The Study Of Many-to-Many Disjoint Path Covers In Digraph

A many-to-many ?-disjoint directed path cover ? k -DDPC for short? of a di-graph D is a set of k vertex-disjoint directed paths connecting two disjoint vertex subsets S = {S1,… , S?} and T = {t1,…,t?} of D , and cover all vertex of the digraph D . In this paper, our main result is that a digraph D of sufficiently large order n with ?0?D? ?[n/2] + ? - 1,then D has a many to many k -DDPC joining any disjoint vertex subsets S = {S1, … , sk and T = {t1, …, t??,(let ?0?D? := min{?+?D?,?^D} be the minimum semi-degree of D .) and the bound on the minimum semi-degree is best.