$\overline{\cal R}(3,4)=17$

Abstract

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.