Multicolor Ramsey numbers for Berge cycles

DOI10.37236/10761zbMath1506.05206arXiv2109.13969OpenAlexW3203115364MaRDI QIDQ2112557

Michael Tait, Hannah Mahon, Zachary DeStefano, Frank Simutis

Publication date: 11 January 2023

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Abstract: In this paper, for small uniformities, we determine the order of magnitude of the multicolor Ramsey numbers for Berge cycles of length $4$, $5$, $6$, $7$, $10$, or $11$. Our result follows from a more general setup which can be applied to other hypergraph Ramsey problems. Using this, we additionally determine the order of magnitude of the multicolor Ramsey number for Berge-$K_{a,b}$ for certain $a$, $b$, and uniformities.

Full work available at URL: https://arxiv.org/abs/2109.13969

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zbMATH Keywords

hypergraph Ramsey numbersBerge-\(G\) hypergraph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Hypergraphs (05C65) Distance in graphs (05C12) Generalized Ramsey theory (05C55) Ramsey theory (05D10)

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