报告题目：Extremal spectral results of planar graphs without vertex-disjoint cycles
报告人：林辉球教授（华东理工大学）
报告时间：2024年5月7日（周二）上午10:00-11:00
报告地点：数学学院B301
报告摘要：Given a planar graph family 𝓕, let exp (n, 𝓕) and spexp (n, 𝓕)be the maximum size and maximum spectral radius over all n-vertex 𝓕 -free planar graphs, respectively. Let tCk be the disjoint union of t copies of k-cycles, and tC be the family of t vertex-disjoint cycles without length restriction.Tait and Tobin [Three conjectures in extremal spectral graph theory, J. Combin. Theory Ser. B 126(2017) 137–161] determined that K2 + Pn−2 is the extremal spectral graph among all planar graphs with sufficiently large order n, which implies the extreme graphs of spexp(n,tCl ) and spexp(n,tC) for t ≥ 3 are K2 +Pn−2 . In this paper, we first determine spexp(n,tCl) and spexp(n,tC) and characterize the unique extremal graph for 1 ≤ t ≤ 2, l≥ 3 and sufficiently large n. Secondly, we obtain the exact values of exp(n,2C4 ) and exp(n,2C), which answers a conjecture of Li [Planar Turán number of disjoint union of C3 and C4 , Discrete Appl. Math. 342 (2024) 260-274]. These present a new exploration of approaches and tools to investigate extremal problems of planar graphs.
报告人简介：林辉球，华东理工大学数学副院长（主持工作）、教授、博士生导师，上海市东方学者特聘教授，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理事。在图论的主流期刊《J. Combin. Theory, Series B》、《Combin. Probab. Comput.》、《J. Graph Theory》、《European J. Comb.》、等发表学术论文60余篇。主持国家自然科学基金项目5项，目前主持在研国家自然科学基金面上项目和数学天元基金项目各一项。