On n-connected splitting matroids

Abstract

In general, the splitting operation on a binary matroid M does not preserve the connectivity of M. In this paper, we provide sufficient conditions to preserve n-connectedness of a binary matroid under splitting operation. As a consequence, for an (n + 1)connected binary matroid M, we give a precise characterization of when the splitting matroid M T is n-connected. c

Connectivity of single-element coextensions of a binary matroid

“…Let M be an n-connected binary matroid. Borse and Mundhe [3] obtained sufficient conditions for the matroid M ′ T \a to be n-connected. In this paper, we obtain a necessary and sufficient condition for M ′ T to be n-connected.…”

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

“…x k y h y 2 y 1 e q q q q q q r r r r r x k v y 1 y 2 y h a e γ q q q q q q G H splitting operation along with some other operations. The notion of connectivity of graphs also has been studied in [6,13] and connectivity of binary matroids has been studied in [3,14]. Suppose G is a graph with n vertices and m edges.…”

On graphic splitting of regular matroids

“…In general, the splitting operation may not preserve some properties of the given matroid; see [1,2,3,4,10]. It is an interesting to check that when the graphic matroids remain graphic under the splitting operation.…”