
TL;DR
This paper establishes a nearly optimal exponential lower bound for the Ramsey number of a specific class of hypergraphs called daisies, extending previous results and matching bounds known for complete hypergraphs.
Contribution
It provides an $(r-2)$-iterated exponential lower bound for the Ramsey number of $(r,m,k)$-daisies in 2-colorings, advancing understanding of hypergraph Ramsey theory.
Findings
Lower bound matches the order of magnitude of complete hypergraph Ramsey numbers
Extends previous work on daisies with improved bounds
Uses combinatorial and probabilistic methods to establish bounds
Abstract
A -uniform hypergraph on vertices is an -daisy if there exists a partition of the vertices with , such that the set of edges of is all the -tuples , where is an -tuple of . Complementing results in ["On the Ramsey number of daisies I"], we obtain an -iterated exponential lower bound to the Ramsey number of an -daisy for -colors. This matches the order of magnitude of the best lower bounds for the Ramsey number of a complete -graph.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory
