论文标题
二项式边缘理想的Cohen-Macaulay特性，图
Cohen-Macaulay Property of Binomial Edge Ideals with Girth of Graphs
论文作者
论文摘要
conca和varbaro（发明数学221（2020），第3号）显示了分级理想的深度相等，并且当初始理想不平方时，在多项式环中的初始理想。在本文中，我们在Cohen-Macaulay二项式边缘理想的研究中给出了一些美丽的应用。我们证明，对于Cohen-Macaulay二项式边缘理想的表征，仅考虑“双连接的图形具有与某些晶须相连”，并且通过研究初始理想来完成。我们给出了几个必要的条件，使二项式边缘在较小的图表方面是Cohen-Macaulay的理想条件。同样，在假设下，我们在图形块方面为二项式边缘理想的Cohen-MaCaulay度提供了足够的条件。此外，我们证明了带有Cohen-Macaulay二项式边缘理想的图形的图形不到$ 5 $或等于Infinity。
Conca and Varbaro (Invent. Math. 221 (2020), no. 3) showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free. In this paper, we give some beautiful applications of this fact in the study of Cohen-Macaulay binomial edge ideals. We prove that for the characterization of Cohen-Macaulay binomial edge ideals, it is enough to consider only "biconnected graphs with some whisker attached" and this done by investigating the initial ideals. We give several necessary conditions for a binomial edge ideal to be Cohen-Macaulay in terms of smaller graphs. Also, under a hypothesis, we give a sufficient condition for Cohen-Macaulayness of binomial edge ideals in terms of blocks of graphs. Moreover, we show that a graph with Cohen-Macaulay binomial edge ideal has girth less than $5$ or equal to infinity.
