list all the edge disjoint Hamiltonian cycles
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Let G be a simple graph. A hamiltonian circuit (HC) is a closed walk that traverses every vertex of G, exactly once, except of course the starting, vertex at which the walk also terminates. Two HCs are said to be edge disjoint if they have no edge in common. For convenience, the vertices are denoted by 1, 2, 3 ... etc.
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