Listing All Potential Maximal Cliques of a Graph
نویسندگان
چکیده
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 5ll-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 5ll-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.
منابع مشابه
Counting and Listing all Potential Maximal Cliques of a Graph
We show that the number of potential maximal cliques for an arbitrary graph G on n vertices is O∗(1.8135n), and that all potential maximal cliques can be listed in O∗(1.8899n) time. As a consequence of this results, treewidth and minimum fill-in can be computed in O∗(1.8899n) time.
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 276 شماره
صفحات -
تاریخ انتشار 2000