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)!.
Read more about this topic: Hamiltonian Path
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)