Decomposing oriented graphs into transitive tournaments

For an oriented graph G with n   vertices, let f(G)f(G) denote the minimum number of transitive subtournaments that decompose G  . We prove several results on f(G)f(G). In particular, if G   is a tournament then f(G)<521n2(1+o(1)) and there are tournaments for which f(G)>n2/3000f(G)>n2/3000. For general G   we prove that f(G)⩽⌊n2/3⌋f(G)⩽⌊n2/3⌋ and this is tight. Some related parameters are also considered.