图的染色与划分及其应用

图论以有限(离散)群组为研究对象，主要研究特定子结构的存在性、相关参数的极值及相应的极值结构.图论研究中的一类基本问题是一个有限集合的二元子集簇整体性质跟局部结构的关系，以及相应极值问题.这类问题在电子信息领域有很强的应用背景.我们拟围绕下列问题展开研究：图的色数与团数关系，Turan问题的Erdos-Sos猜想、LKS猜想，和相关划分问题以及在编码与信息传输等方面的应用.希望本项目各个课题研究在理论和方法上取得较大突破，得到一些有重要国际影响的新结果，对相关问题的研究起到实质推动作用，进一步加强国内外学术交流，培养一批高水平的年轻研究人才，提高我国图论研究的国际影响。

Graph theory studies subsets system on finite (or discrete) set, mainly concerns with the existence of substructures,extremal value and related extremal structure of graph parameters. A basic problem in graph theory is the relation between local structures and global property of 2-subsets systems of a finite set, and their corresponding extremal problem. These problems have very strong background in the field of electronic information. We will study the following problems and their applications: the relation between chromatic number and clique number of graphs, Erdos-Sos Conjecture and LKS Conjecture and their related partition problems. We will also concern with the application of extremal graph theory to coding theory and information transmission. We hope to make great breakthrough on these topics and promote the development of related problems through the study of the project. During the process of the project, we will strengthen the international academic communication, cultivate a group of high level young research talents and improve international influence of graph theory of our country.