一直以来，Cohen-Macaulay性质（简称为CM性质）都是组合代数学家们十分关注的一类代数性质。本项目申请人在前期工作中引进的纯强shellable复形，因其极大面理想的线性商性质和其对应的余一维图等价刻画而成为一类内涵丰富的CM复形。在本申请项目中，我们拟将纯强shellable性质分解成一个被大家所熟知的纯性（对应图上的良好覆盖性质）和一个新定义的半强shellable性质来分别展开研究。在此过程中，余一维图这一图论工具和k阶骨架这一组合手段将成为我们处理非纯复形的重要技术。在上述研究基础上，我们将进一步刻画循环图和f超图等代数图类的良好覆盖性质和半强shellable性质。通过本项目的研究，我们希望以上述代数图类为载体，以半强shellable等组合代数属性为主体，充分地将图论的直观性、组合的技巧性和代数的深刻性结合起来，为CM、强shellable等性质的研究增添新的内涵。

As we know, Cohen-Macaulayness (abbreviated as CM) is an important algebraic property which has attracted the attention of many combinatorial algebraists. In the previous research, we have introduced a special pure shellable property, called strong shellability, which is CM. Pure strongly shellable complexes are very important, not only for the linear quotient property on their facet ideals, but also for the equivalent characterization on their codimension one graphs. In this research project, we intend to study the pure strong shellability by studying pure property, which is equivalent to well-coveredness on the graph, and a newly defined property, semi-strong shellability. During this process, we will make use of codimension one graph and k-skeleton method to deal with the problems on nonpure complex. Based on these studies, we will further characterize well-coveredness and semi-strong shellability of circulant graphs and f-clutters respectively. By the research of this project, we want to explore more connotations in the study about Cohen-Macaulayness and strong shellability by taking advantage of the intuition of graph theory, the skills of combinatorics and the profundity of algebra.