Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
The Structure and Number of Obstructions to Treewidth
SIAM Journal on Discrete Mathematics
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
A New Lower Bound for Tree-Width Using Maximum Cardinality Search
SIAM Journal on Discrete Mathematics
Two Short Proofs Concerning Tree-Decompositions
Combinatorics, Probability and Computing
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Planar Branch Decompositions II: The Cycle Method
INFORMS Journal on Computing
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Pre-processing for triangulation of probabilistic networks
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Degree-Based treewidth lower bounds
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Achievable sets, brambles, and sparse treewidth obstructions
Discrete Applied Mathematics
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
On brambles, grid-like minors, and parameterized intractability of monadic second-order logic
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the characterisation of the treewidth as the maximum order of a bramble of the graph. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a lower bound for the treewidth that is at most a constant factor away from the exact treewidth. For both algorithms, we report on extensive computational experiments that show that the algorithms give often excellent lower bounds, in particular when applied to (close to) planar graphs.