Benedikt Kolbe

On Eigenvalue Bounds for Bounded Genus Graphs and Minor-Free Graphs

In this paper, we resolve a 30-year-old conjecture of Spielman and Teng concerning the performance of the spectral partitioning method on graphs embeddable on an orientable surface of genus $g\ge 1$. In particular, for such a graph $G$ with $n$ vertices and maximum degree $\Delta$, we show that the second-smallest eige...