SAT Modulo Symmetries for Graph Generation

Authors Markus Kirchweger, Stefan Szeider

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Markus Kirchweger
  • Algorithms and Complexity Group, TU Wien, Austria
Stefan Szeider
  • Algorithms and Complexity Group, TU Wien, Austria

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Markus Kirchweger and Stefan Szeider. SAT Modulo Symmetries for Graph Generation. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We propose a novel constraint-based approach to graph generation. Our approach utilizes the interaction between a CDCL SAT solver and a special symmetry propagator where the SAT solver runs on an encoding of the desired graph property. The symmetry propagator checks partially generated graphs for minimality w.r.t. a lexicographic ordering during the solving process. This approach has several advantages over a static symmetry breaking: (i) symmetries are detected early in the generation process, (ii) symmetry breaking is seamlessly integrated into the CDCL procedure, and (iii) the propagator can perform a complete symmetry breaking without causing a prohibitively large initial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of girth and diameter. With our approach, we could confirm the Simon-Murty Conjecture (1979) on diameter-2-critical graphs for graphs up to 18 vertices.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Mathematics of computing → Extremal graph theory
  • symmetry breaking
  • SAT encodings
  • graph generation
  • combinatorial search
  • extremal graphs
  • CDCL


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