# IMO resources for Graph Theory

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:

## “IMO Training 2008: Graph Theory” by Adrian Tung.

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.)

Topics include:

1. Trees and Balancing
2. Friends, Strangers and Cliques
3. Directed Graphs and Tournaments
4. Matchings
5. Hamiltonian/Eulerian Paths/Cycles

## “Graph Theory” by Po-Shen Lo. (2008)

A large collection of problems and topics almost all of which have solutions or hints.

Topics include:

1. Basic facts
2. Extremal Graph Theory
3. Matchings
4. Ramsey Theory
5. Planarity

## “Graph Theory” by Matthew Brennan. (Canada Winter Camp, 2014)

Contains a concise list of important results together with a guided discussion to five example problems that use graph theory.

## “Probabilistic Method/Graph Theory” by James Rickards. (Canada Summer Camp, 2015)

An introduction to the probabilistic method in graph theory along with 10 problems.

## “SIMO Graph Theory Training”. (SIMO training 2003)

A list of about 30 problems and solutions in graph theory.

Topics:

1. Graph Theory
2. Coloring problems

## “Ramsey Theory and the IMO” by Ben Green. (2008)

This is a 4 page article that introduces Ramsey Theory for graphs and arithmetic progressions and its historical relation to the IMO.

## “Coloring Points” at Cut-the-knot

A collection of 12 topics about coloring graphs and planes. There are many problems with solutions.

## “Equivalence of seven major theorems in combinatorics” by Robert Borgersen (2004).

This series of slides states 7 results in extremal combinatorics that are really the same.

Topics:

1. Dilworth’s Theorem
2. Konig’s Bipartite Theorem
3. Hall’s Marriage Theorem
4. Menger’s Theorem
5. (Others)

## One thought on “IMO resources for Graph Theory”

1. Oooh! Nice round-up.

Thanks for posting all this!

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