New Computational Upper Bounds for Ramsey Numbers R(3,k)

  title={New Computational Upper Bounds for Ramsey Numbers R(3,k)},
  author={Jan Goedgebeur and Stanislaw P. Radziszowski},
  journal={Electr. J. Comb.},
Using computational techniques we derive six new upper bounds on the classical twocolor Ramsey numbers: R(3, 10) 6 42, R(3, 11) 6 50, R(3, 13) 6 68, R(3, 14) 6 77, R(3, 15) 6 87, and R(3, 16) 6 98. All of them are improvements by one over the previously best known bounds. Let e(3, k, n) denote the minimum number of edges in any triangle-free graph on n vertices without independent sets of order k. The new upper bounds on R(3, k) are obtained by completing the computation of the exact values of… CONTINUE READING