SEPARATOR THEOREM FOR PLANAR GRAPHS.

Richard J. Lipton; Robert Endre Tarjan

doi:10.1137/0136016

SEPARATOR THEOREM FOR PLANAR GRAPHS.

Richard J. Lipton, Robert Endre Tarjan

Research output: Contribution to journal › Article › peer-review

947 Scopus citations

Abstract

Let G be any n-vertex planar graph. It is proved 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 22** one-half n** one-half vertices. An algorithm is exhibited which finds such a partition A, B, C in O(n) time.

Original language	English (US)
Pages (from-to)	177-189
Number of pages	13
Journal	SIAM J Appl Math
Volume	36
Issue number	2
DOIs	https://doi.org/10.1137/0136016
State	Published - 1979

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1137/0136016

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title = "SEPARATOR THEOREM FOR PLANAR GRAPHS.",

abstract = "Let G be any n-vertex planar graph. It is proved 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 22** one-half n** one-half vertices. An algorithm is exhibited which finds such a partition A, B, C in O(n) time.",

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AB - Let G be any n-vertex planar graph. It is proved 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 22** one-half n** one-half vertices. An algorithm is exhibited which finds such a partition A, B, C in O(n) time.

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SEPARATOR THEOREM FOR PLANAR GRAPHS.

Abstract

All Science Journal Classification (ASJC) codes

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