---
tag: C73GPFD390
kind: statement
role: proposition
name: Planar separator theorem
sources:
  - wikipedia: en:18978005@r1374253333
    locator: Planar separator theorem
    note: adopted
    mention: wikipedia://en/18978005
    sections: [Statement]
same_as:
  wikidata: Q7200963
  wikipedia: Planar separator theorem
inventory: [CJ2EH5WKXN]
---

## Statement

In 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.