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