## Syllabus

Part of the purpose of this blog is to collect enough information on Computational Combinatorics to develop a graduate course on the subject. This page outlines the syllabus of such a course, and how the posts fit within that syllabus.

### Existing Software Tools

1. Using the Sage Graph Library
2. Using `gtools`
3. Using GLPK, CPLEX, and other LP Solvers.
4. Using TreeSearch for Parallel Computation

### Canonical Deletion

1. Introduction to Canonical Deletion
2. Small Graphs are Reconstructible
3. Generating Cubic Graphs
4. Generating Fullerenes
5. Generating 2-connected Graphs using Ears
6. Generating $p$-Extremal Graphs

### Orbit Methods

1. Introduction to Orbital Branching
2. Uniquely $K_r$-Saturated Graphs, Experiment #1
3. There is no Projective Plane of Order 10.

### Planar Graphs

1. Generating planar graphs
2. Hypohamiltonian planar graphs

### Linear and Integer Programming

1. Integer Programming as Blackbox
2. Linear Programming as Subroutine
3. The Nullstellensatz/Linear Algebra Method

### Flag Algebras

1. Introduction to Flag Algebras
2. Hypergraphs Do Jump
3. On the Ramsey Multiplicity of Triangles with Three Colors

### Famous Computer Proofs

1. The Four-Color Theorem
2. Hales’ Proof of the Kepler Conjecture

### The Wilf-Zeilberger Method

1. Introduction to the Wilf-Zeilberger Method