Cycles of Each Length in Regular Tournaments

Abstract

It is known that a strong tournament of order n contains a cycle of each length k, k=3,…, n, ([l], Thm. 7). Moon [2] observed that each vertex in a strong tournament of order n is contained in a cycle of each length k, k = 3,…, n. In this paper we obtain a similar result for each arc of a regular tournament, that is, a tournament in which all vertices have the same score.