Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there are two graphs on a single vertex set (the `people' graph and the `puzzle' graph), and vertices merge to form components if they are joined by an edge of each graph. These components then merge to form larger components if again there is an edge of each graph joining them, and so on. Percolation is said to occur if the process terminates with a single component containing every vertex. In this note we determine the threshold for percolation up to a constant factor, in the case where both graphs are Erdős-Rényi random graphs.
@article{10_37236_6102,
author = {B\'ela Bollob\'as and Oliver Riordan and Erik Slivken and Paul Smith},
title = {The threshold for jigsaw percolation on random graphs},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {2},
doi = {10.37236/6102},
zbl = {1366.05096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6102/}
}
TY - JOUR
AU - Béla Bollobás
AU - Oliver Riordan
AU - Erik Slivken
AU - Paul Smith
TI - The threshold for jigsaw percolation on random graphs
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/6102/
DO - 10.37236/6102
ID - 10_37236_6102
ER -
%0 Journal Article
%A Béla Bollobás
%A Oliver Riordan
%A Erik Slivken
%A Paul Smith
%T The threshold for jigsaw percolation on random graphs
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/6102/
%R 10.37236/6102
%F 10_37236_6102
Béla Bollobás; Oliver Riordan; Erik Slivken; Paul Smith. The threshold for jigsaw percolation on random graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6102
