摘要:对于无向简单图G及正整数a1,…,ak,记G→(a1,…,ak)v当且仅当对于图G的任意一种顶点k染色,一定对某个i∈{1,…,k}存在顶点全染着颜色i的完全子图Kai.对于p>max{a1,…,ak},定义Fv(a1,…,ak;p)=min{|V(G)|:G→(a1,…,ak)v,Kp(∈)G}为顶点Folkman数.证明关于顶点Folkman数Fv(k,k;k+1)的新的迭代不等式,并推广Kolev和 Nenov的一个关于多色顶点Folkman数的不等式.%For an undirected,simple graph G,and positive integers a1,…,ak,we write G→(a1,…,ak)v if and only if for every vertex k-coloring of G,there exists a monochromatic Kai,for some color i∈{1,…,k}.The vertex Folkman number is defined as Fv(a1,…,ak;p)=min {|V(G)|:G→(a1,…,ak)v,Kp(∈)G}for p>max{a1,…,ak}.In this paper,new recurrent inequalities on vertex Folkman numbers Fv(k,k;k+1)are proved.We also generalize an inequality of Kolev and Nenov on multicolor Folkman numbers.