Journal article
The k-core and branching processes
- Abstract:
-
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold $\lambda_c$ for the emergence of a non-trivial k-core in the random graph $G(n,\lambda/n)$, and the asymptotic size of the k-core above the threshold. We give a new proof of this result using a local coupling of the graph to a suitable branching process. This proof extends to a general model of inhomogeneous random graphs with independence between the...
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- Publication status:
- Published
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- Publisher copy:
- 10.1017/S0963548307008589
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Bibliographic Details
- Journal:
- Probability and Computing
- Volume:
- 17
- Issue:
- 1
- Pages:
- 111-136
- Publication date:
- 2005-11-03
- DOI:
- EISSN:
-
1469-2163
- ISSN:
-
0963-5483
- Source identifiers:
-
16715
Item Description
Terms of use
- Copyright date:
- 2005
- Notes:
-
30 pages, 1 figure. Minor revisions. To appear in Combinatorics,
Probability and Computing
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