Arc reversals in tournaments

Abstract We discuss when two tournaments defined on the same set of n vertices are equivalent under a sequence of arc reversals of directed paths or cycles of a fixed length. The results are complete except for directed cycles of length n or n -1 in which case we obtain a general sufficient condition. In particular, any two regular tournaments on the same set with at least 21 vertices are equivalent under a sequence of reversals of directed Hamiltonian cycles.