# Bounds on number of small minimal cut-sets in graph?

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 $\leq \alpha c?$

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