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On the Ramsey numbers of daisies II
Published online by Cambridge University Press: 18 September 2024
Abstract
A $(k+r)$-uniform hypergraph $H$ on $(k+m)$ vertices is an $(r,m,k)$-daisy if there exists a partition of the vertices $V(H)=K\cup M$ with $|K|=k$, $|M|=m$ such that the set of edges of $H$ is all the $(k+r)$-tuples $K\cup P$, where $P$ is an $r$-tuple of $M$. We obtain an $(r-2)$-iterated exponential lower bound to the Ramsey number of an $(r,m,k)$-daisy for $2$-colours. This matches the order of magnitude of the best lower bounds for the Ramsey number of a complete $r$-graph.
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- © The Author(s), 2024. Published by Cambridge University Press
Footnotes
The author was supported by NSF grant DMS 1764385 and US Air Force grant FA9550-23-1-0298.