Phase transitions for modified Erdös-Rényi processes

Details Phase transitions for modified Erdös-Rényi processes Phase transitions for modified Erdös-Rényi processes

2010-05-25

arxiv.org/abs/1005.4494v1

Mathematics

Combinatorics

22 pages

Scientific paper

A fundamental and very well studied region of the Erd\"os-R\'enyi process is the phase transition at 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.

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