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The Hamiltonian Cycle Problem is a well-known problem in graph theory and algorithm design, where the task is to determine whether a given graph contains a cycle that visits each vertex exactly once and returns to the starting vertex. In other words, a Hamiltonian cycle is a closed loop that passes through every vertex of the graph without repetition and ends at the same vertex from which it started. The problem is ________ ____ ______ ___ ________ __________ _____ ______.
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