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

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.