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

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively

Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe

Cycles through arcs in multipartite tournaments and a conjecture of Volkmann

AbstractVolkmann [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148–1150] conjectured that a strong c-partite tournament with c≥3 contains three arcs that belong to a cycle of length m for each m∈{3,4,…,c}. In this work, we prove that Volkmann’s conjecture is true