报告标题:Spectral radius and edge-disjoint spanning trees
报告人：林辉球教授 华东理工大学
报告时间：2022/11/16（周三），9:50-10:30
报告地点：腾讯会议455 861 864
报告摘要:The spanning tree packing number of a graph $G$, denoted by $\tau(G)$, is the maximum number of edge-disjoint spanning trees contained in $G$. The study of $\tau(G)$ is one of the classic problems in graph theory. Cioab\u{a} and Wong initiated to investigate $\tau(G)$ from spectral perspectives in 2012 and since then, $\tau(G)$ has been well studied using the second largest eigenvalue of the adjacency matrix in the past decade. In this paper, we further extend the results in terms of the number of edges and the spectral radius, respectively; and prove tight sufficient conditions to guarantee $\tau(G)\geq k$ with extremal graphs characterized. Moreover, we confirm a conjecture of Ning, Lu and Wang on characterizing graphs with the maximum spectral radius among all graphs with a given order as well as fixed minimum degree and fixed edge connectivity. Our results have important applications in rigidity and nowhere-zero flows. We conclude with some open problems in the end.
报告人简介：林辉球，华东理工大学教授，博士生导师，中国运筹学会图论组合分会青年理事。在图论的主流期刊《J. Combin. Theory Ser. B》、《Combin. Probab. Comput.》、《IEEE Transactions on Computers》、《J. Graph Theory》、《European J. Comb.》等发表SCI论文50余篇，高被引论文1篇，主持国家自然科学基金项目4项。
