License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.53
URN: urn:nbn:de:0030-drops-187061
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18706/
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Geniet, Colin ; Thomassé, Stéphan

First Order Logic and Twin-Width in Tournaments

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LIPIcs-ESA-2023-53.pdf (0.8 MB)

Abstract

We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments T, first-order model checking either is fixed parameter tractable, or is AW[*]-hard. This dichotomy coincides with the fact that T has either bounded or unbounded twin-width, and that the growth of T is either at most exponential or at least factorial. From the model-theoretic point of view, we show that NIP classes of tournaments coincide with bounded twin-width. Twin-width is also characterised by three infinite families of obstructions: T has bounded twin-width if and only if it excludes at least one tournament from each family. This generalises results of Bonnet et al. on ordered graphs.
The key for these results is a polynomial time algorithm which takes as input a tournament T and computes a linear order < on V(T) such that the twin-width of the birelation (T, <) is at most some function of the twin-width of T. Since approximating twin-width can be done in FPT time for an ordered structure (T, <), this provides a FPT approximation of twin-width for tournaments.

BibTeX - Entry

@InProceedings{geniet_et_al:LIPIcs.ESA.2023.53,
  author =	{Geniet, Colin and Thomass\'{e}, St\'{e}phan},
  title =	{{First Order Logic and Twin-Width in Tournaments}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18706},
  URN =		{urn:nbn:de:0030-drops-187061},
  doi =		{10.4230/LIPIcs.ESA.2023.53},
  annote =	{Keywords: Tournaments, twin-width, first-order logic, model checking, NIP, small classes}
}

Keywords: Tournaments, twin-width, first-order logic, model checking, NIP, small classes
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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