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On percolation in random graphs with given vertex degrees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2009 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 14, 87-118 p.Article in journal (Refereed) Published
Abstract [en]

We study the random graph obtained by random deletionof vertices or edges from a random graph with given vertex degrees.A simple trick of exploding vertices instead of deleting them, enablesus to derive results from known results for random graphs with givenvertex degrees. This is used to study existence of giant component andexistence of k-core. As a variation of the latter, we study also bootstrappercolation in random regular graphs.We obtain both simple new proofs of known results and new results.An interesting feature is that for some degree sequences, there are severalor even infinitely many phase transitions for the k-core.

Place, publisher, year, edition, pages
2009. Vol. 14, 87-118 p.
Keyword [en]
random graph, giant component, k-core, bootstrap percolation
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URN: urn:nbn:se:uu:diva-114386ISI: 000263106300001OAI: oai:DiVA.org:uu-114386DiVA: diva2:293868
Available from: 2010-02-15 Created: 2010-02-15 Last updated: 2010-12-14Bibliographically approved

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Janson, Svante
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