Bixby, Robert E.Rajan, Arvind2018-06-182018-06-181986-11Bixby, Robert E. and Rajan, Arvind. "A Short Proof of a Decomposition Theorem for Max-Flow Min-Cut Matroids." (1986) <a href="https://hdl.handle.net/1911/101610">https://hdl.handle.net/1911/101610</a>.https://hdl.handle.net/1911/101610This 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.18 ppengTechnical reportTR86-24