The Turan number of Berge-K_4 in 3-uniform hypergraphs
数学公众报告
报告题目(Title)：The Turan number of Berge-K_4 in 3-uniform hypergraphs
报告人(Speaker)：康丽英教授 （上海大学）
地点(Place)：腾讯会议 ID：992 430 012
时间(Time)：2021 年 09 月 24 日（周五） 15:00--16:00
邀请人(Inviter)：徐敏
报告摘要
For a graph $G=(V, E)$, a hypergraph $H$ is called a Berge-$G$, if there is a bijection $f: E(G)\mapsto E(H)$ such that $e\subseteq f(e)$ for all $e\in E(G)$.
Denoted by $\mathcal{B}(G)$ the family of Berge-$G$ hypergraphs. The maximum number of edges in an $n$-vertex $r$-graph with no subhypergraph isomorphic to any Berge-$G$ is denoted by $ex_r(n, \mathcal{B}(G))$. We determine the Tur$\acute{a}$n number of Berge-$(k+1)K_2$ for the cases when $r\le k-1$ and $r\ge 2k+2$ and we characterize the extremal hypergraphs which achieve $ex_r(n, \mbox{Berge}-(k+1)K_2)$, where $(k+1)K_2$ is a matching of size $k+1$. A recent result, due to Gerbner et al., implies that for $n\ge 9$, $ex_3(n, \mathcal{B}(K_4))=\lfloor\frac{n}{3}\rfloor\lfloor\frac{n+1}{3}\rfloor\lfloor\frac{n+2}{3}\rfloor$. In this talk we prove the remaining cases $n=7$ and $n=8$ for the completeness of the conclusion.
主讲人简介
康丽英,上海大学数学系教授，博士生导师。曾获“上海市三八红旗手”，“上海市曙光学者”称号。中国运筹学会常务理事、中国工业与应用数学学会组合图论专业委员会副主任委员、中国数学会组合图论分会理事。 担任国际期刊《Discrete Mathematics, Algorithms and Applications》、 《Journal of the Operations Research Society of China》、《Communications on Applied Mathematics and Computation》和国内期刊《运筹学学报》编委。 在《SIAM Discrete Mathematics 》、《Journal of Graph Theory》、《European Journal of Combinatorics》等学术期刊上发表学术论文150余篇，主持完成5项国家自然科学基金项目。曾在美国南卡莱罗纳大学、荷兰蒂尔堡大学、法国巴黎十一大等多所大学进行学术访问和合作研究。
