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
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