High-order bootstrap percolation in hypergraphs

Abstract

Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to k-uniform hypergraphs, in which we infect j-sets of vertices for some integer 1 ≤ j ≤ k − 1. We investigate the smallest possible size of an initially infected set which ultimately percolates and determine the exact size in almost all cases of k and j.

Random recursive hypergraphs

“…Statistical physics models on random hypergraphs is another growing area of research, see e.g. [70][71][72][73][74].…”