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Hamiltonian path

Graph theory and combinatorics

A path through a graph visiting every vertex exactly once. A Hamiltonian cycle additionally returns to its starting vertex.

What is usually left out

Deciding whether one exists is NP-complete, which is the standard contrast with Eulerian paths — those traverse every edge once and admit a simple degree criterion checkable in linear time. Two problems that sound alike can sit on opposite sides of the tractability line.

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