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{\bf Julie Cain and Nicholas Wormald}
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{\bf Encores on Cores}
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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 applied to $d$-uniform hypergraphs.
\bye