Source labels openChecked July 26, 2026

Erdős Problem 184

Any graph on $n$ vertices can be decomposed into $O(n)$ many edge-disjoint cycles and edges.

Combinatorics AMS 5

Mathematical statement

Any graph on $n$ vertices can be decomposed into $O(n)$ many edge-disjoint cycles and 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_184

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_184 :    ∃ f : ℕ → ℝ,      (f =O[atTop] fun n : ℕ ↦ (n : ℝ)) ∧      ∀ {V : Type*} [Fintype V] [DecidableEq V] (G : SimpleGraph V),      ∃ (D : Finset G.Subgraph),        (∀ H ∈ D, IsCycleOrEdge H.coe) ∧        IsDecomposition G D ∧        (D.card : ℝ) ≤ f (Fintype.card V) := 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/184background