Instructor: Swastik
Kopparty (swastik.kopparty@rutgers.edu)

Office Hours: Hill 432, Wednesday
2pm – 3pm

Prerequisites: Basic
combinatorics, linear algebra and some discrete probability.

Recommended books:
The Probabilistic Method (Alon & Spencer), Modern
Graph Theory (Bollobas).

There will be problem sets every
2-3 weeks. There are no exams.

__Topics__

·
Matchings, cuts, flows, connectivity

·
Planar
graphs

·
Random
graphs

·
The
local structure of graphs

·
Linear
algebra in graph theory

·
Expander
graphs

·
Random
walks

·
Applications

__Homework__

·
Homework 1 (Due October 6)

·
Homework 2 (Due November 10)

·
Homework 3 (Due December 6)

__Lecture Schedule__

·
September
1: Course Overview

·
September
6: Trees (notes)

·
**September 8: NO CLASS
(Monday Schedule)**

·
September
13: Bipartite Graphs and Matchings (notes)

·
September
15: Flows and Cuts (notes)

·
September
20: Planar Graphs (notes)

·
September
22: Drawing Planar Graphs and Crossing Numbers

·
September
27: Forbidden Subgraphs I (notes)

·
September
29: Forbidden Subgraphs II (notes)

·
October
4: Forbidden Subgraphs III (notes)

·
October
6: Subgraph Counts I (notes)

·
October
11: Subgraph Counts II (notes)

·
October
13: Ramsey Theory (notes)

·
October
18: Random Graphs I

·
October
20: Random Graphs II

·
October
25: Pseudorandom Graphs

·
October
27: The Szemeredi Regularity Lemma

·
November
1: The Szemeredi Regularity Lemma (contd.)

·
November
3: Girth

·
November
8: Expander Graphs (notes)

·
November
10: Expander Graphs (contd.)

·
November
15: R(3, k)

·
November
17: Cayley Graphs (notes)

·
November
22: The Matrix-Tree Theorem (notes)

·
**November 24: NO CLASS
(Thanksgiving)**

·
November
29: Dependent Random Choice (notes)

·
December
1: Applications to Error-Correcting Codes

·
December
6: Lower bounds for the Regularity Lemma

·
December
8: The Planar Separator Theorem

·
December
13: Course Wrap-up