Summary: We consider the on-line Ramsey numbers \(\overline{\mathcal R} (k,l)\) for cliques. Using a high performance computing networks, we `calculated' that \(\overline{\mathcal R}(3,4)=17\). We also present an upper bound of \(\overline{\mathcal R}(k,l)\), study its asymptotic behaviour, and state some open problems.
scientific article; zbMATH DE number 5540972