Abstract: | A -partite tournament is an orientation of a complete -partite graph. In 2006, Volkmann conjectured that every arc of a regular 3-partite tournament is contained in an -, - or -cycle for each , and this conjecture was proved to be correct for . In 2012, Xu et al. conjectured that every arc of an -regular 3-partite tournament with is contained in a - or -cycle for . They proved that this conjecture is true for . In this paper, we confirm this conjecture for , which also implies that Volkmann’s conjecture is correct for . |