Graph Theory
These notes follow Robin J. Wilson's Introduction to Graph Theory, fourth edition, using the local PDF source with 180 pages. Wilson's core route is definitions, connectedness, paths and cycles, trees, planarity, colouring, digraphs, matching, network flows, and matroids. Each page is organized around intuition, precise definitions, theorem statements with proofs or proof sketches, worked examples, and small Python implementations where useful.
The Ramsey page expands Wilson's six-person party puzzle into the basic language of Ramsey numbers. The algebraic/spectral and Erdos-Renyi pages are included because they were requested, but they are supplementary rather than standalone Wilson chapters.
- Definitions and Examples
- Walks Paths and Connectedness
- Eulerian and Hamiltonian Graphs
- Algorithms on Weighted Graphs
- Trees and Spanning Trees
- Counting Trees and Pruefer Sequences
- Planarity and Euler Formula
- Duality Surfaces and Infinite Graphs
- Vertex and Map Colouring
- Edge Colouring and Chromatic Polynomials
- Digraphs Tournaments and Markov Chains
- Matchings Hall and Konig
- Menger Theorem and Network Flows
- Matroids and Graph Duality
- Algebraic Graph Theory Basics
- Ramsey Theory Basics
- Random Graphs Basics