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Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$
Published 11 Oct 2013 in math.CO and cs.DM | (1310.3017v1)
Abstract: 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.
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