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… 
Jigsaw percolation on random hypergraphs
TLDR
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
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
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.
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
TLDR
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.

References

SHOWING 1-10 OF 12 REFERENCES
The Threshold for Jigsaw Percolation on Random Graphs
TLDR
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
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
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?
TLDR
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
TLDR
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.
  • M. Newman
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2001
TLDR
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
TLDR
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.
On random graphs, I
#p
...
1
2
...