Lectures 8 and 9 – Spectral graph theory Uriel

Lectures 8 and 9 – Spectral graph theory

With every graph (or digraph) one can associate several different matrices. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacian. We shall show that spectral properties (the eigenvalues and eigenvectors) of these matrices provide useful information about the structure of the graph. It turns out that for regular graphs, the infor...

Lectures 6, 7 beginning of 8– Treewidth and graph minors

We shall touch upon the theory of Graph Minors by Robertson and Seymour. This theory gives a very general condition under which a graph problem has a polynomial time algorithm (though the algorithms that come out of the theory are often not practical). We shall review a small part of this theory, and illustrate how dynamic programming can be used to solve some NP-hard problems on restricted cla...

Lectures on Algorithmic Spectral Graph Theory

Lectures on Spectral Graph Theory

Contents Chapter 1. Eigenvalues and the Laplacian of a graph 1 1.1. Introduction 1 1.2. The Laplacian and eigenvalues 2 1.3. Basic facts about the spectrum of a graph 6

References on Higher Laplacian Eigenvalues and Combinatorial Graph Properties

This is a collection of references for a series of lectures that I gave in the “boot camp” of the semester on spectral graph theory at the Simons Institute in August, 2014. To keep this document focused, I only refer to results related to the lectures in question, which means that my own work is disproportionally represented. I plan to post a better version of this document in the future, so pl...