Coloring triangle-free graphs with fixed size

被引：9
|
作者：
Gimbel, J [1 ]
Thomassen, C
机构：
[1] Univ Alaska Fairbanks, Fairbanks, AK 99775 USA
[2] Tech Univ Denmark, Inst Math, DK-2800 Lyngby, Denmark
来源：
DISCRETE MATHEMATICS | 2000年 / 219卷 / 1-3期
关键词：
D O I：
10.1016/S0012-365X(00)00087-X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Combining recent results on colorings and Ramsey theory, we show that if G is a triangle-free graph with e edges then the chromatic number of G is at most cel(1/3)(log e)(-2/3) for some constant c. In a previous paper, we found an upper bound on the chromatic number of a triangle-free graph of genus g. Using the new result, we slightly improve this bound to cg(1/3)(log g)(-2/3). Both bounds are best possible, up to a constant multiple. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：275 / 277
页数：3
相关论文
共 50 条
  • [31] Acyclic Edge Coloring of Triangle-free 1-planar Graphs
    Wen Yao SONG
    Lian Ying MIAO
    [J]. ActaMathematicaSinica., 2015, 31 (10) - 1570
  • [32] List Coloring Triangle-Free Hypergraphs
    Cooper, Jeff
    Mubayi, Dhruv
    [J]. RANDOM STRUCTURES & ALGORITHMS, 2015, 47 (03) : 487 - 519
  • [33] Median graphs and triangle-free graphs
    Imrich, W
    Klavzar, S
    Mulder, HM
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1999, 12 (01) : 111 - 118
  • [34] Three-coloring triangle-free graphs on surfaces V. Coloring planar graphs with distant anomalies
    Dvorak, Zdenek
    Kral, Daniel
    Thomas, Robin
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2021, 150 : 244 - 269
  • [35] The Size of Maximally Irregular Graphs and Maximally Irregular Triangle-Free Graphs
    Fengxia Liu
    Zhao Zhang
    Jixiang Meng
    [J]. Graphs and Combinatorics, 2014, 30 : 699 - 705
  • [36] Triangle-free equimatchable graphs
    Buyukcolak, Yasemin
    Ozkan, Sibel
    Gozupek, Didem
    [J]. JOURNAL OF GRAPH THEORY, 2022, 99 (03) : 461 - 484
  • [37] ON MAXIMAL TRIANGLE-FREE GRAPHS
    ERDOS, P
    HOLZMAN, R
    [J]. JOURNAL OF GRAPH THEORY, 1994, 18 (06) : 585 - 594
  • [38] Triangle-free polyconvex graphs
    Isaksen, DC
    Robinson, B
    [J]. ARS COMBINATORIA, 2002, 64 : 259 - 263
  • [39] On the evolution of triangle-free graphs
    Steger, A
    [J]. COMBINATORICS PROBABILITY & COMPUTING, 2005, 14 (1-2): : 211 - 224
  • [40] On triangle-free projective graphs
    Hazan, S
    [J]. ALGEBRA UNIVERSALIS, 1996, 35 (02) : 185 - 196
12345