EXCLUDED-MINORS FOR THE CLASS OF GRAPHIC SPLITTING MATROIDS

This paper is based on the splitting operation for binary matroids that was introduced by Raghunathan, Shikare and Waphare [Discrete Math. 184 (1998), p.267-271] as a natural generalization of the corresponding operation in graphs. Here, we consider the problem of determining precisely which graphs G have the property that the splitting operation, by every pair of edges, on the cycle matroid M(G) yields a graphic matroid. This problem is solved by proving that there are exactly four minor-minimal graphs that do not have this property.