Percolation Processes on Dynamically Grown Graphs

We develop the theory of cluster growth near criticality for a class of “two-choice rules” for dynamically grown graphs. We use scaling theory to compute critical exponents for any two- choice rule, and we show special cases in which we can solve for these exponents explicitly. Finally, we compare our results with the corresponding results for the Erdős-Rényi rule, the simplest two- choice rule for which more explicit calculations are possible. We derive several of its important properties, then show that a large subset of two-choice rules - bounded size rules - behave like Erdős-Rényi near criticality.