论文标题
关于封面理想的力量
On powers of the cover ideals of graphs
论文作者
论文摘要
对于简单的图$ g $，假设$ j（g）$是$ g $的顶点封面理想，$ j（g）^{（s）} $是$ j（g）$的$ s $ th符号功率。我们证明了所有$ s \ geq 1 $和所有奇数周期$ c $的$（j（c）^{（s）}）=（j（c）^s）$。对于简单的复合物$δ$，我们表明$δ$如果$i_Δ^{\ vee} $是弱的polymatoridal，则可以分解顶点。令$ w = g^π$是一个完全旋风的图表，我们证明$ j（w）^s $对于所有$ s \ geq 1 $都是弱的多肌功能。
For a simple graph $G$, assume that $J(G)$ is the vertex cover ideal of $G$ and $J(G)^{(s)}$ is the $s$-th symbolic power of $J(G)$. We prove that $(J(C)^{(s)})=(J(C)^s)$ for all $s\geq 1$ and for all odd cycle $C$. For a simplicial complex $Δ$, we show that $Δ$ is vertex decomposable if $I_Δ^{\vee}$ is weakly polymatroidal. Let $W=G^π$ be a fully clique-whiskering graph, we prove that $J(W)^s$ is weakly polymatroidal for all $s\geq 1$.
