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We consider the problem of ÿnding in an undirected graph a minimum cut that separates exactly a given number k of vertices. For general k (i.e. k is part of the input and may depend on n) this problem is NP-hard. We present for this problem a randomized approximation algorithm, which is useful when k is relatively small. In particular, for k = O(log n) we obtain a polynomial time approximation scheme, and for k = (log n) we obtain an approximation ratio O(k=log n). ?doi:10.1016/s0166-218x(02)00394-3 fatcat:apfgkutjezf4dd7fgc2eadygei