Graph Theory Seminar
Thursday, November 17, 2011 - 12:05pm
1 hour (actually 50 minutes)
A classical result in graph theory states that, if G is a plane graph, then G is Eulerian if and only if its dual, G*, is bipartite. I will talk about an extension of this well-known result to partial duality. (Where, loosely speaking, a partial dual of an embedded graph G is a graph obtained by forming the dual with respect to only a subset of edges of G.) I will extend the above classical connection between bipartite and Eulerian plane graphs, by providing a necessary and sufficient condition for the partial dual of a plane graph to be Eulerian or bipartite. I will then go on to describe how the bipartite partial duals of a plane graph G are completely characterized by circuits in its medial graph G_m. This is joint work with Stephen Huggett.