Written on the Wall II, Graph Conjecture 103

Precise statement

For every connected graph $G$, is $\alpha(G) \le \lfloor b(G) - \log(\operatorname{ecc}_{avg}(G)) \rfloor$, where $b(G)$ is the largest induced-bipartite-subgraph order? An $11$-vertex counterexample - a triangle with four leaves on each of two vertices - has $\alpha = 9$ against bound $8$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT + Codex

The counterexample was found with ChatGPT and Codex and verified in Lean, alongside exhaustive subset enumeration.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Lean-checked counterexample merged into the google-deepmind/formal-conjectures repository.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-22

   formal-conjectures PR #4482 - Disprove WOWII Conjecture 103

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

computation (source-reported)

Source-reported tools: computation.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.