From Width-Based Model Checking to Width-Based Automated Theorem Proving
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In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we introduce a general framework to convert a large class of width-based model-checking algorithms into algorithms that can be used to test the validity of graph-theoretic conjectures on classes of graphs of bounded width. Our framework is modular and can be applied with respect to several well-studied width measures for graphs, including treewidth and cliquewidth. As a quantitative application of our framework, we show that for several long-standing graph-theoretic conjectures, there exists an algorithm that takes a number k as input and correctly determines in time double-exponential in k^O(1) whether the conjecture is valid on all graphs of treewidth at most k. This improves significantly on upper bounds obtained using previously available techniques.
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