  By constructing jointly a random graph and an associated exploration process,
we define the dynamics of a "parking process" on a class of uniform random
graphs as a measure-valued Markov process, representing the empirical degree
distribution of non-explored nodes. We then establish a functional law of large
numbers for this process as the number of vertices grows to infinity, allowing
us to assess the jamming constant of the considered random graphs, i.e. the
size of the maximal independent set discovered by the exploration algorithm.
This technique, which can be applied to any uniform random graph with a given
degree distribution, can be seen as a generalization in the space of measures,
of the differential equation method introduced by Wormald.
