Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Treewidth Lower Bounds with Brambles
Algorithmica
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
New upper bound heuristics for treewidth
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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One of the most important structural parameters of graphs is treewidth , a measure for the "tree-likeness" and thus in many cases an indicator for the hardness of problem instances. The smaller the treewidth, the closer the graph is to a tree and the more efficiently the underlying instance often can be solved. However, computing the treewidth of a graph is NP -hard in general. In this paper we propose an encoding of the decision problem whether the treewidth of a given graph is at most k into the propositional satisfiability problem. The resulting SAT instance can then be fed to a SAT solver. In this way we are able to improve the known bounds on the treewidth of several benchmark graphs from the literature.