A note on Fiedler value of classes with sublinear separators

Jaroslav Nesetril (1) , Patrice Ossona de Mendez (2)

1 IUUK - Computer Science Institute of Charles University [Prague]
2 CAMS - Centre d'Analyse et de Mathématique sociales

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.

Domaines: Combinatoire [math.CO]

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