Karen Gunderson

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Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number r, the r-neighbour bootstrap process is an update rule for vertices of a graph in one of two states: 'infected' or 'healthy'. In consecutive rounds, each healthy vertex with at least r infected(More)
For r ≥ 2, an r-uniform hypergraph is called a friendship r-hypergraph if every set R of r vertices has a unique 'friend' – that is, there exists a unique vertex x / ∈ R with the property that for each subset A ⊆ R of size r − 1, the set A ∪ {x} is a hyperedge. We show that for r ≥ 3, the number of hyperedges in a friendship r-hypergraph is at least r+1 r(More)
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