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 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