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.
Park, Hamilton decompositions of the directed 3-torus: a return-map and odometer view
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The directed five-dimensional torus has a Hamilton decomposition for every odd integer m ≥ 3.
Directed 7-tori D_7(m) for odd m >= 3 admit Hamilton decompositions, established by root-flat certificates for m=3,5 and a uniform prefix-count construction for m>=7, with Lean 4 verification of the boundary cases.
citing papers explorer
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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.
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Hamilton decompositions of the directed 5-torus for odd modulus
The directed five-dimensional torus has a Hamilton decomposition for every odd integer m ≥ 3.
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Hamilton decompositions of the directed 7-torus at odd modulus via root-flat certificates and a prefix-count construction
Directed 7-tori D_7(m) for odd m >= 3 admit Hamilton decompositions, established by root-flat certificates for m=3,5 and a uniform prefix-count construction for m>=7, with Lean 4 verification of the boundary cases.