Longest path partitions in generalizations of tournaments

We consider the so-called Path Partition Conjecture for digraphs which states that for every digraph, D  , and every choice of positive integers, λ1,λ2λ1,λ2, such that λ1+λ2λ1+λ2 equals the order of a longest directed path in D, there exists a partition of D   into two digraphs, D1D1 and D2D2, such that the order of a longest path in DiDi is at most λiλi, for i=1,2i=1,2.We prove that certain classes of digraphs, which are generalizations of tournaments, satisfy the Path Partition Conjecture and that some of the classes even satisfy the conjecture with equality.