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  "body": "\n## Statement\n\nLet $g \\ge 3$ and $t$ be integers.\nThen there is a [[graph|0JD5C82QMB]] $G$ whose [[chromatic number|0C5M7AM6FH]] satisfies $\\chi(G) \u003e t$ and whose [[girth|WZ4JGTG6ZD]] is greater than $g$.\n\n## Remarks\n\nSo a graph can need many colours even though it has no short cycles at all.\nLarge chromatic number does not force a small cycle, such as a triangle, into the graph.\nThe classical proof uses the probabilistic method on a random graph.\n",
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