【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>m ax{a1,…,ak},定义Fv(a1,…,ak;p)=m in{V(G):G→(a1,…,ak)v,Kp G}为顶点Folkm an数.证明关于顶点Folkm an数Fv(k,k;k+1)的新的迭代不等式,并推广K olev和N enov的一个关于多色顶点Folkm an数的不等式.更多还原

【Abstract】 For an undirected,simple graph G,and positive integers a₁,…,a_k,we write G→（a₁,…,a_k）^v if and only if for every vertex k-coloring of G,there exists a monochromatic K_ai,for some color i∈{1,…,k}.The vertex Folkman number is defined as F_v（a₁,…,a_k;p）=min {|V（G）|:G→（a₁,…,a_k）^v,K_pG}for p>max{a₁,…,a_k}.In this paper,new recurrent inequalities on vertex Folkman numbers F_v（k,k;k+1）are proved.We also generalize an inequality of Kolev and Nenov on multicolor Folkman numbers.更多还原