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Babai's Minimal Cayley Graph Problem

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.

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combinatoricsAug 6, 2026Significance 30/100Registry: unreviewed

Babai's Minimal Cayley Graph Problem

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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.

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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.

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Babai's Minimal Cayley Graph Problem — Mathematical Frontier Network