We consider a phenomenon, known as the 'phase transition', which occurs in several random graph processes. At some point during the process, the component structure changes radically through the addition of a relatively small number of random edges, from being a graph consisting of many small components, to containing a unique 'giant' component with a large proportion of the vertices. We consider several different random graph models and we will outline some methods which are used to study the phase transition. In particular we wish to determine the number of edges which have to be added for the phase transition to occur, and describe the behaviour of the graphs in the critical phase, which is the short period of time in which the giant component is formed.
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Benjamin Doerr, 03/12/2007 10:45 -- Created document.