报告主题：On the maximum spread of planar and outerplanar graphs  

报告人： 陆临渊教授

报告时间：2022年9月30日8:30--12:00

报告地点：腾讯会议ID：645-835-410

邀请单位：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

参加对象：感兴趣的老师和学生

报告摘要：

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on $n-1$ vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on $\ceil{(2n-1)/3}$ vertices and $\floor{(n-2)/3}$ isolated vertices. For planar graphs, we show that the extremal $n$-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on $\ceil{(2n-2)/3}$ vertices and $\floor{(n-4)/3}$ isolated vertices. This is a joint work with Zelong Li, William Linz, and Zhiyu Wang.

报告人简介：

陆临渊教授2002年于美国加州大学圣地亚哥分校（UCSD）获得理学博士学位。现在是南卡罗来纳大学教授，天津市千人计划专家，国际知名杂志《Journal of Combinatorics》编委，一直得到美国国家自然科学基金（NSF）的资助。目前，陆临渊教授已经在极值组合与图论、随机网络、图谱理论等众多领域做出了许多出色的工作，在组合图论主流权威刊物发表80多篇论文。著有《Complex graphs and networks》，合作者为金芳蓉院士（Fan Chung）。特别的，因为解决了Erdos提出的关于Folkman数f(3,3)的上界的一个著名猜想，从而获得100美元的奖励，Erdos所悬赏解决的问题都是极其困难的问题。

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