New bounds for off-diagonal hypergraph Ramsey numbers

@misc{conlon2026bounds,
  title = {{New bounds for off-diagonal hypergraph Ramsey numbers}},
  author = {David Conlon and Xiaoyu He and Jiaxi Nie and Logan Post},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14829},
  eprint = {2610.14829},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14829},
}

TY  - UNPB
TI  - New bounds for off-diagonal hypergraph Ramsey numbers
AU  - David Conlon
AU  - Xiaoyu He
AU  - Jiaxi Nie
AU  - Logan Post
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14829
UR  - https://arxiv.org/abs/2610.14829
AB  - We study a conjecture of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstraëte, and Yu, which characterizes the $3$-graphs H for which the off-diagonal Ramsey number r(H,n) is polynomial. We prove the conjecture for $3$-graphs with at most five tight components. Additionally, we show that the full conjecture is equivalent to its specialization to linear $3$-graphs. We prove quasipolynomial upper bounds for a class of `forward-doubleable' $3$-graphs, which includes the Fano plane. Finally, we give an exponential lower bound for `non-forward-laminar' $3$-graphs and use this to completely classify the Ramsey growth of a natural family of 3-graphs called chains.
ER  -