On computing a conditional edge-connectivity of a graph
Information Processing Letters
Restricted arc-connectivity of digraphs
Information Processing Letters
Information Processing Letters
The restricted arc connectivity of Cartesian product digraphs
Information Processing Letters
Restricted arc-connectivity in tournaments
Discrete Applied Mathematics
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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 @l^'(D). The restricted arc-connectivity offers a more refined parameter than the arc-connectivity to measure the reliability of networks. For the investigation of @l^'(D) the minimum arc-degree@x^'(D) is a useful parameter, introduced by S. Wang and S. Lin in [S. Wang, S. Lin, @l^'-optimal digraphs, Inform. Process. Lett. 108 (2008) 386-389]. In this paper, we study the restricted arc-connectivity of bipartite tournaments and show that @l^'(T)@?@x^'(T) for all strong bipartite tournaments except for a family T, where @l^'(T)=21=@x^'(T) for each T@?T. Furthermore, we prove that all strong bipartite tournaments with @d(T)=(n+3)/8 are optimally restricted arc-connected, i.e. @l^'(T)=@x^'(T), and present examples to show the sharpness of this result.