L3

The phase transition is a phenomenon that appears in natural sciences in various contexts. In the random graph theory, the phase transition refers to a dramatic change in the number of vertices in the largest components by addition of a few edges around a critical value, which was first discussed on the standard random graphs in the seminal paper by Erdos and Renyi. Since then, the phase transition has been a central theme of the random graph theory. In this talk we discuss the phase transition in random graphs with a given degree sequence and random graph processes with degree constraints.