题目：Refinement on spectral Tur\'{a}n's theorem

报告人：彭岳建教授

时间：2022年5月13日（周五）下午14:00-16:00

形式：腾讯会议 会议号：620-159-081

Abstract: A well-known result in extremal spectral graph theory,

known as Nosal's theorem, states that if G is a triangle-free graph on n vertices, then \lambda (G) \le \lambda (K_{\lfloor \frac{n}{2}\rfloor, \lceil \frac{n}{2} \rceil }), equality holds if and only if G=K_{\lfloor \frac{n}{2}\rfloor, \lceil \frac{n}{2} \rceil }. Nikiforov [Linear Algebra Appl. 427 (2007)] extended Nosal's theorem to K_{r+1}-free graphs for every integer r\ge 2. This is known as the spectral Tur\'{a}n theorem. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)]

proved a refinement on Nosal's theorem for non-bipartite triangle-free graphs. In this talk, we provide alternative proofs for the result of Nikiforov and the result of Lin, Ning and Wu. Our proof can allow us to extend the later result to non-r-partite K_{r+1}-free graphs. Our result refines the theorem of Nikiforov and it also can be viewed as a spectral version of a theorem of Brouwer. This is a joint work with Yongtao Li.

报告人简介：彭岳建，湖南大学数学学院教授，博士生导师。1989年获湘潭大学数学学士学位，1992年获复旦大学数学硕士学位，2001年获Emory大学（美国）数学博士。主要研究方向为极值组合，在JCT(A,B),CPC,SIDA等知名期刊发表论文多篇，主持国家自然科学基金面上项目和重点项目。