A Separator Theorem for Planar Graphs

@article{Lipton1977AST,
  title={A Separator Theorem for Planar Graphs},
  author={Richard J. Lipton and Robert Endre Tarjan},
  journal={Siam Journal on Applied Mathematics},
  year={1977},
  volume={36},
  pages={177-189}
}
  • R. LiptonR. Tarjan
  • Published 1 October 1977
  • Mathematics
  • Siam Journal on Applied Mathematics
Let G be any n-vertex planar graph. We prove that the vertices of G 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\sqrt 2 \sqrt n $ vertices. We exhibit an algorithm which finds such a partition A, B, C in $O( n )$ time. 
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