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Listing All Potential Maximal Cliques of a Graph

  • Vincent Bouchitté
  • Ioan Todinca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)

Abstract

A potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph. It is known that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fill-in are polynomially tractable for these graphs. We show here that the potential maximal cliques of a graph can be generated in polynomial time in the number of minimal separators of the graph. Thus, the treewidth and the minimum fill-in are polynomially tractable for all graphs with polynomial number of minimal separators.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Vincent Bouchitté
    • 1
  • Ioan Todinca
    • 1
  1. 1.LIP-École Normale Supérieure de LyonLyon Cedex 07France

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