Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.

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  • Eigenvalues of subgraphs of the cube

    Graph theory

    BBB. BollobásJLSL European Journal of Combinatorics

    Hypercube eigenvalues

    Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.

  • Eigenvalues of neutral networks: interpolating between hypercubes

    Graph theory

    TRT. ReevesRFR. FarrJBJ. BlundellAGA. GallagherTFT. Fink Discrete Mathematics

    Eigenvalues of neutral networks

    The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.

  • Transference for the Erdős-Ko-Rado theorem

    Graph theory

    JBBBB. BollobásBN Forum of Mathematics, Sigma

    Erdős-Ko-Rado theorem analogue

    A random analogue of the Erdős-Ko-Rado theorem sheds light on its stability in an area of parameter space which has not yet been explored.

  • Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach

    Statistical physics

    AMA. MozeikaACA. Coolen Journal of Physics A

    Spin systems on Bethe lattices

    Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.