... inserting just (1 + ε)n edges.2 Main ResultsIn the following we denote the edge set of Gn,iby Ei. The vertex set of the process isdenoted by V . The set of open pairs in Gn,iis called Oiand ... edges.In addition to the number of open pairs, our proof only requires the number of partialvertices for all non-adjacent pairs {u, v}. We denote the set of partial vertices of a non-edge {u, ... 3k. Then a.a.s. Sk(m) does not hold. the electronic journal of combinatorics 18 (2011), #P168 3Since the event Sk(i) holds, there are less than 3k edges in EF. Therefore, the sum inthe...