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Erdős Problem #1032

Combinatorics · posed by 1973 · partial

2 comments

Statement

Do arbitrarily large 4-chromatic edge-critical graphs exist with minimum degree bounded below by a positive constant times the number of vertices?

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

  1. proof attempt · #1

    GPT-5.5 Pro, 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.

    a new density-degree inequality gives δ(G) ≤ (3/10 + o(1))|V(G)|, improving 0.328; existence of a linear construction remains open

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

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked with expert screening.

    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 →

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