therefore
Sign up
Open navigation
All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 740

Let m\mathfrak{m} be an infinite cardinal and GG be a graph with chromatic number m\mathfrak{m}. Let r≥1r\geq 1. Must GG contain a subgraph of chromatic number m\mathfrak{m} which does not contain any odd cycle of length ≤r\leq r?

CombinatoricsAMS 5

Mathematical statement

Let m\mathfrak{m} be an infinite cardinal and GG be a graph with chromatic number m\mathfrak{m}. Let r≥1r\geq 1. Must GG contain a subgraph of chromatic number m\mathfrak{m} which does not contain any odd cycle of length ≤r\leq r?

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_740

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_740 :    answer(sorry) ↔      ∀ (V : Type*) (G : SimpleGraph V),        ℵ₀ ≤ G.chromaticCardinal →          ∀ (r : ℕ),            ∃ (H : G.Subgraph), H.coe.chromaticCardinal = G.chromaticCardinal ∧              NoShortOddCycle H.coe r := 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 sourceformalizationerdosproblems.com/740background