# A note on Fiedler value of classes with sublinear separators

* Corresponding author
Abstract : The $n$-th Fiedler value of a class of graphs $\mathcal C$ is the maximum second eigenvalue $\lambda_2(G)$ of a graph $G\in\mathcal C$ with $n$ vertices. In this note we relate this value to shallow minors and, as a corollary, we determine the right order of the $n$-th Fiedler value for some minor closed classes of graphs, including the class of planar graphs.
Document type :
Preprints, Working Papers, ...
2012

https://hal.archives-ouvertes.fr/hal-00724093
Contributor : Patrice Ossona de Mendez <>
Submitted on : Friday, August 17, 2012 - 1:31:24 PM
Last modification on : Wednesday, September 28, 2016 - 4:09:44 PM
Document(s) archivé(s) le : Sunday, November 18, 2012 - 2:30:26 AM

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### Identifiers

• HAL Id : hal-00724093, version 1
• ARXIV : 1208.3581

### Citation

Jaroslav Nesetril, Patrice Ossona de Mendez. A note on Fiedler value of classes with sublinear separators. 2012. <hal-00724093>

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