I will be participating as a trainer for Canada’s 2018 IMO Summer Training camp. I’m giving a session on graph theory. As I prepared my notes I found many resources online that already cover some aspects of graph theory. So here are those resources:
This is an in-depth description of the basic combinatorial and geometric techniques in graph theory. It is a very thorough and helpful document with many Olympiad level problems for each topic. (No solutions are given.)
- Trees and Balancing
- Friends, Strangers and Cliques
- Directed Graphs and Tournaments
- Hamiltonian/Eulerian Paths/Cycles
A large collection of problems and topics almost all of which have solutions or hints.
- Basic facts
- Extremal Graph Theory
- Ramsey Theory
Contains a concise list of important results together with a guided discussion to five example problems that use graph theory.
An introduction to the probabilistic method in graph theory along with 10 problems.
A list of about 30 problems and solutions in graph theory.
- Graph Theory
- Coloring problems
This is a 4 page article that introduces Ramsey Theory for graphs and arithmetic progressions and its historical relation to the IMO.
A collection of 12 topics about coloring graphs and planes. There are many problems with solutions.
This series of slides states 7 results in extremal combinatorics that are really the same.
- Dilworth’s Theorem
- Konig’s Bipartite Theorem
- Hall’s Marriage Theorem
- Menger’s Theorem