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A Brief Tour in Twin-Width (Invited Talk)

Author Stéphan Thomassé

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Stéphan Thomassé
  • Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France

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Stéphan Thomassé. A Brief Tour in Twin-Width (Invited Talk). In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 6:1-6:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICALP.2022.6

Abstract

This is an introduction to the notion of twin-width, with emphasis on how it interacts with first-order model checking and enumerative combinatorics. Even though approximating twin-width remains a challenge in general graphs, it is now well understood for ordered graphs, where bounded twin-width coincides with many other complexity gaps. For instance classes of graphs with linear FO-model checking, small classes, or NIP classes are exactly bounded twin-width classes. Some other applications of twin-width are also presented.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Twin-width
  • matrices
  • ordered graphs
  • enumerative combinatorics
  • model theory
  • algorithms
  • computational complexity
  • Ramsey theory

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References

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