Work

A proof of the rational exponents conjecture

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.18713

Authors: Conlon, David, Janzer, Oliver, Jiang, Tao, Kim, Jaehoon, Lee, Joonkyung, Liu, Hong, Longbrake, Sean, Yepremyan, Liana

Institutions: California Institute of Technology, Emory University, École Polytechnique Fédérale de Lausanne, Miami University, Korea Advanced Institute of Science and Technology, Korea Institute for Advanced Study, Institute for Basic Science

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Awards: G1474807751, G2168000522, G3812690899, G6418436714, G6572798828, Connections in Extremal Combinatorics

OpenAlex ID: W7221791292

Cites: 1

Cited by: 2

Related to: 10