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Pré-Publication, Document De Travail Année : 2014

S-Packing Colorings of Cubic Graphs

Résumé

Given a non-decreasing sequence $S=(s_1,s_2, \ldots, s_k)$ of positive integers, an {\em $S$-packing coloring} of a graph $G$ is a mapping $c$ from $V(G)$ to $\{s_1,s_2, \ldots, s_k\}$ such that any two vertices with color $s_i$ are at mutual distance greater than $s_i$, $1\le i\le k$. This paper studies $S$-packing colorings of (sub)cubic graphs. We prove that subcubic graphs are $(1,2,2,2,2,2,2)$-packing colorable and $(1,1,2,2,3)$-packing colorable. For subdivisions of subcubic graphs we derive sharper bounds, and we provide an example of a cubic graph of order $38$ which is not $(1,2,\ldots,12)$-packing colorable.
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Dates et versions

hal-00967446 , version 1 (28-03-2014)
hal-00967446 , version 2 (29-04-2016)

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Nicolas Gastineau, Olivier Togni. S-Packing Colorings of Cubic Graphs. 2014. ⟨hal-00967446v1⟩
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