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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 596: K4 K3 Exceptional Iff

Whether (K4,K3)(K_4, K_3) is Erdős–Hajnal exceptional is precisely the content of Erdős Problem 595. The finite Ramsey property holds (Folkman 1970, Nešetřil–Rödl [NeRo75]); the open part is whether every K4K_4-free graph is a countable union of triangle-free gr...

Mathematical statement

Whether (K4,K3)(K_4, K_3) is Erdős–Hajnal exceptional is precisely the content of Erdős Problem 595. The finite Ramsey property holds (Folkman 1970, Nešetřil–Rödl [NeRo75]); the open part is whether every K4K_4-free graph is a countable union of triangle-free graphs.

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_596.variants.K4_K3_exceptional_iff

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_596.variants.K4_K3_exceptional_iff : answer(sorry)     IsErdosHajnalExceptional (completeGraph (Fin 4)) (completeGraph (Fin 3)) := 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