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 \Theta Y = fx; y) : x 2 X; y 2 Y g or Y \Theta X or X \Theta Y [Y \Theta 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. 1. Introduction A digraph D on m disjoint vertex classes (partite sets) is called a complete m-partite or multipartite digraph (abbreviated to CMD) if for any two vertices u; v in different partite sets either (u; v) or (v; u) (or both) is an arc of D and there are no arcs between vertices which are found ..