The Maximal Running Time of Hypergraph Bootstrap Percolation

.We show that for every \(r≥ 3\), the maximal running time of the \(Kʳᵣ₊₁\)-bootstrap percolation in the complete \(r\)-uniform hypergraph on \(n\) vertices \(K_n^r\) is \(Θ (n^r)\). This answers a recent question of Noel and Ranganathan in the affirmative and disproves a conjecture of theirs. Moreover, we show that the prefactor is of the form \(r⁻ʳ eO(r)\) as \(r→ ∞\).