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an introduction to clique minimal separator decomposition介绍集团最小分离器分解
Algorithms 2010, 3, 197-215; doi:10.3390/a3020197
OPEN ACCESS
algorithms
ISSN 1999-4893
/journal/algorithms
Review
An Introduction to Clique Minimal Separator Decomposition
,⋆ `
Anne Berry , Romain Pogorelcnik and Genevieve Simonet
´ `
LIMOS UMR CNRS 6158, Ensemble Scientifique des Cezeaux, F-63 173 Aubiere, France;
E-Mail: pogorelc@isima.fr
LIRMM, 161 Rue Ada, F-34392 Montpellier, France; E-Mail: simonet@lirmm.fr
⋆ Author to whom correspondence should be addressed; E-Mail: berry@isima.fr;
Tel.: +033-4734-07769.
Received: 7 April 2010 / Accepted: 28 April 2010 / Published: 14 May 2010
Abstract: This paper is a review which presents and explains the decomposition of graphs by
clique minimal separators. The pace is leisurely, we give many examples and figures. Easy
algorithms are provided to implement this decomposition. The historical and theoretical
background is given, as well as sketches of proofs of the structural results involved.
Keywords: graph decomposition; clique minimal separator; minimal triangulation
1. Introduction
This paper is designed as a presentation for the not so well-known graph decomposition which we
call “clique minimal separator decomposition”. In view of recent applications, this decomposition is a
promising tool.
A separator is a set of vertices (of a connected graph), the removal of which disconnects the graph,
and a clique is a set of pairwise adjacent vertices, a
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