Single Commodity-Flow Algorithms for Lifts of Graphic and Co-graphic Matroids

摘要

Consider a binary matroid M given by its matrix representation. We show that if M is a lift of a graphic or a co-graphic matroid, then in polynomial time we can either solve the single commodity flow problem for M or find an obstruction for which the Max-Flow Min-Cut relation does not hold. The key tool is an algorithmic version of Lehman's Theorem for the set covering polyhedron.