报告题目 (Title)：圈的平面图兰数：一个反例 (Planar Tur\'{a}n number of cycles: a counterexample.)
报告人 (Speaker)： 刘肖男 博士（佐治亚理工学院）
报告时间 (Time)：2023年7月7日(周五) 10:00
报告地点 (Place)：校本部F309
邀请人(Inviter)：康丽英
报告摘要： The planar Tur\'{a}n number $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ is the largest number of edges in an $n$-vertex planar graph with no $\ell$-cycle. For $\ell\in \{3,4,5,6\}$, upper bounds on $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ are known that hold with equality infinitely often. Ghosh, Gy\H{o}ri, Martin, Paulos, and Xiao conjectured an upper bound on $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ for every $\ell\ge 7$ and $n$ sufficiently large. We disprove this conjecture for every $\ell\ge 11$. We also propose two revised versions of the conjecture. Joint work with Dan Cranston, Bernard Lidick\'{y}, and Abhinav Shantanam.