Jigsaw percolation on random hypergraphs

TL;DR

This paper extends the jigsaw percolation model from graphs to hypergraphs, analyzing the critical threshold for percolation in random hypergraph settings, thus broadening understanding of collaborative problem-solving in complex networks.

Contribution

It generalizes the jigsaw percolation process to hypergraphs and determines the asymptotic critical threshold probability for percolation in random hypergraph models.

Findings

Determined the asymptotic order of the critical threshold probability for hypergraph percolation.

Extended previous graph-based results to hypergraphs with various connectedness definitions.

Provided insights into percolation behavior in complex network models.

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.