For every d >= 2 and odd m >= 3 the directed Cayley graph D_d(m) admits a decomposition of its arcs into d directed Hamilton cycles.
Stong, Hamilton decompositions of Cartesian products of graphs,Discrete Mathematics 90 (1991), 169–190
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Hamilton decompositions of all directed tori at odd modulus
For every d >= 2 and odd m >= 3 the directed Cayley graph D_d(m) admits a decomposition of its arcs into d directed Hamilton cycles.