学术报告-侯新民

学术报告


题      目:Spectral extrema of graphs with bounded clique number and matching number


报  告  人:侯新民  教授  (邀请人:尤利华 )

                                   中国科学技术大学


时      间:1月11日  16:00-17:00


        腾讯会议:946-558-145    会议密码:0238


报告人简介:

        侯新民,中国科学技术大学 教授,博士生导师。2002年博士毕业于大连理工大学。2009到2010在西弗吉尼亚大学学术访问,2013到2014在佐治亚理工大学学术访问。研究领域包括结构图论、极值图论及图论应用,已发表学术论文70余篇,主持完成国家自然科学基金4项,省部级项目2项,参与科技部重点专项2项。


摘      要:

For a set of graphs $\mathcal{F}$, let $\ex(n,\mathcal{F})$ and $\spex(n,\mathcal{F})$ denote the maximum number of edges and the maximum spectral radius of an $n$-vertex $\mathcal{F}$-free graph, respectively. Nikiforov ({\em LAA}, 2007) gave the spectral version of the Tur\'an Theorem by showing that $\spex(n, K_{k+1})=\lambda (T_{k}(n))$, where $T_k(n)$ is the $k$-partite Tur\'an graph on $n$ vertices. In the same year, Feng, Yu and Zhang ({\em LAA}) determined the exact value of $\spex(n, M_{s+1})$, where $M_{s+1}$ is a matching with $s+1$ edges. 

Recently, Alon and Frankl~(arXiv2210.15076) gave the exact value of $\ex(n,\{K_{k+1},M_{s+1}\})$.  In this talk, we give the spectral version of the result of Alon and Frankl by determining the exact value of $\spex(n,\{K_{k+1},M_{s+1}\})$ when $n$ is large.

     

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