On internally 4-connected non-regular binary matroids

Abstract

We prove that every internally 4-connected non-regular binary matroid other than F 7 and F 7 ∗ has one of the following matroids as a minor: K 5 , K 5 ∗ , N 10, T 12⧹ e and T 12/ e. As corollaries, we prove a theorem related to Tutte's characterization of graphic matroids and a conjecture by Dharmatilake on excluded minors for the class of binary matroids with branch-width at most 3.