This is a graduate textbook about how to color graphs. Each chapter studies a single method, and presents numerous examples applying that method, generally in order of increasing difficulty. The book is designed to be suitable for a topics course in graph coloring, as well as self-study. The chapters are listed below.
- Greedy Coloring
- Gadgets: Constructions for Lower Bounds
- Recoloring
- Vertex Identification: Coloring Planar Graphs
- The Kernel Method
- Deletion and Contraction: Nowhere-Zero Flows
- Rosenfeld Counting
- The Combinatorial Nullstellensatz
- The Activation Strategy
- The Vertex Shuffle
- Precoloring Extension
- The Potential Method
- The Rest of the Story
This book is (and always will be) freely available for download. It is released under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. License details are available at https://creativecommons.org/licenses/by-nc-nd/4.0.
If you would like a paperback version, you can purchase one on Amazon. In the United States, it costs $24. It is also available in other markets: US CA UK FR IT ES DE AU NL PL SE JP