A graph is induced k-universal if it contains all graphs of order k as an induced subgraph. For over half a century, the question of determining smallest k-universal graphs has been studied. A related question asks for a smallest k-universal tournament containing all tournaments of order k. This paper proposes and compares SAT-based methods for answering these questions exactly for small values of k. Our methods scale to values for which a generate-and-test approach isn't feasible; for instance, we show that an induced 7-universal graph has more than 16 vertices, whereas the number of all connected graphs on 16 vertices, modulo isomorphism, is a number with 23 decimal digits Our methods include static and dynamic symmetry breaking and lazy encodings, employing external subgraph isomorphism testing.
@InProceedings{zhang_et_al:LIPIcs.CP.2023.39, author = {Zhang, Tianwei and Szeider, Stefan}, title = {{Searching for Smallest Universal Graphs and Tournaments with SAT}}, booktitle = {29th International Conference on Principles and Practice of Constraint Programming (CP 2023)}, pages = {39:1--39:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-300-3}, ISSN = {1868-8969}, year = {2023}, volume = {280}, editor = {Yap, Roland H. C.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.39}, URN = {urn:nbn:de:0030-drops-190760}, doi = {10.4230/LIPIcs.CP.2023.39}, annote = {Keywords: Constrained-based combinatorics, synthesis problems, symmetry breaking, SAT solving, subgraph isomorphism, tournament, directed graphs} }
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