(definition)
Definition: A path through a graph that starts and ends at the same vertex and includes every other vertex exactly once.
Also known as tour.
Generalization (I am a kind of ...)
cycle.
Specialization (... is a kind of me.)
traveling salesman.
See also Hamiltonian path, Euler cycle, vehicle routing problem, perfect matching.
Note: Named for Sir William Rowan Hamilton (1805-1865) (a longer biography). A Hamiltonian cycle includes each vertex once; an Euler cycle includes each edge once.
Also known as a Hamiltonian circuit.
Author: PEB
Links to papers on many aspects of Hamiltonian cycles and paths.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 14 September 2006.
HTML page formatted Thu Sep 14 10:28:07 2006.
Cite this as:
Paul E. Black, "Hamiltonian cycle", in
Dictionary of Algorithms and Data
Structures [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 14 September 2006. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/hamiltonianCycle.html
