论文标题
Herzog，Hibi和Ohsugi猜想树木
Herzog, Hibi and Ohsugi conjecture for trees
论文作者
论文摘要
令$ s = \ mathbb {k} [x_1，\ dots，x_n] $为多项式戒指，其中$ \ mathbb {k} $是一个字段，$ g $是$ n $ dertices上的简单图形。令$ j（g）\子集s $为$ g $的顶点封面。 Herzog，Hibi和Ohsugi猜想，所有顶点覆盖弦图的理想都是构成线性的。在这里，我们为树木特殊情况建立了猜想。我们还表明，如果$ g $是一个不包含$ c_3 $或$ c_5 $的独一顶点分解图，则$ j（g）$的符号幂为componentwisewise lineare。
Let $S=\mathbb{K}[x_1,\dots, x_n]$ be a polynomial ring, where $\mathbb{K}$ is a field, and $G$ be a simple graph on $n$ vertices. Let $J(G)\subset S$ be the vertex cover ideal of $G$. Herzog, Hibi and Ohsugi have conjectured that all powers of vertex cover ideals of chordal graph are componentwise linear. Here we establish the conjecture for the special case of trees. We also show that if $G$ is a unicyclic vertex decomposable graph that does not contain $C_3$ or $C_5$, then symbolic powers of $J(G)$ are componentwise linear.
