A note on Fiedler value of classes with sublinear separators

Jaroslav Nesetril; Patrice Ossona De Mendez

A note on Fiedler value of classes with sublinear separators

Combinatorics 2012-08-20 v1

Authors: Jaroslav Nesetril , Patrice Ossona De Mendez

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.

Keywords

graph pebbling graph laplacian graph theory

Cite

@article{arxiv.1208.3581,
  title  = {A note on Fiedler value of classes with sublinear separators},
  author = {Jaroslav Nesetril and Patrice Ossona De Mendez},
  journal= {arXiv preprint arXiv:1208.3581},
  year   = {2012}
}

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