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The Hamiltonian Circuit is a problem in graph theory where the search starts at a vertex 'a', which becomes the root of the implicit tree. The first element of the partial solution is the first intermediate vertex of the Hamiltonian Cycle. If any vertex makes a cycle with any other vertex, a dead end is reached. If this occurs, the search backtracks one step, and the next step is to select another vertex and remove the solution. The search is successful if a Hamiltonian Cycle is obtained.

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