The Path Partition Conjecture is true for some generalizations of tournaments

The Path Partition Conjecture for digraphs states that for every digraph D , and every choice of positive integers λ 1 , λ 2 such that λ 1 + λ 2 equals the order of a longest directed path in D , there exists a partition of D in two subdigraphs D 1 , D 2 such that the order of the longest path in D i is at most λ i for i = 1 , 2 . sent sufficient conditions for a digraph to satisfy the Path Partition Conjecture. Using these results, we prove that strong path mergeable, arc-locally semicomplete, strong 3-quasi-transitive, strong arc-locally in-semicomplete and strong arc-locally out-semicomplete digraphs satisfy the Path Partition Conjecture. Some previous results are generalized.