Win-Loss Sequences for Generalized Roundrobin Tournaments

In a tournament, each of $n$ teams wins or loses against each of the other $n-1$ teams $c$ times. If team $i$ wins a total of $w_i$ games, then the sequence $( w_1, w_2, \ldots , w_n )$ is called the score sequence of the tournament. In this paper we give necessary and sufficient conditions on a sequence in order that it be a score sequence for a tournament.