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A separator theorem for planar graphs

Let G be any n-vertex planar graph. 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(sq.rt 2)(sq. rt n) vertices. An algorithm is exhibited which finds such a partition A, B, C in o(n) time.

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  • "Let G be any n-vertex planar graph. 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(sq.rt 2)(sq. rt n) vertices. An algorithm is exhibited which finds such a partition A, B, C in o(n) time."@en

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  • "A separator theorem for planar graphs"@en
  • "A Separator Theorem for Planar Graphs"@en
  • "A separator theorem for planar graphs"

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