Weakly quasi-Hamiltonian-set-connected multipartite tournaments

A multipartite or cc-partite tournament is an orientation of a complete cc-partite graph. Lu and Guo (submitted for publication) [3] recently introduced strong quasi-Hamiltonian-connectivity of a multipartite tournament DD as follows: For any two distinct vertices xx and yy of DD, there is a path with at least one vertex from each partite set of DD from xx to yy and from yy to xx. We obtain the definition for weak quasi-Hamiltonian-connectivity, where only one of those paths, and weak quasi-Hamiltonian-set-connectivity, where only one such path between every two distinct partite sets has to exist, in a natural way.In this paper, we characterize weakly quasi-Hamiltonian-set-connected multipartite tournaments which extends a result of Thomassen (1980) [6].