On the Excluded Minors for Regular Matroids which Yield Cographic Splitting Matroids

Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. We obtain a forbidden minor characterization of a regular matroid M for which the splitting matroid M-x,M-y is cographic for every pair x, y of elements of M. This problem is solved by proving that there are exactly two minor-minimal graphs and one matrix which has R-10 as a minor does not have this property.