ProbXiv
sign in
Problem archiveProblem record

Babai's Minimal Cayley Graph Problem

Combinatorics · posed by László Babai, 1978 · disproved

1 comment

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.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    James Davies, Meike Hatzel and Liana Yepremyan, using ChatGPT 5.6 Sol

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

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.