报告题目：Spectral radius and the existence of factors in graphs

报 告 人：刘瑞芳教授（上海大学）

报告时间：2024年4月25日  16:30-17:30

报告地点：腾讯会议（726146802）

报告摘要：

A graph $G$ is ID-factor-critical if for every independent set $I$ of $G$ whose size has the same parity as $|V(G)|$, $G-I$ has a perfect matching. In this paper, we prove a tight sufficient condition in terms of the spectral radius for a graph with minimum degree $\delta$ to be ID-factor-critical. Furthermore, we also present a tight sufficient condition based on the spectral radius for a graph to contain a fractional $[a, b]$-factor. Let $b$ be a positive integer. An {\it odd $[1, bl$-factor} of a graph $G$ is a spanning subgraph $F$ such that for each $v\in V(G)$, $d_F(v)$ is odd and $l\leq d_F(v)\leqb$. Motivated by the result of Fan, Lin and Lu [Discrete Math. 345 (2022) 112892] on the existence of an odd $[1, b]$-factor in connected granhs, we first present a tight sufficient condition in terms of the spectral radius for a connected $1$-binding graph to contain an odd $[l, bl$-factor, which generalizes the result of Fan and Lin [Electron. J. Combin, 31 (2024) P1.30]on the existence of a $l$-factor in $l$-binding graphs. Furthermore, we also provide a tight sufficient condition based on the spectral radius for a connected $1$-binding graph to contain a spanning $k$-tree.

报告人简介：

刘瑞芳，郑州大学数学与统计学院教授，博士生导师。2010年博士毕业于华东师范大学。河南省杰青，河南省教育厅学术技术带头人，河南省优青，河南省高等学校青年骨干教师。中国工业与应用数学学会图论组合及应用专业委员会委员，河南省运筹学会常务理事，主要从事图谱理论、谱极值图论的研究工作。在《Electron. J. Combin.》《Adv. Appl. Math.》《Discrete Math.》《Discrete App1. Math.》《Linear Algebra Appl.》等图论主流期刊发表SCI学术论文50余篇。主持国家自然科学基金项目3项，河南省杰青1项，河南省优青1项。曾在美国西弗吉尼亚大学数学系和香港浸会大学数学系进行学术访问。