A totally (Δ + 1)-colorable 1-planar graph with girth at least five

被引：0
作者：
Lin Sun
Jian Liang Wu
Hua Cai
机构：
[1] Shandong University,School of Mathematics
[2] Changji University,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2016年 / 32卷
关键词：
1-planar graph; total coloring; discharging method; girth; 05C15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree Δ(G) ≥ 12 and girth at least five is totally (Δ(G) + 1)-colorable.
引用
收藏
页码：1337 / 1349
页数：12
相关论文
共 40 条
  • [1] Borodin O. V.(1989)On the total coloring of planar graphs J. Reine Angew. Math. 394 180-185
  • [2] Borodin O. V.(1997)List edge and list total colorings of multigraphs J. Combin. Theory Ser. B 71 184-204
  • [3] Kostochka A. V.(1997)Total colorings of planar graphs with large maximum degree J. Graph Theory 26 53-59
  • [4] Woodall D. R.(2013)A note on total colorings of 1-planar graphs Inform. Process. Lett. 113 516-517
  • [5] Borodin O. V.(2013)Neighbor sum distinguishing total colorings via the Combinatorial Nullstellensatz Sci. China Ser. A 57 1875-1882
  • [6] Kostochka A. V.(2008)Total colorings of planar graphs without small cycles Graphs Combin. 24 91-100
  • [7] Woodall D. R.(1996)The total chromatic number of any multigraph with maximum degree five is at most seven Discrete Math. 162 199-214
  • [8] Czap J.(2008)Total-coloring of plane graphs with maximum degree nine SIAM J. Discrete Math. 22 1462-1479
  • [9] Ding L. H.(2014)Neighbor sum distinguishing total colorings of planar graphs J. Comb. Optim. 60 777-791
  • [10] Wang G. H.(1965)Ein Sechsfarbenproblem auf der Kugel Abh. Math. Sem. Univ. Hamburg 29 107-117
1234