A Hamiltonian path is a path in a graph that visits every graph vertex exactly once. Removing any edge from a Hamilton cycle produces a Hamiltonian path. Conversely, a Hamiltonian path closes to a Hamilton cycle exactly when its endpoints are joined by an edge.
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A Hamiltonian path in a graph is a path that visits each vertex exactly once. If a Hamiltonian path exists that also returns to the starting vertex, forming a cycle, it is called a Hamiltonian cycle (or Hamiltonian circuit). Finding Hamiltonian paths and cycles is a well-known problem in graph theory and is closely related to many important problems in computer science, including the Traveling Salesman Problem (TSP).