论文标题
最大最小顶点盖和贝蒂表的大小
Max Min vertex cover and the size of Betti tables
论文作者
论文摘要
令$ g $为$ n $顶点上的有限简单图形，不包含隔离的顶点，让$ i（g）\ subseteq s = k [x_1，\ dots，x_n] $是其优势。在本文中，我们研究了一对衡量投影维度的整数和$ s/i（g）$的规律性。我们表明，如果$ s/i（g）$的投影尺寸达到其最小值$ 2 \ sqrt {n} -2 $，则只有一个例外，它的规律性必须为1。我们还提供了$ s/i（g）$的投影尺寸的完整描述。
Let $G$ be a finite simple graph on $n$ vertices, that contains no isolated vertices, and let $I(G) \subseteq S = K[x_1, \dots, x_n]$ be its edge ideal. In this paper, we study the pair of integers that measure the projective dimension and the regularity of $S/I(G)$. We show that if the projective dimension of $S/I(G)$ attains its minimum value $2\sqrt{n}-2$ then, with only one exception, the its regularity must be 1. We also provide a full description for the spectrum of the projective dimension of $S/I(G)$ when the regularity attains its minimum value 1.
