New computational upper bounds for Ramsey numbers R (3, k)
J Goedgebeur, SP Radziszowski - arXiv preprint arXiv:1210.5826, 2012 - arxiv.org
Using computational techniques we derive six new upper bounds on the classical two-color
Ramsey numbers: R (3, 10)<= 42, R (3, 11)<= 50, R (3, 13)<= 68, R (3, 14)<= 77, R (3, 15)<=
87, and R (3, 16)<= 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 e (3, k, n) for all n with k<= 9 and for all …
Ramsey numbers: R (3, 10)<= 42, R (3, 11)<= 50, R (3, 13)<= 68, R (3, 14)<= 77, R (3, 15)<=
87, and R (3, 16)<= 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 e (3, k, n) for all n with k<= 9 and for all …
[CITATION][C] New computational upper bounds for Ramsey numbers R (3, k). arXiv 1210.5826 (2012)
J Goedgebeur, SP Radziszowski - submitted
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