论文标题
某些加权方向图的无混合性
Unmixedness of some weighted oriented graphs
论文作者
论文摘要
令$ d =（g，\ mathcal {o}，w）$为加权方向的图形，其边缘理想为$ i（d）$。在本文中，我们描述了以下每种情况的$ i（d）$的未混合属性：$ g $是$ scq $ graph; $ g $是和弦图； $ g $是一个简单的图形； $ g $是一个完美的图表； $ g $没有$ 4 $ - 或$ 5 $ -CYCLE； $ g $是一个图形，没有$ 3 $ - 和$ 5 $ -CYCLE；和$ {\ rm girth}（g）\ geqslant 5 $。
Let $D=(G,\mathcal{O},w)$ be a weighted oriented graph whose edge ideal is $I(D)$. In this paper, we characterize the unmixed property of $I(D)$ for each one of the following cases: $G$ is an $SCQ$ graph; $G$ is a chordal graph; $G$ is a simplicial graph; $G$ is a perfect graph; $G$ has no $4$- or $5$-cycles; $G$ is a graph without $3$- and $5$-cycles; and ${\rm girth}(G)\geqslant 5$.
