报告人： 徐子翔博士
报告时间：2024年3月1日16:30--17:30
腾讯会议ID：688-848-004
报告主题：Towards the Bollob\'{a}s-Erd\H{o}s-Tuza conjecture
主 办：数学与统计学院、离散数学及其应用省部共建教育部重点实验室
报告摘要：
Let $h(G)$ denote the smallest size of a subset of vertices $V(G)$ in an $n$-vertex graph $G$ such that it intersects every maximum independent set of $G$. An unresolved conjecture posed by Bollob\'{a}s, Erd\H{o}s, and Tuza asserts that for any $n$-vertex graph $G$, if the independence number $\alpha(G) = cn$ for some constant $c > 0$, then $h(G) = o(n)$. This conjecture remains open and is closely related to the Erd\H{o}s-Hajnal conjecture, another major open problem in graph theory. The only advancement on this conjecture is attributed to Alon, who proved that $h(G)\le O(\sqrt{n\log{n}})$ holds for any $n$-vertex regular graph with $\alpha(G)\ge (\frac{1}{4}+\varepsilon)n$.
In this talk, I will discuss various approaches and demonstrate the validity of the Bollob\'{a}s-Erd\H{o}s-Tuza conjecture for several graph families.
报告人简介：
徐子翔：目前于韩国基础科学研究院极值组合与概率组(Extremal Combinatorics and Probability Group, Institute for Basic Science)从事博士后研究工作。2022年于首都师范大学获得理学博士学位，导师为葛根年教授。目前的研究方向主要为极值组合及其相关领域，在Sci. China. Math、Israel J. Math、Combinatorica、J. Combin. Theory, Ser A 、IEEE Trans. Information theory, SIAM J. Discrete Math等期刊发表论文十余篇。
