SMALL ON-LINE RAMSEY NUMBERS - A NEW APPROACH

In this note, we revisit the problem of calculating small on-line Ramsey numbers (R) over bar (G, H). A new approach is proposed that reduces the running time of the algorithm determining that (R) over bar (K-3, K-4) = 17 by a factor of at least 2 . 10(6) compared to the previously used approach. Using high performance computing networks, we determined that (R) over bar (K-4, K-4) >= 26, (R) over bar (K-3, K-5) >= 25, and that (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 nonsymmetric cases.