Theory
The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory. The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem. Note, however, that unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time.
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“The great tragedy of science—the slaying of a beautiful theory by an ugly fact.”
—Thomas Henry Huxley (1825–1895)