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 leasti+1. Goddard et al. (2008) found an upper bound for the packing chromatic number of hypercubes Q...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2015 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/84368 |
| Online Access: | http://hdl.handle.net/11336/84368 |
| Access Level: | Open access |
| Keyword: | Hypercube Graphs Packing Chromatic Number Upper Bound https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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. |
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