A note on nearly platonic graphs

30 Jul 2016 · Froncek Dalibor, Keith William J., Kreher Donald L. ·

A nearly platonic graph is a k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for a finite graph to have exactly one disparate face, and offer some conjectures, including the conjecture that graphs with two disparate faces come in a small set of families.