On the packing chromatic number of hypercubes

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...

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Detalles Bibliográficos
Autores: Torres, Pablo Daniel, Valencia Pabon, Mario
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/21661
Acceso en línea:http://hdl.handle.net/11336/21661
Access Level:acceso abierto
Palabra clave:Packing Chromatic Number
Upper Bound
Hypercube Graphs
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.