Circular Chromatic Number of Flower Graphs

Abstract

Vince asked whether for each rational $r$ between 2 and 4 there was a planar graph of circular chromatic number $r$. Moser and Zhu showed that the answer is yes, the first for $2<r<3$, the second for $3<r<4$. This paper gives another family of planar graphs with circular chromatic number between 2 and 3.