On traceable powers of digraphs Original Research Article

Let D be a strongly connected digraph of order n. The kth power Dk of D is the digraph with the same set of vertices, a vertex x being joined to a vertex y≠x in Dk if the directed distance from x to y in D is less than or equal to k. We show that for k⩾⌊n/2⌋, Dk is traceable and we characterize the digraphs D of even order n whose (n/2−1)th power is traceable.