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A proof of the rational exponents conjecture
Abstract
The rational exponents conjecture of Erdős and Simonovits asserts that for every rational r∈ [1,2] there exists a graph H such that ex(n,H)=Θ(nr). 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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BibTeX
@misc{conlon2026proof,
title = {{A proof of the rational exponents conjecture}},
author = {David Conlon and Oliver Janzer and Tao Jiang and Jaehoon Kim and Joonkyung Lee and Hong Liu and Sean Longbrake and Liana Yepremyan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18713},
eprint = {2610.18713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18713},
}
RIS
TY - UNPB
TI - A proof of the rational exponents conjecture
AU - David Conlon
AU - Oliver Janzer
AU - Tao Jiang
AU - Jaehoon Kim
AU - Joonkyung Lee
AU - Hong Liu
AU - Sean Longbrake
AU - Liana Yepremyan
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18713
UR - https://arxiv.org/abs/2610.18713
AB - The rational exponents conjecture of Erdős and Simonovits asserts that for every rational r∈ [1,2] there exists a graph H such that 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.
ER -