Espuny Díaz, Alberto, Janzer, Barnabás, Kronenberg, Gal and Lada, Joanna (2024) Long running times for hypergraph bootstrap percolation. European Journal of Combinatorics, 115. ISSN 0195-6698
Text (Long running times for hypergraph bootstrap percolation)
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Abstract
Consider the hypergraph bootstrap percolation process in which, given a fixed r-uniform hypergraph H and starting with a given hypergraph G0, at each step we add to G0 all edges that create a new copy of H. We are interested in maximising the number of steps that this process takes before it stabilises. For the case where H=Kr+1(r) with r≥3, we provide a new construction for G0 that shows that the number of steps of this process can be of order Θ(nr). This answers a recent question of Noel and Ranganathan. To demonstrate that different running times can occur, we also prove that, if H is K4(3) minus an edge, then the maximum possible running time is 2n−⌊log2(n−2)⌋−6. However, if H is K5(3) minus an edge, then the process can run for Θ(n3) steps.
Item Type: | Article |
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Additional Information: | © 2023 The Author(s) |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 03 Oct 2023 23:27 |
Last Modified: | 01 Dec 2024 01:06 |
URI: | http://eprints.lse.ac.uk/id/eprint/120360 |
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