On the packing chromatic number of hypercubes

Autores
Torres, Pablo Daniel; Valencia Pabon, Mario
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i + 1. Goddard et al. [8] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for χρ(Qn) and we compute the exact value of χρ(Qn) for 6 ≤ n ≤ 8.
Fil: Torres, Pablo Daniel. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-nord. Laboratoire D'informatique de L'universite Paris-nord; Francia
Materia
Packing Chromatic Number
Upper Bound
Hypercube Graphs
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/21661
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/21661
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network_name_str CONICET Digital (CONICET)
spelling On the packing chromatic number of hypercubesTorres, Pablo DanielValencia Pabon, MarioPacking Chromatic NumberUpper BoundHypercube Graphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i + 1. Goddard et al. [8] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for χρ(Qn) and we compute the exact value of χρ(Qn) for 6 ≤ n ≤ 8.Fil: Torres, Pablo Daniel. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Valencia Pabon, Mario. Universite de Paris 13-nord. Laboratoire D'informatique de L'universite Paris-nord; FranciaElsevier Science2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/21661Torres, Pablo Daniel; Valencia Pabon, Mario; On the packing chromatic number of hypercubes; Elsevier Science; Electronic Notes in Discrete Mathematics; 44; 11-2013; 263-2681571-0653CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.endm.2013.10.041info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S1571065313002576info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:16:29Zoai:ri.conicet.gov.ar:11336/21661instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:16:30.193CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the packing chromatic number of hypercubes
title On the packing chromatic number of hypercubes
spellingShingle On the packing chromatic number of hypercubes
Torres, Pablo Daniel
Packing Chromatic Number
Upper Bound
Hypercube Graphs
title_short On the packing chromatic number of hypercubes
title_full On the packing chromatic number of hypercubes
title_fullStr On the packing chromatic number of hypercubes
title_full_unstemmed On the packing chromatic number of hypercubes
title_sort On the packing chromatic number of hypercubes
dc.creator.none.fl_str_mv Torres, Pablo Daniel
Valencia Pabon, Mario
author Torres, Pablo Daniel
author_facet Torres, Pablo Daniel
Valencia Pabon, Mario
author_role author
author2 Valencia Pabon, Mario
author2_role author
dc.subject.none.fl_str_mv Packing Chromatic Number
Upper Bound
Hypercube Graphs
topic Packing Chromatic Number
Upper Bound
Hypercube Graphs
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i + 1. Goddard et al. [8] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for χρ(Qn) and we compute the exact value of χρ(Qn) for 6 ≤ n ≤ 8.
Fil: Torres, Pablo Daniel. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-nord. Laboratoire D'informatique de L'universite Paris-nord; Francia
description The packing chromatic number χρ(G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i + 1. Goddard et al. [8] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for χρ(Qn) and we compute the exact value of χρ(Qn) for 6 ≤ n ≤ 8.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/21661
Torres, Pablo Daniel; Valencia Pabon, Mario; On the packing chromatic number of hypercubes; Elsevier Science; Electronic Notes in Discrete Mathematics; 44; 11-2013; 263-268
1571-0653
CONICET Digital
CONICET
url http://hdl.handle.net/11336/21661
identifier_str_mv Torres, Pablo Daniel; Valencia Pabon, Mario; On the packing chromatic number of hypercubes; Elsevier Science; Electronic Notes in Discrete Mathematics; 44; 11-2013; 263-268
1571-0653
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.endm.2013.10.041
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S1571065313002576
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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