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 View the MathML sourcef(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.