报告题目 (Title)：禁用一些奇圈图的最小度稳定性(Minimum degree stability of graphs forbidding some odd cycles)

报告人 (Speaker)：彭岳建 教授（湖南大学）

报告时间 (Time)：2023年4月19日(周三) 19:30

报告地点 (Place)：腾讯会议 739-770-096

邀请人(Inviter)：康丽英 教授

主办部门：理学院数学系

报告摘要： We consider the minimum degree stability of graphs forbidding odd cycles: What is the tight bound on the minimum degree to guarantee that the structure of a $C_{2k+1}$-free graph inherits from the extremal graph (a balanced complete bipartite graph)? Andr\'{a}sfai, Erd\H{o}s and S\'{o}s showed that if a $\{C_3,C_5,\cdots, C_{2k+1}\}$-free graph on $n$ vertices has minimum degree greater than $\frac{2}{2k+3}n$, then it is bipartite. H\"{a}ggkvist showed that for $k\in \{1,2,3,4\}$, if a $C_{2k+1}$-free graph on $n$ vertices has minimum degree greater than $\frac{2}{2k+3}n$, then it is bipartite. H\"{a}ggkvist also pointed out that this result cannot be extended to $k\geq 5$. In this paper, we give a complete answer for any $k\geq 5$.