1.题目: Saturation Numbers for Disjoint Stars

报告人：陆玫 （清华大学）

时间：9月23号下午2：30--3：30

地点：腾讯会议：687-155-588，或点击链接入会：

https://meeting.tencent.com/dm/STNw6LQLNzFF

摘要：A graph $G$ is called an $H$-saturated if $G$ does not contain $H$ as a subgraph, but the addition of any edge between two nonadjacent vertices in $G$ results in a copy of $H$ in $G$. The saturation number $sat(n,H)$ is the minimum number of edges in $G$ for all $H$-saturated graphs $G$ of order $n$. For a graph $F$, let $mF$ denote the disjoint union of $m$ copies of $F$. In 2011, Faudree, Faudree and Schmitt proposed a problem that is to determine $sat(n,mK_{1,k})$ for all $m$ and $k$.  In this talk, I will give a result on $ sat(n,mK_{1,k})$ when $m\ge 2$, $k\ge 4$ and $n\ge 3mk^2$. This work is joint with Zequn Lv and Zhen He. 

2.题目：The maximum number of triangles in Fk-free graphs

报告人：陈耀俊 (南京大学)

时间：9月23号下午3：30--4：30

地点：腾讯会议：687-155-588，或点击链接入会：

https://meeting.tencent.com/dm/STNw6LQLNzFF

摘要：The generalized Tur´an number ex(n, Ks, H) is the maximum number of com- plete graph Ks in an H-free graph on n vertices. Let Fk be the friendship graph con- sisting of k triangles. Erd˝os and S´os (1976) determined the value of ex(n, K3, F2). Alon and Shikhelman (2016) proved that ex(n, K3, Fk) ≤ (9k − 15)(k + 1)n. In this talk, we will report our new result on the exact value of ex(n, K3, Fk) and the extremal graph for any Fk when n ≥ 4k3.