2023/01/30 by Gexin Yu, Yu, Gexin, Rachel Yu +1
Neuroscience · #Nuclear Receptors and Signaling
paper · pdf · doi:10.48550/arxiv.2301.12924
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 χs'(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 χs'(G) ≤ 5Δ+1 if G is a 2-degenerate graph with maximum degree Δ. In this article, we improve it to χs'(G)≤ 5Δ-Δ1/2-ε+2 when Δ>41/(2ε) for any 0<ε<1/2.