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Jigsaw percolation on random hypergraphs

  • Béla Bollobás (a1), Oliver Cooley (a2), Mihyun Kang (a2) and Christoph Koch (a2)

Abstract

The jigsaw percolation process on graphs was introduced by Brummitt et al. (2015) as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex set. Our aim is to extend a result of Bollobás et al. (2017) concerning this process to hypergraphs for a variety of possible definitions of connectedness. In particular, we determine the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.

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Corresponding author

* Postal address: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK. Email address: b.bollobas@dpmms.cam.ac.uk
** Postal address: Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria.
*** Email address: cooley@math.tugraz.at
**** Email address: kang@math.tugraz.at
***** Current address: Mathematics Institute, University of Warwick, Zeeman Building, CV4 7AL Coventry, UK. Email address: c.koch@warwick.ac.uk

References

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[7] Gutiérrez Sanchez, A. (2017). Multi-colored jigsaw percolation on random graphs. Master's Thesis. Graz University of Technology.
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Keywords

MSC classification

Jigsaw percolation on random hypergraphs

  • Béla Bollobás (a1), Oliver Cooley (a2), Mihyun Kang (a2) and Christoph Koch (a2)

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