A note on Fiedler value of classes with sublinear separators

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.