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.

  • Subcritical U-Bootstrap percolation models have non-trivial phase transitions

    Percolation theory

    PBBBB. BollobásMPM. PrzykuckiPSP. Smith Transactions of the American Mathematical Society

    Bootstrap percolation models

    A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.

  • 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.

  • Bootstrap percolation on Galton–Watson trees

    Percolation theory

    BBB. BollobásKGCJMPM. Przykucki Electronic Journal of Probability

    Percolation on Galton-Watson trees

    The critical probability for bootstrap percolation, a process which mimics the spread of an infection in a graph, is bounded for Galton-Watson trees.