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 x(1), x(2), there is a quasi-Hamiltonian path from x(1) to x(2).
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