Plane Graphs are Facially-non-repetitively $10^{4\cdot 10^7}$-Choosable

Abstract

A sequence $\left(x_1,x_2,\dots ,x_{2n}\right)$ of even length is a repetition if $\left(x_1,\dots ,x_n\right)=\left(x_{n+1},\dots ,x_{2n}\right)$. We prove existence of a constant $C<10^{4\cdot 10^7}$ such that given any planar drawing of a graph $G$, and a list $L(v)$ of $C$ permissible colors for each vertex $v$ in $G$, there is a choice of a permissible color for each vertex such that the sequence of colors of the vertices on any facial simple path in $G$ is not a repetition.

References in corpus (2)

• Nonrepetitive Colourings of Planar Graphs with $O(\log n)$ Colours
• Pathwidth and nonrepetitive list coloring