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
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics
Treewidth of chordal bipartite graphs
Journal of Algorithms
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Listing all Minimal Separators of a Graph
SIAM Journal on Computing
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
How to Use the Minimal Separators of a Graph for its Chordal Triangulation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Computing Treewidth and Minimum Fill-In: All You Need are the Minimal Separators
ESA '93 Proceedings of the First 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)
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Abstract We consider the class C* of graphs whose minimal separators have a fixed bounded size. We give an O(nm)-time algorithm computing an optimal tree-decomposition of every graph in C* with n vertices and m edges. Furthermore we make evident that many NP-complete problems are solvable in polynomial time when restricted to this class. Both claims hold although C* contains graphs of arbitrarily large tree-width.