Hamiltonian cycle


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 ...)

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


(Fortran, C, Mathematica, and C++)
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Entry modified 21 December 2020.
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Cite this as:
Paul E. Black, "Hamiltonian cycle", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 21 December 2020. (accessed TODAY) Available from: