Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Algorithms for VLSI layout based on graph width metrics
Algorithms for VLSI layout based on graph width metrics
The Structure and Number of Obstructions to Treewidth
SIAM Journal on Discrete Mathematics
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Safe Reduction Rules for Weighted Treewidth
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
A New Lower Bound for Tree-Width Using Maximum Cardinality Search
SIAM Journal on Discrete Mathematics
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Planar Branch Decompositions I: The Ratcatcher
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
Pre-processing for triangulation of probabilistic networks
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Treewidth computations II. Lower bounds
Information and Computation
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Treewidth lower bounds with brambles
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On switching classes, NLC-width, cliquewidth and treewidth
Theoretical Computer Science
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
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Every lower bound for treewidth can be extended by taking the maximum of the lower bound over all subgraphs or minors. This extension is shown to be a very vital idea for improving treewidth lower bounds. In this paper, we investigate a total of nine graph parameters, providing lower bounds for treewidth. The parameters have in common that they all are the vertex-degree of some vertex in a subgraph or minor of the input graph. We show relations between these graph parameters and study their computational complexity. To allow a practical comparison of the bounds, we developed heuristic algorithms for those parameters that are N P-hard to compute. Computational experiments show that combining the treewidth lower bounds with minors can considerably improve the lower bounds.