Graph Theory
A 27-module path through graph theory, in study order from foundations to the frontier.
Modules
- Graphs and Basic Definitions
- Subgraphs and Special Graph Families
- Degree and the Handshake Lemma
- Degree Sequences and Realizability
- Walks, Paths, and Cycles
- Connectivity and Components
- Vertex and Edge Connectivity
- Trees and Their Properties
- Spanning Trees
- Minimum Spanning Trees and Algorithms
- Cayley's Formula and Matrix-Tree Theorem
- Bipartite Graphs and Characterization
- Eulerian Graphs and Circuits
- Graph Coloring and Chromatic Number
- Bounds on the Chromatic Number
- Matchings and Hall's Theorem
- König's Theorem and Vertex Covers
- Directed Graphs and Digraphs
- Network Flows and Max-Flow Min-Cut
- Menger's Theorem
- Planar Graphs and Euler's Formula
- Consequences of Euler's Formula
- Kuratowski's Theorem
- Graph Isomorphism
- Ramsey Theory Introduction
- The Probabilistic Method Introduction
- Introduction to Spectral Graph Theory