A note on nearly platonic graphs
Combinatorics
2016-08-02 v1
Abstract
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.
Cite
@article{arxiv.1608.00079,
title = {A note on nearly platonic graphs},
author = {Dalibor Froncek and William J. Keith and Donald L. Kreher},
journal= {arXiv preprint arXiv:1608.00079},
year = {2016}
}
Comments
Although we did not find a statement of our main result in a literature search, we remain suspicious that it might be folklore, so we strongly encourage contacting the authors if you know of a previous publication of our main theorem!