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  "body": "\n## Statement\n\nIn graph theory, the **planar separator theorem** is a form of isoperimetric inequality for [[planar graphs|029JQEK15B]], that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of $O(\\sqrt{n})$ vertices from an $n$-vertex graph (where the $O$ invokes big O notation) can partition the graph into disjoint subgraphs each of which has at most $2n/3$ vertices.\n",
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