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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 94-101.doi: 10.6040/j.issn.1671-9352.0.2014.594

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平面图的平方染色数的一个新上界

朱海洋1,顾 毓1,吕新忠2   

  1. 1. 空军勤务学院飞行保障指挥系, 江苏 徐州 221000;2.浙江师范大学数理与信息工程学院, 浙江 金华 321004
  • 收稿日期:2014-12-31 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:朱海洋(1979— ),男,讲师,研究方向为图论与军事运筹学. E-mail:tulunzhuhaiyang7@126.com
  • 基金资助:
    国家自然科学基金资助项目(61170302)

New upper bound on the chromatic number of the square of a planar graph

ZHU Hai-yang1, GU Yu1, LÜ Xin-zhong2   

  1. 1. Department of Flight Support Command, Air Force Logistics College, Xuzhou 221000, Jiangsu, China;
    2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
  • Received:2014-12-31 Online:2016-02-16 Published:2016-03-11

摘要: 令V(G)、E(G)、Δ(G)和χ(G)分别为G的顶点集、边集、最大度和色数。图G的平方图,记为G2,指的是一个图满足条件:V(G2)=V(G),并且uv∈E(G2)当且仅当1≤dG(u,v)≤2。证明了若G是Δ(G)≤6且围长g(G)≥5的平面图,则χ(G2)≤Δ(G)+8。

关键词: 平面图, 染色, 围长, 平方图

Abstract: Let V(G), E(G), Δ(G) and χ(G) denote the vertex set, the edge set, the maximum degree and the chromatic number of a graph G, respectively. The square G2 of a graph G is defined such that V(G2)=V(G), and uv∈E(G2)if and only if 1≤dG(u,v)≤2. It is proved that χ(G2)≤Δ(G)+8 if G is a planar graph with Δ(G)≤6 and girth g(G)≥5.

Key words: planar graph, girth, coloring, squares

中图分类号: 

  • O157.5
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