Characterizations of vertex pancyclic and pancyclic ordinary complete multipartite digraphs

A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a complete multipartite digraph. Such a digraph D is called ordinary if for any pair X, Y of its partite sets the set of arcs with end vertices in X ∪ Y coincides with X × Y = {x, y) : x ∈ X, y ∈ Y } or Y ×X or X×Y ∪Y ×X. We characterize all the pancyclic and vertex pancyclic ordinary complete multipartite digraphs. Our characterizations admit polynomial time algorithms. ∗ This paper forms part of a Ph.D. thesis written by the author under the supervision of Professor N. Alon at Tel Aviv University.