Source labels openChecked July 26, 2026

Erdős Problem 595

*Erdős Problem 595 ( $250)**: Is there an infinite graph$ G $which contains no$ K_4$ and is not the union of countably many triangle-free graphs?

Combinatorics AMS 5

Mathematical statement

*Erdős Problem 595 ( $250)**: Is there an infinite graph$ G $which contains no$ K_4$ and is not the union of countably many triangle-free graphs?

A problem of Erdős and Hajnal [Er87].

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_595

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_595 : answer(sorry) ↔    ∃ (V : Type*) (_ : Infinite V) (G : SimpleGraph V),      G.CliqueFree 4 ∧ ¬IsCountableUnionOfTriangleFree G := 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/595background