素数阶循环图与经典Ramsey数R(8,17)和R(8,19)的新下界

Prime Order Cyclic Graph and New Lower Bounds of Classical Ramsey Numbers R (8,17) and R (8,19)

研究了素数阶循环图的基本性质，提出了寻求有效参数构造正则循环图的新方法，得到了２ 个经典 Ｒａｍｓｅｙ 数的新下界： Ｒ（８ ，１７） ≥７０２ ， Ｒ（８ ，１９） ≥７７０ 。它们超过了目前已知的最好下界 Ｒ（８ ，１７） ≥６０２ 和 Ｒ（８ ，１９） ≥６８４ 。

Some basic character of prime order cyclic graph were studied. The skills for seeking effective parameters to structure regular cyclic graph were proposed. New lower bounds of two classical Ramsey numbers were obtained as follows: R(8,17)≥702, R(8,19)≥770. They are better than the lower bounds of R(8,17)≥602 and R(8,19)≥684 which are known as the best.