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arXiv · 2607.25198

Diamond-free, claw-free cubic graphs are (1, 1, 2, 3)-packing colorable

Sarah E. Anderson·Kirsti Kuenzel·Juan D. Marcano Cuellar
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Abstract

A $(1, 1, 2, k)$-packing coloring of a graph $G$ is a partition of $V(G)$ into two independent sets, a 2-packing, and a $k$-packing. Recently, the question was posed in [A short proof that every claw-free cubic graph is (1, 1, 2, 2)-packing colorable, arXiv:2512.24001v1] as to whether every claw-free cubic graph is $(1, 1, 2, 3)$-packing colorable. We provide an answer in the affirmative in the case that $G$ is a diamond-free, claw-free cubic graph.

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Sarah E. Anderson, Kirsti Kuenzel, Juan D. Marcano Cuellar. 2026-07-28. Diamond-free, claw-free cubic graphs are (1, 1, 2, 3)-packing colorable. https://arxiv.org/abs/2607.25198

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