On Regular $r$-Tournaments

Abstract

The notion of a regular tournament is generalized to $r$-tournaments. By means of a construction, it is shown that if $n\mid (\genfrac{}{}{0ex}{}{n}{r})$ and $(n,r)=p^k$, where $p$ is a prime, and $k\ge 0$, then there exists a regular $r$-tournament on $n$ vertices.