Weakly quasi-Hamiltonian-set-connected multipartite tournaments
A multipartite or c c -partite tournament is an orientation of a complete c c -partite graph. Lu and Guo (submitted for publication)[3] recently introduced strong quasi-Hamiltonian-connectivity of a multipartite tournament D D as follows: For any two distinct vertices x x and y y of D D , there is a path with at least one vertex from each partite set of D D from x x to y y and from y y to x 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].
multipartite tournament quasi-hamiltonian-connectivity weak quasi-hamiltonian-set-connectivity