The London Institute’s papers are the official record of our discoveries. They allow others to build on and apply our work. Each one is the result of many months of research, so we strive to make them clear, inspiring and beautiful, and publish them in leading journals.

Image for the paper "Eigenvalues of subgraphs of the cube"
Graph theory

Hypercube eigenvalues

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

BBBela BollobasJLSL
European Journal of Combinatorics
Image for the paper "Subcritical U-Bootstrap percolation models have non-trivial phase transitions"
Percolation theory

Bootstrap percolation models

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

BBBela BollobasMPMichał PrzykuckiPSPaul SmithPB
Transactions of the American Mathematical Society
Image for the paper "Transference for the Erdős-Ko-Rado theorem"
Graph theory

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.

BBBela BollobasJBBN
Forum of Mathematics, Sigma
Image for the paper "Bootstrap percolation on Galton–Watson trees"
Percolation theory

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.

BBBela BollobasMPMichał PrzykuckiKGCJ
Electronic Journal of Probability