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Written on the Wall II, Graph Conjecture 103

Combinatorics · posed by Graffiti (Written on the Wall II), 1996 · disproved

2 comments

Statement

For every connected graph GG, is α(G)≤⌊b(G)−log⁡(ecc⁡avg(G))⌋\alpha(G) \le \lfloor b(G) - \log(\operatorname{ecc}_{avg}(G)) \rfloor, where b(G)b(G) is the largest induced-bipartite-subgraph order? An 1111-vertex counterexample - a triangle with four leaves on each of two vertices - has α=9\alpha = 9 against bound 88.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. computation · #1

    ChatGPT + Codex

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

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

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

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

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.