ABSTRACT
In 1959, Erdõs and Rényi wrote the first in a series4 '5 , 6 , 7 ' 8 '9 of remarkable papers on the evolution of random graphs, thus giving birth to the now flourishing theory of random graphs. In these papers, Erdõs and Rényi examined the properties of a random graph on n vertices and m edges. Namely, we start with a graph G with no edges. At each time unit, a randomly chosen edge (not yet in G) is added to G. As G acquires more and more edges, various properties and substructures emerge. The problem of interest is to study the typical (sudden) appearance of particular graph properties.
