All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 23

Can every triangle-free graph on 5n5n vertices be made bipartite by deleting at most n2n^2 edges?

Mathematical statement

Can every triangle-free graph on 5n5n vertices be made bipartite by deleting at most n2n^2 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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_23 : answer(sorry)      (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