学术报告

题      目：k-factors, k-extendable and spectral radius in
bipartite graphs

报  告  人：林辉球  教授  (邀请人：尤利华 )

                                    华东理工大学

时      间：7月8日  09：00-10：00

地     点：数科院东楼401

报告人简介:

        林辉球，华东理工大学数学副院长、教授、博士生导师，2013年博士毕业于华东师范大学。中国运筹学会图论组合分会青年理事。在图论的主流期刊《J. Combin. Theory, Series B》、《Combin. Probab. Comput.》、《J. Graph Theory》、《European J. Comb.》、《Linear Algebra Appl.》、《Discrete Math.》等发表学术论文50余篇。主持国家自然科学基金项目4项，目前主持在研国家自然科学基金面上项目和国际联合项目（中俄）各1项，主持完成青年基金1项。

摘      要：

       Let $G$ be a connected graph. If $G$ contains a matching of size $k$, and every matching of size $k$ is contained in a perfect matching of $G$, then $G$ is said to be \emph{$k$-extendable}. A $k$-regular spanning subgraph of $G$ is called a   \textit{$k$-factor}. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree $\delta$ to be $k$-extendable, and for the existence of a $k$-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in \cite{D.F} and \cite{W.L} to $k$-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian \cite{Lu-Liu} to general regular factors. Additionally, using the equivalence of $k$ edge-disjoint perfect matchings and $k$- factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of $k$ edge-disjoint perfect matchings in balanced bipartite graphs.