Abstract
A polynomial test for deciding whether or not a given binary matroid has the max-flow min-cut property is described. In addition polynomial algorithms for finding shortest routes and extreme integral max flows in max-flow min-cut matroids are developed. The algorithms make use of a decomposition result for the max-flow min-cut matroids that was previously established in joint work with F.-T. Tseng. The max-flow algorithm also implies a strengthened version of P. D. Seymour's original characterization of the max-flow min-cut matroids.
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