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

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