Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
Listing all Minimal Separators of a Graph
SIAM Journal on Computing
Triangulating graphs with few P4's
Discrete Applied Mathematics
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient and practical modular decomposition
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A linear time algorithm for minimum fill-in and treewidth for distance hereditary graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Deciding Clique-Width for Graphs of Bounded Tree-Width
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Listing All Potential Maximal Cliques of a Graph
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Algorithms for the Treewidth and Minimum Fill-in of HHD-Free Graphs
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Minimum Fill-in and Treewidth for Graphs Modularly Decomposable into Chordal Graphs
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Counting spanning trees in graphs using modular decomposition
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
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Using the notion of modular decomposition we extend the class of graphs on which both the treewidth and the minimum fill-in problems can be solved in polynomial time. We show that if C is a class of graphs which is modularly decomposable into graphs that have a polynomial number of minimal separators, or graphs formed by adding a matching between two cliques, then both the treewidth and the minimum fill-in problems on C can be solved in polynomial time. For the graphs that are modular decomposable into cycles we give algorithms, that use respectively O(n) and O(n3) time for treewidth and minimum fill-in.