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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… Click to show full abstract
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) proved that, when the two graphs are independent binomial random graphs, whether the jigsaw process percolates undergoes a phase transition when the product of the two probabilities is $\Theta({1}/{(n\ln n)})$. We show that this threshold is sharp, and that it lies at ${1}/{(4n\ln n)}$.
Keywords:
random graphs;
jigsaw;
jigsaw percolation
Journal Title: Advances in Applied Probability
Year Published: 2019
Link to full text (if available)
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Journal Title: Advances in Applied Probability
Year Published: 2019
Link to full text (if available)
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recommendations!