Exponentially many 3-colorings of planar triangle-free graphs with no short separating cycles

被引：1
|
作者：
Thomassen, Carsten [1 ]
机构：
[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, DK-2800 Lyngby, Denmark
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2023年 / 158卷
关键词：
Planar graphs; 3-colorings; ENTROPY;
D O I：
10.1016/j.jctb.2021.01.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The number of proper vertex-3-colorings of every triangle-free planar graph with n vertices and with no separating cycle of length 4 or 5 is at least 2n/17700000. On the other hand, for infinitely many n, there exists a triangle-free planar graph with separating cycles of length 4 and 5 whose number of proper vertex-3-colorings is < 215n/ log2(n). (c) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：301 / 312
页数：12
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