Georgia Institute of Technology College of Sciences

One of the most interesting features of Erdös-Rényi random graphs is the `percolation phase transition', where the global structure intuitively changes from only small components to a single giant component plus small ones. In this talk we discuss the percolation phase transition in the random d-process, which corresponds to a natural algorithmic model for generating random regular graphs (starting with an empty graph on n vertices, it evolves by sequentially adding new random edges so that the maximum degree remains at most d). Our results on the phase transition solve a problem of Wormald from 1997, and verify a conjecture of Balinska and Quintas from 1990. Based on joint work with Nick Wormald (Monash University).