Extension of Line-splitting Operation from Graphs to Binary Matroid

(Lobachevskii Journal of Mathematics, Volume XXIV)

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 an element-set splitting. The resulting matroid is called the es-splitting matroid. We characterize circuits of an es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices. Also, we show that if M is a connected binary matroid then the es-splitting matroid M ^e_X is also connected.