Triangle-free planar graphs with at most 64n0.731 3-colorings

被引：0
|
作者：
Dvorak, Zdenek [1 ]
Postle, Luke [2 ]
机构：
[1] Charles Univ Prague, Prague, Czech Republic
[2] Univ Waterloo, Waterloo, ON, Canada
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2022年 / 156卷
关键词：
Triangle-free; Planar; Number of colorings; 3-COLORINGS;
D O I：
10.1016/j.jctb.2022.05.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Thomassen conjectured that triangle-free planar graphs have exponentially many 3-colorings. Recently, he disproved his conjecture by providing examples of such graphs with n vertices and at most 215n/ log2 n 3-colorings. We improve his construction, giving examples of such graphs with at most 64(nlog9/2 3) < 64n(0.731 3)-colorings. We conjecture this exponent is optimal. (c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：294 / 298
页数：5
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