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 k-restricted 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.