论文信息 - Total colorings of planar graphs without adjacent triangles

Total colorings of planar graphs without adjacent triangles

Let G be a planar graph without adjacent 3-cycles, that is, two cycles of length 3 are not incident with a common edge. In this paper, it is proved that the total coloring conjecture is true for G; moreover, if @D(G)>=9, then the total chromatic number @g^''(G) of G is @D(G)+1. Some other related results are obtained, too.

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

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

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

[4] H. Yap. Total Colourings of Graphs , 1996 .

[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 Colourings of Planar Graphs with Large Girth , 1998, Eur. J. Comb..

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