Listing All Potential Maximal Cliques of a Graph [chapter]

Vincent Bouchitté, Ioan Todinca
2000 Lecture Notes in Computer Science  
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 ÿll-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 ÿll-in are
more » ... ially tractable for all classes of graphs with a polynomial number of minimal separators.
doi:10.1007/3-540-46541-3_42 fatcat:zraegbzjyzfkxdt4xe26icjtla