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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (7): 38-45.doi: 10.6040/j.issn.1671-9352.0.2019.095

• • 上一篇    

不含相交5-圈的平面图的线性2-荫度

陈宏宇,钟斌   

  1. 上海应用技术大学理学院, 上海 201418
  • 发布日期:2020-07-08
  • 作者简介:陈宏宇(1981— ),女,博士,副教授,研究方向为图论. E-mail:hongyuchen86@163.com
  • 基金资助:
    国家自然科学基金青年科学基金资助项目(11401386);上海应用技术大学中青年科技人才发展基金

Linear 2-arboricity of planar graphs without intersecting 5-cycles

CHEN Hong-yu, ZHONG Bin   

  1. School of Science, Shanghai Institute of Technology, Shanghai 201418, China
  • Published:2020-07-08

摘要: 设G是不含相交5-圈的平面图,证明了如果G是连通的并且δ(G)≥2,则G包含一条边xy,使得d(x)+d(y)≤10或者一个2-交错圈。由这个结果可以得到G的线性2-荫度la2(G)≤「Δ/2+5,改进了不含5-圈的平面图的线性2-荫度的已知上界。

关键词: 平面图, 线性2-荫度,

Abstract: Let G be a planar graph without intersecting 5-cycles. If G is connected and δ(G)≥2, then G contains an edge xy with d(x)+d(y)≤10 or a 2-alternating cycle is proved. By this result, its linear 2-arboricity la2(G)≤「Δ/2+5 is obtained, which improves the known upper bound of la2(G) for planar graphs without 5-cycles.

Key words: planar graph, linear 2-arboricity, cycle

中图分类号: 

  • O5
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