摘要
The lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）are investigated.Let K<sub>n</sub><sup>r</sup> be the completer-uniform hypergraph on n points.Define R（l<sub>1</sub>,…,l<sub>q</sub>;r）as the minimal natural number n sothat if the edges of K<sub>n</sub><sup>r</sup> are q-colored,there is a set S of l<sub>i</sub>（i∈{1,…,q}）vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd（?）s and J.Spencer.In this paper,we shall give the lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）.
The lower bounds for any R(l_1,…,l_q;r)are investigated.Let K_n^r be the completer-uniform hypergraph on n points.Define R(l_1,…,l_q;r)as the minimal natural number n sothat if the edges of K_n^r are q-colored,there is a set S of l_i(i∈{1,…,q})vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd(?)s and J.Spencer.In this paper,we shall give the lower bounds for any R(l_1,…,l_q;r).
