报告人： Shagnik Das,  Free University of Berlin, Germany 

报告题目： Perturbed Ramsey problems

报告时间：9月21日 4:00-5:00

报告地点：1208

摘要：

We say a graph G is Ramsey for a pair of graphs (H1, H2) if any red-/blue-colouring of E(G) contains either a red H1 or a blue H2. Much research has been devoted to determining the thresholds at which the Erdős-Rényi random graph G(n,p) becomes Ramsey for (H1, H2). In this talk, we instead consider the perturbed random graph model, where one sprinkles some random edges on top of a deterministic dense graph, and ask how much less randomness is needed to ensure the resulting graph is Ramsey.

This line of research was initiated by Krivelevich, Sudakov and Tetali in 2006, who determined the thresholds for the pairs (K3, Kt) with t ≥ 3. Here we extend their work, considering pairs of larger cliques. We also present results for cycles, and cycles versus cliques.

This is joint work with Andrew Treglown.