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

A many-to-many κ-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,… , Sκ} and T = {t1,…,tκ} 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 δ0（D） ≥[n/2] + ∈ - 1,then D has a many to many k -DDPC joining any disjoint vertex subsets S = {S1, … , sk and T = {t1, …, tκ｝,(let δ0（D） := min{δ+（D）,δ^D} be the minimum semi-degree of D .) and the bound on the minimum semi-degree is best.