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

摘要

For k = 2, a strongly connected digraph D is called. lambda(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 lambda(k)'(D) = min {vertical bar W vertical bar : W is a k-restricted arc-cut}. In this paper we bound lambda(k)' 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) = lambda(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. (c) 2018 Elsevier Inc. All rights reserved.