UVictoria Discrete Math Seminar: Mackenzie Carr

A 2-cell embedding of a graph G in an orientable surface of genus k is an embedding in which each face is homeomorphic to an open disk. The distribution of genus across all 2-cell embeddings of G is called the genus distribution of G. In this talk, we explore embeddings of cubic planar graphs, particularly those with small genus. Using local rotations, we explore ways of describing each embedding of a cubic planar graph and how the face structure differs from that of a planar embedding. We introduce the unstable dual of an embedding of a cubic planar graph, a subgraph of the dual graph, and show how the genus of the corresponding embedding can be determined from properties of this unstable dual.

This is joint work with Bojan Mohar (Simon Fraser University and University of Ljubljana).