Ramsey理论一直是组合数学的研究热点。它是对充分大的结构进行划分的研究，印证了完全的无序是不可能的。而图Ramsey理论是Ramsey理论的重要分支。图的局部（平均）k边染色是一种边染色，使得与任意顶点关联的边（平均）至多染k种不同的颜色。图G的局部（平均）k-Ramsey数定义为最小的正整数N，使得N阶完全图的任意局部（平均）k边染色都包含单色图G。..本项目旨在拓展和深化广义Ramsey数、局部Ramsey数和平均Ramsey数之间的内在联系；研究局部(H,k)边染色导出一般边染色的充要条件；提出新的想法，扩展图Ramsey理论的研究内容，力争取得更有意义的突破。

Ramsey theory has been a research focus in Combinatorics. It refers to the study of partitions of large structures, which indicates that complete disorder is impossible. Graph Ramsey theory is a major branch of Ramsey theory. A local (mean) k-coloring of a graph is a coloring of the edges such that, the edges incident to each vertex are colored with at most k different colors (on average). Given a graph G, the local (mean) k-Ramsey number is defined as the smallest integer N such that, any local (mean) k-coloring of K_N contains a monochromatic copy of G...This project aims at expanding and deepening the interconnections of generalized Ramsey numbers, local Ramsey numbers and mean Ramsey numbers; studying the necessary and sufficient condition for which a local (H,k) edge coloring is in fact a k-edge-coloring; putting forward some new ideas, broadening the scope of graph Ramsey theory, and finally obtaining some significant breakthroughs.