Dec. 17, 2021, Sean English (Lower Bounds on Generalized Ramsey Numbers via Color Energy)

Описание: Title: Lower Bounds on Generalized Ramsey Numbers via Color Energy

Abstract: Let the generalized Ramsey number f(n,p,q) denote the least integer c such that K_n can be edge-colored with c colors such that every set of p vertices spans a clique with at least q colors. in this talk, we will discuss the method of color energy graphs, which borrows some ideas from the concept of additive energy used in additive combinatorics to find new lower bounds on generalized Ramsey numbers, and the connections between generalized Ramsey numbers and the well-known hard problem of determining extremal numbers for different bipartite graphs. Joint work with Jozsef Balogh, Emily Heath and Robert A. Krueger.