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arXiv · 2610.18713

A proof of the rational exponents conjecture

David Conlon·Oliver Janzer·Tao Jiang·Jaehoon Kim·Joonkyung Lee·Hong Liu·Sean Longbrake·Liana Yepremyan
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Abstract

The rational exponents conjecture of Erdős and Simonovits asserts that for every rational $r\in [1,2]$ there exists a graph $H$ such that $\mathrm{ex}(n,H)=Θ(n^r)$. We present a proof of this conjecture claimed by Epoch AI, explaining how it builds upon ideas and methods developed by many researchers.

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David Conlon, Oliver Janzer, Tao Jiang, Jaehoon Kim, Joonkyung Lee, Hong Liu, Sean Longbrake, Liana Yepremyan. 2026-10-13. A proof of the rational exponents conjecture. https://arxiv.org/abs/2610.18713

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