Session I.3 - Graph Theory and Combinatorics
Monday, June 12, 14:00 ~ 15:00
Exponential improvement on diagonal ramsey numbers
Marcelo Campos
University of Oxford, England - This email address is being protected from spambots. You need JavaScript enabled to view it.
The Ramsey Number $R(k)$ is the minimum $n$ such that every red/blue coloring of the edges of $K_n$ contains a monochromatic $K_k$. In this talk I will discuss a recent work where we show that \[R(k)\leq (4-c)^k,\] for some $c \gt 0$. This is the first exponential improvement on the Erd\H{o}s and Szekeres upper bound proved in 1935.
Joint work with Simon Griffiths (PUC - Rio, Brazil), Robert Morris (IMPA, Brazil) and Julian Sahasrabudhe (University of Cambridge, England).