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  "body": "\n## Definition\n\nLet $G$ be a finite [[graph|0JD5C82QMB]] with a nonempty vertex set $V$.\nThe maximum degree of $G$ is\n$$\\Delta(G) = \\max_{v \\in V} \\deg(v),$$\nthe largest [[degree|0T0F6CCS9W]] of a vertex of $G$.\n\n## Remarks\n\nThe complete graph $K_n$ has $\\Delta = n - 1$.\nA [[greedy colouring|04AAKZNXHD]] uses at most $\\Delta(G) + 1$ colours. [[Brooks' theorem|0Y4TV2D5RQ]] improves this to $\\Delta(G)$ in most cases.\n\n## Explanations\n\n### L1 human\n\nThe maximum degree is the largest number of edges at any vertex.\nIn a star with one centre and $5$ leaves, the maximum degree is $5$.\n",
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