On the Complements of Partial k-Trees
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
The structure of obstructions to treewidth and pathwidth
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Achievable sets, brambles, and sparse treewidth obstructions
Discrete Applied Mathematics
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Weighted treewidth algorithmic techniques and results
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Treewidth lower bounds with brambles
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
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For each pair of nonadjacent vertices in a graph, consider the greater of the degrees of the two vertices. The minimum of these maxima is a lower bound on the treewidth of a graph, unless it is a complete graph. This bound has three consequences. First, the obstructions of order w+3 for treewidth w have a simple structural characterization. Second, these graphs are exactly the pathwidth obstructions of order w+3. Finally, although there is only one obstruction of order w+2 for width w, the number of obstructions of order w+3 is bounded below by an exponential function of $\sqrt w$.