Erdős Problem 1175: Threshold Formulation
Threshold reformulation variant.* Replaces chromaticCardinal = λ in the hypothesis of erdos_1175 with λ ≤ chromaticCardinal (a graph of chromatic number ≥ λ has a triangle-free subgraph of chromatic number κ). This is a strengthening of erdos_1175...
Mathematical statement
Threshold reformulation variant.* Replaces chromaticCardinal = λ in the hypothesis
of erdos_1175 with λ ≤ chromaticCardinal (a graph of chromatic number ≥ λ has a
triangle-free subgraph of chromatic number κ). This is a strengthening of erdos_1175
(see erdos_1175.test.threshold_implies_exact).
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
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Pinned Lean formulation 1
erdos_1175.variants.threshold_formulation
theorem erdos_1175.variants.threshold_formulation : answer(sorry) ↔ ∀ (κ : Cardinal), ℵ₀ < κ → ∃ (μ : Cardinal), ∀ (V : Type*) (G : SimpleGraph V), μ ≤ G.chromaticCardinal → ∃ (H : G.Subgraph), H.coe.CliqueFree 3 ∧ H.coe.chromaticCardinal = κ := 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