After winter break and traveling, we met on Monday, Feb 23, for Anita Liebenau's talk on which graphs are Ramsey equivalent to cliques. Here's her abstract. The concept of Ramsey-equivalence was introduced only recently, in 2010, by Szabo, Zumstein and Zürcher. A surprising fact is that the only connected graph that is Ramsey-equivalent to the clique K_k on k vertices is K_k itself. That is, removing a single edge from K_k, or adding a single pendant edge to it, completely changes the Ramsey behavior. In this talk, we will define Ramsey-equivalence of two graphs and see some recent results on Ramsey-equivalence. There are lots of open problems in this area, and I will mention some of them. |

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