An algorithm to generate tournament score sequences

A tournament on n vertices is a directed graph obtained by orienting the edges of Kn, the complete graph on n vertices. The score sequence of a tournament is the sequence of out-degrees of its vertices. There is a well-known criterion due to Havel and Hakimi that checks whether or not a given sequence of integers is the score sequence of a graph. This article presents an algorithm based on the Havel-Hakimi criterion that generates score sequences of all tournaments up to a given size.