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 prepositional 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.
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