Restricted arc-connectivity in tournaments
In [L. Volkmann, Restricted arc-connectivity of digraphs, Inform. Process. Lett. 103 (2007) 234239], L. Volkmann introduced a concept of restricted arc-connectivity  for a digraph D D , where the size of a minimum restricted arc-cut is denoted by ??(D) ? ? ( D ) . The restricted arc-connectivity offers a more refined parameter than the arc-connectivity to measure the reliability of networks. For the investigation of ??(D) ? ? ( D ) the minimum arc-degree ??(D) ? ? ( D ) is a useful parameter, introduced by S. Wang and S. Lin in [S. Wang, S. Lin, ?? ? ? -optimal digraphs, Inform. Process. Lett. 108 (2008) 386389]. In this work we characterize all strong tournaments T T with ??(T)???(T) ? ? ( T ) ? ? ? ( T ) . Furthermore, we prove that all tournaments with minimum degree ?(T)?(n+1)/4 ? ( T ) ? ( n + 1 ) / 4 are ?? ? ? -optimal , i. e. ??(T)=??(T) ? ? ( T ) = ? ? ( T ) , and present examples to show the sharpness of this result.
restricted arc-connectivity arc-degree strong tournaments ?? ? ? -optimal ?? ? ? ?? ? ? ? ?