Graphic Elementary Lift of Cographic Matroids

Abstract

A matroid N is a lift of a binary matroid M , if N = Q\X when Q/X = M for some binary matroid Q and X ⊆ E(Q) and is called an elementary lift of M , if |X| = 1. A splitting operation on a binary matroid can result in an elementary lift. An elementary lift of a cographic or a graphic matroid need not be cographic or graphic. We intend to characterize the cographic matroids whose elementary lift is a graphic matroid.