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Babai's Minimal Cayley Graph Problem

Combinatorics · posed by László Babai, 1978 · disproved

1 attempt

Statement

A Cayley graph is minimal when no proper subset of its connection set generates the group. Babai asked whether minimal Cayley graphs have bounded chromatic number. Resolved negatively: finite minimal Cayley graphs exist with arbitrarily large chromatic number.

Context

A question of Babai's standing open since 1978, in the algebraic graph theory his name anchors, with recent partial results narrowing it just before it fell.

People

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

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  • #1

    Attempt 1

    constructionChatGPT 5.6 Sol with James Davies, Meike Hatzel, Liana Yepremyan ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    ChatGPT 5.6 Sol
    people
    James Davies, Meike Hatzel, Liana Yepremyan

    The paper's statement of AI use: "An initial proof was found by ChatGPT 5.6 Sol given [DHY24] in the input. Substantial parts of Section 2 originate from an early draft created in interaction with ChatGPT 5.6 Sol, which was subsequently edited and improved by the authors." The model found the first proof, given one of the authors' own earlier papers as context.

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