Lower Bounds on Ramsey Numbers R(6, 8), R(7, 9) and R(8, 17)

For integers s, t >= 1, the Ramsey number R(s, t) is defined to be the least positive integer n such that every graph on n vertices contains either a clique of order s or an independent set of order t. In this note, we derive new lower bounds for the Ramsey numbers: R(6,8) >= 129, R(7,9) >= 235 and R(8,17) >= 937. The new bounds are obtained with a constructive method proposed by Xu and Xie et al. and the help of computer algorithm.