Title: The size Ramsey numbers of graphs and hypergraphs
|Affiliation:||London School of Economics|
|Zoom:||Please email Emma Watson|
The s-colour size-Ramsey number of a graph ( hypergraph) H is the minimum number of edges in a graph (hypergraph) G whose every s-edge-colouring contains a monochromatic copy of H. While the study of size Ramsey numbers for graphs goes back to 70's to the work of Erdos, Faudree, Rousseau and Schelp, the systematic study of these numbers for hypergraphs have been initiated much more recently in 2017 by Dudek, La Fleur, Mubayi, and Rödl. In this talk we will present the current known results in the literature, and some recent progress we have made on several questions in the area. We prove a general result that allows us to deduce that powers of tight paths, powers of bounded degree hypergraph trees and of `long subdivisions' of bounded degree hypergraphs have size-Ramsey numbers that are linear in the number of vertices. This result strongly generalizes all families of graphs/hypergraphs for which it was known that that size Ramsey number is linear.
The talk is based on joint work with Shoham Letzter and Alexey Pokrovskiy.