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Written on the Wall II, Graph Conjecture 109

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

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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.

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

  1. construction · #1

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

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

    lean: correctLean

    scope Lean formalization of the result

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

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

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open in Claude →open in ChatGPT →

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