Janson, Svante and Luczak, Malwina J. (2006) A simple solution to the k-core problem. CDAM research report series 2006 (LSE-CDAM-2006-13). Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.
Full text not available from this repository.Abstract
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. We let n ! 1. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that imply that with high probability the k-core is empty, and other conditions that imply that with high probability the k-core is non-empty and the sizes of its vertex and edge sets satisfy a law of large numbers; under suitable assumptions these are the only two possibilities. In particular, we recover the result by Pittel, Spencer andWormald [19] on the existence and size of a k-core in G(n, p) and G(n,m), see also Molloy [17] and Cooper [3]. Our method is based on the properties of empirical distributions of independent random variables, and leads to simple proofs.
| Item Type: | Monograph (Report) |
|---|---|
| Official URL: | http://www.cdam.lse.ac.uk/Reports/ |
| Additional Information: | © 2006 Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 09 Oct 2008 13:56 |
| Last Modified: | 13 Sep 2024 16:34 |
| URI: | http://eprints.lse.ac.uk/id/eprint/13800 |
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