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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (2): 53-58.doi: 10.6040/j.issn.1671-9352.0.2022.557

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不含K1, 3+图的强边染色

袁佳鑫(),黄明芳*()   

  1. 武汉理工大学理学院, 湖北 武汉 430070
  • 收稿日期:2022-10-31 出版日期:2024-02-20 发布日期:2024-02-20
  • 通讯作者: 黄明芳 E-mail:2461634998@qq.com;ds_hmf@126.com
  • 作者简介:袁佳鑫(1999—), 女, 硕士研究生, 研究方向为图论. E-mail: 2461634998@qq.com
  • 基金资助:
    国家自然科学基金资助项目(12261094)

Strong edge-coloring of graphs without K1, 3+

Jiaxin YUAN(),Mingfang HUANG*()   

  1. School of Science, Wuhan University of Technology, Wuhan 430070, Hubei, China
  • Received:2022-10-31 Online:2024-02-20 Published:2024-02-20
  • Contact: Mingfang HUANG E-mail:2461634998@qq.com;ds_hmf@126.com

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摘要：

一个图G的强边染色是将颜色分配给所有的边, 使得每个颜色类的导出子图是一个匹配。在图G的强边染色中所需的最小颜色数称为图G的强边色数, 边e=uv的度记为d(e)=d(u)+d(v), 图G的边度记为d(G)=min{d(e)|e ∈ E(G)}。证明最大度为Δ且图的边度大于顶点数的不含K1, 3+图的强边色数至多是Δ2-Δ+1。

关键词: 强边染色, 强边色数, 边度

Abstract:

The strong edge-coloring of a graph G is to assign colors to all edges, so that the derived subgraphs of each color class are a matching. The minimum number of colors required in the strong edge-coloring of a graph G is called the strong chromatic index of the graph G, the degree of edge e=uv is recorded as d(e)=d(u)+d(v), the edge degree of G is recorded as d(G)=min{d(e)|e ∈ E(G)}. This paper proves that the strong chromatic index of the graph without K1, 3+ with the maximum degree Δ and edge degree of the graph greater than the number of vertices is at most Δ2-Δ+1.

Key words: strong edge-coloring, strong chromatic index, edge degree

中图分类号: 

  • O157

图1

图G中顶点v1、v2的邻点(除v1、v2外)划分为D1、D2、D3这3个顶点集"

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[1] 孟献青. 一类平面图的强边染色[J]. 山东大学学报（理学版）, 2015, 50(08): 10-13.
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