One of the most interesting features of Erdős–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 that differs from the usual configuration model (starting with an empty graph on n vertices, the random d-process 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.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
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