Epsilon-colorings of strips

Abstract

A special case of the Hadwiger-Nelson problem is to color a strip instead of the whole plane.
The aim is to maximize the width of the strip such that it still permits a coloring with $c$ colors.
We present a coloring that improves the recently best known value for 4 colors.
This is discovered by considering colorings that satisfy slightly stronger distance conditions.
Moreover, we can show under a sensible assumption that this value is best possible for the stronger version of the distance conditions.