Encores on Cores

@article{Cain2006EncoresOC,
  title={Encores on Cores},
  author={Julie Cain and Nicholas C. Wormald},
  journal={Electr. J. Comb.},
  year={2006},
  volume={13}
}
We give a new derivation of the threshold of appearance of the $k$-core of a random graph. Our method uses a hybrid model obtained from a simple model of random graphs based on random functions, and the pairing or configuration model for random graphs with given degree sequence. Our approach also gives a simple derivation of properties of the degree sequence of the $k$-core of a random graph, in particular its relation to multinomial and hence independent Poisson variables. The method is also… CONTINUE READING

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