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Written on the Wall II, Graph Conjecture 109

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wow-conjecture-109Combinatoricsposed by Graffiti (Written on the Wall II), 1996recorded: disproved

1 attempt · 1 machine check · no person has looked

Statement

Must every connected graph satisfy the proposed upper bound on its independence number in terms of residue and largest induced-bipartite-subgraph order? The family K‾2r+1∨(Kr⊔Kr)\overline{K}_{2r+1} \vee (K_r \sqcup K_r) violates it for every r≥3r \ge 3.

Context

Machine-generated (Written on the Wall II); real but unfamous by construction.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.6 Sol Max (Codex) ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol Max (Codex)

    The infinite counterexample family was found with GPT-5.6 Sol Max running in Codex; verified in Lean plus independent Python and C++ enumeration.

    Reviews

    0 human reviews · 1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Lean-checked disproof in the google-deepmind/formal-conjectures repository, with independent computational enumeration.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Endorsements

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    Discussion of this attempt

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Discussion

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