Jigsaw percolation on random hypergraphs

Abstract

The jigsaw percolation process on graphs was introduced by Brummitt, Chatterjee, Dey, and Sivakoff as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex set. Our aim is to extend a result of Bollob\'as, Riordan, Slivken, and Smith concerning this process to hypergraphs for a variety of possible definitions of connectedness. In particular, we determine the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.