A note on nearly platonic graphs

William J. Keith, Dalibor Froncek, Donald L. Kreher

Research output: Contribution to journalArticlepeer-review

Abstract

We define a nearly platonic graph to be a finite 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 such a graph to have exactly one disparate face, and offer some conjectures, including the conjecture that nearly platonic graphs with two disparate faces come in a small set of families.

Original languageEnglish (US)
Pages (from-to)86-103
Number of pages18
JournalAustralasian Journal of Combinatorics
Volume70
Issue number1
StatePublished - Feb 2018

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