# 信息来源： 暂无 　 发布日期: 2021-08-03　 浏览次数: _showDynClicks("wbnews", 1756464364, 1311)

Given a family of graphs $\mathcal{F}$, a graph $G$ is said to be $\mathcal{F}$-saturated if $G$ does not contain a copy of $F$ as a subgraph for any $F\in\mathcal{F}$, but the addition of any edge $e\notin E(G)$ creates at least one copy of some $F\in\mathcal{F}$ within $G$. The minimum size of an $\mathcal{F}$-saturated graph on $n$ vertices is called the saturation number, denoted by $\sat(n, \mathcal{F})$. Let $\mathcal{C}_{\ge r}$ be the family of cycles of length at least $r$. Ferrara et al. (2012) gave lower and upper bounds of $\sat(n, C_{\ge r})$ and determined the exact values of $\sat(n, C_{\ge r})$ for $3\le r\le 5$. In this talk, we review some of known results related to this subject and determine the exact value of $\sat(n,\mathcal{C}_{\ge r})$ for $r=6$ and $28\le \frac{n}2\le r\le n$ and give new upper and lower bounds for the other cases.

侯新民，中国科学技术大学数学科学学院，副教授，博士生导师。感兴趣研究领域包括结构图论、极值图论、组合优化等，已发表学术论文50余篇，主持完成国家自然科学基金4项，省部级项目2项。