The bunkbed conjecture is false

2024/10/03 by Gladkov, Nikita, Pak, Igor, Zimin, Aleksandr · 4 citations
#05C80 #60C05 #60K35 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.02545

Abstract

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).

Cited by

• An elementary proof of the bunkbed conjecture for forests
• The bunkbed problem and the random cluster model
• The bunkbed conjecture still holds for cactus graphs and for graphs with certain biconnected components
• The acyclic directed bunkbed conjecture is false

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• Vertex gluing preserves the bunkbed conjecture
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