UNAVOIDABLE PARALLEL MINORS AND SERIES MINORS OF REGULAR MATROIDS
Carolyn Chun, JAMES G. OXLEY · 2009
To the memory of Tom Brylawski, who contributed so much to matroid theory. Abstract. We prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M∗(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtained from K2,k by adding paths through the vertices of each vertex class, or the cycle matroid of the graph obtained from K3,k by adding a complete graph on the vertex class with three vertices. 1.