# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# The largest eigenvalue and bi-average degree of induced subgraphs

Presented by Prof. Vsevolod LEV
Type: Oral presentation
Track: Graph Spectra and its Applications

## Content

We establish a close connection between the largest eigenvalue of a graph and the quantity $$\max \frac{e(X,Y)}{\sqrt{|X||Y|}},$$ where the maximum is over all pairs $(X,Y)$ of subsets of the vertex set of the graph. Our results are best possible up to a logarithmic factor.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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