Browsing by Author "Rajan, Arvind"

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    A Short Proof of a Decomposition Theorem for Max-Flow Min-Cut Matroids
    (1986-11) Bixby, Robert E.; Rajan, Arvind
    This report contains short proofs of two known matroid decomposition results, both of which are based on a decomposition algorithm of Truemper. The main result is a recent theorem of Truemper and Tseng for the class of matroids with the max-flow min-cut property, a class characterized by Seymour. The theorem says essentially that every matroid in this class is either isomorphic to F tau or is decomposable into a 3-sum in a well-defined way. The second result describes the structure of regular matroids, and is an important ingredient in Seymour's decomposition theorem for this class.
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    A Short Proof of the Truemper-Tseng Theorem on Max-Flow Min-Cut Matroids
    (1987-10) Bixby, Robert E.; Rajan, Arvind
    Seymour has characterized the matroids satisfying the integral max-flow min-cut property with respect to a fixed element. Truemper and Tseng subsequently proved a decomposition theorem for this class, similar in spirit to Wagner's characterization of the regular (totally unimodular) matroids. The purpose of this paper is to give a short, self-contained exposition of the Truemper-Tseng result.