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.