JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (2): 94-101.doi: 10.6040/j.issn.1671-9352.0.2014.594

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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

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

CLC Number: 

  • O157.5
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