Hamiltonian Path - Properties

Properties

Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to Hamiltonian cycle only if its endpoints are adjacent.

The line graph of a Hamiltonian graph is Hamiltonian. The line graph of an Eulerian graph is Hamiltonian.

A tournament (with more than 2 vertices) is Hamiltonian if and only if it is strongly connected.

The problem of finding a Hamiltonian cycle may be used as the basis of a zero-knowledge proof.

The number of different Hamiltonian cycles in a complete undirected graph on n vertices is (n - 1)! / 2 and in a complete directed graph on n vertices is (n - 1)!.

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