论文标题
在Castelnuovo-Mumford在Edge Ideass的无平方势力的规律性
On the Castelnuovo-Mumford regularity of squarefree powers of edge ideals
论文作者
论文摘要
假设$ g $是带有edge Idex $ i（g）$的图形和匹配的数字$ {\ rm match}（g）$。对于每个整数$ s \ geq 1 $，我们表示$ s $ th squareFree $ i（g）$ by $ i（g）^{[s]} $。 It is shown that for every positive integer $s\leq {\rm match}(G)$, the inequality ${\rm reg}(I(G)^{[s]})\leq {\rm match}(G)+s$ holds provided that $G$ belongs to either of the following classes: (i) very well-covered graphs, (ii) semi-Hamiltonian graphs, or （iii）顺序的Cohen-Macaulay图。此外，我们证明，对于每个Cameron-Walker Graph $ g $，对于每个正整数$ s \ leq {\ rm match}（g）$，我们都有$ {\ rm reg}（i（g）^{[s} {[s]}）= {\ rm match}（g）+S $
Assume that $G$ is a graph with edge ideal $I(G)$ and matching number ${\rm match}(G)$. For every integer $s\geq 1$, we denote the $s$-th squarefree power of $I(G)$ by $I(G)^{[s]}$. It is shown that for every positive integer $s\leq {\rm match}(G)$, the inequality ${\rm reg}(I(G)^{[s]})\leq {\rm match}(G)+s$ holds provided that $G$ belongs to either of the following classes: (i) very well-covered graphs, (ii) semi-Hamiltonian graphs, or (iii) sequentially Cohen-Macaulay graphs. Moreover, we prove that for every Cameron-Walker graph $G$ and for every positive integer $s\leq {\rm match}(G)$, we have ${\rm reg}(I(G)^{[s]})={\rm match}(G)+s$
