The bunkbed conjecture is false

• 成果类型: Article
• 署名作者: Gladkov, Nikita; Pak, Igor; Zimin, Aleksandr
• 署名单位: University of California System; University of California Los Angeles; Massachusetts Institute of Technology (MIT)
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-12209
• DOI: 10.1073/pnas.2420725122
• 发表日期: 2025-06-17
• 关键词: percolation; probability

摘要

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).