Combinatorics Research Group
The Combinatorics Research Group comprises Professor Mike Grannell, Professor Terry Griggs, Dr Fred Holroyd, Roy Nelson, Dr Kathleen Quinn, Dr Chris Rowley, Dr Bridget Webb and Dr Robin Wilson and also several members of the Technology Faculty (Dr Alan Dolan, Dr Joe Rooney and Dr Jeff Johnson). Members are interested in
- graph theory: colouring (vertex, edge and total colouring and the multicolouring and circular colouring versions of these), graceful labellings, spectral graph theory, topological graph theory;
- design theory: automorphisms, structural properties, configurations and colourings in designs, designs with order, topological design theory, applications to information theory, applications of group theory to designs, graph decomposition problems, defining sets and trades;
- history of combinatorics: early history of combinatorics, history of graph theory, early theory of designs;
- combinatorial computing.
The Group runs the Open University Winter Combinatorics Meeting near the end of January each year.
Research is in progress on:
- variants of the graph colouring problem: in particular, colourings of graphs and hypergraphs (Dr Holroyd, Dr Wilson, Prof Grannell and Prof Griggs), and problems involving colouring with sets of colours and with subintervals of the unit circle (Dr Holroyd);
- the graceful labelling conjecture and variants of it (Prof Grannell, Prof Griggs and Dr Holroyd);
- graph decomposition problems (Prof Griggs, Prof Grannell, Dr Holroyd);
- construction, enumeration and structural analysis of directed designs and other ordered designs (Prof Grannell, Prof Griggs and Dr Quinn);
- determination of which designs can be embedded in surfaces (Prof Grannell and Prof Griggs);
- investigation of the permutation representations on the points and blocks of combinatorial structures (Dr Webb);
- the early history of Kirkman's fifteen schoolgirls problem, which initiated the study of designs in the nineteenth century (Prof Grannell, Prof Griggs and Dr Wilson);
- investigations into the history of combinatorics and graph theory (Dr Wilson).
Some recent books:
- An Atlas of Graphs, containing over 10 000 graphs and many tables of graph parameters, by Dr Wilson together with Prof R. C. Read (Waterloo, Canada), published by Oxford University Press; this book should prove to be a major boon to researchers in graph theory.
- Combinatorial Designs and their Applications, edited by Dr Holroyd, Dr Quinn, Dr Rowley and Dr Webb, the proceedings of a one-day conference held at the OU in 1996, published in the series Chapman & Hall/CRC Press Research Notes in Mathematics.
Publications for
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Mike Grannell
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Terry Griggs
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Fred Holroyd
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Kathleen Quinn
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Bridget Webb
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Robin Wilson
