combinatorics / Graph decompositions

Hamilton Decompositions of the Directed 3-Torus

For $D_3(m) = \vec{C}_m \square \vec{C}_m \square \vec{C}_m$, can the full arc set be partitioned into three directed Hamilton cycles for every integer $m \ge 3$?

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For $D_3(m) = \vec{C}_m \square \vec{C}_m \square \vec{C}_m$, can the full arc set be partitioned into three directed Hamilton cycles for every integer $m \ge 3$?

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