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A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.

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Can we find 3 disjoint directed Hamiltonian cycles in the cube?

It looks like the titled question (d=3) is not directly answered: I will hint at how to show the answer is no. At each vertex, there are two ways that the decomposition can go. I like to call them b …
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