This paper establishes a connection between a certain class of Ramsey numbers for graphs and algebraic constructions. The main case considered here relates the solutions of the systems of equations in Galois fields to the Ramsey numbers r(Ka,a, Ka,s+1) and r(K2,t+1, K2,s+1). Some new lower bounds are given for some bipartite-bipartite graph Ramsey numbers. A new upper bound is given for the bipartite-bipartite graph Ramsey number r(K2,t+1, K2,s+1).%本文在Galois域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系.关键问题是研究了关于Galois域上的代数构造的方程及方程组的解.我们得到了一些关于二部图的新的下界和上界.
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