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The bunkbed conjecture is false

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arxiv 2410.02545 v1 pith:IBGIRUHQ submitted 2024-10-03 math.CO cs.DMmath.PR

Nikita Gladkov , Igor Pak , Aleksandr Zimin This is my paper · ORCID
classification math.COcs.DMmath.PR
keywords bunkbedconjecturecounterexamplebuiltexplicitfalsegivegiven
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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).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Maximum flow and self-avoiding walk on bunkbed graphs

    math.PR 2025-02 conditional novelty 7.0 of 10

    For bunkbed graphs with reflection-symmetric capacities, same-side max flow dominates cross-side max flow, and for K_n x K_2, self-avoiding walks to the mirrored vertex outnumber same-side walks for n=3,4,5 and all su...

  2. The bunkbed conjecture still holds for cactus graphs and for graphs with certain biconnected components

    math.PR 2025-06 conditional novelty 6.0 of 10

    Cactus graphs satisfy the strong bunkbed conjecture, and any graph satisfies the conjecture if and only if all of its biconnected components do.

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