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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] with edge set $E$, and let $C$ be a set of colours.\nAn edge colouring of $G$ is a function $c : E \\to C$ such that $c(e) \\neq c(e')$ for any two distinct edges $e$ and $e'$ with a common end.\nThe chromatic index $\\chi'(G)$ is the smallest number of colours in an edge colouring of a finite graph $G$.\n\n## Remarks\n\nEach colour class is a [[matching|0Z87BHAFTB]]. Thus an edge colouring is a partition of the edges into matchings.\nThe edges at a vertex need different colours, so $\\chi'(G) \\ge \\Delta(G)$.\nVizing's theorem of 1964 says that a simple graph has $\\chi'(G) = \\Delta(G)$ or $\\chi'(G) = \\Delta(G) + 1$.\n\n## Explanations\n\n### L1 human\n\nAn edge colouring colours the lines instead of the points: lines that meet must have different colours.\nIn a sports schedule, each colour is a round, and each team plays at most one game per round.\n",
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