报告题目：Spectral Turan-type problems of graphs
报 告 人：刘瑞芳 教授
工作单位：郑州大学
报告时间：2024-6-7 15:00–16:00
报告地点：我院305
报告摘要：Spectral Tur\'{a}n-type problem is one of central problems in spectral extremal graph theory. Erd\H{o}s et al. [J. Combin. Theory Ser. B 64 (1995) 89-100] obtained the exact Tur\'{a}n number of the friendship graph $F_k$ for $n\geq 50k^2$, and characterized all its extremal graphs. Cioab\u{a} et al. [Electron. J. Combin. 27 (2020) Paper 22] initially introduced Triangle Removal Lemma into a spectral Tur\'{a}n-type problem, and they showed that $SPEX(n, F_k)\subseteq EX(n, F_k)$ for sufficient large $n$, where $EX(n, F_k)$ and $SPEX(n, F_k)$ are the families of $n$-vertex $F_k$-free graphs with maximum size and maximum spectral radius, respectively. We determine the uniqueness of the family $SPEX(n, F_k)$ for sufficiently large $n$. Furthermore, a classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite graph of order $n$ with size $m>\lfloor \frac{n^{2}}{4}\rfloor$ contains a triangle. Lin, Ning and Wu [Comb. Probab. Comput. 30 (2021) 258-270] proved a spectral version of Mantel's theorem for given order $n.$ Zhai and Shu [Discrete Math. 345 (2022) 112630] investigated a spectral version for fixed size $m.$ We prove $Q$-spectral versions of Mantel's theorem.
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，主要从事图谱理论和谱极值图论的研究工作。在《Electronic Journal of Combinatorics》、《Advances in Applied Mathematics 》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Linear Algebra and its Applications》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2项，河南省杰青1项，河南省优青1项，国家自然科学青年基金1项，中国博士后特别资助1项等。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。
