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

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