Introductory description

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.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module 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

Learning outcomes

By the end of the module, students should be able to:

• To state basic results covered by the module.
• To understand main ideas of the underlying mathematics.
• To distinguish between various partial orders on graphs and various graph properties.
• To manipulate with basic graph decomposition techniques.

Indicative reading list

Bollobás, Béla (2004), Extremal Graph Theory, New York: Dover Publications, ISBN 978-0-48643596-1

Diestel, Reinhard (2005), Graph Theory (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3540-26183-4
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View reading list on Talis Aspire

Subject specific skills

See learning outcomes

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.