The Tree Product Conjecture
Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar and Wood conjectured that every graph of degree- polynomial growth embeds into the strong product of trees of linear growth and a bounded clique. False for : a counterexample built from the discrete Heisenberg group.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Structural graph theory
- Posed by
- Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar, Wood
- Year posed
- 2022
- Years open
- 4y
- Solved
- 2026-07-03
- Model
- ChatGPT 5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Freddie Illingworth, Sergey Norin, Raphael Steiner
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
disproved at d = 4; the conjecture for smaller d is untouched
What the AI did
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'.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2607.03041 - Disproof of the tree product conjecture via the Heisenberg group