Extremal graph theory

Extremal graph theory is one of the most active and dynamic branches of combinatorics. The fundamental goal of the area is to understand what conditions force a graph to contain some substructure. For example, Mantel’s theorem – proved more than a century ago – determines how many edges a graph on n vertices needs to guarantee it contains a triangle. In recent years, a number of powerful methods have been developed allowing researchers to answer long-standing questions in extremal graph theory. The aim of this project is for the student to develop an understanding of such tools, including the so-called regularity and absorbing methods, and apply these techniques to further our outstanding of the area.

Entry requirements: 

We are looking for an enthusiastic and highly-motivated graduate with 

– a first class degree in Mathematics at the Master’s level (or equivalent); 

– a strong background in combinatorics, specifically graph theory; 

– good communication skills (oral and written). 

The application procedure and the deadlines for scholarship applications are advertised at https://www.birmingham.ac.uk/schools/mathematics/phd/phd.aspx