On total chromatic number of planar graphs without 4-cycles

被引：0
|
作者：
Min-le SHANGGUAN
机构：
[1] China
[2] College of Mathematics Physics and Information Engineering Zhejiang Normal University
[3] Jinhua 321004
来源：
Science China Mathematics | 2007年 / 01期
基金：
中国国家自然科学基金;
关键词：
total chromatic number; planar graph; F5-subgraph;
D O I：
暂无
中图分类号：
O157.5 [图论];
学科分类号：
070104 ;
摘要：
Let G be a simple graph with maximum degree A(G) and total chromatic number Xve(G). Vizing conjectured thatΔ(G) + 1≤Xve(G)≤Δ(G) + 2 (Total Chromatic Conjecture). Even for planar graphs, this conjecture has not been settled yet. The unsettled difficult case for planar graphs isΔ(G) = 6. This paper shows that if G is a simple planar graph with maximum degree 6 and without 4-cycles, then Xve(G)≤8. Together with the previous results on this topic, this shows that every simple planar graph without 4-cycles satisfies the Total Chromatic Conjecture.
引用
收藏
页码：81 / 86
页数：6
相关论文
共 50 条
  • [1] On total chromatic number of planar graphs without 4-cycles
    Ying-qian Wang
    Min-le Shangguan
    Qiao Li
    [J]. Science in China Series A: Mathematics, 2007, 50 : 81 - 86
  • [2] On total chromatic number of planar graphs without 4-cycles
    Wang, Ying-qian
    Shangguan, Min-le
    Li, Qiao
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2007, 50 (01): : 81 - 86
  • [3] Neighbor sum distinguishing total chromatic number of planar graphs without, 4-cycles
    Ge, Shan
    Li, Jianguo
    Xu, Changqing
    [J]. UTILITAS MATHEMATICA, 2017, 105 : 259 - 265
  • [4] Total Coloring of Planar Graphs without Adacent 4-cycles
    Tan, Xiang
    Chen, Hong-Yu
    Wu, Jian-Liang
    [J]. OPERATIONS RESEARCH AND ITS APPLICATIONS, PROCEEDINGS, 2009, 10 : 167 - 173
  • [5] ON THE NUMBER OF GRAPHS WITHOUT 4-CYCLES
    KLEITMAN, DJ
    WINSTON, KJ
    [J]. DISCRETE MATHEMATICS, 1982, 41 (02) : 167 - 172
  • [6] A note on the total coloring of planar graphs without adjacent 4-cycles
    Wang, Hui-Juan
    Wu, Jian-Liang
    [J]. DISCRETE MATHEMATICS, 2012, 312 (11) : 1923 - 1926
  • [7] FLEXIBILITY OF PLANAR GRAPHS WITHOUT 4-CYCLES
    Masarik, T.
    [J]. ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2019, 88 (03): : 935 - 940
  • [8] Improved upper bound for acyclic chromatic index of planar graphs without 4-cycles
    Wang, Yingqian
    Sheng, Ping
    [J]. JOURNAL OF COMBINATORIAL OPTIMIZATION, 2014, 27 (03) : 519 - 529
  • [9] Improved upper bound for acyclic chromatic index of planar graphs without 4-cycles
    Yingqian Wang
    Ping Sheng
    [J]. Journal of Combinatorial Optimization, 2014, 27 : 519 - 529
  • [10] Total colorings and list total colorings of planar graphs without intersecting 4-cycles
    Liu, Bin
    Hou, Jianfeng
    Wu, Jianliang
    Liu, Guizhen
    [J]. DISCRETE MATHEMATICS, 2009, 309 (20) : 6035 - 6043
12345