学术报告

题      目： Spectral radius and edge-disjoint spanning trees

报  告  人：林辉球   教授  (邀请人：尤利华 )

                                 华东理工大学

时      间：2022-09-30 10:30-12:30

腾 讯 会 议：552-381-478， 密码：123321

报告人简介:

       林辉球，华东理工大学数学副院长、教授、博士生导师，2013年博士毕业于华东师范大学。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, Series B》、《Combin. Probab. Comput.》、《J. Graph Theory》、《European J. Comb.》、《Linear Algebra Appl.》、《Discrete Math.》等发表学术论文50余篇。主持国家自然科学基金项目4项，目前主持在研国家自然科学基金面上项目和国际联合项目（中俄）各1项，主持完成青年基金1项。     

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.