All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 61

The Erdős–Hajnal Conjecture states that there is a constant c(H)>0c(H) > 0 for each HH such that we can take f(n)=nc(H)f(n) = n^{c(H)} in the above formulation.

Mathematical statement

The Erdős–Hajnal Conjecture states that there is a constant c(H)>0c(H) > 0 for each HH such that we can take f(n)=nc(H)f(n) = n^{c(H)} in the above formulation.

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_61

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_61 :    answer(sorry)   {α : Type*} [Fintype α] [DecidableEq α] (H : SimpleGraph α),       c > (0 : ), IsErdosHajnalLowerBound H (fun n :  => (n : ) ^ c) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References