## Hamiltonian problem

(Or "Hamilton's problem") A problem in graph theory posed by William Hamilton: given a graph, is there a path through the graph which visits each vertex precisely once (a "Hamiltonian path")? Is there a Hamiltonian path which ends up where it started (a "Hamiltonian cycle" or "Hamiltonian tour")?

Hamilton's problem is NP-complete. It has numerous applications, sometimes completely unexpected, in computing.

*http://ing.unlp.edu.ar/cetad/mos/Hamilton.html*.

Last updated: 1997-07-18

### Nearby terms:

Hamiltonian path ♦ **Hamiltonian problem** ♦ Hamiltonian tour ♦ Hamilton's problem

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