a tournament r is called transitive if for all uv, vw E A(T), we have uw E A(T) Let be a tournament with n 3 vertices. We will prove the following three statements are equivalent (a) T is transitive. (b) T is acyclic. (c) T has a unique Hamilton dipath. . Show (a) implies (b) by showing that if T has a directed cycle with k vertices for some 3skSn, then T has a cycle with 3 vertices. . Show (b) implies (c). Assume there are two different Hamilton dipaths. There is a pair of vertices u and v such that u appears before v in one Hamilton dipath and u appears after v in the other. . Show (c) implies (a)