Self-Converse Tournaments

Abstract

Let Tn denote a tournament with vertices labelled 1, …, n. Any undefined terms can be found in [5]. The converse of Tn is the tournament obtained by reversing the orientation of all the arcs in Tn. A tournament is called self-converse (s.c.) if . The transitive tournaments are examples of s.c. tournaments. In this paper we provide a structural characterization of s.c. tournaments and we also characterize the score vectors of s.c. tournaments.