We give an introductory course in Graph Theory.
There are several excellent course notes on the web. See for instance the notes of Matt DeVos (SFU) that we will follow quite closely. We give below a list of topics that we cover. At the end of the course I will post a detailed list of the material that has been covered together with references.
There are several good textbooks in Graph Theory. Here is a partial list.
A. Bondy, U.S.R. Murty, Graph Theory (Several copies on reserve in the library)
B. Bollobas, Modern Graph Theory
R. Diestel, Graph Theory
D. B. West, Introduction to Graph Theory
There are several books on specific topics in graph theory. Here are some:
B. Bollobas, Extremal Graph Theory
B. Bollobas, Random graphs
A. Frank, Connections in Combinatorial Optimization
T. R. Jensen, B. Toft, Graph Coloring Problems
L. Lovasz, M. D. Plummer, Matching Theory
Algebraic methods in Graph Theory (and combinatorics) can be found in:
J. Matousek, Thirty-three Miniatures. Mathematical and Algorithmic Applications of Linear Algebra
Exercises are very important in graph theory and are quite different from the numerical applications that are usually given in many courses. The above books contain many of them. For the exam you should be able to solve the easy ones (usually the first ones at the end of the chapters of the above books). Here is a book of exercises (some of them very difficult, but the book contains a solution for all of them) written by a famous mathematician:
L. Lovasz: Combinatorial Problems and Exercises.
Graph theory abounds with conjectures that are very easy to state but are seemingly quite hard to settle. Some of them were formulated long time ago and have been the subject of intensive research. Here is a compendium.
SYLLABUS