Strong edge-coloring of 2-degenerate graphs

A strong edge-coloring of a graph G is an edge-coloring in which every color class is an induced matching, and the strong chromatic index chi(s)' (G) is the minimum number of colors needed in strong edge-colorings of G. A graph is 2-degenerate if every subgraph has minimum degree at most 2. Choi, Kim, Kostochka, and Raspaud (2016) showed chi(s)'(G) <= 5 Delta + 1 if G is a 2-degenerate graph with maximum degree Delta. In this article, we improve it to chi(s)'(G) <= 5 Delta - Delta(1/2-is an element of) + 2 when Delta >= 4(1/(2 is an element of)) for any 0 < is an element of <= 1/2. (c) 2023 Elsevier B.V. All rights reserved.