Abstract
A fundamental and very well studied region of the Erdo{double acute}s-Rényi process is the phase transition at m~n/2 edges in which a giant component suddenly appears. We examine the process beginning with an initial graph. We further examine the Bohman-Frieze process in which edges between isolated vertices are more likely. While the positions of the phase transitions vary, the three processes belong, roughly speaking, to the same universality class. In particular, the growth of the giant component in the barely supercritical region is linear in all cases.
Original language | English (US) |
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Pages (from-to) | 305-329 |
Number of pages | 25 |
Journal | Arkiv for Matematik |
Volume | 50 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2012 |
ASJC Scopus subject areas
- General Mathematics