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

1053 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

Cite this

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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.",

author = "Lipton, \{Richard J.\} and Tarjan, \{Robert Endre\}",

year = "1979",

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AU - Tarjan, Robert Endre

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N2 - 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.

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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U2 - 10.1137/0136016

DO - 10.1137/0136016

M3 - Article

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JO - SIAM J Appl Math

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IS - 2

ER -

SEPARATOR THEOREM FOR PLANAR GRAPHS.

Abstract

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