Bounds on the k-restricted arc connectivity of some bipartite tournaments

Abstract

For k ≥ 2, a strongly connected digraph D is called λ k-connected if it contains a set of arcs W such that D − W contains at least k non-trivial strong components. The krestricted arc connectivity of a digraph D was defined by Volkmann as λ k (D) = min {| W | : W is a k-restricted arc-cut }. In this paper we bound λ k (T) for a family of bipartite tournaments T called projective bipartite tournaments. We also introduce a family of "good" bipartite oriented digraphs. For a good bipartite tournament T we prove that if the minimum degree of T is at least 1. 5 k − 1 then k (k − 1) ≤ λ k (T) ≤ k (N − 2 k − 2) , where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments.