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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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Why is the number of Hamiltonian Cycles of n-octahedron equivalent to the number of Perfect ...
The $n$-dimensional analogue of the octahedron is the complement of a perfect matching of its vertex set. (Every vertex is joined to every other vertex except its antipode.) If you take a Hamilton c …