Affiliation:
1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
2. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA
Abstract
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 χs′(G) is the smallest integer l such that G admits a strong edge coloring using l colors. A K4(t)-minor free graph is a graph that does not contain K4(t) as a contraction subgraph, where K4(t) is obtained from a K4 by subdividing edges exactly t−4 times. The paper shows that every K4(t)-minor free graph with maximum degree Δ(G) has χs′(G)≤(t−1)Δ(G) for t∈{5,6,7} which generalizes some known results on K4-minor free graphs by Batenburg, Joannis de Verclos, Kang, Pirot in 2022 and Wang, Wang, and Wang in 2018. These upper bounds are sharp.
Funder
National Natural Science Foundation of China
Talent Fund Project of Tianjin Normal University, China
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis