论文标题
匹配数字和边缘理想的维度
Matching numbers and dimension of edge ideals
论文作者
论文摘要
令$ g $为有限的简单图形，上面的顶点套装$ v（g）= \ {x_ {1}，\ ldots，x_ {n} \} $和匹配$（g）$，min-match $（g）$和ind-match $（g）$（g）$匹配号码，最小匹配号码，最小匹配号码和$ g $ $ g $的匹配号，相应。令$ k [v（g）] = k [x_ {1}，\ ldots，x_ {n}] $表示在field $ k $和$ k $和$ i（g）\ subset k [v（g）] $ $ g $的边缘的ed y（g）\ subset k $上的多项式环。已经研究了这些图理论不变性和商理论不变性的关系$ k [v（g）/i（g）$之间的关系。在本文中，我们研究了匹配$（g）$，min-match $（g）$，ind-match $（g）$和$ \ dim k [v（g）]/i（g）$之间的关系。
Let $G$ be a finite simple graph on the vertex set $V(G) = \{x_{1}, \ldots, x_{n}\}$ and match$(G)$, min-match$(G)$ and ind-match$(G)$ the matching number, minimum matching number and induced matching number of $G$, respectively. Let $K[V(G)] = K[x_{1}, \ldots, x_{n}]$ denote the polynomial ring over a field $K$ and $I(G) \subset K[V(G)]$ the edge ideal of $G$. The relationship between these graph-theoretic invariants and ring-theoretic invariants of the quotient ring $K[V(G)]/I(G)$ has been studied. In the present paper, we study the relationship between match$(G)$, min-match$(G)$, ind-match$(G)$ and $\dim K[V(G)]/I(G)$.
