A NOTE ON CONNECTIVITY PRESERVING SPLITTING OPERATION FOR MATROIDS REPRESENTABLE OVER GF(p)

The splitting operation on a p-matroid does not necessarily preserve connectivity. It is observed that there exists a single element extension of the splitting matroid which is connected. In this paper, we define the element splitting operation on p-matroids which consist of a splitting operation followed by a single element extension. It is proved that the element splitting operation on a connected p-matroid yields a connected p-matroid. We give a sufficient condition to yield Eulerian p-matroid from Eulerian p-matroid under the element splitting operation. A sufficient condition to obtain Hamiltonian p-matroid by applying the element splitting operation on p-matroid is also provided. The characterization of the paving p-matroid which are closed under the element splitting operation, is also obtained.