erdős #184
Any graph on vertices can be decomposed into many edge-disjoint cycles and edges.
Open — best to date is a honest null, not yet sealed.
graph theory · open · possible · formalized (Lean) · 1 attempt
use this record
vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
honest null
needs verification
attempted via frontier '?' (transfer_strength=n/a) -> no_progress
No solve/partial on this pass. Transfer into the owned frontier was 'n/a'. Do not re-attack cold; needs a new idea or richer accumulated context.
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
What you wrote is **exactly the Erdős–Gallai cycle decomposition conjecture** (from the 1960s):
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 5 · open (literature)
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)formal-conjectures/184.lean ↗status
open