On cycles through two arcs in strong multipartite tournaments
Abstract
A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148--1150], Volkmann proved that a strongly connected c-partite tournament with c 3 contains an arc that belongs to a directed cycle of length m for every m ∈ \3, 4, …, c\. He also conjectured the existence of three arcs with this property. In this note, we prove the existence of two such arcs.
0