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...
| Autores: | , |
|---|---|
| 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 |
| 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. |
|---|