有限结构指一个有限集及其幂集的一个子集合。Ramsey-型问题是指有限结构的规模与其是否包含某些子结构之间的关系。本项目拟研究在某些禁用子结构的条件下有限结构中单色子集的大小，以及一些图或超图Ramsey数和若干相关图参数，目前是极值组合中最活跃最重要的研究领域之一。主要内容是Erdős和Hajnal关于图中不含诱导子图H时单色子集(完全图或独立集)大小的猜想、3-一致超图中单色子集大小的估计、图Ramsey数R(C4,Km)和R(C4,K1,n)及相关的一些图参数。

A finite structure is a finite set V together with a subset of the power set of V. A Ramsey-type problem is the one to consider the relation between the scale of a finite structure and the existence of some sub-structure. In this project, we will consider how large a monochromatic subset of V can be contained in a finite structure without some given sub-structure, calculate some Ramsey numbers concerning graphs or hypographs and some related parameters of graphs. This is one of the most active and important research fields in extremal combinatorics. The main goal of this project is to consider the conjecture of Erdős and Hajnal on the monochromatic subset in a graph containing no some given induced subgraph, estimate the scale of a monochromatic subset in a given 3-uniform hypographs, investigate the Ramsey functions R(C4,Km) and R(C4,K1,n), and some related parameters of graphs.