Every problem here was open when it entered the pool.
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].
∀ 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
What you must prove
import FormalConjectures.ErdosProblems.«617»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos617.erdos_617" := by
sorry
end Bounty
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.