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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).

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