Journal of Combinatorics
Volume 11 (2020)
Multi-coloured jigsaw percolation on random graphs
Pages: 603 – 624
The jigsaw percolation process, introduced by Brummitt, Chatterjee, Dey and Sivakoff, was inspired by a group of people collectively solving a puzzle. It can also be seen as a measure of whether two graphs on a common vertex set are “jointly connected”. In this paper we consider the natural generalisation of this process to an arbitrary number of graphs on the same vertex set. We prove that if these graphs are random, then the jigsaw percolation process exhibits a phase transition in terms of the product of the edge probabilities. This generalises a result of Bollobás, Riordan, Slivken and Smith.
phase transition, random graphs, percolation
2010 Mathematics Subject Classification
O. Cooley was supported by Austrian Science Fund (FWF): I3747.
A. Gutierrez was supported by Austrian Science Fund (FWF): P29355-N35.
Received 30 November 2017
Accepted 13 August 2019
Published 9 October 2020