Lower bounds of Ramsey numbers based on cubic residues

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.