Extending the notion of 3-fold-3-point-splitting from graphs to binary matroids

Abstract

Slater defined r-fold-n-point-splitting operation on graphs and proved that, if G is an n-connected graph and H is a graph obtained from G by an r-fold-n-pointsplitting, then H is n-connected. In this article we extend this notions from graphs to binary matroids and give some similar results to matroids. Moreover, we examine the Eulerianity of the resulting matroid obtained by this operation when the original matriod is Eulerian.