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Twin-Width One

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

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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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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.

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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

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.

References

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