  The Ramsey number $R(C_4,K_m)$ is the smallest $n$ such that any graph on $n$
vertices contains a cycle of length four or an independent set of order $m$.
With the help of computer algorithms we obtain the exact values of the Ramsey
numbers $R(C_4,K_9)=30$ and $R(C_4,K_{10})=36$. New bounds for the next two
open cases are also presented.
