Abstract
The second problem we consider is to find a compact representation of F. We prove that there exists a so-called hypercactus K of size O(|V|), consisting of cycles and (hyper)edges arranged in a tree-like manner, and a mapping from V to V(K) in such a way that there is a bijection between the minimum cuts of K and the members of F. If F corresponds to the minimum cuts of a k-edge-connected graph then K reduces to the well-known cactus representation of minimum cuts due to Dinitz et al.
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Received September 1995 / Revised version received March 1997 Published online March 16, 1999
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Fleiner, T., Jordán, T. Coverings and structure of crossing families. Math. Program. 84, 505–518 (1999). https://doi.org/10.1007/s101070050035
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DOI: https://doi.org/10.1007/s101070050035