Lec #  Topics  KEY DATES 

1 
Course Introduction
Ramsey Theorem 

2 
Additive Number Theory
Theorems of Schur and Van der Waerden 

3 
Lower Bound in Schur’s Theorem
ErdösSzekeres Theorem (Two Proofs) 2Colorability of Multigraphs Intersection Conditions 

4 
More on Colorings
Greedy Algorithm Height Functions Argument for 3Colorings of a Rectangle Erdös Theorem 

5 
More on Colorings (cont.)
ErdösLovász Theorem Brooks Theorem 

6 
5Color Theorem
Vizing’s Theorem 
Problem set 1 due 
7 
Edge Coloring of Bipartite Graphs
Heawood Formula 

8 
Glauber Dynamics
The Diameter Explicit Calculations Bounds on Chromatic Number via the Number of Edges, and via the Independence Number 

9 
Chromatic Polynomial
NBC Theorem 
Problem set 2 due 
10 
Acyclic Orientations
Stanley’s Theorem Two Definitions of the Tutte Polynomial 

11 
More on Tutte Polynomial
Special Values External and Internal Activities Tutte’s Theorem 

12 
Tutte Polynomial for a Cycle
Gessel’s Formula for Tutte Polynomial of a Complete Graph 

13 
Crapo’s Bijection
Medial Graph and Two Type of Cuts Introduction to Knot Theory Reidemeister Moves 

14  Kauffman Bracket and Jones Polynomial  Problem set 3 due 
15 
Linear Algebra Methods
Oddtown Theorem Fisher’s Inequality 2Distance Sets 

16 
Nonuniform RayChaudhuriWilson Theorem
FranklWilson Theorem 

17 
Borsuk Conjecture
KahnKalai Theorem 
Problem set 4 due 
18 
Packing with Bipartite Graphs
Testing Matrix Multiplication 

19 
Hamiltonicity, Basic Results
Tutte’s Counter Example Length of the Longest Path in a Planar Graph 

20 
Grinberg’s Formula
Lovász and Babai Conjectures for Vertextransitive Graphs Dirac’s Theorem 

21 
Tutte’s Theorem
Every Cubic Graph Contains Either no HC, or At Least Three Examples of Hamiltonian Cycles in Cayley Graphs of S_{n} 

22  Hamiltonian Cayley Graphs of General Groups  
23 
Menger Theorem
GallaiMilgram Theorem 
Problem set 5 due 
24 
Dilworth Theorem
Hall’s Marriage Theorem ErdösSzekeres Theorem 

25 
Sperner Theorem
Two Proofs of Mantel Theorem GrahamKleitman Theorem 

26 
Swell Colorings
WardSzabo Theorem Affine Planes 
Problem set 6 due 
27 
Turán’s Theorem
Asymptotic Analogues 

28 
Pattern Avoidance
The case of S_{3} and Catalan Numbers StanleyWilf Conjecture 

29 
Permutation Patterns
Arratia Theorem FurediHajnal Conjecture 

30  Proof by Marcus and Tardos of the StanleyWilf Conjecture  Problem set 7 due 
31 
Nonintersecting Path Principle
GesselViennot Determinants BinetCauchy Identity 

32 
Convex Polyomino
Narayana Numbers MacMahon Formula 

33 
Solid Partitions
MacMahon’s Theorem Hookcontent Formula 

34  Hook Length Formula  
35  Two Polytope Theorem  
36 
Connection to RSK
Special Cases 
Problem set 8 due 
37 
Duality
Number of Involutions in S_{n} 

38  Direct Bijective Proof of the Hook Length Formula  
39 
Introduction to Tilings
Thurston’s Theorem 
Calendar
Course Info
Learning Resource Types
assignment
Problem Sets