The Tree Product Conjecture
Prior state unknown→disproved
disproved at d = 4; the conjecture for smaller d is untouched
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combinatorics / Structural graph theory
The Tree Product Conjecture
Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar and Wood conjectured that every graph of degree-$d$ polynomial growth embeds into the strong product of $d$ trees of linear growth and a bounded clique. False for $d = 4$: a counterexample built from the discrete Heisenberg group.
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Campbell, Distel, Gollin, Harvey, Hendrey, Hickingbotham, Mohar and Wood conjectured that every graph of degree-$d$ polynomial growth embeds into the strong product of $d$ trees of linear growth and a bounded clique. False for $d = 4$: a counterexample built from the discrete Heisenberg group.
disproved at d = 4; the conjecture for smaller d is untouched
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