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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nIf $G$ contains a [[cycle|07CT9RDY7Q]], the girth of $G$ is the smallest length of a cycle in $G$.\nIf $G$ contains no cycle, that is, if $G$ is [[acyclic|0XNN9Z8E5A]], the girth of $G$ is $\\infty$.\n\n## Remarks\n\nIn a simple graph each cycle has length at least $3$, so the girth is at least $3$.\nExample: the [[cycle graph|0QQ0F12962]] $C_n$ with $n \\ge 3$ has girth $n$, since its only cycle has length $n$.\nThe [[complete graph|03WKB2H474]] $K_n$ with $n \\ge 3$ has girth $3$, and the [[complete bipartite graph|0V0GC7BQAN]] $K_{m,n}$ with $m, n \\ge 2$ has girth $4$, since a [[bipartite graph|07DVHJ8N0A]] has no odd cycle.\nThe [[Petersen graph|0NR95CTFCZ]] has girth $5$.\nNon-example: in the path graph $u - v - w$, the closed walk $u, v, u$ has length $2$ but is not a cycle, because it uses the edge $uv$ twice.\nThe path graph has no cycle, so its girth is $\\infty$.\nEvery [[tree|0MJ0JS72DZ]] has girth $\\infty$.\nThe girth is sometimes written $g(G)$.\n",
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