一、题目：Some new results on spectral Turan-type peoblems

二、主讲人：康丽英

三、摘要：

For a simple graph , let and denote set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an -vertex graph without any copy of the graph , respectively. The Turan graph is the complete -partite graph on vertices where its part sizes are as equal as possible. Cioaba, Desai and Tait [The spectral radius of graphs with no odd wheels, European J. Combin., 99 (2022) 103420] posed the following conjecture: Let be any graph such that the graphs in are Turan graphs plus O(1) edges. Then for sufficiently large . In this talk, we consider the graph such that the graphs in are obtained from by adding O(1) edges, and prove that if G has the maximum spectral radius among all n-vertex graphs not containing F, then is a member of for large enough. Thus Cioaba, Desai and Tait’s conjecture is completely solved. We also give the spectral extremal graphs for -fan and the unique spectral extremal graph for .

四、主讲人简介：

康丽英，上海大学理学院教授，博士生导师，研究方向包括图和超图的控制集、匹配问题的理论和算法，图和超图的极值问题，超图的谱和谱极值问题以及图论在社会网络、数据挖掘和人工智能方面的应用；在SIAM DM, JGT, EJC等国际期刊发表论文多篇；主持完成6项国家自然科学基金项目；曾在美国南卡莱罗纳大学、荷兰蒂尔堡大学、法国巴黎十一大等多所大学进行学术访问和合作研究。

五、邀请人：

王光辉 数学学院教授

六、时间：

3月31日（周五）9:30-10:30

七、地点：

腾讯会议

八、联系人：杨帆，联系方式：yangfan5262@163.com

九、主办：山东大学数学学院