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A Separator Theorem for Planar Graphs

Richard J. Lipton and Robert Endre Tarjan
SIAM Journal on Applied Mathematics
Vol. 36, No. 2 (Apr., 1979), pp. 177-189
Stable URL: http://www.jstor.org/stable/2100927
Page Count: 13
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A Separator Theorem for Planar Graphs
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Abstract

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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