David Karger developed an algorithm for estimating graph reliability; a key lemma in this algorithm is that if a graph has minimal cut-set size $c$, then the number of cut-sets of size $\alpha c$ is $\leq n^{2 \alpha}$.

However, these cuts need not be minimal (a cut-set is minimal iff it contains no smaller cut-set). Are there any better bounds on the number of minimal cut-sets of size $\leq \alpha c?$