Hamiltonian path

Path in a graph that visits each vertex exactly once

In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected or directed graph that visits each edge exactly once. A Hamiltonian cycle is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details.

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