A Separator Theorem for Planar Graphs

@inproceedings{Luo2001AST,
  title={A Separator Theorem for Planar Graphs},
  author={Yun Luo},
  year={2001}
}
The vertices of any n-vertex planar graph can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2 2 n vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time by an algorithm.