The Maximal Running Time of Hypergraph Bootstrap Percolation

. We show that for every \ (r 3\), the maximal running time of the \ (K^rₑ+₁\) -bootstrap percolation in the complete \ (r\) -uniform hypergraph on \ (n\) vertices \ (Kₙʳ\) is \ ( (nʳ) \). 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 e^O (r) \) as \ (r \). Keywordsbootstrap percolationmaximal running timecomplete hypergraphMSC codes05C3505C6505D99