Source labels openChecked July 26, 2026

Erdős Problem 944: Dirac Conjecture

Let $k \ge 4$ . Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $>1$ ?

Number theory AMS 11

Mathematical statement

Let $k \ge 4$ . Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $>1$ ?

This was conjectured by Dirac in 1970.

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_944.variants.dirac_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_944.variants.dirac_conjecture :    answer(sorry) ↔ ∀ k ≥ 4, ∃ (V : Type u) (G : SimpleGraph V), G.IsErdos944 k 1 := 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/944background