^⇀c-decompositions of D_v\P and D_v ∪ P where P is a 2-regular Subgraph of D_v

In this paper, we extend the study of C ₄-decompositions of the complete graph with 2-regular leaves and paddings to directed versions. Mainly, we prove that if P is a vertex-disjoint union of directed cycles in a complete digraph D _v , then [InlineMediaObject not available: see fulltext.] and D _v ∪ P can be decomposed into directed 4-cycles, respectively, if and only if v(v-1)-|E(P)|≡0(mod 4) and v(v-1)+|E(P)|≡0(mod 4) where |E(P)| denotes the number of directed edges of P, and v≥8.