应304am永利集团官网张和平教授和高毓平博士邀请，美国佐治亚州立大学陈冠涛教授将于2023年3月30日作线上学术报告。

报告题目：Multiplicity of the second-largest eigenvalue of graphs

报告时间：2023年3月30日19:00

腾讯会议ID：663969747

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(λ₂,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(λ₂,G) for graphs 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(λ₂,G)≤δ(G), where δ(G) is the minimum degree of G. We further prove that if G is a connected planar graph, then m(λ₂,G)≤∆(G); if G is a connected outerplanar graph, then m(λ₂,G)≤max{2,∆(G)-1}, where ∆(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.

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报告人简介

陈冠涛，美国佐治亚州立大学教授(the Regents’Professor)。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。解决了图论领域10余个著名猜想。在组合与图论领域重要学术期刊发表论文150余篇。曾担任SIAM离散数学活动的组织者(2014-2016)，2011年以来任图论组合权威期刊《Graphs and Combinatorics》执行编委。

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2023年3月29日