论文信息 - Total Colorings of Planar Graphs without Small Cycles - 字舞流文

Total Colorings of Planar Graphs without Small Cycles

Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 8 and G is free of k-cycles for some k ∈ {5,6}, then the total chromatic number χ′′(G) of G is Δ + 1.

Jianfeng Hou | Guizhen Liu | Jian-Liang Wu | Yan Zhu | Mei Lan | Jian-Liang Wu | Yan Zhu | G. Liu | Jianfeng Hou | Mei Lan

[1] M. Rosenfeld,et al. On the total coloring of certain graphs , 1971 .

[2] J. A. Bondy,et al. Graph Theory with Applications , 1978 .

[3] Jianfeng Hou,et al. List edge and list total colorings of planar graphs without 4-cycles , 2006, Theor. Comput. Sci..

[4] Ping Wang,et al. A note on total colorings of planar graphs without 4-cycles , 2004, Discuss. Math. Graph Theory.

[5] Yue Zhao,et al. On total 9-coloring planar graphs of maximum degree seven , 1999, J. Graph Theory.

[6] Alexandr V. Kostochka,et al. Total colorings of planar graphs with large maximum degree , 1997, J. Graph Theory.

[7] Uppaluri S. R. Murty,et al. Graph Theory with Applications , 1978 .

[8] V. G. Vizing. SOME UNSOLVED PROBLEMS IN GRAPH THEORY , 1968 .

[9] Abddn SANCHEZ-ARROYO,et al. Determining the total colouring number is np-hard , 1989, Discret. Math..

[10] Alexandr V. Kostochka,et al. The total coloring of a multigraph with maximal degree 4 , 1977, Discret. Math..

[11] Alexandr V. Kostochka,et al. The total chromatic number of any multigraph with maximum degree five is at most seven , 1996, Discret. Math..

[12] N. Vijayaditya. On Total Chromatic Number of a Graph , 1971 .

[13] Oleg V. Borodin,et al. On the total coloring of planar graphs. , 1989 .

[14] Alexandr V. Kostochka,et al. Total Colourings of Planar Graphs with Large Girth , 1998, Eur. J. Comb..