Ringel's Conjecture

formal-conjectures · paper · ams-5

For any tree $T$ with $n$ edges, the complete graph $K_{2n+1}$ decomposes into
$2n+1$ edge-disjoint copies of $T$.

A "copy" of $T$ is the image $T.\text{map}(f_i)$ of $T$ under a vertex embedding
$f_i : V \hookrightarrow \text{Fin}(2n+1)$; the copies are pairwise edge-disjoint
and together cover every edge of $K_{2n+1}$.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Paper/RingelConjecture.lean
Local target: Corpus.PaperRingelConjecture.ringel_conjecture
Source SHA-256: 38dcb7c32bd9d1b8cfb8fda0e36d216c5aa88dfdcb750b75a0730c12806fb2a7
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record