Max-cut and containment relations in graphs

Abstract

We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K 5-minor-free graphs) and identify an open problem which is the missing case for a dichotomy theorem. © 2010 Springer-Verlag.