NIST

Hamiltonian cycle

(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: A Hamiltonian cycle includes each vertex once; an Euler cycle includes each edge once.

Also known as a Hamiltonian circuit.

Named for Sir William Rowan Hamilton (1805-1865).

Author: PEB

Implementation

(Fortran, C, Mathematica, and C++)
Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 15 July 2019.
HTML page formatted Mon Jul 15 12:55:43 2019.

Cite this as:
Paul E. Black, "Hamiltonian cycle", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 15 July 2019. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/hamiltonianCycle.html