Let be the maximum face degree of a graph and its cyclic chromatic number. It is conjectured that for polyhedral graphs (Plummer and Toft 1987).
A number of infinite families satisfying are known, including the stacked 3-prism graphs and two other families noted by Plummer and Toft (1987). The first of these are known in this work as Plummer-Toft graphs, the first few of which are illustrated above.