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运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 232-236.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.018

• • 上一篇    下一篇

不含F5作为子图的平面图的边染色

薛玲1, 吴建良2,†   

  1. 1. 泰山职业技术学院信息技术工程系, 山东 泰安 271000;
    2. 山东大学数学学院, 山东 济南 250100
  • 收稿日期:2024-05-06 发布日期:2026-06-12
  • 通讯作者: 吴建良 E-mail:jlwu@sdu.edu.cn
  • 基金资助:
    国家自然科学基金 (No. 11971270)

Edge colorings of planar graphs without 5-fans

XUE Ling1, WU Jianliang2,†   

  1. 1 Department of Information Engineering, Taishan Polytechnic, Taian 271000, Shandong, China;
    2 School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2024-05-06 Published:2026-06-12

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摘要： 图的$k$-边染色是指用$k$种颜色对它的边进行染色使得相邻的两条边染不同色,用$\chi'(G)$来记图$G$获得这个染色的最小的$k$值。本文证明了:若平面图$G$不含点数为$5$的扇图$F_5$作为子图,则$\chi'(G)\leq\max\{6,\Delta (G)\}$。

关键词: 边染色, 平面图, 圈

Abstract: A $k$-edge-coloring of a graph is an assignment of colors from a set of $k$ colors to the edges of $G$ such that adjacent edges receive distinct colors. $\chi'(G)$ denotes the smallest $k$ for which $G$ admits such a coloring. It is proved here that if a planar graph $G$ contains no $5$-fan $F_5$ as a subgraph, where $F_5$ is a graph of order $5$ with a vertex $v\in V(F_5)$ such that $d(v)=4$ and $F_5-v$ is a path, then $\chi'(G) \leq \max\{6, \Delta(G)\}$.

Key words: edge coloring, planar graph, cycle

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