Excluded-minors for the class of graphic splitting matroids. (English) Zbl 1249.05048

Summary: This paper studies the splitting operation for binary matroids that was introduced by T. T. Raghunathan, M. M. Shikare and B. N. Waphare [Discrete Math. 184, No. 1–3, 267–271 (1998; Zbl 0955.05022)] 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.


05B35 Combinatorial aspects of matroids and geometric lattices
05C75 Structural characterization of families of graphs
05C83 Graph minors


Zbl 0955.05022