Strong Edge Coloring of K4 (t)-Minor Free Graphs

A strong edge coloring of a graph G is a proper coloring of edges in G such that any two edges of distance at most 2 are colored with distinct colors. The strong chromatic index chi'(s) (G) is the smallest integer l such that G admits a strong edge coloring using l colors. A K-4 (t)-minor free graph is a graph that does not contain K-4 (t) as a contraction subgraph, where K-4 (t) is obtained from a K-4 by subdividing edges exactly t - 4 times. The paper shows that every K-4(t)-minor free graph with maximum degree Delta(G) has chi's(G) <= (t - 1)Delta(G) for t is an element of{5, 6, 7} which generalizes some known results on K-4-minor free graphs by Batenburg, Joannis de Verclos, Kang, Pirot in 2022 and Wang, Wang, and Wang in 2018. These upper bounds are sharp.