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On the Twin-Width of Smooth Manifolds

Authors Édouard Bonnet , Kristóf Huszár

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ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Geometric topology
Keywords
  • Smooth manifolds
  • triangulations
  • twin-width
  • Whitney embedding theorem
  • structural graph parameters
  • computational topology

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Abstract

Building on Whitney’s classical method of triangulating smooth manifolds, we show that every compact d-dimensional smooth manifold admits a triangulation with dual graph of twin-width at most d^O(d). In particular, it follows that every compact 3-manifold has a triangulation with dual graph of bounded twin-width. This is in sharp contrast to the case of treewidth, where for any natural number n there exists a closed 3-manifold such that every triangulation thereof has dual graph with treewidth at least n. To establish this result, we bound the twin-width of the dual graph of the d-skeleton of the second barycentric subdivision of the 2d-dimensional hypercubic honeycomb. We also show that every compact, piecewise-linear (hence smooth) d-dimensional manifold has triangulations where the dual graph has an arbitrarily large twin-width.

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Édouard Bonnet and Kristóf Huszár. On the Twin-Width of Smooth Manifolds. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.23

Author Details

Édouard Bonnet
  • Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
Kristóf Huszár
  • Institute of Geometry, Graz University of Technology, Austria

Funding

The authors have been supported by the French National Research Agency through the project TWIN-WIDTH with reference number ANR-21-CE48-0014.
  • Huszár, Kristóf: Partially supported by the Austrian Science Fund (FWF) grant P 33765-N.

Acknowledgements

We thank the anonymous reviewers for their helpful comments and for raising interesting questions for future research.

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