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On the Ramsey numbers of daisies I

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  18 September 2024

Pavel Pudlák ,
Vojtech Rödl  and
Marcelo Sales Open the ORCID record for Marcelo Sales [Opens in a new window]
Pavel Pudlák
Affiliation:
Institute of Mathematics, CAS, Prague, Czech Republic
Vojtech Rödl
Affiliation:
Department of Mathematics, Emory University, Atlanta, GA, USA
Marcelo Sales*
Affiliation:
Department of Mathematics, University of California, Irvine, CA, USA
*
Corresponding author: Marcelo Sales; Email: [email protected]
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Abstract

Daisies are a special type of hypergraph introduced by Bollobás, Leader and Malvenuto. An $r$-daisy determined by a pair of disjoint sets $K$ and $M$ is the $(r+|K|)$-uniform hypergraph $\{K\cup P\,{:}\, P\in M^{(r)}\}$. Bollobás, Leader and Malvenuto initiated the study of Turán type density problems for daisies. This paper deals with Ramsey numbers of daisies, which are natural generalisations of classical Ramsey numbers. We discuss upper and lower bounds for the Ramsey number of $r$-daisies and also for special cases where the size of the kernel is bounded.

Keywords

Ramsey theoryhypergraphs

MSC classification

Primary: 05D10: Ramsey theory
Secondary: 05C65: Hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 33 , Issue 6 , November 2024 , pp. 795 - 806
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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