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{\bf Pawe{\l} Pra{\l}at}
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{\bf $\overline{\cal R}(3,4)=17$}
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In this paper, we consider the on-line Ramsey numbers $\overline{\cal R}
(k,l)$ for cliques. Using a high performance computing networks, we
`calculated' that $\overline{\cal R}(3,4)=17$. We also present an
upper bound of $\overline{\cal R}(k,l)$, study its asymptotic
behaviour, and state some open problems.

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