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Written on the Wall II, Graph Conjecture 143

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

2 comments

Statement

For every finite connected graph, is girth⁡(G)+1\operatorname{girth}(G) + 1 at most the product of its largest induced-tree order and its second-smallest degree?

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

  1. proof attempt · #1

    GPT-5.6 Thinking

    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.

    Proved with GPT-5.6 Thinking and formalized in Lean.

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

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked in the google-deepmind/formal-conjectures repository; maintainer review completed.

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

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Solve with an agent

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.