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In this note, we analyze two random greedy processes on sparse random graphsand hypergraphs with a given degree sequence. First we analyze the matchingprocess, which builds a set of disjoint edges one edge at a time; then weanalyze the independent process, which builds an independent set of verticesone vertex at a time. We use the differential equations method and apply ageneral theorem of Warnke. Our main contribution is to significantly reduce theassociated systems of differential equations and simplify the expression forthe final size of the matching or independent set.

The Matching Process and Independent Process in Random Regular Graphs and Hypergraphs