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Decompositions of large graphs into small subgraphs

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  • Full or part time
    Prof D Kuhn
    Prof D Osthus
  • Application Deadline
    Applications accepted all year round
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

The starting point for the project is the following natural question:
When can the edges of a large `host’ graph G be decomposed into copies of a fixed small graph F? The case when G is complete and F is a triangle corresponds to the famous Kirkman schoolgirl problem. More generally, the case when the host graph G is
complete is well understood. However, much less in known for incomplete host graphs.

Recently major progress been made, involving approaches based on fractional relaxations, Szemeredi’s regularity lemma, as well as probabilistic methods.

The project will build on the above ideas to make further progress on decomposition problems of the type described above.

Some information about Combinatorics at Birmingham is available here:
http://www.birmingham.ac.uk/research/activity/mathematics/pure-maths/combinatorics.aspx

To find out more about studying for a PhD at the University of Birmingham, including full details of the research undertaken in each school, the funding opportunities for each subject, and guidance on making your application, you can now order your copy of the new Doctoral Research Prospectus at: www.birmingham.ac.uk/students/drp.aspx

Funding Notes

This research project is one of a number of projects in the School of Mathematics. It is in competition for funding with one or more of our advertised PhD projects. Usually the project which receives the best applicant will be awarded supported.

Normally scholarships are only available to UK or EU citizens. Other nationals who are normally resident in the UK or those who have been resident in the UK for a period of 3 years or more are also eligible.

All students with the correct qualifications and access to independent funding are also welcome to apply.

Related Subjects

How good is research at University of Birmingham in Mathematical Sciences?

FTE Category A staff submitted: 40.00

Research output data provided by the Research Excellence Framework (REF)

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