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  "body": "\n## Summary\n\nA Hamiltonian path in a graph is a [[path|03NAMV1DHJ]] that visits every vertex exactly once.\nIt is the open form of a [[Hamiltonian cycle|0HF30P75G4]].\nDeciding whether a graph has a Hamiltonian path is NP-complete, and no simple criterion like Euler's parity test for [[Eulerian trails|05NWGBHKSZ]] is known.\nThe node [[Hamiltonian path|AT8GWPWQWT]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nA Hamiltonian path is a tour that visits every city exactly once, without needing to come back home.\nOn a chessboard, a knight's tour that visits every square once is a Hamiltonian path in the knight's move graph.\nThe path graph $1 - 2 - 3 - 4$ is itself a Hamiltonian path, while a star with three arms has none.\n",
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