A path-factor in a graph G is spanning subgraph F of such that every component path. Let d and n be two nonnegative integers with ≥ 2. P -factor its each whose components path at least vertices. called covered if for any e ∈ E ( ), admits containing . , )-factor critical N ⊆ V ) | = the − graph. uniform In this paper, we verify following results: (i) An + 1)-connected order 3 ≥3 satisfies δ >...