无变位色数不是路径有界的
Anagram-Free Chromatic Number is not Pathwidth-Bounded
摘要：
Anagram-free色数是一个新的图形参数，由Kamčev，Zuczak，and Sudakov（2017）和Wilson and Wood（2017）独立引入。本文证明了路宽为3的可平面图具有任意大的Anagram-free色数。更具体地说，我们描述了$2n$ -顶点可平面图的路径宽度为3与anagram自由色数$Ω(\log n)$。我们还描述了在$Ω(k\log n)$中具有任意色数的$kn$顶点图，其路宽为$2k-1$。
英文摘要：
The anagram-free chromatic number is a new graph parameter introduced independently Kamčev, Łuczak, and Sudakov (2017) and Wilson and Wood (2017). In this note, we show that there are planar graphs of pathwidth 3 with arbitrarily large anagram-free chromatic number. More specifically, we describe $2n$-vertex planar graphs of pathwidth 3 with anagram-free chromatic number $Ω(\log n)$. We also describe $kn$ vertex graphs with pathwidth $2k-1$ having anagram-free chromatic number in $Ω(k\log n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
