Compression with wildcards: All spanning trees

02/22/2020

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by   Marcel Wild, et al.

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By processing all minimal cutsets of a graph G, and by using novel wildcards, all spanning trees of G can be compactly encoded. Thus, different from all previous enumeration schemes, the spanning trees are not generated one-by-one. The Mathematica implementation of one of our algorithms generated for a random (11,50)-graph its 819'603'181 spanning trees, in bundles of size about 400, within 52 seconds.