## Hamiltonian problem

Synonyms

## Hamilton's problem

## Hamiltonian cycle

## Hamiltonian path

## Hamiltonian tour

(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.