Georgia Institute of Technology College of Sciences

The Bohman-Frieze process is a simple modification of the Erdős-Rényi random graph that adds dependence between the edges biased in favor of joining isolated vertices. We present new results on the phase transition of the Bohman-Frieze process and show that qualitatively it belongs to the same class as the Erdős-Rényi process. The results include the size and structure of small components in the barely sub- and supercritical time periods. We will also mention a class of random graph processes that seems to exhibit markedly different critical behavior.