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Twin-Width One

Authors Jungho Ahn , Hugo Jacob , Noleen Köhler , Christophe Paul , Amadeus Reinald , Sebastian Wiederrecht

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Author Details

Jungho Ahn
  • Korea Institute for Advanced Study (KIAS), Seoul, South Korea
Hugo Jacob
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Noleen Köhler
  • University of Leeds, UK
Christophe Paul
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Amadeus Reinald
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Sebastian Wiederrecht
  • School of Computing, KAIST, Daejeon, South Korea

Funding

  • Ahn, Jungho: Supported by the KIAS Individual Grant (CG095301) at Korea Institute for Advanced Study.
  • Jacob, Hugo: Supported by the ANR project GODASse ANR-24-CE48-4377.
  • Paul, Christophe: Supported by the ANR project GODASse ANR-24-CE48-4377 and the ANR-DFG project UTMA ANR-20-CE92-0027.
  • Reinald, Amadeus: Supported by the ANR project DIGRAPHS ANR-19-CE48-0013.

Acknowledgements

The authors wish to thank the organisers of the 1st Workshop on Twin-width, which was partially financed by the grant ANR ESIGMA (ANR-17-CE23-0010) of the French National Research Agency. The second author wishes to thank Paul Bastide and Carla Groenland for interesting initial discussions on the topic of this paper.

Cite As Get BibTex

Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht. Twin-Width One. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.6

Abstract

We investigate the structure of graphs of twin-width at most 1, and obtain the following results:  
- Graphs of twin-width at most 1 are permutation graphs. In particular they have an intersection model and a linear structure. 
- There is always a 1-contraction sequence closely following a given permutation diagram. 
- Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a 1-contraction sequence of a graph, or guarantees that it has twin-width more than 1. 
- We characterise distance-hereditary graphs based on their twin-width and deduce a linear time algorithm to compute optimal sequences on this class of graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Twin-width
  • Hereditary graph classes
  • Intersection model

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References

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