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No abstract

In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M (K 4).

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,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.