On the characterization of Eulerian $es$-splitting $p$-matroids

Abstract

The es -splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over GF (p), (p > 2), called p -matroids, the essplitting operation may yield Eulerian matroids. In this work, we introduce es -splitting operation for p -matroids and characterize a class of p -matroids yielding Eulerian matroids after the es -splitting operation. Characterization of circuits, and bases of the resulting matroid, after the es -splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the es -splitting operation on p -matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian pmatroid from Hamiltonian p -matroid under es -splitting operation is also provided.