On Ramsey number of Steiner systems
Ayush Basu, Daniel Dobak, Vojt\v{e}ch R\"odl, Marcelo Sales

TL;DR
This paper proves the existence of certain hypergraphs called partial $(k,k-1)$-systems with Ramsey numbers that grow extremely rapidly, as a tower of height $k-1$, for any number of colors $r \,\geq\, 4$.
Contribution
It establishes the existence of partial $(k,k-1)$-systems with super-exponentially large Ramsey numbers, advancing understanding of hypergraph Ramsey theory.
Findings
Ramsey number grows as a tower of height $k-1$
Existence of such hypergraphs for $r \geq 4$ colors
Significant growth rate of hypergraph Ramsey numbers
Abstract
A -uniform hypergraph is called a partial -system if every set of vertices of is contained in at most one edge of . We prove the existence of a partial -system whose Ramsey number with colors grows as a tower of height .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Advanced Graph Theory Research
