The packing chromatic number of hypercubes

Autores
Torres, Pablo Daniel; Valencia Pabon, Mario
Año de publicación
2015
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 leasti+1. Goddard et al. (2008) 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 improve the lower bounds for χρ (Qn) for 6 ≤ n ≤ 11. In particular we compute the exact value of χρ (Qn) for 6 ≤ n ≤ 8.
Fil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; Argentina
Fil: Valencia Pabon, Mario. Centre National de la Recherche Scientifique; Francia. Université Paris-nord; Francia
Materia
Hypercube Graphs
Packing Chromatic Number
Upper Bound
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:11336/84368
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84368
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The packing chromatic number of hypercubesTorres, Pablo DanielValencia Pabon, MarioHypercube GraphsPacking Chromatic NumberUpper Boundhttps://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 leasti+1. Goddard et al. (2008) 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 improve the lower bounds for χρ (Qn) for 6 ≤ n ≤ 11. In particular we compute the exact value of χρ (Qn) for 6 ≤ n ≤ 8.Fil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; ArgentinaFil: Valencia Pabon, Mario. Centre National de la Recherche Scientifique; Francia. Université Paris-nord; FranciaElsevier Science2015-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84368Torres, Pablo Daniel; Valencia Pabon, Mario; The packing chromatic number of hypercubes; Elsevier Science; Discrete Applied Mathematics; 190-191; 8-2015; 127-1400166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.04.006info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X15001766info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:38:23Zoai:ri.conicet.gov.ar:11336/84368instacron: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:34982025-09-29 10:38:23.371CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The packing chromatic number of hypercubes
title The packing chromatic number of hypercubes
spellingShingle The packing chromatic number of hypercubes
Torres, Pablo Daniel
Hypercube Graphs
Packing Chromatic Number
Upper Bound
title_short The packing chromatic number of hypercubes
title_full The packing chromatic number of hypercubes
title_fullStr The packing chromatic number of hypercubes
title_full_unstemmed The packing chromatic number of hypercubes
title_sort 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 Hypercube Graphs
Packing Chromatic Number
Upper Bound
topic Hypercube Graphs
Packing Chromatic Number
Upper Bound
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 leasti+1. Goddard et al. (2008) 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 improve the lower bounds for χρ (Qn) for 6 ≤ n ≤ 11. In particular we compute the exact value of χρ (Qn) for 6 ≤ n ≤ 8.
Fil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; Argentina
Fil: Valencia Pabon, Mario. Centre National de la Recherche Scientifique; Francia. Université 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 leasti+1. Goddard et al. (2008) 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 improve the lower bounds for χρ (Qn) for 6 ≤ n ≤ 11. In particular we compute the exact value of χρ (Qn) for 6 ≤ n ≤ 8.
publishDate 2015
dc.date.none.fl_str_mv 2015-08
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/11336/84368
Torres, Pablo Daniel; Valencia Pabon, Mario; The packing chromatic number of hypercubes; Elsevier Science; Discrete Applied Mathematics; 190-191; 8-2015; 127-140
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84368
identifier_str_mv Torres, Pablo Daniel; Valencia Pabon, Mario; The packing chromatic number of hypercubes; Elsevier Science; Discrete Applied Mathematics; 190-191; 8-2015; 127-140
0166-218X
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.dam.2015.04.006
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X15001766
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
_version_ 1844614406348996608
score 13.070432

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