报告题目1：Spectral extremal problems for degenerate graphs

报告人：康丽英教授，上海大学

报告时间：2025年11月20日（周四）8:30-9:30

报告地点：20-202

报告摘要：A family of graphs is called degenerate if it contains at least one bipartite graph. In this paper, we investigate the spectral extremal problems for a degenerate family of graphs ℱ. By employing covering and independent covering of graphs, we establish a spectral stability result for ℱ. Using this stability result, we prove two general theorems that characterize spectral extremal graphs for a broad class of graph families ℱ, yielding several new findings as well as reaffirming some known results. Furthermore, we establish the correlation between extremal graphs and spectral extremal graphs for ℱ. In particular, we determine the unique spectral extremal graph when ℱ = {Ms+1, F}, ℱ = {Kr+1, Pk+1}, ℱ = {C≥k, Kr+1} or ℱ = {C≥k, Ms+1}, where Ms+1 denotes a matching of size s+1, F is a color-critical graph, and C≥k represents the set of cycles of length at least k.

报告人简介：康丽英，上海大学数学系教授。曾获得“上海市三八红旗手”、“上海市曙光学者”称号，曾获得“上海大学吴兴华数学奖”。研究兴趣包括极值图论、图和超图的谱。在《Journal of Combinatorial Theory, Series B》、《SIAM Discrete Mathematics 》、《Journal of Graph Theory》、《 European Journal of Combinatorics》等重要学术期刊上发表学术论文180余篇。主持国家自然科学基金项目6项，参加国家自然科学基金重点项目1项，参加重大研究计划1项。现担任中国运筹学会常务理事、中国工业与应用数学学会组合图论专业委员会秘书长、中国数学会组合图论分会理事。担任国际期刊《Discrete Mathematics, Algorithms and Applications》、《Journal of the Operations Research Society of China》、《Communications on Applied Mathematics and Computation》和国内期刊《运筹学学报》编委。

报告题目2：Maximizing the α-spectral radius of hypergraphs with degree stability

报告人：李红海教授，江西师范大学

报告时间：2025年11月20日（周四）9:30-10:30

报告地点：20-202

报告摘要：An r-pattern P is defined as an ordered pair P = ([l] , E), where l is a positive integer and E is a set of r-multisets with elements from [l]. An r- graph H is said to be P-colorable if there is a homomorphism ϕ: V(H)→[l] such that the r-multiset {ϕ (v1),…, ϕ (vr)}is in E for every edge {v1,…, vr} ∈E(H). Let Col(P) denote the family of all P-colorable r-graphs. This paper establishes spectral extremal results for α-spectral radius of hyper- graphs using analytic techniques. We show that for any family ℱ of r- graphs that is degree-stable with respect to Col(P), spectral Turán-type problems can be effectively reduced to spectral extremal problems within Col(P). As an application, we determine the maximum α-spectral radius  (α≥1) among all n-vertex F(r) -free r-graphs, where F(r) represents the r-expansion of the color critical graph F. We also characterize the corresponding extremal hypergraphs. Furthermore, leveraging the spectral method, we derive a corresponding edge Turán extremal result. More precisely, we show that if ℱ is degree-stable with respect to Col(P), then every ℱ -free edge extremal hypergraph must be a P-colorable hypergraph.

报告人简介：李红海，教授、博士生导师。2007年于中国科技大学获理学博士学位。曾应邀访问香港理工大学、加拿大西蒙佛雷泽大学和里贾纳大学。研究兴趣包括图谱理论和超图理论，在Proc. AMS, Disc. Math., Electron. J. Comb., Linear Alg. Appl., J. Comb. Opt.等学术期刊发表论文40余篇，主持国家自然科学基金多项，受江西省“远航工程”资助出国访问。

邀请人：数学研究所