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Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Combinatorics
Erdős problem 617
Let r≥3. If the edges of Kr2+1 are r
-coloured then there exist
r+1
vertices with at
least one colour missing on the edges of the induced
Kr+1
.
In other words, there is no balanced colouring.
A conjecture of Erdős and Gyárfás [ErGy99].
$2,694 bounty·2 pieces from 2 people·last one 20 hours ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
∀ r ≥ 3,
∀ {V : Type} [inst : Fintype V] [DecidableEq V],
Fintype.card V = r ^ 2 + 1 →
∀ (coloring : Sym2 V → Fin r), ∃ S k, S.card = r + 1 ∧ ∀ u ∈ S, ∀ v ∈ S, u ≠ v → coloring s(u, v) ≠ k
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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