Location: Hill 705
Date & time: Thursday, 06 December 2018 at 5:00PM - 5:48PM
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.