The bunkbed conjecture is false
Nikita Gladkov, Igor Pak, Aleksandr Zimin · arXiv (Cornell University) · 2024
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of Hollom (2024).