Weakly quasi-Hamiltonian-connected multipartite tournaments

Abstract

A multipartite or c-partite tournament is an orientation of a complete c-partite graph. In 2013, Lu, Guo and Surmacs introduced the concept of quasi-Hamiltonian paths, that is to say, a directed path containing vertices from each partite set, in multipartite tournaments. They established that every 4-strong multipartite tournament is strongly quasi-Hamiltonian-connected–i.e., for every pair of vertices x1, x2, there is a quasi-Hamiltonian path from x1 to x2.In this paper, we characterize all weakly quasi-Hamiltonian-connected multipartite tournaments–i.e., for every pair of vertices, there is at least one quasi-Hamiltonian path between them. Our results include and extend corresponding ones concerning tournaments due to Thomassen.