顶点Folkman数的上界(英文)

On the Upper Bounds for Vertex Folkman Numbers

证明关于顶点Folkman数上界的新不等式.特别地,用构造性方法证明:对于任意满足0<r<1/2log23-3/4的实数r,存在N(r)>0和c(r)>0使得Fv(k,k;k+1)≤c(r)(k-1)1/4log2(k-1)-r对任意的k≥N(r)成立,其中N(r)和c(r)都是只依赖于r的常数.

Abstract：Some new inequalities on the upper bounds for vertex Folkman numbers are proven in this paper. In particular,we prove the following result by constructive method：for any real number r that satisfies 0〈r〈1/2log;3-3/4,there are（r）〉0 and c（r）〉0 such that Fv（k,k;k＋1）≤c（r）（k-1）^1/4log2（k-1）-rfor any k≥N（r）,in which both N（r） and c（r） are constants only depending on r.