Cycle factors in strongly connected local tournaments (Q965966)

A digraph \(D\) without directed cycles of length one or two is a local tournament if the in-neighbours as well as the out-neighbours of each vertex of \(D\) induce an ordinary tournament. The authors develop a number of rather technical results on the structure of strong local tournaments that are not cycle complementary. From this they deduce, among other things, results on the number of cut-vertices in such local tournaments and a sufficient condition for a local tournament to have a collection of \(k\) disjoint cycles that collectively include all the vertices of \(D\).