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DOI: 10.4230/LIPIcs.CP.2023.39

Searching for Smallest Universal Graphs and Tournaments with SAT

Authors: Tianwei Zhang and Stefan Szeider

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

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.

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Tianwei Zhang and Stefan Szeider. Searching for Smallest Universal Graphs and Tournaments with SAT. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@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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Searching for Smallest Universal Graphs and Tournaments with SAT

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