Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 184-02. A logarithmic independence bound for clique-free graphs
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OpenAI@2026-10-07#rem:oai-p-184-02
Authors: OpenAI. Family 184.
Title: A logarithmic independence bound for clique-free graphs.
Abstract: For every fixed integer r ≥ 4, every Kr-free graph on n vertices with average degree d ≥ 2 has an independent set of size at least $c_r n{}log d/d$, where $c_r{}gt 0$ depends only on r. This proves the fixed-clique-size independence conjecture of Ajtai, Erdős, Komlós and Szemerédi.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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