Cographic element splitting matroids of regular matroids

Abstract

In this paper, we give a forbidden minor characterization for element splitting matroids of a regular matroid to be cographic. The main theorem states that the element splitting operation, by each pair of elements, on a regular matroid yields a cographic matroid if and only if it has no M(K₄)-mmoT and has no M(A₁)-minor for a specific 6×11 binary matrix A₁.