Operations Research Transactions ›› 2022, Vol. 26 ›› Issue (2): 111-127.doi: 10.15960/j.cnki.issn.1007-6093.2022.02.010

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Strong edge-coloring of planar graphs

Yuehua BU1,2,*(), Heng ZHANG1   

  1. 1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
    2. College of Xingzhi, Zhejiang Normal University, Lanxi 321100, Zhejiang, China
  • Received:2019-03-05 Online:2022-06-15 Published:2022-05-27
  • Contact: Yuehua BU E-mail:yhbu@zjnu.edu.cn

Abstract:

A strong edge coloring of graph $G$ is on the basis of the proper edge coloring and requiring any two edges at distance at most 2 receive distinct colors, the smallest integer of strong edge coloring called a figure of colors used strong edge chromatic number of $G$. In this paper, the configuration of the minimal counter example is given, and then the power transfer method is used to prove that the strong chromatic index of plane graphs with $g(G)\geq5$, $\Delta(G)\geq6$ and $5$-cycle do not intersect is at most $4\Delta(G)-1$.

Key words: planar graph, strong edge-coloring, girth, cycle

CLC Number: