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We introduce novel methods for encoding acyclicity and s-t-reachabilityconstraints for propositional formulas with underlying directed graphs. Theyare based on vertex elimination graphs, which makes them suitable for caseswhere the underlying graph is sparse. In contrast to solvers with ad hocconstraint propagators for acyclicity and reachability constraints such asGraphSAT, our methods encode these constraints as standard propositionalclauses, making them directly applicable with any SAT solver. An empiricalstudy demonstrates that our methods together with an efficient SAT solver canoutperform both earlier encodings of these constraints as well as GraphSAT,particularly when underlying graphs are sparse.

Propositional Encodings of Acyclicity and Reachability by using Vertex Elimination