Extendable cycles in multipartite tournaments (Q1889827)

A multipartite tournament is an orientation of a complete multipartite graph. Let \(D\) be a strongly connected multipartite tournament with partite sets \(V_1,V_2,\dots,V_n\) and let \(n\geq 3.\) The authors prove that for each \(i\in \{1,2,\dots,n\}\) there is a vertex \(v\in V_i\) and cycles \(C_3,C_4,\dots,C_n\) such that each \(C_i\) has \(i\) vertices, \(v\in V(C_3)\) and all vertices of \(C_i\) are vertices of \(C_j\) for each \(i<j.\) This generalizes theorems by Bondy, Guo and Volkmann, Gutin, Moon, and Yeo.