Cycles through arcs in multipartite tournaments and a conjecture of Volkmann

Volkmann [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.