# Metadata Source URL:: https://en.wikipedia.org/wiki/Hamiltonian_path Topics:: #mathematic, #graph-theory --- # Hamiltonian path - Wikipedia ## Highlights > [!quote]+ Updated on 280922_195709 > > In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) 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. Determining whether such paths and cycles exist in graphs (the Hamiltonian path problem and Hamiltonian cycle problem) are NP-complete