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  "body": "\n## Statement\n\nLet $G$ be a [[graph|0JD5C82QMB]] and let $e$ be an edge of $G$.\nThen $e$ is a [[bridge|0D81KWH9ZM]] of $G$ if and only if $e$ is not an edge of any [[cycle|07CT9RDY7Q]] of $G$.\n\n## Remarks\n\nProof idea: let $e = uv$. If $e$ lies on a cycle, the rest of the cycle is a path from $u$ to $v$ in $G - e$. Conversely, a path from $u$ to $v$ in $G - e$ together with $e$ gives a cycle.\nA consequence: a graph is a forest if and only if every edge is a bridge.\n\n## Explanations\n\n### L1 human\n\nAn edge on a cycle is never a bridge: if you delete it, you can still go around the other way.\nAn edge on no cycle has no detour, so deleting it splits the graph.\n",
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