English

The bunkbed conjecture is false

Combinatorics 2024-10-04 v1 Discrete Mathematics Probability

Abstract

We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on 72227222 vertices, and is built on the recent work of Hollom (2024).

Cite

@article{arxiv.2410.02545,
  title  = {The bunkbed conjecture is false},
  author = {Nikita Gladkov and Igor Pak and Aleksandr Zimin},
  journal= {arXiv preprint arXiv:2410.02545},
  year   = {2024}
}

Comments

12 pages, 2 figures

R2 v1 2026-06-28T19:07:07.550Z