2025/07/16 by Yunfang Tang, Zoubin Bi, Tang, Yunfang +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2507.11927
openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted by χs'(G), is the minimum number of colors needed for a strong edge coloring of G. The edge weight of a graph G is defined to be maxuv∈ E(G)\(dG(u)+dG(v))\. It was proved in Chen et al in 2020 that every graph with edge weight at most 6 has a strong edge-coloring using at most 10 colors. In this paper, we consider the list version of strong edge-coloring. We strengthen this result by showing that every graph with edge weight at most 6 has a strong list-chromatic index at most 10. Specially, every subcubic graph has a strong list-chromatic index at most 10, which improves a result of Dai et al. in 2018.