What was already known
The 1996 Graph Conjecture 2 asked for this inequality on connected simple graphs.
AI involvement
The DeepMind report credits Agent D with the proof. Human researchers supplied the formal target and explain the incidence-graph and discharging argument.
The paper attributes the proof to the agent, with no human-origin central lemma or repair documented.
Importance
The result settles a named graph inequality.
Limitations
The source identifies a Lean proof, but its definitions were not independently compared with the original conjecture wording.
Technical verification
The paper identifies a Lean proof for the spanning-tree leaf bound. This is source-reported formal verification of the stated graph theorem; the linked file was not rebuilt here.
Independent checking
Agent-generated Lean proof identified as GraphConjecture2.lean
- Checker
- AlphaProof Nexus Lean validator
- Scope
- L_S(G)≥2(ℓ(G)−1) for every finite simple connected graph
- Basis
- Reported by the linked checker
Human understanding
The paper’s appendix explains the incidence-graph degrees, local leaf lemma and final discharging argument.
Correction and publication history
The result settles a named graph inequality.
Read this published revision