Content: Graph theory is a rapidly developing branch of mathematics that finds applications in other areas of mathematics as well as in other fields such as computer science, bioinformatics, statistical physics, chemistry, sociology, etc. In this module we will focus on results from structural graph theory. The module should provide an overview of main techniques with their potential applications. It will include a brief introduction to the basic concepts of graph theory and it will then be structured around the following topics:

Structural graph theory:

• Graph decompositions
• Graph parameters

Extremal graph theory:

• Ramsey’s Theorem with variations
• Properties of almost all graphs

Partial orders on graphs:

• Minor-closed, monotone and hereditary properties
• Well-quasi-ordering and infinite antichains

Aims: To introduce students to advanced methods from structural graph theory.

Objectives: By the end of the module the student should be able to:

• State basic results covered by the module
• Understand covered concepts from graph theory
• Use presented graph theory methods in other areas of mathematics

• Apply basic graph decomposition techniques

Books:

Bollobás, Béla (2004), Extremal Graph Theory, New York: Dover Publications, ISBN 978-0-486-43596-1
Diestel, Reinhard (2005), Graph Theory (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-26183-4