图的Ramsey理论是极值图论的重要分支。其研究对图论的发展有着重要意义。概率方法是在研究极值图论特别是Ramsey理论的过程中产生并发展起来的一种现代方法。该方法可以在不给出具体构造的情况下证明目标结构存在。本项目旨在运用概率方法和正则引理研究随机图空间中Ramsey数的渐近性态，试图加强路与圈的Ramsey数的经典结果。本项目主要研究Erdos-Renyi随机图空间中圈的Ramsey数，随机多部图空间中路的Ramsey数以及随机二部图空间中偶圈的Ramsey数的渐近性态。这项研究是对随机图空间中Ramsey数问题的有益尝试，对于探索无序中的有序规律具有重要意义。

Graph Ramsey theory is an important branch of extremal graph theory, and the research of graph Ramsey theory has great significance to the development of graph theory. The probabilistic method, which is a modern method, is produced and developed in the process of studying extremal graph theory, especially graph Ramsey theory. This method can show the existence of target structure without an explicit construction. This project aims to study asymptotic state of Ramsey number in random graph space via the probabilistic method and regularity lemma, which can strengthen the classical results on path and cycle Ramsey number. We shall study asymptotic state of cycle Ramsey number in Erdos-Renyi random graph space, path Ramsey number in random multipartite graph space and even cycle Ramsey number in random bipartite graph space. It's a useful attempt to the problem of Ramsey number in random graph space, which has great significance for exploring the law of order in disorder.