Source labels openChecked July 26, 2026

Erdős Problem 918: I

Is there a graph with $\aleph_2$ vertices and chromatic number $\aleph_2$ such that every subgraph on $\aleph_1$ vertices has chromatic number $\leq\aleph_0$ ?

Combinatorics AMS 5

Mathematical statement

Is there a graph with $\aleph_2$ vertices and chromatic number $\aleph_2$ such that every subgraph on $\aleph_1$ vertices has chromatic number $\leq\aleph_0$ ?

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_918.variants.all_subgraphs.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_918.variants.all_subgraphs.parts.i :    answer(sorry) ↔ ∃ (V : Type u) (G : SimpleGraph V), #V = ℵ_ 2 ∧ G.chromaticCardinal = ℵ_ 2 ∧      ∀ (H : G.Subgraph) (_ : #H.verts = ℵ₁), H.coe.chromaticCardinal ≤ ℵ₀ := 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/918background