素数阶循环图与经典Ramsey数R(8,19)和R(8,20)的新下界

PRIME ORDER CYCLIC GRAPH AND NEW LOWER BOUNDS OF CLASSICAL RAMSEY NUMBERS R(8,19) AND R(8,20)

该文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数的新的下界：Ｒ（８，１９）≥７０２，Ｒ（８，２０）≥７７０。这两个结果填补了关于Ｒａｍｓｅｙ数综述［４］的上下界表中的２个空白。

Basic characters of prime order cyclic graph were studied.Some skills for seeking effective parameters to structure regular cyclic graph were released.New lower bounds of two classical Ramsey numbers were obtained as follows:R(8,19)≥702,R(8,20)≥770.The above two results have filled in two blanks in the table of upper and lower bounds in the survey on Ramsey numbers.