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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Hamiltonian problem
Hamiltonian cycle
Hamiltonian path
Hamiltonian tour
Hamilton's 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.
(1997-07-18)