A min-max theorem for circuit decompositions of group-labelled graphs

Rose McCarty, University of Waterloo
Fine Hall 224

In-Person 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 "non-zero" if this word does not evaluate to 0. We give a precise min-max theorem for the following problem. Given a vertex v, what is the maximum number of non-zero 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 vertex-minors which is due to Bouchet and Kotzig.