	only	ADV
ejpam-6536	402	14	if	if	SCONJ
ejpam-6536	402	15	s	s	NOUN
ejpam-6536	402	16	=	=	PUNCT
ejpam-6536	402	17	sg	sg	PROPN
ejpam-6536	402	18	∪sh	∪sh	NOUN
ejpam-6536	402	19	,	,	PUNCT
ejpam-6536	402	20	where	where	SCONJ
ejpam-6536	402	21	sg	sg	PROPN
ejpam-6536	402	22	and	and	CCONJ
ejpam-6536	402	23	sh	sh	PROPN
ejpam-6536	402	24	are	be	AUX
ejpam-6536	402	25	inverse	inverse	ADJ
ejpam-6536	402	26	point	point	NOUN
ejpam-6536	402	27	-	-	PUNCT
ejpam-6536	402	28	wise	wise	ADJ
ejpam-6536	402	29	non	non	ADJ
ejpam-6536	402	30	-	-	ADJ
ejpam-6536	402	31	dominating	dominating	ADJ
ejpam-6536	402	32	sets	set	NOUN
ejpam-6536	402	33	of	of	ADP
ejpam-6536	402	34	g	g	PROPN
ejpam-6536	402	35	and	and	CCONJ
ejpam-6536	402	36	h	h	NOUN
ejpam-6536	402	37	,	,	PUNCT
ejpam-6536	402	38	respectively	respectively	ADV
ejpam-6536	402	39	.	.	PUNCT
ejpam-6536	403	1	proof	proof	NOUN
ejpam-6536	403	2	:	:	PUNCT
ejpam-6536	403	3	note	note	VERB
ejpam-6536	403	4	first	first	ADV
ejpam-6536	403	5	that	that	SCONJ
ejpam-6536	403	6	g	g	PROPN
ejpam-6536	404	1	+	+	CCONJ
ejpam-6536	404	2	h	h	NOUN
ejpam-6536	404	3	∈	∈	PROPN
ejpam-6536	404	4	g	g	PROPN
ejpam-6536	404	5	.	.	PUNCT
ejpam-6536	405	1	assume	assume	VERB
ejpam-6536	405	2	that	that	SCONJ
ejpam-6536	405	3	s	s	VERB
ejpam-6536	405	4	is	be	AUX
ejpam-6536	405	5	an	an	DET
ejpam-6536	405	6	inverse	inverse	NOUN
ejpam-6536	405	7	hop	hop	NOUN
ejpam-6536	405	8	dominating	dominating	NOUN
ejpam-6536	405	9	set	set	NOUN
ejpam-6536	405	10	of	of	ADP
ejpam-6536	405	11	g	g	PROPN
ejpam-6536	406	1	+	+	CCONJ
ejpam-6536	406	2	h	h	NOUN
ejpam-6536	406	3	,	,	PUNCT
ejpam-6536	406	4	and	and	CCONJ
ejpam-6536	406	5	let	let	VERB
ejpam-6536	407	1	d	d	PROPN
ejpam-6536	407	2	⊆	⊆	NUM
ejpam-6536	407	3	v	v	NOUN
ejpam-6536	407	4	(	(	PUNCT
ejpam-6536	407	5	g	g	PROPN
ejpam-6536	407	6	+	+	NOUN
ejpam-6536	407	7	h	h	NOUN
ejpam-6536	407	8	)	)	PUNCT
ejpam-6536	407	9	be	be	VERB
ejpam-6536	407	10	a	a	DET
ejpam-6536	407	11	γh	γh	ADV
ejpam-6536	407	12	-	-	PUNCT
ejpam-6536	407	13	set	set	NOUN
ejpam-6536	407	14	of	of	ADP
ejpam-6536	407	15	g	g	PROPN
ejpam-6536	408	1	+	+	CCONJ
ejpam-6536	408	2	h	h	NOUN
ejpam-6536	408	3	such	such	ADJ
ejpam-6536	408	4	that	that	DET
ejpam-6536	408	5	s	s	NOUN
ejpam-6536	408	6	∩	∩	ADJ
ejpam-6536	408	7	d	d	NOUN
ejpam-6536	408	8	=	=	PUNCT
ejpam-6536	408	9	∅.	∅.	X
ejpam-6536	408	10	by	by	ADP
ejpam-6536	408	11	theorem	theorem	NOUN
ejpam-6536	408	12	1	1	NUM
ejpam-6536	408	13	,	,	PUNCT
ejpam-6536	408	14	s	s	PART
ejpam-6536	408	15	=	=	PUNCT
ejpam-6536	408	16	sg	sg	X
ejpam-6536	408	17	∪	∪	VERB
ejpam-6536	408	18	sh	sh	PROPN
ejpam-6536	409	1	and	and	CCONJ
ejpam-6536	409	2	d	d	PROPN
ejpam-6536	409	3	=	=	X
ejpam-6536	409	4	dg	dg	X
ejpam-6536	409	5	∪	∪	PROPN
ejpam-6536	409	6	dh	dh	NOUN
ejpam-6536	409	7	,	,	PUNCT
ejpam-6536	409	8	where	where	SCONJ
ejpam-6536	409	9	sg	sg	NOUN
ejpam-6536	409	10	and	and	CCONJ
ejpam-6536	409	11	dg	dg	NOUN
ejpam-6536	409	12	are	be	AUX
ejpam-6536	409	13	point	point	ADV
ejpam-6536	409	14	-	-	PUNCT
ejpam-6536	409	15	wise	wise	ADJ
ejpam-6536	409	16	non	non	ADJ
ejpam-6536	409	17	-	-	ADJ
ejpam-6536	409	18	dominating	dominating	ADJ
ejpam-6536	409	19	sets	set	NOUN
ejpam-6536	409	20	of	of	ADP
ejpam-6536	409	21	g	g	PROPN
ejpam-6536	409	22	and	and	CCONJ
ejpam-6536	409	23	sh	sh	PROPN
ejpam-6536	409	24	and	and	CCONJ
ejpam-6536	409	25	dh	dh	NOUN
ejpam-6536	409	26	are	be	AUX
ejpam-6536	409	27	point	point	ADV
ejpam-6536	409	28	-	-	PUNCT
ejpam-6536	409	29	wise	wise	ADJ
ejpam-6536	409	30	non	non	ADJ
ejpam-6536	409	31	-	-	ADJ
ejpam-6536	409	32	dominating	dominating	ADJ
ejpam-6536	409	33	sets	set	NOUN
ejpam-6536	409	34	of	of	ADP
ejpam-6536	409	35	h.	h.	PROPN
ejpam-6536	409	36	moreover	moreover	ADV
ejpam-6536	409	37	,	,	PUNCT
ejpam-6536	409	38	dg	dg	PROPN
ejpam-6536	409	39	and	and	CCONJ
ejpam-6536	409	40	dh	dh	NOUN
ejpam-6536	409	41	are	be	AUX
ejpam-6536	409	42	pnd	pnd	NOUN
ejpam-6536	409	43	-	-	PUNCT
ejpam-6536	409	44	sets	set	NOUN
ejpam-6536	409	45	of	of	ADP
ejpam-6536	409	46	g	g	PROPN
ejpam-6536	409	47	and	and	CCONJ
ejpam-6536	409	48	h	h	NOUN
ejpam-6536	409	49	,	,	PUNCT
ejpam-6536	409	50	respectively	respectively	ADV
ejpam-6536	409	51	.	.	PUNCT
ejpam-6536	410	1	thus	thus	ADV
ejpam-6536	410	2	,	,	PUNCT
ejpam-6536	410	3	sg	sg	PROPN
ejpam-6536	410	4	and	and	CCONJ
ejpam-6536	410	5	sh	sh	PROPN
ejpam-6536	410	6	are	be	AUX
ejpam-6536	410	7	inverse	inverse	ADJ
ejpam-6536	410	8	point	point	NOUN
ejpam-6536	410	9	-	-	PUNCT
ejpam-6536	410	10	wise	wise	ADJ
ejpam-6536	410	11	non	non	ADJ
ejpam-6536	410	12	-	-	ADJ
ejpam-6536	410	13	dominating	dominating	ADJ
ejpam-6536	410	14	sets	set	NOUN
ejpam-6536	410	15	of	of	ADP
ejpam-6536	410	16	g	g	PROPN
ejpam-6536	410	17	and	and	CCONJ
ejpam-6536	410	18	h	h	NOUN
ejpam-6536	410	19	,	,	PUNCT
ejpam-6536	410	20	respectively	respectively	ADV
ejpam-6536	410	21	.	.	PUNCT
ejpam-6536	411	1	conversely	conversely	ADV
ejpam-6536	411	2	,	,	PUNCT
ejpam-6536	411	3	suppose	suppose	VERB
ejpam-6536	411	4	that	that	SCONJ
ejpam-6536	411	5	s	s	VERB
ejpam-6536	411	6	=	=	PUNCT
ejpam-6536	411	7	sg	sg	X
ejpam-6536	411	8	∪	∪	ADJ
ejpam-6536	411	9	sh	sh	PROPN
ejpam-6536	411	10	,	,	PUNCT
ejpam-6536	411	11	where	where	SCONJ
ejpam-6536	411	12	sg	sg	ADP
ejpam-6536	411	13	⊆	⊆	NUM
ejpam-6536	411	14	v	v	NOUN
ejpam-6536	411	15	(	(	PUNCT
ejpam-6536	411	16	g	g	NOUN
ejpam-6536	411	17	)	)	PUNCT
ejpam-6536	411	18	and	and	CCONJ
ejpam-6536	411	19	sh	sh	PROPN
ejpam-6536	411	20	⊆	⊆	NUM
ejpam-6536	411	21	v	v	NOUN
ejpam-6536	411	22	(	(	PUNCT
ejpam-6536	411	23	h	h	NOUN
ejpam-6536	411	24	)	)	PUNCT
ejpam-6536	411	25	are	be	AUX
ejpam-6536	411	26	inverse	inverse	ADJ
ejpam-6536	411	27	point	point	NOUN
ejpam-6536	411	28	-	-	PUNCT
ejpam-6536	411	29	wise	wise	ADJ
ejpam-6536	411	30	non	non	ADJ
ejpam-6536	411	31	-	-	ADJ
ejpam-6536	411	32	dominating	dominating	ADJ
ejpam-6536	411	33	sets	set	NOUN
ejpam-6536	411	34	of	of	ADP
ejpam-6536	411	35	g	g	PROPN
ejpam-6536	411	36	and	and	CCONJ
ejpam-6536	411	37	h	h	NOUN
ejpam-6536	411	38	,	,	PUNCT
ejpam-6536	411	39	respectively	respectively	ADV
ejpam-6536	411	40	.	.	PUNCT
ejpam-6536	412	1	then	then	ADV
ejpam-6536	412	2	,	,	PUNCT
ejpam-6536	412	3	there	there	PRON
ejpam-6536	412	4	exist	exist	VERB
ejpam-6536	412	5	pnd	pnd	NOUN
ejpam-6536	412	6	-	-	PUNCT
ejpam-6536	412	7	sets	set	NOUN
ejpam-6536	412	8	dg	dg	VERB
ejpam-6536	412	9	⊆	⊆	NUM
ejpam-6536	412	10	v	v	NOUN
ejpam-6536	412	11	(	(	PUNCT
ejpam-6536	412	12	g	g	NOUN
ejpam-6536	412	13	)	)	PUNCT
ejpam-6536	412	14	and	and	CCONJ
ejpam-6536	412	15	dh	dh	NOUN
ejpam-6536	412	16	⊆	⊆	NUM
ejpam-6536	412	17	v	v	NOUN
ejpam-6536	412	18	(	(	PUNCT
ejpam-6536	412	19	h	h	NOUN
ejpam-6536	412	20	)	)	PUNCT
ejpam-6536	412	21	,	,	PUNCT
ejpam-6536	412	22	such	such	ADJ
ejpam-6536	412	23	that	that	SCONJ
ejpam-6536	412	24	sg	sg	NOUN
ejpam-6536	412	25	∩	∩	NOUN
ejpam-6536	412	26	dg	dg	NOUN
ejpam-6536	412	27	=	=	SYM
ejpam-6536	412	28	∅	∅	NOUN
ejpam-6536	412	29	and	and	CCONJ
ejpam-6536	412	30	sh	sh	PROPN
ejpam-6536	412	31	∩	∩	ADJ
ejpam-6536	412	32	dh	dh	NOUN
ejpam-6536	412	33	=	=	PUNCT
ejpam-6536	412	34	∅.	∅.	X
ejpam-6536	412	35	by	by	ADP
ejpam-6536	412	36	theorem	theorem	NOUN
ejpam-6536	412	37	1	1	NUM
ejpam-6536	412	38	,	,	PUNCT
ejpam-6536	412	39	both	both	PRON
ejpam-6536	412	40	s	s	X
ejpam-6536	412	41	and	and	CCONJ
ejpam-6536	412	42	d	d	NOUN
ejpam-6536	412	43	=	=	X
ejpam-6536	412	44	dg	dg	PROPN
ejpam-6536	412	45	∪	∪	NOUN
ejpam-6536	412	46	dh	dh	PROPN
ejpam-6536	412	47	are	be	AUX
ejpam-6536	412	48	hop	hop	NOUN
ejpam-6536	412	49	dominating	dominating	NOUN
ejpam-6536	412	50	sets	set	NOUN
ejpam-6536	412	51	of	of	ADP
ejpam-6536	412	52	g	g	PROPN
ejpam-6536	412	53	+	+	CCONJ
ejpam-6536	412	54	h.	h.	NOUN
ejpam-6536	412	55	using	use	VERB
ejpam-6536	412	56	the	the	DET
ejpam-6536	412	57	same	same	ADJ
ejpam-6536	412	58	theorem	theorem	NOUN
ejpam-6536	412	59	,	,	PUNCT
ejpam-6536	412	60	it	it	PRON
ejpam-6536	412	61	is	be	AUX
ejpam-6536	412	62	straightforward	straightforward	ADJ
ejpam-6536	412	63	to	to	PART
ejpam-6536	412	64	show	show	VERB
ejpam-6536	412	65	that	that	SCONJ
ejpam-6536	412	66	d	d	NOUN
ejpam-6536	412	67	is	be	AUX
ejpam-6536	412	68	a	a	DET
ejpam-6536	412	69	γh	γh	ADV
ejpam-6536	412	70	-	-	PUNCT
ejpam-6536	412	71	set	set	NOUN
ejpam-6536	412	72	of	of	ADP
ejpam-6536	412	73	g	g	PROPN
ejpam-6536	412	74	+	+	CCONJ
ejpam-6536	412	75	h.	h.	PROPN
ejpam-6536	412	76	since	since	SCONJ
ejpam-6536	412	77	s	s	PART
ejpam-6536	412	78	∩	∩	ADJ
ejpam-6536	412	79	d	d	NOUN
ejpam-6536	412	80	=	=	SYM
ejpam-6536	412	81	∅	∅	NOUN
ejpam-6536	412	82	,	,	PUNCT
ejpam-6536	412	83	s	s	PART
ejpam-6536	412	84	is	be	AUX
ejpam-6536	412	85	an	an	DET
ejpam-6536	412	86	inverse	inverse	NOUN
ejpam-6536	412	87	hop	hop	NOUN
ejpam-6536	412	88	dominating	dominating	NOUN
ejpam-6536	412	89	set	set	NOUN
ejpam-6536	412	90	of	of	ADP
ejpam-6536	412	91	g	g	PROPN
ejpam-6536	412	92	+	+	PROPN
ejpam-6536	412	93	h.	h.	PROPN
ejpam-6536	412	94	■	■	PUNCT
ejpam-6536	412	95	corollary	corollary	ADJ
ejpam-6536	412	96	4	4	NUM
ejpam-6536	412	97	.	.	PUNCT
ejpam-6536	413	1	for	for	ADP
ejpam-6536	413	2	all	all	DET
ejpam-6536	413	3	g	g	NOUN
ejpam-6536	413	4	,	,	PUNCT
ejpam-6536	413	5	h	h	NOUN
ejpam-6536	413	6	∈	∈	PROPN
ejpam-6536	413	7	g	g	PROPN
ejpam-6536	413	8	,	,	PUNCT
ejpam-6536	413	9	γ̃h(g	γ̃h(g	PROPN
ejpam-6536	414	1	+	+	SYM
ejpam-6536	414	2	h	h	X
ejpam-6536	414	3	)	)	PUNCT
ejpam-6536	414	4	=	=	SYM
ejpam-6536	414	5	ipnd(g	ipnd(g	PROPN
ejpam-6536	414	6	)	)	PUNCT
ejpam-6536	414	7	+	+	NUM
ejpam-6536	414	8	ipnd(h	ipnd(h	NOUN
ejpam-6536	414	9	)	)	PUNCT
ejpam-6536	414	10	.	.	PUNCT
ejpam-6536	415	1	(	(	PUNCT
ejpam-6536	415	2	4	4	X
ejpam-6536	415	3	)	)	PUNCT
ejpam-6536	415	4	given	give	VERB
ejpam-6536	415	5	g	g	PROPN
ejpam-6536	415	6	∈	∈	PROPN
ejpam-6536	415	7	g	g	NOUN
ejpam-6536	415	8	,	,	PUNCT
ejpam-6536	415	9	we	we	PRON
ejpam-6536	415	10	use	use	VERB
ejpam-6536	415	11	the	the	DET
ejpam-6536	415	12	symbol	symbol	NOUN
ejpam-6536	415	13	ppnd(g	ppnd(g	NOUN
ejpam-6536	415	14	)	)	PUNCT
ejpam-6536	415	15	to	to	PART
ejpam-6536	415	16	denote	denote	VERB
ejpam-6536	415	17	the	the	DET
ejpam-6536	415	18	family	family	NOUN
ejpam-6536	415	19	of	of	ADP
ejpam-6536	415	20	all	all	DET
ejpam-6536	415	21	pairs	pair	NOUN
ejpam-6536	415	22	(	(	PUNCT
ejpam-6536	415	23	a	a	DET
ejpam-6536	415	24	,	,	PUNCT
ejpam-6536	415	25	b	b	NOUN
ejpam-6536	415	26	)	)	PUNCT
ejpam-6536	415	27	,	,	PUNCT
ejpam-6536	415	28	where	where	SCONJ
ejpam-6536	415	29	a	a	PRON
ejpam-6536	415	30	,	,	PUNCT
ejpam-6536	415	31	b	b	PROPN
ejpam-6536	415	32	⊆	⊆	NUM
ejpam-6536	415	33	v	v	NOUN
ejpam-6536	415	34	(	(	PUNCT
ejpam-6536	415	35	g	g	NOUN
ejpam-6536	415	36	)	)	PUNCT
ejpam-6536	415	37	are	be	AUX
ejpam-6536	415	38	disjoint	disjoint	NOUN
ejpam-6536	415	39	point	point	ADV
ejpam-6536	415	40	-	-	PUNCT
ejpam-6536	415	41	wise	wise	ADJ
ejpam-6536	415	42	non	non	ADJ
ejpam-6536	415	43	-	-	ADJ
ejpam-6536	415	44	dominating	dominating	ADJ
ejpam-6536	415	45	sets	set	NOUN
ejpam-6536	415	46	of	of	ADP
ejpam-6536	415	47	g.	g.	PROPN
ejpam-6536	415	48	by	by	ADP
ejpam-6536	415	49	lemma	lemma	PROPN
ejpam-6536	415	50	1	1	NUM
ejpam-6536	415	51	,	,	PUNCT
ejpam-6536	415	52	ppnd(g	ppnd(g	NOUN
ejpam-6536	415	53	)	)	PUNCT
ejpam-6536	415	54	̸=	̸=	PROPN
ejpam-6536	415	55	∅.	∅.	NOUN
ejpam-6536	415	56	we	we	PRON
ejpam-6536	415	57	define	define	VERB
ejpam-6536	415	58	ppnd(g	ppnd(g	NOUN
ejpam-6536	415	59	)	)	PUNCT
ejpam-6536	416	1	=	=	SYM
ejpam-6536	416	2	min{|a|	min{|a|	NOUN
ejpam-6536	417	1	+	+	CCONJ
ejpam-6536	417	2	|b|	|b|	PROPN
ejpam-6536	417	3	:	:	PUNCT
ejpam-6536	417	4	(	(	PUNCT
ejpam-6536	417	5	a	a	PRON
ejpam-6536	417	6	,	,	PUNCT
ejpam-6536	417	7	b	b	NOUN
ejpam-6536	417	8	)	)	PUNCT
ejpam-6536	417	9	∈	∈	NOUN
ejpam-6536	417	10	ppnd(g	ppnd(g	NOUN
ejpam-6536	417	11	)	)	PUNCT
ejpam-6536	417	12	}	}	PUNCT
ejpam-6536	417	13	.	.	PUNCT
ejpam-6536	418	1	any	any	DET
ejpam-6536	418	2	pair	pair	NOUN
ejpam-6536	418	3	(	(	PUNCT
ejpam-6536	418	4	a	a	PRON
ejpam-6536	418	5	,	,	PUNCT
ejpam-6536	418	6	b	b	NOUN
ejpam-6536	418	7	)	)	PUNCT
ejpam-6536	418	8	∈	∈	NOUN
ejpam-6536	418	9	ppnd(g	ppnd(g	NOUN
ejpam-6536	418	10	)	)	PUNCT
ejpam-6536	418	11	for	for	ADP
ejpam-6536	418	12	which	which	PRON
ejpam-6536	418	13	|a|	|a|	NOUN
ejpam-6536	418	14	+	+	ADJ
ejpam-6536	418	15	|b|	|b|	PROPN
ejpam-6536	418	16	=	=	SYM
ejpam-6536	418	17	ppnd(g	ppnd(g	NOUN
ejpam-6536	418	18	)	)	PUNCT
ejpam-6536	418	19	is	be	AUX
ejpam-6536	418	20	called	call	VERB
ejpam-6536	418	21	ppnd	ppnd	NOUN
ejpam-6536	418	22	-	-	PUNCT
ejpam-6536	418	23	pair	pair	NOUN
ejpam-6536	418	24	of	of	ADP
ejpam-6536	418	25	g.	g.	PROPN
ejpam-6536	418	26	theorem	theorem	VERB
ejpam-6536	418	27	8	8	NUM
ejpam-6536	418	28	.	.	PUNCT
ejpam-6536	419	1	let	let	VERB
ejpam-6536	419	2	g	g	NOUN
ejpam-6536	419	3	,	,	PUNCT
ejpam-6536	419	4	h	h	NOUN
ejpam-6536	419	5	∈	∈	PROPN
ejpam-6536	419	6	g	g	PROPN
ejpam-6536	419	7	,	,	PUNCT
ejpam-6536	419	8	and	and	CCONJ
ejpam-6536	419	9	let	let	VERB
ejpam-6536	419	10	a	a	DET
ejpam-6536	419	11	,	,	PUNCT
ejpam-6536	419	12	b	b	PROPN
ejpam-6536	419	13	⊆	⊆	NUM
ejpam-6536	419	14	v	v	NOUN
ejpam-6536	419	15	(	(	PUNCT
ejpam-6536	419	16	g	g	PROPN
ejpam-6536	419	17	+	+	NOUN
ejpam-6536	419	18	h	h	NOUN
ejpam-6536	419	19	)	)	PUNCT
ejpam-6536	419	20	.	.	PUNCT
ejpam-6536	420	1	then	then	ADV
ejpam-6536	420	2	(	(	PUNCT
ejpam-6536	420	3	a	a	PRON
ejpam-6536	420	4	,	,	PUNCT
ejpam-6536	420	5	b	b	NOUN
ejpam-6536	420	6	)	)	PUNCT
ejpam-6536	420	7	∈	∈	PROPN
ejpam-6536	420	8	phd(g	phd(g	NOUN
ejpam-6536	420	9	+	+	CCONJ
ejpam-6536	420	10	h	h	NOUN
ejpam-6536	420	11	)	)	PUNCT
ejpam-6536	420	12	if	if	SCONJ
ejpam-6536	420	13	and	and	CCONJ
ejpam-6536	420	14	only	only	ADV
ejpam-6536	420	15	if	if	SCONJ
ejpam-6536	420	16	a	a	DET
ejpam-6536	420	17	=	=	X
ejpam-6536	420	18	ag	ag	PROPN
ejpam-6536	420	19	∪	∪	NOUN
ejpam-6536	420	20	ah	ah	INTJ
ejpam-6536	420	21	and	and	CCONJ
ejpam-6536	420	22	b	b	X
ejpam-6536	420	23	=	=	SYM
ejpam-6536	420	24	bg	bg	PROPN
ejpam-6536	420	25	∪	∪	NOUN
ejpam-6536	420	26	bh	bh	PROPN
ejpam-6536	420	27	,	,	PUNCT
ejpam-6536	420	28	where	where	SCONJ
ejpam-6536	420	29	(	(	PUNCT
ejpam-6536	420	30	ag	ag	PROPN
ejpam-6536	420	31	,	,	PUNCT
ejpam-6536	420	32	bg	bg	PROPN
ejpam-6536	420	33	)	)	PUNCT
ejpam-6536	420	34	∈	∈	PROPN
ejpam-6536	420	35	ppnd(g	ppnd(g	NOUN
ejpam-6536	420	36	)	)	PUNCT
ejpam-6536	420	37	and	and	CCONJ
ejpam-6536	420	38	(	(	PUNCT
ejpam-6536	420	39	ah	ah	INTJ
ejpam-6536	420	40	,	,	PUNCT
ejpam-6536	420	41	bh	bh	NOUN
ejpam-6536	420	42	)	)	PUNCT
ejpam-6536	420	43	∈	∈	PROPN
ejpam-6536	420	44	ppnd(h	ppnd(h	PROPN
ejpam-6536	420	45	)	)	PUNCT
ejpam-6536	420	46	.	.	PUNCT
ejpam-6536	421	1	proof	proof	NOUN
ejpam-6536	421	2	:	:	PUNCT
ejpam-6536	421	3	assume	assume	VERB
ejpam-6536	421	4	(	(	PUNCT
ejpam-6536	421	5	a	a	PRON
ejpam-6536	421	6	,	,	PUNCT
ejpam-6536	421	7	b	b	NOUN
ejpam-6536	421	8	)	)	PUNCT
ejpam-6536	421	9	∈	∈	PROPN
ejpam-6536	421	10	phd(g+h	phd(g+h	NOUN
ejpam-6536	421	11	)	)	PUNCT
ejpam-6536	421	12	.	.	PUNCT
ejpam-6536	422	1	by	by	ADP
ejpam-6536	422	2	theorem	theorem	NOUN
ejpam-6536	422	3	1	1	NUM
ejpam-6536	422	4	and	and	CCONJ
ejpam-6536	422	5	since	since	SCONJ
ejpam-6536	422	6	a∩b	a∩b	PROPN
ejpam-6536	422	7	=	=	SYM
ejpam-6536	422	8	∅	∅	NOUN
ejpam-6536	422	9	,	,	PUNCT
ejpam-6536	422	10	a	a	DET
ejpam-6536	422	11	=	=	SYM
ejpam-6536	422	12	ag	ag	PROPN
ejpam-6536	422	13	∪ah	∪ah	PROPN
ejpam-6536	422	14	and	and	CCONJ
ejpam-6536	422	15	b	b	X
ejpam-6536	422	16	=	=	SYM
ejpam-6536	422	17	bg	bg	PROPN
ejpam-6536	422	18	∪	∪	NOUN
ejpam-6536	422	19	bh	bh	PROPN
ejpam-6536	422	20	,	,	PUNCT
ejpam-6536	422	21	where	where	SCONJ
ejpam-6536	422	22	(	(	PUNCT
ejpam-6536	422	23	ag	ag	PROPN
ejpam-6536	422	24	,	,	PUNCT
ejpam-6536	422	25	bg	bg	PROPN
ejpam-6536	422	26	)	)	PUNCT
ejpam-6536	422	27	∈	∈	PROPN
ejpam-6536	422	28	ppnd(g	ppnd(g	NOUN
ejpam-6536	422	29	)	)	PUNCT
ejpam-6536	422	30	and	and	CCONJ
ejpam-6536	422	31	(	(	PUNCT
ejpam-6536	422	32	ah	ah	INTJ
ejpam-6536	422	33	,	,	PUNCT
ejpam-6536	422	34	bh	bh	NOUN
ejpam-6536	422	35	)	)	PUNCT
ejpam-6536	422	36	∈	∈	PROPN
ejpam-6536	422	37	ppnd(h	ppnd(h	PROPN
ejpam-6536	422	38	)	)	PUNCT
ejpam-6536	422	39	.	.	PUNCT
ejpam-6536	423	1	conversely	conversely	ADV
ejpam-6536	423	2	,	,	PUNCT
ejpam-6536	423	3	if	if	SCONJ
ejpam-6536	423	4	a	a	DET
ejpam-6536	423	5	=	=	X
ejpam-6536	423	6	ag	ag	PROPN
ejpam-6536	423	7	∪	∪	NOUN
ejpam-6536	423	8	ah	ah	INTJ
ejpam-6536	423	9	and	and	CCONJ
ejpam-6536	423	10	b	b	X
ejpam-6536	423	11	=	=	SYM
ejpam-6536	423	12	bg	bg	PROPN
ejpam-6536	423	13	∪	∪	NOUN
ejpam-6536	423	14	bh	bh	PROPN
ejpam-6536	423	15	,	,	PUNCT
ejpam-6536	423	16	where	where	SCONJ
ejpam-6536	423	17	(	(	PUNCT
ejpam-6536	423	18	ag	ag	PROPN
ejpam-6536	423	19	,	,	PUNCT
ejpam-6536	423	20	bg	bg	PROPN
ejpam-6536	423	21	)	)	PUNCT
ejpam-6536	423	22	∈	∈	PROPN
ejpam-6536	423	23	ppnd(g	ppnd(g	NOUN
ejpam-6536	423	24	)	)	PUNCT
ejpam-6536	423	25	and	and	CCONJ
ejpam-6536	423	26	(	(	PUNCT
ejpam-6536	423	27	ah	ah	INTJ
ejpam-6536	423	28	,	,	PUNCT
ejpam-6536	423	29	bh	bh	NOUN
ejpam-6536	423	30	)	)	PUNCT
ejpam-6536	423	31	∈	∈	PROPN
ejpam-6536	423	32	ppnd(h	ppnd(h	PROPN
ejpam-6536	423	33	)	)	PUNCT
ejpam-6536	423	34	,	,	PUNCT
ejpam-6536	423	35	then	then	ADV
ejpam-6536	423	36	a	a	PRON
ejpam-6536	423	37	and	and	CCONJ
ejpam-6536	423	38	b	b	NOUN
ejpam-6536	423	39	are	be	AUX
ejpam-6536	423	40	hop	hop	NOUN
ejpam-6536	423	41	dominating	dominating	NOUN
ejpam-6536	423	42	sets	set	NOUN
ejpam-6536	423	43	of	of	ADP
ejpam-6536	423	44	g	g	PROPN
ejpam-6536	423	45	+	+	CCONJ
ejpam-6536	423	46	h	h	NOUN
ejpam-6536	423	47	by	by	ADP
ejpam-6536	423	48	theorem	theorem	NOUN
ejpam-6536	423	49	1	1	NUM
ejpam-6536	423	50	.	.	PUNCT
ejpam-6536	424	1	moreover	moreover	ADV
ejpam-6536	424	2	,	,	PUNCT
ejpam-6536	424	3	since	since	SCONJ
ejpam-6536	424	4	a	a	DET
ejpam-6536	424	5	∩	∩	ADJ
ejpam-6536	424	6	b	b	NOUN
ejpam-6536	424	7	=	=	SYM
ejpam-6536	424	8	∅	∅	NOUN
ejpam-6536	424	9	,	,	PUNCT
ejpam-6536	424	10	(	(	PUNCT
ejpam-6536	424	11	a	a	PRON
ejpam-6536	424	12	,	,	PUNCT
ejpam-6536	424	13	b	b	NOUN
ejpam-6536	424	14	)	)	PUNCT
ejpam-6536	424	15	∈	∈	PROPN
ejpam-6536	425	1	phd(g	phd(g	NOUN
ejpam-6536	425	2	+	+	CCONJ
ejpam-6536	425	3	h	h	NOUN
ejpam-6536	425	4	)	)	PUNCT
ejpam-6536	425	5	.	.	PUNCT
ejpam-6536	426	1	■	■	PUNCT
ejpam-6536	426	2	corollary	corollary	ADJ
ejpam-6536	426	3	5	5	NUM
ejpam-6536	426	4	.	.	PUNCT
ejpam-6536	427	1	for	for	ADP
ejpam-6536	427	2	all	all	DET
ejpam-6536	427	3	g	g	NOUN
ejpam-6536	427	4	,	,	PUNCT
ejpam-6536	427	5	h	h	NOUN
ejpam-6536	427	6	∈	∈	PROPN
ejpam-6536	427	7	g	g	PROPN
ejpam-6536	427	8	,	,	PUNCT
ejpam-6536	427	9	γhh(g	γhh(g	PUNCT
ejpam-6536	427	10	+	+	CCONJ
ejpam-6536	427	11	h	h	NOUN
ejpam-6536	427	12	)	)	PUNCT
ejpam-6536	427	13	=	=	SYM
ejpam-6536	427	14	ppnd(g	ppnd(g	NOUN
ejpam-6536	427	15	)	)	PUNCT
ejpam-6536	428	1	+	+	CCONJ
ejpam-6536	428	2	ppnd(h	ppnd(h	NOUN
ejpam-6536	428	3	)	)	PUNCT
ejpam-6536	428	4	.	.	PUNCT
ejpam-6536	429	1	(	(	PUNCT
ejpam-6536	429	2	5	5	X
ejpam-6536	429	3	)	)	PUNCT
ejpam-6536	429	4	v.	v.	ADP
ejpam-6536	429	5	a	a	DET
ejpam-6536	429	6	besana	besana	PROPN
ejpam-6536	429	7	,	,	PUNCT
ejpam-6536	429	8	f.	f.	PROPN
ejpam-6536	429	9	jamil	jamil	PROPN
ejpam-6536	429	10	,	,	PUNCT
ejpam-6536	429	11	s.	s.	PROPN
ejpam-6536	429	12	canoy	canoy	PROPN
ejpam-6536	429	13	jr	jr	PROPN
ejpam-6536	429	14	.	.	PROPN
ejpam-6536	429	15	/	/	SYM
ejpam-6536	429	16	eur	eur	PROPN
ejpam-6536	429	17	.	.	PUNCT
ejpam-6536	430	1	j.	j.	PROPN
ejpam-6536	430	2	pure	pure	PROPN
ejpam-6536	430	3	appl	appl	PROPN
ejpam-6536	430	4	.	.	PROPN
ejpam-6536	430	5	math	math	PROPN
ejpam-6536	430	6	,	,	PUNCT
ejpam-6536	430	7	18	18	NUM
ejpam-6536	430	8	(	(	PUNCT
ejpam-6536	430	9	3	3	NUM
ejpam-6536	430	10	)	)	PUNCT
ejpam-6536	430	11	(	(	PUNCT
ejpam-6536	430	12	2025	2025	NUM
ejpam-6536	430	13	)	)	PUNCT
ejpam-6536	430	14	,	,	PUNCT
ejpam-6536	430	15	6536	6536	NUM
ejpam-6536	430	16	11	11	NUM
ejpam-6536	430	17	of	of	ADP
ejpam-6536	430	18	17	17	NUM
ejpam-6536	430	19	3.4	3.4	NUM
ejpam-6536	430	20	.	.	PUNCT
ejpam-6536	431	1	in	in	ADP
ejpam-6536	431	2	the	the	DET
ejpam-6536	431	3	corona	corona	NOUN
ejpam-6536	431	4	of	of	ADP
ejpam-6536	431	5	graphs	graph	NOUN
ejpam-6536	431	6	statements	statement	NOUN
ejpam-6536	431	7	(	(	PUNCT
ejpam-6536	431	8	ii	ii	NOUN
ejpam-6536	431	9	)	)	PUNCT
ejpam-6536	431	10	and	and	CCONJ
ejpam-6536	431	11	(	(	PUNCT
ejpam-6536	431	12	iii	iii	NOUN
ejpam-6536	431	13	)	)	PUNCT
ejpam-6536	431	14	of	of	ADP
ejpam-6536	431	15	theorem	theorem	ADJ
ejpam-6536	431	16	3	3	NUM
ejpam-6536	431	17	assert	assert	VERB
ejpam-6536	431	18	that	that	SCONJ
ejpam-6536	431	19	under	under	ADP
ejpam-6536	431	20	some	some	DET
ejpam-6536	431	21	conditions	condition	NOUN
ejpam-6536	431	22	,	,	PUNCT
ejpam-6536	431	23	the	the	DET
ejpam-6536	431	24	value	value	NOUN
ejpam-6536	431	25	of	of	ADP
ejpam-6536	431	26	γh(g	γh(g	PUNCT
ejpam-6536	431	27	◦	◦	NOUN
ejpam-6536	431	28	h	h	NOUN
ejpam-6536	431	29	)	)	PUNCT
ejpam-6536	431	30	is	be	AUX
ejpam-6536	431	31	attainable	attainable	ADJ
ejpam-6536	431	32	by	by	ADP
ejpam-6536	431	33	the	the	DET
ejpam-6536	431	34	value	value	NOUN
ejpam-6536	431	35	of	of	ADP
ejpam-6536	431	36	γ∗t	γ∗t	PROPN
ejpam-6536	431	37	1,2(g	1,2(g	NUM
ejpam-6536	431	38	)	)	PUNCT
ejpam-6536	431	39	or	or	CCONJ
ejpam-6536	431	40	[	[	X
ejpam-6536	431	41	1	1	NUM
ejpam-6536	431	42	+	+	NUM
ejpam-6536	431	43	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-6536	431	44	)	)	PUNCT
ejpam-6536	431	45	.	.	PUNCT
ejpam-6536	432	1	moreover	moreover	ADV
ejpam-6536	432	2	,	,	PUNCT
ejpam-6536	432	3	it	it	PRON
ejpam-6536	432	4	is	be	AUX
ejpam-6536	432	5	shown	show	VERB
ejpam-6536	432	6	in	in	ADP
ejpam-6536	432	7	[	[	X
ejpam-6536	432	8	7	7	X
ejpam-6536	432	9	]	]	PUNCT
ejpam-6536	432	10	that	that	SCONJ
ejpam-6536	432	11	a	a	DET
ejpam-6536	432	12	strict	strict	ADJ
ejpam-6536	432	13	inequality	inequality	NOUN
ejpam-6536	432	14	in	in	ADP
ejpam-6536	432	15	statement	statement	NOUN
ejpam-6536	432	16	(	(	PUNCT
ejpam-6536	432	17	i	i	NOUN
ejpam-6536	432	18	)	)	PUNCT
ejpam-6536	432	19	is	be	AUX
ejpam-6536	432	20	also	also	ADV
ejpam-6536	432	21	attainable	attainable	ADJ
ejpam-6536	432	22	.	.	PUNCT
ejpam-6536	433	1	for	for	ADP
ejpam-6536	433	2	a	a	DET
ejpam-6536	433	3	(	(	PUNCT
ejpam-6536	433	4	1	1	NUM
ejpam-6536	433	5	,	,	PUNCT
ejpam-6536	433	6	2)-total	2)-total	NUM
ejpam-6536	433	7	dominating	dominating	NOUN
ejpam-6536	433	8	set	set	VERB
ejpam-6536	433	9	a	a	PRON
ejpam-6536	433	10	of	of	ADP
ejpam-6536	433	11	a	a	DET
ejpam-6536	433	12	graph	graph	NOUN
ejpam-6536	433	13	g	g	NOUN
ejpam-6536	433	14	,	,	PUNCT
ejpam-6536	433	15	we	we	PRON
ejpam-6536	433	16	write	write	VERB
ejpam-6536	433	17	γ(a	γ(a	NOUN
ejpam-6536	433	18	)	)	PUNCT
ejpam-6536	434	1	=	=	PRON
ejpam-6536	434	2	{	{	PUNCT
ejpam-6536	434	3	v	v	NUM
ejpam-6536	434	4	∈	∈	PROPN
ejpam-6536	434	5	a	a	PRON
ejpam-6536	434	6	:	:	PUNCT
ejpam-6536	434	7	ng(v	ng(v	NUM
ejpam-6536	434	8	)	)	PUNCT
ejpam-6536	434	9	\	\	NOUN
ejpam-6536	435	1	a	a	DET
ejpam-6536	435	2	̸=	̸=	PROPN
ejpam-6536	435	3	∅	∅	NOUN
ejpam-6536	435	4	}	}	PUNCT
ejpam-6536	435	5	.	.	PUNCT
ejpam-6536	436	1	for	for	ADP
ejpam-6536	436	2	each	each	DET
ejpam-6536	436	3	v	v	NUM
ejpam-6536	436	4	∈	∈	PROPN
ejpam-6536	436	5	γ(a	γ(a	NOUN
ejpam-6536	436	6	)	)	PUNCT
ejpam-6536	436	7	,	,	PUNCT
ejpam-6536	436	8	choose	choose	VERB
ejpam-6536	436	9	exactly	exactly	ADV
ejpam-6536	436	10	one	one	NUM
ejpam-6536	436	11	uv	uv	NOUN
ejpam-6536	436	12	∈	∈	PROPN
ejpam-6536	436	13	ng(v	ng(v	PUNCT
ejpam-6536	436	14	)	)	PUNCT
ejpam-6536	436	15	\	\	PROPN
ejpam-6536	437	1	a	a	PRON
ejpam-6536	437	2	,	,	PUNCT
ejpam-6536	437	3	and	and	CCONJ
ejpam-6536	437	4	define	define	VERB
ejpam-6536	437	5	a	a	DET
ejpam-6536	437	6	◦	◦	NOUN
ejpam-6536	437	7	=	=	PUNCT
ejpam-6536	437	8	{	{	PUNCT
ejpam-6536	437	9	uv	uv	NOUN
ejpam-6536	437	10	:	:	PUNCT
ejpam-6536	437	11	v	v	NUM
ejpam-6536	437	12	∈	∈	PROPN
ejpam-6536	437	13	γ(a	γ(a	PROPN
ejpam-6536	437	14	)	)	PUNCT
ejpam-6536	437	15	}	}	PUNCT
ejpam-6536	437	16	.	.	PUNCT
ejpam-6536	438	1	clearly	clearly	ADV
ejpam-6536	438	2	,	,	PUNCT
ejpam-6536	438	3	a	a	DET
ejpam-6536	438	4	∩	∩	ADJ
ejpam-6536	438	5	a	a	DET
ejpam-6536	438	6	◦	◦	NOUN
ejpam-6536	438	7	=	=	PUNCT
ejpam-6536	438	8	∅.	∅.	NOUN
ejpam-6536	438	9	proposition	proposition	NOUN
ejpam-6536	438	10	6	6	NUM
ejpam-6536	438	11	.	.	PUNCT
ejpam-6536	439	1	let	let	VERB
ejpam-6536	439	2	g	g	NOUN
ejpam-6536	439	3	be	be	AUX
ejpam-6536	439	4	an	an	DET
ejpam-6536	439	5	ntc	ntc	NOUN
ejpam-6536	439	6	graph	graph	NOUN
ejpam-6536	439	7	of	of	ADP
ejpam-6536	439	8	order	order	NOUN
ejpam-6536	439	9	n	n	NOUN
ejpam-6536	439	10	and	and	CCONJ
ejpam-6536	439	11	let	let	VERB
ejpam-6536	439	12	h	h	NOUN
ejpam-6536	439	13	be	be	AUX
ejpam-6536	439	14	any	any	DET
ejpam-6536	439	15	graph	graph	NOUN
ejpam-6536	439	16	.	.	PUNCT
ejpam-6536	440	1	then	then	ADV
ejpam-6536	440	2	(	(	PUNCT
ejpam-6536	440	3	i	i	NOUN
ejpam-6536	440	4	)	)	PUNCT
ejpam-6536	440	5	γhh(g	γhh(g	PUNCT
ejpam-6536	440	6	◦	◦	NOUN
ejpam-6536	440	7	h	h	NOUN
ejpam-6536	440	8	)	)	PUNCT
ejpam-6536	440	9	≤	≤	NOUN
ejpam-6536	441	1	[	[	X
ejpam-6536	441	2	1	1	NUM
ejpam-6536	441	3	+	+	NUM
ejpam-6536	441	4	pnd(h	pnd(h	PROPN
ejpam-6536	441	5	)	)	PUNCT
ejpam-6536	441	6	]	]	PUNCT
ejpam-6536	441	7	γγ(g	γγ(g	PRON
ejpam-6536	441	8	)	)	PUNCT
ejpam-6536	441	9	,	,	PUNCT
ejpam-6536	441	10	and	and	CCONJ
ejpam-6536	441	11	this	this	DET
ejpam-6536	441	12	bound	bind	VERB
ejpam-6536	441	13	is	be	AUX
ejpam-6536	441	14	sharp	sharp	ADJ
ejpam-6536	441	15	.	.	PUNCT
ejpam-6536	442	1	(	(	PUNCT
ejpam-6536	442	2	ii	ii	NOUN
ejpam-6536	442	3	)	)	PUNCT
ejpam-6536	442	4	if	if	SCONJ
ejpam-6536	442	5	γh(g	γh(g	NOUN
ejpam-6536	442	6	◦	◦	NOUN
ejpam-6536	442	7	h	h	NOUN
ejpam-6536	442	8	)	)	PUNCT
ejpam-6536	442	9	=	=	SYM
ejpam-6536	442	10	γ∗t	γ∗t	NUM
ejpam-6536	442	11	1,2(g	1,2(g	NUM
ejpam-6536	442	12	)	)	PUNCT
ejpam-6536	442	13	,	,	PUNCT
ejpam-6536	442	14	then	then	ADV
ejpam-6536	442	15	γ̃h(g	γ̃h(g	VERB
ejpam-6536	442	16	◦	◦	NOUN
ejpam-6536	442	17	h	h	NOUN
ejpam-6536	442	18	)	)	PUNCT
ejpam-6536	442	19	≤	≤	NOUN
ejpam-6536	442	20	min{|a	min{|a	NOUN
ejpam-6536	442	21	◦	◦	NOUN
ejpam-6536	442	22	|	|	ADV
ejpam-6536	442	23	+	+	CCONJ
ejpam-6536	442	24	|a	|a	NOUN
ejpam-6536	442	25	◦	◦	NOUN
ejpam-6536	442	26	∩	∩	NOUN
ejpam-6536	442	27	ng(a	ng(a	NOUN
ejpam-6536	442	28	◦	◦	NOUN
ejpam-6536	442	29	)|	)|	PUNCT
ejpam-6536	442	30	+	+	CCONJ
ejpam-6536	443	1	[	[	X
ejpam-6536	443	2	n	n	X
ejpam-6536	443	3	−	−	NOUN
ejpam-6536	443	4	|ng(a	|ng(a	ADP
ejpam-6536	443	5	◦	◦	NOUN
ejpam-6536	443	6	)|]pnd(h	)|]pnd(h	NOUN
ejpam-6536	443	7	)	)	PUNCT
ejpam-6536	443	8	:	:	PUNCT
ejpam-6536	443	9	a	a	PRON
ejpam-6536	443	10	is	be	AUX
ejpam-6536	443	11	a	a	DET
ejpam-6536	443	12	γ∗t	γ∗t	PROPN
ejpam-6536	443	13	1,2set	1,2set	NUM
ejpam-6536	443	14	of	of	ADP
ejpam-6536	443	15	g	g	NOUN
ejpam-6536	443	16	}	}	PUNCT
ejpam-6536	443	17	,	,	PUNCT
ejpam-6536	443	18	and	and	CCONJ
ejpam-6536	443	19	equality	equality	NOUN
ejpam-6536	443	20	is	be	AUX
ejpam-6536	443	21	attained	attain	VERB
ejpam-6536	443	22	for	for	ADP
ejpam-6536	443	23	star	star	NOUN
ejpam-6536	443	24	graphs	graph	NOUN
ejpam-6536	443	25	g	g	NOUN
ejpam-6536	443	26	on	on	ADP
ejpam-6536	443	27	n	n	PRON
ejpam-6536	443	28	≥	≥	NUM
ejpam-6536	443	29	3	3	NUM
ejpam-6536	443	30	vertices	vertex	NOUN
ejpam-6536	443	31	.	.	PUNCT
ejpam-6536	444	1	(	(	PUNCT
ejpam-6536	444	2	iii	iii	X
ejpam-6536	444	3	)	)	PUNCT
ejpam-6536	444	4	if	if	SCONJ
ejpam-6536	444	5	γh(g	γh(g	NOUN
ejpam-6536	444	6	◦	◦	NOUN
ejpam-6536	444	7	h	h	NOUN
ejpam-6536	444	8	)	)	PUNCT
ejpam-6536	444	9	=	=	NOUN
ejpam-6536	445	1	[	[	X
ejpam-6536	445	2	1	1	NUM
ejpam-6536	445	3	+	+	NUM
ejpam-6536	445	4	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-6536	445	5	)	)	PUNCT
ejpam-6536	445	6	,	,	PUNCT
ejpam-6536	445	7	then	then	ADV
ejpam-6536	445	8	γ̃h(g	γ̃h(g	VERB
ejpam-6536	445	9	◦	◦	NOUN
ejpam-6536	445	10	h	h	NOUN
ejpam-6536	445	11	)	)	PUNCT
ejpam-6536	445	12	≤	≤	NOUN
ejpam-6536	446	1	[	[	X
ejpam-6536	446	2	1	1	NUM
ejpam-6536	446	3	+	+	NUM
ejpam-6536	446	4	pnd(h)]γ̃(g	pnd(h)]γ̃(g	PROPN
ejpam-6536	446	5	)	)	PUNCT
ejpam-6536	446	6	.	.	PUNCT
ejpam-6536	447	1	in	in	ADP
ejpam-6536	447	2	particular	particular	ADJ
ejpam-6536	447	3	,	,	PUNCT
ejpam-6536	447	4	if	if	SCONJ
ejpam-6536	447	5	γ(g	γ(g	PROPN
ejpam-6536	447	6	)	)	PUNCT
ejpam-6536	447	7	=	=	SYM
ejpam-6536	447	8	γ̃(g	γ̃(g	NOUN
ejpam-6536	447	9	)	)	PUNCT
ejpam-6536	447	10	,	,	PUNCT
ejpam-6536	447	11	then	then	ADV
ejpam-6536	447	12	γh(g	γh(g	PUNCT
ejpam-6536	447	13	◦	◦	NOUN
ejpam-6536	447	14	h	h	NOUN
ejpam-6536	447	15	)	)	PUNCT
ejpam-6536	447	16	=	=	PUNCT
ejpam-6536	447	17	γ̃h(g	γ̃h(g	ADP
ejpam-6536	447	18	◦	◦	NOUN
ejpam-6536	447	19	h	h	NOUN
ejpam-6536	447	20	)	)	PUNCT
ejpam-6536	447	21	.	.	PUNCT
ejpam-6536	448	1	proof	proof	NOUN
ejpam-6536	448	2	:	:	PUNCT
ejpam-6536	448	3	let	let	AUX
ejpam-6536	448	4	(	(	PUNCT
ejpam-6536	448	5	a	a	DET
ejpam-6536	448	6	,	,	PUNCT
ejpam-6536	448	7	b	b	NOUN
ejpam-6536	448	8	)	)	PUNCT
ejpam-6536	448	9	be	be	AUX
ejpam-6536	448	10	a	a	DET
ejpam-6536	448	11	γγ	γγ	NOUN
ejpam-6536	448	12	-	-	PUNCT
ejpam-6536	448	13	pair	pair	NOUN
ejpam-6536	448	14	of	of	ADP
ejpam-6536	448	15	g.	g.	NOUN
ejpam-6536	448	16	for	for	ADP
ejpam-6536	448	17	each	each	DET
ejpam-6536	448	18	v	v	ADP
ejpam-6536	448	19	∈	∈	PRON
ejpam-6536	448	20	a	a	PRON
ejpam-6536	448	21	,	,	PUNCT
ejpam-6536	448	22	let	let	VERB
ejpam-6536	448	23	sv	sv	PROPN
ejpam-6536	448	24	⊆	⊆	NUM
ejpam-6536	448	25	v	v	X
ejpam-6536	448	26	(	(	PUNCT
ejpam-6536	448	27	hv	hv	NOUN
ejpam-6536	448	28	)	)	PUNCT
ejpam-6536	448	29	be	be	VERB
ejpam-6536	448	30	a	a	DET
ejpam-6536	448	31	pnd	pnd	NOUN
ejpam-6536	448	32	-	-	PUNCT
ejpam-6536	448	33	set	set	NOUN
ejpam-6536	448	34	of	of	ADP
ejpam-6536	448	35	hv	hv	PROPN
ejpam-6536	448	36	.	.	PUNCT
ejpam-6536	449	1	similarly	similarly	ADV
ejpam-6536	449	2	,	,	PUNCT
ejpam-6536	449	3	for	for	ADP
ejpam-6536	449	4	each	each	DET
ejpam-6536	449	5	v	v	ADP
ejpam-6536	449	6	∈	∈	PROPN
ejpam-6536	449	7	b	b	NOUN
ejpam-6536	449	8	,	,	PUNCT
ejpam-6536	449	9	let	let	VERB
ejpam-6536	449	10	tv	tv	NOUN
ejpam-6536	449	11	⊆	⊆	NUM
ejpam-6536	449	12	v	v	NOUN
ejpam-6536	449	13	(	(	PUNCT
ejpam-6536	449	14	hv	hv	NOUN
ejpam-6536	449	15	)	)	PUNCT
ejpam-6536	449	16	be	be	VERB
ejpam-6536	449	17	a	a	DET
ejpam-6536	449	18	pnd	pnd	NOUN
ejpam-6536	449	19	-	-	PUNCT
ejpam-6536	449	20	set	set	NOUN
ejpam-6536	449	21	of	of	ADP
ejpam-6536	449	22	hv	hv	PROPN
ejpam-6536	449	23	.	.	PUNCT
ejpam-6536	450	1	define	define	PROPN
ejpam-6536	450	2	s	s	PART
ejpam-6536	450	3	=	=	PUNCT
ejpam-6536	450	4	a	a	DET
ejpam-6536	450	5	∪	∪	ADJ
ejpam-6536	450	6	(	(	PUNCT
ejpam-6536	450	7	∪v∈asv	∪v∈asv	NOUN
ejpam-6536	450	8	)	)	PUNCT
ejpam-6536	450	9	and	and	CCONJ
ejpam-6536	450	10	t	t	X
ejpam-6536	450	11	=	=	SYM
ejpam-6536	450	12	b	b	X
ejpam-6536	450	13	∪	∪	X
ejpam-6536	450	14	(	(	PUNCT
ejpam-6536	450	15	∪v∈btv	∪v∈btv	NOUN
ejpam-6536	450	16	)	)	PUNCT
ejpam-6536	450	17	.	.	PUNCT
ejpam-6536	451	1	let	let	VERB
ejpam-6536	451	2	x	x	SYM
ejpam-6536	451	3	∈	∈	PROPN
ejpam-6536	451	4	v	v	X
ejpam-6536	451	5	(	(	PUNCT
ejpam-6536	451	6	g	g	NOUN
ejpam-6536	451	7	◦	◦	NOUN
ejpam-6536	451	8	h)\s	h)\s	NOUN
ejpam-6536	451	9	and	and	CCONJ
ejpam-6536	451	10	let	let	VERB
ejpam-6536	451	11	v	v	NUM
ejpam-6536	451	12	∈	∈	PROPN
ejpam-6536	451	13	v	v	NOUN
ejpam-6536	451	14	(	(	PUNCT
ejpam-6536	451	15	g	g	NOUN
ejpam-6536	451	16	)	)	PUNCT
ejpam-6536	451	17	for	for	ADP
ejpam-6536	451	18	which	which	PRON
ejpam-6536	451	19	x	x	SYM
ejpam-6536	451	20	∈	∈	PROPN
ejpam-6536	451	21	v	v	X
ejpam-6536	451	22	(	(	PUNCT
ejpam-6536	451	23	hv	hv	PROPN
ejpam-6536	451	24	+	+	PROPN
ejpam-6536	451	25	v	v	NOUN
ejpam-6536	451	26	)	)	PUNCT
ejpam-6536	451	27	.	.	PUNCT
ejpam-6536	452	1	if	if	SCONJ
ejpam-6536	452	2	x	x	X
ejpam-6536	452	3	=	=	SYM
ejpam-6536	452	4	v	v	NOUN
ejpam-6536	452	5	,	,	PUNCT
ejpam-6536	452	6	then	then	ADV
ejpam-6536	452	7	since	since	SCONJ
ejpam-6536	452	8	a	a	PRON
ejpam-6536	452	9	is	be	AUX
ejpam-6536	452	10	a	a	DET
ejpam-6536	452	11	dominating	dominating	NOUN
ejpam-6536	452	12	set	set	NOUN
ejpam-6536	452	13	and	and	CCONJ
ejpam-6536	452	14	v	v	NOUN
ejpam-6536	452	15	/∈	/∈	PROPN
ejpam-6536	453	1	a	a	PRON
ejpam-6536	453	2	,	,	PUNCT
ejpam-6536	453	3	there	there	PRON
ejpam-6536	453	4	exists	exist	VERB
ejpam-6536	453	5	u	u	PROPN
ejpam-6536	453	6	∈	∈	PROPN
ejpam-6536	453	7	a	a	DET
ejpam-6536	453	8	such	such	ADJ
ejpam-6536	453	9	that	that	DET
ejpam-6536	453	10	uv	uv	PROPN
ejpam-6536	453	11	∈	∈	PROPN
ejpam-6536	453	12	e(g	e(g	PROPN
ejpam-6536	453	13	)	)	PUNCT
ejpam-6536	453	14	.	.	PUNCT
ejpam-6536	454	1	pick	pick	VERB
ejpam-6536	454	2	y	y	PROPN
ejpam-6536	454	3	∈	∈	PROPN
ejpam-6536	454	4	su	su	PROPN
ejpam-6536	454	5	.	.	PUNCT
ejpam-6536	455	1	then	then	ADV
ejpam-6536	455	2	y	y	PROPN
ejpam-6536	455	3	∈	∈	PROPN
ejpam-6536	455	4	s	s	PART
ejpam-6536	455	5	and	and	CCONJ
ejpam-6536	455	6	dg	dg	NOUN
ejpam-6536	455	7	◦	◦	NOUN
ejpam-6536	455	8	h(x	h(x	PROPN
ejpam-6536	455	9	,	,	PUNCT
ejpam-6536	455	10	y	y	PROPN
ejpam-6536	455	11	)	)	PUNCT
ejpam-6536	455	12	=	=	SYM
ejpam-6536	455	13	2	2	X
ejpam-6536	455	14	.	.	X
ejpam-6536	455	15	on	on	ADP
ejpam-6536	455	16	the	the	DET
ejpam-6536	455	17	other	other	ADJ
ejpam-6536	455	18	hand	hand	NOUN
ejpam-6536	455	19	,	,	PUNCT
ejpam-6536	455	20	if	if	SCONJ
ejpam-6536	455	21	x	x	PROPN
ejpam-6536	455	22	̸=	̸=	PROPN
ejpam-6536	455	23	v	v	NOUN
ejpam-6536	455	24	,	,	PUNCT
ejpam-6536	455	25	then	then	ADV
ejpam-6536	455	26	since	since	SCONJ
ejpam-6536	455	27	sv	sv	PROPN
ejpam-6536	455	28	is	be	AUX
ejpam-6536	455	29	a	a	DET
ejpam-6536	455	30	pnd	pnd	NOUN
ejpam-6536	455	31	-	-	PUNCT
ejpam-6536	455	32	set	set	NOUN
ejpam-6536	455	33	of	of	ADP
ejpam-6536	455	34	hv	hv	PROPN
ejpam-6536	455	35	and	and	CCONJ
ejpam-6536	455	36	x	x	PROPN
ejpam-6536	455	37	∈	∈	PROPN
ejpam-6536	455	38	v	v	ADP
ejpam-6536	455	39	(	(	PUNCT
ejpam-6536	455	40	hv	hv	PROPN
ejpam-6536	455	41	)	)	PUNCT
ejpam-6536	455	42	\	\	PROPN
ejpam-6536	455	43	sv	sv	PROPN
ejpam-6536	455	44	,	,	PUNCT
ejpam-6536	455	45	there	there	PRON
ejpam-6536	455	46	exists	exist	VERB
ejpam-6536	455	47	y	y	PROPN
ejpam-6536	455	48	∈	∈	PROPN
ejpam-6536	455	49	sv	sv	INTJ
ejpam-6536	455	50	for	for	ADP
ejpam-6536	455	51	which	which	PRON
ejpam-6536	455	52	xy	xy	X
ejpam-6536	455	53	/∈	/∈	PUNCT
ejpam-6536	455	54	e(hv	e(hv	PROPN
ejpam-6536	455	55	)	)	PUNCT
ejpam-6536	455	56	.	.	PUNCT
ejpam-6536	456	1	this	this	PRON
ejpam-6536	456	2	means	mean	VERB
ejpam-6536	456	3	that	that	SCONJ
ejpam-6536	456	4	y	y	PROPN
ejpam-6536	456	5	∈	∈	PROPN
ejpam-6536	456	6	s	s	PART
ejpam-6536	456	7	and	and	CCONJ
ejpam-6536	456	8	dg	dg	NOUN
ejpam-6536	456	9	◦	◦	NOUN
ejpam-6536	456	10	h(x	h(x	PROPN
ejpam-6536	456	11	,	,	PUNCT
ejpam-6536	456	12	y	y	PROPN
ejpam-6536	456	13	)	)	PUNCT
ejpam-6536	456	14	=	=	SYM
ejpam-6536	456	15	2	2	X
ejpam-6536	456	16	.	.	PUNCT
ejpam-6536	456	17	accordingly	accordingly	ADV
ejpam-6536	456	18	,	,	PUNCT
ejpam-6536	456	19	s	s	VERB
ejpam-6536	456	20	is	be	AUX
ejpam-6536	456	21	a	a	DET
ejpam-6536	456	22	hop	hop	NOUN
ejpam-6536	456	23	dominating	dominating	NOUN
ejpam-6536	456	24	set	set	NOUN
ejpam-6536	456	25	of	of	ADP
ejpam-6536	456	26	g	g	PROPN
ejpam-6536	456	27	◦	◦	PROPN
ejpam-6536	456	28	h.	h.	NOUN
ejpam-6536	456	29	similarly	similarly	ADV
ejpam-6536	456	30	,	,	PUNCT
ejpam-6536	456	31	t	t	PROPN
ejpam-6536	456	32	is	be	AUX
ejpam-6536	456	33	a	a	DET
ejpam-6536	456	34	hop	hop	NOUN
ejpam-6536	456	35	dominating	dominating	NOUN
ejpam-6536	456	36	set	set	NOUN
ejpam-6536	456	37	of	of	ADP
ejpam-6536	456	38	g	g	PROPN
ejpam-6536	456	39	◦	◦	PROPN
ejpam-6536	456	40	h.	h.	PROPN
ejpam-6536	456	41	since	since	SCONJ
ejpam-6536	456	42	s	s	PART
ejpam-6536	456	43	∩	∩	ADJ
ejpam-6536	456	44	t	t	NOUN
ejpam-6536	456	45	=	=	SYM
ejpam-6536	456	46	∅	∅	NOUN
ejpam-6536	456	47	,	,	PUNCT
ejpam-6536	456	48	(	(	PUNCT
ejpam-6536	456	49	s	s	X
ejpam-6536	456	50	,	,	PUNCT
ejpam-6536	456	51	t	t	NOUN
ejpam-6536	456	52	)	)	PUNCT
ejpam-6536	456	53	∈	∈	PROPN
ejpam-6536	456	54	phd(g	phd(g	PROPN
ejpam-6536	456	55	◦	◦	NOUN
ejpam-6536	456	56	h	h	NOUN
ejpam-6536	456	57	)	)	PUNCT
ejpam-6536	456	58	.	.	PUNCT
ejpam-6536	457	1	therefore	therefore	ADV
ejpam-6536	457	2	,	,	PUNCT
ejpam-6536	457	3	γγ(g	γγ(g	PUNCT
ejpam-6536	457	4	◦	◦	NOUN
ejpam-6536	457	5	h	h	NOUN
ejpam-6536	457	6	)	)	PUNCT
ejpam-6536	457	7	≤	≤	NUM
ejpam-6536	457	8	|s|	|s|	PROPN
ejpam-6536	457	9	+	+	CCONJ
ejpam-6536	457	10	|t	|t	PROPN
ejpam-6536	458	1	|	|	ADV
ejpam-6536	458	2	=	=	PUNCT
ejpam-6536	459	1	[	[	X
ejpam-6536	459	2	1	1	NUM
ejpam-6536	459	3	+	+	NUM
ejpam-6536	459	4	pnd(h	pnd(h	PROPN
ejpam-6536	459	5	)	)	PUNCT
ejpam-6536	459	6	]	]	PUNCT
ejpam-6536	459	7	γγ(g	γγ(g	PRON
ejpam-6536	459	8	)	)	PUNCT
ejpam-6536	459	9	.	.	PUNCT
ejpam-6536	460	1	in	in	ADP
ejpam-6536	460	2	particular	particular	ADJ
ejpam-6536	460	3	,	,	PUNCT
ejpam-6536	460	4	if	if	SCONJ
ejpam-6536	460	5	h	h	NOUN
ejpam-6536	460	6	has	have	VERB
ejpam-6536	460	7	an	an	DET
ejpam-6536	460	8	isolated	isolated	ADJ
ejpam-6536	460	9	vertex	vertex	NOUN
ejpam-6536	460	10	,	,	PUNCT
ejpam-6536	460	11	then	then	ADV
ejpam-6536	460	12	γhh(p4	γhh(p4	PROPN
ejpam-6536	460	13	◦	◦	PROPN
ejpam-6536	460	14	h	h	NOUN
ejpam-6536	460	15	)	)	PUNCT
ejpam-6536	460	16	=	=	SYM
ejpam-6536	460	17	4	4	NUM
ejpam-6536	460	18	=	=	SYM
ejpam-6536	460	19	2γγ(g	2γγ(g	NUM
ejpam-6536	460	20	)	)	PUNCT
ejpam-6536	460	21	.	.	PUNCT
ejpam-6536	461	1	this	this	PRON
ejpam-6536	461	2	proves	prove	VERB
ejpam-6536	461	3	(	(	PUNCT
ejpam-6536	461	4	i	i	NOUN
ejpam-6536	461	5	)	)	PUNCT
ejpam-6536	461	6	.	.	PUNCT
ejpam-6536	462	1	to	to	PART
ejpam-6536	462	2	prove	prove	VERB
ejpam-6536	462	3	(	(	PUNCT
ejpam-6536	462	4	ii	ii	NOUN
ejpam-6536	462	5	)	)	PUNCT
ejpam-6536	462	6	,	,	PUNCT
ejpam-6536	462	7	let	let	VERB
ejpam-6536	462	8	a	a	DET
ejpam-6536	462	9	⊆	⊆	NUM
ejpam-6536	462	10	v	v	NOUN
ejpam-6536	462	11	(	(	PUNCT
ejpam-6536	462	12	g	g	PROPN
ejpam-6536	462	13	◦	◦	NOUN
ejpam-6536	462	14	h	h	NOUN
ejpam-6536	462	15	)	)	PUNCT
ejpam-6536	462	16	be	be	VERB
ejpam-6536	462	17	a	a	DET
ejpam-6536	462	18	γ∗t	γ∗t	NUM
ejpam-6536	462	19	1,2	1,2	NUM
ejpam-6536	462	20	-	-	PUNCT
ejpam-6536	462	21	set	set	NOUN
ejpam-6536	462	22	of	of	ADP
ejpam-6536	462	23	g.	g.	PROPN
ejpam-6536	462	24	then	then	ADV
ejpam-6536	462	25	a	a	PRON
ejpam-6536	462	26	is	be	AUX
ejpam-6536	462	27	a	a	DET
ejpam-6536	462	28	γh	γh	ADV
ejpam-6536	462	29	-	-	PUNCT
ejpam-6536	462	30	set	set	NOUN
ejpam-6536	462	31	of	of	ADP
ejpam-6536	462	32	g	g	PROPN
ejpam-6536	462	33	◦	◦	PROPN
ejpam-6536	462	34	h.	h.	NOUN
ejpam-6536	462	35	for	for	ADP
ejpam-6536	462	36	each	each	PRON
ejpam-6536	462	37	v	v	ADP
ejpam-6536	462	38	∈	∈	PROPN
ejpam-6536	462	39	a	a	DET
ejpam-6536	462	40	◦	◦	NOUN
ejpam-6536	462	41	∩	∩	NOUN
ejpam-6536	462	42	ng(a	ng(a	NOUN
ejpam-6536	462	43	◦	◦	NOUN
ejpam-6536	462	44	)	)	PUNCT
ejpam-6536	462	45	,	,	PUNCT
ejpam-6536	462	46	let	let	VERB
ejpam-6536	462	47	sv	sv	PROPN
ejpam-6536	462	48	⊆	⊆	NUM
ejpam-6536	462	49	v	v	X
ejpam-6536	462	50	(	(	PUNCT
ejpam-6536	462	51	hv	hv	NOUN
ejpam-6536	462	52	)	)	PUNCT
ejpam-6536	462	53	be	be	AUX
ejpam-6536	462	54	singleton	singleton	NOUN
ejpam-6536	462	55	.	.	PUNCT
ejpam-6536	463	1	for	for	ADP
ejpam-6536	463	2	each	each	DET
ejpam-6536	463	3	v	v	NUM
ejpam-6536	463	4	∈	∈	PROPN
ejpam-6536	463	5	v	v	NOUN
ejpam-6536	463	6	(	(	PUNCT
ejpam-6536	463	7	g	g	NOUN
ejpam-6536	463	8	)	)	PUNCT
ejpam-6536	463	9	\	\	NOUN
ejpam-6536	463	10	ng(a	ng(a	PUNCT
ejpam-6536	463	11	◦	◦	NOUN
ejpam-6536	463	12	)	)	PUNCT
ejpam-6536	463	13	,	,	PUNCT
ejpam-6536	463	14	let	let	VERB
ejpam-6536	463	15	tv	tv	NOUN
ejpam-6536	463	16	⊆	⊆	NUM
ejpam-6536	463	17	v	v	NOUN
ejpam-6536	463	18	(	(	PUNCT
ejpam-6536	463	19	hv	hv	NOUN
ejpam-6536	463	20	)	)	PUNCT
ejpam-6536	463	21	be	be	VERB
ejpam-6536	463	22	a	a	DET
ejpam-6536	463	23	pnd	pnd	NOUN
ejpam-6536	463	24	-	-	PUNCT
ejpam-6536	463	25	set	set	NOUN
ejpam-6536	463	26	of	of	ADP
ejpam-6536	463	27	hv	hv	PROPN
ejpam-6536	463	28	.	.	PUNCT
ejpam-6536	463	29	define	define	VERB
ejpam-6536	463	30	c	c	PROPN
ejpam-6536	463	31	=	=	PUNCT
ejpam-6536	463	32	a	a	DET
ejpam-6536	463	33	◦	◦	NOUN
ejpam-6536	463	34	∪	∪	ADP
ejpam-6536	463	35	(	(	PUNCT
ejpam-6536	463	36	∪v∈a	∪v∈a	NOUN
ejpam-6536	463	37	◦	◦	NOUN
ejpam-6536	463	38	∩ng(a	∩ng(a	NOUN
ejpam-6536	463	39	◦	◦	NOUN
ejpam-6536	463	40	)sv	)sv	NUM
ejpam-6536	463	41	)	)	PUNCT
ejpam-6536	464	1	∪	∪	ADP
ejpam-6536	464	2	(	(	PUNCT
ejpam-6536	464	3	∪v∈v	∪v∈v	X
ejpam-6536	464	4	(	(	PUNCT
ejpam-6536	464	5	g)\ng(a	g)\ng(a	NOUN
ejpam-6536	464	6	◦	◦	NOUN
ejpam-6536	464	7	)tv	)tv	PUNCT
ejpam-6536	464	8	)	)	PUNCT
ejpam-6536	464	9	.	.	PUNCT
ejpam-6536	465	1	v.	v.	ADP
ejpam-6536	465	2	a	a	DET
ejpam-6536	465	3	besana	besana	PROPN
ejpam-6536	465	4	,	,	PUNCT
ejpam-6536	465	5	f.	f.	PROPN
ejpam-6536	465	6	jamil	jamil	PROPN
ejpam-6536	465	7	,	,	PUNCT
ejpam-6536	465	8	s.	s.	PROPN
ejpam-6536	465	9	canoy	canoy	PROPN
ejpam-6536	465	10	jr	jr	PROPN
ejpam-6536	465	11	.	.	PROPN
ejpam-6536	465	12	/	/	SYM
ejpam-6536	465	13	eur	eur	PROPN
ejpam-6536	465	14	.	.	PUNCT
ejpam-6536	466	1	j.	j.	PROPN
ejpam-6536	466	2	pure	pure	PROPN
ejpam-6536	466	3	appl	appl	PROPN
ejpam-6536	466	4	.	.	PROPN
ejpam-6536	466	5	math	math	PROPN
ejpam-6536	466	6	,	,	PUNCT
ejpam-6536	466	7	18	18	NUM
ejpam-6536	466	8	(	(	PUNCT
ejpam-6536	466	9	3	3	NUM
ejpam-6536	466	10	)	)	PUNCT
ejpam-6536	466	11	(	(	PUNCT
ejpam-6536	466	12	2025	2025	NUM
ejpam-6536	466	13	)	)	PUNCT
ejpam-6536	466	14	,	,	PUNCT
ejpam-6536	466	15	6536	6536	NUM
ejpam-6536	466	16	12	12	NUM
ejpam-6536	466	17	of	of	ADP
ejpam-6536	466	18	17	17	NUM
ejpam-6536	466	19	clearly	clearly	ADV
ejpam-6536	466	20	,	,	PUNCT
ejpam-6536	466	21	c	c	PROPN
ejpam-6536	466	22	∩	∩	PROPN
ejpam-6536	466	23	a	a	DET
ejpam-6536	466	24	=	=	SYM
ejpam-6536	466	25	∅.	∅.	NOUN
ejpam-6536	466	26	we	we	PRON
ejpam-6536	466	27	claim	claim	VERB
ejpam-6536	466	28	that	that	SCONJ
ejpam-6536	466	29	c	c	PROPN
ejpam-6536	466	30	is	be	AUX
ejpam-6536	466	31	a	a	DET
ejpam-6536	466	32	hop	hop	NOUN
ejpam-6536	466	33	dominating	dominating	NOUN
ejpam-6536	466	34	set	set	NOUN
ejpam-6536	466	35	of	of	ADP
ejpam-6536	466	36	g	g	PROPN
ejpam-6536	466	37	◦	◦	PROPN
ejpam-6536	466	38	h.	h.	PROPN
ejpam-6536	466	39	let	let	VERB
ejpam-6536	466	40	v	v	NUM
ejpam-6536	466	41	∈	∈	PROPN
ejpam-6536	466	42	v	v	NOUN
ejpam-6536	466	43	(	(	PUNCT
ejpam-6536	466	44	g	g	NOUN
ejpam-6536	466	45	)	)	PUNCT
ejpam-6536	466	46	\	\	PROPN
ejpam-6536	467	1	a	a	DET
ejpam-6536	467	2	◦	◦	NOUN
ejpam-6536	467	3	.	.	PUNCT
ejpam-6536	468	1	we	we	PRON
ejpam-6536	468	2	consider	consider	VERB
ejpam-6536	468	3	the	the	DET
ejpam-6536	468	4	following	follow	VERB
ejpam-6536	468	5	cases	case	NOUN
ejpam-6536	468	6	:	:	PUNCT
ejpam-6536	468	7	case	case	NOUN
ejpam-6536	468	8	1	1	NUM
ejpam-6536	468	9	:	:	SYM
ejpam-6536	468	10	v	v	NUM
ejpam-6536	468	11	∈	∈	PROPN
ejpam-6536	468	12	a	a	DET
ejpam-6536	468	13	since	since	SCONJ
ejpam-6536	468	14	a	a	PRON
ejpam-6536	468	15	is	be	AUX
ejpam-6536	468	16	a	a	DET
ejpam-6536	468	17	total	total	ADJ
ejpam-6536	468	18	dominating	dominating	NOUN
ejpam-6536	468	19	set	set	NOUN
ejpam-6536	468	20	of	of	ADP
ejpam-6536	468	21	g	g	NOUN
ejpam-6536	468	22	,	,	PUNCT
ejpam-6536	468	23	ng(v	ng(v	PUNCT
ejpam-6536	468	24	)	)	PUNCT
ejpam-6536	468	25	̸=	̸=	PROPN
ejpam-6536	468	26	∅.	∅.	ADP
ejpam-6536	468	27	moreover	moreover	ADV
ejpam-6536	468	28	,	,	PUNCT
ejpam-6536	468	29	because	because	SCONJ
ejpam-6536	468	30	v	v	NUM
ejpam-6536	468	31	/∈	/∈	PUNCT
ejpam-6536	468	32	a	a	DET
ejpam-6536	468	33	◦	◦	NOUN
ejpam-6536	468	34	,	,	PUNCT
ejpam-6536	468	35	ng(v	ng(v	PUNCT
ejpam-6536	468	36	)	)	PUNCT
ejpam-6536	468	37	⊆	⊆	NUM
ejpam-6536	468	38	a.	a.	NOUN
ejpam-6536	468	39	pick	pick	NOUN
ejpam-6536	468	40	w	w	PROPN
ejpam-6536	468	41	∈	∈	PROPN
ejpam-6536	468	42	a	a	DET
ejpam-6536	468	43	∩	∩	NOUN
ejpam-6536	468	44	ng(v	ng(v	NUM
ejpam-6536	468	45	)	)	PUNCT
ejpam-6536	468	46	.	.	PUNCT
ejpam-6536	469	1	first	first	ADV
ejpam-6536	469	2	,	,	PUNCT
ejpam-6536	469	3	suppose	suppose	VERB
ejpam-6536	469	4	that	that	SCONJ
ejpam-6536	469	5	w	w	PROPN
ejpam-6536	469	6	∈	∈	PROPN
ejpam-6536	469	7	γ(a	γ(a	PROPN
ejpam-6536	469	8	)	)	PUNCT
ejpam-6536	469	9	and	and	CCONJ
ejpam-6536	469	10	y	y	PROPN
ejpam-6536	469	11	=	=	SYM
ejpam-6536	469	12	uw	uw	PROPN
ejpam-6536	469	13	∈	∈	PROPN
ejpam-6536	469	14	a	a	DET
ejpam-6536	469	15	◦	◦	NOUN
ejpam-6536	469	16	.	.	PUNCT
ejpam-6536	470	1	since	since	SCONJ
ejpam-6536	470	2	y	y	PROPN
ejpam-6536	470	3	/∈	/∈	PUNCT
ejpam-6536	470	4	ng(v	ng(v	NUM
ejpam-6536	470	5	)	)	PUNCT
ejpam-6536	470	6	,	,	PUNCT
ejpam-6536	470	7	dg(v	dg(v	X
ejpam-6536	470	8	,	,	PUNCT
ejpam-6536	470	9	y	y	NOUN
ejpam-6536	470	10	)	)	PUNCT
ejpam-6536	470	11	=	=	SYM
ejpam-6536	471	1	2	2	X
ejpam-6536	471	2	.	.	PUNCT
ejpam-6536	472	1	next	next	ADV
ejpam-6536	472	2	,	,	PUNCT
ejpam-6536	472	3	suppose	suppose	VERB
ejpam-6536	472	4	that	that	SCONJ
ejpam-6536	472	5	w	w	PROPN
ejpam-6536	472	6	/∈	/∈	PUNCT
ejpam-6536	472	7	γ(a	γ(a	PROPN
ejpam-6536	472	8	)	)	PUNCT
ejpam-6536	472	9	.	.	PUNCT
ejpam-6536	473	1	then	then	ADV
ejpam-6536	473	2	w	w	PROPN
ejpam-6536	473	3	/∈	/∈	PUNCT
ejpam-6536	473	4	ng(a	ng(a	NOUN
ejpam-6536	473	5	◦	◦	NOUN
ejpam-6536	473	6	)	)	PUNCT
ejpam-6536	473	7	and	and	CCONJ
ejpam-6536	473	8	tw	tw	NOUN
ejpam-6536	473	9	is	be	AUX
ejpam-6536	473	10	a	a	DET
ejpam-6536	473	11	pnd	pnd	NOUN
ejpam-6536	473	12	-	-	PUNCT
ejpam-6536	473	13	set	set	NOUN
ejpam-6536	473	14	of	of	ADP
ejpam-6536	473	15	hw	hw	PRON
ejpam-6536	473	16	.	.	PUNCT
ejpam-6536	474	1	pick	pick	VERB
ejpam-6536	474	2	y	y	PROPN
ejpam-6536	474	3	∈	∈	PROPN
ejpam-6536	474	4	tw	tw	PROPN
ejpam-6536	474	5	.	.	PUNCT
ejpam-6536	475	1	then	then	ADV
ejpam-6536	475	2	y	y	PROPN
ejpam-6536	475	3	∈	∈	PROPN
ejpam-6536	475	4	v	v	PROPN
ejpam-6536	475	5	(	(	PUNCT
ejpam-6536	475	6	hw	hw	NOUN
ejpam-6536	475	7	)	)	PUNCT
ejpam-6536	475	8	∩	∩	ADJ
ejpam-6536	475	9	c.	c.	NOUN
ejpam-6536	475	10	case	case	NOUN
ejpam-6536	475	11	2	2	NUM
ejpam-6536	475	12	:	:	SYM
ejpam-6536	475	13	v	v	NOUN
ejpam-6536	475	14	/∈	/∈	PUNCT
ejpam-6536	476	1	a	a	PRON
ejpam-6536	476	2	since	since	SCONJ
ejpam-6536	476	3	a	a	PRON
ejpam-6536	476	4	is	be	AUX
ejpam-6536	476	5	a	a	DET
ejpam-6536	476	6	dominating	dominating	NOUN
ejpam-6536	476	7	set	set	NOUN
ejpam-6536	476	8	of	of	ADP
ejpam-6536	476	9	g	g	NOUN
ejpam-6536	476	10	,	,	PUNCT
ejpam-6536	476	11	there	there	PRON
ejpam-6536	476	12	exists	exist	VERB
ejpam-6536	476	13	w	w	PROPN
ejpam-6536	476	14	∈	∈	PROPN
ejpam-6536	476	15	a	a	DET
ejpam-6536	476	16	∩	∩	NOUN
ejpam-6536	476	17	ng(v	ng(v	NUM
ejpam-6536	476	18	)	)	PUNCT
ejpam-6536	476	19	.	.	PUNCT
ejpam-6536	477	1	since	since	SCONJ
ejpam-6536	477	2	v	v	NUM
ejpam-6536	477	3	∈	∈	NOUN
ejpam-6536	477	4	ng(w	ng(w	NOUN
ejpam-6536	477	5	)	)	PUNCT
ejpam-6536	477	6	\	\	PROPN
ejpam-6536	478	1	a	a	DET
ejpam-6536	478	2	,	,	PUNCT
ejpam-6536	478	3	w	w	PROPN
ejpam-6536	478	4	∈	∈	PROPN
ejpam-6536	478	5	γ(a	γ(a	PROPN
ejpam-6536	478	6	)	)	PUNCT
ejpam-6536	478	7	and	and	CCONJ
ejpam-6536	478	8	there	there	PRON
ejpam-6536	478	9	exists	exist	VERB
ejpam-6536	478	10	y	y	PROPN
ejpam-6536	478	11	=	=	PUNCT
ejpam-6536	478	12	uw	uw	PROPN
ejpam-6536	478	13	∈	∈	PROPN
ejpam-6536	478	14	a	a	DET
ejpam-6536	478	15	◦	◦	NOUN
ejpam-6536	478	16	.	.	PUNCT
ejpam-6536	479	1	if	if	SCONJ
ejpam-6536	479	2	vy	vy	PROPN
ejpam-6536	479	3	/∈	/∈	PUNCT
ejpam-6536	479	4	e(g	e(g	PROPN
ejpam-6536	479	5	)	)	PUNCT
ejpam-6536	479	6	,	,	PUNCT
ejpam-6536	479	7	then	then	ADV
ejpam-6536	479	8	dg(v	dg(v	PUNCT
ejpam-6536	479	9	,	,	PUNCT
ejpam-6536	479	10	y	y	NOUN
ejpam-6536	479	11	)	)	PUNCT
ejpam-6536	479	12	=	=	SYM
ejpam-6536	479	13	2	2	X
ejpam-6536	479	14	.	.	PUNCT
ejpam-6536	479	15	suppose	suppose	VERB
ejpam-6536	479	16	that	that	SCONJ
ejpam-6536	479	17	vy	vy	PROPN
ejpam-6536	479	18	∈	∈	PROPN
ejpam-6536	479	19	e(g	e(g	PROPN
ejpam-6536	479	20	)	)	PUNCT
ejpam-6536	479	21	.	.	PUNCT
ejpam-6536	480	1	if	if	SCONJ
ejpam-6536	480	2	y	y	PROPN
ejpam-6536	480	3	∈	∈	PROPN
ejpam-6536	480	4	ng(a	ng(a	NOUN
ejpam-6536	480	5	◦	◦	NOUN
ejpam-6536	480	6	)	)	PUNCT
ejpam-6536	480	7	,	,	PUNCT
ejpam-6536	480	8	then	then	ADV
ejpam-6536	480	9	v	v	X
ejpam-6536	480	10	(	(	PUNCT
ejpam-6536	480	11	hy	hy	NOUN
ejpam-6536	480	12	)	)	PUNCT
ejpam-6536	480	13	∩	∩	NOUN
ejpam-6536	480	14	c	c	NOUN
ejpam-6536	480	15	=	=	SYM
ejpam-6536	480	16	sy	sy	PROPN
ejpam-6536	480	17	̸=	̸=	PROPN
ejpam-6536	480	18	∅.	∅.	ADV
ejpam-6536	480	19	if	if	SCONJ
ejpam-6536	480	20	y	y	PROPN
ejpam-6536	480	21	/∈	/∈	PUNCT
ejpam-6536	480	22	ng(a	ng(a	PUNCT
ejpam-6536	480	23	◦	◦	NOUN
ejpam-6536	480	24	)	)	PUNCT
ejpam-6536	480	25	,	,	PUNCT
ejpam-6536	480	26	then	then	ADV
ejpam-6536	480	27	v	v	X
ejpam-6536	480	28	(	(	PUNCT
ejpam-6536	480	29	hy	hy	NOUN
ejpam-6536	480	30	)	)	PUNCT
ejpam-6536	480	31	∩	∩	NOUN
ejpam-6536	480	32	c	c	NOUN
ejpam-6536	480	33	=	=	SYM
ejpam-6536	480	34	ty	ty	PROPN
ejpam-6536	480	35	̸=	̸=	PROPN
ejpam-6536	480	36	∅.	∅.	NOUN
ejpam-6536	480	37	by	by	ADP
ejpam-6536	480	38	theorem	theorem	NOUN
ejpam-6536	480	39	2	2	NUM
ejpam-6536	480	40	,	,	PUNCT
ejpam-6536	480	41	c	c	PROPN
ejpam-6536	480	42	is	be	AUX
ejpam-6536	480	43	a	a	DET
ejpam-6536	480	44	(	(	PUNCT
ejpam-6536	480	45	inverse	inverse	NOUN
ejpam-6536	480	46	)	)	PUNCT
ejpam-6536	480	47	hop	hop	NOUN
ejpam-6536	480	48	dominating	dominating	NOUN
ejpam-6536	480	49	set	set	NOUN
ejpam-6536	480	50	of	of	ADP
ejpam-6536	480	51	g	g	PROPN
ejpam-6536	480	52	◦	◦	PROPN
ejpam-6536	480	53	h.	h.	PROPN
ejpam-6536	480	54	thus	thus	ADV
ejpam-6536	480	55	,	,	PUNCT
ejpam-6536	480	56	γ̃h(g	γ̃h(g	VERB
ejpam-6536	480	57	◦	◦	NOUN
ejpam-6536	480	58	h	h	NOUN
ejpam-6536	480	59	)	)	PUNCT
ejpam-6536	480	60	≤	≤	NOUN
ejpam-6536	480	61	|c|	|c|	PROPN
ejpam-6536	480	62	=	=	PUNCT
ejpam-6536	480	63	|a	|a	NOUN
ejpam-6536	480	64	◦	◦	NOUN
ejpam-6536	480	65	|	|	ADV
ejpam-6536	480	66	+	+	CCONJ
ejpam-6536	480	67	|a	|a	NOUN
ejpam-6536	480	68	◦	◦	NOUN
ejpam-6536	480	69	∩	∩	NOUN
ejpam-6536	480	70	ng(a	ng(a	NOUN
ejpam-6536	480	71	◦	◦	NOUN
ejpam-6536	480	72	)|	)|	PUNCT
ejpam-6536	480	73	+	+	CCONJ
ejpam-6536	481	1	[	[	X
ejpam-6536	481	2	n	n	X
ejpam-6536	481	3	−	−	NOUN
ejpam-6536	481	4	|ng(a	|ng(a	ADP
ejpam-6536	481	5	◦	◦	NOUN
ejpam-6536	481	6	)|]pnd(h	)|]pnd(h	NOUN
ejpam-6536	481	7	)	)	PUNCT
ejpam-6536	481	8	.	.	PUNCT
ejpam-6536	482	1	in	in	ADP
ejpam-6536	482	2	particular	particular	ADJ
ejpam-6536	482	3	,	,	PUNCT
ejpam-6536	482	4	if	if	SCONJ
ejpam-6536	482	5	g	g	PROPN
ejpam-6536	482	6	is	be	AUX
ejpam-6536	482	7	the	the	DET
ejpam-6536	482	8	star	star	NOUN
ejpam-6536	482	9	graph	graph	NOUN
ejpam-6536	482	10	k1,n−1	k1,n−1	ADJ
ejpam-6536	482	11	(	(	PUNCT
ejpam-6536	482	12	n	n	CCONJ
ejpam-6536	482	13	≥	≥	NOUN
ejpam-6536	482	14	3	3	NUM
ejpam-6536	482	15	)	)	PUNCT
ejpam-6536	482	16	,	,	PUNCT
ejpam-6536	482	17	then	then	ADV
ejpam-6536	482	18	γh(g	γh(g	PUNCT
ejpam-6536	482	19	◦	◦	NOUN
ejpam-6536	482	20	h	h	NOUN
ejpam-6536	482	21	)	)	PUNCT
ejpam-6536	482	22	=	=	SYM
ejpam-6536	482	23	2	2	NUM
ejpam-6536	482	24	and	and	CCONJ
ejpam-6536	482	25	γ̃h(g	γ̃h(g	NOUN
ejpam-6536	482	26	◦	◦	NOUN
ejpam-6536	482	27	h	h	NOUN
ejpam-6536	482	28	)	)	PUNCT
ejpam-6536	482	29	=	=	SYM
ejpam-6536	482	30	1+(n−1)pnd(h	1+(n−1)pnd(h	NUM
ejpam-6536	482	31	)	)	PUNCT
ejpam-6536	482	32	,	,	PUNCT
ejpam-6536	482	33	for	for	ADP
ejpam-6536	482	34	any	any	DET
ejpam-6536	482	35	graph	graph	NOUN
ejpam-6536	482	36	h.	h.	NOUN
ejpam-6536	482	37	any	any	DET
ejpam-6536	482	38	γ∗t	γ∗t	PROPN
ejpam-6536	482	39	1,2	1,2	NUM
ejpam-6536	482	40	-	-	NUM
ejpam-6536	482	41	set	set	VERB
ejpam-6536	482	42	a	a	DET
ejpam-6536	482	43	contains	contain	VERB
ejpam-6536	482	44	the	the	DET
ejpam-6536	482	45	central	central	ADJ
ejpam-6536	482	46	vertex	vertex	NOUN
ejpam-6536	482	47	,	,	PUNCT
ejpam-6536	482	48	|a	|a	NOUN
ejpam-6536	482	49	◦	◦	NOUN
ejpam-6536	482	50	|	|	NOUN
ejpam-6536	482	51	=	=	SYM
ejpam-6536	482	52	1	1	NUM
ejpam-6536	482	53	and	and	CCONJ
ejpam-6536	482	54	a	a	DET
ejpam-6536	482	55	◦	◦	NOUN
ejpam-6536	482	56	∩ng(a	∩ng(a	NOUN
ejpam-6536	482	57	◦	◦	NOUN
ejpam-6536	482	58	)	)	PUNCT
ejpam-6536	482	59	=	=	NOUN
ejpam-6536	482	60	∅.	∅.	ADP
ejpam-6536	482	61	thus	thus	ADV
ejpam-6536	482	62	,	,	PUNCT
ejpam-6536	482	63	|a	|a	NOUN
ejpam-6536	482	64	◦	◦	NOUN
ejpam-6536	482	65	|+	|+	NOUN
ejpam-6536	482	66	|a	|a	NOUN
ejpam-6536	482	67	◦	◦	NOUN
ejpam-6536	482	68	∩ng(a	∩ng(a	NOUN
ejpam-6536	482	69	◦	◦	NOUN
ejpam-6536	482	70	)|+[n−|ng(a	)|+[n−|ng(a	NOUN
ejpam-6536	482	71	◦	◦	NOUN
ejpam-6536	482	72	)|]pnd(h	)|]pnd(h	NOUN
ejpam-6536	482	73	)	)	PUNCT
ejpam-6536	483	1	=	=	SYM
ejpam-6536	483	2	1+(n−1)pnd(h	1+(n−1)pnd(h	NUM
ejpam-6536	483	3	)	)	PUNCT
ejpam-6536	483	4	.	.	PUNCT
ejpam-6536	484	1	finally	finally	ADV
ejpam-6536	484	2	,	,	PUNCT
ejpam-6536	484	3	to	to	PART
ejpam-6536	484	4	prove	prove	VERB
ejpam-6536	484	5	(	(	PUNCT
ejpam-6536	484	6	iii	iii	NOUN
ejpam-6536	484	7	)	)	PUNCT
ejpam-6536	484	8	,	,	PUNCT
ejpam-6536	484	9	let	let	VERB
ejpam-6536	484	10	b	b	X
ejpam-6536	484	11	⊆	⊆	NUM
ejpam-6536	484	12	v	v	NOUN
ejpam-6536	484	13	(	(	PUNCT
ejpam-6536	484	14	g	g	NOUN
ejpam-6536	484	15	)	)	PUNCT
ejpam-6536	484	16	be	be	AUX
ejpam-6536	484	17	γ̃-set	γ̃-set	VERB
ejpam-6536	484	18	of	of	ADP
ejpam-6536	484	19	g	g	NOUN
ejpam-6536	484	20	and	and	CCONJ
ejpam-6536	484	21	let	let	VERB
ejpam-6536	484	22	a	a	DET
ejpam-6536	484	23	⊆	⊆	NUM
ejpam-6536	484	24	v	v	NOUN
ejpam-6536	484	25	(	(	PUNCT
ejpam-6536	484	26	g	g	NOUN
ejpam-6536	484	27	)	)	PUNCT
ejpam-6536	484	28	be	be	AUX
ejpam-6536	484	29	a	a	DET
ejpam-6536	484	30	γ	γ	NOUN
ejpam-6536	484	31	-	-	PUNCT
ejpam-6536	484	32	set	set	NOUN
ejpam-6536	484	33	of	of	ADP
ejpam-6536	484	34	g	g	NOUN
ejpam-6536	484	35	for	for	ADP
ejpam-6536	484	36	which	which	PRON
ejpam-6536	484	37	a	a	DET
ejpam-6536	484	38	∩	∩	ADJ
ejpam-6536	484	39	b	b	NOUN
ejpam-6536	484	40	=	=	PUNCT
ejpam-6536	484	41	∅.	∅.	NOUN
ejpam-6536	484	42	for	for	ADP
ejpam-6536	484	43	each	each	DET
ejpam-6536	484	44	v	v	ADP
ejpam-6536	484	45	∈	∈	PRON
ejpam-6536	484	46	a	a	PRON
ejpam-6536	484	47	,	,	PUNCT
ejpam-6536	484	48	let	let	VERB
ejpam-6536	484	49	sv	sv	PROPN
ejpam-6536	484	50	⊆	⊆	NUM
ejpam-6536	484	51	v	v	X
ejpam-6536	484	52	(	(	PUNCT
ejpam-6536	484	53	hv	hv	NOUN
ejpam-6536	484	54	)	)	PUNCT
ejpam-6536	484	55	be	be	VERB
ejpam-6536	484	56	a	a	DET
ejpam-6536	484	57	pnd	pnd	NOUN
ejpam-6536	484	58	-	-	PUNCT
ejpam-6536	484	59	set	set	NOUN
ejpam-6536	484	60	of	of	ADP
ejpam-6536	484	61	hv	hv	PROPN
ejpam-6536	484	62	.	.	PUNCT
ejpam-6536	485	1	similarly	similarly	ADV
ejpam-6536	485	2	,	,	PUNCT
ejpam-6536	485	3	for	for	ADP
ejpam-6536	485	4	each	each	DET
ejpam-6536	485	5	v	v	ADP
ejpam-6536	485	6	∈	∈	PROPN
ejpam-6536	485	7	b	b	NOUN
ejpam-6536	485	8	,	,	PUNCT
ejpam-6536	485	9	let	let	VERB
ejpam-6536	485	10	tv	tv	NOUN
ejpam-6536	485	11	⊆	⊆	NUM
ejpam-6536	485	12	v	v	NOUN
ejpam-6536	485	13	(	(	PUNCT
ejpam-6536	485	14	hv	hv	NOUN
ejpam-6536	485	15	)	)	PUNCT
ejpam-6536	485	16	be	be	VERB
ejpam-6536	485	17	a	a	DET
ejpam-6536	485	18	pnd	pnd	NOUN
ejpam-6536	485	19	-	-	PUNCT
ejpam-6536	485	20	set	set	NOUN
ejpam-6536	485	21	of	of	ADP
ejpam-6536	485	22	hv	hv	PROPN
ejpam-6536	485	23	.	.	PUNCT
ejpam-6536	486	1	define	define	PROPN
ejpam-6536	486	2	s	s	PART
ejpam-6536	486	3	=	=	PUNCT
ejpam-6536	486	4	a	a	DET
ejpam-6536	486	5	∪	∪	ADJ
ejpam-6536	486	6	(	(	PUNCT
ejpam-6536	486	7	∪v∈asv	∪v∈asv	NOUN
ejpam-6536	486	8	)	)	PUNCT
ejpam-6536	486	9	and	and	CCONJ
ejpam-6536	486	10	t	t	X
ejpam-6536	486	11	=	=	SYM
ejpam-6536	486	12	b	b	X
ejpam-6536	486	13	∪	∪	X
ejpam-6536	486	14	(	(	PUNCT
ejpam-6536	486	15	∪v∈btv	∪v∈btv	NOUN
ejpam-6536	486	16	)	)	PUNCT
ejpam-6536	486	17	.	.	PUNCT
ejpam-6536	487	1	as	as	SCONJ
ejpam-6536	487	2	shown	show	VERB
ejpam-6536	487	3	in	in	ADP
ejpam-6536	487	4	the	the	DET
ejpam-6536	487	5	proof	proof	NOUN
ejpam-6536	487	6	of	of	ADP
ejpam-6536	487	7	statement	statement	NOUN
ejpam-6536	487	8	(	(	PUNCT
ejpam-6536	487	9	i	i	NOUN
ejpam-6536	487	10	)	)	PUNCT
ejpam-6536	487	11	,	,	PUNCT
ejpam-6536	487	12	(	(	PUNCT
ejpam-6536	487	13	s	s	X
ejpam-6536	487	14	,	,	PUNCT
ejpam-6536	487	15	t	t	NOUN
ejpam-6536	487	16	)	)	PUNCT
ejpam-6536	487	17	∈	∈	PROPN
ejpam-6536	487	18	phd(g	phd(g	PROPN
ejpam-6536	487	19	◦	◦	NOUN
ejpam-6536	487	20	h	h	NOUN
ejpam-6536	487	21	)	)	PUNCT
ejpam-6536	487	22	.	.	PUNCT
ejpam-6536	488	1	moreover	moreover	ADV
ejpam-6536	488	2	,	,	PUNCT
ejpam-6536	488	3	since	since	SCONJ
ejpam-6536	488	4	|s|	|s|	PROPN
ejpam-6536	488	5	=	=	SYM
ejpam-6536	489	1	[	[	X
ejpam-6536	489	2	1	1	NUM
ejpam-6536	489	3	+	+	NUM
ejpam-6536	489	4	pnd(h)]γ(g	pnd(h)]γ(g	NOUN
ejpam-6536	489	5	)	)	PUNCT
ejpam-6536	489	6	,	,	PUNCT
ejpam-6536	489	7	t	t	PROPN
ejpam-6536	489	8	is	be	AUX
ejpam-6536	489	9	an	an	DET
ejpam-6536	489	10	inverse	inverse	NOUN
ejpam-6536	489	11	hop	hop	NOUN
ejpam-6536	489	12	dominating	dominating	NOUN
ejpam-6536	489	13	set	set	NOUN
ejpam-6536	489	14	of	of	ADP
ejpam-6536	489	15	g	g	PROPN
ejpam-6536	489	16	◦	◦	PROPN
ejpam-6536	489	17	h.	h.	PROPN
ejpam-6536	489	18	therefore	therefore	ADV
ejpam-6536	489	19	,	,	PUNCT
ejpam-6536	489	20	γ̃h(g	γ̃h(g	VERB
ejpam-6536	489	21	◦	◦	NOUN
ejpam-6536	489	22	h	h	NOUN
ejpam-6536	489	23	)	)	PUNCT
ejpam-6536	489	24	≤	≤	NOUN
ejpam-6536	489	25	|t	|t	VERB
ejpam-6536	490	1	|	|	ADV
ejpam-6536	490	2	=	=	SYM
ejpam-6536	491	1	[	[	X
ejpam-6536	491	2	1	1	NUM
ejpam-6536	491	3	+	+	NUM
ejpam-6536	491	4	pnd(h)]γ̃(g	pnd(h)]γ̃(g	PROPN
ejpam-6536	491	5	)	)	PUNCT
ejpam-6536	491	6	.	.	PUNCT
ejpam-6536	492	1	■	■	PUNCT
ejpam-6536	492	2	the	the	DET
ejpam-6536	492	3	corona	corona	NOUN
ejpam-6536	492	4	g	g	PROPN
ejpam-6536	492	5	◦	◦	NOUN
ejpam-6536	492	6	h	h	NOUN
ejpam-6536	492	7	,	,	PUNCT
ejpam-6536	492	8	where	where	SCONJ
ejpam-6536	492	9	pnd(h	pnd(h	PROPN
ejpam-6536	492	10	)	)	PUNCT
ejpam-6536	492	11	≥	≥	NOUN
ejpam-6536	492	12	2	2	NUM
ejpam-6536	492	13	and	and	CCONJ
ejpam-6536	492	14	g	g	PROPN
ejpam-6536	492	15	is	be	AUX
ejpam-6536	492	16	the	the	DET
ejpam-6536	492	17	graph	graph	NOUN
ejpam-6536	492	18	in	in	ADP
ejpam-6536	492	19	figure	figure	NOUN
ejpam-6536	492	20	5	5	NUM
ejpam-6536	492	21	,	,	PUNCT
ejpam-6536	492	22	shows	show	VERB
ejpam-6536	492	23	that	that	SCONJ
ejpam-6536	492	24	strict	strict	ADJ
ejpam-6536	492	25	inequality	inequality	NOUN
ejpam-6536	492	26	may	may	AUX
ejpam-6536	492	27	be	be	AUX
ejpam-6536	492	28	attained	attain	VERB
ejpam-6536	492	29	in	in	ADP
ejpam-6536	492	30	proposition	proposition	NOUN
ejpam-6536	492	31	6(ii	6(ii	NOUN
ejpam-6536	492	32	)	)	PUNCT
ejpam-6536	492	33	.	.	PUNCT
ejpam-6536	493	1	here	here	ADV
ejpam-6536	493	2	a	a	PRON
ejpam-6536	493	3	=	=	X
ejpam-6536	493	4	{	{	PUNCT
ejpam-6536	493	5	z	z	NOUN
ejpam-6536	493	6	,	,	PUNCT
ejpam-6536	493	7	w	w	NOUN
ejpam-6536	493	8	}	}	PUNCT
ejpam-6536	493	9	is	be	AUX
ejpam-6536	493	10	the	the	DET
ejpam-6536	493	11	unique	unique	ADJ
ejpam-6536	493	12	γh	γh	NOUN
ejpam-6536	493	13	-	-	PUNCT
ejpam-6536	493	14	set	set	NOUN
ejpam-6536	493	15	of	of	ADP
ejpam-6536	493	16	g	g	PROPN
ejpam-6536	493	17	◦	◦	NOUN
ejpam-6536	493	18	h	h	NOUN
ejpam-6536	493	19	and	and	CCONJ
ejpam-6536	493	20	γ̃h(g	γ̃h(g	VERB
ejpam-6536	493	21	◦	◦	NOUN
ejpam-6536	493	22	h	h	NOUN
ejpam-6536	493	23	)	)	PUNCT
ejpam-6536	493	24	=	=	SYM
ejpam-6536	493	25	2	2	NUM
ejpam-6536	493	26	+	+	NUM
ejpam-6536	493	27	pnd(h	pnd(h	NUM
ejpam-6536	493	28	)	)	PUNCT
ejpam-6536	493	29	.	.	PUNCT
ejpam-6536	494	1	now	now	ADV
ejpam-6536	494	2	,	,	PUNCT
ejpam-6536	494	3	choose	choose	VERB
ejpam-6536	494	4	a	a	DET
ejpam-6536	494	5	◦	◦	NOUN
ejpam-6536	494	6	=	=	SYM
ejpam-6536	494	7	{	{	PUNCT
ejpam-6536	494	8	y	y	NOUN
ejpam-6536	494	9	}	}	PUNCT
ejpam-6536	494	10	.	.	PUNCT
ejpam-6536	495	1	then	then	ADV
ejpam-6536	495	2	|a	|a	VERB
ejpam-6536	495	3	◦	◦	NOUN
ejpam-6536	495	4	|	|	ADV
ejpam-6536	495	5	+	+	CCONJ
ejpam-6536	495	6	|a	|a	NOUN
ejpam-6536	495	7	◦	◦	NOUN
ejpam-6536	495	8	∩	∩	NOUN
ejpam-6536	495	9	ng(a	ng(a	NOUN
ejpam-6536	495	10	◦	◦	NOUN
ejpam-6536	495	11	)|	)|	PUNCT
ejpam-6536	495	12	+	+	CCONJ
ejpam-6536	496	1	[	[	X
ejpam-6536	496	2	4	4	NUM
ejpam-6536	496	3	−	−	NOUN
ejpam-6536	496	4	|ng(a	|ng(a	ADP
ejpam-6536	496	5	◦	◦	NOUN
ejpam-6536	496	6	)|]pnd(h	)|]pnd(h	NOUN
ejpam-6536	496	7	)	)	PUNCT
ejpam-6536	496	8	=	=	SYM
ejpam-6536	496	9	1	1	NUM
ejpam-6536	496	10	+	+	NUM
ejpam-6536	496	11	2pnd(h	2pnd(h	NUM
ejpam-6536	496	12	)	)	PUNCT
ejpam-6536	496	13	>	>	X
ejpam-6536	496	14	γ̃h(g	γ̃h(g	VERB
ejpam-6536	496	15	◦	◦	NOUN
ejpam-6536	496	16	h	h	NOUN
ejpam-6536	496	17	)	)	PUNCT
ejpam-6536	496	18	.	.	PUNCT
ejpam-6536	497	1	....................................	....................................	PUNCT
ejpam-6536	497	2	....................................	....................................	PUNCT
ejpam-6536	498	1	....................................	....................................	PUNCT
ejpam-6536	498	2	....................................	....................................	PUNCT
ejpam-6536	498	3	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-6536	499	1	.......................................................................................................................	.......................................................................................................................	PUNCT
ejpam-6536	499	2	..........................	..........................	PUNCT
ejpam-6536	500	1	.........................	.........................	PUNCT
ejpam-6536	500	2	.........................	.........................	PUNCT
ejpam-6536	500	3	.........................	.........................	PUNCT
ejpam-6536	500	4	.........................	.........................	PUNCT
ejpam-6536	501	1	.........	.........	PUNCT
ejpam-6536	501	2	........	........	PUNCT
ejpam-6536	501	3	........	........	PUNCT
ejpam-6536	501	4	........	........	PUNCT
ejpam-6536	501	5	........	........	PUNCT
ejpam-6536	501	6	........	........	PUNCT
ejpam-6536	501	7	........	........	PUNCT
ejpam-6536	501	8	........	........	PUNCT
ejpam-6536	501	9	........	........	PUNCT
ejpam-6536	501	10	...	...	PUNCT
ejpam-6536	502	1	g	g	NOUN
ejpam-6536	502	2	x	x	PUNCT
ejpam-6536	502	3	y	y	PROPN
ejpam-6536	502	4	z	z	PROPN
ejpam-6536	502	5	w	w	PROPN
ejpam-6536	502	6	•	•	NUM
ejpam-6536	502	7	•	•	NUM
ejpam-6536	502	8	figure	figure	NOUN
ejpam-6536	502	9	5	5	NUM
ejpam-6536	502	10	:	:	PUNCT
ejpam-6536	502	11	graph	graph	VERB
ejpam-6536	502	12	g	g	NOUN
ejpam-6536	502	13	for	for	ADP
ejpam-6536	502	14	illustration	illustration	NOUN
ejpam-6536	502	15	of	of	ADP
ejpam-6536	502	16	proposition	proposition	NOUN
ejpam-6536	502	17	6(ii	6(ii	NOUN
ejpam-6536	502	18	)	)	PUNCT
ejpam-6536	502	19	let	let	VERB
ejpam-6536	502	20	h	h	NOUN
ejpam-6536	502	21	be	be	AUX
ejpam-6536	502	22	a	a	DET
ejpam-6536	502	23	graph	graph	NOUN
ejpam-6536	502	24	with	with	ADP
ejpam-6536	502	25	isolated	isolated	ADJ
ejpam-6536	502	26	vertex	vertex	NOUN
ejpam-6536	502	27	.	.	PUNCT
ejpam-6536	503	1	for	for	ADP
ejpam-6536	503	2	n	n	PRON
ejpam-6536	503	3	≥	≥	NOUN
ejpam-6536	503	4	2	2	NUM
ejpam-6536	503	5	,	,	PUNCT
ejpam-6536	503	6	γ̃h(k1,n	γ̃h(k1,n	NOUN
ejpam-6536	503	7	◦	◦	NOUN
ejpam-6536	503	8	h	h	NOUN
ejpam-6536	503	9	)	)	PUNCT
ejpam-6536	503	10	=	=	SYM
ejpam-6536	503	11	n	n	PROPN
ejpam-6536	503	12	+	+	CCONJ
ejpam-6536	503	13	1	1	NUM
ejpam-6536	503	14	<	<	X
ejpam-6536	503	15	2n	2n	NUM
ejpam-6536	504	1	=	=	PUNCT
ejpam-6536	505	1	[	[	X
ejpam-6536	505	2	1	1	NUM
ejpam-6536	505	3	+	+	NUM
ejpam-6536	505	4	pnd(h)]γ̃(k1,n	pnd(h)]γ̃(k1,n	NOUN
ejpam-6536	505	5	)	)	PUNCT
ejpam-6536	505	6	.	.	PUNCT
ejpam-6536	506	1	this	this	PRON
ejpam-6536	506	2	means	mean	VERB
ejpam-6536	506	3	that	that	SCONJ
ejpam-6536	506	4	inequality	inequality	NOUN
ejpam-6536	506	5	in	in	ADP
ejpam-6536	506	6	proposition	proposition	NOUN
ejpam-6536	506	7	6(iii	6(iii	NOUN
ejpam-6536	506	8	)	)	PUNCT
ejpam-6536	506	9	is	be	AUX
ejpam-6536	506	10	also	also	ADV
ejpam-6536	506	11	attainable	attainable	ADJ
ejpam-6536	506	12	.	.	PUNCT
ejpam-6536	507	1	v.	v.	ADP
ejpam-6536	507	2	a	a	DET
ejpam-6536	507	3	besana	besana	PROPN
ejpam-6536	507	4	,	,	PUNCT
ejpam-6536	507	5	f.	f.	PROPN
ejpam-6536	507	6	jamil	jamil	PROPN
ejpam-6536	507	7	,	,	PUNCT
ejpam-6536	507	8	s.	s.	PROPN
ejpam-6536	507	9	canoy	canoy	PROPN
ejpam-6536	507	10	jr	jr	PROPN
ejpam-6536	507	11	.	.	PROPN
ejpam-6536	507	12	/	/	SYM
ejpam-6536	507	13	eur	eur	PROPN
ejpam-6536	507	14	.	.	PUNCT
ejpam-6536	508	1	j.	j.	PROPN
ejpam-6536	508	2	pure	pure	PROPN
ejpam-6536	508	3	appl	appl	PROPN
ejpam-6536	508	4	.	.	PROPN
ejpam-6536	508	5	math	math	PROPN
ejpam-6536	508	6	,	,	PUNCT
ejpam-6536	508	7	18	18	NUM
ejpam-6536	508	8	(	(	PUNCT
ejpam-6536	508	9	3	3	NUM
ejpam-6536	508	10	)	)	PUNCT
ejpam-6536	508	11	(	(	PUNCT
ejpam-6536	508	12	2025	2025	NUM
ejpam-6536	508	13	)	)	PUNCT
ejpam-6536	508	14	,	,	PUNCT
ejpam-6536	508	15	6536	6536	NUM
ejpam-6536	508	16	13	13	NUM
ejpam-6536	508	17	of	of	ADP
ejpam-6536	508	18	17	17	NUM
ejpam-6536	508	19	3.5	3.5	NUM
ejpam-6536	508	20	.	.	PUNCT
ejpam-6536	509	1	in	in	ADP
ejpam-6536	509	2	the	the	DET
ejpam-6536	509	3	lexicographic	lexicographic	ADJ
ejpam-6536	509	4	product	product	NOUN
ejpam-6536	509	5	of	of	ADP
ejpam-6536	509	6	graphs	graph	NOUN
ejpam-6536	509	7	a	a	DET
ejpam-6536	509	8	subset	subset	NOUN
ejpam-6536	509	9	s	s	VERB
ejpam-6536	509	10	⊆	⊆	NUM
ejpam-6536	509	11	v	v	NOUN
ejpam-6536	509	12	(	(	PUNCT
ejpam-6536	509	13	g	g	NOUN
ejpam-6536	509	14	)	)	PUNCT
ejpam-6536	509	15	is	be	AUX
ejpam-6536	509	16	a	a	DET
ejpam-6536	509	17	ρh	ρh	NOUN
ejpam-6536	509	18	-	-	PUNCT
ejpam-6536	509	19	set	set	NOUN
ejpam-6536	509	20	of	of	ADP
ejpam-6536	509	21	g	g	PROPN
ejpam-6536	509	22	if	if	SCONJ
ejpam-6536	509	23	s	s	VERB
ejpam-6536	509	24	is	be	AUX
ejpam-6536	509	25	a	a	DET
ejpam-6536	509	26	hop	hop	NOUN
ejpam-6536	509	27	dominating	dominating	NOUN
ejpam-6536	509	28	set	set	NOUN
ejpam-6536	509	29	of	of	ADP
ejpam-6536	509	30	g	g	NOUN
ejpam-6536	509	31	with	with	ADP
ejpam-6536	509	32	ρh(g	ρh(g	NOUN
ejpam-6536	509	33	)	)	PUNCT
ejpam-6536	509	34	=	=	SYM
ejpam-6536	509	35	|s	|s	PROPN
ejpam-6536	509	36	∩	∩	NOUN
ejpam-6536	509	37	ng(s	ng(s	CCONJ
ejpam-6536	509	38	,	,	PUNCT
ejpam-6536	509	39	2)|	2)|	NUM
ejpam-6536	509	40	+	+	CCONJ
ejpam-6536	509	41	pnd(h)|s	pnd(h)|s	NOUN
ejpam-6536	509	42	\	\	PROPN
ejpam-6536	509	43	ng(s	ng(s	PUNCT
ejpam-6536	509	44	,	,	PUNCT
ejpam-6536	509	45	2)|	2)|	NUM
ejpam-6536	509	46	.	.	PUNCT
ejpam-6536	510	1	theorem	theorem	NOUN
ejpam-6536	510	2	9	9	NUM
ejpam-6536	510	3	.	.	PUNCT
ejpam-6536	511	1	let	let	VERB
ejpam-6536	511	2	g	g	NOUN
ejpam-6536	511	3	and	and	CCONJ
ejpam-6536	511	4	h	h	NOUN
ejpam-6536	511	5	be	be	AUX
ejpam-6536	511	6	ntc	ntc	NOUN
ejpam-6536	511	7	graphs	graph	NOUN
ejpam-6536	511	8	with	with	ADP
ejpam-6536	511	9	γ(g	γ(g	NOUN
ejpam-6536	511	10	)	)	PUNCT
ejpam-6536	511	11	̸=	̸=	PROPN
ejpam-6536	511	12	1	1	NUM
ejpam-6536	511	13	.	.	PUNCT
ejpam-6536	512	1	then	then	ADV
ejpam-6536	512	2	γ̃h(g[h	γ̃h(g[h	PROPN
ejpam-6536	512	3	]	]	PUNCT
ejpam-6536	512	4	)	)	PUNCT
ejpam-6536	512	5	=	=	SYM
ejpam-6536	512	6	γth(g	γth(g	NOUN
ejpam-6536	512	7	)	)	PUNCT
ejpam-6536	512	8	.	.	PUNCT
ejpam-6536	513	1	proof	proof	NOUN
ejpam-6536	513	2	:	:	PUNCT
ejpam-6536	513	3	since	since	SCONJ
ejpam-6536	513	4	γ(g	γ(g	PROPN
ejpam-6536	513	5	)	)	PUNCT
ejpam-6536	513	6	̸=	̸=	PROPN
ejpam-6536	513	7	1	1	NUM
ejpam-6536	513	8	,	,	PUNCT
ejpam-6536	513	9	g	g	PROPN
ejpam-6536	513	10	admits	admit	VERB
ejpam-6536	513	11	a	a	DET
ejpam-6536	513	12	total	total	ADJ
ejpam-6536	513	13	hop	hop	NOUN
ejpam-6536	513	14	dominating	dominating	NOUN
ejpam-6536	513	15	set	set	NOUN
ejpam-6536	513	16	.	.	PUNCT
ejpam-6536	514	1	let	let	VERB
ejpam-6536	514	2	s	s	PRON
ejpam-6536	514	3	⊆	⊆	NUM
ejpam-6536	514	4	v	v	NOUN
ejpam-6536	514	5	(	(	PUNCT
ejpam-6536	514	6	g	g	NOUN
ejpam-6536	514	7	)	)	PUNCT
ejpam-6536	514	8	be	be	AUX
ejpam-6536	514	9	a	a	DET
ejpam-6536	514	10	γth	γth	NOUN
ejpam-6536	514	11	-	-	PUNCT
ejpam-6536	514	12	set	set	NOUN
ejpam-6536	514	13	of	of	ADP
ejpam-6536	514	14	g	g	NOUN
ejpam-6536	514	15	,	,	PUNCT
ejpam-6536	514	16	and	and	CCONJ
ejpam-6536	514	17	let	let	VERB
ejpam-6536	514	18	u	u	NOUN
ejpam-6536	514	19	,	,	PUNCT
ejpam-6536	514	20	v	v	PROPN
ejpam-6536	514	21	∈	∈	PROPN
ejpam-6536	514	22	v	v	NOUN
ejpam-6536	514	23	(	(	PUNCT
ejpam-6536	514	24	h	h	NOUN
ejpam-6536	514	25	)	)	PUNCT
ejpam-6536	514	26	with	with	ADP
ejpam-6536	514	27	u	u	NOUN
ejpam-6536	514	28	̸=	̸=	PROPN
ejpam-6536	514	29	v.	v.	ADV
ejpam-6536	514	30	by	by	ADP
ejpam-6536	514	31	theorem	theorem	NOUN
ejpam-6536	514	32	4	4	NUM
ejpam-6536	514	33	,	,	PUNCT
ejpam-6536	514	34	c1	c1	PROPN
ejpam-6536	514	35	=	=	PROPN
ejpam-6536	514	36	s	s	PART
ejpam-6536	514	37	×	×	NOUN
ejpam-6536	514	38	{	{	PUNCT
ejpam-6536	514	39	u	u	NOUN
ejpam-6536	514	40	}	}	PUNCT
ejpam-6536	514	41	and	and	CCONJ
ejpam-6536	514	42	c2	c2	PROPN
ejpam-6536	514	43	=	=	PROPN
ejpam-6536	514	44	s	s	PROPN
ejpam-6536	514	45	×	×	NOUN
ejpam-6536	514	46	{	{	PUNCT
ejpam-6536	514	47	v	v	NOUN
ejpam-6536	514	48	}	}	PUNCT
ejpam-6536	514	49	are	be	AUX
ejpam-6536	514	50	hop	hop	NOUN
ejpam-6536	514	51	dominating	dominating	NOUN
ejpam-6536	514	52	sets	set	NOUN
ejpam-6536	514	53	of	of	ADP
ejpam-6536	514	54	g[h	g[h	NOUN
ejpam-6536	514	55	]	]	PUNCT
ejpam-6536	514	56	.	.	PUNCT
ejpam-6536	515	1	since	since	SCONJ
ejpam-6536	515	2	|c1|	|c1|	PROPN
ejpam-6536	515	3	=	=	SYM
ejpam-6536	515	4	γth(g	γth(g	NOUN
ejpam-6536	515	5	)	)	PUNCT
ejpam-6536	515	6	,	,	PUNCT
ejpam-6536	515	7	c1	c1	PROPN
ejpam-6536	515	8	is	be	AUX
ejpam-6536	515	9	a	a	DET
ejpam-6536	515	10	γh	γh	ADV
ejpam-6536	515	11	-	-	PUNCT
ejpam-6536	515	12	set	set	NOUN
ejpam-6536	515	13	of	of	ADP
ejpam-6536	515	14	g[h	g[h	NOUN
ejpam-6536	515	15	]	]	PUNCT
ejpam-6536	515	16	by	by	ADP
ejpam-6536	515	17	corollary	corollary	ADJ
ejpam-6536	515	18	1	1	NUM
ejpam-6536	515	19	.	.	PUNCT
ejpam-6536	516	1	consequently	consequently	ADV
ejpam-6536	516	2	,	,	PUNCT
ejpam-6536	516	3	c2	c2	PROPN
ejpam-6536	516	4	is	be	AUX
ejpam-6536	516	5	an	an	DET
ejpam-6536	516	6	inverse	inverse	NOUN
ejpam-6536	516	7	hop	hop	NOUN
ejpam-6536	516	8	dominating	dominating	NOUN
ejpam-6536	516	9	set	set	NOUN
ejpam-6536	516	10	of	of	ADP
ejpam-6536	516	11	g[h	g[h	PROPN
ejpam-6536	516	12	]	]	PUNCT
ejpam-6536	516	13	.	.	PUNCT
ejpam-6536	517	1	thus	thus	ADV
ejpam-6536	517	2	,	,	PUNCT
ejpam-6536	517	3	γth(g	γth(g	NOUN
ejpam-6536	517	4	)	)	PUNCT
ejpam-6536	517	5	=	=	SYM
ejpam-6536	517	6	γh(g[h	γh(g[h	NOUN
ejpam-6536	517	7	]	]	X
ejpam-6536	517	8	)	)	PUNCT
ejpam-6536	517	9	≤	≤	NOUN
ejpam-6536	518	1	γ̃(g[h	γ̃(g[h	CCONJ
ejpam-6536	518	2	]	]	SYM
ejpam-6536	518	3	)	)	PUNCT
ejpam-6536	519	1	≤	≤	NUM
ejpam-6536	519	2	|c2|	|c2|	NOUN
ejpam-6536	519	3	=	=	SYM
ejpam-6536	519	4	γth(g	γth(g	NOUN
ejpam-6536	519	5	)	)	PUNCT
ejpam-6536	519	6	.	.	PUNCT
ejpam-6536	520	1	■	■	PUNCT
ejpam-6536	520	2	theorem	theorem	ADJ
ejpam-6536	520	3	10	10	NUM
ejpam-6536	520	4	.	.	PUNCT
ejpam-6536	521	1	let	let	VERB
ejpam-6536	521	2	g	g	NOUN
ejpam-6536	521	3	and	and	CCONJ
ejpam-6536	521	4	h	h	NOUN
ejpam-6536	521	5	be	be	AUX
ejpam-6536	521	6	ntc	ntc	NOUN
ejpam-6536	521	7	graphs	graph	NOUN
ejpam-6536	521	8	with	with	ADP
ejpam-6536	521	9	γ(g	γ(g	PROPN
ejpam-6536	521	10	)	)	PUNCT
ejpam-6536	521	11	=	=	SYM
ejpam-6536	521	12	1	1	NUM
ejpam-6536	521	13	and	and	CCONJ
ejpam-6536	521	14	h	h	NOUN
ejpam-6536	521	15	∈	∈	PROPN
ejpam-6536	521	16	g	g	PROPN
ejpam-6536	521	17	.	.	PUNCT
ejpam-6536	522	1	let	let	VERB
ejpam-6536	522	2	c	c	NOUN
ejpam-6536	522	3	=	=	SYM
ejpam-6536	522	4	∪x∈s	∪x∈s	PROPN
ejpam-6536	522	5	(	(	PUNCT
ejpam-6536	522	6	{	{	PUNCT
ejpam-6536	522	7	x	x	NOUN
ejpam-6536	522	8	}	}	PUNCT
ejpam-6536	522	9	×	×	PROPN
ejpam-6536	522	10	tx	tx	PROPN
ejpam-6536	522	11	)	)	PUNCT
ejpam-6536	522	12	⊆	⊆	NUM
ejpam-6536	522	13	v	v	NOUN
ejpam-6536	522	14	(	(	PUNCT
ejpam-6536	522	15	g[h	g[h	PROPN
ejpam-6536	522	16	]	]	PUNCT
ejpam-6536	522	17	)	)	PUNCT
ejpam-6536	522	18	with	with	ADP
ejpam-6536	522	19	tx	tx	PROPN
ejpam-6536	522	20	̸=	̸=	PROPN
ejpam-6536	522	21	v	v	PROPN
ejpam-6536	522	22	(	(	PUNCT
ejpam-6536	522	23	h	h	NOUN
ejpam-6536	522	24	)	)	PUNCT
ejpam-6536	522	25	for	for	ADP
ejpam-6536	522	26	x	x	PROPN
ejpam-6536	522	27	∈	∈	PROPN
ejpam-6536	522	28	s.	s.	PROPN
ejpam-6536	522	29	then	then	ADV
ejpam-6536	522	30	c	c	PROPN
ejpam-6536	522	31	is	be	AUX
ejpam-6536	522	32	an	an	DET
ejpam-6536	522	33	inverse	inverse	NOUN
ejpam-6536	522	34	hop	hop	NOUN
ejpam-6536	522	35	dominating	dominating	NOUN
ejpam-6536	522	36	set	set	NOUN
ejpam-6536	522	37	of	of	ADP
ejpam-6536	522	38	g[h	g[h	PROPN
ejpam-6536	522	39	]	]	PUNCT
ejpam-6536	522	40	if	if	SCONJ
ejpam-6536	522	41	and	and	CCONJ
ejpam-6536	522	42	only	only	ADV
ejpam-6536	522	43	if	if	SCONJ
ejpam-6536	522	44	each	each	PRON
ejpam-6536	522	45	of	of	ADP
ejpam-6536	522	46	the	the	DET
ejpam-6536	522	47	following	follow	VERB
ejpam-6536	522	48	holds	hold	VERB
ejpam-6536	522	49	:	:	PUNCT
ejpam-6536	522	50	(	(	PUNCT
ejpam-6536	522	51	i	i	NOUN
ejpam-6536	522	52	)	)	PUNCT
ejpam-6536	522	53	s	s	VERB
ejpam-6536	522	54	is	be	AUX
ejpam-6536	522	55	a	a	DET
ejpam-6536	522	56	hop	hop	NOUN
ejpam-6536	522	57	dominating	dominating	NOUN
ejpam-6536	522	58	set	set	NOUN
ejpam-6536	522	59	of	of	ADP
ejpam-6536	522	60	g	g	NOUN
ejpam-6536	522	61	;	;	PUNCT
ejpam-6536	522	62	(	(	PUNCT
ejpam-6536	522	63	ii	ii	NOUN
ejpam-6536	522	64	)	)	PUNCT
ejpam-6536	522	65	tx	tx	PROPN
ejpam-6536	522	66	is	be	AUX
ejpam-6536	522	67	a	a	DET
ejpam-6536	522	68	point	point	NOUN
ejpam-6536	522	69	-	-	PUNCT
ejpam-6536	522	70	wise	wise	ADJ
ejpam-6536	522	71	non	non	ADJ
ejpam-6536	522	72	-	-	ADJ
ejpam-6536	522	73	dominating	dominating	ADJ
ejpam-6536	522	74	set	set	NOUN
ejpam-6536	522	75	of	of	ADP
ejpam-6536	522	76	h	h	NOUN
ejpam-6536	522	77	for	for	ADP
ejpam-6536	522	78	all	all	PRON
ejpam-6536	522	79	x	x	PART
ejpam-6536	522	80	∈	∈	PROPN
ejpam-6536	522	81	s	s	PART
ejpam-6536	522	82	\	\	NOUN
ejpam-6536	522	83	ng(s	ng(s	NUM
ejpam-6536	522	84	,	,	PUNCT
ejpam-6536	522	85	2	2	NUM
ejpam-6536	522	86	)	)	PUNCT
ejpam-6536	522	87	;	;	PUNCT
ejpam-6536	522	88	(	(	PUNCT
ejpam-6536	522	89	iii	iii	X
ejpam-6536	522	90	)	)	PUNCT
ejpam-6536	522	91	there	there	PRON
ejpam-6536	522	92	exists	exist	VERB
ejpam-6536	522	93	a	a	DET
ejpam-6536	522	94	ρh	ρh	ADV
ejpam-6536	522	95	-	-	PUNCT
ejpam-6536	522	96	set	set	VERB
ejpam-6536	522	97	s∗	s∗	NOUN
ejpam-6536	522	98	of	of	ADP
ejpam-6536	522	99	g	g	NOUN
ejpam-6536	522	100	such	such	ADJ
ejpam-6536	522	101	that	that	PRON
ejpam-6536	522	102	for	for	ADP
ejpam-6536	522	103	each	each	DET
ejpam-6536	522	104	x	x	SYM
ejpam-6536	522	105	∈	∈	PROPN
ejpam-6536	522	106	(	(	PUNCT
ejpam-6536	522	107	s	s	X
ejpam-6536	522	108	∩	∩	NOUN
ejpam-6536	522	109	s∗	s∗	PROPN
ejpam-6536	522	110	)	)	PUNCT
ejpam-6536	522	111	\	\	PROPN
ejpam-6536	522	112	ng(s∗	ng(s∗	PROPN
ejpam-6536	522	113	,	,	PUNCT
ejpam-6536	522	114	2	2	NUM
ejpam-6536	522	115	)	)	PUNCT
ejpam-6536	522	116	,	,	PUNCT
ejpam-6536	522	117	v	v	X
ejpam-6536	522	118	(	(	PUNCT
ejpam-6536	522	119	h	h	NOUN
ejpam-6536	522	120	)	)	PUNCT
ejpam-6536	522	121	\	\	PROPN
ejpam-6536	522	122	tx	tx	PROPN
ejpam-6536	522	123	admits	admit	VERB
ejpam-6536	522	124	a	a	DET
ejpam-6536	522	125	pnd	pnd	NOUN
ejpam-6536	522	126	-	-	PUNCT
ejpam-6536	522	127	set	set	NOUN
ejpam-6536	522	128	of	of	ADP
ejpam-6536	522	129	h.	h.	PROPN
ejpam-6536	522	130	more	more	ADV
ejpam-6536	522	131	particularly	particularly	ADV
ejpam-6536	522	132	,	,	PUNCT
ejpam-6536	522	133	for	for	ADP
ejpam-6536	522	134	each	each	DET
ejpam-6536	522	135	x	x	SYM
ejpam-6536	522	136	∈	∈	PROPN
ejpam-6536	522	137	(	(	PUNCT
ejpam-6536	522	138	s	s	NOUN
ejpam-6536	522	139	∩	∩	NOUN
ejpam-6536	522	140	s∗)\(ng(s	s∗)\(ng(s	NOUN
ejpam-6536	522	141	,	,	PUNCT
ejpam-6536	522	142	2	2	NUM
ejpam-6536	522	143	)	)	PUNCT
ejpam-6536	522	144	∪	∪	X
ejpam-6536	522	145	ng(s∗	ng(s∗	NUM
ejpam-6536	522	146	,	,	PUNCT
ejpam-6536	522	147	2	2	NUM
ejpam-6536	522	148	)	)	PUNCT
ejpam-6536	522	149	)	)	PUNCT
ejpam-6536	522	150	,	,	PUNCT
ejpam-6536	522	151	tx	tx	PROPN
ejpam-6536	522	152	is	be	AUX
ejpam-6536	522	153	an	an	DET
ejpam-6536	522	154	inverse	inverse	NOUN
ejpam-6536	522	155	point	point	NOUN
ejpam-6536	522	156	-	-	PUNCT
ejpam-6536	522	157	wise	wise	ADJ
ejpam-6536	522	158	non	non	ADJ
ejpam-6536	522	159	-	-	ADJ
ejpam-6536	522	160	dominating	dominating	ADJ
ejpam-6536	522	161	set	set	NOUN
ejpam-6536	522	162	of	of	ADP
ejpam-6536	522	163	h.	h.	NOUN
ejpam-6536	522	164	proof	proof	NOUN
ejpam-6536	522	165	:	:	PUNCT
ejpam-6536	522	166	first	first	ADV
ejpam-6536	522	167	,	,	PUNCT
ejpam-6536	522	168	assume	assume	VERB
ejpam-6536	522	169	that	that	SCONJ
ejpam-6536	522	170	c	c	PROPN
ejpam-6536	522	171	is	be	AUX
ejpam-6536	522	172	an	an	DET
ejpam-6536	522	173	inverse	inverse	NOUN
ejpam-6536	522	174	hop	hop	NOUN
ejpam-6536	522	175	dominating	dominating	NOUN
ejpam-6536	522	176	set	set	NOUN
ejpam-6536	522	177	of	of	ADP
ejpam-6536	522	178	g[h	g[h	NOUN
ejpam-6536	522	179	]	]	PUNCT
ejpam-6536	522	180	.	.	PUNCT
ejpam-6536	523	1	by	by	ADP
ejpam-6536	523	2	theorem	theorem	NOUN
ejpam-6536	523	3	4	4	NUM
ejpam-6536	523	4	,	,	PUNCT
ejpam-6536	523	5	both	both	PRON
ejpam-6536	523	6	(	(	PUNCT
ejpam-6536	523	7	i	i	NOUN
ejpam-6536	523	8	)	)	PUNCT
ejpam-6536	523	9	and	and	CCONJ
ejpam-6536	523	10	(	(	PUNCT
ejpam-6536	523	11	ii	ii	NOUN
ejpam-6536	523	12	)	)	PUNCT
ejpam-6536	523	13	hold	hold	VERB
ejpam-6536	523	14	for	for	ADP
ejpam-6536	523	15	s.	s.	PROPN
ejpam-6536	523	16	since	since	SCONJ
ejpam-6536	523	17	c	c	PROPN
ejpam-6536	523	18	is	be	AUX
ejpam-6536	523	19	an	an	DET
ejpam-6536	523	20	inverse	inverse	NOUN
ejpam-6536	523	21	hop	hop	NOUN
ejpam-6536	523	22	dominating	dominating	NOUN
ejpam-6536	523	23	set	set	NOUN
ejpam-6536	523	24	,	,	PUNCT
ejpam-6536	523	25	there	there	PRON
ejpam-6536	523	26	exists	exist	VERB
ejpam-6536	523	27	a	a	DET
ejpam-6536	523	28	γh	γh	ADV
ejpam-6536	523	29	-	-	PUNCT
ejpam-6536	523	30	set	set	VERB
ejpam-6536	523	31	c∗	c∗	NOUN
ejpam-6536	523	32	=	=	SYM
ejpam-6536	523	33	∪x∈s∗	∪x∈s∗	PROPN
ejpam-6536	523	34	(	(	PUNCT
ejpam-6536	523	35	{	{	PUNCT
ejpam-6536	523	36	x	x	NOUN
ejpam-6536	523	37	}	}	PUNCT
ejpam-6536	523	38	×	×	PROPN
ejpam-6536	523	39	t	t	PROPN
ejpam-6536	523	40	∗	∗	NOUN
ejpam-6536	523	41	x	x	SYM
ejpam-6536	523	42	)	)	PUNCT
ejpam-6536	523	43	of	of	ADP
ejpam-6536	523	44	g[h	g[h	NOUN
ejpam-6536	523	45	]	]	PUNCT
ejpam-6536	523	46	for	for	ADP
ejpam-6536	523	47	which	which	PRON
ejpam-6536	523	48	c	c	PROPN
ejpam-6536	523	49	⊆	⊆	NUM
ejpam-6536	523	50	v	v	NOUN
ejpam-6536	523	51	(	(	PUNCT
ejpam-6536	523	52	g[h	g[h	PROPN
ejpam-6536	523	53	]	]	PUNCT
ejpam-6536	523	54	)	)	PUNCT
ejpam-6536	523	55	\	\	NOUN
ejpam-6536	523	56	c∗.	c∗.	NOUN
ejpam-6536	523	57	by	by	ADP
ejpam-6536	523	58	corollary	corollary	ADJ
ejpam-6536	523	59	1	1	NUM
ejpam-6536	523	60	,	,	PUNCT
ejpam-6536	523	61	s∗	s∗	PROPN
ejpam-6536	523	62	is	be	AUX
ejpam-6536	523	63	a	a	DET
ejpam-6536	523	64	ρh	ρh	NOUN
ejpam-6536	523	65	-set	-set	ADJ
ejpam-6536	523	66	of	of	ADP
ejpam-6536	523	67	g	g	PROPN
ejpam-6536	523	68	and	and	CCONJ
ejpam-6536	523	69	t	t	PROPN
ejpam-6536	523	70	∗	∗	NOUN
ejpam-6536	523	71	x	x	PUNCT
ejpam-6536	523	72	is	be	AUX
ejpam-6536	523	73	a	a	DET
ejpam-6536	523	74	pnd	pnd	NOUN
ejpam-6536	523	75	-	-	PUNCT
ejpam-6536	523	76	set	set	NOUN
ejpam-6536	523	77	of	of	ADP
ejpam-6536	523	78	h	h	NOUN
ejpam-6536	523	79	for	for	ADP
ejpam-6536	523	80	each	each	DET
ejpam-6536	523	81	x	x	PROPN
ejpam-6536	523	82	∈	∈	PROPN
ejpam-6536	523	83	s∗	s∗	PROPN
ejpam-6536	523	84	\	\	PROPN
ejpam-6536	523	85	ng(s∗	ng(s∗	PROPN
ejpam-6536	523	86	,	,	PUNCT
ejpam-6536	523	87	2	2	NUM
ejpam-6536	523	88	)	)	PUNCT
ejpam-6536	523	89	.	.	PUNCT
ejpam-6536	524	1	let	let	VERB
ejpam-6536	524	2	x	x	X
ejpam-6536	524	3	∈	∈	PROPN
ejpam-6536	524	4	(	(	PUNCT
ejpam-6536	524	5	s	s	X
ejpam-6536	524	6	∩	∩	NOUN
ejpam-6536	524	7	s∗	s∗	PROPN
ejpam-6536	524	8	)	)	PUNCT
ejpam-6536	524	9	\	\	PROPN
ejpam-6536	524	10	ng(s∗	ng(s∗	PROPN
ejpam-6536	524	11	,	,	PUNCT
ejpam-6536	524	12	2	2	NUM
ejpam-6536	524	13	)	)	PUNCT
ejpam-6536	524	14	.	.	PUNCT
ejpam-6536	525	1	because	because	SCONJ
ejpam-6536	525	2	c	c	PROPN
ejpam-6536	525	3	∩	∩	ADJ
ejpam-6536	525	4	c∗	c∗	NOUN
ejpam-6536	525	5	=	=	SYM
ejpam-6536	525	6	∅	∅	NOUN
ejpam-6536	525	7	,	,	PUNCT
ejpam-6536	525	8	t	t	PROPN
ejpam-6536	525	9	∗	∗	NOUN
ejpam-6536	525	10	x	x	X
ejpam-6536	525	11	⊆	⊆	NUM
ejpam-6536	525	12	v	v	ADP
ejpam-6536	525	13	(	(	PUNCT
ejpam-6536	525	14	h	h	NOUN
ejpam-6536	525	15	)	)	PUNCT
ejpam-6536	525	16	\	\	PROPN
ejpam-6536	525	17	tx	tx	PROPN
ejpam-6536	525	18	.	.	PUNCT
ejpam-6536	526	1	more	more	ADV
ejpam-6536	526	2	particularly	particularly	ADV
ejpam-6536	526	3	,	,	PUNCT
ejpam-6536	526	4	if	if	SCONJ
ejpam-6536	526	5	x	x	SYM
ejpam-6536	526	6	∈	∈	PROPN
ejpam-6536	526	7	(	(	PUNCT
ejpam-6536	526	8	s	s	X
ejpam-6536	526	9	∩	∩	NOUN
ejpam-6536	526	10	s∗	s∗	PROPN
ejpam-6536	526	11	)	)	PUNCT
ejpam-6536	526	12	\	\	PUNCT
ejpam-6536	526	13	(	(	PUNCT
ejpam-6536	526	14	ng(s	ng(s	NUM
ejpam-6536	526	15	,	,	PUNCT
ejpam-6536	526	16	2	2	X
ejpam-6536	526	17	)	)	PUNCT
ejpam-6536	526	18	∪	∪	X
ejpam-6536	526	19	ng(s∗	ng(s∗	NUM
ejpam-6536	526	20	,	,	PUNCT
ejpam-6536	526	21	2	2	NUM
ejpam-6536	526	22	)	)	PUNCT
ejpam-6536	526	23	)	)	PUNCT
ejpam-6536	526	24	,	,	PUNCT
ejpam-6536	526	25	then	then	ADV
ejpam-6536	526	26	tx	tx	PROPN
ejpam-6536	526	27	is	be	AUX
ejpam-6536	526	28	a	a	DET
ejpam-6536	526	29	point	point	NOUN
ejpam-6536	526	30	-	-	PUNCT
ejpam-6536	526	31	wise	wise	ADJ
ejpam-6536	526	32	non	non	ADJ
ejpam-6536	526	33	-	-	ADJ
ejpam-6536	526	34	dominating	dominating	ADJ
ejpam-6536	526	35	set	set	NOUN
ejpam-6536	526	36	of	of	ADP
ejpam-6536	526	37	h.	h.	PROPN
ejpam-6536	526	38	further	far	ADV
ejpam-6536	526	39	,	,	PUNCT
ejpam-6536	526	40	since	since	SCONJ
ejpam-6536	526	41	tx	tx	PROPN
ejpam-6536	526	42	⊆	⊆	NUM
ejpam-6536	526	43	v	v	NOUN
ejpam-6536	526	44	(	(	PUNCT
ejpam-6536	526	45	h	h	NOUN
ejpam-6536	526	46	)	)	PUNCT
ejpam-6536	526	47	\	\	PROPN
ejpam-6536	526	48	t	t	PROPN
ejpam-6536	526	49	∗	∗	NOUN
ejpam-6536	526	50	x	x	X
ejpam-6536	526	51	,	,	PUNCT
ejpam-6536	526	52	tx	tx	PROPN
ejpam-6536	526	53	is	be	AUX
ejpam-6536	526	54	an	an	DET
ejpam-6536	526	55	inverse	inverse	NOUN
ejpam-6536	526	56	point	point	NOUN
ejpam-6536	526	57	-	-	PUNCT
ejpam-6536	526	58	wise	wise	ADJ
ejpam-6536	526	59	non	non	ADJ
ejpam-6536	526	60	-	-	ADJ
ejpam-6536	526	61	dominating	dominating	ADJ
ejpam-6536	526	62	set	set	NOUN
ejpam-6536	526	63	of	of	ADP
ejpam-6536	526	64	h.	h.	PROPN
ejpam-6536	526	65	this	this	PRON
ejpam-6536	526	66	proves	prove	VERB
ejpam-6536	526	67	(	(	PUNCT
ejpam-6536	526	68	iii	iii	NOUN
ejpam-6536	526	69	)	)	PUNCT
ejpam-6536	526	70	.	.	PUNCT
ejpam-6536	527	1	conversely	conversely	ADV
ejpam-6536	527	2	,	,	PUNCT
ejpam-6536	527	3	suppose	suppose	VERB
ejpam-6536	527	4	that	that	SCONJ
ejpam-6536	527	5	c	c	PROPN
ejpam-6536	527	6	satisfies	satisfy	VERB
ejpam-6536	527	7	all	all	DET
ejpam-6536	527	8	conditions	condition	NOUN
ejpam-6536	527	9	(	(	PUNCT
ejpam-6536	527	10	i	i	NOUN
ejpam-6536	527	11	)	)	PUNCT
ejpam-6536	527	12	,	,	PUNCT
ejpam-6536	527	13	(	(	PUNCT
ejpam-6536	527	14	ii	ii	NOUN
ejpam-6536	527	15	)	)	PUNCT
ejpam-6536	527	16	and	and	CCONJ
ejpam-6536	527	17	(	(	PUNCT
ejpam-6536	527	18	iii	iii	NOUN
ejpam-6536	527	19	)	)	PUNCT
ejpam-6536	527	20	.	.	PUNCT
ejpam-6536	528	1	then	then	ADV
ejpam-6536	528	2	,	,	PUNCT
ejpam-6536	528	3	by	by	ADP
ejpam-6536	528	4	theorem	theorem	NOUN
ejpam-6536	528	5	4	4	NUM
ejpam-6536	528	6	,	,	PUNCT
ejpam-6536	528	7	c	c	PROPN
ejpam-6536	528	8	is	be	AUX
ejpam-6536	528	9	a	a	DET
ejpam-6536	528	10	hop	hop	NOUN
ejpam-6536	528	11	dominating	dominating	NOUN
ejpam-6536	528	12	set	set	NOUN
ejpam-6536	528	13	of	of	ADP
ejpam-6536	528	14	g[h	g[h	NOUN
ejpam-6536	528	15	]	]	PUNCT
ejpam-6536	528	16	.	.	PUNCT
ejpam-6536	529	1	we	we	PRON
ejpam-6536	529	2	construct	construct	VERB
ejpam-6536	529	3	a	a	DET
ejpam-6536	529	4	γh	γh	ADV
ejpam-6536	529	5	-	-	PUNCT
ejpam-6536	529	6	set	set	VERB
ejpam-6536	529	7	c∗	c∗	NOUN
ejpam-6536	529	8	=	=	SYM
ejpam-6536	529	9	∪x∈s∗	∪x∈s∗	PROPN
ejpam-6536	529	10	(	(	PUNCT
ejpam-6536	529	11	{	{	PUNCT
ejpam-6536	529	12	x	x	NOUN
ejpam-6536	529	13	}	}	PUNCT
ejpam-6536	529	14	×	×	PROPN
ejpam-6536	529	15	t	t	PROPN
ejpam-6536	529	16	∗	∗	NOUN
ejpam-6536	529	17	x	x	PUNCT
ejpam-6536	529	18	)	)	PUNCT
ejpam-6536	529	19	for	for	ADP
ejpam-6536	529	20	which	which	PRON
ejpam-6536	529	21	c	c	NOUN
ejpam-6536	529	22	⊆	⊆	NUM
ejpam-6536	529	23	v	v	NOUN
ejpam-6536	529	24	(	(	PUNCT
ejpam-6536	529	25	g[h	g[h	PROPN
ejpam-6536	529	26	]	]	PUNCT
ejpam-6536	529	27	)	)	PUNCT
ejpam-6536	529	28	\	\	PROPN
ejpam-6536	529	29	c∗	c∗	PROPN
ejpam-6536	529	30	as	as	SCONJ
ejpam-6536	529	31	follows	follow	VERB
ejpam-6536	529	32	:	:	PUNCT
ejpam-6536	529	33	let	let	VERB
ejpam-6536	529	34	x	x	X
ejpam-6536	529	35	∈	∈	PROPN
ejpam-6536	529	36	s∗.	s∗.	ADJ
ejpam-6536	529	37	case	case	NOUN
ejpam-6536	529	38	1	1	NUM
ejpam-6536	529	39	:	:	PUNCT
ejpam-6536	529	40	suppose	suppose	VERB
ejpam-6536	529	41	that	that	SCONJ
ejpam-6536	529	42	x	x	PROPN
ejpam-6536	529	43	∈	∈	PROPN
ejpam-6536	529	44	s.	s.	PROPN
ejpam-6536	529	45	if	if	SCONJ
ejpam-6536	529	46	x	x	PROPN
ejpam-6536	529	47	∈	∈	PROPN
ejpam-6536	529	48	ng(s∗	ng(s∗	NOUN
ejpam-6536	529	49	,	,	PUNCT
ejpam-6536	529	50	2	2	NUM
ejpam-6536	529	51	)	)	PUNCT
ejpam-6536	529	52	,	,	PUNCT
ejpam-6536	529	53	then	then	ADV
ejpam-6536	529	54	we	we	PRON
ejpam-6536	529	55	take	take	VERB
ejpam-6536	529	56	t	t	PROPN
ejpam-6536	529	57	∗	∗	NOUN
ejpam-6536	529	58	x	x	X
ejpam-6536	529	59	=	=	SYM
ejpam-6536	529	60	{	{	PUNCT
ejpam-6536	529	61	y	y	NOUN
ejpam-6536	529	62	}	}	PUNCT
ejpam-6536	529	63	,	,	PUNCT
ejpam-6536	529	64	where	where	SCONJ
ejpam-6536	529	65	y	y	PROPN
ejpam-6536	529	66	∈	∈	PROPN
ejpam-6536	529	67	v	v	PROPN
ejpam-6536	529	68	(	(	PUNCT
ejpam-6536	529	69	h)\tx	h)\tx	PROPN
ejpam-6536	529	70	.	.	NOUN
ejpam-6536	530	1	if	if	SCONJ
ejpam-6536	530	2	x	x	X
ejpam-6536	530	3	/∈	/∈	SYM
ejpam-6536	530	4	ng(s∗	ng(s∗	PROPN
ejpam-6536	530	5	,	,	PUNCT
ejpam-6536	530	6	2	2	NUM
ejpam-6536	530	7	)	)	PUNCT
ejpam-6536	530	8	,	,	PUNCT
ejpam-6536	530	9	then	then	ADV
ejpam-6536	530	10	as	as	SCONJ
ejpam-6536	530	11	provided	provide	VERB
ejpam-6536	530	12	by	by	ADP
ejpam-6536	530	13	condition	condition	NOUN
ejpam-6536	530	14	(	(	PUNCT
ejpam-6536	530	15	iii	iii	NOUN
ejpam-6536	530	16	)	)	PUNCT
ejpam-6536	530	17	,	,	PUNCT
ejpam-6536	530	18	we	we	PRON
ejpam-6536	530	19	take	take	VERB
ejpam-6536	530	20	a	a	DET
ejpam-6536	530	21	pnd	pnd	NOUN
ejpam-6536	530	22	-	-	PUNCT
ejpam-6536	530	23	set	set	VERB
ejpam-6536	530	24	t	t	NOUN
ejpam-6536	530	25	∗	∗	NOUN
ejpam-6536	530	26	x	x	PUNCT
ejpam-6536	530	27	of	of	ADP
ejpam-6536	530	28	h	h	NOUN
ejpam-6536	530	29	with	with	ADP
ejpam-6536	530	30	which	which	PRON
ejpam-6536	530	31	tx	tx	ADP
ejpam-6536	530	32	⊆	⊆	NUM
ejpam-6536	530	33	v	v	NOUN
ejpam-6536	530	34	(	(	PUNCT
ejpam-6536	530	35	h	h	NOUN
ejpam-6536	530	36	)	)	PUNCT
ejpam-6536	530	37	\	\	PROPN
ejpam-6536	530	38	t	t	PROPN
ejpam-6536	530	39	∗	∗	NOUN
ejpam-6536	530	40	x	x	PUNCT
ejpam-6536	530	41	.	.	PUNCT
ejpam-6536	531	1	case	case	NOUN
ejpam-6536	531	2	2	2	NUM
ejpam-6536	531	3	:	:	PUNCT
ejpam-6536	531	4	suppose	suppose	VERB
ejpam-6536	531	5	that	that	SCONJ
ejpam-6536	531	6	x	x	PROPN
ejpam-6536	531	7	/∈	/∈	PROPN
ejpam-6536	531	8	s.	s.	PROPN
ejpam-6536	532	1	if	if	SCONJ
ejpam-6536	532	2	x	x	PROPN
ejpam-6536	532	3	∈	∈	PROPN
ejpam-6536	532	4	ng(s∗	ng(s∗	NOUN
ejpam-6536	532	5	,	,	PUNCT
ejpam-6536	532	6	2	2	NUM
ejpam-6536	532	7	)	)	PUNCT
ejpam-6536	532	8	,	,	PUNCT
ejpam-6536	532	9	then	then	ADV
ejpam-6536	532	10	choose	choose	VERB
ejpam-6536	532	11	t	t	PROPN
ejpam-6536	532	12	∗	∗	NOUN
ejpam-6536	532	13	x	x	PUNCT
ejpam-6536	533	1	=	=	PRON
ejpam-6536	533	2	{	{	PUNCT
ejpam-6536	533	3	y	y	NOUN
ejpam-6536	533	4	}	}	PUNCT
ejpam-6536	533	5	for	for	ADP
ejpam-6536	533	6	any	any	DET
ejpam-6536	533	7	y	y	PROPN
ejpam-6536	533	8	∈	∈	PROPN
ejpam-6536	533	9	v	v	PROPN
ejpam-6536	533	10	(	(	PUNCT
ejpam-6536	533	11	h	h	NOUN
ejpam-6536	533	12	)	)	PUNCT
ejpam-6536	533	13	.	.	PUNCT
ejpam-6536	534	1	if	if	SCONJ
ejpam-6536	534	2	x	x	X
ejpam-6536	534	3	/∈	/∈	SYM
ejpam-6536	534	4	ng(s∗	ng(s∗	PROPN
ejpam-6536	534	5	,	,	PUNCT
ejpam-6536	534	6	2	2	NUM
ejpam-6536	534	7	)	)	PUNCT
ejpam-6536	534	8	,	,	PUNCT
ejpam-6536	534	9	then	then	ADV
ejpam-6536	534	10	we	we	PRON
ejpam-6536	534	11	choose	choose	VERB
ejpam-6536	534	12	any	any	DET
ejpam-6536	534	13	pnd	pnd	NOUN
ejpam-6536	534	14	-	-	PUNCT
ejpam-6536	534	15	set	set	VERB
ejpam-6536	534	16	t	t	NOUN
ejpam-6536	534	17	∗	∗	NOUN
ejpam-6536	534	18	x	x	PUNCT
ejpam-6536	534	19	of	of	ADP
ejpam-6536	534	20	h.	h.	PROPN
ejpam-6536	534	21	v.	v.	ADP
ejpam-6536	534	22	a	a	DET
ejpam-6536	534	23	besana	besana	PROPN
ejpam-6536	534	24	,	,	PUNCT
ejpam-6536	534	25	f.	f.	PROPN
ejpam-6536	534	26	jamil	jamil	PROPN
ejpam-6536	534	27	,	,	PUNCT
ejpam-6536	534	28	s.	s.	PROPN
ejpam-6536	534	29	canoy	canoy	PROPN
ejpam-6536	534	30	jr	jr	PROPN
ejpam-6536	534	31	.	.	PROPN
ejpam-6536	534	32	/	/	SYM
ejpam-6536	534	33	eur	eur	PROPN
ejpam-6536	534	34	.	.	PUNCT
ejpam-6536	535	1	j.	j.	PROPN
ejpam-6536	535	2	pure	pure	PROPN
ejpam-6536	535	3	appl	appl	PROPN
ejpam-6536	535	4	.	.	PROPN
ejpam-6536	535	5	math	math	PROPN
ejpam-6536	535	6	,	,	PUNCT
ejpam-6536	535	7	18	18	NUM
ejpam-6536	535	8	(	(	PUNCT
ejpam-6536	535	9	3	3	NUM
ejpam-6536	535	10	)	)	PUNCT
ejpam-6536	535	11	(	(	PUNCT
ejpam-6536	535	12	2025	2025	NUM
ejpam-6536	535	13	)	)	PUNCT
ejpam-6536	535	14	,	,	PUNCT
ejpam-6536	535	15	6536	6536	NUM
ejpam-6536	535	16	14	14	NUM
ejpam-6536	535	17	of	of	ADP
ejpam-6536	535	18	17	17	NUM
ejpam-6536	535	19	define	define	VERB
ejpam-6536	535	20	c∗	c∗	PROPN
ejpam-6536	535	21	=	=	SYM
ejpam-6536	535	22	∪x∈s∗	∪x∈s∗	PROPN
ejpam-6536	535	23	(	(	PUNCT
ejpam-6536	535	24	{	{	PUNCT
ejpam-6536	535	25	x	x	NOUN
ejpam-6536	535	26	}	}	PUNCT
ejpam-6536	535	27	×	×	PROPN
ejpam-6536	535	28	t	t	NOUN
ejpam-6536	535	29	∗	∗	NOUN
ejpam-6536	535	30	x	x	PUNCT
ejpam-6536	535	31	)	)	PUNCT
ejpam-6536	535	32	.	.	PUNCT
ejpam-6536	536	1	then	then	ADV
ejpam-6536	536	2	c∗	c∗	PROPN
ejpam-6536	536	3	is	be	AUX
ejpam-6536	536	4	a	a	DET
ejpam-6536	536	5	hop	hop	NOUN
ejpam-6536	536	6	dominating	dominating	NOUN
ejpam-6536	536	7	set	set	NOUN
ejpam-6536	536	8	of	of	ADP
ejpam-6536	536	9	g[h	g[h	PROPN
ejpam-6536	536	10	]	]	PUNCT
ejpam-6536	536	11	by	by	ADP
ejpam-6536	536	12	theorem	theorem	NOUN
ejpam-6536	536	13	4	4	NUM
ejpam-6536	536	14	.	.	PUNCT
ejpam-6536	537	1	moreover	moreover	ADV
ejpam-6536	537	2	,	,	PUNCT
ejpam-6536	537	3	c	c	PROPN
ejpam-6536	537	4	∩	∩	ADJ
ejpam-6536	537	5	c∗	c∗	NOUN
ejpam-6536	537	6	=	=	SYM
ejpam-6536	537	7	∅	∅	NOUN
ejpam-6536	537	8	and	and	CCONJ
ejpam-6536	537	9	|c∗|	|c∗|	VERB
ejpam-6536	537	10	=	=	SYM
ejpam-6536	537	11	∑	∑	PUNCT
ejpam-6536	537	12	x∈s∗∩ng(s∗,2	x∈s∗∩ng(s∗,2	PROPN
ejpam-6536	537	13	)	)	PUNCT
ejpam-6536	537	14	|t	|t	PROPN
ejpam-6536	538	1	∗	∗	NOUN
ejpam-6536	538	2	x	x	PUNCT
ejpam-6536	539	1	|	|	ADV
ejpam-6536	539	2	+	+	CCONJ
ejpam-6536	539	3	∑	∑	PROPN
ejpam-6536	539	4	x∈s∗\ng(s∗,2	x∈s∗\ng(s∗,2	PROPN
ejpam-6536	539	5	)	)	PUNCT
ejpam-6536	539	6	|t	|t	PROPN
ejpam-6536	540	1	∗	∗	NOUN
ejpam-6536	540	2	x	x	PUNCT
ejpam-6536	541	1	|	|	ADV
ejpam-6536	541	2	=	=	SYM
ejpam-6536	541	3	|s∗	|s∗	PROPN
ejpam-6536	541	4	∩	∩	NOUN
ejpam-6536	541	5	ng(s∗	ng(s∗	NUM
ejpam-6536	541	6	,	,	PUNCT
ejpam-6536	541	7	2)|	2)|	NUM
ejpam-6536	541	8	+	+	CCONJ
ejpam-6536	541	9	pnd(h)|s∗	pnd(h)|s∗	PROPN
ejpam-6536	541	10	\	\	PROPN
ejpam-6536	541	11	ng(s∗	ng(s∗	PROPN
ejpam-6536	541	12	,	,	PUNCT
ejpam-6536	541	13	2)|	2)|	NUM
ejpam-6536	541	14	=	=	SYM
ejpam-6536	541	15	ρh(g	ρh(g	NOUN
ejpam-6536	541	16	)	)	PUNCT
ejpam-6536	541	17	.	.	PUNCT
ejpam-6536	542	1	therefore	therefore	ADV
ejpam-6536	542	2	,	,	PUNCT
ejpam-6536	542	3	c	c	PROPN
ejpam-6536	542	4	is	be	AUX
ejpam-6536	542	5	an	an	DET
ejpam-6536	542	6	inverse	inverse	NOUN
ejpam-6536	542	7	hop	hop	NOUN
ejpam-6536	542	8	dominating	dominating	NOUN
ejpam-6536	542	9	set	set	NOUN
ejpam-6536	542	10	of	of	ADP
ejpam-6536	542	11	g[h	g[h	NOUN
ejpam-6536	542	12	]	]	PUNCT
ejpam-6536	542	13	.	.	PUNCT
ejpam-6536	543	1	■	■	PUNCT
ejpam-6536	543	2	corollary	corollary	ADJ
ejpam-6536	543	3	6	6	NUM
ejpam-6536	543	4	.	.	PUNCT
ejpam-6536	544	1	if	if	SCONJ
ejpam-6536	544	2	g	g	PROPN
ejpam-6536	544	3	and	and	CCONJ
ejpam-6536	544	4	h	h	NOUN
ejpam-6536	544	5	are	be	AUX
ejpam-6536	544	6	ntc	ntc	NOUN
ejpam-6536	544	7	graphs	graph	NOUN
ejpam-6536	544	8	with	with	ADP
ejpam-6536	544	9	γ(g	γ(g	PROPN
ejpam-6536	544	10	)	)	PUNCT
ejpam-6536	545	1	=	=	SYM
ejpam-6536	545	2	1	1	NUM
ejpam-6536	545	3	and	and	CCONJ
ejpam-6536	545	4	h	h	NOUN
ejpam-6536	545	5	∈	∈	PROPN
ejpam-6536	545	6	g	g	PROPN
ejpam-6536	545	7	,	,	PUNCT
ejpam-6536	545	8	then	then	ADV
ejpam-6536	545	9	γ̃h(g[h	γ̃h(g[h	PROPN
ejpam-6536	545	10	]	]	PUNCT
ejpam-6536	545	11	)	)	PUNCT
ejpam-6536	546	1	≤	≤	NUM
ejpam-6536	546	2	min{|s	min{|s	PROPN
ejpam-6536	546	3	∩	∩	NOUN
ejpam-6536	546	4	ng(s	ng(s	CCONJ
ejpam-6536	546	5	,	,	PUNCT
ejpam-6536	546	6	2)|	2)|	NUM
ejpam-6536	546	7	+	+	CCONJ
ejpam-6536	546	8	ipnd(h)|s	ipnd(h)|s	VERB
ejpam-6536	546	9	\	\	NOUN
ejpam-6536	546	10	ng(s	ng(s	PUNCT
ejpam-6536	546	11	,	,	PUNCT
ejpam-6536	546	12	2)|	2)|	NUM
ejpam-6536	546	13	:	:	PUNCT
ejpam-6536	546	14	s	s	VERB
ejpam-6536	546	15	∈	∈	NOUN
ejpam-6536	546	16	hd(g	hd(g	NOUN
ejpam-6536	546	17	)	)	PUNCT
ejpam-6536	546	18	}	}	PUNCT
ejpam-6536	546	19	.	.	PUNCT
ejpam-6536	547	1	proof	proof	NOUN
ejpam-6536	547	2	:	:	PUNCT
ejpam-6536	547	3	put	put	VERB
ejpam-6536	547	4	ρ̃h(g	ρ̃h(g	NOUN
ejpam-6536	547	5	)	)	PUNCT
ejpam-6536	548	1	=	=	SYM
ejpam-6536	548	2	min{|s	min{|s	PROPN
ejpam-6536	548	3	∩	∩	NOUN
ejpam-6536	548	4	ng(s	ng(s	CCONJ
ejpam-6536	548	5	,	,	PUNCT
ejpam-6536	548	6	2)|	2)|	NUM
ejpam-6536	548	7	+	+	CCONJ
ejpam-6536	548	8	ipnd(h)|s	ipnd(h)|s	VERB
ejpam-6536	548	9	\	\	NOUN
ejpam-6536	548	10	ng(s	ng(s	PUNCT
ejpam-6536	548	11	,	,	PUNCT
ejpam-6536	548	12	2)|	2)|	NUM
ejpam-6536	548	13	:	:	PUNCT
ejpam-6536	548	14	s	s	VERB
ejpam-6536	548	15	∈	∈	NOUN
ejpam-6536	548	16	hd(g	hd(g	NOUN
ejpam-6536	548	17	)	)	PUNCT
ejpam-6536	548	18	}	}	PUNCT
ejpam-6536	548	19	.	.	PUNCT
ejpam-6536	549	1	let	let	VERB
ejpam-6536	549	2	s	s	PRON
ejpam-6536	549	3	⊆	⊆	NUM
ejpam-6536	549	4	v	v	NOUN
ejpam-6536	549	5	(	(	PUNCT
ejpam-6536	549	6	g	g	NOUN
ejpam-6536	549	7	)	)	PUNCT
ejpam-6536	549	8	be	be	AUX
ejpam-6536	549	9	a	a	DET
ejpam-6536	549	10	ρh	ρh	NOUN
ejpam-6536	549	11	-set	-set	ADJ
ejpam-6536	549	12	of	of	ADP
ejpam-6536	549	13	g	g	PROPN
ejpam-6536	549	14	,	,	PUNCT
ejpam-6536	549	15	y	y	PROPN
ejpam-6536	549	16	∈	∈	PROPN
ejpam-6536	549	17	v	v	ADP
ejpam-6536	549	18	(	(	PUNCT
ejpam-6536	549	19	h	h	NOUN
ejpam-6536	549	20	)	)	PUNCT
ejpam-6536	549	21	and	and	CCONJ
ejpam-6536	549	22	a	a	DET
ejpam-6536	549	23	⊆	⊆	NUM
ejpam-6536	549	24	v	v	NOUN
ejpam-6536	549	25	(	(	PUNCT
ejpam-6536	549	26	h	h	NOUN
ejpam-6536	549	27	)	)	PUNCT
ejpam-6536	549	28	an	an	DET
ejpam-6536	549	29	inverse	inverse	NOUN
ejpam-6536	549	30	point	point	NOUN
ejpam-6536	549	31	-	-	PUNCT
ejpam-6536	549	32	wise	wise	ADJ
ejpam-6536	549	33	non	non	ADJ
ejpam-6536	549	34	-	-	ADJ
ejpam-6536	549	35	dominating	dominating	ADJ
ejpam-6536	549	36	sets	set	NOUN
ejpam-6536	549	37	of	of	ADP
ejpam-6536	549	38	h.	h.	NOUN
ejpam-6536	549	39	define	define	VERB
ejpam-6536	549	40	c	c	PROPN
ejpam-6536	549	41	=	=	SYM
ejpam-6536	549	42	∪x∈s	∪x∈s	PROPN
ejpam-6536	549	43	(	(	PUNCT
ejpam-6536	549	44	{	{	PUNCT
ejpam-6536	549	45	x	x	NOUN
ejpam-6536	549	46	}	}	PUNCT
ejpam-6536	549	47	×	×	PROPN
ejpam-6536	549	48	tx	tx	PROPN
ejpam-6536	549	49	)	)	PUNCT
ejpam-6536	549	50	,	,	PUNCT
ejpam-6536	549	51	where	where	SCONJ
ejpam-6536	549	52	tx	tx	VERB
ejpam-6536	549	53	=	=	PUNCT
ejpam-6536	549	54	{	{	PUNCT
ejpam-6536	549	55	y	y	NOUN
ejpam-6536	549	56	}	}	PUNCT
ejpam-6536	549	57	for	for	ADP
ejpam-6536	549	58	all	all	DET
ejpam-6536	549	59	x	x	SYM
ejpam-6536	549	60	∈	∈	NOUN
ejpam-6536	549	61	s	s	PART
ejpam-6536	549	62	∩	∩	NOUN
ejpam-6536	549	63	ng(s	ng(s	CCONJ
ejpam-6536	549	64	,	,	PUNCT
ejpam-6536	549	65	2	2	NUM
ejpam-6536	549	66	)	)	PUNCT
ejpam-6536	549	67	and	and	CCONJ
ejpam-6536	549	68	tx	tx	VERB
ejpam-6536	549	69	=	=	PUNCT
ejpam-6536	549	70	a	a	PRON
ejpam-6536	549	71	for	for	ADP
ejpam-6536	549	72	all	all	DET
ejpam-6536	549	73	x	x	PART
ejpam-6536	549	74	∈	∈	PROPN
ejpam-6536	549	75	s	s	PART
ejpam-6536	549	76	\	\	NOUN
ejpam-6536	549	77	ng(s	ng(s	PUNCT
ejpam-6536	549	78	,	,	PUNCT
ejpam-6536	549	79	2	2	NUM
ejpam-6536	549	80	)	)	PUNCT
ejpam-6536	549	81	.	.	PUNCT
ejpam-6536	550	1	by	by	ADP
ejpam-6536	550	2	theorem	theorem	NOUN
ejpam-6536	550	3	10	10	NUM
ejpam-6536	550	4	,	,	PUNCT
ejpam-6536	550	5	c	c	PROPN
ejpam-6536	550	6	is	be	AUX
ejpam-6536	550	7	an	an	DET
ejpam-6536	550	8	inverse	inverse	NOUN
ejpam-6536	550	9	hop	hop	NOUN
ejpam-6536	550	10	dominating	dominating	NOUN
ejpam-6536	550	11	set	set	NOUN
ejpam-6536	550	12	of	of	ADP
ejpam-6536	550	13	g[h	g[h	PROPN
ejpam-6536	550	14	]	]	PUNCT
ejpam-6536	550	15	.	.	PUNCT
ejpam-6536	551	1	thus	thus	ADV
ejpam-6536	551	2	,	,	PUNCT
ejpam-6536	551	3	γ̃h(g[h	γ̃h(g[h	NOUN
ejpam-6536	551	4	]	]	PUNCT
ejpam-6536	551	5	)	)	PUNCT
ejpam-6536	551	6	≤	≤	NUM
ejpam-6536	551	7	|c|	|c|	PROPN
ejpam-6536	551	8	=	=	SYM
ejpam-6536	551	9	|s	|s	PROPN
ejpam-6536	551	10	∩	∩	NOUN
ejpam-6536	551	11	ng(s	ng(s	CCONJ
ejpam-6536	551	12	,	,	PUNCT
ejpam-6536	551	13	2)|	2)|	NUM
ejpam-6536	551	14	+	+	CCONJ
ejpam-6536	551	15	ipnd(h)|s	ipnd(h)|s	VERB
ejpam-6536	551	16	\	\	NOUN
ejpam-6536	551	17	ng(s	ng(s	NUM
ejpam-6536	551	18	,	,	PUNCT
ejpam-6536	551	19	2)|	2)|	NUM
ejpam-6536	551	20	.	.	PUNCT
ejpam-6536	552	1	since	since	SCONJ
ejpam-6536	552	2	s	s	NOUN
ejpam-6536	552	3	is	be	AUX
ejpam-6536	552	4	arbitrary	arbitrary	ADJ
ejpam-6536	552	5	,	,	PUNCT
ejpam-6536	552	6	γ̃h(g[h	γ̃h(g[h	NOUN
ejpam-6536	552	7	]	]	PUNCT
ejpam-6536	552	8	)	)	PUNCT
ejpam-6536	552	9	≤	≤	ADV
ejpam-6536	552	10	ρ̃h(g	ρ̃h(g	NOUN
ejpam-6536	552	11	)	)	PUNCT
ejpam-6536	552	12	.	.	PUNCT
ejpam-6536	553	1	■	■	PUNCT
ejpam-6536	553	2	corollary	corollary	ADJ
ejpam-6536	553	3	7	7	NUM
ejpam-6536	553	4	.	.	PUNCT
ejpam-6536	554	1	for	for	ADP
ejpam-6536	554	2	all	all	DET
ejpam-6536	554	3	h	h	NOUN
ejpam-6536	554	4	∈	∈	PROPN
ejpam-6536	554	5	g	g	PROPN
ejpam-6536	554	6	and	and	CCONJ
ejpam-6536	554	7	m	m	PROPN
ejpam-6536	554	8	≥	≥	NOUN
ejpam-6536	554	9	2	2	NUM
ejpam-6536	554	10	,	,	PUNCT
ejpam-6536	554	11	γ̃h(km[h	γ̃h(km[h	X
ejpam-6536	554	12	]	]	PUNCT
ejpam-6536	554	13	)	)	PUNCT
ejpam-6536	554	14	=	=	PUNCT
ejpam-6536	554	15	m	m	PUNCT
ejpam-6536	554	16	·	·	PUNCT
ejpam-6536	554	17	ipnd(h	ipnd(h	NOUN
ejpam-6536	554	18	)	)	PUNCT
ejpam-6536	554	19	.	.	PUNCT
ejpam-6536	555	1	proof	proof	NOUN
ejpam-6536	555	2	:	:	PUNCT
ejpam-6536	555	3	note	note	VERB
ejpam-6536	555	4	first	first	ADV
ejpam-6536	555	5	that	that	PRON
ejpam-6536	555	6	s	s	VERB
ejpam-6536	555	7	=	=	X
ejpam-6536	555	8	v	v	PROPN
ejpam-6536	555	9	(	(	PUNCT
ejpam-6536	555	10	km	km	PROPN
ejpam-6536	555	11	)	)	PUNCT
ejpam-6536	555	12	is	be	AUX
ejpam-6536	555	13	the	the	DET
ejpam-6536	555	14	unique	unique	ADJ
ejpam-6536	555	15	hop	hop	NOUN
ejpam-6536	555	16	dominating	dominating	NOUN
ejpam-6536	555	17	set	set	NOUN
ejpam-6536	555	18	of	of	ADP
ejpam-6536	555	19	km	km	PROPN
ejpam-6536	555	20	and	and	CCONJ
ejpam-6536	555	21	nkm(s	nkm(s	PROPN
ejpam-6536	555	22	,	,	PUNCT
ejpam-6536	555	23	2	2	NUM
ejpam-6536	555	24	)	)	PUNCT
ejpam-6536	555	25	=	=	NOUN
ejpam-6536	555	26	∅.	∅.	ADP
ejpam-6536	555	27	thus	thus	ADV
ejpam-6536	555	28	,	,	PUNCT
ejpam-6536	555	29	corollary	corollary	ADJ
ejpam-6536	555	30	6	6	NUM
ejpam-6536	555	31	yields	yield	NOUN
ejpam-6536	555	32	γh(km[h	γh(km[h	ADP
ejpam-6536	555	33	]	]	SYM
ejpam-6536	555	34	)	)	PUNCT
ejpam-6536	555	35	≤	≤	NUM
ejpam-6536	556	1	m	m	VERB
ejpam-6536	556	2	·	·	PUNCT
ejpam-6536	556	3	ipnd(h	ipnd(h	NOUN
ejpam-6536	556	4	)	)	PUNCT
ejpam-6536	556	5	.	.	PUNCT
ejpam-6536	557	1	now	now	ADV
ejpam-6536	557	2	,	,	PUNCT
ejpam-6536	557	3	let	let	VERB
ejpam-6536	557	4	c	c	PROPN
ejpam-6536	557	5	⊆	⊆	NUM
ejpam-6536	557	6	v	v	NOUN
ejpam-6536	557	7	(	(	PUNCT
ejpam-6536	557	8	km	km	NOUN
ejpam-6536	557	9	)	)	PUNCT
ejpam-6536	557	10	be	be	VERB
ejpam-6536	557	11	a	a	DET
ejpam-6536	557	12	γ̃h	γ̃h	NOUN
ejpam-6536	557	13	-	-	PUNCT
ejpam-6536	557	14	set	set	NOUN
ejpam-6536	557	15	of	of	ADP
ejpam-6536	557	16	km[h	km[h	PROPN
ejpam-6536	557	17	]	]	PUNCT
ejpam-6536	557	18	.	.	PUNCT
ejpam-6536	558	1	by	by	ADP
ejpam-6536	558	2	theorem	theorem	NOUN
ejpam-6536	558	3	10	10	NUM
ejpam-6536	558	4	,	,	PUNCT
ejpam-6536	558	5	c	c	NOUN
ejpam-6536	558	6	=	=	SYM
ejpam-6536	558	7	∪x∈v	∪x∈v	PROPN
ejpam-6536	558	8	(	(	PUNCT
ejpam-6536	558	9	km	km	PROPN
ejpam-6536	558	10	)	)	PUNCT
ejpam-6536	558	11	(	(	PUNCT
ejpam-6536	558	12	{	{	PUNCT
ejpam-6536	558	13	x	x	NOUN
ejpam-6536	558	14	}	}	PUNCT
ejpam-6536	558	15	×	×	PROPN
ejpam-6536	558	16	tx	tx	PROPN
ejpam-6536	558	17	)	)	PUNCT
ejpam-6536	558	18	,	,	PUNCT
ejpam-6536	558	19	where	where	SCONJ
ejpam-6536	558	20	tx	tx	PROPN
ejpam-6536	558	21	⊆	⊆	NUM
ejpam-6536	558	22	v	v	NOUN
ejpam-6536	558	23	(	(	PUNCT
ejpam-6536	558	24	h	h	NOUN
ejpam-6536	558	25	)	)	PUNCT
ejpam-6536	558	26	is	be	AUX
ejpam-6536	558	27	an	an	DET
ejpam-6536	558	28	inverse	inverse	NOUN
ejpam-6536	558	29	point	point	NOUN
ejpam-6536	558	30	-	-	PUNCT
ejpam-6536	558	31	wise	wise	ADJ
ejpam-6536	558	32	non	non	ADJ
ejpam-6536	558	33	-	-	ADJ
ejpam-6536	558	34	dominating	dominating	ADJ
ejpam-6536	558	35	set	set	NOUN
ejpam-6536	558	36	of	of	ADP
ejpam-6536	558	37	h	h	NOUN
ejpam-6536	558	38	for	for	ADP
ejpam-6536	558	39	each	each	DET
ejpam-6536	558	40	x	x	SYM
ejpam-6536	558	41	∈	∈	PROPN
ejpam-6536	558	42	v	v	NOUN
ejpam-6536	558	43	(	(	PUNCT
ejpam-6536	558	44	km	km	PROPN
ejpam-6536	558	45	)	)	PUNCT
ejpam-6536	558	46	.	.	PUNCT
ejpam-6536	559	1	thus	thus	ADV
ejpam-6536	559	2	,	,	PUNCT
ejpam-6536	559	3	γ̃h(km[h	γ̃h(km[h	X
ejpam-6536	559	4	]	]	PUNCT
ejpam-6536	559	5	)	)	PUNCT
ejpam-6536	559	6	=	=	PUNCT
ejpam-6536	559	7	∑	∑	PUNCT
ejpam-6536	559	8	x∈v	x∈v	PROPN
ejpam-6536	559	9	(	(	PUNCT
ejpam-6536	559	10	km	km	NOUN
ejpam-6536	559	11	)	)	PUNCT
ejpam-6536	559	12	|tx|	|tx|	PROPN
ejpam-6536	559	13	≥	≥	NUM
ejpam-6536	559	14	m	m	PROPN
ejpam-6536	559	15	·	·	PUNCT
ejpam-6536	559	16	ipnd(h	ipnd(h	NOUN
ejpam-6536	559	17	)	)	PUNCT
ejpam-6536	559	18	.	.	PUNCT
ejpam-6536	560	1	■	■	PUNCT
ejpam-6536	560	2	equality	equality	NOUN
ejpam-6536	560	3	in	in	ADP
ejpam-6536	560	4	corollary	corollary	ADJ
ejpam-6536	560	5	6	6	NUM
ejpam-6536	560	6	can	can	AUX
ejpam-6536	560	7	be	be	AUX
ejpam-6536	560	8	attained	attain	VERB
ejpam-6536	560	9	even	even	ADV
ejpam-6536	560	10	with	with	ADP
ejpam-6536	560	11	a	a	DET
ejpam-6536	560	12	noncomplete	noncomplete	ADJ
ejpam-6536	560	13	g.	g.	NOUN
ejpam-6536	560	14	consider	consider	VERB
ejpam-6536	560	15	,	,	PUNCT
ejpam-6536	560	16	for	for	ADP
ejpam-6536	560	17	example	example	NOUN
ejpam-6536	560	18	,	,	PUNCT
ejpam-6536	560	19	g	g	PROPN
ejpam-6536	560	20	=	=	PROPN
ejpam-6536	560	21	p3	p3	PROPN
ejpam-6536	560	22	=	=	PUNCT
ejpam-6536	561	1	[	[	X
ejpam-6536	561	2	x1	x1	PROPN
ejpam-6536	561	3	,	,	PUNCT
ejpam-6536	561	4	x2	x2	PROPN
ejpam-6536	561	5	,	,	PUNCT
ejpam-6536	561	6	x3	x3	ADJ
ejpam-6536	561	7	]	]	PUNCT
ejpam-6536	561	8	.	.	PUNCT
ejpam-6536	562	1	then	then	ADV
ejpam-6536	562	2	g	g	PROPN
ejpam-6536	562	3	has	have	VERB
ejpam-6536	562	4	only	only	ADV
ejpam-6536	562	5	three	three	NUM
ejpam-6536	562	6	distinct	distinct	ADJ
ejpam-6536	562	7	hop	hop	NOUN
ejpam-6536	562	8	dominating	dominating	NOUN
ejpam-6536	562	9	sets	set	NOUN
ejpam-6536	562	10	,	,	PUNCT
ejpam-6536	562	11	namely	namely	ADV
ejpam-6536	562	12	s1	s1	NOUN
ejpam-6536	562	13	=	=	SYM
ejpam-6536	562	14	{	{	PUNCT
ejpam-6536	562	15	x1	x1	PROPN
ejpam-6536	562	16	,	,	PUNCT
ejpam-6536	562	17	x2	x2	PROPN
ejpam-6536	562	18	}	}	PUNCT
ejpam-6536	562	19	,	,	PUNCT
ejpam-6536	562	20	s2	s2	NOUN
ejpam-6536	562	21	=	=	SYM
ejpam-6536	562	22	{	{	PUNCT
ejpam-6536	562	23	x2	x2	PROPN
ejpam-6536	562	24	,	,	PUNCT
ejpam-6536	562	25	x3	x3	ADJ
ejpam-6536	562	26	}	}	PUNCT
ejpam-6536	562	27	and	and	CCONJ
ejpam-6536	562	28	s3	s3	PROPN
ejpam-6536	562	29	=	=	SYM
ejpam-6536	562	30	v	v	PROPN
ejpam-6536	562	31	(	(	PUNCT
ejpam-6536	562	32	g	g	NOUN
ejpam-6536	562	33	)	)	PUNCT
ejpam-6536	562	34	.	.	PUNCT
ejpam-6536	563	1	in	in	ADP
ejpam-6536	563	2	view	view	NOUN
ejpam-6536	563	3	of	of	ADP
ejpam-6536	563	4	proposition	proposition	NOUN
ejpam-6536	563	5	2	2	NUM
ejpam-6536	563	6	,	,	PUNCT
ejpam-6536	563	7	for	for	ADP
ejpam-6536	563	8	any	any	DET
ejpam-6536	563	9	graph	graph	NOUN
ejpam-6536	563	10	h	h	NOUN
ejpam-6536	563	11	∈	∈	PROPN
ejpam-6536	563	12	g	g	PROPN
ejpam-6536	563	13	,	,	PUNCT
ejpam-6536	563	14	s3	s3	PROPN
ejpam-6536	563	15	is	be	AUX
ejpam-6536	563	16	the	the	DET
ejpam-6536	563	17	unique	unique	ADJ
ejpam-6536	563	18	ρh	ρh	NOUN
ejpam-6536	563	19	-set	-set	PUNCT
ejpam-6536	563	20	of	of	ADP
ejpam-6536	563	21	g.	g.	PROPN
ejpam-6536	563	22	thus	thus	ADV
ejpam-6536	563	23	,	,	PUNCT
ejpam-6536	563	24	γ̃h(g[h	γ̃h(g[h	PROPN
ejpam-6536	563	25	]	]	PUNCT
ejpam-6536	563	26	)	)	PUNCT
ejpam-6536	564	1	=	=	SYM
ejpam-6536	564	2	ρ̃h(g	ρ̃h(g	NOUN
ejpam-6536	564	3	)	)	PUNCT
ejpam-6536	564	4	=	=	SYM
ejpam-6536	564	5	2	2	NUM
ejpam-6536	564	6	+	+	NUM
ejpam-6536	564	7	ipnd(h	ipnd(h	PROPN
ejpam-6536	564	8	)	)	PUNCT
ejpam-6536	564	9	.	.	PUNCT
ejpam-6536	565	1	proposition	proposition	NOUN
ejpam-6536	565	2	7	7	NUM
ejpam-6536	565	3	.	.	PUNCT
ejpam-6536	566	1	let	let	VERB
ejpam-6536	566	2	g	g	NOUN
ejpam-6536	566	3	and	and	CCONJ
ejpam-6536	566	4	h	h	NOUN
ejpam-6536	566	5	be	be	AUX
ejpam-6536	566	6	ntc	ntc	NOUN
ejpam-6536	566	7	graphs	graph	NOUN
ejpam-6536	566	8	with	with	ADP
ejpam-6536	566	9	γ(g	γ(g	NOUN
ejpam-6536	566	10	)	)	PUNCT
ejpam-6536	566	11	̸=	̸=	PROPN
ejpam-6536	566	12	1	1	NUM
ejpam-6536	566	13	.	.	PUNCT
ejpam-6536	567	1	then	then	ADV
ejpam-6536	567	2	γhh(g[h	γhh(g[h	NUM
ejpam-6536	567	3	]	]	PUNCT
ejpam-6536	567	4	)	)	PUNCT
ejpam-6536	567	5	=	=	PUNCT
ejpam-6536	567	6	2γth(g	2γth(g	NOUN
ejpam-6536	567	7	)	)	PUNCT
ejpam-6536	567	8	.	.	PUNCT
ejpam-6536	568	1	v.	v.	ADP
ejpam-6536	568	2	a	a	DET
ejpam-6536	568	3	besana	besana	PROPN
ejpam-6536	568	4	,	,	PUNCT
ejpam-6536	568	5	f.	f.	PROPN
ejpam-6536	568	6	jamil	jamil	PROPN
ejpam-6536	568	7	,	,	PUNCT
ejpam-6536	568	8	s.	s.	PROPN
ejpam-6536	568	9	canoy	canoy	PROPN
ejpam-6536	568	10	jr	jr	PROPN
ejpam-6536	568	11	.	.	PROPN
ejpam-6536	568	12	/	/	SYM
ejpam-6536	568	13	eur	eur	PROPN
ejpam-6536	568	14	.	.	PUNCT
ejpam-6536	569	1	j.	j.	PROPN
ejpam-6536	569	2	pure	pure	PROPN
ejpam-6536	569	3	appl	appl	PROPN
ejpam-6536	569	4	.	.	PROPN
ejpam-6536	569	5	math	math	PROPN
ejpam-6536	569	6	,	,	PUNCT
ejpam-6536	569	7	18	18	NUM
ejpam-6536	569	8	(	(	PUNCT
ejpam-6536	569	9	3	3	NUM
ejpam-6536	569	10	)	)	PUNCT
ejpam-6536	569	11	(	(	PUNCT
ejpam-6536	569	12	2025	2025	NUM
ejpam-6536	569	13	)	)	PUNCT
ejpam-6536	569	14	,	,	PUNCT
ejpam-6536	569	15	6536	6536	NUM
ejpam-6536	569	16	15	15	NUM
ejpam-6536	569	17	of	of	ADP
ejpam-6536	569	18	17	17	NUM
ejpam-6536	569	19	proof	proof	NOUN
ejpam-6536	569	20	:	:	PUNCT
ejpam-6536	569	21	applying	apply	VERB
ejpam-6536	569	22	corollary	corollary	ADJ
ejpam-6536	569	23	1	1	NUM
ejpam-6536	569	24	and	and	CCONJ
ejpam-6536	569	25	theorem	theorem	VERB
ejpam-6536	569	26	9	9	NUM
ejpam-6536	569	27	,	,	PUNCT
ejpam-6536	569	28	we	we	PRON
ejpam-6536	569	29	have	have	AUX
ejpam-6536	569	30	2γth(g	2γth(g	NOUN
ejpam-6536	569	31	)	)	PUNCT
ejpam-6536	569	32	=	=	PUNCT
ejpam-6536	569	33	2γh(g[h	2γh(g[h	NUM
ejpam-6536	569	34	]	]	PUNCT
ejpam-6536	569	35	)	)	PUNCT
ejpam-6536	569	36	≤	≤	NUM
ejpam-6536	569	37	γhh(g[h	γhh(g[h	NUM
ejpam-6536	569	38	]	]	NOUN
ejpam-6536	569	39	)	)	PUNCT
ejpam-6536	569	40	≤	≤	NOUN
ejpam-6536	569	41	γh(g[h	γh(g[h	NOUN
ejpam-6536	569	42	]	]	X
ejpam-6536	569	43	)	)	PUNCT
ejpam-6536	570	1	+	+	CCONJ
ejpam-6536	570	2	γ̃h(g[h	γ̃h(g[h	NOUN
ejpam-6536	570	3	]	]	PUNCT
ejpam-6536	570	4	)	)	PUNCT
ejpam-6536	570	5	=	=	PUNCT
ejpam-6536	570	6	2γth(g	2γth(g	NOUN
ejpam-6536	570	7	)	)	PUNCT
ejpam-6536	570	8	.	.	PUNCT
ejpam-6536	571	1	■	■	PUNCT
ejpam-6536	571	2	the	the	DET
ejpam-6536	571	3	following	following	NOUN
ejpam-6536	571	4	follows	follow	VERB
ejpam-6536	571	5	immediately	immediately	ADV
ejpam-6536	571	6	from	from	ADP
ejpam-6536	571	7	theorem	theorem	ADJ
ejpam-6536	571	8	4	4	NUM
ejpam-6536	571	9	.	.	PUNCT
ejpam-6536	571	10	theorem	theorem	NOUN
ejpam-6536	571	11	11	11	NUM
ejpam-6536	571	12	.	.	PUNCT
ejpam-6536	572	1	let	let	VERB
ejpam-6536	572	2	g	g	NOUN
ejpam-6536	572	3	and	and	CCONJ
ejpam-6536	572	4	h	h	NOUN
ejpam-6536	572	5	be	be	AUX
ejpam-6536	572	6	ntc	ntc	NOUN
ejpam-6536	572	7	graphs	graph	NOUN
ejpam-6536	572	8	with	with	ADP
ejpam-6536	572	9	γ(g	γ(g	PROPN
ejpam-6536	572	10	)	)	PUNCT
ejpam-6536	572	11	=	=	SYM
ejpam-6536	572	12	1	1	NUM
ejpam-6536	572	13	and	and	CCONJ
ejpam-6536	572	14	h	h	NOUN
ejpam-6536	572	15	∈	∈	PROPN
ejpam-6536	572	16	g	g	PROPN
ejpam-6536	572	17	.	.	PUNCT
ejpam-6536	573	1	let	let	VERB
ejpam-6536	573	2	c	c	NOUN
ejpam-6536	573	3	=	=	SYM
ejpam-6536	573	4	∪x∈s	∪x∈s	PROPN
ejpam-6536	573	5	(	(	PUNCT
ejpam-6536	573	6	{	{	PUNCT
ejpam-6536	573	7	x	x	NOUN
ejpam-6536	573	8	}	}	PUNCT
ejpam-6536	573	9	×	×	PROPN
ejpam-6536	573	10	tx	tx	PROPN
ejpam-6536	573	11	)	)	PUNCT
ejpam-6536	573	12	,	,	PUNCT
ejpam-6536	573	13	c∗	c∗	PROPN
ejpam-6536	573	14	=	=	SYM
ejpam-6536	573	15	∪x∈s∗	∪x∈s∗	PROPN
ejpam-6536	573	16	(	(	PUNCT
ejpam-6536	573	17	{	{	PUNCT
ejpam-6536	573	18	x	x	NOUN
ejpam-6536	573	19	}	}	PUNCT
ejpam-6536	573	20	×	×	PROPN
ejpam-6536	573	21	t	t	PROPN
ejpam-6536	573	22	∗	∗	NOUN
ejpam-6536	573	23	x	x	X
ejpam-6536	573	24	)	)	PUNCT
ejpam-6536	573	25	⊆	⊆	NUM
ejpam-6536	573	26	v	v	NOUN
ejpam-6536	573	27	(	(	PUNCT
ejpam-6536	573	28	g[h	g[h	PROPN
ejpam-6536	573	29	]	]	PUNCT
ejpam-6536	573	30	)	)	PUNCT
ejpam-6536	573	31	with	with	ADP
ejpam-6536	573	32	tx	tx	PROPN
ejpam-6536	573	33	̸=	̸=	PROPN
ejpam-6536	573	34	v	v	PROPN
ejpam-6536	573	35	(	(	PUNCT
ejpam-6536	573	36	h	h	NOUN
ejpam-6536	573	37	)	)	PUNCT
ejpam-6536	573	38	for	for	ADP
ejpam-6536	573	39	x	x	PROPN
ejpam-6536	573	40	∈	∈	PROPN
ejpam-6536	573	41	s	s	PART
ejpam-6536	573	42	and	and	CCONJ
ejpam-6536	573	43	t	t	PROPN
ejpam-6536	573	44	∗	∗	NOUN
ejpam-6536	573	45	x	x	PUNCT
ejpam-6536	573	46	̸=	̸=	PROPN
ejpam-6536	573	47	v	v	NOUN
ejpam-6536	573	48	(	(	PUNCT
ejpam-6536	573	49	h	h	NOUN
ejpam-6536	573	50	)	)	PUNCT
ejpam-6536	573	51	for	for	ADP
ejpam-6536	573	52	all	all	DET
ejpam-6536	573	53	x	x	SYM
ejpam-6536	573	54	∈	∈	PRON
ejpam-6536	573	55	s∗.	s∗.	INTJ
ejpam-6536	573	56	then	then	ADV
ejpam-6536	573	57	(	(	PUNCT
ejpam-6536	573	58	c	c	X
ejpam-6536	573	59	,	,	PUNCT
ejpam-6536	573	60	c∗	c∗	ADJ
ejpam-6536	573	61	)	)	PUNCT
ejpam-6536	573	62	∈	∈	PROPN
ejpam-6536	573	63	phd(g[h	phd(g[h	NUM
ejpam-6536	573	64	]	]	PUNCT
ejpam-6536	573	65	)	)	PUNCT
ejpam-6536	574	1	if	if	SCONJ
ejpam-6536	574	2	and	and	CCONJ
ejpam-6536	574	3	only	only	ADV
ejpam-6536	574	4	if	if	SCONJ
ejpam-6536	574	5	each	each	PRON
ejpam-6536	574	6	of	of	ADP
ejpam-6536	574	7	the	the	DET
ejpam-6536	574	8	following	follow	VERB
ejpam-6536	574	9	holds	hold	VERB
ejpam-6536	574	10	:	:	PUNCT
ejpam-6536	574	11	(	(	PUNCT
ejpam-6536	574	12	i	i	NOUN
ejpam-6536	574	13	)	)	PUNCT
ejpam-6536	574	14	both	both	PRON
ejpam-6536	574	15	s	s	VERB
ejpam-6536	574	16	and	and	CCONJ
ejpam-6536	574	17	s∗	s∗	PROPN
ejpam-6536	574	18	satisfy	satisfy	VERB
ejpam-6536	574	19	the	the	DET
ejpam-6536	574	20	conditions	condition	NOUN
ejpam-6536	574	21	(	(	PUNCT
ejpam-6536	574	22	i	i	NOUN
ejpam-6536	574	23	)	)	PUNCT
ejpam-6536	574	24	and	and	CCONJ
ejpam-6536	574	25	(	(	PUNCT
ejpam-6536	574	26	ii	ii	NOUN
ejpam-6536	574	27	)	)	PUNCT
ejpam-6536	574	28	of	of	ADP
ejpam-6536	574	29	theorem	theorem	NOUN
ejpam-6536	574	30	4	4	NUM
ejpam-6536	574	31	;	;	PUNCT
ejpam-6536	574	32	and	and	CCONJ
ejpam-6536	574	33	(	(	PUNCT
ejpam-6536	574	34	ii	ii	NOUN
ejpam-6536	574	35	)	)	PUNCT
ejpam-6536	574	36	tx	tx	PROPN
ejpam-6536	574	37	∩	∩	PROPN
ejpam-6536	574	38	t	t	PROPN
ejpam-6536	574	39	∗	∗	NOUN
ejpam-6536	574	40	x	x	X
ejpam-6536	574	41	=	=	NOUN
ejpam-6536	574	42	∅	∅	NOUN
ejpam-6536	574	43	for	for	ADP
ejpam-6536	574	44	all	all	DET
ejpam-6536	574	45	x	x	PART
ejpam-6536	574	46	∈	∈	NOUN
ejpam-6536	574	47	s	s	PART
ejpam-6536	574	48	∩	∩	NOUN
ejpam-6536	574	49	s∗.	s∗.	ADJ
ejpam-6536	574	50	more	more	ADV
ejpam-6536	574	51	particularly	particularly	ADV
ejpam-6536	574	52	,	,	PUNCT
ejpam-6536	574	53	(	(	PUNCT
ejpam-6536	574	54	tx	tx	PROPN
ejpam-6536	574	55	,	,	PUNCT
ejpam-6536	574	56	t	t	PROPN
ejpam-6536	574	57	∗	∗	NOUN
ejpam-6536	574	58	x	x	X
ejpam-6536	574	59	)	)	PUNCT
ejpam-6536	574	60	∈	∈	PROPN
ejpam-6536	574	61	ppnd(h	ppnd(h	PROPN
ejpam-6536	574	62	)	)	PUNCT
ejpam-6536	574	63	for	for	ADP
ejpam-6536	574	64	all	all	DET
ejpam-6536	574	65	x	x	SYM
ejpam-6536	574	66	∈	∈	PROPN
ejpam-6536	574	67	(	(	PUNCT
ejpam-6536	574	68	s	s	X
ejpam-6536	574	69	∩	∩	NOUN
ejpam-6536	574	70	s∗	s∗	PROPN
ejpam-6536	574	71	)	)	PUNCT
ejpam-6536	574	72	\	\	PUNCT
ejpam-6536	574	73	(	(	PUNCT
ejpam-6536	574	74	ng(s	ng(s	NUM
ejpam-6536	574	75	,	,	PUNCT
ejpam-6536	574	76	2	2	X
ejpam-6536	574	77	)	)	PUNCT
ejpam-6536	574	78	∪	∪	X
ejpam-6536	574	79	ng(s∗	ng(s∗	NUM
ejpam-6536	574	80	,	,	PUNCT
ejpam-6536	574	81	2	2	NUM
ejpam-6536	574	82	)	)	PUNCT
ejpam-6536	574	83	)	)	PUNCT
ejpam-6536	574	84	.	.	PUNCT
ejpam-6536	575	1	corollary	corollary	ADJ
ejpam-6536	575	2	8	8	NUM
ejpam-6536	575	3	.	.	PUNCT
ejpam-6536	576	1	for	for	ADP
ejpam-6536	576	2	all	all	DET
ejpam-6536	576	3	graphs	graph	NOUN
ejpam-6536	576	4	h	h	NOUN
ejpam-6536	576	5	∈	∈	PROPN
ejpam-6536	576	6	g	g	PROPN
ejpam-6536	576	7	and	and	CCONJ
ejpam-6536	576	8	m	m	PROPN
ejpam-6536	576	9	≥	≥	NOUN
ejpam-6536	576	10	2	2	NUM
ejpam-6536	576	11	,	,	PUNCT
ejpam-6536	576	12	γhh(km[h	γhh(km[h	X
ejpam-6536	576	13	]	]	X
ejpam-6536	576	14	)	)	PUNCT
ejpam-6536	576	15	=	=	PUNCT
ejpam-6536	576	16	m	m	PUNCT
ejpam-6536	576	17	·	·	PUNCT
ejpam-6536	576	18	ppnd(h	ppnd(h	NOUN
ejpam-6536	576	19	)	)	PUNCT
ejpam-6536	576	20	.	.	PUNCT
ejpam-6536	577	1	proof	proof	NOUN
ejpam-6536	577	2	:	:	PUNCT
ejpam-6536	577	3	put	put	VERB
ejpam-6536	577	4	s	s	NOUN
ejpam-6536	577	5	=	=	X
ejpam-6536	577	6	v	v	ADJ
ejpam-6536	577	7	(	(	PUNCT
ejpam-6536	577	8	km	km	PROPN
ejpam-6536	577	9	)	)	PUNCT
ejpam-6536	577	10	and	and	CCONJ
ejpam-6536	577	11	let	let	VERB
ejpam-6536	577	12	c	c	NOUN
ejpam-6536	577	13	=	=	SYM
ejpam-6536	577	14	∪x∈s	∪x∈s	PROPN
ejpam-6536	577	15	(	(	PUNCT
ejpam-6536	577	16	{	{	PUNCT
ejpam-6536	577	17	x	x	NOUN
ejpam-6536	577	18	}	}	PUNCT
ejpam-6536	577	19	×	×	PROPN
ejpam-6536	577	20	tx	tx	PROPN
ejpam-6536	577	21	)	)	PUNCT
ejpam-6536	577	22	,	,	PUNCT
ejpam-6536	577	23	c∗	c∗	PROPN
ejpam-6536	577	24	=	=	SYM
ejpam-6536	577	25	∪x∈s	∪x∈s	PROPN
ejpam-6536	577	26	(	(	PUNCT
ejpam-6536	577	27	{	{	PUNCT
ejpam-6536	577	28	x	x	NOUN
ejpam-6536	577	29	}	}	PUNCT
ejpam-6536	577	30	×	×	PROPN
ejpam-6536	577	31	t	t	PROPN
ejpam-6536	577	32	∗	∗	NOUN
ejpam-6536	577	33	x	x	X
ejpam-6536	577	34	)	)	PUNCT
ejpam-6536	578	1	∈	∈	PROPN
ejpam-6536	578	2	v	v	NOUN
ejpam-6536	578	3	(	(	PUNCT
ejpam-6536	578	4	km[h	km[h	PROPN
ejpam-6536	578	5	]	]	PUNCT
ejpam-6536	578	6	)	)	PUNCT
ejpam-6536	578	7	such	such	ADJ
ejpam-6536	578	8	that	that	SCONJ
ejpam-6536	578	9	(	(	PUNCT
ejpam-6536	578	10	tx	tx	PROPN
ejpam-6536	578	11	,	,	PUNCT
ejpam-6536	578	12	t	t	PROPN
ejpam-6536	578	13	∗	∗	NOUN
ejpam-6536	578	14	x	x	PUNCT
ejpam-6536	578	15	)	)	PUNCT
ejpam-6536	578	16	is	be	AUX
ejpam-6536	578	17	a	a	DET
ejpam-6536	578	18	ppnd	ppnd	NOUN
ejpam-6536	578	19	-	-	PUNCT
ejpam-6536	578	20	pair	pair	NOUN
ejpam-6536	578	21	of	of	ADP
ejpam-6536	578	22	h	h	NOUN
ejpam-6536	578	23	for	for	ADP
ejpam-6536	578	24	each	each	DET
ejpam-6536	578	25	x	x	PROPN
ejpam-6536	578	26	∈	∈	PROPN
ejpam-6536	578	27	s.	s.	PROPN
ejpam-6536	579	1	then	then	ADV
ejpam-6536	579	2	(	(	PUNCT
ejpam-6536	579	3	c	c	X
ejpam-6536	579	4	,	,	PUNCT
ejpam-6536	579	5	c∗	c∗	ADJ
ejpam-6536	579	6	)	)	PUNCT
ejpam-6536	579	7	∈	∈	PROPN
ejpam-6536	579	8	phd(km[h	phd(km[h	PROPN
ejpam-6536	579	9	]	]	PUNCT
ejpam-6536	579	10	)	)	PUNCT
ejpam-6536	579	11	by	by	ADP
ejpam-6536	579	12	theorem	theorem	NOUN
ejpam-6536	579	13	4	4	NUM
ejpam-6536	579	14	.	.	PUNCT
ejpam-6536	579	15	thus	thus	ADV
ejpam-6536	579	16	,	,	PUNCT
ejpam-6536	579	17	γhh(km[h	γhh(km[h	PROPN
ejpam-6536	579	18	]	]	X
ejpam-6536	579	19	)	)	PUNCT
ejpam-6536	579	20	≤	≤	PROPN
ejpam-6536	579	21	|c|	|c|	PROPN
ejpam-6536	579	22	+	+	CCONJ
ejpam-6536	579	23	|c∗|	|c∗|	VERB
ejpam-6536	579	24	=	=	X
ejpam-6536	579	25	∑	∑	PUNCT
ejpam-6536	579	26	x∈v	x∈v	PROPN
ejpam-6536	579	27	(	(	PUNCT
ejpam-6536	579	28	km	km	PROPN
ejpam-6536	579	29	)	)	PUNCT
ejpam-6536	579	30	(	(	PUNCT
ejpam-6536	579	31	|tx|	|tx|	NOUN
ejpam-6536	579	32	+	+	CCONJ
ejpam-6536	579	33	|t	|t	PROPN
ejpam-6536	579	34	∗	∗	NOUN
ejpam-6536	579	35	x	x	PUNCT
ejpam-6536	579	36	|	|	ADV
ejpam-6536	579	37	)	)	PUNCT
ejpam-6536	579	38	=	=	PUNCT
ejpam-6536	580	1	m	m	PUNCT
ejpam-6536	580	2	·	·	PUNCT
ejpam-6536	580	3	ppnd(h	ppnd(h	NOUN
ejpam-6536	580	4	)	)	PUNCT
ejpam-6536	580	5	.	.	PUNCT
ejpam-6536	581	1	now	now	ADV
ejpam-6536	581	2	let	let	VERB
ejpam-6536	581	3	(	(	PUNCT
ejpam-6536	581	4	c	c	X
ejpam-6536	581	5	,	,	PUNCT
ejpam-6536	581	6	c∗	c∗	PROPN
ejpam-6536	581	7	)	)	PUNCT
ejpam-6536	581	8	be	be	VERB
ejpam-6536	581	9	a	a	DET
ejpam-6536	581	10	γhh	γhh	NOUN
ejpam-6536	581	11	-	-	PUNCT
ejpam-6536	581	12	pair	pair	NOUN
ejpam-6536	581	13	of	of	ADP
ejpam-6536	581	14	km[h	km[h	NOUN
ejpam-6536	581	15	]	]	PUNCT
ejpam-6536	581	16	.	.	PUNCT
ejpam-6536	582	1	by	by	ADP
ejpam-6536	582	2	theorem	theorem	NOUN
ejpam-6536	582	3	11(i	11(i	NUM
ejpam-6536	582	4	)	)	PUNCT
ejpam-6536	582	5	,	,	PUNCT
ejpam-6536	582	6	c	c	X
ejpam-6536	582	7	=	=	SYM
ejpam-6536	582	8	∪x∈s	∪x∈s	PROPN
ejpam-6536	582	9	(	(	PUNCT
ejpam-6536	582	10	{	{	PUNCT
ejpam-6536	582	11	x	x	NOUN
ejpam-6536	582	12	}	}	PUNCT
ejpam-6536	582	13	×	×	PROPN
ejpam-6536	582	14	tx	tx	PROPN
ejpam-6536	582	15	)	)	PUNCT
ejpam-6536	582	16	and	and	CCONJ
ejpam-6536	582	17	c∗	c∗	PROPN
ejpam-6536	582	18	=	=	SYM
ejpam-6536	582	19	∪x∈s∗	∪x∈s∗	PROPN
ejpam-6536	582	20	(	(	PUNCT
ejpam-6536	582	21	{	{	PUNCT
ejpam-6536	582	22	x	x	NOUN
ejpam-6536	582	23	}	}	PUNCT
ejpam-6536	582	24	×	×	PROPN
ejpam-6536	582	25	t	t	PROPN
ejpam-6536	582	26	∗	∗	NOUN
ejpam-6536	582	27	x	x	PUNCT
ejpam-6536	582	28	)	)	PUNCT
ejpam-6536	582	29	for	for	ADP
ejpam-6536	582	30	some	some	DET
ejpam-6536	582	31	hop	hop	NOUN
ejpam-6536	582	32	dominating	dominating	NOUN
ejpam-6536	582	33	sets	set	NOUN
ejpam-6536	582	34	s	s	PART
ejpam-6536	582	35	and	and	CCONJ
ejpam-6536	582	36	s∗	s∗	PROPN
ejpam-6536	582	37	of	of	ADP
ejpam-6536	582	38	km	km	PROPN
ejpam-6536	582	39	with	with	ADP
ejpam-6536	582	40	tx	tx	PROPN
ejpam-6536	582	41	a	a	DET
ejpam-6536	582	42	point	point	NOUN
ejpam-6536	582	43	-	-	PUNCT
ejpam-6536	582	44	wise	wise	ADJ
ejpam-6536	582	45	non	non	ADJ
ejpam-6536	582	46	-	-	ADJ
ejpam-6536	582	47	dominating	dominating	ADJ
ejpam-6536	582	48	sets	set	NOUN
ejpam-6536	582	49	of	of	ADP
ejpam-6536	582	50	h	h	NOUN
ejpam-6536	582	51	for	for	ADP
ejpam-6536	582	52	each	each	DET
ejpam-6536	582	53	x	x	SYM
ejpam-6536	582	54	∈	∈	PROPN
ejpam-6536	582	55	s	s	PART
ejpam-6536	582	56	\	\	ADJ
ejpam-6536	582	57	nkm(s	nkm(s	PROPN
ejpam-6536	582	58	,	,	PUNCT
ejpam-6536	582	59	2	2	NUM
ejpam-6536	582	60	)	)	PUNCT
ejpam-6536	582	61	and	and	CCONJ
ejpam-6536	582	62	t	t	PROPN
ejpam-6536	582	63	∗	∗	NOUN
ejpam-6536	582	64	x	x	PUNCT
ejpam-6536	582	65	a	a	DET
ejpam-6536	582	66	point	point	NOUN
ejpam-6536	582	67	-	-	PUNCT
ejpam-6536	582	68	wise	wise	ADJ
ejpam-6536	582	69	non	non	ADJ
ejpam-6536	582	70	-	-	ADJ
ejpam-6536	582	71	dominating	dominating	ADJ
ejpam-6536	582	72	set	set	NOUN
ejpam-6536	582	73	of	of	ADP
ejpam-6536	582	74	h	h	NOUN
ejpam-6536	582	75	fo	fo	INTJ
ejpam-6536	582	76	all	all	PRON
ejpam-6536	582	77	x	x	PROPN
ejpam-6536	582	78	∈	∈	PROPN
ejpam-6536	582	79	s∗	s∗	PROPN
ejpam-6536	582	80	\	\	PROPN
ejpam-6536	582	81	nkm(s∗	nkm(s∗	X
ejpam-6536	582	82	,	,	PUNCT
ejpam-6536	582	83	2	2	NUM
ejpam-6536	582	84	)	)	PUNCT
ejpam-6536	582	85	.	.	PUNCT
ejpam-6536	583	1	since	since	SCONJ
ejpam-6536	583	2	v	v	NOUN
ejpam-6536	583	3	(	(	PUNCT
ejpam-6536	583	4	km	km	PROPN
ejpam-6536	583	5	)	)	PUNCT
ejpam-6536	583	6	is	be	AUX
ejpam-6536	583	7	the	the	DET
ejpam-6536	583	8	unique	unique	ADJ
ejpam-6536	583	9	hop	hop	NOUN
ejpam-6536	583	10	dominating	dominating	NOUN
ejpam-6536	583	11	set	set	NOUN
ejpam-6536	583	12	of	of	ADP
ejpam-6536	583	13	km	km	PROPN
ejpam-6536	583	14	,	,	PUNCT
ejpam-6536	583	15	s	s	PART
ejpam-6536	583	16	=	=	X
ejpam-6536	583	17	s∗	s∗	PROPN
ejpam-6536	583	18	=	=	SYM
ejpam-6536	583	19	v	v	PROPN
ejpam-6536	583	20	(	(	PUNCT
ejpam-6536	583	21	km	km	PROPN
ejpam-6536	583	22	)	)	PUNCT
ejpam-6536	583	23	and	and	CCONJ
ejpam-6536	583	24	nkm(s	nkm(s	PROPN
ejpam-6536	583	25	,	,	PUNCT
ejpam-6536	583	26	2	2	X
ejpam-6536	583	27	)	)	PUNCT
ejpam-6536	583	28	=	=	SYM
ejpam-6536	583	29	nkm(s∗	nkm(s∗	X
ejpam-6536	583	30	,	,	PUNCT
ejpam-6536	583	31	2	2	NUM
ejpam-6536	583	32	)	)	PUNCT
ejpam-6536	583	33	=	=	NOUN
ejpam-6536	583	34	∅.	∅.	VERB
ejpam-6536	583	35	further	far	ADV
ejpam-6536	583	36	,	,	PUNCT
ejpam-6536	583	37	by	by	ADP
ejpam-6536	583	38	theorem	theorem	NOUN
ejpam-6536	583	39	11(ii	11(ii	NUM
ejpam-6536	583	40	)	)	PUNCT
ejpam-6536	583	41	,	,	PUNCT
ejpam-6536	583	42	(	(	PUNCT
ejpam-6536	583	43	tx	tx	PROPN
ejpam-6536	583	44	,	,	PUNCT
ejpam-6536	583	45	t	t	PROPN
ejpam-6536	583	46	∗	∗	NOUN
ejpam-6536	583	47	x	x	X
ejpam-6536	583	48	)	)	PUNCT
ejpam-6536	583	49	∈	∈	PROPN
ejpam-6536	583	50	ppnd(h	ppnd(h	PROPN
ejpam-6536	583	51	)	)	PUNCT
ejpam-6536	583	52	.	.	PUNCT
ejpam-6536	584	1	thus	thus	ADV
ejpam-6536	584	2	,	,	PUNCT
ejpam-6536	584	3	γhh(km[h	γhh(km[h	X
ejpam-6536	584	4	]	]	X
ejpam-6536	584	5	)	)	PUNCT
ejpam-6536	585	1	=	=	SYM
ejpam-6536	585	2	|c|	|c|	PROPN
ejpam-6536	585	3	+	+	CCONJ
ejpam-6536	585	4	|c∗|	|c∗|	PROPN
ejpam-6536	585	5	=	=	X
ejpam-6536	585	6	∑	∑	PUNCT
ejpam-6536	585	7	x∈v	x∈v	PROPN
ejpam-6536	585	8	(	(	PUNCT
ejpam-6536	585	9	km	km	PROPN
ejpam-6536	585	10	)	)	PUNCT
ejpam-6536	585	11	(	(	PUNCT
ejpam-6536	585	12	|tx|	|tx|	NOUN
ejpam-6536	585	13	+	+	CCONJ
ejpam-6536	585	14	|t	|t	PROPN
ejpam-6536	585	15	∗	∗	NOUN
ejpam-6536	585	16	x	x	PUNCT
ejpam-6536	585	17	|	|	NOUN
ejpam-6536	585	18	)	)	PUNCT
ejpam-6536	585	19	≥	≥	NOUN
ejpam-6536	585	20	m	m	PROPN
ejpam-6536	585	21	·	·	PUNCT
ejpam-6536	585	22	ppnd(h	ppnd(h	NOUN
ejpam-6536	585	23	)	)	PUNCT
ejpam-6536	585	24	.	.	PUNCT
ejpam-6536	586	1	■	■	PUNCT
ejpam-6536	586	2	acknowledgements	acknowledgement	VERB
ejpam-6536	586	3	this	this	DET
ejpam-6536	586	4	research	research	NOUN
ejpam-6536	586	5	project	project	NOUN
ejpam-6536	586	6	is	be	AUX
ejpam-6536	586	7	fully	fully	ADV
ejpam-6536	586	8	supported	support	VERB
ejpam-6536	586	9	by	by	ADP
ejpam-6536	586	10	the	the	DET
ejpam-6536	586	11	dost	dost	NOUN
ejpam-6536	586	12	-	-	PUNCT
ejpam-6536	586	13	asthrdp	asthrdp	ADJ
ejpam-6536	586	14	,	,	PUNCT
ejpam-6536	586	15	philippines	philippine	NOUN
ejpam-6536	586	16	,	,	PUNCT
ejpam-6536	586	17	and	and	CCONJ
ejpam-6536	586	18	the	the	DET
ejpam-6536	586	19	office	office	NOUN
ejpam-6536	586	20	of	of	ADP
ejpam-6536	586	21	the	the	DET
ejpam-6536	586	22	vice	vice	NOUN
ejpam-6536	586	23	chancellor	chancellor	NOUN
ejpam-6536	586	24	for	for	ADP
ejpam-6536	586	25	research	research	NOUN
ejpam-6536	586	26	and	and	CCONJ
ejpam-6536	586	27	enterprise	enterprise	NOUN
ejpam-6536	586	28	of	of	ADP
ejpam-6536	586	29	the	the	DET
ejpam-6536	586	30	msu	msu	PROPN
ejpam-6536	586	31	-	-	PUNCT
ejpam-6536	586	32	iit	iit	PROPN
ejpam-6536	586	33	,	,	PUNCT
ejpam-6536	586	34	philippines	philippine	NOUN
ejpam-6536	586	35	.	.	PUNCT
ejpam-6536	587	1	the	the	DET
ejpam-6536	587	2	authors	author	NOUN
ejpam-6536	587	3	would	would	AUX
ejpam-6536	587	4	like	like	VERB
ejpam-6536	587	5	to	to	PART
ejpam-6536	587	6	thank	thank	VERB
ejpam-6536	587	7	the	the	DET
ejpam-6536	587	8	reviewers	reviewer	NOUN
ejpam-6536	587	9	for	for	ADP
ejpam-6536	587	10	reading	read	VERB
ejpam-6536	587	11	and	and	CCONJ
ejpam-6536	587	12	recommending	recommend	VERB
ejpam-6536	587	13	invaluable	invaluable	ADJ
ejpam-6536	587	14	suggestions	suggestion	NOUN
ejpam-6536	587	15	to	to	ADP
ejpam-6536	587	16	the	the	DET
ejpam-6536	587	17	improvement	improvement	NOUN
ejpam-6536	587	18	of	of	ADP
ejpam-6536	587	19	the	the	DET
ejpam-6536	587	20	paper	paper	NOUN
ejpam-6536	587	21	.	.	PUNCT
ejpam-6536	588	1	v.	v.	ADP
ejpam-6536	588	2	a	a	DET
ejpam-6536	588	3	besana	besana	PROPN
ejpam-6536	588	4	,	,	PUNCT
ejpam-6536	588	5	f.	f.	PROPN
ejpam-6536	588	6	jamil	jamil	PROPN
ejpam-6536	588	7	,	,	PUNCT
ejpam-6536	588	8	s.	s.	PROPN
ejpam-6536	588	9	canoy	canoy	PROPN
ejpam-6536	588	10	jr	jr	PROPN
ejpam-6536	588	11	.	.	PROPN
ejpam-6536	588	12	/	/	SYM
ejpam-6536	588	13	eur	eur	PROPN
ejpam-6536	588	14	.	.	PUNCT
ejpam-6536	589	1	j.	j.	PROPN
ejpam-6536	589	2	pure	pure	PROPN
ejpam-6536	589	3	appl	appl	PROPN
ejpam-6536	589	4	.	.	PROPN
ejpam-6536	589	5	math	math	PROPN
ejpam-6536	589	6	,	,	PUNCT
ejpam-6536	589	7	18	18	NUM
ejpam-6536	589	8	(	(	PUNCT
ejpam-6536	589	9	3	3	NUM
ejpam-6536	589	10	)	)	PUNCT
ejpam-6536	589	11	(	(	PUNCT
ejpam-6536	589	12	2025	2025	NUM
ejpam-6536	589	13	)	)	PUNCT
ejpam-6536	589	14	,	,	PUNCT
ejpam-6536	589	15	6536	6536	NUM
ejpam-6536	589	16	16	16	NUM
ejpam-6536	589	17	of	of	ADP
ejpam-6536	589	18	17	17	NUM
ejpam-6536	589	19	references	reference	NOUN
ejpam-6536	589	20	[	[	X
ejpam-6536	589	21	1	1	NUM
ejpam-6536	589	22	]	]	X
ejpam-6536	589	23	f.	f.	PROPN
ejpam-6536	589	24	buckley	buckley	PROPN
ejpam-6536	589	25	and	and	CCONJ
ejpam-6536	589	26	f.	f.	PROPN
ejpam-6536	589	27	harary	harary	PROPN
ejpam-6536	589	28	.	.	PUNCT
ejpam-6536	590	1	distance	distance	NOUN
ejpam-6536	590	2	in	in	ADP
ejpam-6536	590	3	graphs	graph	NOUN
ejpam-6536	590	4	.	.	PUNCT
ejpam-6536	591	1	addison	addison	PROPN
ejpam-6536	591	2	-	-	PUNCT
ejpam-6536	591	3	wesley	wesley	PROPN
ejpam-6536	591	4	,	,	PUNCT
ejpam-6536	591	5	redwood	redwood	NOUN
ejpam-6536	591	6	city	city	NOUN
ejpam-6536	591	7	,	,	PUNCT
ejpam-6536	591	8	ca	ca	NOUN
ejpam-6536	591	9	,	,	PUNCT
ejpam-6536	591	10	1990	1990	NUM
ejpam-6536	591	11	.	.	PUNCT
ejpam-6536	592	1	[	[	X
ejpam-6536	592	2	2	2	NUM
ejpam-6536	592	3	]	]	PUNCT
ejpam-6536	592	4	c.	c.	PROPN
ejpam-6536	592	5	berge	berge	PROPN
ejpam-6536	592	6	.	.	PUNCT
ejpam-6536	593	1	the	the	DET
ejpam-6536	593	2	theory	theory	NOUN
ejpam-6536	593	3	of	of	ADP
ejpam-6536	593	4	graphs	graph	NOUN
ejpam-6536	593	5	and	and	CCONJ
ejpam-6536	593	6	its	its	PRON
ejpam-6536	593	7	applications	application	NOUN
ejpam-6536	593	8	.	.	PUNCT
ejpam-6536	594	1	wiley	wiley	PROPN
ejpam-6536	594	2	,	,	PUNCT
ejpam-6536	594	3	new	new	PROPN
ejpam-6536	594	4	york	york	PROPN
ejpam-6536	594	5	,	,	PUNCT
ejpam-6536	594	6	1962	1962	NUM
ejpam-6536	594	7	.	.	PUNCT
ejpam-6536	595	1	[	[	X
ejpam-6536	595	2	3	3	X
ejpam-6536	595	3	]	]	X
ejpam-6536	595	4	e.	e.	PROPN
ejpam-6536	595	5	cockayne	cockayne	PROPN
ejpam-6536	595	6	and	and	CCONJ
ejpam-6536	595	7	s.	s.	PROPN
ejpam-6536	595	8	hedetniemi	hedetniemi	PROPN
ejpam-6536	595	9	.	.	PUNCT
ejpam-6536	596	1	towards	towards	ADP
ejpam-6536	596	2	a	a	DET
ejpam-6536	596	3	theory	theory	NOUN
ejpam-6536	596	4	of	of	ADP
ejpam-6536	596	5	domination	domination	NOUN
ejpam-6536	596	6	in	in	ADP
ejpam-6536	596	7	graphs	graph	NOUN
ejpam-6536	596	8	.	.	PUNCT
ejpam-6536	597	1	networks	network	NOUN
ejpam-6536	597	2	,	,	PUNCT
ejpam-6536	597	3	7(3):247–261	7(3):247–261	NUM
ejpam-6536	597	4	,	,	PUNCT
ejpam-6536	597	5	1977	1977	NUM
ejpam-6536	597	6	.	.	PUNCT
ejpam-6536	598	1	[	[	X
ejpam-6536	598	2	4	4	X
ejpam-6536	598	3	]	]	X
ejpam-6536	598	4	t.w	t.w	PROPN
ejpam-6536	598	5	.	.	PROPN
ejpam-6536	598	6	haynes	haynes	PROPN
ejpam-6536	598	7	,	,	PUNCT
ejpam-6536	598	8	s.t	s.t	PROPN
ejpam-6536	598	9	.	.	PROPN
ejpam-6536	598	10	hedetniemi	hedetniemi	PROPN
ejpam-6536	598	11	,	,	PUNCT
ejpam-6536	598	12	and	and	CCONJ
ejpam-6536	598	13	p.j	p.j	PROPN
ejpam-6536	598	14	.	.	PROPN
ejpam-6536	598	15	slater	slater	PROPN
ejpam-6536	598	16	.	.	PUNCT
ejpam-6536	599	1	fundamentals	fundamental	NOUN
ejpam-6536	599	2	of	of	ADP
ejpam-6536	599	3	domination	domination	NOUN
ejpam-6536	599	4	in	in	ADP
ejpam-6536	599	5	graphs	graph	NOUN
ejpam-6536	599	6	.	.	PUNCT
ejpam-6536	600	1	marcel	marcel	PROPN
ejpam-6536	600	2	dekker	dekker	PROPN
ejpam-6536	600	3	,	,	PUNCT
ejpam-6536	600	4	inc	inc	PROPN
ejpam-6536	600	5	.	.	PROPN
ejpam-6536	600	6	,	,	PUNCT
ejpam-6536	600	7	new	new	PROPN
ejpam-6536	600	8	york	york	PROPN
ejpam-6536	600	9	,	,	PUNCT
ejpam-6536	600	10	1998	1998	NUM
ejpam-6536	600	11	.	.	PUNCT
ejpam-6536	601	1	[	[	X
ejpam-6536	601	2	5	5	NUM
ejpam-6536	601	3	]	]	X
ejpam-6536	601	4	f.p	f.p	PROPN
ejpam-6536	601	5	.	.	PROPN
ejpam-6536	601	6	jamil	jamil	PROPN
ejpam-6536	601	7	and	and	CCONJ
ejpam-6536	601	8	h.n	h.n	PROPN
ejpam-6536	601	9	.	.	PROPN
ejpam-6536	601	10	maglanque	maglanque	PROPN
ejpam-6536	601	11	.	.	PUNCT
ejpam-6536	602	1	cost	cost	NOUN
ejpam-6536	602	2	effective	effective	ADJ
ejpam-6536	602	3	domination	domination	NOUN
ejpam-6536	602	4	in	in	ADP
ejpam-6536	602	5	the	the	DET
ejpam-6536	602	6	join	join	NOUN
ejpam-6536	602	7	,	,	PUNCT
ejpam-6536	602	8	corona	corona	NOUN
ejpam-6536	602	9	and	and	CCONJ
ejpam-6536	602	10	composition	composition	NOUN
ejpam-6536	602	11	of	of	ADP
ejpam-6536	602	12	graphs	graph	NOUN
ejpam-6536	602	13	.	.	PUNCT
ejpam-6536	603	1	european	european	ADJ
ejpam-6536	603	2	journal	journal	PROPN
ejpam-6536	603	3	of	of	ADP
ejpam-6536	603	4	pure	pure	ADJ
ejpam-6536	603	5	and	and	CCONJ
ejpam-6536	603	6	applied	applied	ADJ
ejpam-6536	603	7	mathematics	mathematic	NOUN
ejpam-6536	603	8	,	,	PUNCT
ejpam-6536	603	9	12(3):978–998	12(3):978–998	NUM
ejpam-6536	603	10	,	,	PUNCT
ejpam-6536	603	11	2019	2019	NUM
ejpam-6536	603	12	.	.	PUNCT
ejpam-6536	604	1	[	[	X
ejpam-6536	604	2	6	6	NUM
ejpam-6536	604	3	]	]	PUNCT
ejpam-6536	604	4	o.	o.	PROPN
ejpam-6536	604	5	ore	ore	PROPN
ejpam-6536	604	6	.	.	PUNCT
ejpam-6536	605	1	theory	theory	NOUN
ejpam-6536	605	2	of	of	ADP
ejpam-6536	605	3	graphs	graph	NOUN
ejpam-6536	605	4	,	,	PUNCT
ejpam-6536	605	5	volume	volume	NOUN
ejpam-6536	605	6	38	38	NUM
ejpam-6536	605	7	of	of	ADP
ejpam-6536	605	8	american	american	PROPN
ejpam-6536	605	9	mathematical	mathematical	PROPN
ejpam-6536	605	10	society	society	NOUN
ejpam-6536	605	11	colloquium	colloquium	NOUN
ejpam-6536	605	12	publications	publication	NOUN
ejpam-6536	605	13	.	.	PUNCT
ejpam-6536	606	1	american	american	PROPN
ejpam-6536	606	2	mathematical	mathematical	PROPN
ejpam-6536	606	3	society	society	NOUN
ejpam-6536	606	4	,	,	PUNCT
ejpam-6536	606	5	providence	providence	NOUN
ejpam-6536	606	6	,	,	PUNCT
ejpam-6536	606	7	ri	ri	NOUN
ejpam-6536	606	8	,	,	PUNCT
ejpam-6536	606	9	1962	1962	NUM
ejpam-6536	606	10	.	.	PUNCT
ejpam-6536	607	1	[	[	X
ejpam-6536	607	2	7	7	X
ejpam-6536	607	3	]	]	X
ejpam-6536	607	4	s.r	s.r	PROPN
ejpam-6536	607	5	canoy	canoy	PROPN
ejpam-6536	607	6	jr	jr	PROPN
ejpam-6536	607	7	.	.	PROPN
ejpam-6536	607	8	,	,	PUNCT
ejpam-6536	607	9	r.v	r.v	PROPN
ejpam-6536	607	10	.	.	NOUN
ejpam-6536	607	11	mollejon	mollejon	NOUN
ejpam-6536	607	12	,	,	PUNCT
ejpam-6536	607	13	and	and	CCONJ
ejpam-6536	607	14	j.g	j.g	PROPN
ejpam-6536	607	15	.	.	PROPN
ejpam-6536	607	16	canoy	canoy	PROPN
ejpam-6536	607	17	.	.	PUNCT
ejpam-6536	608	1	hop	hop	PROPN
ejpam-6536	608	2	dominating	dominating	NOUN
ejpam-6536	608	3	sets	set	NOUN
ejpam-6536	608	4	in	in	ADP
ejpam-6536	608	5	graphs	graph	NOUN
ejpam-6536	608	6	under	under	ADP
ejpam-6536	608	7	binary	binary	ADJ
ejpam-6536	608	8	operations	operation	NOUN
ejpam-6536	608	9	.	.	PUNCT
ejpam-6536	609	1	european	european	ADJ
ejpam-6536	609	2	journal	journal	PROPN
ejpam-6536	609	3	of	of	ADP
ejpam-6536	609	4	pure	pure	ADJ
ejpam-6536	609	5	and	and	CCONJ
ejpam-6536	609	6	applied	applied	ADJ
ejpam-6536	609	7	mathematics	mathematic	NOUN
ejpam-6536	609	8	,	,	PUNCT
ejpam-6536	609	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-6536	609	10	,	,	PUNCT
ejpam-6536	609	11	2019	2019	NUM
ejpam-6536	609	12	.	.	PUNCT
ejpam-6536	610	1	[	[	X
ejpam-6536	610	2	8	8	NUM
ejpam-6536	610	3	]	]	SYM
ejpam-6536	610	4	v.r	v.r	PROPN
ejpam-6536	610	5	.	.	PROPN
ejpam-6536	610	6	kulli	kulli	PROPN
ejpam-6536	610	7	and	and	CCONJ
ejpam-6536	610	8	s.c	s.c	PROPN
ejpam-6536	610	9	.	.	PROPN
ejpam-6536	610	10	sigarkanti	sigarkanti	PROPN
ejpam-6536	610	11	.	.	PROPN
ejpam-6536	610	12	inverse	inverse	ADJ
ejpam-6536	610	13	domination	domination	NOUN
ejpam-6536	610	14	in	in	ADP
ejpam-6536	610	15	graphs	graph	NOUN
ejpam-6536	610	16	.	.	PUNCT
ejpam-6536	611	1	national	national	PROPN
ejpam-6536	611	2	academy	academy	PROPN
ejpam-6536	611	3	science	science	PROPN
ejpam-6536	611	4	letters	letter	NOUN
ejpam-6536	611	5	,	,	PUNCT
ejpam-6536	611	6	14:473–475	14:473–475	PROPN
ejpam-6536	611	7	,	,	PUNCT
ejpam-6536	611	8	1991	1991	NUM
ejpam-6536	611	9	.	.	PUNCT
ejpam-6536	612	1	[	[	X
ejpam-6536	612	2	9	9	NUM
ejpam-6536	612	3	]	]	X
ejpam-6536	612	4	p.g	p.g	PROPN
ejpam-6536	612	5	.	.	PROPN
ejpam-6536	612	6	bhat	bhat	PROPN
ejpam-6536	612	7	and	and	CCONJ
ejpam-6536	612	8	s.r	s.r	PROPN
ejpam-6536	612	9	.	.	PROPN
ejpam-6536	612	10	bhat	bhat	PROPN
ejpam-6536	612	11	.	.	PUNCT
ejpam-6536	613	1	inverse	inverse	ADJ
ejpam-6536	613	2	independence	independence	NOUN
ejpam-6536	613	3	number	number	NOUN
ejpam-6536	613	4	of	of	ADP
ejpam-6536	613	5	a	a	DET
ejpam-6536	613	6	graph	graph	NOUN
ejpam-6536	613	7	.	.	PUNCT
ejpam-6536	614	1	international	international	ADJ
ejpam-6536	614	2	journal	journal	PROPN
ejpam-6536	614	3	of	of	ADP
ejpam-6536	614	4	computer	computer	NOUN
ejpam-6536	614	5	applications	application	NOUN
ejpam-6536	614	6	,	,	PUNCT
ejpam-6536	614	7	42(5	42(5	NUM
ejpam-6536	614	8	)	)	PUNCT
ejpam-6536	614	9	,	,	PUNCT
ejpam-6536	614	10	2012	2012	NUM
ejpam-6536	614	11	.	.	PUNCT
ejpam-6536	615	1	[	[	X
ejpam-6536	615	2	10	10	NUM
ejpam-6536	615	3	]	]	X
ejpam-6536	615	4	g.s	g.s	PROPN
ejpam-6536	615	5	.	.	PROPN
ejpam-6536	615	6	domke	domke	PROPN
ejpam-6536	615	7	,	,	PUNCT
ejpam-6536	615	8	j.e	j.e	PROPN
ejpam-6536	615	9	.	.	PROPN
ejpam-6536	615	10	dunbar	dunbar	PROPN
ejpam-6536	615	11	,	,	PUNCT
ejpam-6536	615	12	and	and	CCONJ
ejpam-6536	615	13	l.r	l.r	PROPN
ejpam-6536	615	14	.	.	PROPN
ejpam-6536	615	15	markus	markus	PROPN
ejpam-6536	615	16	.	.	PUNCT
ejpam-6536	616	1	the	the	DET
ejpam-6536	616	2	inverse	inverse	ADJ
ejpam-6536	616	3	domination	domination	NOUN
ejpam-6536	616	4	number	number	NOUN
ejpam-6536	616	5	of	of	ADP
ejpam-6536	616	6	a	a	DET
ejpam-6536	616	7	graph	graph	NOUN
ejpam-6536	616	8	.	.	PUNCT
ejpam-6536	617	1	ars	ars	PROPN
ejpam-6536	617	2	combinatoria	combinatoria	PROPN
ejpam-6536	617	3	,	,	PUNCT
ejpam-6536	617	4	72:149–160	72:149–160	PROPN
ejpam-6536	617	5	,	,	PUNCT
ejpam-6536	617	6	2004	2004	NUM
ejpam-6536	617	7	.	.	PUNCT
ejpam-6536	618	1	[	[	X
ejpam-6536	618	2	11	11	NUM
ejpam-6536	618	3	]	]	X
ejpam-6536	618	4	e.m	e.m	PROPN
ejpam-6536	618	5	.	.	PROPN
ejpam-6536	618	6	kiunisala	kiunisala	PROPN
ejpam-6536	618	7	and	and	CCONJ
ejpam-6536	618	8	f.p	f.p	PROPN
ejpam-6536	618	9	.	.	PROPN
ejpam-6536	618	10	jamil	jamil	PROPN
ejpam-6536	618	11	.	.	PUNCT
ejpam-6536	619	1	inverse	inverse	PROPN
ejpam-6536	619	2	domination	domination	NOUN
ejpam-6536	619	3	numbers	number	NOUN
ejpam-6536	619	4	and	and	CCONJ
ejpam-6536	619	5	disjoint	disjoint	NOUN
ejpam-6536	619	6	domination	domination	NOUN
ejpam-6536	619	7	numbers	number	NOUN
ejpam-6536	619	8	of	of	ADP
ejpam-6536	619	9	graphs	graph	NOUN
ejpam-6536	619	10	under	under	ADP
ejpam-6536	619	11	some	some	DET
ejpam-6536	619	12	binary	binary	ADJ
ejpam-6536	619	13	operations	operation	NOUN
ejpam-6536	619	14	.	.	PUNCT
ejpam-6536	620	1	applied	apply	VERB
ejpam-6536	620	2	mathematical	mathematical	ADJ
ejpam-6536	620	3	sciences	sciences	PROPN
ejpam-6536	620	4	,	,	PUNCT
ejpam-6536	620	5	8(107):5303–5315	8(107):5303–5315	PROPN
ejpam-6536	620	6	,	,	PUNCT
ejpam-6536	620	7	2014	2014	NUM
ejpam-6536	620	8	.	.	PUNCT
ejpam-6536	621	1	[	[	X
ejpam-6536	621	2	12	12	NUM
ejpam-6536	621	3	]	]	X
ejpam-6536	621	4	e.m	e.m	PROPN
ejpam-6536	621	5	.	.	PROPN
ejpam-6536	621	6	kiunisala	kiunisala	PROPN
ejpam-6536	621	7	and	and	CCONJ
ejpam-6536	621	8	f.p	f.p	PROPN
ejpam-6536	621	9	.	.	PROPN
ejpam-6536	621	10	jamil	jamil	PROPN
ejpam-6536	621	11	.	.	PUNCT
ejpam-6536	622	1	on	on	ADP
ejpam-6536	622	2	pairs	pair	NOUN
ejpam-6536	622	3	of	of	ADP
ejpam-6536	622	4	disjoint	disjoint	ADJ
ejpam-6536	622	5	dominating	dominating	NOUN
ejpam-6536	622	6	sets	set	NOUN
ejpam-6536	622	7	in	in	ADP
ejpam-6536	622	8	a	a	DET
ejpam-6536	622	9	graph	graph	NOUN
ejpam-6536	622	10	.	.	PUNCT
ejpam-6536	623	1	international	international	ADJ
ejpam-6536	623	2	journal	journal	PROPN
ejpam-6536	623	3	of	of	ADP
ejpam-6536	623	4	mathematical	mathematical	ADJ
ejpam-6536	623	5	analysis	analysis	NOUN
ejpam-6536	623	6	,	,	PUNCT
ejpam-6536	623	7	10(13):623–637	10(13):623–637	NUM
ejpam-6536	623	8	,	,	PUNCT
ejpam-6536	623	9	2016	2016	NUM
ejpam-6536	623	10	.	.	PUNCT
ejpam-6536	624	1	[	[	X
ejpam-6536	624	2	13	13	NUM
ejpam-6536	624	3	]	]	SYM
ejpam-6536	624	4	s.m	s.m	PROPN
ejpam-6536	624	5	.	.	PROPN
ejpam-6536	624	6	hedetniemi	hedetniemi	PROPN
ejpam-6536	624	7	,	,	PUNCT
ejpam-6536	624	8	s.t	s.t	PROPN
ejpam-6536	624	9	.	.	PROPN
ejpam-6536	624	10	hedetniemi	hedetniemi	PROPN
ejpam-6536	624	11	,	,	PUNCT
ejpam-6536	624	12	r.c	r.c	PROPN
ejpam-6536	624	13	.	.	PROPN
ejpam-6536	624	14	laskar	laskar	PROPN
ejpam-6536	624	15	,	,	PUNCT
ejpam-6536	624	16	l.	l.	PROPN
ejpam-6536	624	17	markus	markus	PROPN
ejpam-6536	624	18	,	,	PUNCT
ejpam-6536	624	19	and	and	CCONJ
ejpam-6536	624	20	p.j	p.j	PROPN
ejpam-6536	624	21	.	.	PROPN
ejpam-6536	624	22	slater	slater	PROPN
ejpam-6536	624	23	.	.	PUNCT
ejpam-6536	625	1	disjoint	disjoint	NOUN
ejpam-6536	625	2	dominating	dominating	NOUN
ejpam-6536	625	3	sets	set	NOUN
ejpam-6536	625	4	in	in	ADP
ejpam-6536	625	5	graphs	graph	NOUN
ejpam-6536	625	6	.	.	PUNCT
ejpam-6536	626	1	in	in	ADP
ejpam-6536	626	2	proceedings	proceeding	NOUN
ejpam-6536	626	3	of	of	ADP
ejpam-6536	626	4	the	the	DET
ejpam-6536	626	5	international	international	ADJ
ejpam-6536	626	6	conference	conference	NOUN
ejpam-6536	626	7	on	on	ADP
ejpam-6536	626	8	discrete	discrete	ADJ
ejpam-6536	626	9	mathematics	mathematic	NOUN
ejpam-6536	626	10	,	,	PUNCT
ejpam-6536	626	11	volume	volume	NOUN
ejpam-6536	626	12	7	7	NUM
ejpam-6536	626	13	of	of	ADP
ejpam-6536	626	14	ramanujan	ramanujan	PROPN
ejpam-6536	626	15	mathematical	mathematical	ADJ
ejpam-6536	626	16	society	society	NOUN
ejpam-6536	626	17	lecture	lecture	NOUN
ejpam-6536	626	18	notes	note	NOUN
ejpam-6536	626	19	series	series	NOUN
ejpam-6536	626	20	,	,	PUNCT
ejpam-6536	626	21	pages	page	NOUN
ejpam-6536	626	22	87–100	87–100	PROPN
ejpam-6536	626	23	.	.	PUNCT
ejpam-6536	626	24	2008	2008	NUM
ejpam-6536	626	25	.	.	PUNCT
ejpam-6536	627	1	[	[	X
ejpam-6536	627	2	14	14	NUM
ejpam-6536	627	3	]	]	X
ejpam-6536	627	4	c.	c.	PROPN
ejpam-6536	627	5	natarajan	natarajan	PROPN
ejpam-6536	627	6	and	and	CCONJ
ejpam-6536	627	7	s.k	s.k	PROPN
ejpam-6536	627	8	.	.	PROPN
ejpam-6536	627	9	ayyaswamy	ayyaswamy	PROPN
ejpam-6536	627	10	.	.	PUNCT
ejpam-6536	628	1	hop	hop	PROPN
ejpam-6536	628	2	domination	domination	NOUN
ejpam-6536	628	3	in	in	ADP
ejpam-6536	628	4	graphs	graph	NOUN
ejpam-6536	628	5	–	–	PUNCT
ejpam-6536	628	6	ii	ii	NOUN
ejpam-6536	628	7	.	.	PUNCT
ejpam-6536	628	8	versita	versita	PROPN
ejpam-6536	628	9	,	,	PUNCT
ejpam-6536	628	10	23(2):187–199	23(2):187–199	PROPN
ejpam-6536	628	11	,	,	PUNCT
ejpam-6536	628	12	2015	2015	NUM
ejpam-6536	628	13	.	.	PUNCT
ejpam-6536	629	1	[	[	X
ejpam-6536	629	2	15	15	NUM
ejpam-6536	629	3	]	]	X
ejpam-6536	629	4	m.a	m.a	PROPN
ejpam-6536	629	5	.	.	PROPN
ejpam-6536	629	6	bonsocan	bonsocan	PROPN
ejpam-6536	629	7	and	and	CCONJ
ejpam-6536	629	8	f.p	f.p	PROPN
ejpam-6536	629	9	.	.	PROPN
ejpam-6536	629	10	jamil	jamil	PROPN
ejpam-6536	629	11	.	.	PUNCT
ejpam-6536	630	1	transversal	transversal	PROPN
ejpam-6536	630	2	hop	hop	PROPN
ejpam-6536	630	3	domination	domination	NOUN
ejpam-6536	630	4	in	in	ADP
ejpam-6536	630	5	graphs	graph	NOUN
ejpam-6536	630	6	.	.	PUNCT
ejpam-6536	631	1	european	european	ADJ
ejpam-6536	631	2	journal	journal	PROPN
ejpam-6536	631	3	of	of	ADP
ejpam-6536	631	4	pure	pure	ADJ
ejpam-6536	631	5	and	and	CCONJ
ejpam-6536	631	6	applied	applied	ADJ
ejpam-6536	631	7	mathematics	mathematic	NOUN
ejpam-6536	631	8	,	,	PUNCT
ejpam-6536	631	9	16(1):192–206	16(1):192–206	NUM
ejpam-6536	631	10	,	,	PUNCT
ejpam-6536	631	11	2023	2023	NUM
ejpam-6536	631	12	.	.	PUNCT
ejpam-6536	632	1	[	[	X
ejpam-6536	632	2	16	16	NUM
ejpam-6536	632	3	]	]	X
ejpam-6536	632	4	m.a	m.a	PROPN
ejpam-6536	632	5	.	.	PROPN
ejpam-6536	632	6	henning	henning	PROPN
ejpam-6536	632	7	,	,	PUNCT
ejpam-6536	632	8	s.	s.	PROPN
ejpam-6536	632	9	pal	pal	PROPN
ejpam-6536	632	10	,	,	PUNCT
ejpam-6536	632	11	and	and	CCONJ
ejpam-6536	632	12	d.	d.	PROPN
ejpam-6536	632	13	pradhan	pradhan	PROPN
ejpam-6536	632	14	.	.	PUNCT
ejpam-6536	633	1	algorithm	algorithm	PROPN
ejpam-6536	633	2	and	and	CCONJ
ejpam-6536	633	3	hardness	hardness	NOUN
ejpam-6536	633	4	results	result	NOUN
ejpam-6536	633	5	on	on	ADP
ejpam-6536	633	6	hop	hop	NOUN
ejpam-6536	633	7	domination	domination	NOUN
ejpam-6536	633	8	in	in	ADP
ejpam-6536	633	9	graphs	graph	NOUN
ejpam-6536	633	10	.	.	PUNCT
ejpam-6536	634	1	information	information	NOUN
ejpam-6536	634	2	processing	processing	NOUN
ejpam-6536	634	3	letters	letter	NOUN
ejpam-6536	634	4	,	,	PUNCT
ejpam-6536	634	5	153:105872	153:105872	NUM
ejpam-6536	634	6	,	,	PUNCT
ejpam-6536	634	7	2020	2020	NUM
ejpam-6536	634	8	.	.	PUNCT
ejpam-6536	635	1	[	[	X
ejpam-6536	635	2	17	17	NUM
ejpam-6536	635	3	]	]	X
ejpam-6536	635	4	m.a	m.a	PROPN
ejpam-6536	635	5	.	.	PROPN
ejpam-6536	635	6	henning	henning	PROPN
ejpam-6536	635	7	and	and	CCONJ
ejpam-6536	635	8	n.j	n.j	PROPN
ejpam-6536	635	9	.	.	PROPN
ejpam-6536	635	10	rad	rad	PROPN
ejpam-6536	635	11	.	.	PROPN
ejpam-6536	636	1	on	on	ADP
ejpam-6536	636	2	2	2	NUM
ejpam-6536	636	3	-	-	PUNCT
ejpam-6536	636	4	step	step	NOUN
ejpam-6536	636	5	and	and	CCONJ
ejpam-6536	636	6	hop	hop	NOUN
ejpam-6536	636	7	dominating	dominating	NOUN
ejpam-6536	636	8	sets	set	NOUN
ejpam-6536	636	9	in	in	ADP
ejpam-6536	636	10	graphs	graph	NOUN
ejpam-6536	636	11	.	.	PUNCT
ejpam-6536	637	1	graphs	graph	NOUN
ejpam-6536	637	2	and	and	CCONJ
ejpam-6536	637	3	combinatorics	combinatoric	NOUN
ejpam-6536	637	4	,	,	PUNCT
ejpam-6536	637	5	33:913–927	33:913–927	NUM
ejpam-6536	637	6	,	,	PUNCT
ejpam-6536	637	7	2017	2017	NUM
ejpam-6536	637	8	.	.	PUNCT
ejpam-6536	638	1	[	[	X
ejpam-6536	638	2	18	18	NUM
ejpam-6536	638	3	]	]	X
ejpam-6536	638	4	c.	c.	PROPN
ejpam-6536	638	5	natarajan	natarajan	PROPN
ejpam-6536	638	6	,	,	PUNCT
ejpam-6536	638	7	s.k	s.k	PROPN
ejpam-6536	638	8	.	.	PROPN
ejpam-6536	638	9	ayyaswamy	ayyaswamy	PROPN
ejpam-6536	638	10	,	,	PUNCT
ejpam-6536	638	11	and	and	CCONJ
ejpam-6536	638	12	g.	g.	PROPN
ejpam-6536	638	13	sathiamoorthy	sathiamoorthy	PROPN
ejpam-6536	638	14	.	.	PUNCT
ejpam-6536	639	1	a	a	DET
ejpam-6536	639	2	note	note	NOUN
ejpam-6536	639	3	on	on	ADP
ejpam-6536	639	4	hop	hop	NOUN
ejpam-6536	639	5	domination	domination	NOUN
ejpam-6536	639	6	number	number	NOUN
ejpam-6536	639	7	of	of	ADP
ejpam-6536	639	8	some	some	DET
ejpam-6536	639	9	special	special	ADJ
ejpam-6536	639	10	families	family	NOUN
ejpam-6536	639	11	of	of	ADP
ejpam-6536	639	12	graphs	graph	NOUN
ejpam-6536	639	13	.	.	PUNCT
ejpam-6536	640	1	international	international	ADJ
ejpam-6536	640	2	journal	journal	NOUN
ejpam-6536	640	3	of	of	ADP
ejpam-6536	640	4	pure	pure	ADJ
ejpam-6536	640	5	and	and	CCONJ
ejpam-6536	640	6	applied	applied	ADJ
ejpam-6536	640	7	mathematics	mathematic	NOUN
ejpam-6536	640	8	,	,	PUNCT
ejpam-6536	640	9	119(12):14165–14171	119(12):14165–14171	NUM
ejpam-6536	640	10	,	,	PUNCT
ejpam-6536	640	11	2018	2018	NUM
ejpam-6536	640	12	.	.	PUNCT
ejpam-6536	641	1	v.	v.	ADP
ejpam-6536	641	2	a	a	DET
ejpam-6536	641	3	besana	besana	PROPN
ejpam-6536	641	4	,	,	PUNCT
ejpam-6536	641	5	f.	f.	PROPN
ejpam-6536	641	6	jamil	jamil	PROPN
ejpam-6536	641	7	,	,	PUNCT
ejpam-6536	641	8	s.	s.	PROPN
ejpam-6536	641	9	canoy	canoy	PROPN
ejpam-6536	641	10	jr	jr	PROPN
ejpam-6536	641	11	.	.	PROPN
ejpam-6536	641	12	/	/	SYM
ejpam-6536	641	13	eur	eur	PROPN
ejpam-6536	641	14	.	.	PUNCT
ejpam-6536	642	1	j.	j.	PROPN
ejpam-6536	642	2	pure	pure	PROPN
ejpam-6536	642	3	appl	appl	PROPN
ejpam-6536	642	4	.	.	PROPN
ejpam-6536	642	5	math	math	PROPN
ejpam-6536	642	6	,	,	PUNCT
ejpam-6536	642	7	18	18	NUM
ejpam-6536	642	8	(	(	PUNCT
ejpam-6536	642	9	3	3	NUM
ejpam-6536	642	10	)	)	PUNCT
ejpam-6536	642	11	(	(	PUNCT
ejpam-6536	642	12	2025	2025	NUM
ejpam-6536	642	13	)	)	PUNCT
ejpam-6536	642	14	,	,	PUNCT
ejpam-6536	642	15	6536	6536	NUM
ejpam-6536	642	16	17	17	NUM
ejpam-6536	642	17	of	of	ADP
ejpam-6536	642	18	17	17	NUM
ejpam-6536	642	19	[	[	SYM
ejpam-6536	642	20	19	19	NUM
ejpam-6536	642	21	]	]	X
ejpam-6536	642	22	s.	s.	PROPN
ejpam-6536	642	23	shanmugavelan	shanmugavelan	PROPN
ejpam-6536	642	24	and	and	CCONJ
ejpam-6536	642	25	c.	c.	PROPN
ejpam-6536	642	26	natarajan	natarajan	PROPN
ejpam-6536	642	27	.	.	PROPN
ejpam-6536	643	1	on	on	ADP
ejpam-6536	643	2	hop	hop	PROPN
ejpam-6536	643	3	domination	domination	NOUN
ejpam-6536	643	4	number	number	NOUN
ejpam-6536	643	5	of	of	ADP
ejpam-6536	643	6	some	some	DET
ejpam-6536	643	7	generalized	generalized	ADJ
ejpam-6536	643	8	graph	graph	NOUN
ejpam-6536	643	9	structures	structure	NOUN
ejpam-6536	643	10	.	.	PUNCT
ejpam-6536	644	1	ural	ural	ADJ
ejpam-6536	644	2	mathematical	mathematical	ADJ
ejpam-6536	644	3	journal	journal	NOUN
ejpam-6536	644	4	,	,	PUNCT
ejpam-6536	644	5	7(2):121–135	7(2):121–135	NUM
ejpam-6536	644	6	,	,	PUNCT
ejpam-6536	644	7	2021	2021	NUM
ejpam-6536	644	8	.	.	PUNCT
ejpam-6536	645	1	[	[	X
ejpam-6536	645	2	20	20	NUM
ejpam-6536	645	3	]	]	X
ejpam-6536	645	4	w.	w.	PROPN
ejpam-6536	645	5	desormeaux	desormeaux	PROPN
ejpam-6536	645	6	,	,	PUNCT
ejpam-6536	645	7	t.	t.	PROPN
ejpam-6536	645	8	w.	w.	PROPN
ejpam-6536	645	9	haynes	haynes	PROPN
ejpam-6536	645	10	,	,	PUNCT
ejpam-6536	645	11	and	and	CCONJ
ejpam-6536	645	12	m.	m.	PROPN
ejpam-6536	645	13	a.	a.	PROPN
ejpam-6536	645	14	henning	henning	PROPN
ejpam-6536	645	15	.	.	PUNCT
ejpam-6536	646	1	a	a	DET
ejpam-6536	646	2	note	note	NOUN
ejpam-6536	646	3	on	on	ADP
ejpam-6536	646	4	non	non	ADJ
ejpam-6536	646	5	-	-	ADJ
ejpam-6536	646	6	dominating	dominating	ADJ
ejpam-6536	646	7	set	set	VERB
ejpam-6536	646	8	partitions	partition	NOUN
ejpam-6536	646	9	in	in	ADP
ejpam-6536	646	10	graphs	graph	NOUN
ejpam-6536	646	11	.	.	PUNCT
ejpam-6536	647	1	discussiones	discussione	NOUN
ejpam-6536	647	2	mathematicae	mathematicae	PROPN
ejpam-6536	647	3	graph	graph	NOUN
ejpam-6536	647	4	theory	theory	NOUN
ejpam-6536	647	5	,	,	PUNCT
ejpam-6536	647	6	36:1043–1050	36:1043–1050	PROPN
ejpam-6536	647	7	,	,	PUNCT
ejpam-6536	647	8	2016	2016	NUM
ejpam-6536	647	9	.	.	PUNCT