报告题目：Eigenvalues and triangles in graphs
报 告 人: 宁博（南开大学 副教授）
报告摘要：A well-known result in spectral graph theory states that a graph G on m edges has a triangle if the spectral radius $\lambda_1(G)>\sqrt{m}$. Bollob\'as and Nikiforov proposed a conjecture in 2007 that if $G$ is $K_{r+1}$-free then $\lambda_1^2+\lambda_2^2\leq \frac{k-1}{k}\cdot 2m$. We confirm this conjecture in the case of $r=2$ and find all extremal graphs for this case. Furthermore, we mention some other spectral results on triangles motivated by classical results due to Erd\H{o}s.
报告时间: 2020年11月6日(周五) 15:30-17:00
报告地点: 腾讯会议室：237-987-694
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科学技术处
2020年11月3日