Author/Authors :
Wenlong Su، نويسنده , , Qiao Li، نويسنده , , Haipeng Luo، نويسنده , , Guiqing Li، نويسنده ,
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.
