Skip to main content Accessibility help
×
Home
Hostname: page-component-79b67bcb76-c5xhk Total loading time: 0.402 Render date: 2021-05-12T18:29:11.548Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Jigsaw percolation on random hypergraphs

Published online by Cambridge University Press:  30 November 2017

Béla Bollobás
Affiliation:
University of Cambridge, University of Memphis, and London Institute for Mathematical Sciences
Oliver Cooley
Affiliation:
Graz University of Technology
Mihyun Kang
Affiliation:
Graz University of Technology
Christoph Koch
Affiliation:
Graz University of Technology

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

Access options

Get access to the full version of this content by using one of the access options below.

References

[1] Ball, P. (2014). Crowd-sourcing: strength in numbers. Nature 506, 422423. CrossRefGoogle ScholarPubMed
[2] Barabási, A. L. et al. (2002). Evolution of the social network of scientific collaborations. Phys. A 311, 590614. CrossRefGoogle Scholar
[3] Bollobás, B., Riordan, O., Slivken, E. and Smith, P. (2017). The threshold for jigsaw percolation on random graphs. Electron. J. Combin. 24, 2.36. Google Scholar
[4] Brummitt, C. D., Chatterjee, S., Dey, P. S. and Sivakoff, D. (2015). Jigsaw percolation: what social networks can collaboratively solve a puzzle? Ann. Appl. Prob. 25, 20132038. CrossRefGoogle Scholar
[5] Cooley, O., Kang, M. and Koch, C. (2016). Threshold and hitting time for high-order connectedness in random hypergraphs. Electron. J. Combin. 23, 2.48. Google Scholar
[6] Gravner, J. and Sivakoff, D. (2017). Nucleation scaling in jigsaw percolation. Ann. Appl. Prob. 27, 395438. CrossRefGoogle Scholar
[7] Gutiérrez Sanchez, A. (2017). Multi-colored jigsaw percolation on random graphs. Master's Thesis. Graz University of Technology. Google Scholar
[8] Newman, M. E. J. (2001). Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64, 016131. CrossRefGoogle ScholarPubMed
[9] Newman, M. E. J. (2001). Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016132. CrossRefGoogle ScholarPubMed
[10] Newman, M. E. J. (2001). The structure of scientific collaboration networks. Proc. Nat. Acad. Sci. USA 98, 404409. CrossRefGoogle ScholarPubMed
[11] Tebbe, J. (2011). Book review: Where good ideas come from: the natural history of innovation. J. Psychological Issues Organizational Culture 2, 106110. CrossRefGoogle Scholar

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Jigsaw percolation on random hypergraphs
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Jigsaw percolation on random hypergraphs
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Jigsaw percolation on random hypergraphs
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *