Tutte Colloquium -Rutger Campbell-The excluded minors for Z3 -gainable biased graphs

Abstract: A biased graph is a pair (G,B) consisting of a graph G and a collection B of “balanced" cycles in G. Biased graphs arise naturally as the cycles that have identity weight in a group-labelling of arcs where opposite arcs have inverse weight. I present an excluded minor characterization for biased graphs that have such a group-labelling over Z₃.