BAP: Lecture 8 (Mar 7, 2002)

The notes for this lecture are available in

In this lecture, we proved that the laplacian matrices of degree d planar graphs have second-smallest eigenvalue at most 8d/n. This result appeared in the paper Spectral Partitioning Works: Planar graphs and finite element meshes.
A proof of Koebe's embedding theorem may be found in my lecture notes from Applied Extremal Combinatorics