On the circuits of splitting matroids representable over GF(p)

Abstract

We extend the splitting operation from binary matroids (Raghunathan et al., 1998) to p -matroids, where p -matroids refer to matroids representable over GF (p). We also characterize circuits, bases, and independent sets of the resulting matroid. Sufficient conditions to yield Eulerian p -matroids from Eulerian and non-Eulerian p -matroids by applying the splitting operation are obtained. A class of connected p -matroids that gives connected p -matroids under the splitting operation is characterized.