专家报告

题      目：Some local results on Tur\'{a}n problems

报  告  人： 袁西英 教授  (邀请人：尤利华)

                                         上海大学

时      间： 4月7日  09：00-10:00

腾讯会议：786-655-170

报告人简介:

       袁西英，上海大学数学系教授，博士生导师。中国运筹学会组合与图论分会理事，主要从事图与超图谱理论的研究，先后主持多项国家自然基金项目。先后在美国Memphis 大学、香港理工大学、美国威廉玛丽学院以及日本东北大学等高校访问交流。

摘      要：

       In 2002, Nikiforov proved a spectral Tur\'{a}n inequality in terms of the clique number and edge number. In 2026, Liu and Ning prove a local version of this spectral Tur\'{a}n inequality. In this talk we will give a local version for a bound on the high order spectral radius. Furthermore, we define a weight function for each hyperedge in an $n$-vertex uniform hypergraph $H$ according to the number of hyperedges in the largest Berge star containing the hyperedge. We prove that the sum of the weight function values over all hyperedges of $H$ is at most $n$, and characterize the extremal hypergraphs that achieve this bound. Our result extends the hypergraph version of the classical Tur\'{a}n result for stars, providing a local version of the classic result.

          欢迎老师、同学们参加、交流！