2026-07-24T19:05:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19076 2024-03-06T11:03:27Z ddc:004 open_access

Searching for Smallest Universal Graphs and Tournaments with SAT Zhang, Tianwei Szeider, Stefan Constrained-based combinatorics synthesis problems symmetry breaking SAT solving subgraph isomorphism tournament directed graphs 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tianwei Zhang and Stefan Szeider 2023 Is Part Of LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CP.2023.39 urn:nbn:de:0030-drops-190760 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.39 eng https://creativecommons.org/licenses/by/4.0/legalcode