Internally 4-connected binary matroids with cyclically sequential orderings

Abstract

We characterize all internally 4-connected binary matroids M with the property that the ground set of M can be ordered (e0,…,en−1) in such a way that {ei,…,ei+t} is 4-separating for all 0≤i,t≤n−1 (all subscripts are read modulo n). We prove that in this case either n≤7 or, up to duality, M is isomorphic to the polygon matroid of a cubic or quartic planar ladder, the polygon matroid of a cubic or quartic Möbius ladder, a particular single-element extension of a wheel, or a particular single-element extension of the bond matroid of a cubic ladder