Small on-line Ramsey numbers---a new approach

In this note, we revisit the problem of calculating small on-line Ramsey numbers R(G,H). A new approach is proposed that reduces the running time of the algorithm determining that R(K_3,K_4)=17 by a factor of at least 2*10^6 comparing to the previously used approach. Using high performance computing networks, we determined that R(K_4,K_4) <= 26, R(K_3,K_5) < 25, and that R(K_3,K_3,K_3) <= 20 for a natural generalization to three colours. All graphs on 3 or 4 vertices are investigated as well, including non-symmetric cases