# On the packing chromatic number of hypercubes

4 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : The packing chromatic number $\chi_\rho(G)$ 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. \cite{Goddard08} found an upper bound for the packing chromatic number of hypercubes $Q_n$. Moreover, they compute $\chi_\rho(Q_n)$ for $n \leq 5$ leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for $\chi_\rho(Q_n)$ and we compute the exact value of $\chi_\rho(Q_n)$ for $6 \leq n \leq 8$.
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Journal articles

Cited literature [9 references]

https://hal.archives-ouvertes.fr/hal-00926875
Contributor : Mario Valencia <>
Submitted on : Friday, January 10, 2014 - 2:04:32 PM
Last modification on : Thursday, February 7, 2019 - 5:47:53 PM
Long-term archiving on : Thursday, April 10, 2014 - 10:50:30 PM

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• HAL Id : hal-00926875, version 1

### Citation

Pablo Torres, Mario Valencia-Pabon. On the packing chromatic number of hypercubes. Electronic Notes in Discrete Mathematics, Elsevier, 2013, 44 (5), pp.263-268. ⟨hal-00926875⟩

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