Source labels openChecked July 26, 2026

Erdős Problem 64

Does every finite graph with minimum degree at least $3$ contain a cycle of length $2^k$ for some $k \geq 2$ ?

Combinatorics AMS 5

Mathematical statement

Does every finite graph with minimum degree at least $3$ contain a cycle of length $2^k$ for some $k \geq 2$ ?

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_64

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_64 :    answer(sorry) ↔ ∀ (V : Type*) (G : SimpleGraph V) [Fintype V] [DecidableRel G.Adj],        G.minDegree ≥ 3 → ∃ (k : ℕ) (v : V) (c : G.Walk v v),            k ≥ 2 ∧ c.IsCycle ∧ c.length = 2^k := 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/64background