Graph limits and Hansen--Aouchiche conjecture

发布时间：2024-04-16 作者：浏览次数：

Speaker:	刘乐乐	DateTime:	2024年5月11日（周六）上午10：00-11：00
Brief Introduction to Speaker: 刘乐乐，2019年博士毕业于上海大学，导师是康丽英教授。于2017年9月至2019年3月访问南卡罗莱纳大学。研究方向为代数图论、超图谱理论，在SIAM Journal on Discrete Mathematics, European Journal of Combinatorics, Electronic Journal of Combinatorics, Linear and Multilinear Algebra 等杂志发表论文20余篇。主持国家自然科学基金青年项目一项。		Place:	6号楼2楼报告厅
Abstract:Let $\lambda(G)$ be the largest eigenvalue of the adjacency matrix of a graph $G$, and $\overline{G}$ be the complement of $G$. The Hansen--Aouchiche conjecture states that the graph on $n$ vertices maximizing $\lambda(G) + \lambda(\overline{G})$ is the join of a clique and an independent set, with $\lfloor n/3\rfloor$ and $\lceil 2n/3\rceil$ (also $\lceil n/3\rceil$ and $\lfloor 2n/3\rfloor$ if $n \equiv 2 \pmod{3}$) vertices, respectively. We resolve this conjecture for sufficiently large $n$ using the theory of graph limits. In this talk, we will show how to use graph limits method to confirm this conjecture.