Optional for: All MSci programmes in Mathematics, BSc Mathematical Sciences, BSc Mathematical Sciences with Study in Continental Europe, All programmes including a Major in Mathematics, All JH programmes

The module will give an introduction to fundamental results and concepts in graph theory. This is an area of Pure Mathematics which underpins much of the digital economy. Topics are likely to include Hamilton cycles, graph matchings, connectivity, graph colourings, planar graphs and extremal graph problems. For example, a fundamental result in Graph Theory is Hall’s marriage theorem, which characterizes all bipartite graphs that can be split into compatible pairs. Another famous result is the four colour theorem, which states that every planar map can be coloured with at most four colours such that adjacent regions have different colours (this can be translated into a graph colouring problem and has applications to scheduling).

Learning Outcomes

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

Be familiar with basic graph parameters and their relationships, such as connectivity, vertex covers and chromatic number.

Understand and be able to apply fundamental results on graphs (such as Hall’s theorem, Menger’s theorem, Dirac’s theorem and Turan’s theorem).

Apply the basic techniques introduced in the lectures.

Assessment

19592-04 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions

3 hour Written Unseen Examination (80%); In-course Assessment (20%).

Other

Reading List

Bondy, J A & Murty, U S R. 1976. Graph Theory with Applications. North-Holland.
Electronic version: http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html
West, D. 2001. Introduction to Graph Theory. Prentice Hall.
Diestel, R. 2000. Graph Theory. 2nd ed. Springer Verlag.