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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] with vertex set $V$, and let $C$ be a set, the set of colours.\nA colouring of $G$ with colours in $C$ is a function $c : V \\to C$ such that $c(u) \\neq c(v)$ for any two adjacent vertices $u$ and $v$.\n\n## Remarks\n\nSuch a colouring is also called proper. A colouring with a set of $k$ colours is a $k$-colouring.\nEach colour class $c^{-1}(x)$ is an [[independent set|0KZJ82WEPP]].\nA graph has a $2$-colouring if and only if it is [[bipartite|07DVHJ8N0A]].\nThe subject started with the colouring of maps. Francis Guthrie stated the four colour conjecture in 1852.\n\n## Explanations\n\n### L1 human\n\nColour the vertices of a graph so that the two ends of each edge have different colours.\nFor example, a timetable gives each exam a time slot, so that exams with a common student are at different times.\n",
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