A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable
Combinatorics
2026-01-01 v1
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 Bre\v{s}ar, Kuenzel, and Rall [Discrete Mathematics 348 (8) (2025), 114477]. In this paper, we provide a simpler and shorter proof.
Cite
@article{arxiv.2512.24001,
title = {A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable},
author = {Maidoun Mortada and Ayman El Zein},
journal= {arXiv preprint arXiv:2512.24001},
year = {2026}
}