# ͼϵн֮ʮţ

ʱ䣺2020-11-03

ĿEigenvalues and triangles in graphs

: Ͽѧ ڣ

ժҪA 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.

ʱ: 2020116()  15:30-17:00

ص: Ѷң237-987-694

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2020113

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