Circular choosability is rational

The circular choosability or circular list chromatic number of a graph is a list-version of the circular chromatic number, that was introduced by Mohar in 2002 and has been studied by several groups of authors since then. One of the nice properties that the circular chromatic number enjoys is that it is a rational number for all finite graphs G, and a fundamental question, posed by Zhu and reiterated by others, is whether the same holds for the circular choosability. In this paper we show that this is indeed the case.