報告題目：Extremal spectral results of planar graphs without vertex-disjoint cycles
報告人：林輝球教授（華東理工大學）
報告時間：2024年5月7日（周二）上午10:00-11:00
報告地點：伟德bvB301
報告摘要：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.
報告人簡介：林輝球，華東理工大學數學副院長（主持工作）、教授、博士生導師，上海市東方學者特聘教授，2013年博士畢業于華東師範大學。中國運籌學會圖論組合分會理事。在圖論的主流期刊《J. Combin. Theory, Series B》、《Combin. Probab. Comput.》、《J. Graph Theory》、《European J. Comb.》、等發表學術論文60餘篇。主持國家自然科學基金項目5項，目前主持在研國家自然科學基金面上項目和數學天元基金項目各一項。