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. 1