  We analyse the size of an independent set in a random graph on $n$ vertices
with specified vertex degrees, constructed via a simple greedy algorithm: order
the vertices arbitrarily, and, for each vertex in turn, place it in the
independent set unless it is adjacent to some vertex already chosen. We find
the limit of the expected proportion of vertices in the greedy independent set
as $n \to \infty$, expressed as an integral whose upper limit is defined
implicitly, valid whenever the second moment of a random vertex degree is
uniformly bounded. We further show that the random proportion of vertices in
the independent set converges to the jamming constant as $n \to \infty$. The
results hold under weaker assumptions in a random multigraph with given degrees
constructed via the configuration model.
