The class of binary matroids with no M(K-3,K-3)-, M*(K-3,K-3)-, M(K-5)- or M*(K-5)-minor

摘要

We prove that an internally 4-connected binary matroid with no minor isomorphic to M(K-3,(3)),M*(K-3,(3)),M(K-5), or M*(K-5) is either planar or isomorphic to F-7 or F-7*. As a corollary, we prove an extremal result for the class of binary matroids without these minors. (C) 2003 Elsevier Inc. All rights reserved. [References: 11]