Department of
Applied
Mathematics

Circular choosability is rational

Tobias Mueller

Technische Universiteit Eindhoven

Abstract

The circular chromatic number of a graph is a refinement of the ordinary chromatic number that has attracted considerable attention since its introduction by Vince in 1988. One of the nice properties it enjoys that it is a rational number that lies between the chromatic number and the chromatic number minus one.

In 2002 Mohar introduced a ``list version'' of the circular chromatic number, the circular choosability. After a brief overview of known results and open problems on circular choosability, I will give a proof of the (nontrivial) fact that the circular choosability is a rational number for all graphs.