The es-splitting Operation for Matroids Representable Over Prime Fields GF(p)

The es-splitting operation for binary matroids is a natural generalization of Slater’s n-line splitting operation on graphs. The present paper extends the es-splitting operation to the matroids representable over the field GF(p),  called the p-matoids. We characterize circuits, and bases of the resulting matroid in terms of the circuits, and the bases of the original matroid, respectively. It is proved that the es-splitting operation preserves the connectivity of the p-matoids. A Sufficient condition to obtain a 3-connected p-matroid from a 3-connected p-matroid using the es-splitting operation is also provided. In the last section, we obtain a sufficient condition to produce an Eulerian p-matroid from an Eulerian p-matroid using es-splitting operation.