(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.

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