Total coloring of planar graphs without chordal 7-cycles

被引:0
作者
Hua Cai
机构
[1] Shandong University,School of Mathematics
[2] Changji University,Department of Mathematics
来源
Acta Mathematica Sinica, English Series | 2015年 / 31卷
关键词
Planar graph; total coloring; chordal 7-cycle; 05C15;
D O I
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中图分类号
学科分类号
摘要
A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color. In this paper, it is proved that if G is a planar graph with Δ(G) ≥ 7 and without chordal 7-cycles, then G has a (Δ(G)+1)-total-coloring.
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页码:1951 / 1962
页数:11
相关论文
共 84 条
  • [1] Borodin O. V.(1987)Coupled colorings of graphs on a plane (in Russian) Metody Diskret. Analiz 45 21-27
  • [2] Borodin O. V.(1989)On the total coloring of planar graphs J. Reine Angew. Math. 394 180-185
  • [3] Borodin O. V.(1997)Total colorings of planar graphs with large maximum degree J. Graph Theory 26 53-59
  • [4] Kostochka A. V.(1997)List edge and list total colourings of multigarphs J. Combin. Theory Ser. B 71 184-204
  • [5] Woodall D. R.(1998)Total colourings of planar graphs with large girth European J. Combin. 19 19-24
  • [6] Borodin O. V.(2011)Local condition for planar graphs of maximum degree 7 to be 8-totally colorable Discrete Appl. Math. 159 760-768
  • [7] Kostochka A. V.(2013)Total coloring of planar graphs with maximum degree 8 and without 5-cycles with two chords Theoret. Comput. Sci. 476 16-23
  • [8] Woodall D. R.(2014)Total colorings of Electron. J. Combin. 21 56-2784
  • [9] Borodin O. V.(2009)-free planar graphs with maximum degree 8 Discrete Appl. Math. 157 2778-163
  • [10] Kostochka A. V.(2011)Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable Discrete Appl. Math. 159 157-214