The k-Core and Branching Processes

  title={The k-Core and Branching Processes},
  author={Oliver Riordan},
  journal={Combinatorics, Probability and Computing},
  pages={111 - 136}
  • O. Riordan
  • Published 3 November 2005
  • Mathematics
  • Combinatorics, Probability and Computing
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 λc for the emergence of a non-trivial k-core in the random graph G(n, λ/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 edges. As an… 
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