学术报告报告主题: Some stability results for Berge-$K_{s,t}$ hypergraphs and their application
报 告 人: 袁西英教授
报告时间: 2024年 5月16日（星期四）下午16:00-17:00
报告地点: 腾讯会议：361-233-901
邀 请 人: 林鸿莺副教授
欢迎广大师生前往！
数学学院
2024年5月13日
报告摘要：An $r$-uniform hypergraph ($r$-graph) is linear if any two edges intersect at most one vertex. For a graph $F$, a hypergraph $H$ is Berge-$F$ if there is a bijection $\phi:E(F)\rightarrow E(H)$ such that $e\subseteq\phi(e)$ for all $e$ in $E(F)$. For an $r$-graph $H$, let $\mathcal{A}(H)$ be the adjacency tensor of $H$. The spectral radius of $H$ is the spectral radius of the tensor $\mathcal{A}(H)$. In this report, a kind of stability result for Berge-$K_{3,t}$ linear $r$-graphs is established. Based on this stability result, an upper bound for the linear Tur\'{a}n number of Berge-$K_{3,t}$ is determined, and some bounds for the maximum spectral radius of connected Berge-$K_{3,t}$-free linear $r$-graphs are obtained. Moreover, a kind of stability result for Berge-$K_{2,t}$ linear $r$-graphs and a kind of stability result for Berge-$K_{s,t}$ linear $r$-graphs are obtained, where $t\geq s\geq4$. As applications, the upper bound for linear Tur\'{a}n number of Berge-$K_{2,t}$ in [Gerbner et al., J. Comb. Theory, Ser. B, 137 (2019) 264-290] may be slightly improved, and an upper bound for the maximum spectral radius of connected Berge-$K_{s,t}$-free linear $r$-graphs is obtained, where $t\geq s\geq4$.
报告人介绍：袁西英，上海大学数学系教授，博士生导师。中国运筹学会组合与图论分会第四、第五届理事会理事，主要从事图与超图谱理论的研究，2008年毕业于同济大学，博士学位论文《图的特征值》获得上海市研究生优秀成果（学位论文）。曾先后主持四项国家自然基金项目。