关于图与偏序集的饱和数问题研究

极值图论是图论研究的一个重要内容，关于饱和图和饱和数的研究是目前极值图论研究的热点方向之一，研究内容主要包括饱和数的界、特殊图类的饱和数等，目前仍有大量极具理论意义的问题值得研究。本项目将围绕该领域的几个猜想和公开问题，研究特殊图类和偏序集的饱和数问题，主要内容包括：(1)刻画若干线性森林图的饱和图，确定饱和数；(2)确定特殊图类的饱和数边谱；(3)研究关于偏序集、拟阵的饱和数问题。本项目成果将以学术论文形式呈现，拟发表一批较高水平论文，力争在饱和数相关研究上有所突破。

Extremal graph theory is an important branch of the graph theory. Within the fields of extremal graph theory, saturated graph and saturation number are two major topics that has always been discussed hotly. The main research aims at the bound of saturation number, saturation number of special graphs, etc., while there are still a large number of theoretical problems worthy studying. In this project we will focus on several open problems and important conjectures in this field. We will deal with the saturation number of forest graphs and posets. The main contents include: (1) to describe the saturated graph of some linear forest graphs and determine their saturated numbers; (2) to determine the edge spectrum of saturation number of some special graphs; (3) to further explore the problem about saturation number of the posets and matroids. The results of this project will be presented in the form of academic papers, published on high level journals, and we would like to make some breakthroughs in the field of saturation number.