# Computing all small cuts in undirected networks

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## Abstract

Let *λ(N)* denote the weight of a minimum cut in an edge-weighted undirected network *N*, where *n* and *m* are the numbers of vertices and edges, respectively. It is known that *O*(*n*^{2k}) is an upper bound on the number of cuts with weights less than *kλ(N)*. We first show that all cuts of weights less than *kλ(N)* can be enumerated in *O*(*mn*^{3} + *n*^{2k+2}) time without using the maximum flow algorithm. We then prove for *k*<4/3 that ( _{2} ^{n} ) is a tight upper bound on the number of cuts of weights less than *kλ(N)*.

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© Springer-Verlag Berlin Heidelberg 1994