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The Tree Product Conjecture

Combinatorics · posed by Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar, Wood, 2022 · disproved

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Statement

Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar and Wood conjectured that every graph of degree-dd polynomial growth embeds into the strong product of dd trees of linear growth and a bounded clique. False for d=4d = 4: a counterexample built from the discrete Heisenberg group.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Freddie Illingworth, Sergey Norin and Raphael Steiner, using ChatGPT 5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The AI disclosure is narrow and specific: the model was used to help work out the details of the compactness argument. The Heisenberg group counterexample is the authors'.

    disproved at d = 4; the conjecture for smaller d is untouched

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.