Name
Abstract | ||
|---|---|---|
A method to improve the lower bounds for Ramsey numbers R(k,l) is provided: one may construct cyclic graphs by using cubic residues modulo the primes in the form p = 6m + 1 to produce desired examples. In particular, we obtain 16 new lower bounds, which are R(6, 12) ≥ 230, R(5,15) ≥ 242, R(6,14) ≥ 284, R(6,15) ≥ 374, R(6, 16) ≥ 434, R(6,17) ≥ 548, R(6,18) ≥ 614, R(6,19) ≥ 710, R(6,20) ≥ 878, R(6,21) ≥ 884, R(7,19) ≥ 908, R(6,22) ≥ 1070, R(8,20) ≥ 1094, R(7,21) ≥ 1214, R(9,20) ≥ 1304, R(8,21) ≥ 1328. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0012-365X(01)00283-7 | Discrete Mathematics |
Keywords | Field | DocType |
ramsey numbers r,cubic residue,form p,new lower bound,lower bound,lower boumds,cyclic graph,ramsey number | Graph,Discrete mathematics,Combinatorics,Upper and lower bounds,Ramsey's theorem,Mathematics | Journal |
Volume | Issue | ISSN |
250 | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
3 | 0.55 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wenlong Su | 1 | 7 | 2.77 |
| Qiao Li | 2 | 59 | 3.61 |
| Haipeng Luo | 3 | 37 | 8.18 |
| Guiqing Li | 4 | 129 | 19.25 |