题目：The spectral Turan problem:Characterizing spectral-consistent graphs
报告人：方龙飞（滁州学院）
报告时间：2025年11月19日，10:00
报告地点：1C207
报告摘要：Let EX(n,H) and SPEX(n,H)denote the families of n-vertex H-free graphs with the maximum size and the maximum spectral radius, respectively.A graph H is said to be spectral-consistent if SPEX(n,H)is a subset of EX(n,H) for sufficiently large n.A fundamental problem in spectralextremal graph theory is to determine which graphs are spectral-consistent.Cioaba, Desai, and Tait [European J. Combin. 99 (2022)] proposed the following conjecture:Let H be any graph such that the graphs in EX(n,H) are Turan graph plus O(1) edges.Then H is spectral-consistent.Wang, Kang, and Xue [J. Combin. Theory Ser. B 159 (2023)]confirmed this conjecture,along with a stronger result.Recently, Liu and Ning posed the following problem:Characterize all graphs H that are spectral-consistent.In this talk, we further investigate the spectral-consistent problem.We prove that for any finite graph H,if M(H) is matching-good, then H is spectral-consistent.As an application, this result enables us to characterize spectral-consistency for several important classes of forbidden graphs,including generalized color-critical graphs (such as the Petersen graph and the dodecahedron graph).This is a joint work with Huiqiu Lin and Mingqing Zhai.
报告人简介：方龙飞，滁州学院数学与金融学院专任教师，目前主要研究方向为极值图论和图谱理论。主持国家自然科学基金青年项目和安徽省自然科学研究一般项目，以第一作者身份在图论权威SCI期刊Journal of Graph Theory, Electronic Journal of Combinatorics，Discrete Mathematics及Discrete Applied Mathematics等发表论文10余篇。