Long running times for hypergraph bootstrap percolation
نویسندگان
چکیده
Consider the hypergraph bootstrap percolation process in which, given a fixed r-uniform H and starting with G0, at each step we add to G0 all edges that create new copy of H. We are interested maximising number steps this takes before it stabilises. For case where H=Kr+1(r) r≥3, provide construction for shows can be order Θ(nr). This answers recent question Noel Ranganathan. To demonstrate different running times occur, also prove that, if is K4(3) minus an edge, then maximum possible time 2n−⌊log2(n−2)⌋−6. However, K5(3) run Θ(n3) steps.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2024
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2023.103783