Editing Hamiltonian path problem (section)

=== Brute force ===
To decide if a graph has a Hamiltonian path, one would have to check each possible path in the input graph G. There are ''n''! different sequences of vertices that ''might'' be Hamiltonian paths in a given ''n''-vertex graph (and are, in a [[complete graph]]), so a [[brute force search]] algorithm that tests all possible sequences would be very slow.