A short proof that $R(3,k)=\Theta (k^2/\log k)$

Abstract

We give a nibble-free construction proving $R(3,k)\ge (1/200+o(1))k^2/\log k$. We also include Shearer's proof bounding the independence number of a triangle-free graph, which implies $R(3,k)\le (1+o(1))(k^2/\log k)$.

7 pages