Eplett's theorem for self-converse generalised tournaments

TL;DR

This paper extends Eplett's theorem, which characterizes score sequences of self-converse tournaments, to the broader class of generalised tournaments, providing a comprehensive criterion for their score sequences.

Contribution

The paper generalizes Eplett's theorem from standard to generalised tournaments, offering a necessary and sufficient condition for score sequences of self-converse structures.

Findings

Extended Eplett's theorem to generalised tournaments

Provided a complete characterization of score sequences

Enhanced understanding of self-converse tournament structures

Abstract

The converse of a tournament is obtained by reversing all arcs. If a tournament is isomorphic to its converse, it is called self--converse. Eplett provided a necessary and sufficient condition for a sequence of integers to be realisable as the score sequence of a self--converse tournament. In this paper we extend this result to generalised tournaments.