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  "body": "\n## Definition\n\nLet $k$ be a natural number.\nA [[graph|0JD5C82QMB]] $G$ is $k$-colourable if it has a [[colouring|0874138YP6]] with the set of colours $\\{1, 2, \\dots, k\\}$.\n\n## Remarks\n\nA $k$-colourable graph is also $(k+1)$-colourable.\nA graph is $2$-colourable if and only if it is [[bipartite|07DVHJ8N0A]].\nThe [[complete graph|03WKB2H474]] $K_n$ is $k$-colourable if and only if $k \\ge n$.\n\n## Explanations\n\n### L1 human\n\nA graph is $k$-colourable when $k$ colours are enough to colour it properly.\nA triangle needs three colours, so it is $3$-colourable but not $2$-colourable.\n",
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