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The interests of the Combinatorics Research Group include:

• Graph theory: total, fractional, and star colourings of graphs; well-quasi-ordering; degree-diameter problem and cages
• Combinatorial designs: automorphisms and embeddings; infinite designs
• Latin squares
• Pattern-avoiding permutations and their connection with graph theory
• Theory of symmetric maps on surfaces
• Optimal network design
• Automorphism groups of combinatorial objects

The Group holds a one day OU Winter Combinatorics Meeting each January.