### Hamilton's problem ==>

# Hamiltonian problem

<*computability*> (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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<*2001-03-16*>

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**Nearby terms:**
halting problem « Hamiltonian cycle « Hamiltonian path « Hamiltonian problem » Hamiltonian tour » Hamilton's problem » Hamilton William