2026/06/22 by Yanli Hao, Tianchi Yang, Xingxing Yu · 1 citation
#math.CO
An edge-coloring of a graph G is called a strong edge-coloring if all its color classes are induced matchings in G; the minimum number of colors required for such a coloring, denoted by χs'(G), is known as the strong chromatic index of G. For each vertex v of a graph G, let dG(v) denote the degree of v in G. Let G be a bipartite graph with partite sets A and B, and let ΔA=max\dG(a): a∈ A\ and ΔB=max\dG(b): b∈ B\. A conjecture of Brualdi and Quinn Massey asserts that \( χs'(G) ≤ ΔA ΔB\). In this paper, we show that \(χs'(G) ≤ 1.676 ΔA ΔB\) provided that the product ΔAΔB is sufficiently large.