Multi-coloured jigsaw percolation on random graphs
@article{Cooley2020MulticolouredJP,
title={Multi-coloured jigsaw percolation on random graphs},
author={Oliver Cooley and Abraham Guti'errez},
journal={Journal of Combinatorics},
year={2020}
}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
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References
SHOWING 1-10 OF 12 REFERENCES
The Threshold for Jigsaw Percolation on Random Graphs
- MathematicsElectron. J. Comb.
- 2017
In this note, the threshold for percolation up to a constant factor is determined, in the case where both graphs are Erd\H{o}s--R\'enyi random graphs.
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…
Nucleation scaling in jigsaw percolation
- Mathematics
- 2013
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic \puzzle graph" by using connectivity properties of a random \people graph" on the same set of…
JIGSAW PERCOLATION: WHAT SOCIAL NETWORKS CAN COLLABORATIVELY SOLVE A PUZZLE?
- Computer Science
- 2015
This model suggests a mechanism for recent empirical claims that innovation increases with social density, and it might begin to show what social networks stifle creativity and what networks collectively innovate.
Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs
- MathematicsElectron. J. Comb.
- 2016
A hitting time result is deduced for the random hypergraph process – the hypergraph becomes $j-connected at exactly the moment when the last isolated $j$-set disappears.
The structure of scientific collaboration networks.
- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 2001
It is shown that these collaboration networks form "small worlds," in which randomly chosen pairs of scientists are typically separated by only a short path of intermediate acquaintances.
Crowd-sourcing: Strength in numbers
- ArtNature
- 2014
Inspired by the online citizen-science movement, Gowers, a mathematician at the University of Cambridge, UK, posted an esoteric theorem on his blog and challenged his readers to prove it — together, and this open approach has taken root as an ongoing crowd-sourcing project called Polymath.