Sufficient conditions for k-factors and spanning trees of graphs
科研大讨论系列报告
报告题目(Title)：Sufficient conditions for k-factors and spanning trees of graphs
报告人(Speaker)：刘瑞芳 教授 (郑州大学)
地点(Place)：腾讯会议 ID：102 705 853
时间(Time)：2023 年 5 月 12 日(周五), 16:30-17:30
邀请人(Inviter)：徐敏
报告摘要
For any integer k≥1, a graph G has a k-factor if it contains a k-regular spanning subgraph. In this paper, motivated by a question proposed by F\"{u}redi, Kostochka and Luo, we prove a sufficient condition in terms of the number of $r$-cliques to guarantee the existence of a k-factor in a graph with minimum degree at least δ. For any integer k≥2, a spanning k-tree of a connected graph G is a spanning tree in which every vertex has degree at most k. We present a tight spectral condition for an m-connected graph to have a spanning k-tree, which extends the result of Fan, Goryainov, Huang and Lin. Let T be a spanning tree of a connected graph. The leaf degree of T is the maximum number of leaves adjacent to v in T for any v ∈ V(T). Inspired by the work of Ao, Liu and Yuan, we provide a sharp spectral condition for the existence of a spanning tree with leaf degree at most k in a connected graph with minimum degree δ, where k≥1 is an integer.
主讲人简介
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。河南省教育厅学术技术带头人，河南省优青基金获得者。现任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。主要从事图谱理论与谱极值图论的研究工作。在《Electron. J. Combin.》、《Adv. Appl. Math.》、《Theoret. Comput. Sci.》、《Discrete Math.》、《Discrete Appl. 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面上项目与河南省优青基金。曾在美国西弗吉尼亚大学数学系和香港浸会大学数学系学术访问。
