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

For k¿=¿2, a strongly connected digraph D is called -connected if it contains a set of arcs W such that contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by Volkmann as . In this paper we bound 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 then where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments.Peer ReviewedPostprint (author's final draft

Vertex-disjoint cycles in bipartite tournaments

Let k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.Peer ReviewedPostprint (author's final draft