A note on reducible cycles in multipartite tournaments (Q698553)

The main lemma (Lemma 4) of this note is an easy consequence of the following more general result by Guo and Volkmann [cf. \textit{Y. Guo}, Semicomplete multipartite digraphs: A generalization of tournaments (Habilitation Thesis, RWTH Aachen) (1998)]. Let \(D\) be a strongly connected \(c\)-partite tournament. Then every partite set of \(D\) has at least one vertex which lies on a cycle \(C_m\) of length \(m\) for each \(m\in\{3,4,\ldots,c\}\) such that \(V(C_3)\subset V(C_4)\subset\cdots \subset V(C_c)\). Also Corollary 9 of this note is well known (cf. Corollary 6.2 of the Habilitation Thesis by Y. Guo). Revievers remark: In 1998, Y. Guo has sent his Habilitation Thesis to the third author Ke-Min Zhang.