The 3 and 4-dichromatic tournaments of minimum order Original Research Article

The dichromatic number dc(D) of a digraph D is the minimum number of acyclic sets in which V(D) can be partitioned. If dc(D) = r, D is said r-dichromatic. In this paper it is proved that the minimum order of a 3-dichromatic (resp. 4-dichromatic) tournament is 7 (resp. 11). It is also proved that there are exactly four nonisomorphic 3-dichromatic tournaments of order 7 and a unique 4-dichromatic tournament of order 11. All these tournaments are characterized.