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Off-diagonal Ramsey numbers of 3-graphs
Abstract
We prove a conjecture of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstraëte, and Yu that for a $3$-graph H, the off-diagonal Ramsey number R(H,n) is polynomial in n if and only if H is isomorphic to a subgraph of the "depth-t iterated blowup" textsfBt for an integer t≥ 0. Here, the $3$-graphs textsfBt are defined recursively: textsfB0 has one vertex, and textsfBt for t≥ 1 is obtained from the disjoint union of three copies of textsfBt−1 by adding all transversal hyperedges.
Related
BibTeX
@misc{gishboliner2026offdiagonal,
title = {{Off-diagonal Ramsey numbers of 3-graphs}},
author = {Lior Gishboliner and Sepehr Hajebi and Xiangyu Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32644},
eprint = {2610.32644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32644},
}
RIS
TY - UNPB
TI - Off-diagonal Ramsey numbers of 3-graphs
AU - Lior Gishboliner
AU - Sepehr Hajebi
AU - Xiangyu Li
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32644
UR - https://arxiv.org/abs/2610.32644
AB - We prove a conjecture of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstraëte, and Yu that for a $3$-graph H, the off-diagonal Ramsey number R(H,n) is polynomial in n if and only if H is isomorphic to a subgraph of the "depth-t iterated blowup" textsfB_t for an integer t≥ 0. Here, the $3$-graphs textsfB_t are defined recursively: textsfB_0 has one vertex, and textsfB_t for t≥ 1 is obtained from the disjoint union of three copies of textsfB_t−1 by adding all transversal hyperedges.
ER -