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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 Ramseynumbers $R(C_4,K_9)=30$ and $R(C_4,K_{10})=36$. New bounds for the next twoopen cases are also presented.

Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$