报告人： 陈冠涛教授，美国佐治亚州立大学
报告时间：2022年2月25日10:00--14:00
腾讯会议ID：194488503
报告主题：Multiplicity of the second-largest eigenvalue of graphs
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：
The multiplicity of the second-largest eigenvalue of the adjacency matrix $A(G)$ of a connected graph $G$, denoted by $m(\lambda_2, G)$, is the number of times of the second-largest eigenvalue of $A(G)$ appears. In 2019, Jiang, Tidor, Yao, Zhang and Zhao gave an upper bound on $m(\lambda_2, G)$ forgraphs $G$ with bounded degrees, and applied it to solve a longstanding problem on equiangular lines. We showed that if $G$ is a $3$-connected planar graph or $2$-connected outerplanar graph, then $m(\lambda_2, G)\le\delta(G)$, where $\delta(G)$ is the minimum degree of $G$. We further prove that if $G$ is a connected planar graph, then $m(\lambda_2, G)\le\Delta(G)$; if $G$ is a connected outerplanar graph, then $m(\lambda_2, G)\le\max\{2, \Delta(G)-1\}$, where $\Delta(G)$ is the maximum degree of $G$. Moreover, these two upper bounds for connected planar graphs and outerplanar graphs, respectively, are best possible. We will discuss general techniques and specific methods we used in the proofs of these results.
报告人简介：
陈冠涛，佐治亚州立大学教授，数学与统计系主任。主要研究方向为图论及其应用。主要研究图的结构问题，如图的圈和路、图染色和图的Ramsey理论。近年来，他的主要工作是研究对图的边进行重新着色的技巧，并利用它们解决该领域的一些经典问题。他在组合学和图论的主要期刊上发表了120多篇论文，并与他的许多合作者解决了许多长期存在的猜想。曾担任SIAM离散数学活动组的组织者(2014-2016)，以及《图与组合学》杂志的执行主编(2011年以来)。
