Let $T=(V,E)$ be a tournament. We call it *regular* if all vertices have the same out-degree. It is not hard to see that there are no regular tournaments on an even number of points.


Let $n>0$ be an integer. If $T\_1, T\_2$ are regular tournaments on $2n+1$ vertices, do we always have $T\_1\cong T\_2$?



Regular tournaments
No. Start with a $K\_9$ and compose a tournament of directed cycles built by chords of same "length" in the 9-gon. So there are three $C\_9$ and one $3C\_3$ involved. Now if you reverse the orientation of just one $C\_3$, the resulting tournament should be non isomorphic.


