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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 147-154.doi: 10.6040/j.issn.1671-9352.0.2022.221

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不含相邻短圈的可嵌入图的线性荫度

杜红军(),王慧娟*()   

  1. 青岛大学数学与统计学院,山东 青岛 266071
  • 收稿日期:2022-04-18 出版日期:2023-11-20 发布日期:2023-11-07
  • 通讯作者: 王慧娟 E-mail:dhjqdu@163.com;sduwhj@163.com
  • 作者简介:杜红军(1997—),女,硕士研究生,研究方向为图论与组合最优化. E-mail: dhjqdu@163.com
  • 基金资助:
    山东省自然科学基金资助项目(ZR2020MA045)

Linear arboricity on embedded graphs without adjacent short cycles

Hongjun DU(),Huijuan WANG*()   

  1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2022-04-18 Online:2023-11-20 Published:2023-11-07
  • Contact: Huijuan WANG E-mail:dhjqdu@163.com;sduwhj@163.com

摘要:

线性荫度是一种非正常的边染色,图的线性荫度是指将它的边集划分为线性森林的最小数目。利用权转移方法,证明得到:对于任意的一个最大度Δ≥7的可嵌入到欧拉示性数非负的曲面图G而言,如果存在着两个固定的整数i, j∈{3, 4, 5, 6},使得图G中不包含相邻的i-圈和j-圈,那么它的线性荫度是$\left\lceil\frac{\varDelta}{2}\right\rceil $

关键词: 欧拉示性数, 曲面, 线性荫度

Abstract:

Linear arboricity is an improper edge coloring. The linear arboricity of a graph refers to the minimum number that the edge set is divided into linear forests. By using discharging method, we proved a conclusion about a graph G which can be embedded in a surface of non-negative Euler characteristic with maximum degree Δ≥7. If there exist two fixed integers i, j∈{3, 4, 5, 6} such that G has no adjacent i- cycles or j- cycles, then its linear arboricity is $\left\lceil\frac{\Delta}{2}\right\rceil $.

Key words: Euler characteristic, surface, linear arboricity

中图分类号: 

  • O157.5

图1

图G不含的结构"

图2

7-点关联3-面的个数是3时,3-面的分布方式"

图3

8-点关联4个3-面时,3-面的分布方式"

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