ON THE PARAMETERIZED COMPLEXITY OF COUNTING SMALL-SIZED MINIMUM (S,T)-CUTS

The counting of minimum edge (S, T)-cuts in undirected graphs, parameterized by the size p of these cuts, is FPT. The best performance in the literature is O\ast(2O(p2)). We treat a more general problem of counting minimum (S, T)-cuts composed of vertices instead of edges. We propose an FPT algorithm with running time O\ast(2O(p log p)). As it may be applied to the edge version as well, we improve the time complexity of the minimum edge (S, T )-cuts counting.