Ramsey numbers of sparse graphs and hypergraphs

Ramsey numbers of sparse graphs and hypergraphs

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Jakob Fox, Princeton University
Fine Hall 314

The Ramsey number $r(G)$ of a graph $G$ is the minimum $N$ such that every 2-coloring of the edges of the complete graph on $N$ vertices contains a monochromatic copy of $G$. Determining or estimating Ramsey numbers is one of the central problem in Ramsey theory. Besides the complete graph, the next most classical topic in this area concerns the Ramsey number of sparse graphs. The study of these Ramsey numbers was initiated by Burr and Erdos in 1975, and this topic has since placed a central role in graph Ramsey theory. In this talk we will discuss recent progress in this area. Joint work with Benny Sudakov.