Babai's Minimal Cayley Graph Problem
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
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.
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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