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  "body": "\n## Definition\n\nLet $r$ and $s$ be positive integers.\nThe Ramsey number $R(r, s)$ is the least positive integer $n$ with this property.\nColour each edge of the [[complete graph|03WKB2H474]] $K_n$ blue or red, in any way.\nThen there is a blue [[clique|0G52BPNPKG]] with $r$ vertices or a red clique with $s$ vertices.\n\n## Remarks\n\nSuch an $n$ exists by [[Ramsey's theorem|00TQV3F5S4]].\n$R(r, s) = R(s, r)$ and $R(r, 2) = r$. The [[theorem on friends and strangers|0NYM0ZGAK9]] gives $R(3, 3) = 6$.\nWith more colours there are similar numbers, for example $R(3, 3, 3) = 17$.\n\n## Explanations\n\n### L1 human\n\nThe Ramsey number $R(r, s)$ is the size of a party that is large enough for one of two things to happen.\nThere are $r$ people who all know each other, or $s$ people who are all strangers to each other.\n",
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