一类广义Ramsey数R(B2,Kn)界的研究

The bound research of a generalized Ramsey number R(B 2,K n)

Ramsey数的确定是一个非常困难并尚未完全解决的问题.利用构造特殊图的方法准确界定Ramsey数,目前只解决了较少的经典Ramsey数.经典Ramsey数R(4,n)目前已有的界均为组合数形式或者递推式,均为构造特殊图的方法得出.文章主要利用概率的方法给出了一类广义Ramsey数R(B2,Kn)的非线性界.由于B2是完全图K4的子图,因此上述非线性界同样也适用于R(4,n).

Determining the Ramsey number is very difficult and uncompleted solved problem.Applying the construction method of special graph,a small quantity Ramsey number is found at present.Classical Ramsey number R(4,n)have the bound of combination or recursion now.The bounds are obtained by constructing special graph.This paper will provide the nonlinear bound of a generalized Ramsey number R(B 2,K n)applying probability method.As B 2 is a subgraph of complete graph K 4,the nonlinear bound is suitable for R(4,n).