# Multi-coloured jigsaw percolation on random graphs

@article{Cooley2017MulticolouredJP, title={Multi-coloured jigsaw percolation on random graphs}, author={Oliver Cooley and Abraham Guti'errez}, journal={arXiv: Combinatorics}, year={2017} }

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…

## 5 Citations

Jigsaw percolation on random hypergraphs

- MathematicsJ. Appl. Probab.
- 2017

This work determines the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.

C O ] 4 D ec 2 01 7 Multi-coloured jigsaw percolation on random graphs

- Mathematics
- 2018

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…

The sharp threshold for jigsaw percolation in random graphs

- MathematicsAdvances in Applied Probability
- 2019

Abstract We analyse the jigsaw percolation process, which may be seen as a measure of whether two graphs on the same vertex set are ‘jointly connected’. Bollobás, Riordan, Slivken, and Smith (2017)…

The size of the joint-giant component in a binomial random double graph.

- Mathematics
- 2019

We study the joint components in a random `double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices. A joint component is a maximal set of vertices, which…

The Size of the Giant Joint Component in a Binomial Random Double Graph

- MathematicsElectron. J. Comb.
- 2021

It is shown that there are critical pairs of red and blue edge densities at which a giant joint component appears in a random ‘double graph’ that is obtained by superposing red andblue binomial random graphs on n vertices.

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C O ] 4 D ec 2 01 7 Multi-coloured jigsaw percolation on random graphs

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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…

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