All open problems
Source labels openChecked July 26, 2026
Erdős Problem 23
Can every triangle-free graph on vertices be made bipartite by deleting at most edges?
Mathematical statement
Can every triangle-free graph on vertices be made bipartite by deleting at most edges?
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_23
Complete statement target, proof intentionally absentLean 4
theorem erdos_23 : answer(sorry) ↔ ∀ (n : ℕ) (V : Type) [Fintype V], Fintype.card V = 5 * n → ∀ (G : SimpleGraph V), G.CliqueFree 3 → ∃ (H : SimpleGraph V), H ≤ G ∧ H.IsBipartite ∧ (G.edgeFinset \ H.edgeFinset).card ≤ n^2 := 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