### An exponential improvement for diagonal Ramsey

Combinatorics Seminar

21st November 2023, 11:00 am – 12:00 pm

Fry Building, 2.04

The Ramsey number R(k) is the minimum natural number n such that every red-blue colouring of the edges of the complete graph K_n on n vertices contains a monochromatic copy of K_k. In this talk I will present a recent result which shows that R(k) \le (4 - \eps)^k for some constant \eps > 0. This is the first exponential improvement on the upper bound of Erdos and Szekeres, proved in 1935. Joint work with Simon Griffiths, Robert Morris and Julian Sahasrabudhe.

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