Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics
Treewidth of chordal bipartite graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Listing all Minimal Separators of a Graph
SIAM Journal on Computing
Minimum fill-in on circle and circular-arc graphs
Journal of Algorithms
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Dynamic Algorithms for Graphs of Bounded Treewidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Algorithms for Maximum Matching and Minimum Fill-in on Chordal Bipartite Graphs
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Reduction Algorithms for Constructing Solutions in Graphs with Small Treewidth
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Computing Treewidth and Minimum Fill-In: All You Need are the Minimal Separators
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Erratum: Computing Treewidth and Minimum Fill-In: All You Need are the Minimal Separators
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Approximating the Bandwidth for Asteroidal Triple-Free Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Minimal Triangulations for Graphs with "Few" Minimal Separators
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Treewidth and minimum fill-in of weakly triangulated graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Computing the Treewidth and the Minimum Fill-in with the Modular Decomposition
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximating the Treewidth of AT-Free Graphs
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
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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.