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A note on the logarithmic exponent of Ramsey number r(4,t)
Abstract
In this short note, we point out that the recent lower bounds for off-diagonal Ramsey numbers r(s,t) with fixed s≥ 5, together with the recent proof of the Ajtai--Erdős--Komlós--Szemerédi independence conjecture, imply r(4,t)=t3/((log t)2+o(1)). This note is solely for informal circulation and will not be submitted for publication.
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BibTeX
@misc{chen2026note,
title = {{A note on the logarithmic exponent of Ramsey number $r(4,t)$}},
author = {Kaizhe Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15293},
eprint = {2610.15293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15293},
}
RIS
TY - UNPB
TI - A note on the logarithmic exponent of Ramsey number r(4,t)
AU - Kaizhe Chen
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15293
UR - https://arxiv.org/abs/2610.15293
AB - In this short note, we point out that the recent lower bounds for off-diagonal Ramsey numbers r(s,t) with fixed s≥ 5, together with the recent proof of the Ajtai--Erdős--Komlós--Szemerédi independence conjecture, imply r(4,t)=t^3/((log t)^2+o(1)). This note is solely for informal circulation and will not be submitted for publication.
ER -