Decomposition by clique separators

Robert E. Tarjan

doi:10.1016/0012-365X(85)90051-2

Decomposition by clique separators

Robert E. Tarjan

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

321 Scopus citations

Abstract

We consider the problem of decomposing a graph by means of clique separators, by which we mean finding cliques (complete graphs) whose removal disconnects the graph. We give an O(nm)-time algorithm for finding a decomposition of an n-vertex, m-edge graph. We describe how such a decomposition can be used in divide-and-conquer algorithms for various graph problems, such as graph coloring and finding maximum independent sets. We survey classes of graphs for which such divide-and-conquer algorithms are especially useful.

Original language	English (US)
Pages (from-to)	221-232
Number of pages	12
Journal	Discrete Mathematics
Volume	55
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(85)90051-2
State	Published - Jul 1985
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(85)90051-2

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abstract = "We consider the problem of decomposing a graph by means of clique separators, by which we mean finding cliques (complete graphs) whose removal disconnects the graph. We give an O(nm)-time algorithm for finding a decomposition of an n-vertex, m-edge graph. We describe how such a decomposition can be used in divide-and-conquer algorithms for various graph problems, such as graph coloring and finding maximum independent sets. We survey classes of graphs for which such divide-and-conquer algorithms are especially useful.",

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AB - We consider the problem of decomposing a graph by means of clique separators, by which we mean finding cliques (complete graphs) whose removal disconnects the graph. We give an O(nm)-time algorithm for finding a decomposition of an n-vertex, m-edge graph. We describe how such a decomposition can be used in divide-and-conquer algorithms for various graph problems, such as graph coloring and finding maximum independent sets. We survey classes of graphs for which such divide-and-conquer algorithms are especially useful.

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Decomposition by clique separators

Abstract

All Science Journal Classification (ASJC) codes

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