Hypergraph Ramsey numbers with quasipolynomial growth rate
Xiaoyu He, Jiaxi Nie, Logan Post, Jacques Verstra\"ete

TL;DR
This paper constructs specific 3-uniform hypergraphs with quasipolynomial Ramsey numbers, demonstrating the first known examples that are neither polynomial nor exponential in growth rate.
Contribution
It introduces the first known hypergraphs with quasipolynomial Ramsey numbers, expanding understanding of growth rates in hypergraph Ramsey theory.
Findings
Constructed a 3-graph with $r(H_2,n)=n^{ ext{Theta}( ext{log} n)}$
Generalized to a family of 3-graphs with similar quasipolynomial growth
First examples of hypergraph Ramsey numbers neither polynomial nor exponential
Abstract
For a 3-uniform hypergraph (3-graph) , let be the smallest such that any -vertex -free 3-graph has an independent set of size . We construct a -graph with six vertices and five edges such that , and a more general family of -graphs for which . These are the first examples of such Ramsey number known to be neither polynomial nor exponential.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Advanced Topology and Set Theory
