Listing all potential maximal cliques of a graph
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 classes of graphs with a polynomial number of minimal separators. (C) 2002 Elsevier Science B.V. All rights reserved.
potential maximal cliques treewidth minimal separators graph algorithms