Duncan Adamson

Postgraduate researcher at the University of Liverpool, focusing on combinatorics of crystal energy graphs

Contact Information



I am a post-graduate research student at the University of Liverpool Department of Computer Science, in the algorithms and complexity research group. My PhD thesis is titled "Combinatorial analysis of the energy graphs under operations of composition", supervised by Prof. Igor Potapov, with secondary supervisors Matthew Dyer and Vladimir Gusev. I am currently funded by the Leverhulme Research Centre for Functional Materials Design.

My main interests are in Combinatorics and complexity theory, in particular working out complexity classes of problems, and determining combinatorial rules for hard problems. I am specifically interested in matching problems, and the impact on problems through the operations of composition (swapping, addition and deletion). Also I am interested in the use of Integer Programming as a method for tackling hard problems.

Research Interests

My current research interests are in the analysis of the effects of using operations of composistion on graphs, particularly for energy graphs embedded in real space with euclidean distance (where the energy value is calculated by the pairwise distance between the two points) with the objective being to minimise the total energy. Our goal with this is to find ways to find the bounds on the energy for structures, with the aim of using this for predicting the structure crystals.

During my masters project I worked on finding maximum cardinality matchings with a minimum number of blocking pairs, supervised by David Manlove at the University of Glasgow. In this project I developed a new IP model for finding matchings, as well as discovering several combinatorial rules for the problem. My dissertation is available here.

Other Interests

Outside of computer science, I also enjoy making board games, often based on problems I am working on (I am currently working one on the vertex cover problem). If you run into me at a conforence I will be more than happy to test them out.

Short CV

  • 2013-2018

    Unveristy of Glasgow

    Undergraduate Masters in Science

    Master's Thesis: Maximum least-unstable matchings using Integer Programming

  • 2016


    Summer Intern

    Developed Online Services for existing software

  • 2018-Present

    Univeristy of Liverpool

    Post Graduate Researcher

    Combinatorial analysis of the energy graphs under operations of composition