Sandra Kingan, City University of New York

Abstract

 Regular matroids are binary matroids with no minors isomorphic to the Fano matroid or its dual. The Fano matroid is the binary projective plane PG(2, 2). Seymour proved that 3-connected regular matroids are either graphs, cographs, or a special matroid R10 called a splitter, or else can be decomposed along a non-minimal exact 3-separation induced by another special matroid R12 called a 3-decomposer. Quasiregular matroids are binary matroids with no minor isomorphic to E4, where E4 is a 10-element rank 5 self-dual binary matroid. The class of quasiregular matroids properly contains the class of regular matroids. I will describe how I decomposed quasiregular matroids in a manner similar to regular matroids. There is a compuatational aspect to this result which will be the focus of this talk. A portion of this talk is joint work with Manoel Lemos.