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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA Hamiltonian cycle of $G$ is a [[cycle|07CT9RDY7Q]] in $G$ that contains every vertex of $G$.\n\n## Remarks\n\nA Hamiltonian path is a [[path|0JDE56HWQ8]] that contains every vertex of $G$.\nThe names come from William Rowan Hamilton. His icosian game asks for a Hamiltonian cycle on the edges of a dodecahedron.\nTo decide whether a graph has a Hamiltonian cycle is an NP-complete problem.\n\n## Explanations\n\n### L1 human\n\nA Hamiltonian cycle is a round trip that visits every vertex exactly once.\nIt is about visiting all vertices, while an Eulerian circuit is about using all edges.\n",
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