【廿周年院庆·学术会议】2023杭州图论研讨会

主题：Maximizing the signless Laplacian spectral radius of minimally $3$-connected graphs with given size

主讲人：盐城师范学院  郭曙光 教授

摘要：In this talk, we provide an upper bound on the signless Laplacian spectral radius of minimally $3$-connected graphs with $m$ edges, and completely characterize the corresponding extremal graph in the case when $m$ is even. As a corollary, we determine the unique graph  with the maximal  signless Laplacian spectral radius among all Halin graphs with $m$ edges. This is a joint work with Rong Zhang.

个人简介：郭曙光，江苏省盐城师范学院教授，主要从事代数图论和组合数论的研究。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，曾被评为江苏省高校“青蓝工程”中青年学术带头人和江苏省“333工程”培养对象，先后主持国家自然科学基金面上项目、江苏省自然科学基金面上项目多项，在《J. Number Theory》《Linear Algebra Appl.》《Discrete Math.》等重要学术刊物上发表论文60余篇，出版江苏省高等学校重点教材1部，获江苏省教育科学研究成果二等奖1项。

主题：The nullity of a graph

主讲人：华东理工大学  郭继明 教授

摘要：Let G = (V (G), E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). Its adjacency matrix A(G) = (a_{ij}) is defined as n by n matrix (a_{ij}), where a_{ij} = 1, if v_i is adjacent to v_j ; and a_{ij} = 0, otherwise.

The nullity n(G) of G is the multiplicity of 0 as an eigenvalue of A(G). In this topic, we will introduce some old and new results on the nullity of a graph.

个人简介：郭继明，华东理工大学数学学院教授、博士生导师。中国高等教育学会教育数学专业委员会常务理事、上海市数学会常务理事、中国工业与应用数学学会理事。主要研究方向为图论与组合数学，先后主持多项国家自然科学基金面上项目，在国内外杂志上发表论文80余篇、出版学术专著一部。

主题：Brualdi-Hoffman-Tur'{a}n-type problem

主讲人：滁州学院 翟明清 教授

摘要：Spectral extremal problem was firstly proposed by Brualdi and Solheid in 1986. In 2010, a variation of spectral extremal problem and Tur'{a}n-type problem was given by Nikiforov, who asked what is the maximum spectral radius of an H-free graph of order n? In the past decades, much attention has been paid to this spectral Tur'{a}n-type problem. In this talk, we introduce a variation of spectral Tur'{a}n-type problem, namely, Brualdi-Hoffman-Tur'{a}n-type problem.

个人简介：翟明清，滁州学院教授，博士生导师。近年来在组合数学顶级期刊JCTB以及组合图论权威期刊 JGT, EJC, EUJC, LAA, DM等期刊发表学术论文40余篇，主持国家自然科学基金2项。研究方向：图谱理论、谱极值图论。

主题：Sufficient conditions for k-factors and spanning trees of graphs

主讲人：郑州大学  刘瑞芳 教授

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 \delta. 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 in 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 \delta, where k>=1 is an integer. This is a joint work with Guoyan Ao, Jinjiang Yuan, C.T. Ng and T.C.E. Cheng.

个人简介：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，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项目2项，河南省优青基金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。