Multi-coloured jigsaw percolation on random graphs

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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
JournalJournal of combinatorics
Publication statusAccepted/In press - 13 Aug 2019

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Random Graphs
Graph in graph theory
Vertex of a graph
Phase Transition
Generalise
Arbitrary

Keywords

  • math.CO
  • 05C80

Cite this

Multi-coloured jigsaw percolation on random graphs. / Cooley, Oliver; Gutiérrez, Abraham.

In: Journal of combinatorics, 13.08.2019.

Research output: Contribution to journalArticleResearchpeer-review

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