The Closure Operator of es-Splitting Matroids

Abstract

The es-splitting operation for binary matroids is a natural generalization of Slater's n-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid M e X in terms of the closure operator of the original binary matroid M . We also characterize the flats of the es-splitting binary matroid M e X in terms of the flats of the original binary matroid M .