Abstract
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-Hamiltonian-connectivity of a multipartite tournament D as follows: For any two distinct vertices x and y of D, there is a path with at least one vertex from each partite set of D 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].
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