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Communication Dans Un Congrès Année : 2023

First Order Logic and Twin-Width in Tournaments

Résumé

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.
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Dates et versions

hal-04249625 , version 1 (19-10-2023)

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Colin Geniet, Stéphan Thomassé. First Order Logic and Twin-Width in Tournaments. 31st Annual European Symposium on Algorithms (ESA 2023), Sep 2023, Amsterdam, Netherlands. pp.53:1--53:14, ⟨10.4230/LIPIcs.ESA.2023.53⟩. ⟨hal-04249625⟩
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