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arXiv · 2512.24001

A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable

Maidoun Mortada·Ayman El Zein
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Abstract

It was recently proved that every claw-free cubic graph admits a (1, 1, 2, 2)-packing coloring--that is, its vertex set can be partitioned into two 1-packings and two 2-packings. This result was established by Brešar, Kuenzel, and Rall [Discrete Mathematics 348 (8) (2025), 114477]. In this paper, we provide a simpler and shorter proof.

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Maidoun Mortada, Ayman El Zein. 2025-12-30. A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable. https://arxiv.org/abs/2512.24001

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