摘要
设K_n^r为具有n个点的完全r-一致超图。著名的Ramsey数R(l_1,…,l_4;r)可定义为这样的最小整数n,使得无论怎样对K_n^r的每条边用q种颜色一着色,总存在某个完全r-一致子超图K_l_1~r,i∈{1,…,q},其所有边均为第i种色。在[1]与[2]中,P.Erdos与J.Spencer分别对R(l,l;2)给出了下界,作者在[4]中首先给出了任意Ramsey数R(l_1,…l_q;r)的下界。本文是[4]的续篇.我们先将著名的Loua'sy Local Theorem推广成关于概率的一条引理,然后利用它得到一般形式的Ramsey数的新的下界。
Let KnT be a complete r-uniform (hyper) graph on n points. The well-known Ramsey manlier R(l1,…,l6;r) in the least integer n so that after coloring each (hyper) edge of KnT with one of q colors,there is always a complete r-uniform Kl1T (i∈{1,…,q}) with all its (hyper) edges in the samet-thhcolor Jn [1] and [2],P. Erdos and J. Spencer gave lower bounds to R(1.1:2) separately. In this paper,we prove a lemma about probability and use it to obtain lower bounds for any R(l1,…,l4;r).
出处
《工程数学学报》
CSCD
1990年第1期72-75,共4页
Chinese Journal of Engineering Mathematics
