Vertex critical r-dichromatic tournaments (Q788737)

The dichromatic number d(D) of a directed graph D is the smallest number of colours needed to colour the vertices of D in such a way that D contains no monochromatic directed cycle. If \(d(D)=r\) but \(d(D-v)=r-1\) for every vertex v of D, then D is a critical r-dichromatic digraph. The authors construct an infinite family of critical r-dichromatic regular tournaments for every r such that \(r=3\) or \(r\geq 5\).