论文标题
对二项式边缘理想规律性的猜想的证明
A proof for a conjecture on the regularity of binomial edge ideals
论文作者
论文摘要
在本文中，我们在图中介绍了集团脱节边缘集的概念。然后，对于图形$ g $，我们将不变的$η（g）$定义为$ g $中的集团分离边缘的最大尺寸。我们表明，$ g $的二项式边缘理想的规律性在上面是$η（g）$。尤其是，这完全解决了完全普遍性的二项式边缘理想的规律性的猜想。
In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a graph $G$, we define the invariant $η(G)$ as the maximum size of a clique disjoint edge set in $G$. We show that the regularity of the binomial edge ideal of $G$ is bounded above by $η(G)$. This, in particular, settles a conjecture on the regularity of binomial edge ideals in full generality.
