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  "body": "\n## Statement\n\nLet $G$ be a finite simple [[graph|0JD5C82QMB]] with $n \\ge 3$ vertices.\nSuppose that $\\deg(u) + \\deg(v) \\ge n$ for any two distinct vertices $u$ and $v$ that are not adjacent.\nThen $G$ is [[Hamiltonian|090WPKFABX]].\n\n## Remarks\n\n[[Dirac's theorem|0TC99BRSSB]] is a special case.\nThe Bondy–Chvátal theorem of 1976 extends it. It says that $G$ is Hamiltonian if and only if its closure is Hamiltonian.\nThe closure comes from $G$ when you add edges $uv$ with $\\deg(u) + \\deg(v) \\ge n$ again and again.\n\n## History\n\nØystein Ore proved the theorem in 1960.\n\n## Explanations\n\n### L1 human\n\nOre's theorem looks only at pairs of vertices that are not neighbours.\nIf each such pair has many edges together, the graph has a round trip through all vertices.\n",
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