Abstract
We examine the necessary and sufficient conditions for a complete symmetric digraph $K_n^\ast$ to admit a resolvable decomposition into directed cycles of length $m$. We give a complete solution for even $m$, and a partial solution for odd $m$.
Highlights
In this paper, we consider the problem of decomposing the complete symmetric digraphKn∗ into spanning subgraphs, each a vertex-disjoint union of directed cycles of length m
We examine the necessary and sufficient conditions for a complete symmetric digraph Kn∗ to admit a resolvable decomposition into directed cycles of length m
We consider the problem of decomposing the complete symmetric digraph
Summary
We consider the problem of decomposing the complete symmetric digraph. We solve the problem completely for all even cycle lengths m 6, and partially for odd cycle lengths m 5, proving the following main result. There exists a resolvable decomposition of Kn∗ into directed cycles of length m if and only if m divides n and (m, n) = (6, 6). There exists a resolvable decomposition of Kn∗ into directed cycles of length m whenever n ≡ 0 (mod 4m), except possibly for n = 8m.
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