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Communication Dans Un Congrès Année : 2023

Twin-width and permutations

Édouard Bonnet
  • Fonction : Auteur
Jaroslav Nešetřil
  • Fonction : Auteur
Sebastian Siebertz
  • Fonction : Auteur
Stephan Thomassé
  • Fonction : Auteur

Résumé

Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomassé, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been further extended to binary structures, in several (basically equivalent) ways. We prove that a class of binary relational structures (that is: edge-colored partially directed graphs) has bounded twin-width if and only if it is a first-order transduction of a proper permutation class. As a by-product, we show that every class with bounded twin-width contains at most $2^{O(n)}$ pairwise non-isomorphic $n$-vertex graphs.

Dates et versions

hal-04314372 , version 1 (29-11-2023)

Identifiants

Citer

Édouard Bonnet, Jaroslav Nešetřil, Patrice Ossona de Mendez, Sebastian Siebertz, Stephan Thomassé. Twin-width and permutations. Eurocomb 2023, Aug 2023, Prague (CZ), Czech Republic. pp.156-162, ⟨10.5817/CZ.MUNI.EUROCOMB23-022⟩. ⟨hal-04314372⟩

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