论文标题
在带有晶须的块方面
Cohen-Macaulay Binomial edge ideals in terms of blocks with whiskers
论文作者
论文摘要
对于图$ g $，Bolognini等。已经显示出$ j_ {g} $是强烈未混合的$ \ rightarrow $ $ j_ {g} $是cohen-macaulay $ \ rightarrow $ $ g $是可访问的，其中$ j_ {g} $表示$ g $的二项式边缘理想。可访问且强烈的未混合性能纯粹是组合。我们提供一些动机，只专注于带有晶须的块，以用Cohen-Macaulay $ J_ {G} $表征所有$ G $。我们表明，$ g $的易于访问且无形的属性仅取决于其带有晶须的块的相应属性，反之亦然。另外，我们提供了无限类的图形，其二项式边缘理想是Cohen-Macaulay，因此，我们对所有$ r $ r $ r $ r $ r $ r $ r $连接的图进行了分类，从而将一些特殊的晶须附加到其上，二项式边缘理想成为cohen-macaulay。最后，我们定义了一个新的图形，称为\ textit {强烈$ r $ cut-cut-connected}，并证明任何强烈的$ r $ r $ cut连接的可访问图的二项式边缘最多都有三个切割顶点是Cohen-Macaulay。
For a graph $G$, Bolognini et al. have shown $J_{G}$ is strongly unmixed $\Rightarrow$ $J_{G}$ is Cohen-Macaulay $\Rightarrow$ $G$ is accessible, where $J_{G}$ denotes the binomial edge ideals of $G$. Accessible and strongly unmixed properties are purely combinatorial. We give some motivations to focus only on blocks with whiskers for the characterization of all $G$ with Cohen-Macaulay $J_{G}$. We show that accessible and strongly unmixed properties of $G$ depend only on the corresponding properties of its blocks with whiskers and vice versa. Also, we give an infinite class of graphs whose binomial edge ideals are Cohen-Macaulay, and from that, we classify all $r$-regular $r$-connected graphs such that attaching some special whiskers to it, the binomial edge ideals become Cohen-Macaulay. Finally, we define a new class of graphs, called \textit{strongly $r$-cut-connected} and prove that the binomial edge ideal of any strongly $r$-cut-connected accessible graph having at most three cut vertices is Cohen-Macaulay.
