Multi-coloured jigsaw percolation on random graphs

Oliver Cooley, Abraham Gutiérrez

Research output: Contribution to journalArticlepeer-review


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 Bollob\'as, Riordan, Slivken and Smith.
Original languageEnglish
Pages (from-to)603-624
JournalJournal of Combinatorics
Issue number4
Publication statusPublished - 2020


  • math.CO
  • 05C80


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