A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian

Jørgen Bang-Jensen, Gregory Gutin, Jing Huang
1996 Discrete Mathematics  
A multipartite tournament is an orientation of a complete k-partite graph for some k ≥ 2. A factor of a digraph D is a collection of vertex disjoint cycles covering all the vertices of D. We show that there is no degree of strong connectivity which together with the existence of a factor will guarantee that a multipartite tournament is Hamiltonian. Our main result is a sufficient condition for a multipartite tournament to be Hamiltonian. We show that this condition is general enough to provide
more » ... asy proofs of many existing results on paths and cycles in multipartite tournaments. Using this condition, we obtain a best possible lower bound on the length of a longest cycle in any strongly connected multipartite tournament.
doi:10.1016/0012-365x(95)00272-x fatcat:cqhpnnleyjg7ll3w75foe4mvrm