Regular tournament
= Regular tournament
{title2=$d^+(v)=d^-(v)=(N-1)/2$}
A regular <tournament> has equal <outdegree> and indegree at every vertex. On $2k+1$ vertices, label by residues modulo $2k+1$ and direct $i\to j$ when $j-i\in\{1,\ldots,k\}$. This gives an explicit regular tournament. It contains no outward-oriented star with more than $k$ leaves.