Erdős–Faudree–Rousseau–Schelp cycle-versus-clique Ramsey conjecture

For graphs $G$ and $H$, let $R(G,H)$ denote the least integer $N$ such that every red-blue colouring of the edges of $K_N$ contains a red copy of $G$ or a blue copy of $H$. Erdős–Faudree–Rousseau–Schelp conjecture. If $n\geq m\geq 3$, then

$$R(C_n,K_m)=(n-1)(m-1)+1.$$

The source says this remains open, although it is known in several broad parameter ranges.