A separator theorem for nonplanar graphs

Noga Alon; Paul Seymour; Robin Thomas

doi:10.1090/S0894-0347-1990-1065053-0

A separator theorem for nonplanar graphs

Noga Alon, Paul Seymour, Robin Thomas

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

159 Scopus citations

Abstract

Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete 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 (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h^½ n^½m) where m = V(G) + E(G).

Original language	English (US)
Pages (from-to)	801-808
Number of pages	8
Journal	Journal of the American Mathematical Society
Volume	3
Issue number	4
DOIs	https://doi.org/10.1090/S0894-0347-1990-1065053-0
State	Published - Oct 1990
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0894-0347-1990-1065053-0

Cite this

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title = "A separator theorem for nonplanar graphs",

abstract = "Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete 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 (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h½ n½m) where m = V(G) + E(G).",

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AU - Seymour, Paul

AU - Thomas, Robin

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N2 - Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete 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 (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h½ n½m) where m = V(G) + E(G).

AB - Let G be an n-vertex graph with no minor isomorphic to an h-vertex complete 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 (Eqution presented) vertices. This extends a theorem of Lipton and Tarjan for planar graphs. We exhibit an algorithm which finds such a partition (A, B, C) in time O(h½ n½m) where m = V(G) + E(G).

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A separator theorem for nonplanar graphs

Abstract

All Science Journal Classification (ASJC) codes

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