Internally 4-connected binary matroids with cyclically sequential orderings

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 M

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Jeremy Aikin, Carolyn Chun, Rhiannon Hall, Dillon Mayhew
• Keywords: 4-connected Binary Matroids, DM 2010, Matroid, Particular Single-element Extension