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arXiv · 2209.09135

$S$-Packing Coloring of Cubic Halin Graphs

Batoul Tarhini·Olivier Togni
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Abstract

Given a non-decreasing sequence $S = (s_{1}, s_{2}, \ldots , s_{k})$ of positive integers, an $S$-packing coloring of a graph $G$ is a partition of the vertex set of $G$ into $k$ subsets $\{V_{1}, V_{2}, \ldots , V_{k}\}$ such that for each $1 \leq i \leq k$, the distance between any two distinct vertices $u$ and $v$ in $V_{i}$ is at least $s_{i} + 1$. In this paper, we study the problem of $S$-packing coloring of cubic Halin graphs, and we prove that every cubic Halin graph is $(1,1,2,3)$-packing colorable. In addition, we prove that such graphs are $(1,2,2,2,2,2)$-packing colorable.

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Batoul Tarhini, Olivier Togni. 2024-02-06. $S$-Packing Coloring of Cubic Halin Graphs. https://arxiv.org/abs/2209.09135

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