Weakly quasi-Hamiltonian-set-connected multipartite tournaments

A multipartite or c-partite tournament is an orientation of a complete c-partite graph. Lu and Guo (submitted for publication) [3] recently introduced strong quasi-Hamiltonianconnectivity of a multipartite tournament D as follows: For any two distinct vertices x and y ofD, there is a pathwith at least one vertex from each partite set ofD from x to y and from y to x. 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]. © 2012 Elsevier B.V. All rights reserved.