The Tree Product Conjecture
Statement
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.
Context
disproved at d = 4; the conjecture for smaller d is untouched
A 2022 conjecture from the product structure theory programme, put forward by eight authors and cited as a target in that literature.
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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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