A minmax theorem for circuit decompositions of grouplabelled graphs
A minmax theorem for circuit decompositions of grouplabelled graphs

Rose McCarty, University of Waterloo
Fine Hall 224
InPerson Talk
This talk focuses on Eulerian graphs whose arcs are directed and labelled in a group. Each circuit yields a word over the group, and we say that a circuit is "nonzero" if this word does not evaluate to 0. We give a precise minmax theorem for the following problem. Given a vertex v, what is the maximum number of nonzero circuits in a circuit decomposition where each circuit begins and ends at v? This is joint work with Jim Geelen and Paul Wollan. Our main motivation is a surprising connection with vertexminors which is due to Bouchet and Kotzig.