报告地点：行健楼学术活动室526
邀请人：许宝刚教授
Talk One
Title: A new proof of Dirac’s theorem on Hamilton cycles
Abstract:In 1952, Dirac proved that every graph on n\geq 3 vertices with minimum degree at least n/2 has a Hamilton cycle, which is a cornerstone result of graph theory. The classic proof is by Posa’s rotation. In this short talk, we present a new proof by induction on the order of a graph avoiding Posa’s rotation. We hope the proof is friendly to all the graduate students.
Talk Two
Title：Graph operations and a unified method for kinds of Turan-type problems on paths, cycles and matchings
Abstract:We present a method that offers a unified approach to addressing several Tur´an-type and generalized Tur´an-type problems, degree power problems, and extremal spectra problems on paths, cycles, and matching. Specifically, we generalize classical results on cycles and matchings by Kopylov and Erdos-Gallai, respectively, and provide a positive resolution to an open problem originally proposed by Nikiforov. Besides, we enhance and expand upon the spectral extremal results on paths, building on the work of Nikiforov, Nikiforov and Yuan. Additionally, we deliver a comprehensive solution to a connected version of a problem related to the degree power sum of a graph that contains no Pk, a topic initially investigated by Caro and Yuster.
报告人简介：宁博，南开大学副教授、博士生导师，南开大学百名青年学科带头人。研究兴趣是结构图论和极值图论、谱图论，与人合作解决了Bondy和Murty撰写的1976年出版的经典图论教科书《Graph Theory with Applications》附录中50个未解决问题的问题7。曾获得中国运筹学会青年科技奖，并受邀在第九届世界华人数学家大会作45分钟特邀报告。目前主持国家自然科学基金面上项目1项。
