Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 Jun 17;122(24):e2420725122.
doi: 10.1073/pnas.2420725122. Epub 2025 Jun 13.

The bunkbed conjecture is false

Nikita Gladkov #  1 , Igor Pak #  1 , Aleksandr Zimin #  2
Affiliations

The bunkbed conjecture is false

Nikita Gladkov et al. Proc Natl Acad Sci U S A. .

Abstract

We give an explicit counterexample to the bunkbed conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on 7,222 vertices and is built on the recent work of Hollom (2024).

Keywords: bunkbed conjecture; counterexample; hypergraph; percolation on graphs; random network.

PubMed Disclaimer

Conflict of interest statement

Competing interests statement:The authors declare no competing interest.

References

    1. van den Berg J., Kahn J., A correlation inequality for connection events in percolation. Ann. Probab. 29, 123–126 (2001).
    1. Bollobás B., Riordan O., Percolation (Cambridge University Press, New York, NY, 2006), p. 323.
    1. G. R. Grimmett, Percolation (Springer, Berlin, Germany, ed. 2, 1999), p. 444.
    1. H. Duminil-Copin, “Sixty years of percolation” in Proceedings of the ICM (World Scientific, Hackensack, NJ, 2018), vol. IV, pp. 2829–2856.
    1. Werner W., Percolation et Modèle d’Ising (Société Mathématique de France, Paris, France, 2009), p. 161.

LinkOut - more resources