(C)over-right-arrow(4)-decompositions of D-v\P and D-v boolean OR P where P is a 2-regular subgraph of D-v

Abstract

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 D-v\P and D-v boolean OR Pcan be decomposed into directed 4-cycles, respectively, if and only if v(v-1) - vertical bar E(P)vertical bar = 0 (mod 4) and v(v-1) + vertical bar E(P)vertical bar = 0 (mod 4) where vertical bar E(P)vertical bar denotes the number of directed edges of P, and v >= 8.