On the (1,25)-packing edge-colorings of claw-free subcubic graphs

Abstract

A graph is called (1l,2k)-packing edge-colorable if its edge set decomposes into l matchings and k induced matchings. A graph is called claw-free if it does not contain an induced subgraph isomorphic to the complete bipartite graph K1,3. This paper shows that every claw-free subcubic graph without triangular prism components is (1,25)-packing edge-colorable, which is best possible.