Restricted arc-connectivity of bipartite tournaments

In [L. Volkmann, Restricted arc-connectivity of digraphs, Inform. Process. Lett. 103 (2007) 234–239], L. Volkmann introduced a concept of restricted arc-connectivity for a digraph D, where the size of a minimum restricted arc-cut is denoted by λ′(D). The restricted arc-connectivity offers a more refined parameter than the arc-connectivity to measure the reliability of networks. For the investigation of λ′(D) the minimum arc-degreeξ′(D) is a useful parameter, introduced by S. Wang and S. Lin in [S. Wang, S. Lin, λ′-optimal digraphs, Inform. Process. Lett. 108 (2008) 386–389]. In this paper, we study the restricted arc-connectivity of bipartite tournaments and show that λ′(T)≤ξ′(T) for all strong bipartite tournaments except for a family T, where λ′(T)=2>1=ξ′(T) for each T∈T. Furthermore, we prove that all strong bipartite tournaments with δ(T)≥(n+3)/8 are optimally restricted arc-connected, i.e. λ′(T)=ξ′(T), and present examples to show the sharpness of this result.