A step forwards on the Erdős-Sós problem concerning the Ramsey numbers $R(3,k)$

Rujie Zhu, Xiaodong Xu, Stanisław Radziszowski

Let ${\Delta }_s=R(K_3,K_s)-R(K_3,K_{s-1})$, where $R(G,H)$ is the Ramsey number of graphs $G$ and $H$ defined as the smallest $n$ such that any edge coloring of $K_n$ with two colors cont…