On the Parameterized Complexity of Counting Small-Sized Minimum \(\boldsymbol{(S,T)}\)-Cuts.

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