[1] A preprint giving a proposed counterexample to the conjecture was posted on the arXiv in October 2024 by Nikita Gladkov, Igor Pak, and Alexander Zimin.
A random subgraph of the bunkbed graph is then formed by independently deleting each edge based on the assigned probability.
This is intuitive, and similar questions for random walks and Ising model were resolved positively.
[5] Despite intuitiveness, proving this conjecture is not straightforward and is an active area of research in percolation theory.
[11][12] Counterexamples for generalizations of the bunkbed conjecture have been published for site percolation, hypergraphs, and directed graphs.