Multicolor Ramsey numbers for Berge cycles

TL;DR

This paper determines the order of magnitude of multicolor Ramsey numbers for Berge cycles of specific lengths and extends the results to Berge bipartite graphs, providing insights into hypergraph Ramsey problems.

Contribution

It establishes the order of magnitude for multicolor Ramsey numbers of Berge cycles and bipartite graphs for small uniformities, introducing a general framework applicable to other hypergraph Ramsey problems.

Findings

Order of magnitude results for Berge cycles of lengths 4, 5, 6, 7, 10, 11

Order of magnitude results for Berge-$K_{a,b}$ for certain parameters

A general setup applicable to various hypergraph Ramsey problems

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.