Abstract
A random graph process, G1(n), is a sequence of graphs on n vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after (1+o(1))n=2 edges (a phenomenon known as "the double jump"), i.e., at time t = 1 when using a timescale of n/2 edges in each step.
Original language | English (US) |
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Pages (from-to) | 1853-1888 |
Number of pages | 36 |
Journal | Indiana University Mathematics Journal |
Volume | 59 |
Issue number | 6 |
DOIs | |
State | Published - 2010 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Giant component
- Random graphs
- Wormald's differential equation method