有限域与Ramsey数R_n(k)的下界

Finite Fields and Lower Bounds for Ramsey Numbers R_n(k)

研究有限域GF(ps)上的循环图的结构性质,给出一些图的团数的解析表达式,并给出计算Ramsey数Rn(k)下界的一种算法,得到一个Ramsey数的新下界:R3(8)≥4111。

The structure and properties of the circulant graphs over a finite field GF(ps) are studied in this paper. Some explicit formulas for the clique numbers of some graphs are given. An algorithm for the computation of the lower bound of the Ramsey number Rn(k) is presented. A new lower bound for a Ramsey number is obtained,that is,R3(8)≥4111.