Extension of line-splitting operation from graphs to binary matroids

Abstract

In this paper, we characterize the n-line splitting operation of graphs in terms of cycles of respective graphs and then extend this operation to binary matroids. In matroids, we call this operation as element-set splitting. For convenience, we call the resulting matroid, es-splitting matroid. We characterize circuits of es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices. We also show that if M is a connected binary matroid then es-splitting matroid is also connected.