Computing the minimum cut in hypergraphic matroids

Hypergraphic matroids were de ned by Lorea as generalizations of graphic matroids. We show that the minimum cut (co-girth) of a multiple of a hypergraphic matroid can be computed in polynomial time. It is well-known that the size of the minimum cut (co-girth) of a graph can be computed in polynomial time. For connected graphs, this is equivalent to computing the co-girth of the circuit matroid. On the other hand, it is NP-hard to determine the girth of a transversal matroid (see McCormick [6]), so the problem of nding the co-girth is hard for fairly simple matroid classes such as gammoids. It would be useful to have new classes of matroids where the problem is tractable. In the rst section of this note we brie y review the known results on the co-girth of multiples of graphic matroids, and in the second section we show that the problem remains tractable for hypergraphic matroids.