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.
We obtain some results concerning the planarity and graphicness of the splitting matroids. Further, we explore the effect of splitting operation on the sum of two matroids.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.