The name "Plummer-Toft graphs" is used in this work for the first of two infinite families noted by Plummer and Toft (1987) that attain the conjectured bound described below.
Let 
be the maximum number of vertices incident with a graph
face of a graph (the maximum face degree) and 
its cyclic chromatic
number. It is conjectured that 
for polyhedral
graphs (Plummer and Toft 1987).
The first few Plummer-Toft graphs are illustrated above in three different types of embeddings.
The 2-Plummer-Toft graph is an outer-cylindrical forbidden minor 
(No. 12; Archdeacon et al. 2001).
