-Decompositions of and Dv∪P where P is a 2-Regular Subgraph of Dv

In this paper, we extend the study of C4-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 Dv, then and Dv∪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.