On n-connected minors of the es-splitting binary matroids

Abstract

The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor of rank-(r + 1) having |E(M )| + 1 elements.