Abstract
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.
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